Consider a plate of infinite length with a crack of length 2a perpendicular to the direction of loading (see figure belo

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Consider A Plate Of Infinite Length With A Crack Of Length 2a Perpendicular To The Direction Of Loading See Figure Belo 1 (80.77 KiB) Viewed 56 times

Consider a plate of infinite length with a crack of length 2a perpendicular to the direction of loading (see figure below). The material is assumed to behave as an elastic-perfectly plastic solid (no strain hardening) with a tensile yield stress equal to 0. 2a 22 Consider the asymptotic solution by Westergaard for the 2D local stress field at the crack tip in a purely linear elastic solid (we will assume a plane stress condition only), i.e., K е Ꮎ 30 011 cos-1-sin-sin /2xr 2 2 = 022 K /2r rl COS soll 30 1+ sin sin 2 2 09 K 012 = Varli 30 sin x cos x cos 2 2 2 033 = 0 23=013=0 Questions: (1) Determine the plastic zone size r, for 0=0, 7, and 1/2, as a function of K, and or by applying the von Mises criterion such that: for rsp, Sla)= 1,(3) - VE 0 f)<0 Recall: 31," = (0,20x} +60,-0.) +(02-03) +6l6,22 +0,4 +0,,) (2) Now find the plastic zone size re for 0= Tt and 1/2, for r>r,) > (3) Using the solutions of (1) and (2), schematically represent the shape of the plastic zone at the crack tip under an applied stress intensity K.