Fracture analysis of a steel sandwich with hardened core

2-D elasticity was employed to solve a thermal stress problem of a three layer laminated beam, in which each layer has different thermal expansion coefficient. The thermal stresses arise as a result that initially the layers of the beam were bonded at some high temperature T_Hschand then quenched to some low temperature T_l. Elastic stress field can be derived and expressed in closed form by following the algorithm presented. A numerical example is presented to show that stress concentration due to this thermal effect at the ends of a laminated beam is high and steep enough to cause failure in an ultra-high carbon content and hardened steel.