Importance of Inertia Term in Dynamic Crack Problems Considering Lord–shulman Theory of Thermoelasticity

Abstract

A numerical technique is presented for the accurate calculation of stress intensity factors as a function of time for generalized coupled thermoelastic problems. In this task, the effect of the inertia term is investigated, considering different theories of thermoelasticity, and its importance is shown.A boundary element method using the Laplace transform in time domain is developed for the analysis of fracture mechanics; dynamic coupled thermoelasticity problems with relaxation time are considered in the two-dimensional finite domain. The Laplace transform method is applied to the time domain and the resulting equations in the transformed field are discretized using the boundary element method. Actual physical quantities in the time domain are obtained using the numerical inversion of the Laplace transform method.The singular behavior of the temperature and displacement fields in the vicinity of the crack tip is modeled by quarter-point elements. The thermal dynamic stress intensity factor for mode I is evaluated using the J-integral method. The accuracy of the method is investigated through comparison of the results with the data available in literature.The J integral, which represents the dynamic energy release rate for propagating cracks, contains a boundary integral and a domain integral. The boundary integral contains strain energy, tractions, and strains whereas the domain integral contains inertia and strains. The J-integral method allows these two terms to be calculated separately. In this way, the importance of each term may be investigated by considering different theories of dynamic thermoelasticity.