FAILURE MODES and MATERIALS PROPERTIES. Component failures. Ductile and Brittle Fracture COMPONENT FAILURES. COMPONENT FAILURE MODES examples:

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1 FAILURE MODES and MATERIALS PROPERTIES MECH Materials Lecture 10 R. W. Truss Materials Engineering COMPONENT FAILURES Structures lectures es on component es cause response in component that may lead to failure (failure = cease to perform design function) COMPONENT FAILURE MODES examples: Excessive Elastic deformation Plastic deformation High /short term Low /long term/high temperature Static load Fatigue Wear Corrosion / degradation etc Component failures Important to match failure mode to material property used in design mode may change with conditions Failure Mode Material Property Elastic deformation Modulus (E) Plastic deformation Yield strength (σ y ) Creep resistance Brittle fracture Fracture toughness (K 1c, G 1c ) Fatigue crack propagation Wear hardness, fracture toughness Corrosion half cell potential, etc Degradation UV stability, etc. Ductile and Brittle Fracture Ductile fracture brittle fracture - substantial bulk plastic - little bulk deformation deformation of sample failure is often sudden and catastrophic

2 Toughness Def n : Toughness - energy required to cause failure/fracture Measured by: 1) Area under strain curve to failure 2) Impact energy (Charpy/Izod) Failure modes change with conditions eg Charpy energy v Temp 3) Fracture mechanics (see later) Ductile/ brittle transition Depends on: alloy composition bcc or fcc metals (transition at much higher temperatures in bcc metals) Presence of notches Corrected fig. Example: brittle failure of welded ships Brittle fracture likely Ductile fracture likely 1/T Ductile / Brittle transition in Polymers As a function of temperature or rate Ductile at high temperatures or slow rates Brittle at high rates or low temperatures Ductile/Brittle transition in Polymers As a function of time under load Example: failure modes in HDPE Pipes Short term failures - ductile Long term failures - Brittle

3 time to failure increases with decreasing load design pressure decreases as design failure time increases But type of failure changes with time Caused by different time dependency of ductile and brittle failure modes Toughness: fracture mechanics approach Basis of Fracture Mechanics all materials are imperfect i.e. they contain flaws or small cracks these cracks can grow to cause brittle fracture cracks propagate only when specific energy or conditions met Stress, σ, at point near tip of a crack y σ x = {K / πr} f x (θ) σ y = {K / πr} f y (θ) r θ σ z = {K / πr} f z (θ) crack z r - distance from crack tip θ - angle from the plane of the crack σ y σ x τ xy σ z x near crack tip described by term K intensity factor crack begins to grow at critical value of K, K 1c (fracture toughness) K 1c =Yσ f (πa) 1/2 Y = geometry term a = crack length For internal notch of length 2a, in a infinite sheet, Y=1 For a surface notch of length a, Y~ 1.12 Design against Brittle Fracture Brittle fracture occurs when K 1c =Yσ f (πa) 1/2 Fracture toughness, K 1c,fixed from materials selection, σ, from design Flaw size, a, from non destructive testing or inspection Case study: Failure of a loaded bolt Possible failure modes: Yield Corrosion Elastic deformation Creep??? D d

4 Will the bolt deform and yield or undergo brittle fracture when loaded with an axial load P D d Yield governed by yield, σ y related to fracture toughness, K 1c Brittle fracture of bolt Bolt thread can act as flaw Stress Intensity Factor for circumferential notch in a rod (bolt thread is approximately this geometry) is given to ~1% accuracy by K 1 D 3/2 / P = 1.72 D/d 1.27 for 0.5 < d/d < 0.8, where D is diameter of rod; d is diameter of notched region; P is tensile load on rod. {cf K 1c = Yσ f (πa) 1/2 } For Brittle fracture: K 1c D 3/2 / P f = 1.72 D/d 1.27 where P f is load at fracture for bolt with D = 25 mm, d = 20mm K 1c = P f *222.6 (D,d in m ) Medium carbon steel Steel properties Yield MPa 260 Fracture Toughness MPam 1/2 54 For yield/ductile failure: Tool steel (hardened & tempered) σ y = P y / 3.14 x10-4 (based on inner diameter) where P y is the load to yield High strength alloy steel Medium carbon steel Tool steel (hardened & tempered) High strength alloy steel Failure loads in bolt Load for Yield (kn) Load for Brittle fracture (kn) brittle fracture as a statistical quantity materials contain distribution of flaws K 1c is a material property - invariant (for given conditions) measured brittle failure must change with flaw size distribution of failure es

5 Design depends on acceptable failure rate Stress for 10% failure failure Mean failure 50% fail Wiebull Modulus probability of failure F = f (σ, V) σ = applied V = volume under σ σ t F= 1 exp{ dv} σ V σ t is below which the probability of failure is zero σ 0 is a normalising parameter m is the Wiebull modulus 0 m Wiebull modulus measure of strength variation high m - narrow distribution in failure low m - wide distribution of failure note : for many ceramics and glasses 5 < m < 20 how do you select design? based on some probability of failure at which there is 10% chance of failure question if I measure the tensile strength of a ceramic in 3pt bending, 4 pt bending and in tension σ f (3pt) > σ f (4pt) > σ f (tension) WHY IS IT SO?

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