PSI - Issue 59

Jesús Toribio et al. / Procedia Structural Integrity 59 (2024) 104–111 Jesús Toribio / Procedia Structural Integrity 00 (2024) 000 – 000

108

5

A classical model of compressive residual stresses in the vicinity of the crack tip after loading/unloading a material element is that proposed by James R. Rice in the past (Rice, 1967, Gortemaker at al., 1981), applicable to an elastic ideally plastic material under cyclic loading, and predictive of the residual stress distribution ahead of the crack tip at the end of the final fatigue pre-cracking step, and therefore prior to a SCC or HAC test. During this test the residual stresses in front of the crack tip are redistributed as the external load increases, and the compressions become tensions when the externally applied load is sufficiently high. Fig. 4 shows the stress distribution proposed by Rice for the maximum (K = K max ) and minimum (K = K min ) fatigue loads. In both cases the maximum and minimum stresses are equal to the yield strength of the material  Y (with positive and negative sign, respectively). Distribution corresponding to K = K min represents the residual stress state after a cyclic loading/unloading process similar to that of fatigue pre-cracking (prior to any SCC test with pre cracked specimens). As depicted in this plot, cyclic residual stresses ahead of the crack tip are compressions. Rice's model does not take into account the strain hardening of the material, and therefore the compressive residual stress at the boundary (crack tip) is always equal to the yield strength of the material. Despite this objection, its predictions seem to be reasonable, according to available numerical estimations (Gortemaker at al., 1981). Moreover, the model is able to predict the depth of the maximum hydrostatic stress point, whose importance is determinant in HAC processes governed by stress-assisted hydrogen diffusion.

Fig. 4. Schematic representation of the cyclic residual stress distribution ahead of a crack tip which has (previously) been subjected to far-field cyclic tension, according to the Rice's model for en elastic ideally plastic material (Rice, 1967, Gortemaker at al., 1981). The values of  and ∆  represent the depth of the monotonic (K max ) and cyclic (K min ) plastic zones as:  = (  /8) (K max /  Y ) 2 (1) ∆  = (  /32) (  K/  Y ) 2 (2) where  Y is the yield strength of the material, K max the maximum SIF during fatigue pre-cracking (last step of loading, just prior to the SCC test), and ∆K the stress intensity range in that step (∆K = K max – K min ). In the tests performed in this work K min = 0, and therefore ∆K = K max . In order to analyze the results of the SCC tests (either LAD or HAC) on the basis of the previous mode and to evaluate interactions between crack-tip plasticity and hydrogen , it is useful to estimate the near-tip plastic zone size during fatigue pre-cracking and at the end of the SCC test. Defining  f = K max / K IC as the dimensionless ratio of the maximum SIF during fatigue pre-cracking K max to the fracture toughness K IC (  f = 0.28, 0.45, 0.60 0.80), it is:  f = (  /8) (K IC /  Y ) 2  f 2 (3)