The concept and numerical evaluation of M-integral based on domain integral method in cracked viscoelastic materials

Abstract

A new form of M-integral associated with time dependence parameters, is presented herein for viscoelastic materials. Based on the equivalent domain integral method, this time-dependent M-integral is numerically implemented as an effective and accepted fracture mechanical parameter for damage induced by crack growth in viscoelastic materials. Based on the linear viscoelastic model defined through Prony series, the conservation of the time-dependent M-integral for viscoelasticity is verified by applying user defined Python scripts. The results show that the newly proposed time-dependent M-integral can be successfully calculated numerically. Furthermore, numerical examples are given to demonstrate the validity and relevance of the time-dependent M-integral in viscoelastic material. In particular, the variations of the time-dependent M-integral for different loading rates are considered, which show that the crack growth behavior over a period of time in viscoelastic material can be evaluated based on the value of the time-dependent M-integral. In addition, the time-dependent M-integral is calculated to assess the damage degree induced by two collinear cracks.