Fracture, Toughness, Fatigue, and Creep MATERIALS SCIENCE & MANUFACTURING PROCESSES Why Study Failure In order to know the reasons behind the occurrence of failure so that we can prevent failure of products by improving design in the light of failure reasons 2 Mechanical Failure ISSUES TO ADDRESS... • How do flaws in a material initiate failure? • How is fracture resistance quantified; how do different material classes compare? • How do we estimate the stress to fracture? • How do loading rate, loading history, and temperature affect the failure stress? Ship-cyclic loading from waves. Computer chip-cyclic thermal loading. 3 Hip implant-cyclic loading from walking. What is a Fracture? Fracture is the separation of a body into two or more pieces in response to an imposed stress that is static and at temperatures that are low relative to the melting temperature of the material. The applied stress may be tensile, compressive, shear, or torsional Any fracture process involves two steps—crack formation and propagation—in response to an imposed stress. Fracture Modes Ductile fracture 5 Occurs with plastic deformation Material absorbs energy before fracture Crack is called stable crack: plastic deformation occurs with crack growth. Also, increasing stress is required for crack propagation. • Brittle fracture – Little or no plastic deformation – Material absorb low energy before fracture – Crack is called unstable crack. – Catastrophic Ductile vs Brittle Failure • Classification: 6 Fracture behavior: Very Ductile Moderately Ductile Brittle Moderate Small (%EL)=100% Large • Ductile fracture is usually desirable! Ductile: warning before fracture, as increasing is required for crack Brittle: No warning Example: Failure of a Pipe • Ductile failure: --one/two piece(s) --large deformation • Brittle failure: --many pieces --small deformation 7 Moderately Ductile Failure- Cup & Cone Fracture • Evolution to failure: necking s • Resulting fracture surfaces void nucleation void growth and linkage shearing at surface fracture 50 50mm mm (steel) 100 mm particles serve as void nucleation sites. crack occurs perpendicular to tensile force applied 8 Ductile vs. Brittle Failure 9 cup-and-cone fracture brittle fracture Transgranular vs Intergranular Fracture Transgranular Fracture Intergranular Fracture Brittle Fracture Surfaces • Transgranular • Intergranular (between grains) (within grains) 304 S. Steel (metal) 316 S. Steel (metal) 160 mm 4 mm Polypropylene (polymer) Al Oxide (ceramic) 1 mm 11 3 mm Stress Concentration- Stress Raisers 12 σm › σo t Suppose an internal flaw (crack) already exits in a material and it is assumed to have a shape like a elliptical hole: The maximum stress (σm) occurs at crack tip: 1/ 2 a s m 2so t K t so where t = radius of curvature so = applied stress sm = stress at crack tip Theoretical fracture strength is higher Kt = Stress concentration factor than practical one; Why? Concentration of Stress at Crack Tip 13 Engineering Fracture Design • Avoid sharp corners! 14 so sm Stress Conc. Factor, K t = so w smax r, fillet 2.5 h Kt 2.0 increasing w/h radius 1.5 1.0 0 0.5 sharper fillet radius 1.0 r/h Crack Propagation 15 Cracks propagate due to sharpness of crack tip A plastic material deforms at the tip, “blunting” the crack. deformed plastic region When σm › σy brittle Effect of stress raiser is more significant in brittle materials than in ductile materials. When σm exceeds σy , plastic deformation of metal in the region of crack occurs thus blunting crack. However, in brittle material, it does not happen. Fracture Toughness: Design Against Crack Growth • Crack growth condition: Kc = Ys c a • Largest, most stressed cracks grow first! --Result 1: Max. flaw size --Result 2: Design stress dictates design stress (max allowable stress). dictates max. allowable flaw 2 size. Kc s design Y amax σc amax 1 K c Ys design amax fracture no fracture fracture no fracture amax 16 σc Fracture Toughness Brittle materials do not undergo large plastic deformation, so they posses low KIC than ductile ones. KIC increases with increase in temp and with reduction in grain size if other elements are held constant KIC reduces with increase in strain rate Design Example: Aircraft Wing • Material has Kc = 26 MPa-m0.5 • Two designs to consider... Design A --use same material --largest flaw is 4 mm --failure stress = ? --largest flaw is 9 mm --failure stress = 112 MPa • Use... sc Design B Kc Y a • Key point: Y and Kc are the same in both designs. --Result: 112 MPa 9 mm s a s a c A c 4 mm B Answer: (sc )B 168 MPa • Reducing flaw size pays off! 18 Impact Tests A material may have a high tensile strength and yet be unsuitable for shock loading conditions Impact testing is testing an object's ability to resist high-rate loading. An impact test is a test for determining the energy absorbed in fracturing a test piece at high velocity Types of Impact Tests -> Izod test and Charpy Impact test In these tests a load swings from a given height to strike the specimen, and the energy dissipated in the fracture is measured A. Charpy Test 20 (Charpy) Impact energy= Kinetic energy + energy absorbed by specimen Energy absorbed during test is determined from difference of pendulum height final height initial height b. Izod Test Izod test varies from charpy in respect of holding of specimen Effect of Temperature on Toughness • Increasing temperature... --increases %EL and Kc • Ductile-to-Brittle Transition Temperature (DBTT)... Impact Energy Low strength FCC metals (e.g., Cu, Ni) Low strength BCC metals (e.g., iron at T < 914°C) polymers Brittle More Ductile High strength materials ( s y > E/150) Temperature Ductile-to-brittle transition temperature 22 Fatigue Test Fatigue is a form of failure that occurs in structures subjected to dynamic and fluctuating loads (e.g. bridges, aircrafts, ships and m/c components) The term Fatigue is used because this type of failure occurs after a lengthy period of repeated stress of strain cycling. Failure stress in fatigue is normally lower than yield stress under static loading. Fatigue failure is brittle in nature even in ductile metals The failure begins with initiation and propagation of cracks Types of Cyclic Stresses Types of Cyclic Stresses Random Stress Cycle Terms Related to Cyclic Stresses Mean stress: Range of stress: Stress Amplitude: Stress Ratio: 4. Creep Creep is defined as time dependent plastic deformation under constant static load/stress (steam turbines blades under centrifugal force, pipes under steam pressure) at elevated temperatures At relatively high temperatures creep appears to occur at all stress levels, But the creep rate increases with increasing stress at a given temperature. 4. Creep Test A creep test involves a tensile specimen under a Constant Load OR Constant Stress maintained at a constant temperature. Temperature: Greater than 0.4Tm Stress & Temp Effects on Creep Time to rupture decreases as imposed stress or temperature increases 2. Steady creep rate increases with increase of stress and temperature 1. Good Luck