A new <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si3.svg" display="inline" id="d1e1208"> <mml:mrow> <mml:mi mathvariant="bold">M</mml:mi> <mml:mi>θ</mml:mi> </mml:mrow> </mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si4.svg" display="inline" id="d1e1216"> <mml:mrow> <mml:mi mathvariant="bold">A</mml:mi> <mml:mi>θ</mml:mi> </mml:mrow> </mml:math> fractional-integrals for crack initiation and mixed modes growth in hygro-viscoelastic orthotropic materials

Abstract

This paper deals with the development of new path-independent integral formulations for the analysis of crack initiation and mixed-mode crack propagation in orthotropic materials subjected to coupled hygro-mechanical loading with time-dependent viscoelastic effects. The analytical framework is based on an energetic approach to fracture mechanics derived from conservation laws. An automatic crack initiation detection algorithm is proposed and implemented within a finite element software using incremental hygro-viscoelastic constitutive laws. Hygro-viscoelastic behavior is modeled through a fractional Zener formulation, composed of a spring in series with a fractional Kelvin cell. A sensitivity analysis is performed to investigate the influence of the fractional fracture model parameters on crack propagation kinetics. The newly introduced invariant integrals, denoted as M θ visco and A θ visco , allow the evaluation of fracture parameters such as stress intensity factors and energy release rates, while ensuring a proper separation of the elementary fracture modes. This separation is first established in the absence of moisture variations and subsequently extended to account for hygro-mechanical coupling effects. Numerical validations are carried out using a Mixed Mode Crack Growth (MMCG) specimen under combined hygro-mechanical mixed-mode loading at different crack propagation rates. • A new analytical formulation of fractional-integral for path independency. • Initiation and mixed mode crack propagation for viscoelastic orthotropic materials. • A new algorithm including process zone in mixed mode configuration. • Impact velocity and time on viscoelastic energy release rate. • Finite element application with the impact of fractional order.