Polycrystalline microstructure, cubic elasticity, and nucleation of high-cycle fatigue cracks

Abstract

It is well-known that high-cycle fatigue cracks usually nucleate in surface well-oriented grains with a high Schmid factor. A numerical evaluation of the effect of crystalline elasticity anisotropy (which is often neglected) on the stress state in well-oriented grains is presented. Each of these grains is located at the free surface of an aggregate. The other crystallographic orientations are random. Numerous finite element computations are carried out for evaluating the effect of the neighboring grain orientations. Resolved shear stress and normal stress averages are given, as well as scatter parameters and histograms. Several metals, orientations, and loading conditions are considered. For common (anisotropic) metals/alloys such as copper and austenitic steels, the local average resolved shear stress is about 18% smaller than the macroscopic value which induces a Schmid factor value with respect to the macroscopic tensile stress of 0.41 instead of the classical 0.5 value. Relative scatters in resolved shear stress and corresponding normal stress are high (respectively ±22% and ±38%). These high scatter values computed for small applied loads can explain many observations taken from the literature showing a large scatter in the plastic slip line feature, dislocation microstructure, microstructurally short M. Sauzay (B) · T. Jourdan DEN-DMN-SRMA, CEA, bât. 455, crack nucleation, and propagation rate among welloriented surface grains. Finally, the effects of some geometrical parameters are evaluated (2D/3D effects, subsurface grains….).

Fatigue crack nucleation: Mechanistic modelling across the length scales

“…It's also explicitly recognised that Schmid factors calculated based on macro-level applied loading and crystallographic orientation are often misleading by virtue again of the effects of microtexture, since local stress states are often vastly different to that of the macro-level loading. The role of combination of crystallographic orientations in hcp grain pairs was examined systematically in [23,34] in which it was found that a worst case combination of orientations exists in terms of interfacial stress levels and that the effects of elastic anisotropy can be quite significant, also observed by Sauzay [41]. Experimental observations in a largegrained hcp Ti alloy sample [42] using speckle interferometry to measure grain-level strain demonstrate the development of strong strain concentrations resulting from grain orientation combinations which are captured by CP modelling, and a non-local failure criterion presented captures the experimentally observed crack nucleation site.…”

“…Lebensohn [40] developed a full field fast Fourier transform crystal plasticity technique which represents microstructural input from orientation imaging microscopy which achieves good agreement with experimental studies and demonstrates that only models which explicitly account for the interaction of grains (such as CP techniques) are able to capture local microtexture formation and its subsequent behaviour. Computational CP studies [41] have also shown the importance of grain orientation combinations in determining local behaviour, and demonstrate the importance of elastic anisotropy. It's also explicitly recognised that Schmid factors calculated based on macro-level applied loading and crystallographic orientation are often misleading by virtue again of the effects of microtexture, since local stress states are often vastly different to that of the macro-level loading.…”

TEM observations and finite element modelling of channel deformation in pre-irradiated austenitic stainless steels – Interactions with free surfaces and grain boundaries

“…They have been used recently for studying the influence of crystalline elasticity on the resolved shear stress distribution at the free surface of multicrystals [40,41]. The meshes are 3D ones, made of tetrahedra.…”

Finite element modeling of periodic polycrystalline aggregates with intergranular cracks

“…This is due to the presence of harder constituents (reinforcing phase or precipitates) and also simply to the anisotropy of individual crystallites or "grains". Significant stress concentrations occur at the junction of adjacent grains so that grain boundaries and triple junctions are often regarded as preferential crack nucleation sites ( Luther and Könke, 2009;McDowell and Dunne, 2010;Onck and van der Giessen, 1998;Sauzay and Jourdan, 2006;Simonovski and Cizelj, 2015;Yan et al, 2016 ). Computational modeling of the latter phenomena requires three ingredients: (i) a valid representation of the mechanical responses of microscopic constituents, (ii) the definition of a "digital microstructure" that is statistically representative of the real polycrystalline aggregate, and (iii) a robust and efficient numerical solver.…”