Crack propagation due to time-dependent creep in quasi-brittle materials under sustained loading

Abstract

This research considers static mode I fracture under sustained loading and time-dependent creep resulting from the visco-elasticity of the bulk material outside the fracture process zone, and cohesive crack rate dependence. Under sustained loading, the magnitude of the bulk creep deformations are taken to be related to the elastic deformations, material parameters and time. The finite element model formulation used for the analysis of quasi-brittle fracture of Attard and Tin-Loi [M.M. Attard, F. Tin-Loi, Numerical simulation of quasibrittle fracture in concrete, Engrg. Fract. Mech. 72 (2005) 387–411] is extended to include time-dependent behaviour. Fracture is lumped and assumed to occur only at interface nodes by means of a softening-fracture law. The formulation is based on an assembled structural piecewise-linear constitutive law and is set in the form of a “linear complementarity problem” (LCP). In order to include time effects, two main sources of time dependence including bulk creep and crack rate dependency are taken into consideration. The simple concept of a creep coefficient is adopted to account for bulk creep. A simplified crack rate model is proposed and used to represent rate-dependent crack opening. The model is applied to predicting the time-dependent crack propagation in quasi-brittle materials subjected to sustained loading. The experimental results of Zhou [F.P. Zhou, Time-dependent crack growth and fracture in concrete, Doctoral Dissertation, Lund University, Lund, Sweden, 1992] are used to compare with the results of simulations. The crucial aspects of time-dependent behaviour are simulated and presented.