Energy analysis of crack interaction with an elastic inclusion

Abstract

This paper gives an energy analysis of an elastic solid with a crack which penetrates an elastic inclusion. The purpose of our work is to evaluate the energy release rates (ERR) associated with crack tip extension while the inclusion is stationary, and to evaluate the ERR due to inclusion translation, rotation and expansion with respect to the crack tip. Reduction and increase in the crack ERR caused by an inclusion (shielding and amplification effects of the inclusion) are expressed in terms of the inclusion elastic properties normalized by Young's modulus of the bulk material. The variation in ERR as a crack approaches and passes through a circular inclusion is also examined.

The stress intensity factor Green's function for a crack interacting with a circular inclusion

“…This element with the shift of the midpoint to the quarterpoint simulates the singular elastic fields at the crack tip. The finite element discretization is similar to that employed in our previous work [11]. The inclusion is identified by the parameter that represents the material properties of the elements.…”

“…This master curve therefore may only depend on dipole force location ~(~ = 1 -x/a) and the relative distance d/D. Noticing this, we propose a function q defined by (11) This function is shown in Fig. 6.…”

“…Problems of the crack interaction with an elastic inclusion have been extensively discussed by various authors, for example, Atkinson [1], Erdogan and Gupta [2], Tlrosh and Tetelman [3]; Hutchinson [4], Steif [5], Ortiz [6], Wu [7]; Wu and Chen [8], Patton and Santare [9], Chudnovsky and Li [ 10] and [ 11 ]; details of their works can be found in numerous publications. Some of the analytical solutions in their essential part were based on the dislocation solutions which were earlier works of Dundurs et al in [12][13].…”

Examination of the fatigue crack growth equations

“…In general, energy release rate due to a perturbation of the system is defined as the variational derivative of potential energy with respect to a system characteristic ERR def t~II = 64 (6) where in this case ~II is the potential energy variation due to crack extension Aa, and ~ stands for the crack length a. The energy release due to variation of crack growth direction as well as due to variation of PZ configuration is reported elsewhere [27,28]. The finite element mesh is automatically regenerated every step when the crack t~p ,~uvances to a new position.…”

“…The process zone affects the stress field in the vicinity of the crack tip. Microcracks, crazes, voids and other microdefects in general reduce the stiffness of the material, and thus impose a shielding on the main crack as pointed out by many authors [27,28,[31][32][33][34][35][36][37].…”