The physics of fatigue crack initiation

X-ray diffraction contrast tomography (DCT) is a technique for mapping grain shape and orientation in plastically undeformed polycrystals. In this paper, we describe a modified DCT data acquisition strategy which permits the incorporation of an innovative Friedel pair method for analyzing diffraction data. Diffraction spots are acquired during a 360 degrees rotation of the sample and are analyzed in terms of the Friedel pairs ((hkl) and (hkl) reflections, observed 180 degrees apart in rotation). The resulting increase in the accuracy with which the diffraction vectors are determined allows the use of improved algorithms for grain indexing (assigning diffraction spots to the grains from which they arise) and reconstruction. The accuracy of the resulting grain maps is quantified with reference to synchrotron microtomography data for a specimen made from a beta titanium system in which a second phase can be precipitated at grain boundaries, thereby revealing the grain shapes. The simple changes introduced to the DCT methodology are equally applicable to other variants of grain mapping.

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Three-dimensional grain mapping by x-ray diffraction contrast tomography and the use of Friedel pairs in diffraction data analysis.

Tensile behavior of columnar grained Cu with preferentially oriented nanoscale twins

http://publish.illinois.edu/mechse-html/files/imported/sangid_maier_sehitogliu_ijp.20110408.4d9f59ff0c48a8.29327594.pdf

The role of grain boundaries on fatigue crack initiation - An energy approach

In this paper a crystal plasticity-based crack nucleation model is developed for polycrystalline microstructures undergoing cyclic dwell loading. The fatigue crack nucleation model is developed for dual-phase titanium alloys admitting room temperature creep phenomenon. It is a non-local model that accounts for the cumulative effect of slip on multiple slip systems, and involves evolving mixed-mode stresses in the grain along with dislocation pileups in contiguous grains. Rate dependent, highly anisotropic behavior causes significant localized stress concentration that increases with loading cycles. The crystal plasticity finite element (CPFE) model uses rate and size-dependent anisotropic elasto-crystal plasticity constitutive model to account for these effects. Stress rise in the hard grain is a consequence of time-dependent load shedding in adjacent soft grains, and is the main cause of crack nucleation in the polycrystalline titanium microstructure. CPFE simulation results are post-processed to provide inputs to the crack nucleation model. The nucleation model is calibrated and satisfactorily validated using data available from acoustic microscopy experiments for monitoring crack evolution in dwell fatigue experiments.

Dwell fatigue crack nucleation model based on crystal plasticity finite element simulations of polycrystalline titanium alloys

We report about plastic strain controlled High Cycle Fatigue (HCF) experiments on an austenitic stainless steel (26% Ni, 15% Cr, 23% Ti, 13% Mn, 12% Mo, 03% Al) for both annealed and age hardened conditions Since twin boundary cracking phenomena were dominant for both conditions, most of the research focused on annealed steel The local orientation of more than 190 grains was measured by a modified electron channeling technique In a simplifying model [P Neumann and A Tonnessen, Proc Conf Fatigue, Charlottsville, USA, Vol 1, pp 3–22 (1987); P Neumann and A Tonnessen, Proc Int Conf Strength of Metals and Alloys, Tampere, Finland, Vol 1, p 743–748 (1987)] these orientation data were used to calculate the local stress concentrations near the twin boundaries By this method for 89% of the examined twin boundaries we could predict whether a crack would develop or not A laser interferometric method was used to measure the local plastic strain across different selected twin boundaries These experiments show that local plasticity is the most important parameter in HCF of fcc polycrystals

Crack initiation during high cycle fatigue of an austenitic steel

A convenient method for the description of orientation data for cubic, hexagonal, tetragonal and orthorhombic crystals is given. The method can also be used for the representation of disorientation data, where disorientations between any two crystals of the specified symmetry lattices are considered. It is based on the quaternion formalism introduced into the discussion of orientations and disorientations by Grimmer [Acta Cryst. (1974), A30, 685–688], Frank [(1987). Proc. Int. Conf. on Texture of Materials 8 (INCOTOM 8), Santa Fe, USA, pp. 3–13] and others. Since orientations and disorientations can be interpreted as rotations which in turn can be represented by only three parameters a vector description is used. These vectors span a rotation space corresponding to the usual space of Eulerian angles. It is called Rodrigues vector space [Rodrigues (1840). J. Math. Pure Appl. 5, 380–440; Becker & Panchanadeeswaran (1989). Text. Microstruct. 10, 167]. The direction of a Rodrigues vector is parallel to the rotation axis and its length is tan (θ/2), where θ describes the rotation angle. A method for selecting a unique representative out of the numerous symmetrically equivalent Rodrigues vectors is given. Since these selection rules depend on the symmetry of the crystal lattices considered they yield compact domains in the Rodrigues vector space which are typical for each type of lattice or lattice pair. These domains are always bounded by planes. Frank (1987) called them fundamental zones and described them for the orientations of cubic, hexagonal and orthorhombic crystals.

A. Heinz

Papers

Crack initiation during high cycle fatigue of an austenitic steel

Representation of orientation and disorientation data for cubic, hexagonal, tetragonal and orthorhombic crystals