A non-local model for the description of twinning in polycrystalline materials in the context of infinitesimal strains: application to a magnesium alloy
Charles Mareau, Hamidreza Abdolvand
发表信息：
Journal of Theoretical, Computational and Applied Mechanics (March 7, 2022) jtcam:7562
A polycrystalline plasticity model, which incorporates the contribution of deformation twinning, is proposed. For this purpose, each material point is treated as a composite material consisting of a parent constituent and multiple twin variants. In the constitutive equations, the twin volume fractions and their spatial gradients are treated as external state variables to account for the contribution of twin boundaries to free energy. The set of constitutive relations is implemented in a spectral solver, which allows solving the differential equations resulting from equilibrium and compatibility conditions. The proposed model is then used to investigate the behavior of a AZ31 magnesium alloy. For the investigated loading conditions, the mechanical behavior is controlled by the joint contribution of basal slip and tensile twinning. Also, according to the numerical results, the development of crystallographic texture, morphological texture and internal stresses is consistent with the experimental observations of the literature.
Plastic deformation of metallic alloys usually takes place through slip, but occasionally involves twinning. In particular, twinning is important in hexagonal close packed materials where the easy slip systems are insufficient to accommodate arbitrary deformations. While deformation by slip mechanisms is reasonably well understood, less remains known about deformation by twinning. Indeed, the identification of relevant twinning modes remains an art. In this paper, we develop an universal framework combining fundamental kinematic definition of twins with large scale atomistic calculations to pr…
Twinning is an important deformation mode of hexagonal close-packed metals. The crystallographic theory is based on the 150-years old concept of simple shear. The habit plane of the twin is the shear plane, it is invariant. Here we present Electron BackScatter Diffraction observations and crystallographic analysis of a millimeter size twin in a magnesium single crystal whose straight habit plane, unambiguously determined both the parent crystal and in its twin, is not an invariant plane. This experimental evidence demonstrates that macroscopic deformation twinning can be obtained by a mechanis…
Contraction twinning in magnesium alloys leads to new grains that are misoriented from the parent grain by a rotation of 56 deg around the a-axis. The classical theory of deformation twinning does not precise the atomic displacements and does not explain why contractions twinning is less frequent than extension twinning. The paper proposes a new model in the continuity of our previous works on martensitic transformations and extension twinning. A continuous angular distortion matrix that transforms the initial hcp crystal into a final hcp crystal is determined such that the atoms move as hard …
A crystallographic displacive model is proposed for the extension twins in magnesium. It is based on a hard-sphere assumption previously used for martensitic transformations. The atomic displacements are established, and the homogeneous lattice distortion is analytically expressed as a continuous angular-distortive matrix that takes the usual form of shear when the distortion is complete. The calculations prove that a volume change of 3 percents occurs for the intermediate states and that the twinning plane, even if untilted and restored when the distortion is complete, is not fully invariant …
Deformation twinning is a form of permanent deformation that is commonly observed in low symmetry crystals such as hexagonal close-packed (hcp) metals. With recent increased interest in using hcp metals, such as magnesium, in structural, automotive, and armor applications due to their high strength to weight ratio, there is a need for a comprehensive understanding of deformation twinning and its interaction with dislocation slip. A great deal has been learned at the microscopic level where individual dislocations interact with twin boundaries through atomistic simulations, and at the macroscop…
A theoretical-computational framework is proposed for predicting the failure behavior of two anisotropic brittle materials, namely, single crystal magnesium and boron carbide. Constitutive equations are derived, in both small and large deformations, by using thermodynamics in order to establish a fully coupled and transient twin and crack system. To study the common deformation mechanisms (e.g., twinning and fracture), which can be caused by extreme mechanical loading, a monolithically-solved Ginzburg--Landau-based phase-field theory coupled with the mechanical equilibrium equation is implemen…
The {11-22} and {11-26} twinning modes were recently put in evidence by Ostapovets et al. (Phil. Mag, 2017)and interpreted as {101-2}-{101-2} double-twins formed by a simultaneous action of two twinning shears. We propose another interpretation in which the twinning modes result from a one-step mechanism based on the same (58deg, a+2b) prototype stretch twin. . The two twins differ from the prototype twin by their obliquity correction. The results are compared with the classical theory of twinning and with Westlake-Rosenbaum model of {11-22} twinning. An unconventional twinning mode recently d…
Magnesium (Mg) and its alloys hold great potential as an energy-saving structural material for automative, aerospace applications. However, the use of Mg alloys has been limited due to poor ductility and formability. Poor mechanical properties of Mg alloys origin from the insufficient number of slip systems, and deformation twinning plays an important role to accommodate plastic deformation. Here, we report a comprehensive experimental and modeling study to understand crystal size effect on the transformation in deformation modes in twin oriented Mg single crystals. The experiments reveal two …
The cyclic deformation behavior of extruded Mg-8.5wt.%Al alloy with a conventional extrusion texture and a modified texture is systematically investigated by in-situ neutron diffraction and elastic viscoplastic self-consistent (EVPSC) modeling incorporating a twinning/de-twinning (TDT) scheme. The role of twinning and de-twinning on the deformation behavior of Mg-8.5wt.% Al alloy is investigated in terms of the macroscopic stress-strain response, the evolution of the activities of various deformation mechanisms, the texture evolution, the evolution of the internal elastic strains, and the evol…
Precipitation on deformation defects is essential for enhancing mechanical properties of age-hardenable alloys. {10-12} twinning is common in deformed alloys with hexagonal-close-packed structure. In this work, we revealed how {10-12} twin boundary (TB) influences beta-Mg17Al12 precipitation in Mg-9Al-1Zn alloy. The precipitates on the TB are rod-like, while others are lath-shape. The precipitates hold the Burgers orientation relationship (OR) only with twin or matrix, contrary to traditional wisdom in others alloys that precipitates on TB symmetrically keep an OR with both twin and matrix. Mo…
The deformation mechanisms of an extruded Mg-5Y-0.08Ca (wt. %) alloy were analyzed by means of micropillar compression tests on single crystals along different orientations -- selected to activate specific deformation modes -- as well as slip trace analysis, transmission electron microscopy and transmission Kikuchi diffraction. The polycrystalline alloy presented a remarkable ductility in tension (~32%) and negligible differences in the yield strength between tension and compression. It was found that the presence of Y and Ca in solid solution led to a huge increase in the CRSS for <a> basal s…
Defect-controlled twin activation in crystallographically equivalent magnesium micropillars
RWTH Aachen University（亚琛工业大学）；CNRS, Université de Lorraine, Arts et Métiers Institute of Technology（法国国家科学研究中心，洛林大学，国立工艺学院）；Helmholtz Zentrum Hereon（海姆霍兹HEREON中心）
Schrodinger-type wave equations with logarithmic nonlinearity occur in hydrodynamic models of Korteweg-type materials with capillarity and surface tension, which can undergo liquid-solid or liquid-gas phase transitions. One of the predictions of the theory is a periodic pattern of density inhomogeneities occurring in the form of either bubbles (topological phase), or cells (non-topological phase). Such inhomogeneities are described by solitonic solutions of a logarithmic wave equation, gaussons and kinks, in the vicinity of the liquid-solid phase transition. During the solidification process, …
Strain-controlled fatigue of Mg-1Mn-0.5Nd (wt.\%) alloy were studied by experiment and simulation. The microstructure was made up of a dispersion of strongly texture grains (13\%) embedded in a matrix of grains with a random texture. The cyclic stress-strain curves showed limited tension-compression anisotropy because of the limited texture. Cyclic hardening under compression and cyclic softening under tension occurred due to the presence of twinning. Moreover, the twin volume fraction of the broken samples depended on whether the sample was broken in tension or compression, indicating that tw…
Uncertainty quantification (UQ) plays a major role in verification and validation of computational engineering models and simulations, and establishes trust in the predictive capability of computational models. In the materials science and engineering context, where the process-structure-property-performance linkage is well known to be the only road mapping from manufacturing to engineering performance, numerous integrated computational materials engineering (ICME) models have been developed across a wide spectrum of length-scales and time-scales to relieve the burden of resource-intensive exp…
Temperature-Aware Recurrent Neural Operator for Temperature-Dependent Anisotropic Plasticity in HCP Materials
organization= Mechanics \& Materials Laboratory, Department of Mechanical；Process Engineering, ETH Zürich , city= Zürich , postcode= 8092 , country= Switzerland；organization= Department of Engineering, University of Cambridge , addressline= Trumpington Street , city= Cambridge , postcode= CB2 1PZ , country= UK
