The Effect of Temperature on Interfacial Gradient Plasticity in Metallic Thin Films

The material microstructural interfaces have a profound impact on the scale-dependent yield strength and strain hardening when the surface-to-volume ratio of the medium increases such as in micro and nanosystems. In this paper, the framework of higher-order strain gradient plasticity with interfacial energy effect is used to investigate the coupling of thermal and mechanical responses of materials in small scales and fast transient processes. In addition to the nonlocal yield condition for the material bulk, a temperature and rate dependent microscopic yield condition for the interface is presented, which determines the stress at which the interface begins to deform plastically and harden. In order to address the strengthening and hardening mechanisms, the theory is developed based on the decomposition of the mechanical state variables into energetic and dissipative counterparts. This, consecutively, provides the constitutive equations to have both energetic and dissipative gradient length scales ℓ _en and ℓ _dis respectively. Hence four material length scales are introduced: two for the bulk and the other two for the interface. In addition, the effect of temperature on the yield strength and hardening of the interface is included in the formulation by postulating that the interfacial energy decreases as temperature increases. Finally the developed framework is solved numerically to investigate the size effect of unaxial loading of a film substrate system.