Shakedown analysis of multilayered beams coupled with ductile damage

Shakedown behavior of multilayered beams under cyclic thermo-mechanical loadings was analyzed based on Armstrong–Fredrick nonlinear kinematic hardening model coupled with ductile damage. The shakedown limit loads were determined by the accumulation of plastic straining after enough cycles under various loading combinations and presented by the Bree-like diagram. The effects of the thickness ratio of film/substrate as well as damage parameters on shakedown behavior were also addressed. The calculated results indicated that the twice yield stress limit for shakedown evaluation is considerable conservative compared with the shakedown domain obtained by nonlinear kinematic hardening model. However, shakedown limit loads decreases remarkably considering the ductile damage and the twice yield stress limit for shakedown estimation may be unsafe for engineering designs, especially when the thermal load is prominent.