Standard and strain gradient crystal plasticity modelsapplication to Titanium

Resumen

The mechanical response of metallic alloys is the consequence of deformation mechanisms operating at different length and time scales being these mechanisms strongly influenced by the alloy microstructure. The improvement of the existing alloys and the design of new ones require a deep understanding of these mechanisms and their dependency with the material microstructure. At the mesoscopic level, individual atoms and defects are not considered and the material microstructure can be viewed as the aggregation of single crystalline grains with a given distribution of shapes, sizes and orientation. At this length scale, the discrete plastic deformation of the crystals caused by the dislocation movement and interaction can be homogenized and accounted using continuum theories. Among them, crystal plasticity is a very common approach due to its clear physical basis and proven ability to reproduce the main features of the mechanical behavior in crystalline solids including irreversible plastic response and anisotropy. This thesis proposes some new steps towards the understanding of the relation between microstructure and mechanical behavior of polycrystalline metals at the mesoscopic level using crystal plasticity models to account for the crystal behavior. In the first part, standard crystal plasticity theory is used to model the effect of grain shape and orientation in the mechanical behavior of a polycrystalline metal. In this context the attention is focused on Ti, a metal where the crystal anisotropy and the crystallographic texture play a major role in the microstructure-behavior relation. In particular, nanostructured pure Ti, a novel material for biological applications, was studied using a crystal plasticity finite element (CPFE) polycrystalline model. The actual polycrystalline microstructure (grain shape and orientation distributions) was accounted in voxel-based representative volume elements and the crystal behavior was described using a physically based crystal plasticity model in which plastic slip rate was based on the theory of thermally activated dislocation motion. Prismatic, basal and pyramidal < c + a > slip systems were considered. The parameters of the crystal plasticity model were obtained combining direct microscopic measurements and an inverse analysis of macroscopic experimental results. The resulting polycrystalline model was able to predict the material response as a function of temperature, applied strain rate and loading orientation. The model response was validated by the accurate prediction of independent experimental tests performed at different temperatures and strain rates. Moreover, the model allowed to successfully reproduce the evolution with the temperature of the ratios between the critical resolved shear stresses (CRSS) of the different slip systems. However, it is well known that the actual values of the CRSS are strongly dependent on the grain size and the standard plasticity approach used for this study does not allow to predict this effect. On the contrary, the CRSS obtained by the inverse technique is only valid for that particular grain size. For this reason, in the second part of this thesis a strain gradient crystal plasticity model is proposed to allow the introduction of size effects such as grain size in the polycrystalline modeling framework previously developed. The model here proposed follows a low-order theory and is developed following a continuum thermodynamic framework. The choice of a low order crystal plasticity model is motivated by their ability to reproduce strain gradient effects on the plastic response using a conventional framework and at a relatively low computational cost, compared to high order crystal plasticity theories. However, the computation of slip gradients is still a controversial step in low order crystal plasticity models. In this second part of the thesis, a benchmark problem is proposed first to assess strain gradient crystal plasticity formulations from a numerical standpoint, with the aim to determine the robustness and accuracy. The benchmark consists on a bending beam, especially suitable for lower-order strain gradient crystal plasticity theories because it does not involve higher-order boundary conditions. The most common approach to compute strain gradients, the use of a non-local element first proposed by Busso et al. (2000) is compared with a recovery technique proposed by Han et al. (2007) and the analytical solution. It has been found that the non-local element presents convergence problems that discourage its use, while the recovery technique shows satisfactory results and proves to be a feasible technique. Consequently, a recovery technique is implemented within the finite element framework using a phenomenological crystal plasticity model in which gradients enter in the hardening rate. The resulting model is used to predict the size effect on the single-crystalline bending beam and the expected result, smaller is stronger, is reproduced.