Rise of correlations of transformation strains in random polycrystals

We investigate the statistics of the transformation strains that arise in random martensitic polycrystals as boundary conditions cause its component crystallites to undergo martensitic phase transitions. In our laminated polycrystal model the orientation of the n grains (crystallites) is given by an uncorrelated random array of the orientation angles θ_i, i = 1, . . . ,n. Under imposed boundary conditions the polycrystal grains may undergo a martensitic transformation. The associated transformation strains ε_i, i = 1, . . . ,n depend on the array of orientation angles, and they can be obtained as a solution to a nonlinear optimization problem. While the random variables θ_i, i = 1, . . . ,n are uncorrelated, the random variables ε_i, i = 1, . . . ,n may be correlated. This issue is central in our considerations. We investigate it in following three different scaling limits: (i) Infinitely long grains (laminated polycrystal of height L = ∞); (ii) Grains of finite but large height (L » 1); and (iii) Chain of short grains (L = l_0/(2n), l_0 « 1). With references to de Finetti’s theorem, Riesz’ rearrangement inequality, and near neighbor approximations, our analyses establish that under the scaling limits (i), (ii), and (iii) the arrays of transformation strains arising from given boundary conditions exhibit no correlations, long-range correlations, and exponentially decaying short-range correlations, respectivel

The anisotropic grain size effect on the mechanical response of polycrystals: The role of columnar grain morphology in additively manufactured metals

Additively manufactured (AM) metals exhibit highly complex microstructures, particularly with respect to grain morphology which typically features heterogeneous grain size distribution, anomalous and anisotropic grain shapes, and the so-called columnar grains. In general, the conventional morphological descriptors are not suitable to represent complex and anisotropic grain morphology of AM microstructures. The principal aspect of microstructural grain morphology is the state of grain boundary spacing or grain size whose effect on the mechanical response is known to be crucial. In this paper, we formally introduce the notions of axial grain size and grain size anisotropy as robust morphological descriptors which can concisely represent highly complex grain morphologies. We instantiated a discrete sample of polycrystalline aggregate as a representative volume element (RVE) which has random crystallographic orientation and misorientation distributions. However, the instantiated RVE incorporates the typical morphological features of AM microstructures including distinctive grain size heterogeneity and anisotropic grain size owing to its pronounced columnar grain morphology. We ensured that any anisotropy arising in the macroscopic mechanical response of the instantiated sample is mainly associated with its underlying anisotropic grain size. The RVE was then used for meso-scale full-field crystal plasticity simulations corresponding to uniaxial tensile deformation along different axes via a spectral solver and a physics-based crystal plasticity constitutive model. Through the numerical analyses, we were able to isolate the contribution of anisotropic grain size to the anisotropy in the mechanical response of polycrystalline aggregates, particularly those with the characteristic complex grain morphology of AM metals. Such a contribution can be described by an inverse square relation

Revealing per-grain and neighbourhood stress interactions of a deforming ferritic steel via three-dimensional X-ray diffraction

The structural performance of polycrystalline alloys is strongly controlled by the characteristics of individual grains and their interactions, motivating this study to understand the dynamic micromechanical response within the microstructure. Here, a high ductility single-phase ferritic steel during uniaxial deformation is explored using three-dimensional X-ray diffraction. Grains well aligned for dislocation slip are shown to possess a wide intergranular stress range, controlled by per-grain dependent hardening activity. Contrariwise, grains orientated poorly for slip have a narrow stress range. A grain neighbourhood effect is observed of statistical significance: the Schmid factor of serial adjoining grains influences the stress state of a grain of interest, whereas parallel neighbours are less influential. This phenomenon is strongest at low plastic strains, with the effect diminishing as grains rotate during plasticity to eliminate any orientation dependent load shedding. The ability of the ferrite to eliminate such neighbourhood interactions is considered key to the high ductility possessed by these materials

Revealing per-grain and neighbourhood stress interactions of a deforming ferritic steel via three-dimensional X-ray diffraction

The structural performance of polycrystalline alloys is strongly controlled by the characteristics of individual grains and their interactions, motivating this study to understand the dynamic micromechanical response within the microstructure. Here, a high ductility single-phase ferritic steel during uniaxial deformation is explored using three-dimensional X-ray diffraction. Grains well aligned for dislocation slip are shown to possess a wide intergranular stress range, controlled by per-grain dependent hardening activity. Contrariwise, grains orientated poorly for slip have a narrow stress range. A grain neighbourhood effect is observed of statistical significance: the Schmid factor of serial adjoining grains influences the stress state of a grain of interest, whereas parallel neighbours are less influential. This phenomenon is strongest at low plastic strains, with the effect diminishing as grains rotate during plasticity to eliminate any orientation dependent load shedding. The ability of the ferrite to eliminate such neighbourhood interactions is considered key to the high ductility possessed by these materials

Modelling Polycrystalline Materials: An Overview of Three-Dimensional Grain-Scale Mechanical Models

International audienc

Review of the Synergies Between Computational Modeling and Experimental Characterization of Materials Across Length Scales

With the increasing interplay between experimental and computational approaches at multiple length scales, new research directions are emerging in materials science and computational mechanics. Such cooperative interactions find many applications in the development, characterization and design of complex material systems. This manuscript provides a broad and comprehensive overview of recent trends where predictive modeling capabilities are developed in conjunction with experiments and advanced characterization to gain a greater insight into structure-properties relationships and study various physical phenomena and mechanisms. The focus of this review is on the intersections of multiscale materials experiments and modeling relevant to the materials mechanics community. After a general discussion on the perspective from various communities, the article focuses on the latest experimental and theoretical opportunities. Emphasis is given to the role of experiments in multiscale models, including insights into how computations can be used as discovery tools for materials engineering, rather than to "simply" support experimental work. This is illustrated by examples from several application areas on structural materials. This manuscript ends with a discussion on some problems and open scientific questions that are being explored in order to advance this relatively new field of research.Comment: 25 pages, 11 figures, review article accepted for publication in J. Mater. Sc

Interplay of Analysis and Probability in Physics

[no abstract available

The behavior of grain boundaries in the Fe-based superconductors

The Fe-based superconductors (FBS) are an important new class of superconducting materials. As with any new superconductor with a high transition temperature and upper critical field, there is a need to establish what their applications potential might be. Applications require high critical current densities, so the usefulness of any new superconductor is determined both by the capability to develop strong vortex pinning and by the absence or ability to overcome any strong current-limiting mechanisms of which grain boundaries in the cuprates are a cautionary example. In this review we first consider the positive role that grain boundary properties play in the metallic, low temperature superconductors and then review the theoretical background and current experimental data relating to the properties of grain boundaries in FBS polycrystals, bi-crystal thin films, and wires. Based on this evidence, we conclude that grain boundaries in FBS are weak linked in a qualitatively similar way to grain boundaries in the cuprate superconductors, but also that the effects are a little less marked. Initial experiments with the textured substrates used for cuprate coated conductors show similar benefit for the critical current density of FBS thin films too. We also note that the particular richness of the pairing symmetry and the multiband parent state in FBS may provide opportunities for grain boundary modification as a better understanding of their pairing state and grain boundary properties are developed.Comment: To appear in Reports on Progress in Physic