Discrete modelling of continuous dynamic recrystallisation by modified Metropolis algorithm

Continuous dynamic recrystallisation (CDRX) is often the primary mechanism for microstructure evolution during severe plastic deformation (SPD) of polycrystalline metals. Its physically realistic simulation remains challenging for the existing modelling approaches based on continuum mathematics because they do not capture important local interactions between microstructure elements and spatial inhomogeneities in plastic strain. An effective discrete method for simulating CDRX is developed in this work. It employs algebraic topology, graph theory and statistical physics tools to represent an evolution of grain boundary networks as a sequence of conversions between low-angle grain boundaries (LAGBs) and high-angle grain boundaries (HAGBs) governed by the principle of minimal energy increase, similar to the well-known Ising model. The energy is minimised by a modified Metropolis algorithm. The model is used to predict the equilibrium fractions of HAGBs in several SPD-processed copper alloys. The analysis captures non-equilibrium features of the transitions from sub-grain structures to new HAGB-dominated grain structures and provides estimations of critical values for HAGB fractions and accumulated strain at these transitions

Dynamics of structural defects and plasticity: models and numerical implementation for dynamical problems

We report the plasticity model with explicit description of kinetics of the material defects (dislocations, grain boundaries). This method becomes especially effective for computation of the dynamical deformation of materials at high strain rates because it allows for a simple accounting of the strain rate effects. The equation system is written out and discussed; its implementation is demonstrated for the problem of the plastic flow localization

Triple junction disclinations in severely deformed Cu-0.4%Mg alloys

Stress fields arising from triple junction disclinations (TJDs) play a significant role in the microstructure evolution during the plastic deformation of metals. The calculation of TJD strengths from grain orientation data was developed by Bollmann more than 50 years ago, but so far applied only to collections of a few grains. Developed here is a new methodology for calculating TJD strengths and the associated stress fields in large polycrystalline assemblies using experimental electron back-scattered diffraction (EBSD) maps. The methodology combines Bollmann's approach with a representation of materials as cell complexes. It is computationally efficient and allows for obtaining the spatial distribution of TJD strengths from EBSD images containing thousands of grains. Analysed are the fraction, distribution, and strengths of TJDs within statistically representative microstructures of Cu-0.4%Mg alloy subjected to severe plastic deformation (SPD) by equal channel angular pressing. It is shown that the formation of low-angle grain boundaries (dislocation walls) during SPD leads to an increasing number of TJDs, whose spatial distribution is progressively more uniform and whose strength distribution remains nearly constant. This result suggests that the SPD reduces the internal stresses associated with disclinations in large regions of the material, as closely situated disclinations screen each other's fields. Regions with high local stresses can be expected between sparsely distributed TJDs with the highest strengths. The average distance between such TJDs could be considered as a natural length scale in a material

Defect-induced fracture topologies in Al₂O₃ ceramic-graphene nanocomposites

Models of ceramic-graphene nanocomposites are used to study how the manufacturing process-dependent arrangement of reduced graphene oxide (rGO) inclusions governs nano-crack network development. The work builds upon recent studies of such composites where a novel combinatorial approach was used to investigate the effect of rGO arrangements on electrical conductivity and porosity. This approach considers explicitly the discrete structure of the composite and represents it as a collection of entities of different dimensions - grains, grain boundaries, triple junctions, and quadruple points. Here, the combinatorial approach is developed further by considering the effects of rGO agglomerations, stress concentrators and adhesion energies on intergranular cracking. The results show that the fracture networks can be effectively controlled by the local ordering of rGO inclusions to allow for a concurrent increase in the strength and conductivity of the ceramic composites. It is shown that the ratio of local stress concentrators related to rGO inclusions and cracks is the most significant factor affecting the nano-crack network topology. The local spatial arrangement of rGO inclusions becomes an effective tool for controlling nano-crack network topology only when this ratio approaches one. It is anticipated that these results will inform future design of toughness-enhanced composites

Discrete model for discontinuous dynamic recrystallisation applied to grain structure evolution inside adiabatic shear bands

Discontinuous dynamic recrystallisation (DDRX) is a well-known phenomenon playing a significant role in the high-temperature processing of metals, including industrial forming and severe plastic deformations. The ongoing discussion on the Zener–Hollomon (Z–H) parameter as a descriptor of materials’ propensity to DDRX and a measure of microstructure homogeneity leaves more questions than answers and prevents its practical application. Most of the existing DDRX models are continuous, and so the geometry and topology of real grain microstructures cannot be considered. The present study uses a fully discrete representation of polycrystalline aluminium alloys as 2D/3D Voronoi space tessellations corresponding to EBSD maps. Such tessellations are geometric realisations of combinatorial structures referred to as polytopal cell complexes. Combining discrete models with FEM LS-Dyna simulations of shock-wave propagation in AA1050 and AW5083 aluminium alloys makes it possible to estimate for the first time the contribution of DDRX to the final material microstructure inside adiabatic shear bands. It is shown that the increase of the initial fraction of high-angle grain boundaries, caused by preliminary deformation, significantly increases the spatial homogeneity and decreases the clustering of DDRX grains. The obtained results contradict the conventional assumption that the microstructures obtained by severe plastic deformation under quasi-static and dynamic deformation conditions are similar due to the similar value of the Z–H parameter: competition between the two recrystallisation mechanisms leads to almost unpredictable final grain structures inside share bands that require further comprehensive experimental studies. This agrees with experimental evidence for high material sensitivity to the Z–H parameter

Kinetic model for mechanical twinning and its application for intensive loading of metals

In this report, we present our twinning model intended for simulation of the dynamic deformation of metals with low values of the stacking fault energy, as well as the results of application of the model to numerical simulation of intensive loading of metals. Generation of a twin is described as an appearance of a stacking fault with size more than some critical value, while growth of a twin is considered as a cooperative movement of partial dislocation along the stacking fault. The twin nucleation rate is expressed through the energy released due to annihilation of dislocations. Movement of partial dislocations in the course of twin growth passes under the action of elastic stress field and phonon drag. The surface energy of the growing twin continuously increases which leads to the appearance of an additional force. Application of this model allows us to investigate plastic response of metals at various dynamic loading conditions and initial defect structures. Influence of twinning at Taylor rod compaction experiments is analyzed including formation of the shape of the lateral surface

Dynamical Models of Plasticity with Nonmonotonic Deformation Curves for Nanomaterials

Nanomaterials are widely used in different fields, such as microelectronics, industry, and nanocomposites, and they can exhibit unstable deformation behaviour depending on the strain rates. Under strain rates of 10−4–10−1 s−1, the deformation of nanomaterials, unlike the quasi-static deformation of micromaterials, is characterized by the presence of the rate sensitivity as a possible scale phenomenon in dynamic plasticity. In this paper, the relaxation model of plasticity for the prediction of deformation curves at different strain rates is used. It allows us to comprehensively study the effects of strain hardening in a wide range of deformation conditions for coarse-grained materials and nanomaterials. Considering the plastic deformation of the nanosized samples in the early stages, dynamical softening, associated with a generation of new defects, and dynamic hardening, are crucial. The proposed model, using one parameter or the classical hardening law as an example of nanosized gold whisker crystals, tungsten single-crystal pillars, and single-crystalline Au-Ag alloy nanowires, is verified. Calculated sets of parameters of characteristic time, as a parameter of rate sensitivity of a material, and hardening parameters for different nanomaterials are compared. It is shown that the characteristic relaxation times for the single-crystal nanomaterials (100–103 s) are greater than for the nanostructured materials (10−6–10−4 s). Despite the manifestation of dynamics at different strain rates of nanomaterials, single crystal and nanostructured materials, the proposed model can be successfully applied to materials with different degrees of hardening or softening