FAILURE MODES and MATERIALS PROPERTIES MECH2300 - Materials Lecture 10 R. W. Truss Materials Engineering R.Truss@uq.edu.au COMPONENT FAILURE MODES examples: • Excessive Elastic deformation • Plastic deformation – High stress/short term – Low stress/long term/high temperature • Brittle fracture – Static load – Fatigue • Wear • Corrosion / degradation • etc Failure Mode Material Property ------------------------------------------------------Elastic deformation Plastic deformation Brittle fracture Wear Corrosion Degradation Modulus (E) Yield strength (σy) Creep resistance Fracture toughness (K1c, G1c) Fatigue crack propagation hardness, fracture toughness half cell potential, etc UV stability, etc. COMPONENT FAILURES • Structures lectures → stresses on component • stresses cause response in component that may lead to failure (failure = cease to perform design function) Component failures • Important to match failure mode to material property used in design • mode may change with conditions Ductile and Brittle Fracture Ductile fracture - substantial bulk plastic deformation of sample brittle fracture - little bulk deformation failure is often sudden and catastrophic Toughness Defn : Toughness - energy required to cause failure/fracture Failure modes change with conditions eg Charpy energy v Temp Measured by: 1) Area under stress strain curve to failure 2) Impact energy (Charpy/Izod) 3) Fracture mechanics (see later) Example: brittle failure of welded ships Ductile/ brittle transition Depends on: • alloy composition • bcc or fcc metals (transition at much higher temperatures in bcc metals) • Presence of notches Corrected fig. 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 • 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 stress conditions met Stress, σ, at point near tip of a crack y σx= {K /√πr} fx (θ) σy σx σy= {K /√πr} fy (θ) τxy r σz= {K /√πr} fz (θ) σz θ crack r - distance from crack tip θ - angle from the plane of the crack z Design against Brittle Fracture Brittle fracture occurs when K1c = Yσf (πa)1/2 • Fracture toughness, K1c, fixed from materials selection • stress, σ, from design • Flaw size, a, from non destructive testing or inspection x • stress near crack tip described by term K – stress intensity factor • crack begins to grow at critical value of K, K1c (fracture toughness) K1c = Yσf (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 Case study: Failure of a loaded bolt Possible failure modes: • Yield • Brittle fracture • Corrosion • Elastic deformation • Creep • ??? D d Will the bolt deform and yield or undergo brittle fracture when loaded with an axial load P D • Yield governed by yield stress, σy • Brittle fracture related to fracture toughness, K1c d For Brittle fracture: K1c D3/2 / Pf = 1.72 D/d –1.27 where Pf is load at fracture For yield/ductile failure: σy = Py / 3.14 x10-4 (based on inner diameter) where Py is the load to yield Failure loads in bolt Load for Yield Load for Brittle fracture (kN) (kN) 81.7 242.6 Tool steel 817 (hardened & tempered) High strength alloy 459 steel 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 K1 D3/2 / 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 K1c = Yσf (πa)1/2} Steel properties for bolt with D = 25 mm , d = 20mm (D,d in ‘m’) K1c = Pf *222.6 Medium carbon steel Brittle fracture of bolt 98.8 440 Medium carbon steel Yield stress Fracture Toughness MPa MPam 1/2 260 54 Tool steel 2600 (hardened & tempered) High strength alloy 1460 steel 22 98 brittle fracture stress as a statistical quantity • materials contain distribution of flaws • K1c is a material property - invariant (for given conditions) • measured brittle failure stress must change with flaw size • distribution of failure stresses Design stress depends on acceptable failure rate Mean failure stress 50% fail Stress for 10% failure Wiebull Modulus probability of failure F = f (σ, V) σ = applied stress V = volume under stress f ailur e st r ess m ⎛ σ −σt ⎞ ⎟ dV} F =1−exp{−∫ ⎜ σ ⎝ 0 ⎠ V σt is stress below which the probability of failure is zero σ0 is a normalising parameter m is the Wiebull modulus how do you select design stress? • based on some probability of failure • stress at which there is 10% chance of failure Wiebull modulus measure of strength variation high m - narrow distribution in failure stress low m - wide distribution of failure stress note : for many ceramics and glasses 5 < m < 20 question if I measure the tensile strength of a ceramic in 3pt bending, 4 pt bending and in tension σf (3pt) > σf (4pt) > σf (tension) WHY IS IT SO?