Fracture of Materials - Intro to Intermediate Mechanics of Materials - Lecture Slide, Slides of Mechanics of Materials

Download Fracture of Materials - Intro to Intermediate Mechanics of Materials - Lecture Slide and more Slides Mechanics of Materials in PDF only on Docsity! 3 – Fracture of Materials Docsity.com Part of the top of an Aloha Airlines jet peeled of during the flight Docsity.com Fracture: separation of a body into pieces due to stress, at temperatures below the melting point. Steps in fracture: Crack formation Crack propagation Depending on the ability of material to undergo plastic deformation before the fracture two fracture modes can be defined - ductile or brittle Fracture Docsity.com 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 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 Ductile Fracture 450 - maximum Shear shear Fibrous stress (d) fe) (d) Crack propagation, (e) Fracture Docsity.com Ductile Fracture (Cap-and-cone fracture in Al) 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 A.Transgranular fracture: Fracture cracks pass through grains. Fracture surface have faceted texture because of different orientation of cleavage planes in grains. B. Intergranular fracture: Fracture crack propagation is along grain boundaries (grain boundaries are weakened or embrittled by impurities segregation etc.) Docsity.com Brittle Fracture 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 Says r x Position along X—X’ (a) Docsity.com Stress Concentration For a long crack oriented perpendicular to the applied stress the maximum stress near the crack is: σm ≈ 2σ (a/ρ)1/2 where σ is the applied external stress, a is the half- length of the crack, and ρ 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). (1) 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 Substitute K into Equation (3): a ee = eos 3 1 sin 3 sin] é 36 o,- qc[ae (1 + sin sin )} (4) K _ 8 é 34 Ty = mr [sin 5 cos 5 eos Docsity.com Stress Concentration Fracture Modes Opening In-plane Shear Out-of-Plane Shear 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 Plain Stress vs. Plain Strain Plane Stress Plane Strain THICKNESS Docsity.com Crack Tip Plasticity Irwin Approach Oyy Elastic Elastic-Plastic Docsity.com Crack Tip Plasticity Irwin Approach 2 ry =f Ki 20\ oys 2 tH) t ® Docsity.com Fracture Toughness Measurement MEASURE STRENGTH WITH A CRACK OF KNOWN LENGTH SHARP CRACK LINEAR ELASTIC? SMALL PROCESS ZONE RULES ASTM STANDARDS: E-399 Docsity.com SUMMARY Types of Fracture: Brittle Fracture Ductile Fracture Ductile Fracture: Crack initiation, crack growth, fracture, fractography Brittle Fracture: Intergranular & Transgranular (Cleavage) Brittle to Ductile Transition: DBTT 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