The equilibrium concentration of hydrogen atoms ahead of a mixed mode I-Mode III crack tip in single crystal iron
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INTRODUCTION
THE interaction between interstitial hydrogen atoms and the large tensile stresses present at the tip of a loaded crack has long been recognized.[1,2] Li et al.[3] assumed a spherical distortion around an interstitial atom in a crystal lattice and derived an expression for the equilibrium enhancement of the interstitial species in a stressed solid. The pure dilatation assumed for the interstitial solute only couples to the hydrostatic stress component of the applied stress state. This concept has been used to rationalize the time-dependent hydrogen embrittlement of cracked solids under mode I loading for both internal and external sources of hydrogen.[4–7] In such experiments, the cracking is controlled by the diffusion of hydrogen to the crack tip region. The cracking is typically discontinuous in nature and is observed to follow the plane of maximum normal and hydrostatic tensile stresses.[4,5,6] The site of hydrogen induced cracking has even been found to coincide with the peak in normal and hydrostatic stresses under conditions of internal hydrogen embrittlement in a high strength steel.[7] As a test of the dominance of the hydrostatic stress component in time-dependent hydrogen assisted cracking, several authors have compared the behavior of material loaded in mode I vs mode III. The stress field around a mode III crack does not include any hydrostatic component. Therefore, it has been argued that reduced or nonexistent timedependent hydrogen assisted cracking under mode III loading conditions would be strong evidence of the correctness of any contributions of the deviatoric stresses to hydrogen accumulation in stressed solids.[8,9,10] The experimental findings to date have been mixed. While several studies have shown no detectable time-dependent hydrogen assisted
crack growth in steel and aluminum alloys,[8,9,10] Chu et al. did find evidence for crack growth in mode III in tests conducted on both precharged samples[11] and those tested in solutions known to induce stress corrosion cracking (SCC).[12] In both cases, cracks were found to proceed along planes at 45 deg to the tensile axis on twisted smooth and circumferentially notched bars of high strength steel. Although it is known that surface roughness can confuse the proper determination of the stress intensity factors when mode III loading is applied,[13,14] crack initiation under pure mode III loading does imply an effect of deviatoric stresses on sustained load cracking. Chou et al.[15] discussed the possibility of additional crack tip enhancement of hydrogen in steels as a result of the tetragonal nature of the distortion induced by common interstitial elements in bcc metals. Recently, Zhang et al.[16,17] have used values of the principal strains induced by hydrogen in an iron lattice determined by Bai et al.[18] to examine the potential influence of the deviatoric component of crack tip stresses on hydrogen redistribution. They found that the shear components of the distortion field couple strongly with the crack tip stress field for a
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