A finite element analysis of plane strain dynamic crack growth in materials displaying the Bauschinger effect

Abstract

In this paper dynamic crack growth in an elastic-plastic material is analyzed under mode I plane strain small-scale yielding conditions using a finite element procedure. The main objective of this paper is to investigate the influence of anisotropic strain hardening on the material resistance to rapid crack growth. To this end, materials that obey an incremental plasticity theory with linear isotropic or kinematic hardening are considered. A detailed study of the near-tip stress and deformation fields is conducted for various crack speeds. The results demonstrate that kinematic hardening does not oppose the role of inertia in decreasing the plastic strains and stresses near the crack tip with increase in crack speed to the same extent as isotropic strain hardening. A ductile crack growth criterion based on the attainment of a critical crack opening displacement at a small micro-structural distance behind the tip is used to obtain the dependence of the theoretical dynamic fracture toughness with crack speed. It is found that for any given level of strain hardening, the dynamic fracture toughness displays a much more steep increase with crack speed over the quasi-static toughness for the kinematic hardening material as compared to the isotropic hardening case.

A finite element analysis of plane strain dynamic crack growth at a ductile-brittle interface

“…The difference in ~b due to changing L from L1 to L2 is given by ~2 --~1 = eln(L2/L1). (11) In the present small-scale yielding formulation, (8), (9) radius L. The domain modelled along with a coarse representation of the finite element mesh is shown in Figure 1. In this figure, the interface is located along :~2 = 0 and the crack line along (~2 = 0, ~t < 0).…”

“…The motivation for employing this criterion stems from experimental observations of self-similar crack profiles during crack growth in homogeneous ductile solids. On employing the above criterion for both quasi-static crack growth and crack propagation at a higher speed, the ratio of the dynamic fracture toughness I Kal to the quasi-static limit I Kqs I can be obtained (see [8] for details).…”

“…In this work, the critical value ofu2/(e~l)r) is taken as 35 (see also [8]). Results are presented for two stiffness ratios, E (l)/E (2) = 1.0 and 0.2, (but with no density mismatch) and two values of strain hardening, o~ = 0.25 and 0.10.…”

“…Also, many finite element studies (see, for example, [7,8]) have been conducted to validate these asymptotic solutions and to investigate the effect of inertia in enhancing the resistance of an elastic-plastic material to high speed crack growth. Dynamic crack growth along an interface between two dissimilar elastic solids with arbitrary anisotropy was sudied by Yang et al [9].…”

Asymptotic and finite element analyses of mode III dynamic crack growth at a ductile-brittle interface

“…[14] and Lam and Freund [15]. The role of strain hardening in off-setting the effects of material inertia was examined by Achenbach et al [16], 0stlund and Gudmundson [ 17], Venkatesha and Narasimhan [ 18] and Narasimhan and Venkatesha [ 19].…”