Effect of Grain Size on Collective Damage of Short Cracks and Fatigue Life Estimation for a Stainless Steel

In the short crack regime of the fatigue process, grain boundaries in steels are barriers against crack growth. In this paper, we use: (1) a method involving crack density; and (2) a method of dimensional analysis, to evaluate the effects of grain size and grain-boundary resistance on short crack behaviour and fatigue life. The results show that the fatigue life increases with a decrease in grain size and an enlargement in the obstacle effect of a grain boundary. An experimental investigation is consequently performed and four groups of stainless steel specimens are used with different grain sizes. The experimental measurements show the dependence of fatigue properties on grain size, which are in good agreement with the theoretical results. Keywords—Short fatigue cracks; Fatigue life; Grain size effect; Stainless steel; Crack density; Dimensional analysis. NOMENCLATURE A(c)=non-dimensional crack growth rate A*=characteristic crack growth rate Ad=crack growth rate at c=1 c=non-dimensional crack length c1=the maximum crack length in the long-crack regime ccr=critical crack length characterizing the termination of the short-crack regime d=non-dimensional grain diameter d0=average grain diameter d:=normalized grain diameter (=d/Ad) D=damage variable D0=total number of cracks or zero-th order of the damage moment D1=first order of the damage moment G=cohesive energy of material M=parameter related to elastic modulus and Poisson’s ratio of the material n (c, t)=crack density n*=characteristic crack density nN(c)=crack nucleation rate n*N=characteristic crack nucleation rate Nf=number of loading cycles to fracture Ng=non-dimensional coefficient= (n* NΩd/n*ΩA*) P=parameter with respect to energy dispersion Q=energy release rate of the damage system r= linear correlation coefficient t=time tcr=critical time characterizing the termination of the short-crack regime c=non-dimensional factor s=effective stress s0=nominal stress s*=threshold stress for fatigue crack growth smax=maximum stress in cyclic loading