Sequential simulation of thermal stresses in disc brakes for repeated braking

In this paper, an efficient sequential approach for simulating thermal stresses in brake discs for repeated braking is presented. First, a frictional heat analysis is performed by using an Eulerian formulation of the disc. Then, by using the temperature history from the first step of the sequence, a plasticity analysis with temperature dependent material data is performed in order to determine the corresponding thermal stresses. Three-dimensional geometries of a disc and a pad to a heavy truck are considered in the numerical simulations. The contact forces are computed at each time step taking the thermal deformations of the disc and pad into account. In such manner, the frictional heat power distribution will also be updated in each time step, which in turn will influence the development of heat bands. The plasticity model is taken to be the von Mises yield criterion with linear kinematic hardening, where both the hardening and the yield limit are temperature dependent. The results show that during hard braking, high compressive stresses are generated on the disc surface in the circumferential direction which cause yielding. But when the disc cools down, these compressive stresses transform to tensile residual stresses. For repeated hard braking when this kind of stress history is repeated, we also show that stress cycles with high amplitudes are developed which might generate low cycle fatigue cracks after a few braking cycles.