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Chapter 6 Fatigue Failure

1- surface factor ka

a, b table 6-

2- size factor kb

a- rotating shaft for bending or torsion

b- For axial load kb = 1

c- Non rotating shaft

3- Loading factor kc

For combined loading use kc = 1

4- Temperature factor kd (table 6-4)

5- Reliability factor ke (table 6-5)

6- Miscellaneous factor kf = 1 in all cases

7- Determine S'e

Safety factor

For localized yield n =

a m

Sy

For Torsion

Replace σm and σa with τm and τa. Replace Sut with Ssu = 0.67 Sut and replace Sy with Ssy = 0.577Sy

Using Goodman

ut

m e

a

f

S S

n

For localized yield

a m

Sy

n

Useful Tables 1035

Table A–

Charts of Theoretical Stress-Concentration Factors K*t ( Continued )

w / d = `

Kt

r

r / d

1.0 0 0.05 0.10 0.15 0.20 0.25 0.

M w (^) d M

Figure A–15–

Notched rectangular bar in bending. s 0 5 Mc y I , where c 5 d y2, I 5 td^3 y12, and t is the thickness.

Kt

r / d

1.0 0 0.05 0.10 0.15 0.20 0.25 0.

r D d

D / d = 1.

3 1.1 1.

1.05 M M

Figure A–15–

Rectangular filleted bar in bending. s 0 5 Mc y I , where c 5 d y2, I 5 td^3 y12, t is the thickness.

Kt

r / d

1.0 0 0.05 0.10 0.15 0.20 0.25 0.

r D d

D / d = 1.

F F

Figure A–15–

Rectangular filleted bar in tension or simple compression. s 0 5 F y A , where A 5 dt and t is the thickness.

*Factors from R. E. Peterson, “Design Factors for Stress Concentration,” Machine Design, vol. 23, no. 2, February 1951, p. 169; no. 3, March 1951, p. 161, no. 5, May 1951, p. 159; no. 6, June 1951, p. 173; no. 7, July 1951, p. 155. Reprinted with permission from Machine Design, a Penton Media Inc. publication.

( Continued )

1036 Mechanical Engineering Design

Table A–

Charts of Theoretical Stress-Concentration Factors K*t ( Continued )

Kt

r / d

1.0 0 0.05 0.10 0.15 0.20 0.25 0.

r F F

D / d = 1.

D d

Figure A–15–

Round shaft with shoulder fillet in tension. s 0 5 F y A , where A 5 p d^2 y4.

Kt

r / d

1.0 0 0.05 0.10 0.15 0.20 0.25 0.

D / d = 3

r M D d M

Figure A–15–

Round shaft with shoulder fillet in bending. s 0 5 Mc y I , where c 5 d y2 and I 5 p d^4 y64.

Kts

r / d

1.0 0 0.05 0.10 0.15 0.20 0.25 0.

D / d = 2

1.20 (^) 1.

r

T D^ d T

Figure A–15–

Round shaft with shoulder fillet in torsion. t 0 5 Tc y J , where c 5 d y2 and J 5 p d^4 y32.

1038 Mechanical Engineering Design

Table A–

Charts of Theoretical Stress-Concentration Factors K*t ( Continued )

Kt

r / d

1.0 0 0.05 0.10 0.15 0.20 0.25 0.

D / d = 1.

d

r

F D F

Figure A–15–

Grooved round bar in tension. s 0 5 F y A , where A 5 p d^2 y4.

Kts

r / d

1.0 0 0.05 0.10 0.15 0.20 0.25 0.

D / d = 1.

d

r

D

T T

Figure A–15–

Grooved round bar in torsion. t 0 5 Tc y J , where c 5 d y 2 and J 5 p d^4 y32.

Kt

r / d

1.0 0 0.05 0.10 0.15 0.20 0.25 0.

1.02 D / d = 1.

d

r

M D M

Figure A–15–

Grooved round bar in bending. s 0 5 Mc y I , where c 5 d y 2 and I 5 p d^4 y64.

*Factors from R. E. Peterson, “Design Factors for Stress Concentration,” Machine Design, vol. 23, no. 2, February 1951, p. 169; no. 3, March 1951, p. 161, no. 5, May 1951, p. 159; no. 6, June 1951, p. 173; no. 7, July 1951, p. 155. Reprinted with permission from Machine Design, a Penton Media Inc. publication.

Useful Tables 1039

Table A–

Charts of Theoretical Stress-Concentration Factors K*t ( Continued )

Figure A–15–

Round shaft with flat-bottom groove in bending and/or tension.

s 0 5 4 F p d^2 1 32 M p d^3 Source: W. D. Pilkey and D. F. Pilkey, Peterson’s Stress- Concentration Factors, 3rd ed. John Wiley & Sons, Hoboken, NJ, 2008, p. 115. Kt

1.00.5 0.6 0.7 0.8 0.91.0 2.0 (^) a/t 3.0 4.0 5.0 6.

d

ra r D (^) MF

t M

F

r t

( Continued )

Useful Tables 1041

The nominal bending stress is s 0 5 M y Z net where Znet is a reduced value of the section modulus and is defined by

Z net 5 p A 32 D ( D

(^4 2) d (^4) )

Values of A are listed in the table. Use d 5 0 for a solid bar

d/D 0.9 0.6 0 a/D A Kt A K (^) t A K (^) t 0.050 0.92 2.63 0.91 2.55 0.88 2. 0.075 0.89 2.55 0.88 2.43 0.86 2. 0.10 0.86 2.49 0.85 2.36 0.83 2. 0.125 0.82 2.41 0.82 2.32 0.80 2. 0.15 0.79 2.39 0.79 2.29 0.76 2. 0.175 0.76 2.38 0.75 2.26 0.72 2. 0.20 0.73 2.39 0.72 2.23 0.68 2. 0.225 0.69 2.40 0.68 2.21 0.65 2. 0.25 0.67 2.42 0.64 2.18 0.61 2. 0.275 0.66 2.48 0.61 2.16 0.58 1. 0.30 0.64 2.52 0.58 2.14 0.54 1.

M M

D d

Table A–16 a

Approximate Stress-

Concentration Factor Kt

of a Round Bar or Tube

with a Transverse Round

Hole and Loaded in

Bending

Source: R. E. Peterson, Stress- Concentration Factors, Wiley, New York, 1974, pp. 146, 235.

( Continued )

1048 Mechanical Engineering Design

Table A–

Deterministic ASTM Minimum Tensile and Yield Strengths for Some Hot-Rolled (HR) and Cold-Drawn (CD) Steels

[The strengths listed are estimated ASTM minimum values in the size range 18 to 32 mm ( 34 to 1^14 in). These

strengths are suitable for use with the design factor defi ned in Sec. 1–10, provided the materials conform to ASTM

A6 or A568 requirements or are required in the purchase specifi cations. Remember that a numbering system is not a

specifi cation.] Source: 1986 SAE Handbook, p. 2.15.

Tensile Yield SAE and/or Process- Strength, Strength, Elongation in Reduction in Brinell UNS No. AISI No. ing MPa (kpsi) MPa (kpsi) 2 in, % Area, % Hardness G10060 1006 HR 300 (43) 170 (24) 30 55 86 CD 330 (48) 280 (41) 20 45 95 G10100 1010 HR 320 (47) 180 (26) 28 50 95 CD 370 (53) 300 (44) 20 40 105 G10150 1015 HR 340 (50) 190 (27.5) 28 50 101 CD 390 (56) 320 (47) 18 40 111 G10180 1018 HR 400 (58) 220 (32) 25 50 116 CD 440 (64) 370 (54) 15 40 126 G10200 1020 HR 380 (55) 210 (30) 25 50 111 CD 470 (68) 390 (57) 15 40 131 G10300 1030 HR 470 (68) 260 (37.5) 20 42 137 CD 520 (76) 440 (64) 12 35 149 G10350 1035 HR 500 (72) 270 (39.5) 18 40 143 CD 550 (80) 460 (67) 12 35 163 G10400 1040 HR 520 (76) 290 (42) 18 40 149 CD 590 (85) 490 (71) 12 35 170 G10450 1045 HR 570 (82) 310 (45) 16 40 163 CD 630 (91) 530 (77) 12 35 179 G10500 1050 HR 620 (90) 340 (49.5) 15 35 179 CD 690 (100) 580 (84) 10 30 197 G10600 1060 HR 680 (98) 370 (54) 12 30 201 G10800 1080 HR 770 (112) 420 (61.5) 10 25 229 G10950 1095 HR 830 (120) 460 (66) 10 25 248

1050 Mechanical Engineering Design

Table A–21 ( Continued )

Mean Mechanical Properties of Some Heat-Treated Steels

[These are typical properties for materials normalized and annealed. The properties for quenched and tempered

(Q&T) steels are from a single heat. Because of the many variables, the properties listed are global averages. In all

cases, data were obtained from specimens of diameter 0.505 in, machined from 1-in rounds, and of gauge length 2 in.

unless noted, all specimens were oil-quenched.] Source: ASM Metals Reference Book, 2d ed., American Society for Metals,

Metals Park, Ohio, 1983.

1 2 3 4 5 6 7 8 Tensile Yield Temperature Strength Strength, Elongation, Reduction Brinell AISI No. Treatment °C (°F) MPa (kpsi) MPa (kpsi) % in Area, % Hardness 4130 Q&T* 205 (400) 1630 (236) 1460 (212) 10 41 467 Q&T* 315 (600) 1500 (217) 1380 (200) 11 43 435 Q&T* 425 (800) 1280 (186) 1190 (173) 13 49 380 Q&T* 540 (1000) 1030 (150) 910 (132) 17 57 315 Q&T* 650 (1200) 814 (118) 703 (102) 22 64 245 Normalized 870 (1600) 670 (97) 436 (63) 25 59 197 Annealed 865 (1585) 560 (81) 361 (52) 28 56 156 4140 Q&T 205 (400) 1770 (257) 1640 (238) 8 38 510 Q&T 315 (600) 1550 (225) 1430 (208) 9 43 445 Q&T 425 (800) 1250 (181) 1140 (165) 13 49 370 Q&T 540 (1000) 951 (138) 834 (121) 18 58 285 Q&T 650 (1200) 758 (110) 655 (95) 22 63 230 Normalized 870 (1600) 1020 (148) 655 (95) 18 47 302 Annealed 815 (1500) 655 (95) 417 (61) 26 57 197 4340 Q&T 315 (600) 1720 (250) 1590 (230) 10 40 486 Q&T 425 (800) 1470 (213) 1360 (198) 10 44 430 Q&T 540 (1000) 1170 (170) 1080 (156) 13 51 360 Q&T 650 (1200) 965 (140) 855 (124) 19 60 280

*Water-quenched

1051

Strength (Tensile)

Yield

Ultimate

Fracture,

Coefficient

Strain

S^ y

,^

S^ u

,^

S

,^ f

S^0

,^

Strength,

Fracture

Number

Material

Condition

MPa (kpsi)

MPa (kpsi)

MPa (kpsi)

MPa (kpsi)

Exponent

m

Strain

f

Steel

Annealed

†^

Steel

Annealed

†^

Steel

HR

†^

Steel

Q&T 600°F

†^

Steel

Q&T 600°F

†^

Stainless

Annealed

†^

steel

Stainless

Annealed

†^

steel

Aluminum

T

†^

alloy

Aluminum

T

†^

alloy

Aluminum

T

†^

alloy

Table A–22 Results of Tensile Tests of Some Metals* *Values from one or two heats and believed to be attainable using proper purchase specifications. The fracture strain may vary as much as 100 percent.†Derived value.

Source:

J. Datsko, “Solid Materials,” chap. 32 in Joseph E. Shigley, Charles R. Mischke, and Thomas H. Brown, Jr.

(eds.-in-chief),

Standard Handbook of Machine Design,

3rd ed., McGraw-Hill, New York, 2004, pp. 32.49–32.52.