Thermal effect of plastic dissipation at the crack tip on the stress intensity factor under cyclic loading

Abstract

is an open access repository that collects the work of Arts et Métiers ParisTech researchers and makes it freely available over the web where possible. a b s t r a c tPlastic dissipation at the crack tip under cyclic loading is responsible for the creation of an heterogeneous temperature field around the crack tip. A thermomechanical model is proposed in this paper for the theoretical problem of an infinite plate with a semi-infinite through crack under mode I cyclic loading both in plane stress or in plane strain condition. It is assumed that the heat source is located in the reverse cyclic plastic zone. The proposed analytical solution of the thermo-mechanical problem shows that the crack tip is under compression due to thermal stresses coming from the heterogeneous stress field around the crack tip. The effect of this stress field on the stress intensity factor (its maximum and its range) is calculated analytically for the infinite plate and by finite element analysis. The heat flux within the reverse cyclic plastic zone is the key parameter to quantify the effect of dissipation at the crack tip on the stress intensity factor.

About the effect of plastic dissipation in heat at the crack tip on the stress intensity factor under cyclic loading

“…As was noticed by the authors in 2011 [6], the dissipated energy in the reverse cyclic plastic zone also generates a heterogeneous temperature field which depends on the intensity of the heat source associated with the plasticity and the thermal boundary conditions of the cracked structure. Due to the thermal expansion of the material, the temperature gradient near the crack tip creates thermal stresses which contribute to the stress field in this region.…”

“…In order to determine the temperature field, it is possible to consider the thermal problem associated with the fatigue crack propagation as a line heat source centered in the reverse cyclic plastic zone along the crack tip in an infinitely thick body. Ranc et al [6] have compared the numerical solution (by finite element analysis) of the thermal problem in the case of a uniform heat source in a cylinder with a radius equal to the radius of the reverse cyclic plastic zone ( Figure 1) and the analytical solution of the thermal problem with a line heat source. The temperature variation fields obtained with the line heat source or the uniform heat source hypothesis are very close to eachother outside the reverse cyclic plastic zone: the relative difference is equal to about 0.03%.…”

“…Within all these assumptions, the thermal problem is axisymmetric. The authors [6] have solved the associated heat transfer equation considering that there is a homogeneous temperature T 0 in the plate at time t = 0. The temperature variation field ϑ(r, t) = T (r, t) − T 0 can be expressed by:…”

“…The hypothesis and the main results associated to this problem, solved by the authors in 2011 [6], are recalled to understand the most significant phenomena. Then, the heat source within the reverse cyclic plastic zone is identified from temperature field measurement (with an infrared camera) at the surface of a central cracked specimen.…”

“…The previous paper by the authors [6] was devoted to the theoretical problem of an infinite plate with a semi-infinite through crack without any heat loss. Indeed, there are two significant problems to solve when estimating the thermal stresses: the first one is the quantification of the heat source associated with the plasticity near the crack tip; the second one is to make a good estimation of the boundary conditions of the thermal problem (convection from the surface of the cracked structure, for example).…”