A theoretical and computational investigation of mixed mode creep crack growth along an interface

Elsiddig Elmukashfi,Alan C F Cocks

doi:10.1007/s10704-021-00534-x

Abstract

In this paper, we propose a theoretical framework for studying mixed mode (I and II) creep crack growth under steady state creep conditions. In particular, we focus on the problem of creep crack growth along an interface, whose fracture properties are weaker than the bulk material, located either side of the interface. The theoretical framework of creep crack growth under mode I, previously proposed by the authors, is extended. The bulk behaviour is described by a power-law creep, and damage zone models that account for mode mixity are proposed to model the fracture process ahead of a crack tip. The damage model is described by a traction-separation rate law that is defined in terms of effective traction and separation rate which couple the different fracture modes. Different models are introduced, namely, a simple critical displacement model, empirical Kachanov type damage models and a micromechanical based model. Using the path independence of the C^{*}-integral and dimensional analysis, analytical models are developed for mixed mode steady-state crack growth in a double cantilever beam specimen (DCB) subjected to combined bending moments and tangential forces. A computational framework is then implemented using the Finite Element method. The analytical models are calibrated against detailed Finite Element models and a scaling function (C_{k}) is determined in terms of a dimensionless quantity phi _{0} (which is the ratio of geometric and material length scales), mode mixity chi and the deformation and damage coupling parameters. We demonstrate that the form of the C_{k}-function does not change with mode mixity; however, its value depends on the mode mixity, the deformation and damage coupling parameters and the detailed form of the damage zone. Finally, we demonstrate how parameters within the models can be obtained from creep deformation, creep rupture and crack growth experiments for mode I and II loading conditions.

Highlights

The effective displacement jump across ature, structural components exhibit significant timethe damage zone (m) dependent inelastic deformation, which might lead to δe
We have developed a theoretical framework wherein the bulk material is described by a power-law creep law and the interface behaviour is assumed to be described by a generalised traction-rate of separation law
The damage zone models have been extended to the mixed mode loading case such that the deformation and damage processes are expressed in terms of effective traction and rate of separation which determine the coupling between normal and tangential deformation and a representative separation, respectively

Summary

Introduction

The effective displacement jump across ature, structural components exhibit significant timethe damage zone (m) dependent inelastic deformation, which might lead to δe. Studying creep the damage zone (m/s) crack growth (CCG) has been an active area of research δc. The representative separation at which over the last four decades, with the aim of designing damage initiates in the damage zone at structures with high integrity and safety. The crack tip (m) we aim to devise analytical models for steady-state δf. The representative separation at failure in crack growth under mixed mode loading conditions the crack tip (m) which can be calibrated against detailed Finite Element δim. Such models can be used to investigate vector in the crack tip (i = 1, 2, 3) (m/s) the effect of different material parameters and damage δem

Objectives

Results

Conclusion