The more precise crack line analyses for antiplane quasistatically propagating crack

Abstract

Achenbach and Dunayevsky [1], and Guo and Li [2] investigated the near crack line fields of stress and deformation for an antiplane growing crack in an elastic perfectly-plastic material. In both [1] and [2], the elastic dominant terms (K-dominated terms) of the stress and deformation fields have been used to match with the plastic fields at the elastic plastic boundary. In this paper, the K-dominated terms have not been adopted but the precise elastic solutions for cracked bodies have been used as the elastic fields outside the crack-tip plastic region. Thus the solutions of this paper are more reasonable than the solutions of [1] and [2] for an antiplane quasistatically growing crack in an elastic perfectly-plastic material.For the typical mode III crack in an infinite body as shown in Fig. 1, the precise elastic solutions have been obtained by using Westergaard's complex stress function. Linear elastic fracture mechanics is generally concerned with the dominant terms of the stresses and displacements near the crack tip. The author, however, is more interested in the stresses and deformations near the crack line.Expanding Westergaard's precise elastic stresses and displacement in a power series of the angle 0 to the crack line, we have x r r -a r(a+r) ] -L j0 + 0(0) 3 x= "#r(2a + r) 2 x [ ( 2a2r + a 3 L21 ---4 -x"-~lr(2a +r)(a + r ) -~2-~+~-~2Ju j+o~t~ ) "C .r a+r ] W =--d'~lr(2a + r ~ ~a + r 0+0(03) (la) (ib) (2)where G is the elastic shear modulus.Equations (la,b) and (2) are valid near the crack line from r----> 0 to r--->~.In the plastic region, by the basic equations (the equilibrium equations, the Int Journ of Fracture 55 (1992)

Elastic-plastic crack line fields for a growing crack in a centre cracked plate with finite dimensions

“…Although one of the small scale yielding conditions, which states that the plastic zone is small enough that the elastic field out of the plastic zone is the dominant field for a crack (i.e., the K-dominant field), had been abandoned by using the exact elastic field to match with the plastic field; another condition of the small scale yielding, that the elastic field is moved to some location along the crack line, had not been given up. Further analyses corresponding to [1] and [2] have been given by Yi [3,4], where the small scale yielding conditions have been given up entirely. Meanwhile, a cracked plate with finite dimensions under stationary condition has been successfully analysed in [3].…”