Strain-gradient effect on the crack tip dislocations density

Andrey Tumanov,Ruslan Khamidullin,Valery Shlyannikov

doi:10.3221/igf-esis.54.14

Abstract

In this study, the influence of a material’s plastic properties on the crack tip fields and dislocation density behavior is analytically and numerically analyzed using the conventional mechanism-based strain-gradient plasticity (CMSGP) theory established using the Taylor model. The material constitutive equation is implemented in a commercial finite element code by a user subroutine, and the crack tip fields are evaluated with novel parameters in the form of the intrinsic material length, characterizing the scale over which gradient effects become significant. As a consequence of the strain-gradient contribution, FE results show a significant increase in the magnitude of the stress fields of CMSGP when the material length parameter is considered. It is found that the density of geometrically necessary dislocations (GND) is large around the crack tip, but it rapidly decreases away from the crack tip. On the contrary, the density of statistically stored dislocations (SSD) is not as large as geometrically necessary dislocations around the crack tip, but it decreases much slower than GND away from the crack tip. A couple effect of material work hardening and the crack tip distance is identified.

Highlights

The last quarter of a century witnessed increasing attention being drawn to problems of gradient plasticity
Once the distance to the crack tip is less than 0.3r/l, the effective stress predicted by conventional mechanism-based strain gradient (CMSG) plasticity increases considerably more rapidly than its counterpart in conventional HRR plasticity, which is dependent on the applied stress intensity factor level K1 and the plastic work hardening exponent N value
A s a consequence of the strain-gradient contribution, FE results show a significant increase in the magnitude and the extent of the difference between the crack tip stress fields of conventional mechanism-based strain-gradient plasticity (CMSGP) and conventional HRR theories when the material length parameter is considered

Summary

Introduction

The last quarter of a century witnessed increasing attention being drawn to problems of gradient plasticity. Fleck and Hutchinson [1,2] and Fleck et al [3] developed a phenomenological gradient theory of the plasticity of materials and structures whose dimensions control plastic deformation, in the range of approximately a tenth of a micron to tens of microns They have been applied to numerous problems where strain gradient effects are expected to play significant roles in the behavior of the material, including in the analysis of stress fields at the crack tip (Huang et al.[4,5], Xia and Hutchinson [6]). Characteristic length l was introduced to scale the components of the rotational gradient of coupled stresses (Fleck and Hutchinson,[1], Fleck et al, [3]) This length scale was considered as an internal parameter of the material structure associated with the dislocation density. The purpose of our study is to investigate the crack tip dislocation behavior in CMSG plasticity

Objectives

Results

Conclusion