Prior-to-failure extension of flaws under monotonic and pulsating loadings

An equation governing the prior to failure crack propagation is proposed. For a rate-sensitive solid containing two-dimensional crack and subject to the tensile mode of fracture the differential equations are integrated numerically for the loads increasing monotonically in time. The resulting integral curves gs = σ(l) and l= l(t), i.e. load vs crack length and length vs time, indicate that the growth of cracks in the subcritical range is strongly rate dependent.The fatigue growth, viewed as a sequence of slow growth periods, is simulated on EAI 380 analogue computer. The fourth power law proposed by Paris is confirmed only within certain range of high-cycle fatigue propagation and for a rate-insensitive solid. Otherwise, that is for a more pronounced rate dependency induced by viscosity of a solid and/or in the proximity of the final instability point the growth is markedly enhanced. For sufficiently small ratios of the applied stress intensity range ΔK to the toughness K_c, the suggested fatigue growth law consists of two terms, i.e.

$\text{d}\text{l}\text{d}\text{n}\text{=}\text{l}{}_1\text{12}\text{4}\text{ΔK}\text{K}{}_{\mathrm{c}}{}^4\text{+Cf}{}^{\mathrm{?1}}\text{ΔK}\text{K}{}_{\mathrm{c}}{}^2\text{, l}{}_1\text{=}\text{πK}{}^2{}_{\mathrm{c}}\text{8Y}{}^2$

First term is the familiar Paris expression while the second one accounts for the rate-dependent contribution; f denotes frequency and Y is the yield strength. Rate-sensitivity C is defined by eq. (1.13).