Thiebaud Richeton

Analytical expressions of incompatibility stresses at Σ3⟨111⟩ twin boundaries and consequences on single-slip promotion parallel to twin plane

Strong incompatibility stresses may develop at grain or twin boundaries because of elastic and plastic anisotropies. Their knowledge at twin boundaries may be of interest for a better understanding of the mechanical behaviour of fcc materials that can display lamellar twin structures, such as twinning-induced plasticity (TWIP) steels or general nanotwinned materials. In this paper, incompatibility stresses arising at general twin boundaries are explicitly derived for a given twin volume fraction. They are deduced from the solutions of the general infinite bicrystal, which is equivalent to a periodic layered structure. In the case of pure elasticity and twin boundaries, the result is of remarkable simplicity. The incompatibility stress field reduces to a shear stress acting upon a plane orthogonal to twin plane. Simple analytical expressions of the resolved shear stresses are also determined according to the twin-boundary orientation, the twin volume fraction and the elastic anisotropy factor. Such expressions allow performing a comprehensive study of slip initiation. In particular, there exists a large physical domain, depending on the three above parameters, where simultaneous slip parallel to twin plane in the parent and in the twin is greatly promoted. There is also a restricted domain where simultaneous single slip parallel to twin plane is promoted. The conditions for these promotions are realistic considering the literature data on TWIP steels. The present results, hence, support the high ductility and strong contribution of kinematic hardening observed in TWIP steels and agree with composite hardening models with single- and multi-slip-deforming grains.

Variant selection of twins with low Schmid factors in cross grain boundary twin pairs in a magnesium alloy

Samples of magnesium AZ31 alloys are deformed in compression at room temperature under a strain rate of 1×10−3 s−1. The initial texture with respect to the loading direction is favorable for {10-12} extension twinning during the deformation. At an engineering strain of 2.75%, many extension twins are found to be connected with each other at grain boundaries, forming cross grain boundary twin pairs. Some have low positive or even negative Schmid factors (SFs). The variant selection of them are interpreted in terms of shear accommodations. The observed twin variants require the least or no accommodation through deformation modes with high CRSSs, but the most or more accommodation through those with low CRSSs.

Combined Effects of Texture and Grain Size Distribution on the Tensile Behavior of α-Titanium

This work analyzes the role of both the grain size distribution and the crystallographic texture on the tensile behavior of commercially pure titanium. Specimens with different microstructures, especially with several mean grain sizes, were specifically prepared for that purpose. It is observed that the yield stress depends on the grain size following a Hall–Petch relationship, that the stress–strain curves have a tendency to form a plateau that becomes more and more pronounced with decreasing mean grain size and that the hardening capacity increases with the grain size. All these observations are well reproduced by an elasto-visco-plastic self-consistent model that incorporates grain size effects within a crystal plasticity framework where dislocations’ densities are the state variables. First, the critical resolved shear stresses are made dependent on the individual grain size through the addition of a Hall–Petch type term. Then, the main originality of the model comes from the fact that the multiplication of mobile dislocation densities is also made grain size dependent. The underlying assumption is that grain boundaries act mainly as barriers or sinks for dislocations. Hence, the smaller the grain size, the smaller the expansion of dislocation loops and thus the smaller the increase rate of mobile dislocation density is. As a consequence of this hypothesis, both mobile and forest dislocation densities increase with the grain size and provide an explanation for the grain size dependence of the transient low work hardening rate and hardening capacity.

Micromechanical Modeling of the Elasto-Viscoplastic Behavior and Incompatibility Stresses of β-Ti Alloys

Near β titanium alloys can now compete with quasi-α or α/β titanium alloys for airframe forging applications. The body-centered cubic β-phase can represent up to 40% of the volume. However, the way that its elastic anisotropy impacts the mechanical behavior remains an open question. In the present work, an advanced elasto-viscoplastic self-consistent model is used to investigate the tensile behavior at different applied strain rates of a fully β-phase Ti alloy taken as a model material. The model considers crystalline anisotropic elasticity and plasticity. It is first shown that two sets of elastic constants taken from the literature can be used to well reproduce the experimental elasto-viscoplastic transition, but lead to scattered mechanical behaviors at the grain scale. Incompatibility stresses and strains are found to increase in magnitude with the elastic anisotropy factor. The highest local stresses are obtained toward the end of the elastic regime for grains oriented with their <111> direction parallel to the tensile axis. Finally, as a major result, it is shown that the elastic anisotropy of the β-phase can affect the distribution of slip activities. In contrast with the isotropic elastic case, it is predicted that {112} <111> slip systems become predominant at the onset of plastic deformation when elastic anisotropy is considered in the micromechanical model.

Complexity and Anisotropy of Plastic Flow of α-Ti Probed by Acoustic Emission and Local Extensometry

Current progress in the prediction of mechanical behavior of solids requires understanding of spatiotemporal complexity of plastic flow caused by self-organization of crystal defects. It may be particularly important in hexagonal materials because of their strong anisotropy and combination of different mechanisms of plasticity, such as dislocation glide and twinning. These materials often display complex behavior even on the macroscopic scale of deformation curves, e.g., a peculiar three-stage elastoplastic transition, the origin of which is a matter of debates. The present work is devoted to a multiscale study of plastic flow in α-Ti, based on simultaneous recording of deformation curves, 1D local strain field, and acoustic emission (AE). It is found that the average AE activity also reveals three-stage behavior, but in a qualitatively different way depending on the crystallographic orientation of the sample axis. On the finer scale, the statistical analysis of AE events and local strain rates testifies to an avalanche-like character of dislocation processes, reflected in power-law probability distribution functions. The results are discussed from the viewpoint of collective dislocation dynamics and are confronted to predictions of a recent micromechanical model of Ti strain hardening.

Three-Stage Character of Strain Hardening of α-Ti in Tension Conditions

The plasticity of hexagonal materials is strongly anisotropic and involves different microscopic mechanisms such as mechanical twinning and dislocation glide. Twins are often considered to be responsible for a particular three-stage shape of compression curves, unusual for polycrystals with cubic structure. However, the role of twins remains a matter of debate and it is not clear if the same features appear in other testing conditions. We performed tensile tests on commercially-pure Ti samples cut along the rolling and the transverse direction, which yielded several unexpected results. In particular, the work hardening rate was found to be lower in the latter case, although the EBSD measurements revealed for them a larger volume fraction of twins. Also, the two kinds of specimens showed an opposite sign for the strain-rate effect on the proneness to the three-stage shape of the deformation curves. As a first approach, these observations are compared to the results derived from a simple Kocks-Mecking model. The possible role of twinning and dislocation glide on the anisotropy of mechanical behavior of titanium is then discussed.