Fracture of Materials - Intermediate Mechanics of Materials - Lecture Slides, Slides of Classical Mechanics

Download Fracture of Materials - Intermediate Mechanics of Materials - Lecture Slides and more Slides Classical Mechanics in PDF only on Docsity! 3 – Fracture of Materials Docsity.com Fracture of Materials Types of Fracture Brittle Fracture Ductile Fracture Brittle to Ductile Transition Fracture Mechanics Stress Concentration LEFM K & G Kc Appendix - Griffith Theory Outline Docsity.com Brittle vs. Ductile Fracture Ductile materials - extensive plastic deformation and energy absorption (“toughness”) before fracture Brittle materials - little plastic deformation and low energy absorption before fracture Docsity.com Brittle vs. Ductile Fracture (a)Brittle fracture; (b) Shearing fracture in single crystal (c) Completely ductile (d) Ductile fracture Docsity.com Ductile Fracture (a)Necking, (b) Cavity Formation, (c) Cavity coalescence to form a crack, Docsity.com Ductile Fracture Scanning Electron Microscopy: Fractographic studies at high resolution. Spherical “dimples” correspond to micro-cavities that initiate crack formation. Docsity.com Brittle Fracture 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) Docsity.com Brittle Fracture Brittle fracture in a mild steel Docsity.com Ductile-to-Brittle Transition Ductile-to-Brittle Transition: As temperature decreases a ductile material can become brittle 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. Docsity.com Ductile-to-Brittle Transition 100 |— 80 ;— _. 100 5 [ —— # = Impact . Bo — energy — — 80 5 5 40 Shear £ 2 fracture = Z [_ - a — 60 8 E ~ 40 a L — 40 20 -— +20 phil y tity fy ty ty | 40 -20 0 20 40 60 8006100) «120-140 Temperature (°C) DBTT: Ductile-Brittle Transition Temperature Docsity.com Fracture Mechanics & Fracture Toughness • Stress Concentration • Energy Release Rate • Crack Tip Plasticity • Fracture Toughness Docsity.com Stress Concentration Factor 1/ 22( )mt aK σ σ ρ = = The ratio of the maximum stress and the nominal applied tensile stress is denoted as the stress concentration factor, Kt, where Kt can be calculated by Equation 1. The stress concentration factor is a simple measure of the degree to which an external stress is amplified at the tip of a small crack. Docsity.com Stress Concentration The stress distribution at the crack tip in a thin plate for an elastic solid is given by: (2) Docsity.com Stress Concentration K: Stress Intensity Factor Unit of K: psi√in, MN/(m3/2), or MPa√m (3) K f aσ π= Docsity.com Energy Release Rate Energy Release Rate: In 1956, Irwin defined an energy release rate, G, which is a measure of the energy available for an increment of crack extension: G = - dU/dA Since G is obtained from the derivative of a potential, it is also called the crack extension force or crack driving force Docsity.com Energy Release Rate Griffith Approach: G = πσ2a/E Where σ is the nominal stress, a is half-length of crack, E is Young’s Modulus Docsity.com Relationship between K and G Plain Stress: G = KI2/E Plain Strain: G = KI2(1-ν2)/E Mode I Docsity.com Crack Tip Plasticity Irwin Approach 2 ry =f Ki 20\ oys 2 tH) t ® Docsity.com Crack Tip Plastic Zone Shape Docsity.com Fracture Toughness Kc: If we assume a material fails locally at some combination of stresses and strains, then crack extension must occur at a critical K value. This Kc value, which is a measure of fracture toughness, is a material constant that is independent of the size and geometry of the cracked body. Docsity.com SUMMARY – Cont’d Stress Concentration Stress distribution in front of the crack tip Stress concentration factor Linear Elastic Fracture Mechanics K: Stress Intensity Factor G: Energy Release Rate Relationship between K & G Crack tip plasticity Fracture Toughness Docsity.com Appendix - Griffith Theory for Brittle Fracture For defect-free material: 0 2 a E th γσ = Where E – Young’s modulus γ – specific surface energy a0 – lattice parameter σth – theoretical strength of the material σth ~ E/10 is orders of magnitude higher than usually observed Docsity.com Energy criterion for brittle fracture (Griffith Theory) Energy criterion: when rate of change of the release of elastic energy with respect to crack size ≥ rate at which energy is consumed to create new surfaces, fracture occurs ( )a da d E a da d sγ σπ 4 2 2 =           Onset: Where σ – Griffith’s stress (the critical stress) γs – surface energy/per unit area Docsity.com