A study of size effects and length scales in fracture and fatigue of metals by second gradient modelling

As the dimensions of structures are scaled down to the micro- and nano-domains, the mechanical behaviour becomes size dependent and thus, we cannot expect the classical elasticity solutions to hold. In particular, recent experimental investigations of fatigue strength of metals show pronounced strengthening due to the influences of small geometrical dimensions. Based on second gradient elasticity framework as particularized on beams, closed form solutions to idealized problems of elastic cantilever bending, elastic three-point bending and elasto-plastic torsion have been found, showing considerable stiffening, toughening and hardening, respectively, compared to the classical theory predictions. In these models, the intrinsic material length scale was taken to be constant. Furthermore, we describe a gradient solid with a characteristic length which is not a fixed material parameter but depends on the amount of plastic effective strain amplitude, as obtained from cyclic strain hardening. A respective evolution law is suggested and discussed.