A Proposed Criterion for Fatigue Threshold: Dislocation Substructure Approach

Abstract

A model for fatigue threshold has been proposed based on the dislocation subgrain cell structure that evolves at the crack tip in steels during the fatigue deformation process. The stabilized subgrain cells that develop in the material act as impenetrable barriers to dislocations in slip band pile-ups that emanate from the fatigue crack tip. The blocking of these dislocations tends to limit crack growth that occurs by crack tip emission of dislocations, thereby leading ultimately to the fatigue threshold condition. The grain size effect on threshold is deduced to be an indirect effect as it is proposed that the subgrain cell size is the controlling substructural parameter at the threshold stress intensity level. The subgrain cell size is shown to be proportional to the one-third power of the initial grain size. NOMENCLATURE a = constant b = Burger's vector = constant p, = cyclic strain hardening exponent D = average grain size E = elastic modulus G = shear modulus E , E,,, eya = total, plastic and yield strains AKTH = threshold stress intensity range factor M = Taylor's factor p, = mobile dislocation density Rf = reversed plastic zone size r = length parameter X = subgrain cell size 0 = plasticity factor 6 = constant o y s = yield strength AK = stress intensity range.

Variability of large-crack fatigue-crack-growth thresholds in structural alloys

“…According to this analysis, [50] the threshold arises because a dislocation emitted from the crack tip must overcome the resistance provided by dislocations in the cellular structure in order for the activation of cyclic slip in the vicinity of the crack tip to occur. The threshold model is given by [50] [5] ⌬K th ϭ 2 a fr m Ebd…”

“…These multiple transitions of the near-tip stress fields are analogous to those postulated for explaining the onset [10] of cleavage fracture in a plastic field by the transitions of the K field to the J field and then back to the K field, due to formation of an elastic enclave near the crack tip. [63,64] The intrinsic threshold for large cracks in cell-forming materials proposed by Lucas and Gerberich [50] (shown in Eq. [5]) is comprised of two terms, both of which depend on the dislocation-cell size, d. The term is analogous to Eq.…”

“…The threshold model proposed by Lucas and Gerberich [50,51] is based on the development of a dislocation-cell structure by cyclic slip in the near-tip region. According to this analysis, [50] the threshold arises because a dislocation emitted from the crack tip must overcome the resistance provided by dislocations in the cellular structure in order for the activation of cyclic slip in the vicinity of the crack tip to occur.…”

“…[52] In particular, the cyclic plastic-zone size can be expressed in terms of the yield stress and the stress-intensity range by the expression given by [50,52] [6] which can be rearranged to give [7] at the cyclic plastic-zone boundary. Since the stress-range distribution ahead of the tip of the fatigue crack is reasonably described by the elastic or K field and exhibits a r Ϫ1/2 dependence, as shown schematically in Figure 2(a), where r is distance from the crack tip, one can replace ys by ⌬ e and by r s at the FCG threshold to give [8] with [9] where ⌬ e is the fatigue limit and M is the Taylor factor.…”