A second gradient elasto-plastic model for fatigue of small-scale metal components

Purpose – As the dimensions of structures are scaled down to the micro and nanodomains, the mechanical behavior becomes size dependent and thus, the classical elasticity solutions cannot be expected to hold. In particular, recent experimental investigations of fatigue strength of metals show pronounced strengthening due to the influences of both grain size and small geometrical dimensions. This paper aims to provide a simple, yet rigorous analytical model in order to address the aforementioned size effects. Design/methodology/approach – The present study employs a framework based on the type II, strain gradient elasticity theory by Mindlin, embedded into a thermodynamicsbased formulation which considers both mechanical behavior parameters and material lengths, as internal variables, in order to model metal fatigue. Findings – A thermodynamicsbased, second gradient elastoplastic formulation with an explicit material length, which captures the size effects in fatigue of smallscale metal components, has been established. From a physical viewpoint, the evolution of the internal length in the constitutive equations with the evolution of the intrinsic wavelength (e.g. persistent slip bands spacing) can be identified signifying the splitting of the grains into subregions and consequently, the softening of the material. Originality/value – The major novelty of the proposed modeling is that the internal characteristic length considered is not a fixed parameter, but evolves with the plastic effective strain amplitude obtained from cyclic loading.