An axisymmetric ordinary state-based peridynamic model for thermal cracking of linear elastic solids

Abstract

This paper proposes an axisymmetric ordinary state-based peridynamic model considering the thermal expansion effect for temperature-induced cracking of linear elastic solids. Both the force state and bond failure criterion of the model are built in axisymmetric domain. The direct calculation for peridynamic bond energy density of the axisymmetric model considering thermal terms is given. The adaptive dynamic relaxation method is adopted for the quasi-static peridynamic simulations. Validity and reliability of the proposed axisymmetric model are illustrated by numerical examples of cold-induced fracture in a pipe with an inner crack. It is shown that the displacement predicted by the proposed peridynamic model is in good agreement with the corresponding finite element method. The critical bond energy density criterion for thermal cracking is verified via comparisons with the critical fracture temperature loads computed from the virtual crack closure technique and released energy based on Griffith’s theory. The sensitivity of the present model on the peridynamic discretization is investigated and discussed in both the continuous deformation and cracking cases. The performance of the peridynamic model is further demonstrated for cold-induced fracture of double-layered pipes with inner cracks, and the cracking behaviors influenced by the interfacial toughness and number of inner cracks are captured, respectively. The present model is capable of solving axisymmetric thermal cracking problems of linear elastic solids effectively, and it can be applied in more advanced axisymmetric structures which involve more complicated cracking issues.