Simplified estimate of elastic–plastic J-integral of cracked components subjected to secondary stresses by the enhanced reference stress method and elastic follow-up factors

A simple method to estimate elastic follow-up factors for transient creep parameter C(t) under secondary stress

“…However, values of Z converge to constant values at larger secondary loadings, which is consistent with the findings by Fujioka. 8 As assumed by Fujioka, 8 those constant values will be chosen as an approximate elastic follow-up factor in this study, which is then used to estimate C ( t ).…”

“…For elastic properties, an isotropic material was assumed with Young's modulus E = 200 GPa and Poisson's ratio n = 0.3. For elastic-plastic analyses, the material was assumed to follow equation (8) with s o = 300 MPa. Two values of the strain hardening exponent m were considered, m = 5 and m = 10.…”

“…Based on the reference stress approach, 1 a number of researchers have proposed elastic-plastic and creep fracture mechanics analysis methods for combined primary and secondary stresses. 2–13 An important issue in nonlinear fracture mechanics analyses for combined loadings is the ‘elastic follow-up’ phenomenon which can lead to large local inelastic (plastic or creep) strain. For uncracked components, such a phenomenon occurs due to differences in structural stiffness.…”

“…Although Lei’s method would be useful to calculate the Z value, it is not a predictive one and not suitable in practical situations as detailed elastic-plastic-creep FE analyses are required. Recently, Fujioka 8 proposed an estimation method of the elastic follow-up factor Z for elastic-plastic J estimations under secondary stresses. Based on FE analysis of simple cracked plates under displacement controlled loading, he showed that the calculated Z value approached a saturated one.…”

“…In this article, a semi-analytical method to estimate elastic follow-up factor as input to estimating the transient creep C ( t ) parameter under secondary loading is presented and validated against systematic FE analysis results of cracked two-bar problems. The method can be regarded as an extension of that by Fujioka 8 for elastic-plastic problems to elastic-creep ones and requires only one elastic-plastic FE analysis but not creep FE analysis. This article first reviews the existing equations to estimate the transient creep parameter C ( t ) for secondary stresses in section ‘Approximate C ( t ) estimates for secondary stress: review’.…”