Statistical approach to roughness‐induced shielding effects

Abstract

A B S T R A C T A new theoretical concept is introduced to describe the roughness-induced shielding effects in metallic materials. This approach is based on the statistics of the local ratio between the characteristic microstuctural distance and the plastic zone size. A general equation involving both the crack branching and the crack closure phenomena is derived in the frame of linear elastic fracture mechanics under the assumption of remote mode I loading. It enables the determination of the intrinsic values of both the fracture toughness and the fatigue crack growth threshold. Moreover, the roughness-induced component can be separated from other closure components, such as the plasticity or oxide-induced closure. In order to estimate the total roughness-induced shielding effect only standard materials data such as the yield stress, the mean grain size, the surface roughness and the fracture mode are necessary. Examples of applications concerning static fracture and fatigue are presented for selected metallic materials.A = coefficient in the Paris-Erdogan relation a = length of the fatigue pre-crack B = specimen thickness C pcl = closure ratio (other than roughness-induced) D = length of the kinked part of the crack path D dm = standard deviation of the mean grain size data D R = standard deviation of the surface roughness d c = critical (boundary) characteristic microstructural distance d m = mean characteristic microstructural distance da/dN = fatigue crack growth rate dW = elementary energy release (or fracture energy) d = characteristic microstructural distance g * = mean normalized local effective crack driving force g r eff = local effective crack driving force normalized to G G eff = remote effective crack driving force g eff = local effective crack driving forcē g * = normalized local effective crack driving force averaged along the fatigue crack path G I , G II , G III = remote crack driving forces (modes I, II, III) G u I = crack driving force related to the crack instability K = general denotation of the remote stress intensity factor k * = mean local effective stress intensity factor normalized to K I k 1 , k 2 , k 3 = local stress intensity factors (modes 1, 2, 3) K cl = remote closure stress intensity factor K eff,g = global effective stress intensity factor for brittle fracture

Dislocation-based model of plasticity and roughness-induced crack closure

“…In this case, the grain or phase boundaries constitute obstacles for crack growth which results in microscopically rough crack flanks and a highly asymmetric crack-wake plasticity as shown in Fig. 4 (see e.g., [1,11,17] for more details). In the case of S R ( 1, the plastic zone embraces many grains or particles and the grain/phase boundaries do not constitute obstacles for the crack growth.…”

“…6 for an extremely asymmetric dislocation array. Such an array produces RICC far behind the crack tip, in contrast to shear displacements generated by the short-range RICC at the crack tip (see e.g., [4,17] and hereafter). Thus, both the asymmetry of crack-wake dislocations and the roughness of fracture surfaces can be assumed to be the necessary conditions for an occurrence of the long-range RICC.…”

“…A lot of experimental evidence about a significant role of the mean size ratio S Rm = d m /r p (d m is the mean value of the characteristic microstructural distance and r p is the plastic zone size) was collected during the last three decades of fracture and fatigue research, e.g., [17][18][19]. Numerous experiments revealed that the crack path is particularly influenced by microstructure (grain boundaries, phase boundaries, large precipitates, inclusions) when S Rm P 1, i.e., when the static plastic zone at the crack front is constrained within individual grains or between large particles of secondary phases.…”

Influence of phosphorus enrichment at grain boundaries on energy of intergranular fracture in Fe–Si–P alloys

“…Therefore, one has to correct the measured values of K Ic to separate the shielding effect. 11 Another difficulty of Eqn (7) could consist in a possible dependence of elastic moduli on the concentration of segregated phosphorus in the grain boundary layer. However, a recent ab initio analysis showed that there is no significant difference in the modulus values up to 50% of the phosphorus concentration.…”

Microstructural aspects of fatigue in Ni-base superalloys

“…figures 22, 23 and 25), other explanations for microstructural effects have been put forward. For example, it has been posited that the regime of strong microstructural effect depends upon the ratio of the plastic zone to a characteristic microstructural dimension [56,57]. The gist of this idea is that the effects of microstructure become averaged out as this ratio increases since the larger the plastic zone, the smaller the tendency for crack deflection at microstructural barriers.…”