TCC - ...so [1] - autor waloddi weibull - ano 1960 - weibull-1960book-2, Teses (TCC) de Engenharia Mecânica
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TCC - ...so [1] - autor waloddi weibull - ano 1960 - weibull-1960book-2, Teses (TCC) de Engenharia Mecânica

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FATIGUE TESTING AND ANALYSIS OF RESULTS

r (d) Mechanical propert, Defiexion method, brittle coating method, bonded

wire technique, moist coating method, vibration methods involving frequency and damping or damping changes during fatigue test.

(e) Penetrating radiation tests. (f) Ultrasonic testing Reflection or through transmission methods. (g) Magneto-inductive tests. (h) Electrical tests. Electrical resistance or tribo-electrical methods.

Destructive Tests

(a) Heat tinting method (b) Chemical etching method (c) Recrystallization method (d) Damage line method (e) Impact method (f) Tensile pulling (g) Slow-bend test (h) Sectioning techniques

A review ofexperimental data on the initiation and propagation of fatigue cracks in test specimens is given in Part 2 of the reference cited.

For more detailed description of the various methods reference is made to thebibliography of thereport byDemer containingabout 200 references, and to the bibliography below.

References: BENNETT (1956), BUCHANAN and THUIt5TON (1956), DECK (1956), DEMEs (1955), FROST and DUGDALE (1958), FROST and PHILLIPs (1956), HARDRATHRndLEYBOLD (1958), HUL’r(1957a, 1957b, 1958a, 1958b), MCCLINTOcIC (1956), YEor~Incsand BELLONCA (1956), WEIBULL (1 954a, 1956a, 1956b).

SECTION 30. GENERAL

Fatigue testing machines may be classified from different view-points such as: purpose of the test, type of stressing, means of producing the load, operation characteristics, type of load, etc. The most appropriate sequence of these alternatives for building up a classification system depends upon who is going to use it. One system may be preferred by the manufacturer of testing machines and another by the research worker. The attitude of the latter will be taken in this chapter, which is aimed at being helpful to investigators trying to select the testing machine most suitable to their purposes. For this same reason it was decided to avoid detailed descriptions of individual machines, but to provide an ample number of references. Comprehensive reviews of the whole field are to be found in the following books: CAZAUn (1949), HORGER (1949), and OscHATz and HEMPEL (1958).

The purpose of the investigation is the most important item for the investigator, and he generally knows, when starting his investigation, what type of stressing he is going to use, whereas it may be of minor importance whether he is to use a mechanical or an electrical machine; the above- mentioned sequence will therefore be used for the classification system.

The purpose of the test will be chosenas the basis of the first-orderdivision, the type of stressing as that of the second-order division, and the design characteristic as that of the third-order division. Each of these classes may be subdivided according to the operating characteristic, i.e. the machines may be either of the resonant type, which operate at or close to the natural frequencyofthemass-spring system, or ofthe non-resonant type which do not.

A further basis ofdivision is the type ofload; a machine belongs either to the constant-stress amplitude type or to the constant-strain amplitude type, although some machines may easily be transformed from one type to the other, for exasnplc by inserting or removing a spring.

The first-order division consists of the following classes: (1) machines for general purposes; (2) machines for special purposes; (3) equipments for testing parts and assemblies; (4) components of fatigue testing machines; (5) calibration and checking of testing machines; and (6) accuracies of actual testing machines and equipments.

The second-order division, which will be primarily applied to the general purpose machines, but also, when possible, to other machines and equip- ments, consists of the following classes; (I) axial loading; (2) repeated bending; (3) rotating bending; (4) torsion; (5) combined bending and torsion; and (6) biaxial and triaxial loading.

tests.

CHAPTER III

FATIGUE TESTING MACHINES AND EQUIPMENTS

24 25

FATIGUE TESTING AND ANALYSIS or RESULTS FATIGUE TESTING MACHINES AND EQUIPMENT

The third-order division consists of the following classes: (1) load pro- duced by mechanical deflexion combined, in some cases, with variable spring forces and/or reciprocating masses; (2) load produced by dead weights and/or constant spring forces; (3) load produced by centrifugal forces; (4) load produced by electro-magnetic forces; (5) load produced by hydraulic forces; (6) load produced by pneumatic forces; and (7) load produced by thermal dilatation.

The testing machines for special purposes are basically similar to general purpose machines, with some modifications and additional devices. They will be classified into: (1) high frequencies; (2) elevated or low tempera- tures and cyclic thermal stresses; (3) corroding environments and fretting corrosion; (4) multi-stress level tests; (5) contact stresses; (6) repeated impact; and (7) combined creep and fatigue tests.

Equipments for testing parts and assemblies have been designed for the purpose of adapting the component to conventional testing machines, but sometimes the equipment is attached directly to full-scale test pieces, such as aeroplane wings, pressurized cabins, etc. Equipment for testing of the following components will be discussed: (1) wires, tires, and ropes; (2) coil and leaf springs; (3) turbine and propeller blades; (4) large specimens, structures, beams, rails; (5) aircraft structures.

Any component of a fatiguetesting machine belongs to oneofthe following functional parts of the machine: (1) load-producing mechanism; (2) load- transmittingmembers; (3) measuring device; (4) control device and shut-off apparatus; (5) counter; and (6) framework.

A careful and correct calibration and checking of the testing machine is an indispensable condition for obtaining reliable results; the calibration may be subdivided into: (1) static calibration and checking; and (2) dynamic calibration and checking.

Data on theaccuracies of actual testing machines and equipments are given at the end of this chapter.

References: CAzAUD (1948), F öPPL, BECKER and v. HEYDENKAMPF (1929), GOUGH (1926), GRAF (1929), GROVER, GORDON and JACKsON (1954), HORGER (1949), JOHNSTON (1946), LEna (1940), MAILANDER (1924), MOORE and KOMMER5 (1927), MOORE and KROU5E (1934), O5CHATZ (1936), O5CHATz and HEMPEL (1958), QUINLAN (1946), RU5SENBERGER (1952), SCHULZ and BUCHHOLTZ (1931), LOCATI (1950).

SECTION 31. MACHINES FOR GENERAL PURPOSES

31.1 Axial Loading 31.11 Load produced by mechanical defiexion and variable

springs and/or masses.—The simplest way of applying a constant-stress amplitude to a specimen consists of attaching one end of a coil spring to the specimen and imposing a reciprocating motion to theother end by means of a direct crank drive. This type of testing machine was, in fact, used by WOHLER (1871) in his fundamental investigations. Weak springs and a heavy leverage caused a low natural frequency of the system and conse- quently the speed of the machine had to be limited to less than 100 c/mm.

The same principle with small modifications and improvements has been used repeatedly. MOORE and JASPER (1924) introduced a variable-throw crank and a connecting-rod mechanism, which were also incorporated in a machine by MATTHAES (1935); TEMPLIN (1933) used two variable eccentrics, and Moome and KROUSE (1934) used a cam-operated lever system. This last machine could be operated at a speed of 1000 rev/mm, but in general a reduced speed of 100 to 200 rev/mm was recommended to prevent vibration and to reduce undesirable inertia forces.

If the reciprocating motion is applied directly to one end of the specimen, the spring being omitted, a constant-strain amplitude machine will result, provided the testing machine, including the dynamometer, is very stiff compared to the test piece—a condition which is not always fulfilled. Machines ofthis type using a crank and lever system have been described by WILsoN and THOMAS (1938) and LANE (1956). A study of the inertia forces acting on the specimen mounted in a large machine having a capacity of +200,000 lb showed that even at 180 rev/mm the additional forces pro- duced by the masses was some 3 per cent. A similar machine, used by ROBERTS and MCDONALD (1954), with a capacity of 100 tons and intended for testing rivet and screw joints of large sizes, had also to be limited to a speed of 18() rev/mm.

For small amplitudes, difficulties may arisewith the usual types ofbearing, but these may be eliminated by means offlexure plate pivots as demonstrated by EASTMAN (1935), also used by ERLINGER (1941). This useful machine part is discussed in paragraph 34.2.

A double eccentric coupled to a lever system, originally introduced by Mona (1923) and later adopted by TEMPLIN (1939) for testing structural parts, allowed an operating speed of 500 rev/mm at a capacity of +50,000 lb. Other machines of this type are described by FINDLEY (1947). Reference is also made to a simplified dynamic strain equipment by WORLEY (1948).

Aningenious design, using a differential strip mechanism and eliminating the disadvantages of loose bearings, was developed by PIRKL and von LAIZNER (1938). Another way of solving this problem by means of two counteracting, conventional bearings has been proposed by KLfiFPEL and applied in commercial testing machines.

The reciprocating motion may also be imposed on the specimen to which a mass is attached, thus producing the load in the form ofinertia forces as was proposed by REYNOLDS and SMITn (1902). Further descriptions are given by SMITN (1905, 1910). A machine based on the same principle was developed by Stanton and Bairstow at the National Physical Laboratory, and by STANTON (1905). This machine had four reciprocating masses attached to two pairs of opposed cranks, thus giving complete balance in both horizontal and vertical directions. Four specimens were tested simul- taneously at a speed of 1000 c/mm.

A convenient machine, incorporated in the current production of the Baldwin-Lima-Hamilton Corporation consists of a shake table to which various test pieces and components can be attached. The motion of the

26 27

FATIGUE TESTING AND ANALYSIS OF RESULTS FATIGUE TESTING MACnINES AND EQUIPMENT

table is obtained by the use of rotating out-of-balance weights, but the load on the specimens is actually produced by reciprocating masses.

An advantage of this type of machine is the high speed that can be achieved, but on the other hand, avery close control is necessary because an error in speed gives twice as large an error in load; complicated speed- regulating devices are therefore usually needed.

An ingenious method of producing resonant vibrations by mechanical means, called “the shipping clutch”, was originated by AUGHTIE (1931) and further developed by Cox and COLEMAN (1956).

References: AUGHTIE (1931), CAZAUD (1948), Cox and COLEMAN (1956), ERLINGER (1941), FINDLEY (1947), HORGEE (1949), LANE (1956), LEna (1940), MATTHAES (1935), MOHE (1923), MOORE and JAsPER (1924), MoORE and KOMMERS (1927, p. 91), MOORE and KROUSE (1934) OscnATZ (1943), OscnATz and HEMPEL (1958), PIRKL and v. LAIZNER (1938), ROBERTS and MCDONALD (1954), TEMPLIN (1933, 1939), WILSON and TMosas (1938), WORLEY (1948), WöHLER (1871).

31.12 Load produced by dead weights and/or constant spring forces.—Springs are not always reliable, and errors in the nominal load are easily introduced by overstressing, temperature effects, and inertia. The best guarantee against suck errors appears to be to use gravity forces from suspended weights. The first machine of this type was designed by Jasper as described in the book by MOORE and KOMMERS (1927, p. 91). By rotating the specimen, a stationary weight, suspended at the outer end of a lever, produces reversed axial load in the specimen.

Another design based on a similar principle was proposed by PROT and manufactured by Matra. This Construction ~S described in a paper by OSCHATE (1943) and in the book by OSCHATZ and HEMPEL (1958). Fluctua- ting axial load is transmitted from the suspended weights to the Specimen by means of a member rotating on a specially shaped curved track. The speed is low, not more than 120 rev/mm, and the diameter of thespecimen only 2~5mm.

References: CAZAUD (1948), HORGEE (1949), MOORE and KOMMERS (1927), O5CHATZ (1943) O5CFIATZ and HEMPEL (1958).

31.13 Load produced by centrifugal forces.-—This method of pro- ducing loads has found wide application. An early machine was designed by SMITH (1909) and later by THUM at the Material-Priifungs-Amt, Darm- stadt, as reported by TnUM and BERGMANN (1937), TnuM andJACoul (1939), and THUM and L0RENZ (1941). One single out-of-balance weight was rotated at a constant speed of 1500 rev/mm. The centrifugal force could be changed in steps while the machine was stationary.

A few years earlier, a more complieated machine had been designed by LEMR (1930, 1931) and by LEHR and PRAGER (1939). Two pairs of weights rotating at a speed of 3000 rev/mm produeed a load in the horizontal direction only. The load could be changed by aphase shift while themachine was in operation.

The two preceding types did not use the principle of resonance by which the forces can be multiplied many times. As an example of such a resonant

machine may be mentioned one by ERLINGER (1936, 1938), also described by OSCHATZ (1936), in which a single rotating weight produced vibrations in a cantilever spring; in a later design (ERLINGER, 1943) this was replaced by a coil spring in order to reduce damping effects. A similar principle has been used by Sonntag.

Mechanical oscillators of this type are frequently used in modern com- mercial machines (Sehenek, Baldwin, etc.), also as convenient means of vibrating full-scale structures and assemblies for fatigue testing purposes.

A machine of this type has also been applied to the testing of textiles as described by AMsLEE (1946) and TENOT (1947).

References: ERLINGER (1936, 1938, 1943), AMSLER (1946), LEHE (1930, 1931), LEHR and PEAGER (1939), OSCI-IATZ (1936), OSCnATZ and HEMPEL (1958), SMITH (1909), SONNTAG (1947), TENOT (1947), THUM and BERGMAN (1937), THUM and JACoBI (1939), THUM and LoluINz (1941).

31.14 Load produced by electro-magnetic forces.—Electro- magnetieally excited machines have the advantage of allowing very high frequencies. The first machine ofthis type was designed by KAPP (1911) and by HOPKIN5ON (1911, 1912), who attained a speed of 7000 c/mm, and by HAIGH (1912, 1917). Haigh’s machine, which has later been described by FOSTER (1932), has an armature placed between two magnets. One end of the specimen is attached to theframework and theother end to the armature which is eonneeted to a double cantilever spring. The natural frequency of the system without specimen is tuned to resonance by changing the length of the cantilever. The introduction of the specimen increases the natural frequency of the system and consequently the machine operates below resonanee but with compensated inertia forees.

The same principle was adopted by LEHR (1925). His machine operated with a frequency of up to 30,000 c/mm and was incorporated in the pro- duction of Schenck and Co., Darmstadt. A similar design has beenproposed by ESAU and VOIGT (1928).

A modern machine of this type has been developed by RUS5ENBERGER (1945), also described by RUSIENBERGER and FöLDES (1955), and is now incorporated in the current production of the Amsier Co. The system, conSisting of two masses connected through the specimen and the dynamo- meter in series, vibrates at its natural frequency which, by changing one of the masses, can be tuned to a frequency from 3000 to 18,000 e/Inin with a capacity of + 1 ton and +5 tons.

\ T

ery high frequencies (30,000 c/mm) have been attained by VOIGT and CFIRISTENSEN (1932) and KORBER and HEMPEL (1933) and up to 60,000 c/mm in a machine by THOMPSON, WArnwoaTn and LOUAT (1956).

References: ERLINGER (1936, 1938), ESAU and VOIGT (1928), FOSTER (1932), HAIGH (1912, 1917), HOPKIN5ON (1911, 1912), JC&pp (1911, 1912, 1917), KöRBER and HEMPEL (1933), LEMR (1925), RUS5ENBERGER (1945), RUIIEN- BERGER and FÔLDE5 (1955), SCHULZ and BUCFIHOLTZ (1931), THOMPSON, W~4nswoRTn and LOUAT (1956), VOIGT and CISRISTENIEN (1932).

31.15 Load produced by hydraulic forces.—Very high loads (up to + 100 tons or more) and large dynamic amplitudes are obtainable by means

28 29

FATIGUE TESTING AND ANALYSIS OF RESULTS FATIGUE YESTING MACHINES AND EQUIPMENT

of hydraulic machines, and various types of commercial machine are now available. The first machines consisted of a pulsator attached to the con- ventional tensile testing equipments. Later on, designs for the specific purpose of fatigue testing have been evolved.

The problem of changing the load while the machine is in operation has beensolved in two different ways. In one, thepump consists of two identical pivoted cylinders, and by changing the angle between them the resultant volume fed to another cylinder in series with the specimen is adjusted to give the required load (Amsler); instead of pivoting one of the cylinders, both cylinders may have a fixed position, and the phase is then changed by means of a differential gear (MAN). Alternatively, the stroke of thepump piston of a single cylinder may be changed (Losenhausen).

A description of an Amsler machine, using the first method, is given by SGHICR (1934) and of the Losenhausen machines, using the second method, by RAYIIRE (1931) and POMP and HEMPEL (1933, 1936). A hydraulic pulsator, developed by General Motors Corporation, is described by UNDERWOOD and GRIFFIN (1946). The design is somewhat different from the preceding types in that oil at high pressure is discharged to either or both sides of a large-diameter piston connected to thespecimen. The travel of the piston is controlled by leakage and bleed-off.

A French pulsator which is combined with a Trayvou universal testing machine is mentioned in the book by CAZAUD (1948, p. 91).

The characteristic feature of hydraulic fatigue testing machines is that the speed is rather limited. For large machinesa speed of 500 to 1000 c/mm is possible. For smaller machines, as for example the Losenhausenmachines with a capacity of +3 tons and + 10 tons, speeds from 500 to 3000 c/mm may be used. The load capacity of the above-mentioned GMC pulsator is + 100,000 lb at a maximum speed of 2000 c/mm and a stroke of 017 in.

References: CAZAUD (1948), DIEP5cHLAG, MATTING and OLDENBURG (1935), POMP and HEMPEL (1933, 1936), RATEKE (1931), ScHICK (1934), UNDERWOOD and GRIFFIN (1946).

31.16 Load produced by pneumatic forces.—--The only machine of this type has been proposed by Lehr, and a description will be found in the book by OscHATz and HEMPEL (1958, p. 183). The main data are: load +100 tons, stroke +5 mm and speed 1200 c/mm. The load is regulated with the machine in operation by changing a volume between the pump, which works at a constant stroke, and the cylinder attached to the specimen.

Reference: O5CHATZ and HEMPEL (1958, p. 183) 31.17 Load produced by thermal dilatation.—An original idea for

producing cyclic strains was introduced by COFFIN and HE~&D(1956). The device was based on the principle of heating and cooling columns in parallel with the test specimen. The thermal expansion and contraction were controlled by thermocouples spot-welded to each column. The cycling speed is of necessity very low. Two full cycles of strain were imposed per minute. This device was used for a study of the fatigue behaviour of cold- worked metal.

The joint effect of temperature and stress cycling was investigated in an apparatus developed by COFFIN and WESLEY (1953). A thin-walled tubular specimen was constrained at each end and alternately heated and cooled. The inner diameter of the specimen was0~5in. and the thickness of the wall 0~02in. which allowed a cycling rate of 4 c/mm.

A more complicated stress distribution in the specimen is applied by means ofthermal dilatation in a method used at the Westinghouse Research Laboratories for the purpose of screening or grading materials according to their resistance to cyclic temperature conditions. This method which was mentioned by Kemeny in a discussion ofa paper by COFFIN (I954b) consists of thermal cycling by induction heating ofsmall disks. The desired tempera- ture is reached after 3 or 4 see, and is limited to a thin layer around the periphery. After the heating cycle, the test piece is allowed to cool in air until all surfaces are below 800°F,when the specimen is quenched in water. In this way, cracks can be produced within 50 to 100 temperature cycles.

References: COFFIN (1954b), COFFIN and READ (1956), COFFIN and WEsLEy (1953)

31.2 Repeated Bending 31.21 Load produced by mechanical deflexion.—All machines

belonging to this type work on the constant-strain amplitude principle, although a constant moment would be easily maintained in many of the machines by an adjustment while the machine is in operation.

The simple principle of this type of machine consists of bending backand forth in the same plane of the specimen. The forced motion ofone or of two points of the specimen is usually produced by an adjustable crank. Various mechanisms aredescribed by HORGER (1949, p. 10). In someofthe machines, the stroke can be changed while the machine is in operation, as mentioned by JAeQUEssoN and LAURENT (1950).

The bending moment may either vary or be constant over the length ofthe specimen. The former usually results in a simpler design, but the second alternative is preferable from the testing view-point because a larger volume is tested, and irregularities in the material are consequently easier to detect.

The earlier machines were of the first type. In the machines by UPTON and LEwIs (1912), modified by LAUDENDALE, DOWDELL and CA55ELMAN (1939), and in those by MOORE (1930), the free end of the specimen is given a hack and birth motion by means of a crank. The 1 ~nnding moment conse- quently increases linearly over the length of the specimen. Sometimes the ~vidtlsof the specimen is made to decrease linearly, so t 1 Iat a constant stress is produced over the larger part of the specimen.

A convenient method ofeliminating failure in the grips is to load thespeci- men as a buckling column; as the moment is proportional to the deviation from the straight line through the ends of the specimen, the moment is a maximum in the middle portion of the specimen and is zero at the grips.

A uniform bending moment over the length of the specimen is realized in many different ways. In a DVL machine developed by MATTHAE5 (1933); the specimen is attached to two levers, one having a fixed end and the other

30 31

FATIGUE TESTING AND ANALYSIS OF RESULTS FATIGUE TESTING MACHINES AND EQUIPMENT

given a reciprocating motion by means of an adjustable crank. Another design by ERLINGER (1938) solves the problem by having the midpoint of the specimen fixed and applying movements along circular arcs to the ends of thespecimen. A third machine, designed and constructed at the National Physical Laboratory, is deseribed by Low (1956). The ends of the flat test piece are given appropriate angular movements and all tensile loads are eliminated by leverages; the curvature at the test section and thus the maximum Strain is measured by a spherometer. The speed of this machine was controllable between limits of 300 and 600 c/mm. By means of ahand rig a speed of about 3 c/mm eould be attained. In order to localize the strain in the test section as far as possible, steel plates were clamped to the ends of test pieces from sheet material, while in test pieces from bars the test section was reduced in thickness.

The bending machines are easily adapted for testing a large number of specimens simultaneously. An early design at the Bell Laboratory is de- scribed by TOWNSEND and GREENALL (1929) and by GREENALL and GOHN (1937), allowing the simultaneous testing of 126 specimens. In a modified construction by GOHN and MORTON (1949) and by GOIIN (1952), the number of specimens was reduced to 24. Both mean static strain and alternating strain are adjustable. The speed of this machine (3000 c/mm) is excep- tionally high for this type ofmachine. Another fast machine intended for 12 specimens is described by JOHNSTONE (1946).

These machines seldom exceed 1000 c/mm because of the low natural frequency of the system, but a machine for 18,000 c/mm is mentioned by JACQUES5ON and LAURENT (1950).

A quite different principle for producing bending moments was intro- duced by OrnERY (1936, 1938). A cantilever specimen is rotated and its free end is loaded through a ball bearing by the constant force of a coil spring. A steady bending moment can be superimposed by means of a beam spring rotating together with the Specimen.

References: DIETZ (1944), ERLINGER (1938), GOHN (1952), GORN and MORTON (1949), GREENALL and GOHN (1937), HORGER (1949), JACQUE5SON and LAURENT (1950), J0HNSTONE (1946), LAUDENDALE, DOwDELL and CASSELMAN (1939), Low (1956), MATTHAES (1933), MOORE (1930), OSCHATZ and HEMPEL (1958), TOWNSEND and GREENALL (1929), UPTON and LEWIS CASSELMAN (1939), Low (1956), MATTHAES (1933), MOORE (1930), OICHATZ and HEMPEL (1958), TOWNSEND and GREENALL (1929), UPTON and LEWIS (1912), OTTIZKY (1936, 1938).

31.22 Load produced by dead weights.—This way of producing bending moments rotating in relation to the specimen has been used frequently, but does not appear to have been used for producing fluctuating bending moments in a fixed plane of the specimen.

31.23 Loadproduced by centrifugalforces.—A very convenient and frequently used method of producing repeated bendingstresses in specimens consists of mechanical oscillators attached to the test piece. An early investigation by GOUGH (1926) used a single out-of-balance weight attached to the free end of leaf springs.

The meehanical exciter may also be mounted in the centre of the span between the nodes. Tests of this type have been carried out on various test pieces by many investigators, including those named in the references below.

Mechanical oscillators having two opposed out-of-balance weights in order to produce a resultant centrifugal force acting in one plane only were designated by BERNHARD (1937) and by LAZAN (1942). Commercial

oscillators of this type were being built in 1927 by Losenhausen and are now available also from Schenek, Baldwin, and other manufacturers. They are almost always run with a speed close to the natural frequency of the specimen system. Further references are given in Section 33.

References: BANKS (1950), BENDA and GALLANT (1954), BERNHARD (1937), GALLANT and BENDA (1954), GOUGH (1926), LAZAN (1942), MAILANDER (1939), NEWMAN and COATEI (1956), PERCIVAL and WECK (1947), UNKSOv (1956).

31.24 Load produced by electro-magnetic forces.—Most of the machines of this type are based on the same principle as the preceding type, in which a cantilever specimen or a beam is excited to vibrate in resonance. If the specimen is supported at the nodes and vibrates in its fundamental free-free bending mode, failure in the grip portion of the specimen is definitely eliminated.

One of the earlier machines was designed by JENKINS (1925), a wire- bending machine which operated at a frequency of 1000 C/S. A similar machine developed by RUTTMAN (1933) used a cantilever specimen which was excited by magnets alternately energized by an inertia switch attached to the free end of the specimen. Other machines of this type was described by vo~HEYnENKAMPF (1929), MULLER (1937), WILKINsoN (1939), ROBERTS and GREGORY (1951), and DOLAN (1951). In the Dolan machine, the diffi- culty of controlling the amplitude of the resonant vibration within narrow limits was solved by employing a new and simple circuit actuated from a micrometer screw used to pre-set the amplitude desired.

A modification was introduced by LE5IELL5 and BRODRICK (1956) which made it possible to apply the Prot method of determining the fatigue limit. This method requires a continuously increasing amplitude of vibration at any desired rate. Failure of the specimen at an early stage was detected by the reduction in tIm natural frequency, which was used also to control the a toma tic shut—off.

In some cases, e.g. when testing the specimen at elevated temperatures, ii ~nay he more convenient to have the vibrating system as a separate unit and to produce the forces on the test member by a mechanical connexion. This method was used by BLEAKNEY (1938) and by BRUEGGEMAN, KRUPEN and Roop (1944) for testing aeroplane wing-beam specimens, and by WELCII and WILsON (1941) for testing material at high temperatures.

An interesting torsional vibrator producing bending moments was developed by WADE and GROOTENRUIS (1954, 1956) by which a wide range of frequeneies was attained (from 24 to 3835 c/s). The specimen had a rectangular Cross-section and was made to vibrate in the free-free mode by purely torsional oscillations at one of the nodal points.

32 33

FATIGUE TESTING AND ANALYSIS OF RESULTS

References: BLEAKNEY (1938), BRUEGGEMAN, KRUPEN and Roo~ (1944), DOLAN (1951), VON HEYDEKAMPF (1929), JENKIN (1925), LES5ELLS and BRODEICK (1956), MULLER (1937, 1939) ROBERTS and GREGORY (1951), RUTTMAN (1933), WADE and GROOTENHUIS (1954, 1956), WELCH and WILSON (1941), WILKINsON (1939)

31.25 Loadproduced by hydraulic forces.—No reference to machines of this type have been found in the literature, but by means of suitable attachments axial-load or torsional machines may be used for this purpose.

31.26 Load produced by pneumatic forces.—Extremely high frequencies may be attained by this type of machine. The first machine of this type was designedbyJENKIN and LEHMAN (1929). Small beam specimens were made to resonate in the free-free modeby an air stream. The frequency was 18,000 c/s. A similar machine, designed and constructed at theNational Bureau of Standards, is described by VON ZEERLEDER (1930). The frequency was 12,000 to 20,000 c/s. A method of testing turbine blades with pneumatic oscillators is discussed by KRO0N (1940).

A machine by QUINLAN (1946, 1947) consists oftwo small pistons connected to the free end of a cantilever specimen which is vibrated at its natural frequencyby air pressure. A pneumatic column is tuned so that its resonance frequency coincides with that of the specimen. It is of considerable interest that fatigue cracks too small to be detected by X-ray or Zyglo tests have a measurable influence on the frequency, which gradually decreases with the growth of thecrack. This method also allows internal cracks to be detected before they appear at the surface. The same principle of generating vibra- tions has been used by MEREDITH and PHELAN (1948) and also by LOMAS, WARD, RAIT and COLBECK (1956) who studied the speed effect on several different materials.

References: JENKIN and LEHMAN (1929), KROON (1940), LOMAS, WARD, RAIT and COLBECK (1956), MEREDITH and PHELAN (1948), QUINLAN (1946, 1947), ROBERTS and NORTHCLIFFE (1947), VON ZEERLEDERER (1930).

31.3 Rotating Bending

31.31 Load produced by mechanical deflesion.—If a bent wire is rotated about its curved axis, a simple and efficient method of producing constant strain amplitudes is obtained. Machines of this type were designed by KENvON (1935) and are also described and used by VOTTA (1948). If the wire arc is circular, a constant bending moment over the length of the specimen results. This is of advantage, if the specimen can be given such a shape that failure does not occur in the grip portion of the specimen, but otherwise it is desirable that the end moments be small. This problem was solved by Haigh and Robertson who introduced the principle ofloading the test piece as a buckling column. This idea was adopted by SHELTON (1931, 1933, 1935) and by GILL and GOODACRE (1934).

Instead of using an axial load, CORTEN and SINCLAIR (1955) attained the same result by having the drive end of the wire rigidly fixed, the other end of the spe~menbeing free to rotate in the plane of bending and following a curved path of such a form that the fixed end of the specimen is subjected

34

FATIGUE TESTING MACHINE5 AND EQUIPMENT

to zero moment. The movable end of the specimen fits into a miniature bearing and housing which are free to rotate and assume the configuration imposed by the specimen. Rapid changes of deflexion are possible due to the small masses, and this machine is therefore suitable for programme testing.

References: CORTEN and SINCLAIR (1955), GILL and GOODACRE (1934), KENY0N (1935), SHELTON (1931, 1933, 1935), VOTTA (1948)

31.32 Load produced by dead weights and/or constant spring forces.—T his type of machine employs either a rotating specimen or a rotating load. The first design constitutes the classical high-speed fatigue machine, introduced by WöHLER (1871). The merit of this principle lies in the fact that all inertia forces are easily eliminated.

In its simplest form, the rotating-beam specimen is provided at the free end with a ball bearing which is loaded by a dead weight or a constant spring force calibrated by a dead weight. An early design developed by KROU5E (1934) and also described by MOORE and KROUSE (1934) was capable of speeds up to 30,000 rev/mm. Such machines are extensively used and have a wide application. Specimens ofdiameter from 0~05in. (PETERSON, 1930) up to 12 in. have been tested, the latter specimens requiring bending moments of 8,000,000 lb in.

In these machines, the bending moment varies linearly over the length of the specimen. This may be quite acceptable if the specimen is notched, but in an unnotched specimen a uniform stress over the length is preferable. For this purpose MCADAM (1921) introduced a tapered specimen which satisfies this condition.

Another method of producing uniform stresses over the length is to apply a constant bending moment over the length of the specimen. Four-point loading provides a good solution of this problem, the specimen being supported by two ball bearings while two other bearings are loaded by weights. Ifa largebattery ofmachines is used simultaneously, it is convenient to replace theweightsby coil springs and to set their elongations by acommon calibrated weight. Machines of this type were introduced by LEHR (1925) and also by R. R. Moore as described by OBERG and JoHNsoN (1937). A spring-loaded machine has recently been described by CORON (1953).

A rotating-beam machine with superimposed fluctuating axial loading was developedi by ROMUALDI, CHANG and PECK (1954).

There arc methods other titan the four-point loading method for producing constant moments. LEI-IR (1 ¶140) attached a cross-lever to the free end of the cantilever specimen and loaded it by two springs acting in opposite directions. This construction was simplified by using one spring only. In this way the axial load is not completely eliminated, but it can be made negligible by using a lever of sufficient length. This modification was introduced by THUM and BERGMANN (1937) and is discussed also by THUM (1942) and by SAUL (1942).

Machines ofthis type, allowing the simultaneous testing ofa largenumber of specimens, have been designed by PROT (1937) capable of testing thirty specimens and also by KELTON (1946).

35

i

4

FATIGUE TESTING AND ANALYSIS OF RESULTS FATIGUE TESTING MACHINES AND EQUIPMENT

The constant-moment machines make it necessary to give the specimen a suitable shape to avoid failure in the grips. In some cases, where this measure is undesirable—as for example when testing wires—it is better to apply a non-uniform bending moment to the specimen.

The second method of producing a bending stress rotating in relation to the specimen, is to keep the specimen stationary and to rotate the bending moment. This principle was used by GOUGH (1926) and by MOORE and KOMMERS (1927). A similar machine was designed by DORGELOH (1929). The specimen is held rigidly in a support, while theother end is rotated in a small circle by a revolving load arrangement. An advantage of the non- rotating specimen is that it can be examined and cracks can be detected while the machine is in operation. Also at elevated temperatures, where the measurement of the surface temperature is needed, the rotation introduces complications.

References: CORON (1953), DORGERLOH (1929), ERLINGER (1941), GOUGH (1926), GUTFREUND (1951), HOWELL and HOWARTII (1937), JATZKEwITSCH (1949), KELTON (1946), KROU5E (1934), LEHR (1925, 1940), MCADAMS (1921), MOKEowN and BLACK (1948), MOORE and ALLEMAN (1931), MooRE and KOMMER5 (1927), MOORE and KROUSE (1934), OBERG and JOHNSON (1937), O5CHATZ and HEMPEL (1958), PROT (1937), ROMUALDI, CHANG and PECK (1954), SAUL (1942), THUM (1942), THUM and BERGMANN (1937), TIEDEMANN, PARDUE and VIGNE55 (1955), WöHLER (1871).

31.4 Torsion

31.41 Load produced by mechanical defiesion and inertia forces.—Machines of this type were developed by WoHLER (1871), FöPPL (1909) and ROwETT (1913) using acrank drive acting directly on aspecimen in series with a coil spring or a torsion weight bar or even an optical system recording the hysteresis ioop and thus allowing a study of the damping at different stages of the damage process (LEHR, 1930). Other contributions to the development of this type of machine has been described by MASON (1917, 1921), MooRE and KOMMER5 (1921) and others. Commercial machines of different capacity are now available.

A different principle was introduced by STROMEYEE (1914) who used a crank drive connected to one end of the specimen while aflywheel producing the load was attached to the opposite end of the specimen. Two specimens could be tested simultaneously. This machine did not operate at resonance.

A resonant machine was designed by MCADAM (1920) and by BUSEMANN (1925). As a torque bar and a flywheel constitute a System with very small damping, the amplitude is very dependent on the speed of the machine, and artificial damping is sometimes needed.

Torsional oscillations may also be maintained by means of a slipping clutch. This principlewas used by Krouse and later by Aughtie and by Cox and Coleman as explained in paragraph 34.1.

References: BU5EMANN (1925), FöFPL (1909), GUTFREUND (1950), HAN- STOCK and MURRAY (1946), LEHR (1930), MAILANDER (1939), MAILANDER and BAUER5FELD (1934), MASON (1917, 1921), MCADAM (1920), MOORE and

KOMMER5 (1921), OScHATZ (1934), PAUL and BRIsTow (1952), ROWETT (1913), SPATH (1938), STROMEYER (1914), WöHLER (1871).

31.42 Load produced by dead weights.—This principle has not been used very muchbecause of the limited speed due to inertia forces. A machine of this type, however, developed by H. F. Moore and by Stanton and Batson as reported in thebook by MOORE and KOMMERS (1927, p. 102). The torsional moment was produced by a rotating cantilever beam provided with a dead weight which was attached to one end of the specimen. A speed of 1000 rev/mm could be used.

A more complicated design of a similar kind has been produced by PROT (1937). The torsional loading is produced by suspended weights by means of an internal conical gear.

References: MOORE and KOMMERS (1927, p. 102), PROT (1937) 31.43 Load produced by centrifugal forces.—Mechardcal oscillators

mentioned in paragraphs 31.13 and 31.23 may quite well be used for producing reversed torsional vibrations. Crankshafts of diesel engines have been tested in this way by LEIIR and RUEF (1943) and full-size marine shaftings of ~1in. diameter by DOREV (1948) using a planetary system in which out-of-balance wheelswere geared to a sun wheel and planet pinions. An electronic method ofspeed control wasclaimed to be capable ofregulating the nominal stresses in the specimenwithin 1 per cent.

THUM and BERGMANN (1937) tested specimens in reversed torsion using a two-mass resonant system excited by a rotating out-of-balance weight. The same method was applied to the testing of tractor engine crankshafts by ROSEN and KING (1946) and by PAUL and BaHTow (1953) for testing large erankshafts. The torsional moment was 28,000 kg cm at a speed of 300 rev/mm.

Mechanical oscillators are now incorporated in the current production of several manufacturers.

References: DOREY (1948), HORGER (1949), LEHR and RUEF (1943), PAUL and BRISTOW (1953), ROSEN and KING (1946), THUM and BERGMANN (1937).

31.44 Load produced by electro-magnetic forces.—Several machines of this type have been designed, all being of the resonant type. Most of them consist of an armature acting as a flywheel connected in series with the specimen and excited! either by feeding into the stator an electric current of a 1Icqueucy close to tile natural frequency of the system, as in the Loscuuhauiscn machine described by vo~BouUsxEwlCz and SPATH (1928), or by sonic autonlatic device as fir example a swinging contact hammer mounted 00 the flywheel as done by Holzer and described by FöPPL, BECKER and vo~HEYDENKAMPF (1929). In some eases two flywheels are introduced in the Iwinging system for the purpose of eliminating bending vibrations (FUPPL and PERTZ, 1928). A similar design wasfurther developed by EIAU and KORTUM (1930), KORTUM (1930), HOLT5CHMIDT (1935).

The preceding machines apply reversed torsion to the specimen and it is difficult to introduce a steady torsional moment. An improvement in this respect is incorporated in the production of Amsier and also by HENT5cIIEL and SCIIWEIZEEHOF (1954).

36 37

FATIGUE TESTING AND ANALYSIS OF RESULTS FATIGUE TESTING MACHINES AND EQUIPMENT

References: VON BOHUIZEwICZ and SPATH (1928), EIAU and KORTUM (1930), FOPPL, BECKER and VON HEYDEKAMPF (1929), HENTSCHEL and SCHwEIZERHOF (1954), HOLT5CHMIDT (1935), HUBRIG (1936), KORTUM (1930), PERTZ (1928).

31.45 Load produced by pneumatic forces.—By a slight modifi- cation, QUINLAN (1946) hadadapted his machine for exciting high-frequency bending vibrations into a torsional machine. This machine is particularly fitted for tests at elevated temperatures.

Reference: QUINLAN (1946).

31.5 Combined Bending and Torsion

31.51 Load produced by mechanical deftexion.—Conventional testing machines may be used to apply combined bending and torsional loads to the specimen by means of suitable attachments. Such devices are described by BRUDER (1943) and by NIIHINARA and KAVAMOTO (1943). Designs and features of such attachments for converting Krouse plate- bending fatigue machines and Sonntag vibratory fatigue machines have been developed by FINDLEY (1945) and FINDLEY and MITcHELL (1953) and also by PUcHNER (1946) and have been incorporated in the current pro- duction of Krouse.

References: BRUDER (1943), FINDLEY (1945), FINDLEY and MITCHELL (1953), FRITH (1948) NISHINARA and KAVAMOTO (1943), PUCHNER (1946).

31.52. Load produced by centrifugal forces.—Machines for the specific purpose of combining bending and torsional loads are generally based on centrifugal forces. A machine designed by LEHR and PEAGER (1933) consisted of a mechanical oscillator with four rotating out-of-balance weights which produced axial loading, while a cross-lever having mechanical oscillators at each endprovided reversed torsional loading. This machine is a non-resonant machine. Further details are given by HOHENEMSER and PRAGER (1933).

Another machine for similar purposes was designed by GOUGH and POLLARD (1935, 1936, 1937). Any combination of bending and torsional stresses was possible by means of a vibrating arm attached thrdulgh a pivoted joint to one end of thespecimen. This arm, which could be operated in any angular position with reference to the longitudinal axis of the specimen, wasexcited by a rotating out-of-balance disk, operated at the resonant fre- quency. Additional steady loads could be produced by the cantilever spring supporting the mechanical oscillator as described by G0UGIL (1949, 1950).

The use of mechanical oscillators for producing reversed bending and torsion is also reported by THUM and BERGMAN (1937) and by THUM and KIRM5ER (1943).

References: GOUGH (1949, 1950), GOUGH and Cox (1932), GOUGH and POLLARD (1935, 1936, 1937), HOHENEM5ER and PRAGER (1933), LEHR and PRAGER (1933), STANTON and BAT5ON (1916), THUM and BERGMAN (1937), TIIUM and KIRMIER (1943). 31.53 Load produced by electro-magnetic forces.—Starting from

conventional rotating-beam machines, additional steady or fluctuating

torsional moments were applied to the specimen by ON0 (1921), by LEA and BUDGEN (1926) and by Bohlenrath as reported by Osca&vz (1936).

References: LEA and BUDGEN (1926), ONO (1921), O5CHATZ (1936), OICHATZ and HEMPEL (1958).

31.6 Biaxial and Triaxial Loading

The majority of the combined fatigue stress tests reported have been made by subjecting aspecimen of circular cross-section to combined bending and torsion as described above. The range of biaxial principal stress ratios is restricted by this method to from 0 to — l~0,i.e. to biaxial stresses of opposite Signs.

A wider rangeofpossible stress combinations can be obtained by subjecting tubular Specimens to internal fluctuating pressure and static or fluctuating axial stress, or by combining torsional fatigue and external static pressure.

In the case oftubular specimens subjected to internal pressure, the thick- ness of the wall decides whether biaxial or triaxial stress result. Biaxial stress is obtained by means of thin-walled tubular specimens, whereas a thick cylinder, subjected to internal pressure andsupporting its own end load, can be considered to be subjected to a uniform triaxial tensile stress acting thrbughout the wall thickness with a superimposed shear stress varying from a minimuln at the outside to a maximum at the bore. The ratio of the triaxial tension to the shear stress changes with the ratio of the external to the internal diamneters of the cylinder.

Biaxial fluctuating stresses are obviously easier to produce, because a thin-walled tube requires a comparatively small pressure, which may be produced by means of oil from a pump. Such apparatuses, test specimens and methods of testing are described by MARIN (1947, 1948, 1 949a, 1949b), MARIN and SMEL5ON (1949), MARIN and HUGHES (1958), BUNDY and MARIN (1954) and also by MAJORS, MILLS and MCGREGOR (1949). Similar arrange- ments will be found in publications by MASER (1934), MORSKAwA and GRIFFY (1945), LATIN (1950), and Red and EICHINGER (1950).

Fatigue under triaxial stress has been studied by MORRISON, CROISLAND and PARRy (1956). This paper gives a detailed description of the machine used and a discussion of special features required in a machine for this purpose, such as glands, core bar, and pressure measurements. The high- presSure system consists of a rain reciprocating in a closed cylinder filled with oil driven by a variable-Stroke mechanism (PARRV, 1956). Aremarkable observation is reported. It was found that the fatigue limit for unprotected cylinders subjected to repeated internal pressures was astonishingly low. The fatigue strength of the cylinder could, however, be raised considerably either by honing the bore after heat-treatment or by protecting the bore from the fluid by a thin film ofrubber. If the cylinder after honing was heat- treated at 600°C[the material used was Vibrac V 30 (En 25T)j in vacuo, then the strengthening effect was removed.

Another way of producing triaxial stresses is to subject a specimen to torsional fatigue with superimposed high static fluid pressure as described by CRO5SLAND (1956). The most difficult part of the machine is obviously

38 39

FATIGUE TESTING AND ANALYSIS OF RESULTS FATIGUE TESTING MACHINES AND EQUIPMENT

the seal surrounding the oscillating shaft which is heavily loaded by the high fluid pressure. A successfulconstruction, called the Morrison seal, is described in detail by CROI5LAND (1954).

Finally, reference is made to a method of producing triaxial loads by means of cube-shaped test pieces, developed by WELTER (1948).

References: BUNDY and MARIN (1954), CRO5SLAND (1954, 1956), LATIN (1950), MASER (1934), MAJORS, MILLS and MCGREGOR (1949), MARIN (1947, 1948, 1949), MARIN and HUGHES (1942), MARIN and SHEL5ON (1949), MORIKAWA and GRIFFY (1945), MORRISON, CEO5ILAND and PARRY (1956), PARRY (1956) Red and EICHINGER (1950), WELTER (1948).

SECTION 32. MACHINES FOR SPECIAL PURPOSES

32.1 High Frequencies

The classification into high and low frequencies is rather arbitrary. Since there are now commercially available fatigue testing machines which are capable of speeds up to 12,000 and even 18,000 c/mm, it seems reasonable to put the lower limit of high frequency at 30,000 c/mm.

The only workable wayof obtaining these high frequencies by mechanical means is by using rotating-beam machines. This method was developed by KROU5E (1934) who attained a speed up to 30,000 rev/mm using an air- turbine driven rotating-beam machine.

Other high-frequency machines are of the resonant type, the vibrations being excited either electromagnetically or pneumatically.

Of the first type may be mentioned some axial-load machines. SCHULZ and BUCHHOLTZ (1931), V0IGT and CHRISTENSEN (1932), and KöRBER and HEMPEL (1933) achieved frequencies of 30,000 c/mi whereas THOMP- SON, WADSWORTH and LOUAT (1956) reached 60,000 c/mm and VIDAL, GIRARD and LANU5SE (1956) even 480,000 c/mm. Electromagnetic wire- bending machines by JENKIN (1925) and by WADE and CEOOTENHUIS (1954) were capable of 30,000 and 230,000 c/mm respectively. A resonant torsion machine by HANSTOCK and MURRAY (1946) operates at a frequency of 90,000 c/mm.

The highest frequencies so far produced were obtained by means of pneumatic bending machines. A machine simulating the vibrations of turbine blades attained speeds of 150,000 c/mi while another machine using small beam specimens which were made to resonate in the free-free mode by an air excitation method developed by JENKIN and LEHMAN (1929) reached the highest frequency so far recorded for testing purpose, namely 1,080,000 c/mm.

References: HANITOeK and MURRAY (1946), JENKIN (1925), JENEIN and LEHMAN (1929), KROUSE (1934), KöRBER and HEMPEL (1933), L0MAI, WARD, RAIT and COLEECK (1956), SCHULx and BUCHHOLTZ (1931), THOMPSON, WADSWORTH and LOUAT (1956), VIDAL, GIRARD and LANUISE (1956), VOIGT and CHRISTENSEN (1932), WADE and GROOTENHUIS (1954, 1956).

32.2 Elevated or Low Temperatures and Cyclic Thermal Stresses

Some modifications of conventional fatigue testing machines aregenerally needed to enable them to be used for testing at elevated temperatures. The rotating-beam machine arenot easilyarranged for this purpose but a note on such a machine for tests at 200°Cis given by PHILLIPS and THURITON (1951). For this reason machines have been designed where thespecimenis stationary and the load rotates. Such machines were developed by DORGERLOR (1929), JATZKEWITSeH (1949), and MCKEOwN and BACK (1948).

Machines specifically intended for testing at elevated temperatures have been designed by HOWELL and HOWARTH (1937), BERNSTEIN (1949), and MARKOWITZ, SMIJAN and MICHAJEW (1949) and special machines for ceramic materials by DICK and WILLIAMS (1952). Test equipments and technique are described by SMITH (1944), REGGIORI and ERRA (1953). VIDAL (1955) combined the temperature with a corroding atmosphere of combustion gases.

Pneumatic, bending, or torsional machines are easily adapted for tests at elevated temperatures by placing a cylindrical, resistance-wound furnace around the specimen as demonstrated by QUINLAN (1946).

Fatigue tests of welds at elevated temperatures were conducted by AMATULLY and HENRY (1938).

An apparatus for testing at low temperatures is described by RUSSELL and WELCKER (1931) and fatigue machines for low temperatures and for miniature specimens have been developed by FINDLEY, JONES, MITCHELL and SUTHERLAND (1952).

A comparatively new field of research is the resistance of materials to cyclic thermal stresses. Thermal fatigue is due either to the anisotropic thermal expansion of the crystals or to temperature gradients as explained by ALLEN and FORREsT (1956) who postulate that resistance to thermal fatigue can be determined only from dynamic experiments. A simple method consists of subjecting the specimen, rigidly clamped at its ends, to thermal cycles.

Alternatively, fatigue tests for purposes of comparison can be made at a number of constant temperatures under conditions of constant alternating

strain. It is important that tIme frequency of the stress cycle should be comparable with tisat occurring in service, since at high temperatures dynamic ductility depends on the frequency.

An apparatus for carrying out either of the two types of tests indicated above has been developed by COFFIN and WESLEY (1953) and is also described by COFFIN (I954a). A detailed investigation of the behaviour of an austenitic steel was carried out by COFFIN (I954b). The apparatus was quite simple; a thin-walled tubular specimen (inner diam. 05 in., wall thickness 0~02in.) was constrained at each end and alternately heated and cooled. The cycling rate was 4 c/mm.

Another test, used at the Westinghouse Research Laboratories, and described by Kemeny in the discussion of the paper by COFFIN (1 954b) uses disks 1 to l~65in. in diameter and 0.11 to 0~25in. thick which are

40 41

FATIGUE TESTING AND ANALYSIS OF RE5ULTS FATIGUE TESTING MACHINES AND EQUIPMENT

thermally cycled by induction heating. A thin layer around the periphery is brought to the desired temperature in 3 to 4 sec. After the heating cycle the pieces are allowed to cool in air down to 800°F,when the specimens are quenched in water. The temperature distribution may be controlled by using the indicating paint “Tempilaq”. Cracks can be produced within 50 to 100 temperature cycles.

References: AMATULLY and HENRY (1938), BERNSTEIN (1949), COFFIN (1954a,b), COFFIN and WESLEY (1953), DICK and WILLIAMS (1952), DORGER- LOH (1929), FINDLEY, JONES, MITCHELL and SUTHERLAND (1952), HOWELL and HOWARTH (1937), JATZKEWITSCH (1949), MARKOWITZ, SMIJAN and MICHAJEW (1949), MCKEOWN and BAcK (1948), PHILLIPS and THURSTON (1951), QUINLAN (1946), REGGIORI and ERRA (1953), RUSSELL and WELCKER (1931), SMITH (1944).

32.3 Corroding Environments and Fretting Corrosion

Conventional fatigue testing machines of any type may be used for corrosion fatigue tests with the addition of ameans for applying thecorrosive solution or atmosphere to the specimens under test. It is essential that the action of corrosion and stressing be simultaneous, and that the temperature be kept constant. It was found by GOULD (1936) that tests in a constant temperature room give points which plot with less scatter than tests con- ducted in the open laboratory.

Although any type of stressing may be used, different types produce very different results. In theregion of normal working stresses, axial stresses give about five times as long a fatigue life as do rotating bending stresses of the same value, as demonstrated by GOULD (1949). This result is explained by the fact that the electric currents flowing under axial loading are of lower intensity than those flowing under the rotating-bending action, thus pro- ducing slower fatigue damage.

Some remarkable comments made by Gould have a bearing on corrosion tests and may be presented here. He states that when deciding the way in which the corrosive is to be applied, it may be realistic to consider the fact that with industrial metals it is highly probable that pure mechanical fatigue is a phenomenon which is perhaps non-existent in actual service and even in the laboratory is realized only by invoking the ultimate of refinement in technique. It has been found that the air fatigue limit of the metal was raised appreciably by running the test in a hard vacuum and by excluding oxygen (GOUGH and SOPwITH, 1932) or in a concentrated, pure solution of corrosion inhibitor (GOULD, 1933).

The first systematic investigations into corrosion fatigue were made by HAIGH (1917) and by MCADAM (1926, 1927a,b,c) who used a stream of the corrosive guided along the test piece. Other ways of serving the corrosive are as a spray (GOUGH and SOPWITH, 1933) or as a drip on to a tape which carries a meniscus of fluid over a selected portion of the specimen (GOULD and EVANS, 1939) or by pouring sea-water on to torsional and rotating-beam specimens from an overhead tank (HARA, 1956). Technique and apparatus for testing in an atmosphere of combustion gases are described by VIDAL

(1955). Recently, a comprehensive review relating to corrosion fatigue has been made by GOULD (1956).

References: GOUGH and SOPWITH (1933), GOULD (1936, 1949, 1956), GOULD and EVANS (1939), HAIGH (1917), MCADAM (1926, 1927a,b,c), VIDAL (1955).

Fretting corrosion in connexion with contact friction and its detrimental influence on the fatigue limit was first observed as premature failure of fatigue test Specimens in the grip portion. It has beenfound that the degree of damage of this type is greatest under perfectly dry conditions.

Conventional rotating-beam tests on shafts with pressed-on collars have been carried out by PETERSON and WAML (1935). Extensive investigations using a similar method are reported by HORGER (1953, 1956).

Another way of producing the necessary pressure is to use clamps in which known high lateral pressures can be applied to specimens under test in a fatigue testing machine, either in plane bending (CORTEN, 1955) or in axial loading (CORNELIUS, 1944). The latter method has been extensively used by FENNER, WRIGHT and MANN (1956).

A third method has beenapplied by ODING and IvANOvA (1956). A speci- men was vibrated in reversed bending and was provided with two bent plates attached to the specimen, thus producing the desired contact friction at the critical part of the specimen. It was found that the fatigue limit was equal to zero or, at any rate, was very small.

References: CORNELIUS (1944), CORTEN (1955), FENNER, WRIGHT and MANN (1956), HORGER (1953, 1956), ODING and IvANOVA (1956), PETERSON and WAHL (1935).

32.4 Multi-stress Level Tests

In order to simulate service loads, the stress levels must be changed during the lifetime of each individual specimen. This can be done either by means of programme testing or by spectrum testing. In the first method, a limited number of stress amplitudes are selected and to each of them is attributed a certain number of stress reversals, chosen on the basis ofextensive records of statistical frequencies. Each stress cycle of a given amplitude is repeated a certain number of times, large amplitudes a smaller number than small

amplitudes. The programme is composed of these stress levels following after each otlser either according to a fixed pattern or at random. The second method, spectrum testing, is defined by the condition that two eonse cutive stress cycles always differ in amplitude. In this ease too the sequence of stress amplitudes either follows a fixed pattern or is completely random.

A non-random programme testing may, of course, be performed by hand in any conventional testing machine, but an improvement is obtained by using automatically controlled machines.

The simplest programme consists of two stress levels only. Axial fatigue testing machines for applying a sequence of loads of two amplitudes have been developed by SMITH, HOWARD, SMITH and HARWELL (1951) and by MCPHERSON (1952). A dual-amplitude rotating-bending machine was designed by CORTEN and SINCLAIR (1955).

42 43

FATIGUE TESTING AND ANALYSIS OF RE5ULTI FATIGUE TESTING MACHINES AND EQUIPMENT

Several commercial machines capable of subjecting the specimen to a preassigned programme until fatigue failure occurs are now available. Descriptions and details ofsuch machines are given by BECKER (1949, 1950), HALL and SINNAMON (1952), DRYDEN, RHODE and KUIIN (1952), ZUNKLER (1956), and DEUTLER (1956). One of the most complete programme machines constructed by Schenck and based on proposals by Gassner and Federn is provided with twin drives. Small, fast stress reversals are pro- duced by a crankshaft with constant stroke acting on a spring system in resonance, while high, slow stress cycles are produced by hydraulic means. The programme can be changed within a wide range.

A more realistic simulation ofservice load is obtained by means of random programme testing. A machine for this purpose was designed and con- structed by FREUDENTHAL (1953, 1956). This machine operates on the prin- ciple ofa conventional vertical rotating-beam machine with theadded feature that the load can be arbitrarily varied between zero and amaximum so as to form a prescribed sequence of sufficient length to eliminate any effect of the periodicity. The sequence is recorded on a tape which is run through mi reading device consisting of a group of contact springs and a group of relays closing a combination of circuits delivering the prescribed current pulses through the loading coil. Random load fatigue tests on simple specimens have also been carried out by FINNEY and JOHNSTONE (1955). BRUTON, COHEN and HIND (1956) developed a random load controller for fatigue testing of full-scale structures.

The simplest pattern of spectrum testing is that proposed by PROT (1937) for the specific purpose of determining the fatigue limit rapidly. The specimen is subjected to a linearly increasing stress amplitude until failure occurs. This type of spectrum is usually produced by a rotating-beam machine in which the loading weight, consisting of water, increases con- tinuously.

Another solution of the problem is given by BRODRICK, KHEIRALLA and BABCOCK (1956) and LE5SELL5 and BRODEICK (1956). In this machine the specimen is magnetically excited in a free-free bending mode. A system of electronic controls is provided, so as to produce a continuously increasing amplitude at any desired rate.

For service simulating purposes, HARDRATH and UTLEv (1952) used a rotating-beam machine with a mechanism by which the stress amplitude is varied according to a predetermined pattern. A cam is rotated at 1 rev/mm and the specimen at 10,000 rev/mm. Two different cams were used, one producing a stress amplitude which varied sinusoidally with time while the other produced stress amplitudes varying according to an exponential function for most of its travel.

A similar machine was designed by L0CATI (1952), and another by SERENIEN (1956).

An interesting method of producing random spectrum loading is intro- duced by HEAD and HOOKE (1956). The “random noise generator” consists essentially of a thyraton valve giving a large random output voltage which is amplified and excites a moving-coil vibrator which produces an equivalent

bending moment in thefatigue specimen. The average output voltage of the amplifier is maintained at a constant value by a stabilizer.

FilIally, a machine of quite a different type may be mentioned. STARKEY and MAECO (1954) have designed a machine which produces a multi- harmoonie, uniaxial stress by superposition of fundamental and second- harmonic sinusoidal stress-time waves. The load is produced by cam- operated plungers on a common volume of hydraulic fluid. A machine for similar purposes has been designed and constructed by SEEENIEN (1956). Torsional load is produced by two pairs of out-of-balance weights, rotating at different speeds and resulting in stress cycles of polyharmonic form. Different combinations of the first and second harmonics were investigated.

References: BECKER (1949, 1950), BENDA and GALLANT (1954), BRODRICK, KHEIRALLA and BABCOCK (1956), BEUTON, COHEN and HIND (1956), COETEN and SINCLAIR (1955), DEUTLER (1956), DRYDEN, RHODE and KUHN (1952), FINNEv and JOMN5TONE (1955), FREUDENTHAL (1953, 1956), HALL and SINNAMON (1952), HARDRATH and UTLEY (1952), HEAD and HOOKE (1956), LES5ELL5 and BRODRICK (1956), LEBER (1954), LOCATI (1952), MCPHERsON (1952), NISNIHARA and YAMADA (1950), PEOT (1937), SEREN5EN (1956), SMITH, HOWARD, SMITH and HAEWELL (1951), STARKEY and MARCO (1954), TAPLIN and FINDLEY (1952), ZUNKLER (1956).

32.5 Contact Stresses

A very direct method of testing specimens subjected to pulsating contact stresses was devised by KENNEDY (1956). He used two steel balls which were pressed against eaels other by means of a rig consisting of a rotating shaft which, through two cranks, caused an oscillatory motion in a second shaft, arranged to impart its motion to the loading device. The mating sizes of the pairs of balls were respectively 2 in. and 4 in. diameter. The larger ball was considered to be the test specimen. An important feature of this testing device is an ultrasonic flaw detector.

A different method of producing contact stresses is described by MACKS (1953) and by BUTLER, BEAR and CARTER (1957). The rig consists of two balls driven at lsigls speed on the inner surface of a cylinder race by an air jet from three nozzles. Ball loading results from centrifugal forces. Speed control and automatic failure shut-down systems are provided.

The most common method of producing contact stresses is by rotating a pair of cylindrical disks wlsich are pressed against each other. In some machines one of the disks is driven (WAY, 1935 and BIJCKINGHAM, 1944), whereas in other designs botis are driven thus allowing a definite amount of slip at the contact surface.

Conical disks are also used to simulate helical gear tooth action in a laboratory machine by WALKER (1947).

A convenient method of testing complete gears is to connect two pairs of wheels in a closed circuit and to apply the load by meansoftorquebars or coil springs. In this way the effect circulates within theassembly andonly thelosses dueto friction have to be produced bythemotor. Asan exampleof this arrange- ment an investigation by KNOWLTON and SNYDER (1940) is mentioned.

44 45

FATIGUE TESTING AND ANALYSIS OF RESULTS FATIGUE TESTING MACHINES AND EQUIPMENT

Extremely high contact stresses are developed in ball and roller bearings, and machines for testing complete bearings are used by all manufacturers. Loads are produced by weight or spring-loaded leverages. Some methods of life testing of both plain bearings and ball and roller bearings are described in ASTM STP No. 70 (1946): Synsposiusn on testing of bearings and also in a book byJURGEN5MEYER (1937).

References: BUCKINGHAM (1944), GUYOT and SCHIMKAT (1950), HORGER (1949), JURGEN5MEYER (1937), KNOWLTON and SNYDER (1940), KENNEDY (1956), MACKS (1958), MELDAHL (1939), NI5HIHARA and YAMADA (1950), VIDAL, GIRARD and LANU5SE (1956), WALKER (1947), WAY (1935).

32.6 Repeated Impact

The effect of an impact depends entirely upon the shape of the test piece and the rigidity of the framework, and in consequence reproducible results are difficult to obtain. This makes the impact method of testing less reliable than conventional fatigue testing and it is now not verymuch used. As early as 1864 Fairbairn carried out “experiments to determine theeffect ofimpadt vibratory action and long continued changes of load on wrought iron girders”.

A typical wayof producing repeated impacts is tlse one used by STANToN (1906). A cam raises a weight which strikes a beam Specimen midway between two knife edge supports at a rate of 100 blows per minute. The specimen is rotated 180°between impacts. The speed is restricted, due to the condition that the vibrations have to vanish between the blows. This delay depends, of course, on the shape of the specimen and on the material.

Amachine of similar design was developed by Amsler and Co. as described by SCHICK (1934). The test piece permitted an operation speed of 600 strokes per mm. Arrangements were provided for tension, bending, and compression impact tests.

A somewhat different principle was used by Roos (1912). His machine consisted of a pair of swinging pendulum hammers acting on a cantilever specimen which was fixed at one end and struck alternately from two sides by the hammers. Fifty double blows were applied per sninute. A similar machine was developed by MOORE and KOMMER5 (1927). The rate was slightly higher, being 65 blows per minute. Reference is also made to a paper by SEAGEE and TAIT (1938).

For the purpose of testing the resistance of plastics to impact, FINDLEY and HINTZ (1943) employed a novel method. Balls were lifted by a large wheel with pockets and deposited in a runway from which they dropped on the specimen. It is of interest to note that calculations of stress produced by impact permitted correlation with fatigue test. A somewhat modified method of transporting the balls was used by LUaIN and WINAN5 (1944).

References: FINDLEY and HINTZ (1943), LUBIN and WINANI (1944), MOORE and KOMMERS (1927), Roos (1912), SCHICK (1934), SEAGER and TAIT (1938), STANTON (1906).

32.7 Combined Creep and Fatigue Tests

The development of high-temperature machines such as gas turbines, operating under complex stressing conditions, depends to a large extent on the production and use of special metals. Simple creep and fatigue tests alone are inadequate in determining the behaviour of metals under inter- mittent working conditions. From a practical point of view it may be advantageous to simulate the essential features of thestress and temperature conditions imposed on a particular machine component during its working life.

From this viewpoint KENNEDY (1956) and KENNEDY and SLADE (1956) have designedand developedan apparatus to examine themore fundamental aspects of these problems, permitting a complex stress programme to be applied and the deformationrecorded. In addition, facilities are incorporated for examining the stress relaxation at constant strain or the strain relaxation at constant stress.

The new feature of the machine is the electromechanical stressing system, and particularly its application to creep testing. The stress is imposed by meaos of a mechanical spring. The extension of the spring is automatically regulated so that the test is conducted at either constant Stress or constant load. The test piece is mounted in a temperature-controlled enclosure, its upper essd connected through a set of parallel-motion springs to an electro- magnetic vibrator. A pick-up in parallel with the vibrator enables the motion of the upper end of the test piece to be measured. The variable force is measured by a barium titanate crystal. The creep stress is applied by driving a reversible motor to pull dowss the lower end of a spring. Any desired intermittent stressing sequence can be applied by a programmer which switches the motor on or off.

Another machine of this type, combining the rupture test and fatigue test, is described by MANJOINE (1949).

References: KENNEDY (1956), KENNEDY and SLADE (1956), MANJOINE (1949).

33.0 General

SECTION 33. EQUIPMENTS FOR TESTING PARTS AND ASSEMBLIES

Thie dihlieulty of correlating the fhtigue properties of standard test speci- messs with those of actual machine parts and components is explained by differences in material propert es, Sllape and fabrication. As an illustration we may take a gas-turbine blade Itaving a crescent-like cross-section. In cast blades, the metal usually has a finer grain structure at the points of the crescent than ill the heavier mid-section. As grain structure has a pro- nounced effect on the fatigue properties, conclusions based on tests on standard specimens from the same material may be quite misleading. In the same way, differences in stress distribution due to the shape and differences in surface condition due to the fabrication make tests on actual components a necessity.

46 47

FATIGUE TESTING AND ANALYSIS OF RESULTS FATIGUE TESTING MACHINES AND EQUIPMENT

The testing of actual design membersand assemblies is, in fact, older than the testing. of standardized specimens. Fairbairn in 1864 carried out experiments on full-size wrought iron girders subjected to impact vibratory loads and Wohler (1858—1870) started his famous investigations by applying rotating-bending tests to full-size railway axles.

The shape and the size of many components prevent the use of standard fatigue machines and accordingly several testing machines and equipments have been designed for specific and limited purposes.

The following items will be discussed in the present section: (1) wires, tyres, and ropes; (2) coil and leafsprings; (3) turbine and propeller blades; (4) large specimens, structures, beams, rails; (5) aircraft structures.

33.1 Wires, Tyres and Ropes

The purpose of testing wires in fatigue is to examine the properties of the material and the effect of heat treatment, cold working, and metallographic and mechanical surface condition. A particular difficulty arises from the fact that the test piece cannot be givena suitable shape to prevent failure in the grips and does not permit surface preparation for this purpose. This condition restricts the choice of testing machine. The most common type of stressing is bending and torsion for the reason that they are more sensitive to changes in the surface properties.

There are also, however, a few wire testing machines in which axial loading is applied to the specimen. POMP and DUcKWITz (1931) and POMP and HEMPEL (1938), for example, used an electro-magnetic machine based on a d.c. motor vibrated in resonance by an a.c. current. Another type of machine by KENYON (1940) employs the inertia forces of three masses connected to three specimens inserted between two wobble plates which produce reciprocating motions with a phase difference of 120°. A third machine by AMSLER (1946) is based on resonant vibrations produced by centrifugal forces acting on two Specimens in series, one on each side of a vibrating lever.

Fatigue testing ofwires by meansof conventional rotating-beam machines with constant moment over the length of thespecimenwas used by WAMPLER and ALLEMAN (1939), while KENYON (1935) and similarly VOTTA (1948) developed rotating wire-arc machines with the specimen submerged in an oil bath to prevent transverse vibrations. The constant moment over the length of the specimen makes it difficult to eliminate failure at the grip. For this purpose SHELTON (1931, 1933, 1935) and GILL and GOODAcRE (1934) used thebuckling column principle introduced by Haigh and Robert- son by means of which the moment in the grip portion is practically zero. Instead of loading the wires as a pin-ended column, CORTEN and SINCLAIR (1955) attained the same effect by automatically keeping the distance between the ends of the curved wire at the correct distance for a moment- free end load. RossET’rI (1953) developed a new machine for testing wire ropes, the load being a combination of bending and tension.

Thepreceding machines may be used for purposesother than testing Wires. A more realistic simulation of service loads on ropes and cables is obtained

in a machine by FOREST and HOPKINs (1932) who used the old principle of flexing the cable over rotating pulleys of different diameters, and simul- taneously rotating the cablewhich was subjected to a constant tension. The friction was reduced by a slow rotation of the pulley. A similar idea was used by WOERNLE (1930) with the modification that both ends of the cable were driven in order to reduce torsional moments on the cable.

A special machine for testing car tyre cords was invented by MALLORY (U.S. Patent No. 2,412,524) and further developed and used by KENYON (1945), BRADSHAW (1945), BUDD and LARRICK (1945) and LARRICK (1945). An axial oscillator-type machine for testing textiles and rubber is described by TENOT (1947).

References: AMSLER (1946), B1t&Dsa&w (1945), BUDD and LARRIGK (1945), CORTEN and SINcLAIR (1955), DEFoREsT and HOPKINS (1932), GILL and GooDAcm~(1934), KENYON (1935, 1940, 1945), LARRIGK (1945), MALLORY (U.S.patent No. 2,412,524), POMP and DUcKwITZ (1931), POMP and HEMPEL (1938), ROSSEYTI (1953), SHELTON (1931, 1933, 1935), TATNALL (1937), TENOT (1947), VOTTA (1948), WAMPLER and ALLEMAN (1939), WOERNLE (1930).

33.2 Coil and Leaf Springs

Earlier machines for testing of coil sprjngs were of thedirect displacement type in which somemechanism, such as d~cam, applied a known compressive distortion to the spring. Some were desitned for a single specimen, whereas others allowed the simultaneous testing of alarge number ofspecimens. An example of the first type is a machine by ZIMMERLI (1940), and ofthe second type machines described by TATNALL (1937) and by Oscavrz (1940).

The force necessary to apply direct compressive deformation to a heavy Spring of this type is considerable and requires a large input of power. Due to the weight of the moving parts these machines are slow.

A considerable increase in speed can be obtained by using a machine working on the resonance principle, in which the spring-mass system is oscillated at its natural frequency (LEA and HEYwOOD, 1927). Another machine of this type is described by COATE5 and POPE (1956), in which the oscillating system consists of two masses arranged between four springs in

series. A periodic force produced by. a pair of out-of-balance weights is applied to the lower mass. This particular system has two degrees of freedom: the first, in which the two masses move in phase, thus causing no fluctuating stresses in the two central springs; and the second, in which the two masses move in opposite directions, with a central collar acting as a node. The forces are determined by the amplitudes of oscillation which are measured to an accuracy of +0~005inch by means of vibrographs fastened on the two masses and the collar. When fracture of any spring occurs, the balance of the system is destroyed and the central collar starts moving, thereby acting on a cut-off system which breaks the power supply to the main driving motor.

Resonant machines for the simultaneous testing of a large number of springs have also been constructed. As an example may be mentioned one

48 49

FATIGUE TESTING AND ANALYSIS OF RESULTS FATIGUE TESTING MACNINES AND EQUIPMENT

of Bauart Reicherter, described in the book by Oseswrz and HEMPEL (1958, p. 231). At the same time, 100 to 180 springs may be subjected to a displacement of 40 mm at a speed of 1800 to 2400 c/mm.

The testing of leaf springs is also based either on constant displacement amplitude or on resonance of the spring-mass system. Several commercial machines of thefirst type are available. An early design ofthe second type was developed by BAT5ON and BRADLEY (1931) in which the excitation force wasproduced by a crank, leverage and coil spring system. A similar machine was designed by LEHR (1932).

References: BAT5ON and BRADLEY (1931), COATE5 and POPE (1956), LEA and HEYWOOD (1927), LEHR (1932), OscMATz (1940), OscrsATz and HEMPEL (1958), TATNALL (1937), ZIMMERLI (1940).

33.3 Turbine and Propeller Blades

Special fatigue-testing machines in which the blade of a propeller is excited to its natural mode of vibration by means of mechanical oscillators are discussed by GARDINER (1949).

Turbine blades may be excited electro-magnetically. Such devices operate at high frequencies and require very small power consumption. Electrical methods of inducing and detecting such vibrations are described by SNOWBALL (1949). An electrostatic method for the same purpose has been developed by STRAND—HAGEN and SOMMER (1956).

References: GARDINER (1949), SNOWBALL (1949), STRANDNAGEN and SOMMER (1956).

33.4 Large Specimens, Structures, Beams, Rails Fatigue testing of large specimens and full-size members requires special

testing machines or equipment attached direct to the test piece. A frequently used device is the mechanical oscillator consisting of a single rotating eccentric, as developed by Losenhausen Werke already in 1927, or of two opposed out-of-balance weights as described by O5GHATZ (1934), TIIUM and BERGMAN (1937), LAZAN (1942) and others. Vibration-testing techniques for large specimens are reviewed by SCREEYER and YOST (1956).

Electromagnetic excitation is also used. A convenient method ofvibrating a test member is to use a mechanical connexion from a moving-coil type loudspeaker as described by BLEAKNEY (1938).

Similar methods may be used for testing structures. Fatigue machines fir testing structural units are discussed by TEMPLIN (1939). The fatigue testing of structures by the resonance method is discussed by HEYwOOD (1953) and by MEYER (1954). Notes on the automatic control of testing equipment are given by HEwsoN (1954) and a new resonance vibration excitor and controller was developed by LAEAN, a al. (1952).

In some cases it may be convenient to attach hydraulic equipment to a structure to produce the load. Arrangements of levers, jacks, loading frames, and special supports are reviewed by OWEN (1943).

A control equipment for the fatigue testing by means of hydraulic jacks of a large variety of components such as highly loaded undercarriage, wing

or tailplane attachments, and pressurized components such as radoms and

parts of the air, fuel and hydraulic system has been developed at the English Electric Company Ltd. by MOORE (1956). This equipment is capable of subjecting the component to a programme loading consisting of six loading steps with a number of load cycles arbitrarily selected between one and 999 cycles.

The main part of the equipment consists of a load setting and counting unit wluchi controls the number of cycles of each stress level. This unit controls the supply of hydraulic fluid to the loading rig by means of a solenoid-operated valve. The load applied to the test component is measured by resistance strain gauges included in a bridge network. The bridge can be unbalanced by a number of potentiometers, one for each value of maxi- mum and minimum load. On starting the cycle, the load is gradually increased until tile maximum value is reached. At this point, the bridge network will be balanced and the output signal from the bridge will pass through zero and change in phase. This causes the bi-stable switch to reverse the flow, and the load returns to the minimum load value, from which the cycling is started again.

A typical method (If testing large welded beams by means of mechanical exeitors mounted in the centre of the span between thenodes is described by PERCIVAL and WECK (1947). A similar test on thin-gauge box-section beams was carried out by NEWMAN and C0ATE5 (1956) with the modification that the excitor was mounted at one end of the beam with a balancing mass at the other. To keep the test frequencies within 3500 to 5000 c/mm the beams were made 6 ft in length.

Similar tests on rails have been conducted by BANKS (1950). A length of 15 ft gave a natural frequency of 1920 c/mirs.

In tests by R0E5LI, LOEWER and ENEY (1954) the passage of trucks over bridge members was simulated.

References: BANKS (1950), BLEAKNEY (1938), HEWSON (1954), HEYWOOD (1953), LAzAN (1942), LAZAN, BROWN, GANN5ETT, KIRMSER and KLUMPP (1952), MEYER (1954), MOORE (1956), NEWMAN and COATES (1956), OseHA’rz (1934), OWEN (1943), PERCIVAL and WECK (1947), ROESLI, LOEWER and ItNRY (1954), SCIIREYER and YosT (195fi), TEMPLIN (1939), TFIUM and BERGMAN (1937).

33.5 Aircraft Structures

NI ((h iai I cal scihha ((IS h avc tisquclst hy blecil used for subjecting aircraft structures to ahternatiug stresses, as described by FosrER and SELIGER (1944) and by MOLYNEUX and BROADnENT (1946). A comparison of the endurance of various aircraft structures under fluctuating load was made by FISHER (1949). Aeroplane wing-beams were tested by BLEAKNEY (1938) and by BRUECGEMAN, KRUPEN and Row’ (1944) by using a mechanical connexion from a moving-coil type loudspeaker. Tests for studying crack propagation in fuselages and smahh- and full-scale cylinders were made by HARPUR (1958) and impact tests on aircraft undercarriage by BROWN (1947). Cams Were used to lift and drop weights on the test member.

50 51

FATIGUE TEsTING AND ANALYSIS OP RESULTS

Developments in methods of strength testing pressurized fuselages are reported by HoTsoN (1949). Observed failures of pressurized fuselages varied in character from minor rupture to catastrophic explosion. In order to answer the question of whether the character of the failure can be con- trolled, Dow and PETERS (1955) subjected stiffened cylinders of 2024 aluminium alloy to internal pressure and cyclic torsion, thus simulating stress conditions of cutouts in the side of a pressurized cabin in flight.

Full-scale aeroplane wing structures have been tested to destruction by several investigators. FEARNOW (1951) subjected two C-46D wings to resonant vibrations of constant amplitude by means of a testing rig which consisted of prime mover, reduction gear box, line shafting, adjustable eccentric, and an excited spring. Concentrated masses were attached to the wing to reproduce flight Stresses corresponding to load factor values of 1 ±0~625g over approximately 45 per cent of the span. Each wing was instrumented with fatigue-detector wires at points where previous tests by brittle-lacquer techniques had indicated high local stress concentrations. It is remarkable that the decrease in natural frequency was small and could not be used to detect incipient cracks, a method which has been used with great advantage when testing specimens of simple shape (cf. QUJNLAN, 1946). In this case, the frequency did not decrease more than 2 c/mm out of 106 c/mm when as much as 55 per cent of the tension material had failed.

A detailed description of a similar fatigue rig and the preparation of the wing specimen is given by MGGUIGAN (1953). Tests on C—46 “Commando” aeroplane wings with this machine are reported by MCGUIGAN, BRYAN and WHALEY (1954). The tests were conducted at a resonant frequency of 108 c/mm at four different stress levels (each wing subjected to one stress level only). The wings were instrumented with a number of wire resistance strain gauges and crack-detecting copper wires in the vicinity of expected stress raisers. Fatigue tests on typical two-spar light alloy structures (Meteor 4 tailplanes) were conducted by RAITHBY (1951).

The fatigue strength of CA—12 “Boomerang” wings was determined in a similar manner byjouNsToNE, PATCHING and PAYNE (1950). The vibrations were excited by a stroking machine driving through a spring. The load was controlled by a deflexion indicator. The wing was excited on one side only. The bending restraint at the supporting points must therefore be small to obtain sympathetic vibration of the other side.

The vibration method is not suitable for applying high load ranges of low frequencies. For this purpose hydraulic loading rigs are preferable. Such a rig is described by PATCHING (1951) in an interim note on fatigue testing of P51D “Mustang” wings. The frequency is very low, being only 10 c/mm. An extension of this investigation including not less than 72 Mustang mainpianes and using a combination of the previously mentioned vibration and hydraulic methods is reported by KEPERT and PAYNE (1956) and by PAYNE (1956). The hydraulic loading rig was used for stress levels leading to fatigue failure in less than 50 kc in combination with dead weights and screw jacks, whereas tests at low load ranges were made in the vibration

FATIGUE TESTING MACHINES AND EQUIPMENT

loading rig. Each wing was subjected to one stress level only until failure occurred, with the exception that some of thewing specimens were subjected to pre-loads of different magnitude, some as high as 95 per cent of the ultimate failing load.

The preceding investigations were all of the constant-amplitude type, i.e. each specimen was subjected to one stress level only. A fatigue equipment for simulating the flight stresses on aircraft by a programme loading is described by JOMNSTONE and MOODY (1953). Fatigue machines of this type have been used extensively for testing aircraft structures and various com-

ponents in Germany since 1939 (GASSNER) and are now commercially available (Schenck and others).

References: BLEAKNEY (1938), BROWN (1947), BRUEGGEMAN, KRUPEN and Row’ (1944), Dow and PETERS (1955), FEARNOW (1951), FIsHER (1949), FOSTER and SELtGER (1944), HARPUR (1958), HoTsoN (1949), JOHNSTONE and MOODY (1953), J0HN5T0NE, PATCHING and PAYNE (1950), KEPERT and PAYNE (1956), MCGUIGAN (1953), MCGUIGAN, BRYAN and WHALEY (1954), MOLYNEUx and BROADBENT (1946), PATCH5NG (1951), PAYNE (1956), RAsTrsnv (1951).

SECTION 34. COMPONENTS OF FATIGUE TESTING MACHINES

34.0 General

Any fatigue testing machine is composed of the following structural components: (1) a load-producing mechanism which generates the alter- nating load (or displacement) to which in some cases is added a steady load; (2) load-transmitting members such as grips, guide fixtures, flexure joints etc., by which the load produced is transmitted in such a way as to produce the desired stress distribution within the specimen; (3) measuring devices which permit the setting of the nominal upper and lower load limits; (4) a control device for maintaining the load throughout the test and sometimes automatically correcting changes in force or deformation arising

during the test; (5) counter and shut-off apparatus which counts the number of Stress reversals imposed on the specimen and stops the testing machine after a given number of cycles, at complete fracture of the specimen, or at sonic prcassigocd clsaoge ill deformatiots or frequency; (6) a framework, suppurtissg the various parts of the machine and, if necessary, arranged to reduce the vibratory energy transmitted to the foundations.

34.1 Load-producing Mechanisms

The loads may be produced by various methods: mechanical, electro- magnetic, etc., as mentioned in Section 30.

The simplest way is to attach one end of a coil spring to the specimen and to give the other end of the spring a reciprocating movement by means of a crank. The use of single tandem spriugs will often produce torsional vibrations which may be eliminated by the addition of a detuning inertia. Parallel-motion springs are described by JONEs (1951). If the speed of the

52 53

FATIGUE TESTING AND ANALYSIS OF RESULTS FATIGUE TESTING MACHINES AND EQUIPMENT

crank shaft is well below the natural frequency of the spring-mass system, the forces on the crank are approximately equal to the forces acting on the specimen. A considerable reduction of the load on the crank is possible, however, by running the crankshaft at a speed close to the natural frequency of the system.

Another convenientmethod of producing the excitingforcesby mechanical means is to use oscillators consisting of one, two, or even four rotating out-of- balance weights. With fourweights it is possible to adjust the force while the machine is in operation by shifting the relative phase between the two pail-s of weights.

A third method of excitingthe spring-mass system, known as the “slipping clutch”, was originated by AUGHTIE (1931) and further developed and used by Cox and COLEMAN (1950). An application of this device is also described by O’CONNOR and MORRISON (1956). The clutch is moved back and forth by a variable throw crank, rubbing against a surface of themass and exciting the system to vibrate at its natural frequency. The force transmitted to the Specimen is constant within a reasonable rangeofspeeds of the driving motor; its magnitude depending on the spring System and the throw of the driving crank, which in some applications by Cox could be varied while the machine is running.

The fact that very small bbrces are required to maintain a spring-mass system in vibration at its natural frequency makes electromagnetic excitation very Suitable for testing purpose. Various machines based on this principle have beendesigned. As an illustration, a device developed by DOLAN (1951) will be described because of its simplicity. The vibrating system consists of two lseavy masses attached to the ends of the specimen which acts as a bending spring. This assembly is suspended by links and soft springs from a frame that allows the assembly to vibrate as a tuning fork. One of themasses is excited by means of a short drive rod actuated by the electromagnetic excitor. Attached to the second mass is a velocity-sensitive pickup which generates an electric signal that is amplified and fed back to the driving coil of the excitor. The main difficulty arising when operating a system in resonant vibrations is the control of the amplitude within narrow limits. This problem has been solved in a very simple and successful way whicls will be described in paragraph 31.4.

Hydraulic machines are convenient to use wlscn a large capacity is required and low frequencies can be tolerated. The loading rigs Ilsay easily be adapted to a wide range of applications, in particular by controlling the supply of hydraulic fluid to the loading rig by means of a solenoid- operated valve. Such an equipment, developed by MOORE (1956), has heeo described in paragraph 33.4.

Although hydraulic methods do not permit high frequencies, the contrary is true of pneumatic methods. As already mentioned (32.1), LOMAS, WARD, RAIT and COLBECK (1956) could easily attain speeds up to 150,000 c/mm with an extremely simple design of fatigue machine. A tuning cavity adjustable by a piston, a tube, and the specimen is all that is needed. Another advantage is that theresonant peak in apneumatic circuit is quite broad and

flat, unlike reson;mce in an electrical circuit. Automatic amplitude control is, therefore, is most cases unnecessary.

References: AUGHTIE (1931), Cox and COLEMAN (1950), DOLAN (1951), JONES (1951), LEHR (1930), L0MA5, WARD, RAIT and COLBECK (1956), MOORE (1956), O’CONNOR and MORRISON (1956).

34.2 Load-transmitting Members

An essential feature of a fatigue testing machine, which is of extreme importance if the machine is to function efficiently and give reliable results, is the way in which the load is transmitted from the machine to thespecimen, i.e. the design of the grips. The grips must fulfil two conditions; first, they must not introduce extraneous stresses leading to failure in the grip portion of the specimen, and second, they must not distort the prescribed stress distribution within the specimen.

The first condition is particularly difficult to satisfy when no surface preparation of the specimen is permitted and the specimen cannot be shaped to prevent such failure. Under these conditions only certain types of machine are acceptable, e.g. repeated bending machines or machines of the pin-ended column type.

Even if the Specimen is given a suitable shape to satisfy the first condition, the second difficulty remains, i.e. the prevention of unexpected stresses introduced into the specimen when it is mounted in the machine. In parti- cular, precautions must be taken in connexioD with axial-loading machines.

It is easy to show that in order to limit the error to not more than I per cent of tue stress applied to a rectangular specimen of cross-section b x h, the line of load must not deviate from the geometrical axis of the specimen by nsore than 0~002h. This problem hasbeendiscussed by MoRRISoN (1940). It is obvious that no specimen which depends upon screwed ends for load application is satisfactory in this respect, as pointed out by O’CONNOR and MORRISON (1956), who also suggest that appalling inaccuracies which may easily range from ten to twenty or more per cent have been incurred by tisose who have taken insufficient care with this one requirement. This statement appears to be in good agreement with their own results. The Specimens of a pssSh-pull fatigue testiug macisine were finished not only on time gauge lcugtis smith nieticmdous care, but also Isad their ends ground to extremely close limits (-1-00001 in.). Each end was thus secured, by means of Split coilets ssud a nut, axially in a loading bar. These bars were them- selves supported ill a massive stress—free cast—il-un frame in wlsich were four holeS, bored amsd lapped wit Is extreme care to guide the bars coaxially. In spite of tisese prccautions—-certainly surpassing current practice—careful dynamic calibration, using triple resistance strain-gauge extensometers attached to the specimen, and statically checked by triple optical extenso- meters, indicated that the maximum stress exceeded the mean stress by about I ~ per cent.

These results ame cossfirmed by an investigation by FINDLEY (1947). By means of an apparatus which will be described in the following paragraph (3), ise found that the specimen was distorted when mounted in the testing

54 55

FATIGUE TESTING AND ANALYSIS OF RESULTS FATIGUE TESTING MACHINES AND EQUIPMENT

machine by an amount corresponding to bending stresses seldom less than 10 or 20 per cent of the mean stress. These distortions could be considerably reduced by means of a six-component correction system incorporated in the testing machine.

Self-aiming grips are described by RUSSELL, JACKSON, GROVER and BEAVER (1944) and by GROVER, BIsHOP and JACKSON (1951). Measurements with bonded wire strain gauges have shown that, with careful loading, the grips gave uniformity of stresses in a sheet specimen to about ±500lb/in2, which was 5 per cent of the maximum stress.

Five different systems of grips for fatigue testing wires are described by SOETE and VANCROMBRUGGE (1949).

A torsion grip to ensure that only pure torque is applied to thespecimen is described by CHODOROWSKI (1956). The square end of the specimen is keyed to an inner member, whose inclined faces are positioned in the machine by four hardened steel balls held in an outer member. The balls arebacked by grub screws and bear against hardened steel rollers.

An interesting method of mounting specimens in a torsional vibrator hi such a way that reversed plain bending in the free-free mode resulted was developed by WADE and GROOTENHUI5 (1956). After having tried several ways, the ultimate form described in the paper consisted of transmitting the torque through a hardened knife-edge integral with a silver-steel shaft. The specimen, supported only at one node, was located on the opposite face by a central probe.

Another detail of practical use for supported levers in testing machines, which is a simple and effective means of overcoming difficulties experienced with the usual type of bearing and knife edges, is the cross-spring pivot which consists of one or two pairs of crossed flat springs. It is of practical use in cases where only a limited angle of rotation is required. The points where the springs intersect functions primarily as the pivot point. Since a cross-spring pivot has no sliding parts there is no need of lubrication. The deflexion is, however, accompanied by reaction forces, though they are usually very small. This constructional element has been examined by EAsTMAN (1935). It has been studied experimentally by YOUNG (1944) and theoretically by HARINGx (1949).

The application of the load to structural members, aircraft wings, and the like, is not always easy. A device which in many cases has rendered good service is the tension pad which is glued to the test piece. It has been examined by OAKS and HOWELL (1956).

Thin sheet specimens in compression are inclined to buckle. A means of preventing buckling is to clamp the specimen between guide plates. A description of such guides is given by BRUEGGEMAN and MAYER (1944, 1948) and also by RONDELL and DUYN (1950). In papers by GROVER, BISHOP and JACKSON (1951) and by GROVER, HYLER, KUHN, LANDERS and HOWELL (1953) somefeatures of this device and the influence on theaccuracy are presented.

It was found that if the guide plates are too tight and specimens are not perfectly flat, an appreciable fraction of the applied load goes in friction,

but ifthe guide plates are too loose, the specimen buckles on thecompression part of the cycle and bending Stresses may become large. On the basis of previous experience, the guide plates were made to allow a clearance of 0~0025in. between either surface of thespecimen and an oiled paper. With

clearance increased by a 0~005in. shim separating the guide plates, however, there was evidence of significant buckling.

A difficult problem is to transmit an axial or torsional load to a specimen inside a thick cylinder to which high internal pressure is applied. A solution of this problem is reported by MORRISON, CROSSLAND and PARRY (1956), the main feature being a gland which provides simultaneously little friction and little leakage. The gland described is of the “unsupported area” principle, in that aheavy block called the gland body is forced by the liquid pressure on to a rubber packing-ring whose extrusion is prevented by chamfer rings. The inner surfaceof the rubber presses on a thin extension of the gland body. It is reported that since the technique of producing a really good finish on the ram and in the gland with the correct clearance had been mastered, and the optimum packing thickness ascertained, the leakage was extremely small—of the order of a drop per minute—yet the ram could be easily pushed to and fro and rotated by hand when the pressure held was 20 tons/in1.

References: BRUEGGEMAN and MAYER (1944, 1948), CH0D0R0w5KI (1956), CRO55LAND (1954), EASTMAN (1935), GROVER, HYLER, KUHN, LANDERS and HOWELL (1953), HARINGx (1949), MORRISON (1940), MoRRISON, CRO5SLAND and PARRY (1956), OAKS and HOWELL (1956), O’CONNOR and MORRISON (1956), RONDELL and DUYN (1950), SOETE and VANCROMBRUGGE (1949), WADE and GROOTENHUIS (1956), YOUNG (1944).

34.3 Measuring Devices

In the machines producing a constant amplitude of deflexion and those where the load is produced by dead weights or constant spring forces no measuring device is required. This is also the case when a variable load is measured by the extension or compression of a calibrated Spring with the reservation that the modulus of elasticity for steel, measured statically, does not rensain unchanged at frequencies above 5000 c/mm as stated by ERLINGER (1935). Otherwise sonic nscans of measuring either a deflexion or a force is needed.

A very simmiple device for measuring large amplitudes is the vibrograph, which consists essentially of two diagrams with sloping lines, one of them fastened to tise vibratissg mass, the otiser stationary. Vertical oscillations of such a diagram causes an apparent hsorizontal movement of the point of intersection of the lines. Readings to an accuracy of 0~002in. are obtainable.

Various otiser optical methods such as microscopes or mirrors are fre- quently used.

A convenient electrical method, easily adapted for control purposes, is the resistor transducer. As an example, the stressing unit by KENNEDY and SLADE (1956) may be mentioned, where the transducers were able to detect a movement of 0~00Iin. over a total range of 0~5in.

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FATIGUE TESTING AND ANALYSIS OP RESULTS PATIGUE TESTING MACHINES AND EQUIPMENT

An interesting method of measuring the applied load in an axial-loading machine based on centrifugal forces was developed by LEHR (1930). The frame-work of the machine was free to move in horizontal direction and its amplitude, measured by a microscope, was used as a measure of the applied load.

Torsional moments are easily and precisely measured optically by observing the twist of a torque-bar calibrated against a dead weight. This type ofspring is less affected by inertia forces than coil and leaf springs and is therefore applicable at high frequencies. An application is reported by CROS5LAND (1956) and by CHoDoRowsKs (1956). By using interchangeable bars, a sensitivity of measurement always better than +1 per cent could he expected.

By making use of an idea suggested by Parry, it was possible to measure the torque at any point in the cycle while the machine was running at full speed. The method consists of fitting a contactbreaker on the driving shaft, so arranged that it may be manually placed in an arbitrary angular position of the stress cycle. This contact breaker triggers a stroboscope which illuminates the scale, used in conjunction with a telescope and mirrors on the torque bar.

The measurement of forces may be done by mechanical dynamometers of various designs. A versatile electrical method is obtained by the use of bonded wire strain gauges. As the change in resistance is very small, a precise measurement of high-frequency variable forces requires a specialized technique. A null method for this purpose has been developed by ROBERTS (1952), another by GUsTAvssoN and OLssoN (1956).

The strain gauge may be bonded to a calibrated bar, thus serving as a high-frequency dynamometer. It may also be bonded directly to the test piece without adding any perceptible inertia, and is then an excellent means of controlling the desired stress distribution within the specimen.

In hydraulic testing machines, the problem arises of measuring the fluid pressure. Up to pressures of 30 tons/in1 the approximate pressure may be measured by a Bourdon tube gauge, but for more accurate measurements, or for higher pressures, a dead-Weight piston gauge may be used. The weight carrier of the dead-weight gauge is continuously rotated as described by PEARCE (1952). For fluctuating pressures, the pressure effect on tlse resis- tance of a manganin coil has been extensively used by Bridgman. Another straightforward method is to measure, optically or by strain gauges, the diametral expansion of a thick-walled cylinder. The latter method isas been used, for example, by MoRRISoN, CROSSLAND and PARRY (1956).

References: CHODORWSKI (1956), ERLINGER (1935), GUSTAFSSON and OLssoN (1956), KENNEDY and SLADE (1956), LEHR (1930), MoRRIsoN, CROSSLAND and PARRY (1956), PEARCE (1952), ROnERTS (1952).

34.4 Control Devices and Shut-off Apparatuses In most cases the selected stress level remains the same throughout the

greater part of the test, but many machines require a certain time before a stationary state is reached, and in the later stage of the damage processwhen

localized yielding or cracking of the test piece occurs, a substantial change may occssr. Possible changes are revealed by the measuring devices indicated in the preceding paragraph, and appropriate adjustment may then follow either by hand or automatically. The first alternative is, in general, used during the starting period, but in modern machines and equipments an automatic control throughout the test is frequently required, particularly in equipments of the resonant type. This procedure is, of course, easier When the load is produced by electrical forces but it is quite feasible in connexion with other machines.

As an example of such control methods in eonnexion with mechanical oscillators, reference is made to a paper by PERCIVAL and WECK (1947). A similar device is used in spring fatigue testing machines developed by COATES and POPE (1956). A spring and dash-pot lever mechanism is actuated by one of the vibrating masses and controls a Servo-motor which varies a resistance in the electrical circuit of the main driving motor.

A simple control system which has been found to operate in a stable and satisfactory manner for long periods of continuous operation was developed by DOLAN (1951). A micrometer screw is attached to one ofthe two vibrating masses. At a given amplitude which can be pre-set to give a desired magni- tude the contact made by this screw develops a small pulse from a battery. This pulse is smoothed and spread out over approximately a half period of the vibration and then subtracted from the generating current. The control circuit can be adjusted during operation so that the micrometer makes contact, say, every second or third cycle ofvibration. The shut-off apparatus consisted of a piece of piano wire on which was slipped a small brass weight flee to slide up and down thewire. The length of wire was adjusted to give a natural frequency slightly higher than the resonant frequency ofthe spring-mass system. Any drop in amplitude or frequency of the exciter caused the small weight to slide down the wire and actuated the shut-off.

In the torsional vibrator by WADE and GROOTENHUI5 (1956), mentioned in paragraph (32.1), resonance was maintained by using an electrical feed- back system, tise initial signal Iseing derived from the motion of the specimen by means of an induction coil pick-up. An elaborate, completely electronic amplitude and control system is described in the publication.

A load-control system in connexion with a hydraulic, non-resonant fatigue tistiug maclime by MooRE (1956) has already been described in paragraph (33.4).

A load-control System of quite a different character is that developed by KENNEDY (1952, 1953) in a unit for combined creep and fatigue testing. It is required that the applied load be decreased in relation to thechanging cross-section in order to maintain a constant stress. Assuming that there is no change in the density of the metal, this condition is equivalent to the conditiois that the product of the load applied and the specimen length sisall be constant. i~isiscondition is simply achieved by arranging that the resistances in the opposite arms ofa Wheatstone bridge vary according to the load and the length. For this purpose, two resistor transducers were con- nected across a load spring and a creep spring, respectively.

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FATIGUE TESTING AND ANALYSIS OF RESULTS FATIGUE TESTING MACHINES AND EQUIPMENT

References: COATES and POPE (1956), DOLAN (1961), KENNEDY (1952, 1953), MOORE (1956), PERCIVAL and WECK (1947), WADEand GROOTENHUIS (1956).

34.5 Counters

The fatiguelife is defined by thenumber ofcycles imposed on thespecimen until failure or some other specified event occurs. When the testing machine is driven by a rotating motor, the life is simply measured by a counter giving the number of revolutions from the start until the motor is stopped. This method is not feasible, however, in electrically excited resonant-type machines. In this case, it may be possible to measure the fatigue life directly in time (minutes) on condition that the frequency does not change by a measurable amount, and then to obtain the number of cycles by direct multiplication of the time and the frequency. This method WaS used by DOLAN (1951).

It is, of course, better to measure the exact number of cycles by means of an electric clock as done, for example, by WA.rE and GROOTENHUIS (1956).

In programme testing machines it is required that the load be changed automatically after a prescribed number of cycles. This may be realized by means of mechanical or electrical counters. A review of various counters of these types used in Germany is given by BECKER (1950). High-frequency pulses and electrical signals are conveniently counted by means of dekatron counters as done, for example, by KENNEDY and SLADE (1956). Another application in programme testing of this type of counter is described by MOORE (1956).

References: BECKER (1950), DOLAN (1951), KENNEDY and SLADE (1956), MOORE (1956), WADE and GROOTENHUIS (1956).

34.6 Frameworks The different components of a testing machine such as guiding bars,

loading frames, leverage, pivots and bearings are assembled and supported by a framework.

In order to reduce to a minisuum the energy transmitted to the foundation and to isolate the testing machine and its parts from vibrations ofsurrounding machines, the framework sometimes includes a suspension rig, or is mounted on suitable springs, or placed on rubber mounts or cork. Undamped dynamic vibration absorbers have also been used (O’CONNOR and MORRISON, 1956).

As already mentioned, LEHR (1930) providedtheframework with means to allow free horizontal vibrations, which were used as a measure of tise load.

References: LEHR (1930), O’CONNOR and MORRISON (1956). SECTION 35. CALIBRATION AND CHECKING OF TESTING

MACHINES

35.0 General

The purpose of a fatigue-testing machine is to apply to the test piece an alternating load producing a well-defined stress distribution. This distri- bution should be reproducible within narrow limits, a requirement which

includes two aspects: the load should be reproduced with sufficient accuracy, and it should be transmitted to the test piece without undue scatter. For this purpose, the measuring devices of the machine should be calibrated and the proper function ofits components should be checked at intervals in order to detect and eliminate the many errors which are so easily introduced. The demand of reduced scatter is—or should be—particularly severe in relation to fatigue machines. The reason why errors in these machines are so detrimental is explained by the fact that the end product ofa conventional fatigue test is an observed fatiguelife and this life is greatly affected by errors in load. This statement is easilydemonstrated by an elementary calculation.

Suppose that the relation between load S and life N is represented by the expression (cf. Section 85)

It then follows that

or, for large values of N

S= (S~—S6)(N/B+l)-~-~-S~

dS dN (~~~e) N S (N+B)

Taking as a common averagevalue a = 05 and supposing that (S — S~)/S = 01, which corresponds to a stress level approximately 10 per cent above the fatigue limit, then it follows that

dN/N= 20 dS/S

which implies that an error in the load of —3 per cent (which is frequently exceeded) corresponds to an increase in fatigue life of no less than 60 per cent. A stress level closer to the fatigue limit, say 5 per cent above it, implies that an error of 3 per cent in load corresponds to an error in life of 120 per cent.

The behaviour of a stationary fatigue machine is quite different from the machine under operating conditions with regard to the sources of errors, and, therefore, a static calibration is not sufficient but must be completed by the more consplicated dynamic calibration.

35.1 Static Calibration and Checking

From tIme preceding it follows tisat the examination of the testing machine should include not only the load—producing mechanism but also the trans- mitting elements.

Tise calibration depends, ofcourse, upon the method by which the load is produced. In machines where the load is generated by dead weights and constant spring forces or by lever and poise mechanism and transmitted to the specimen through a lever system, weights and forces have to be carefully controlled including weighing of all levers and other parts of the loading system, together with an experimental determination of the centres ofgravity of these parts. This information, together with the geometry of the lever system, can be employed to calculate a calibration constant or to construct

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FATIGUE TESTING AND ANALYSIS OP RESULTS

a calibration chart relating the applied dead weight or position of the poise or the reading of the spring deflexion to the load, bending moment, or torque actually applied to the specimen.

In machines where the load is produced by reciprocating masses or by centrifugal forces, it is of paramount importance to know exactly the speed of the machine, as an error in speed corresponds to a doubled error in load.

In hydraulic and pneumatic machines, pressure gauges should be carefully calibrated at intervals.

The greatest source of scatter in a fatigue testing machine appears, however, to be the grips and the guiding fixtures. For tisis reason, extraneous bending moments and twisting, introduced iiy the grips in axial-loading machines in particular, and friction caused by guide fixtures should be measured and, if possible, eliminated. There is reason to believe that appalling inaccuracies, easily ranging from ten to twenty or more per cent, may be incurred, if sufficient and meticulous care is neglected, as stated by O’CONNOR and MORRISON (1956).

A valuable contribution to the solving of this problem has been presented by FSNDLEY (1947) by an apparatus which was designed with provision for detecting and correcting strains introduced into the specimen when it is fixed in the testing machine. The device consists of means for measuring six components of distortion in the upper end ofthe specimen with respect to the lower end. Axial load is detected by readings of a dynamometer dial. Displacement in either of two horizontal directions, bending in either of two planes, and twisting are indicated by means of five small dials indicating relative movement of two aluminium plates which are clamped by split collets to the upper and lower straight sections of the specimen. This detector is balanced statically about the centre-line of the specimen. Before a specimen is placed in the testing machine, the detector is clamped to the specimen and the five dials are set to zero. The specimen is then fastened to the testing machine by means of special collet-type chucks, wisich are so designed that the specimen and detector can be inserted in the machine without moving the heads of the machine from their normal position. Results obtained by means of this detector are indicated below.

The joint effect of all factors mentioned above (except the grips) may be determined by placing a weighing scale or a dynamonscter in the machine and measuring repeatedly the result for different readings on the load scaie.

A reliable and simple dynamometer is the “Morclsouse proving ring” whicis is an elastic steel ring, designed primarily for determining static loads by micrometer measurements ofthe deflexiun of the ring. Rings of less tisan 100,000 lb capacity can be carefully calibrated in precision dead-weight machines. A calibration factor, varying with deulcxion, may thus be obtained for tension and compression, together with atemperature correction factor. The calibration factor remains constant over several years with normal care. This device has been thoroughly examined by WILSON, TATA and B0RK0wSKI (1946). In an adaption of a 25,000 lb ring by WILSON and JOHNSON (1937), where the micrometer and reed were replaced by an adjustable screw and an electrical contact with a neon glow lamp as

rATsc.UE TESTING MACnINES AND EQUIPMENT

indicator, time sclssitivity of the device when controlled by dead-weight loading was found to be less than 2 lb.

References: FSNISLEY (1947), WILSON and JOHNSON (1937), WILSON, TATA and BORKOWSKI (1946).

35.2 Dynamic Calibration and Checking

When the testing machine is in operation, a new source oferror, sometimes of considerable magnitude and non-existent in a stationary machine, appears due to unintentional inertia forces. In combination with springs or other flexible mensijers, resolIant vibrations will be generated which result in an appreciable increase in the errors in load.

An inertia effect which actually exists in every fatigue testing machine is introduced by the deflexion of the test piece in the load direction, thus imposing vibratory movements to the grips. In many cases this effect may be negligible but in others, as for example in hydraulic machines, this effect may result in errors in the load amounting to come 30 per cent of the maximum iliad. These inertia forces, acting on the specimen, may be eiimina ted by applying a spring force to the grip of such a magnitude that this spring-mass system has a natural frequency equal to that of the testing machine. This idea was introduced by HAtCH (1912) in his electromagnetic testing machine, lint is not easily applied to many types of machine. It is, however, possible to calculate a correction factor which may be applied to the nominal loads. As the additional forces on the grips are proportional to the masses and to the square of die speed, which are known, and to the deflexion of the specimen, which can be measured, a chart relating the correction factor with the deflexion of the specimen per unit load and the speed consists of a family (if straight lines, each one corresponding to a

certain frequency. This problem has been discussed by HEMPEL (1939), VON PHILIPP (1942) and P55cHEL (1953) and has also been applied by HEMPEL and FINK (1953).

The influence of other inertia forces on the actual load is generally much more difficult to detect and eliminate. The flexibility of parts supposed to be rigid and the complicated distribution of masses in many machines make it hard to anticipate tise natural frequencies of many possible spring-mass System that mmiay develop within tise machine. Suds resonance regions are usually- Imcc;iusc mmf small rlamping—very narrow. ‘l’hese difficulties and emmimstrmmet icc uieamms fir deahimsg with them arc (htdlisSed us papers by MASON

1917, 1921), MooRe (1921), MCAuAM (1924), and utisers. Many nsaeluncs are mathcr weak in transverse directions, and this may

result in large tramssverse vibrations at one or more specific speeds of the ns;sclsine.

The precediug considerations emphasize the necessity of dynamic cali- bration. Some ofthese methods do not simulate closely enough the properties of the specimen. Methods of this type are those using a dynamometer or a proving ring as, for example, demonstrated by THURSTON (1948). Valuable and even indispensable as they may he, the effect of the grip is not revealed, as only the total load and not its eccentricity is measured.

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FATIGUE TESTING AND ANALYSIS OP RESULTS FATIGUE TESTING MACHINES AND EQUIPMENT

For this purpose, the most reliable method of measuring the load distri- bution within the specimen is, for the present, the application of electrical resistance strain gauges directly to the test piece. The technique of this valuable tool of measurement is now very well developed, and some of its merits wiil be indicated in Chapter IV. Reference will here be given to two comprehensive reviews, viz, one by ROBERTS (1946) and another by HUGGENBERGER and SCHWAIGERER (1958).

Suffice it to mention here, that an accuracy better than one per cent will require an advanced technique, and that strain gauges are not very resistant to repeated strains. Fatigue failure will be expected to occur after a few thousand cycles at strain amplitudes of the magnitude 0~2per cent.

References: HAIGH (1912), HEMPEL (1939), HUGGENBERGER and SC5WAI- GERER (1958), MASON (1917, 1921), MCADAM (1924), MOORE (1921), v. PHILLIPP (1942), PI5cHEL (1953) ROBERTS (1946), THURSTON (1948), WILSON and JOHNSON (1937)

SECTION 36. ACCURACIES OF ACTUAL TESTING MACHINES

AND EQUIPMENTS

In this section, data will be given of accuracies actually attained and measured in fatigue testing machines. Up to the present, however, such data arescarce and not easilygiven in general form, as theaccuracy depends upon the individual care of calibration, static and dynamic, and on the proper maintenance of the machine and its function. This problem has been discussed by EKLINGER (1936).

According to a comprehensive survey of various conventional macisines, FINK and HEMPEL (1951) and HEMPEL and FINK (1953) found that the accuracy depends upon three different factors: (1) the design of themachine; (2) the useof themachine and resulting wear in the bearings; (3) theproper

- manipulation of the machine according to establislsed instructions. In the above-mentioned investigations which were carried out by means of

electrical strain gauges, deviations of the actual load from the nominal load of more than 30 to 40 per cent were observed in some cases. When caused by uncorrected inertia forces, the accuracy could lie substantially improved by applying correction factors as mentioned above, but in some machines the errors resulted from the design of the machine or neglected maintenassce of its proper function. The latter objection applied particularly to hydraulic machines.

Even if errors of this magnitude, though actually existing perhaps inure frequently than anticipated, may be removed without excessive difficulty, it appears, on the other hand, that accuracies better than 3 per cent will require considerable skill. As previously mentioned, this statement is con- firmed by theresults obtained by O’CONNOR and MORRISON (1956), who after many precautions could attain an accuracy in the load of about 14 per cent.

In the fatigue testing of coil springs by COATES and POPE (1956), the stresses produced under dynamic straining conditions were determined by electrical straingauges. Examination ofthe results showed that an accuracy

of +24 per cent was attainable in the middle ranges of load amplitude, but ths’ iii the lower ranges the percentage accuracy was not so high. GROVER, HYLER, KUHN, LANDERS and HOWELL (1953) found that the

accuracy ofload-measuring apparatus is approximately I per cent. Frequent monitoring revealed, however, that the loads sometimes but rarely changed as muds as 3 per cent during any given test. If guide plates were used, (in compression tests) tise accuracy of the load was estimated to be about

±~per cent. KEPERT and PAYNE (1956) examined the fatigue characteristics of a

typical metal wing using a vibration rig. The accuracy of loading was checked by numerous electric strain gauge readings and also by deflexion measurements during the test. They concluded that the applied load is accurately known within ±5per cent.

As a general conclusion, it may be stated that an accuracy of±~per cent seems to be generally accepted as satisfactory, that in some cases the error may be considerably much larger, and that an accuracy of 1 per cent is comparatively seldom attained.

These results may perhaps appear to be too pessimistic when rotating bending machines are concerned, but, in fact, in the author’s experience errors in the load of ten or more per cent may easily occur, ifvibrations due to eccentric mounting of the specimen are not effectively eliminated by inserting sufficiently weak suspension springs between the dead weight and the specimen.

References: COATE and POPE (1956), ERLINGER (1936), FINK and HEMPEL (1951), GROVER, HYLER, KUHN, LANDERS and HOWELL (1953), HISMPEL and FINK (1953), KEPERT and PAYNE (1956), O’CONNOR and MORRISON (1956).

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