Brittle Fracture, Slides of Engineering

Download Brittle Fracture and more Slides Engineering in PDF only on Docsity! 1MSE 2090: Introduction to Materials Science Chapter 8, Failure How do Materials Break? Chapter Outline: Failure Ductile vs. brittle fracture Principles of fracture mechanics Stress concentration Impact fracture testing Fatigue (cyclic stresses) Cyclic stresses, the S—N curve Crack initiation and propagation Factors that affect fatigue behavior Creep (time dependent deformation) Stress and temperature effects Alloys for high-temperature use Not tested: in 8.5 Fracture Toughness 8.14 Data extrapolation methods 2MSE 2090: Introduction to Materials Science Chapter 8, Failure Fracture: separation of a body into pieces due to stress, at temperatures below the melting point. Steps in fracture: crack formation 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): Extensive plastic deformation ahead of crack Crack is “stable”: resists further extension unless applied stress is increased • Brittle fracture - ceramics, ice, cold metals: Relatively little plastic deformation Crack is “unstable”: propagates rapidly without increase in applied stress Ductile fracture is preferred in most applications 5MSE 2090: Introduction to Materials Science Chapter 8, Failure Ductile Fracture (Dislocation Mediated) (a) Necking (b) Formation of microvoids (c) Coalescence of microvoids to form a crack (d) Crack propagation by shear deformation (e) Fracture Crack grows 90o to applied stress 45O - maximum shear stress Cup-and-cone fracture 6MSE 2090: Introduction to Materials Science Chapter 8, Failure Ductile Fracture (Cup-and-cone fracture in Al) Scanning Electron Microscopy: Fractographic studies at high resolution. Spherical “dimples” correspond to microvoids that initiate crack formation. tensile failure shear failure 7MSE 2090: Introduction to Materials Science Chapter 8, Failure No appreciable plastic deformation Crack propagation is very fast Crack propagates nearly perpendicular to the direction of the applied stress 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 10MSE 2090: Introduction to Materials Science Chapter 8, Failure Stress Concentration where σ0 is the applied external stress, a is the half-length of the crack, and ρt the radius of curvature of the crack tip. (note that a is half-length of the internal flaw, but the full length for a surface flaw). The stress concentration factor is: 2/1 t 0m a2 ⎟⎟ ⎠ ⎞ ⎜⎜ ⎝ ⎛ ρ σ≈σ For a long crack oriented perpendicular to the applied stress the maximum stress near the crack tip is: 2/1 t0 m t a2K ⎟⎟ ⎠ ⎞ ⎜⎜ ⎝ ⎛ ρ ≈ σ σ = 11MSE 2090: Introduction to Materials Science Chapter 8, Failure Crack propagation Energy balance on the crack Elastic strain energy: energy stored in material as it is elastically deformed this energy is released when the crack propagates creation of new surfaces requires energy ductile Cracks with sharp tips propagate easier than cracks having blunt tips 2/1 t 0m a2 ⎟⎟ ⎠ ⎞ ⎜⎜ ⎝ ⎛ ρ σ≈σ In ductile materials, plastic deformation at a crack tip “blunts” the crack. brittle deformed region 212 /s c πa Eγσ ⎟ ⎠ ⎞ ⎜ ⎝ ⎛=Critical stress for crack propagation: γs = specific surface energy for ductile materials γs should be replaced with γs + γp where γp is plastic deformation energy Griffith's criterion 12MSE 2090: Introduction to Materials Science Chapter 8, Failure 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) CharpyIzod h’ h Energy ~ h - h’ 15MSE 2090: Introduction to Materials Science Chapter 8, Failure V. Bulatov et al., Nature 391, #6668, 669 (1998) “Dynamic" Brittle-to-Ductile Transition (not tested) (from molecular dynamics simulation of crack propagation) Ductile Brittle 16MSE 2090: Introduction to Materials Science Chapter 8, Failure Under fluctuating / cyclic stresses, failure can occur at loads considerably lower than tensile or yield strengths of material under a static load: Fatigue Estimated to causes 90% of all failures of metallic structures (bridges, aircraft, machine components, etc.) Fatigue failure is brittle-like (relatively little plastic deformation) - even in normally ductile materials. Thus sudden and catastrophic! Applied stresses causing fatigue may be axial (tension or compression), flextural (bending) or torsional (twisting). Fatigue failure proceeds in three distinct stages: crack initiation in the areas of stress concentration (near stress raisers), incremental crack propagation, final catastrophic failure. Fatigue (Failure under fluctuating / cyclic stresses) 17MSE 2090: Introduction to Materials Science Chapter 8, Failure Fatigue: Cyclic Stresses (I) Periodic and symmetrical about zero stress Periodic and asymmetrical about zero stress Random stress fluctuations 20MSE 2090: Introduction to Materials Science Chapter 8, Failure Fatigue: S—N curves (II) Fatigue limit (endurance limit) occurs for some materials (e.g. some Fe and Ti alloys). 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. 21MSE 2090: Introduction to Materials Science Chapter 8, Failure 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 a specified number of cycles (e.g. 107) Fatigue life: Number of cycles to fail at a specified stress level 22MSE 2090: Introduction to Materials Science Chapter 8, Failure Fatigue: Crack initiation and propagation (I) Three stages of fatigue failure: 1. crack initiation in the areas of stress concentration (near stress raisers) 2. incremental crack propagation 3. final rapid crack propagation after crack reaches critical size The total number of cycles to failure is the sum of cycles at the first and the second stages: Nf = Ni + Np Nf : Number of cycles to failure Ni : Number of cycles for crack initiation Np : Number of cycles for crack propagation High cycle fatigue (low loads): Ni is relatively high. With increasing stress level, Ni decreases and Np dominates 25MSE 2090: Introduction to Materials Science Chapter 8, Failure Factors that affect fatigue life: environmental effects Thermal Fatigue. Thermal cycling causes expansion and contraction, hence thermal stress, if component is restrained. Solutions: eliminate restraint by design use materials with low thermal expansion coefficients Corrosion fatigue. Chemical reactions induce pits which act as stress raisers. Corrosion also enhances crack propagation. Solutions: decrease corrosiveness of medium, if possible add protective surface coating add residual compressive stresses 26MSE 2090: Introduction to Materials Science Chapter 8, Failure Creep Furnace Creep is a time-dependent and permanent deformation of materials when subjected to a constant load at a high temperature (> 0.4 Tm). Examples: turbine blades, steam generators. Creep testing: 27MSE 2090: Introduction to Materials Science Chapter 8, Failure 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. 30MSE 2090: Introduction to Materials Science Chapter 8, Failure Creep: stress and temperature effects The stress/temperature dependence of the steady-state creep rate can be described by ⎟ ⎠ ⎞ ⎜ ⎝ ⎛−σ=ε RT QexpK cn2s& where Qc is the activation energy for creep, K2 and n are material constants. (Remember the Arrhenius dependence on temperature for thermally activated processes that we discussed for diffusion) 31MSE 2090: Introduction to Materials Science Chapter 8, Failure Mechanisms of Creep Different mechanisms are responsible for creep in different materials and under different loading and temperature conditions. The mechanisms include Stress-assisted vacancy diffusion Grain boundary diffusion Grain boundary sliding Dislocation motion Different mechanisms result in different values of n, Qc. Grain boundary diffusion Dislocation glide and climb 32MSE 2090: Introduction to Materials Science Chapter 8, Failure Alloys for high-temperature use (turbines in jet engines, hypersonic airplanes, nuclear reactors, etc.) Creep is generally minimized in materials with: High melting temperature High elastic modulus Large grain sizes (inhibits grain boundary sliding) Following alloys are especially resilient to creep: Stainless steels Refractory metals (containing elements of high melting point, like Nb, Mo, W, Ta) “Superalloys” (Co, Ni based: solid solution hardening and secondary phases)