On a possible model of crack propagation in a solid subjected to a cyclic loading

Abstract

By the use of the Griffith model, the propagation of a crack in a solid subjected to a cyclic loading is studied. It is assumed that all the energy lost per cycle in the Bauschinger process is transferred to the crack to increase its size.The paper is divided in two parts, the first dealing with materials which do not undergo work-hardening and the second with materials subjected to said phenomenon during cyclic loading. Notwithstanding the crude approximation of this model, it is shown that the main features of fatigue phenomena are accounted for.

A low-cycle fatigue approach to fatigue crack propagation

“…The energy input must be greater than or equal to the energy dissipated in the form of heat together with the formation energies of the crack tip plastic zone and new crack surface for a fatigue crack to extend. This concept, in one form or another, has been used [15][16][17][18][19] in the derivation of crack growth rate equations.…”

“…Because material elements start experiencing plastic strain amplitudes as soon as they cross the monotonic plastic zone boundary, Kma x (Jmax) instead of AK (A J) appears in the growth rate equation. However, K~ax and AK are simply related according to /(max = AK/(1 -R) (15) where R is the ratio of the minimum to maximum stress intensity factor. So, Equation 14a can be rearranged in the following form dl/dN = f4(eF, 8pZB, fly, fl, C, R) AK 2 (16) to account for the mean stress effects.…”

Crack propagation during fatigue experiments

“…Such a phenomenon is a direct consequence of work-hardening itself. To account for work-hardening effects, it was assumed [1] very simply, that (71 is a linear function of n. Consequently, an.asymptotic expression for the fatigue curve was obtained as…”

“…Therefore, if AE is the energy lost during one hysteresis loop, a, the length of the crack at a given moment, and E(a)Aa the energy required to increase a by Aa, the following equation will result' E(a)Aa = c~AE (1) c~__< 1 being a certain constant assumed independent of crack size, stress, and number of cycles. For analytic treatment it will be convenient to replace (1) with its differential form OW(a) da = c~AEdn (2) Oa where W (a) is the internal energy of the specimen containing a crack of length a and n the number of cycles.…”

“…Equations (1) and (2) are quite general and certainly valid" the problem is to specify the analytical forms of W(a) and AE. This will be done by means of purely phenomenological considerations without claiming any a priori justification of the hypotheses to be put forward.…”