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Failure
Ship-cyclic loading from waves.
Computer chip-cyclic thermal loading.
Introduction to Materials Science, Chapter 8, Failure
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How do Materials Break?
Chapter Outline: Failure
Ductile vs. brittle fracture
Principles of fracture mechanics
9 Stress concentration
Impact fracture testing
Fatigue (cyclic stresses)
9 Cyclic stresses, the S—N curve
9 Crack initiation and propagation
9 Factors that affect fatigue behavior
Creep (time dependent deformation)
9 Stress and temperature effects
9 Alloys for high-temperature use
Not tested: 8.10 Crack propagation rate
8.15 Data extrapolation methods
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- Stress-strain behavior (Room T):
E/
E/
0.
perfect mat’l-no flaws carefully produced glass fiber
typical ceramic (^) typical strengthened metal typical polymer
TSengineering << TS
materials
perfect materials
• DaVinci (500 yrs ago!) observed...
--the longer the wire, the
smaller the load to fail it.
• Reasons:
--flaws cause premature failure.
--Larger samples are more flawed!
IDEAL VS REAL MATERIALS
Introduction to Materials Science, Chapter 8, Failure
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Fracture: separation of a body into pieces due to stress, at temperatures below the melting point. Steps in fracture: ¾ crack formation ¾ crack propagation
Fracture
Depending on the ability of material to undergo plastic deformation before the fracture two fracture modes can be defined - ductile or brittle
- Ductile fracture - most metals (not too cold): ¾ Extensive plastic deformation ahead of crack ¾ Crack is “stable”: resists further extension unless applied stress is increased
- Brittle fracture - ceramics, ice, cold metals: ¾ Relatively little plastic deformation ¾ Crack is “unstable”: propagates rapidly without increase in applied stress
Ductile fracture is preferred in most applications
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Ductile Fracture (Dislocation Mediated)
(a) Necking, (b) Cavity Formation, (c) Cavity coalescence to form a crack,
(d) Crack propagation, (e) Fracture
Crack grows 90 o^ to applied stress
45 O^ -
maximum shear stress
Introduction to Materials Science, Chapter 8, Failure
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Ductile Fracture
Typical Cup-and-Cone fracture in ductile Al
Scanning Electron Microscopy: Fractographic studies at
high resolution. Spherical “dimples” correspond to
micro-cavities that initiate crack formation.
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¾ No appreciable plastic deformation
¾ Crack propagation is very fast
¾ Crack propagates nearly perpendicular to the direction of the applied stress
¾ Crack often propagates by cleavage - breaking of atomic bonds along specific crystallographic planes (cleavage planes).
Brittle Fracture (Limited Dislocation Mobility)
Brittle fracture in a mild steel
Introduction to Materials Science, Chapter 8, Failure
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A. Transgranular fracture : Fracture cracks pass through grains. Fracture surface have faceted texture because of different orientation of cleavage planes in grains.
B. Intergranular fracture : Fracture crack propagation is along grain boundaries (grain boundaries are weakened or embrittled by impurities segregation etc.)
A B
Brittle Fracture
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Simulation courtesy of Farid Abraham. Used with permission from International Business Machines Corporation.
- Tensile loading (horizontal dir.) of a FCC metal with **notches in the top and bottom surface.
- Over 1 billion atoms modeled in 3D block.
- Note the large increase in disl. density.**
SIMULATION: DISLOCATION MOTION/GENERATION
Introduction to Materials Science, Chapter 8, Failure
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ENGINEERING FRACTURE DESIGN
- Avoid sharp corners!
r/h
sharper fillet radius
increasing w/h
Stress Conc. Factor, Kt
σ max
o
=
r , fillet radius
w
h
σ o
σ max
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Two standard tests, the Charpy and Izod, measure the impact energy (the energy required to fracture a test piece under an impact load), also called the notch toughness.
Impact Fracture Testing
(testing fracture characteristics under high strain rates)
Izod Charpy
h’
h
Energy ~ h - h’
Introduction to Materials Science, Chapter 8, Failure
University of Tennessee, Dept. of Materials Science and Engineering (^) 16
As temperature decreases a ductile material can become
brittle - ductile-to-brittle transition
Alloying usually increases the ductile-to-brittle transition temperature. FCC metals remain ductile down to very low temperatures. For ceramics, this type of transition occurs at much higher temperatures than for metals.
The ductile-to-brittle transition can be measured by impact testing: the impact energy needed for fracture drops suddenly over a relatively narrow temperature range – temperature of the ductile-to-brittle transition.
Ductile-to-brittle transition
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Fatigue: Cyclic Stresses (II)
Periodic and symmetrical about zero stress
Periodic and asymmetrical about zero stress
Random stress fluctuations
Introduction to Materials Science, Chapter 8, Failure
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Fatigue: S—N curves (I)
(stress-number of cycles to failure)
Fatigue properties of a material (S-N curves) are tested in rotating-bending tests in fatigue testing apparatus:
Result is commonly plotted as S (stress) vs. N (number of cycles to failure)
Low cycle fatigue: high loads, plastic and elastic deformation
High cycle fatigue: low loads, elastic deformation (N > 105 )
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Fatigue: S—N curves (II)
Fatigue limit (endurance limit) occurs for some materials (some Fe and Ti allows). In this case, the S—N curve becomes horizontal at large N. The fatigue limit is a maximum stress amplitude below which the material never
fails, no matter how large the number of cycles is.
Introduction to Materials Science, Chapter 8, Failure
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Fatigue: S—N curves (III)
In most alloys, S decreases continuously with N. In this cases the fatigue properties are described by
Fatigue strength : stress at which fracture occurs after specified number of cycles (e.g. 10 7 )
Fatigue life : Number of cycles to fail at specified stress level
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Factors that affect fatigue life
Magnitude of stress (mean, amplitude...)
Quality of the surface (scratches, sharp transitions and edges).
Solutions:
¾ Polishing (removes machining flaws etc.)
¾ Introducing compressive stresses (compensate for applied tensile stresses) into thin surface layer by “Shot Peening”- firing small shot into surface to be treated. High-tech solution - ion implantation, laser peening.
¾ Case Hardening - create C- or N- rich outer layer in steels by atomic diffusion from the surface. Makes harder outer layer and also introduces compressive stresses
¾ Optimizing geometry - avoid internal corners, notches etc.
Introduction to Materials Science, Chapter 8, Failure
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Factors that affect fatigue life: environmental effects
Thermal Fatigue. Thermal cycling causes expansion and contraction, hence thermal stress, if component is restrained.
Solutions: ¾ eliminate restraint by design ¾ use materials with low thermal expansion coefficients
Corrosion fatigue. Chemical reactions induce pits which act as stress raisers. Corrosion also enhances crack propagation. Solutions: ¾ decrease corrosiveness of medium, if possible ¾ add protective surface coating ¾ add residual compressive stresses
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Creep
Furnace
Creep is a time-dependent and permanent deformation of materials when subjected to a constant load at a high temperature (> 0.4 T (^) m ). Examples: turbine blades, steam generators.
Creep testing:
Introduction to Materials Science, Chapter 8, Failure
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Stages of creep
1. Instantaneous deformation , mainly elastic. 2. Primary/transient creep. Slope of strain vs. time decreases with time: work-hardening 3. Secondary/steady-state creep. Rate of straining is constant: balance of work-hardening and recovery. 4. Tertiary. Rapidly accelerating strain rate up to failure: formation of internal cracks, voids, grain boundary separation, necking, etc.
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Creep: stress and temperature effects
The stress/temperature dependence of the steady-state
creep rate can be described by
ε = σ − RT
Q K exp c n &s 2
where Qc is the activation energy for creep, K 2 and n
are material constants.
(Remember the Arrhenius dependence on temperature for thermally activated processes that we discussed for diffusion?)
Introduction to Materials Science, Chapter 8, Failure
g (^) 32
Mechanisms of Creep
Different mechanisms are responsible for creep in different materials and under different loading and temperature conditions. The mechanisms include
¾ Stress-assisted vacancy diffusion
¾ Grain boundary diffusion
¾ Grain boundary sliding
¾ Dislocation motion
Different mechanisms result in different values of n, Q (^) c.
Grain boundary diffusion Dislocation glide and climb
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Alloys for high-temperature use
(turbines in jet engines, hypersonic airplanes, nuclear
reactors, etc.)
Creep is generally minimized in materials with:
9 High melting temperature 9 High elastic modulus 9 Large grain sizes (inhibits grain boundary sliding)
Following materials (discussed in Chapter 12) are especially resilient to creep:
9 Stainless steels 9 Refractory metals (containing elements of high melting point, like Nb, Mo, W, Ta) 9 “Superalloys” (Co, Ni based: solid solution hardening and secondary phases)
Introduction to Materials Science, Chapter 8, Failure
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Summary
¾ Brittle fracture ¾ Charpy test ¾ Corrosion fatigue ¾ Creep ¾ Ductile fracture ¾ Ductile-to-brittle transition ¾ Fatigue ¾ Fatigue life ¾ Fatigue limit ¾ Fatigue strength ¾ Fracture toughness ¾ Impact energy ¾ Intergranular fracture ¾ Izod test ¾ Stress raiser ¾ Thermal fatigue ¾ Transgranular fracture
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