Twinning is a primary deformation mechanism in hcp metals and {101¯2} twins are prevalent in nearly every hcp metal. The 3D morphology and growth of twins is controlled by faceted structures at twin boundaries. We characterize the 3D faceted boundaries of {101¯2} twins in Ti using HR-TEM and compare them with Mg. We find eight characteristic facets in Ti, three of which were not observed in Mg. The revealed 3D facets provide the basic information for studying the kinetics, morphology, and transmission of the 3D twins and provide better understanding of differences in the deformation mechanisms of these materials.

Plastic anisotropy is observed during plastic flow in samples from the axial and transverse directions of Zr-2.5Nb pressure tubes used in CANDU1 nuclear reactors tested in uniaxial tension. Plastic anisotropy was also measured in shear by testing in torsion 'mini' pressure tubes from the same material. Room temperature results from these experiments were analysed using a visco-plastic self-consistent model that takes into account the crystallographic texture of the material and allows for the single crystal work hardening behaviour to be described by means of a deformation law specific to each slip system. The visco-plastic self-consistent model was used to derive: (i) the evolution with strain of the critical resolved shear stress values consistent with prismatic, basal and pyramidal dislocation glide, (ii) the evolution of slip system activity as a function of strain, and (iii) the values of Hill's plastic anisotropy coefficients that are consistent with the observed anisotropy of yielding and their dependence on accumulated strain. The model also allows for the prediction of the components of the flow stress tensor that cannot be measured experimentally and their dependence on the work hardening behaviour of pressure tube material. Moreover, the yield surface after different amounts of plastic strain was calculated using the visco-plastic self-consistent model, compared to the one that results from using the Hill's anisotropy coefficients. Our work exposes the limitations of the Hill ellipsoid for describing plastic yield when microstructural evolution is present.

The mechanical response of hexagonal close-packed metals is mediated by the formation of three-dimensional twin domain networks. To assess the morphology of these networks and statistically characterize their fingerprint, a three-dimensional twin network in cryogenically compressed high-purity Ti was reconstructed using serial sectioning and electron backscatter diffraction (EBSD). Adjoining intergranular twin pairs, high order twin intersections (e.g. triple junctions of twins), and twin network hubs with over 15 separate intergranular and intragranular contacts are found to be salient morphological features of these networks. Using kinematics, the interfacial incompatibilities arising from these twin contact at grain boundaries are studied. The analysis reveals that numerous misaligned paired twin configurations generate high incompatibilities, likely resulting from the contact between two initially distinct twin chains. These configurations generally induce higher incompatibilities than the ones of the individual twins, equivalent to introducing a dense wall of dislocations at twin-grain boundary facets with a dislocation spacing on the order of 1.3 nm or less. In contrast, the shear incompatibilities resulting from the formation of aligned twin pairs are generally reduced compared to non- transmitting twins. Further, twin triple junctions and branches - consisting of intergranular contact of three co-located twins - induce higher incompatibilities on average compared to adjoining twin pairs and represent sources of high shear localization in the domain network.

This work presents a dislocation density-based crystal plasticity constitutive model for glide kinetics, strengthening and dislocation density evolution, implemented in the effective medium-based visco-plastic self consistent (VPSC) framework and the spatially resolved, rho-CP crystal plasticity finite element framework. Additionally, a distribution of intragranular stresses is introduced in the VPSC framework, instead of the conventionally used mean value of grain stress for effective medium calculations. The rho-CP model is first calibrated to predict the mechanical response of a bcc ferritic steel with an initial rolled texture. The same set of constitutive model parameters are then used in VPSC to predict the aggregate stress-strain response and total dislocation densities. For these VPSC simulations, the interaction parameter governing the interaction between the grain and the effective medium in the Eshelby inclusion formalism, and a scalar parameter representative of the distribution of intragranular stresses within a grain, are used to calibrate the VPSC predictions in order to match the predictions of the rho-CP model. A parametric study is performed to understand the effect of these two parameters on the VPSC predictions. Further, simulations are also performed for a random untextured polycrystal to identify the corresponding VPSC simulation parameters for predicting a similar response as the rho-CP model. The novelty of the work is in the same set of constitutive models and associated parameters have been implemented in VPSC and rho-CP to predict similar aggregate stress-strain response and total dislocation densities. This finite element-calibrated effective medium crystal plasticity approach reduces the computational time by at least two orders of magnitude and represents an advance towards the development of multiscale crystal plasticity modeling tools.

Zirconium transforms from the alpha+omega phase under high hydrostatic pressures. The critical transformation pressure is expected to be affected by internal stresses associated with defects. This study focuses on the effects of dis-locations and twins and their associated stress fields on the transformation. Samples are pre-loaded to seed dislocations or twins. In-situ high-hydrostatic-pressure X-ray synchrotron experiments are performed revealing that microstructures with pre-existing prismatic (a) dislocations and {101 over bar 2} twins promote the transformation more effectively than pyramidal (c + a) dislocations or {112 over bar 2} twins. Post-mortem electron backscatter diffraction further shows that pre-seeded defects stabilize the omega-phase at ambient conditions. In-situ stress-hold neutron diffraction experiments are also performed combining both hydrostatic and deviatoric stresses capturing the role of deviatoric stresses on phase transformation kinetics. These results support the findings of recent atomistic simulations indicating flow of prismatic (a) dislocations at an alpha-omega interface promotes the growth of the omega domain.

Two recently proposed elasto-visco-plastic self-consistent (EVPSC) models, based on solving for stress or stress increment, are discussed, and their results are compared with the ones of the visco-plastic self-consistent (VPSC) approach. The advantages and shortcomings of the models are demonstrated, with emphasis on how the grain responses are affected by the time increment and inclusion-medium interaction strength used. Experimental data obtained for an FCC stainless steel is used as the benchmark system for performing the simulations and assessing the reliability of the results. Predictions of stress-strain response of the aggregate, standard deviations in intergranular stress and strain rate, along with the evolution of internal lattice strain are presented and compared, with special focus on their dependence on the incremental approach chosen. We find that the chosen time increment may significantly affect predicted grain responses. To avoid such effect a method based on using two separate time increments is proposed, one for approximating the stress rate and another for actual integration of stress, strain, and state variables. The proposed method successfully eliminates the dependence of results on the time increment used, thus allowing more reliable computations while preserving the computational efficiency of the elasto-visco-plastic model.

Uranium polycrystal aggregates accumulate large plastic deformation during thermal cycling in a process known as thermal ratcheting. This process is induced by highly anisotropic single crystal properties, texture, and a complex coupling between thermal, elastic, and plastic mechanisms of deformation. In this study, a thermo-elasto-visco-plastic polycrystal model is developed and applied to the prediction of thermal ratcheting in uranium. The model is based on the evolution of dislocation density on individual slip systems and accounts for static recovery effects. The model captures the plastic relaxation of intergranular stresses induced by thermal cycling and leads to quantitative understanding of the coupling between thermal, elastic and plastic mechanisms, and the important role played by static dislocation recovery in uranium. Results are compared with thermal ratcheting measurements.

Diffusionless transformations (DTs), such as twinning, are key plastic deformation modes in metals with a limited number of slip systems. DTs can simultaneously confer excellent strength and ductility to these materials under thermomechanical loads. The efficiency of DTs is fundamentally governed by the balance between plastic dissipation (as the domains grow) and the buildup of internal elastic strain energy in the matrix. The present study examines this duality by quantitatively mapping the mechanical fields at the nanometer scale near the propagation front of a deformation twin under load in hexagonal close-packed Mg. To this end, a novel combination of in situ straining and patterned-probe four-dimensional scanning transmission electron microscopy (4D-STEM) strain mapping is utilized. Cross-examination of the experimental results using an atomistically-informed phase field model suggests that the junctions between interfaces/facets bounding twin domains can shield the matrix from a large fraction of the transformation-induced rotations, thereby significantly lowering the buildup of elastic strain energy that is induced by twinning. This sheds new light on the effects of twinning on the evolution of the internal energy landscape during plasticity.

Ceramic-metal composites, or cermets, exhibit beneficial properties resulting in their use in many industrial applications. One challenge with cermets is mismatches in the coefficient of thermal expansion (CTE) values between the ceramic and metal phases that lead to residual stresses after processing, plasticity in the metal phase, internal stresses, and instability after thermal cycling. In order to make predictions of these properties to inform the design of cermets, we employ an incremental elasto-viscoplastic, self-consistent formulation to calculate the thermal, elastic, and plastic strains in two-phase polycrystalline cermet materials. This framework is extended to include temperature dependent properties, which are called implicitly within the temperature-dependent, incremental elasto-viscoplastic, self-consistent (TE-VPSC) model. Temperature-induced cooling and thermal cycling simulations are conducted using the TE-VPSC framework to study the residual stresses and plastic strains in the metal phases. Two materials are discussed in detail exhibiting stark differences based on the CTE between their ceramic and metal phases, WC/57-vol% Cu (exhibiting a pronounced CTE mismatch) and Y2O3/27-vol% Nb (exhibiting a negligible CTE mismatch). The model demonstrates high residual stresses in the Cu phase during processing and reverse plasticity leading to recovery of plastic strain during thermal cycling of the WC/Cu cermet. Moreover, the model demonstrates relatively low residual stresses and plasticity in Y2O3/Nb and a thermal stability point of 1251°C, below which no plasticity develops in the cermet. We employ the TE-VPSC model as a design tool for cermets to systematically investigate the effects of process-induced microstructure variations (volume fraction, grain aspect ratio, and crystallographic texture are investigated) and compositional differences (19 compositions are explored) on the residual stress, degree of plasticity in the metal phase, and thermal stability point. The computational efficiency of the TE-VPSC framework makes it a desktop design tool that can be used to quantify the impact of changing composition, processing, and thermo-mechanical loading on the performance of the cermet, which can help reduce the number of time intensive and costly high temperature experiments.

Under ambient conditions, Zn is a hexagonal metal with a large c/a ratio of 1.856. Plastic deformation is predominantly accommodated by basal 〈a〉 slip and compression twins on the {101¯2} planes. Increasing hydrostatic pressure drastically reduces the c/a ratio of Zn and, when a critical threshold of c/a=3 at about 10 GPa is crossed, the {101¯2} twins are predicted to change from compressive to tensile in nature. What happens at the transition point, when c/a=3, remains unknown. Here, we strain-cycle a textured polycrystalline sample of pure Zn at uniform hydrostatic pressures ranging between 2 and 17 GPa, over which the c/a ratio crosses the c/a=3 compressive-tensile transition for {101¯2} twins. During deformation, the state of the sample is monitored through x-ray diffraction to extract texture and internal strain evolution. By comparing the experimental results with the predictions of an elastoviscoplastic polycrystal simulation, we confirm the androgynous nature of {101¯2} twin response at low and high pressures. When c/a=3, polycrystalline Zn does not display any evidence of twinning and its plastic behavior is controlled by mostly basal and pyramidal 〈c+a〉 slip activity, with a very small contribution of prismatic 〈a〉 slip. Evidence for the activity of other {101¯n} twinning modes, which have been suggested for Zn under high pressure, are not observed. Published by the American Physical Society 2024

Under ambient conditions, Zn is a hexagonal metal with a large c/a ratio of 1.856. Plastic deformation is predominantly accommodated by basal (a) slip and compression twins on the {1012} planes. Increasing hydrostatic pressure drastically reduces the c/a ratio of Zn and, when a critical threshold of c/a = 3 at about 10 GPa is crossed, the {1012} twins are predicted to change from compressive to tensile in nature. What happens at the transition point, when c/a = 3, remains unknown. Here, we strain-cycle a textured polycrystalline sample of pure Zn at uniform hydrostatic pressures ranging between 2 and 17 GPa, over which the c/a ratio crosses the c/a = 3 compressive-tensile transition for {1012} twins. During deformation, the state of the sample is monitored in situ through x-ray diffraction to extract texture and internal strain evolution. By comparing the experimental results with the predictions of an elastoviscoplastic polycrystal simulation, we confirm the androgynous nature of {1012} twin response at low and high pressures. When c/a = 3, polycrystalline Zn does not display any evidence of twinning and its plastic behavior is controlled by mostly basal and pyramidal (c + a) slip activity, with a very small contribution of prismatic (a) slip. Evidence for the activity of other {101n} twinning modes, which have been suggested for Zn under high pressure, are not observed.

Chapter 6 presents several examples meant to familiarize the reader with the various capabilities of the VPSC code by addressing practical cases and materials with different crystal symmetry. Among them are the use of different constitutive laws and plastic strain paths, the enforcement of mixed boundary conditions, and the calculation of polycrystal yield surfaces.

This chapter provides a comprehensive derivation of a viscoplastic self-consistent (VPSC) model for polycrystal aggregates. The VPSC model, used to simulate the plastic response of polycrystals, is based on treating grains as ellipsoidal viscoplastic inclusions interacting with an effective medium having the average viscoplastic properties of the polycrystal. The polycrystal is represented by a discrete set of crystal orientations with associated volume fractions chosen to reproduce the texture of the aggregate. The deformation of the grains is based on the activation of crystallographic slip and twinning. The VPSC model is fully anisotropic and applicable to aggregates with arbitrary crystal symmetry, including multiphase aggregates. The stress and strain rates at the crystal level are related by a rate-sensitive power law. Other constitutive laws, described in Chapter 4, can be implemented within the VPSC framework. The model predicts the evolution of stress, strain, and crystal orientation of the individual grains, and the hardening and texture evolution of aggregates subjected to combined and evolving stress and strain rate conditions.

In this chapter we describe the basic concepts associated with crystal symmetry, crystal elasticity, crystal plasticity, and continuum mechanics (kinematics) used throughout the book. Basic constitutive laws such as linear elasticity, linear viscosity, and viscoplasticity are introduced, with an emphasis on anisotropy, which gives the tensorial character to such laws. Basic concepts concerning the treatment of tensors, texture representation, and plastic yield surface of single crystals are presented. We describe the fundamental concepts associated with stress and strain, accounting for heterogeneity and anisotropy, and the corresponding equations that determine the mechanical behavior of deformable solids, in particular polycrystalline materials: constitutive equations that provide a relation between local or overall stress and strain, and governing equations that provide the conditions that stress and strain fields obey in a deformed solid.

This chapter provides a comprehensive derivation of a thermo-elastic self-consistent (TESC) model for polycrystal aggregates. The TESC model, used to simulate the elastic and thermal mechanical response of polycrystals, is based on treating grains as ellipsoidal thermo-elastic inclusions interacting with an effective medium having the average thermal and elastic properties of the polycrystal. The polycrystal is represented by a discrete set of crystal orientations with associated volume fractions chosen to reproduce the texture of the aggregate. The model predicts the evolution of stress and strain in both, the aggregate and the individual grains, when subjected to combined and evolving stress, strain, and temperature conditions.

The advent of techniques enabling three-dimensional (3D) analysis of objects, defects, and fields has been key to discoveries and paradigm shifts in molecular biology, astrophysics, medicine, quantum physics, etc. In materials science, the 3D nature of materials microstructures remains largely hidden; leading to a fragmented under-standing of microstructure-property linkages. Current tools cannot characterize large volumes of 3D micro-structures at fine resolution. To this end, this study introduces a graph-theory-based framework to automatically extract 3D microstructures and statistics of electron-backscatter diffraction datasets. Further, leveraging network science, the study introduces a new approach to classify and compare microstructures; the keystone to materials taxonomy. The significance of this tool is demonstrated by studying deformation twin structures in Titanium. The study reveals extraordinarily complex and tortuous twin networks never observed via traditional two-dimensional analysis. This changes our perception of the ability of metals to withstand severe microstructure changes without failing.

Under extreme conditions, α-Ti becomes unstable and transforms either into β-Ti at high temperature or into ω-Ti at high pressure. In what concerns the α to ω phase transformation (PT), there has been a wide range of experimentally reported transition pressures from approximately 2 to 15 GPa at room temperature. Deviatoric stresses and internal defects are often assumed to be the root cause of this variation. In this study, these postulates are revisited using both continuum mechanics and molecular dynamics (MD) simulations. First, a simple continuum model, assuming linear elasticity and isotropic plasticity, is developed to describe the effects of applied stress and dislocations on the stability of an ω nucleus in an infinite α domain. Second, a new MD simulation method is developed to generate an ω nucleus in the α domain utilizing the displacement field identified from the topological analysis. Results from MD simulations show that despite the fact that phase diagrams typically delineate the limits between two phases in terms of only P and T, deviatoric stress promotes the α to ω phase transformation by reducing the critical radius above which an ω nucleus is stable. Furthermore, the required deviatoric stress to nucleate and stabilize a nanoscale ω nucleus is likely emanating from the internal stress of defects such as dislocations. The MD-informed micromechanics models are used to identify favorable configurations where dislocations help favor the α to ω transformation. These configurations show that the interaction with a basal or prismatic dislocation reduces the critical radius of a ω nucleus by about 10 or 16 %, respectively. In addition, prismatic edge dislocations are found to promote the growth of ω nucleus when interacting with the (1¯1¯20)α//(0001)ω interface. Importantly, a simple model of the arrival of dislocation at an ω nucleus suggests that PT does not necessarily require a pile-up to be present but could alternatively be mediated by a constant rapid flow of dislocations.

Chapter 5 documents the implementation of the VPSC formulation in the VPSC code and describes the latter in detail: its structure, input/output files, subroutines, and the derivation of the algorithms used.

The present study investigates the effect of strain path on microstructure and micro-texture evolution in AA8090 alloy during single point incremental forming (SPIF). In this regard, 45° and 60° wall angle truncated pyramidal geometries have been formed to attain different strain paths at wall and corner regions. The effect of wall angle on thickness reduction and strain evolution in pyramidal geometries has been studied in detail employing finite element (FE) simulations. A multiscale FE coupled visco-plastic self-consistent (VPSC) simulation has been conducted to elucidate the effect of shear strains on SPIF deformation behaviour from the perspective of micro-texture evolution. The micro-textures predicted using variable velocity gradients (considering shear components) are in good agreement with the experimental ones, unlike the micro-texture simulated employing monotonic velocity gradient (excluding shear components). The VPSC simulation demonstrates that the presence of shear components deviates the rotation path of orientations from developing stable texture components, resulting in spread of orientation. The shear components are also observed to reduce the lattice reorientation rate which weakens the micro-texture evolution. It can be contemplated that the evolution of shear strains reduces the sharpness of microtexture which could be attributed to higher formability during SPIF process. Further, the anisotropy evolution (r-values) is estimated for simulated micro-texture using VPSC simulation. A correlation is established between plastic anisotropy and micro-texture evolution which could be used to predict the material response towards deformation at intermediate stages during multi-stage forming.