Model For Inelastic Deformation Research Articles

Relativistic constitutive modeling of inelastic deformation of continua moving in space-time

Since Einstein introduced the theory of relativity, several scientific observations have proven that it thoroughly approximates the motion of materials in space-time. Thus, efforts have been made to expand classical continuum mechanics to relativistic continuum models to consider relativistic effects. However, most models consider only the elastic range without accounting for inelastic deformation. A relativistic inelasticity model should provide objective measures of the inelastic deformation for different observers with nonzero relative velocities over a wide speed range, even when the moving speed is close to the speed of light. This study presents a mathematical modeling structure of the relativistic constitutive equations of the inelastic deformation of a material moving over a wide speed range to provide objective measures for observers. In this model, the deformation tensors of classical mechanics are expanded to four-dimensional tensors (referred to relativistic Cauchy–Green deformation tensors) in space-time, based on which constitutive equations of inelastic deformation are introduced. The four-dimensional tensors are objective about the homogeneous Lorentz transformation in the Minkowski space-time, and the material dissipation, determined employing the proposed modeling of inelastic deformation, satisfies the second law of thermodynamics. In addition, an example illustrates the application of this theory by explaining the physical meaning of modeling. Finally, it is also demonstrated that the proposed relativistic inelasticity model collapses into a classical inelasticity model when the speed of motion is much slower than the speed of light.

Identification of Initial Critical Resolved Shear Stresses Using of a Two-Level Model of Inelastic Deformation

Identification of Initial Critical Resolved Shear Stresses Using of a Two-Level Model of Inelastic Deformation

Grain Structure Rearrangement by Means the Advanced Statistical Model Modified for Describing Dynamic Recrystallization

The study of grain and defect structure evolution in materials subjected to thermomechanical processing is still an urgent problem because the state of a structure substantially determines the physical and mechanical macro properties of polycrystals and polycrystalline products. Significant changes in the structure of polycrystalline materials are associated with the process of dynamic recrystallization (DRX). To investigate DRX, an extended statistical model of inelastic deformation with internal variables is proposed, which takes into consideration contact interactions between neighboring grains. We constructed a geometric image of the grain structure by applying a Laguerre polyhedron in order to describe such interactions in the statistical framework. During the recrystallization simulation, this image is being reconstructed as new recrystallized grains emerge. This leads to the problem of establishing correspondence between an initial grain structure and a reconstructed structure with the required statistical consistency. To provide such consistency, an optimization problem is formulated to preserve the stress and strain parameters and the recrystallization driving force from changes in a statistical sense. This problem is posed with respect to the distributions of differences in defect-stored energy, mutual misorientation angles between grains and sizes of these grains. A genetic algorithm is applied for resolution. By the example of simulating inelastic deformation of a representative volume element (a macrosample analogue) of polycrystalline copper, the influence of the mentioned distributions on the material response upon structure reconstruction is shown. Reasonable values for the objective weights and the genetic algorithm parameters were obtained. This paper presents a detailed description of the grain structure correspondence establishment method, the formulation of the optimization problem and the algorithm to resolve it.

Some Issues with Statistical Crystal Plasticity Models: Description of the Effects Triggered in FCC Crystals by Loading with Strain-Path Changes.

The justification of the applicability of constitutive models to exploring technological processes requires a detailed analysis of their performance when they are used to describe loadings including the complex loading mode that is characteristic of these processes. This paper considers the effect of equivalent stress overshooting after the strain-path changes known to occur in metals and alloys. The macrophenomenological and multilevel models, which are based on crystal plasticity, account for this effect by applying anisotropic yield criteria at the macro- and mesolevels, respectively. We introduce a two-level constitutive statistical inelastic deformation model (identified for aluminum) that incorporates the popular simple phenomenological anisotropic hardening law for describing the behavior of FCC polycrystals. The results of the numerical simulation are in satisfactory agreement with existing experimental data. Statistical analysis of the motion of a mesostress in the stress space on the crystallite yield surface is performed. The obtained data are compared with the results found using the isotropic hardening law. The results clarify the simulation details of statistical crystal plasticity models under loading with strain-path changes in materials and demonstrate their suitability for describing the processes under consideration.

Subgrain Coalescence Simulation by Means of an Advanced Statistical Model of Inelastic Deformation

The development of technological methods for processing and manufacturing of functional (with a priori targeted properties) polycrystalline materials and products made of these materials still remains an acute problem. A multilevel modeling approach offers researchers the opportunity to describe inelastic deformation by applying internal variables that give an effective characterization of the material structure at different structural scale levels. High temperature plastic deformation is accompanied by these processes, which leads to a significant rearrangement of the meso- and microstructure of the material. The most substantial contribution to changing the properties of polycrystals is made by the evolution of grain and defect structures at the expense of dynamic recrystallization, which significantly depends on dynamic recovery. In this paper, we consider the problem of the coalescence of subgrains undergoing rotation during inelastic hot deformation. This process is called subgrain coalescence, and it is one of the dynamic recovery mechanisms responsible for changes in the fine subgrain structure. Under applied thermomechanical loads, the coalescence process promotes the formation of recrystallization nuclei and their subsequent growth, which can greatly change the grain structure of a polycrystal. The problem was solved in terms of the advanced statistical model of inelastic deformation, modified to describe the subgrain coalescence process. The model takes into account the local interactions between contacting structural elements (subgrains). These have to be considered so that the grain coalescence caused by a decrease in subboundary energies during their progressive merging can be adequately analyzed. For this purpose, a subgrain structure quite similar to the real structure was modeled using Laguerre polyhedra. Subgrain rotations were investigated using the developed model, which relies on the consideration of the excess density edge component of the same sign dislocations on incidental subgrain boundaries. The results of modeling of a copper polycrystal are presented, and the effects of temperature and strain rate on the subgrain coalescence process is demonstrated.

Description of Dynamic Recrystallization by Means of An Advanced Statistical Multilevel Model: Grain Structure Evolution Analysis

Physical multilevel models of inelastic deformation that take into account the material structure evolution hold promise for the development of functional materials. In this paper, we propose an advanced (modified via analyzing the mutual arrangement of crystallites) statistical multilevel model for studying thermomechanical processing of polycrystals that includes a description of the dynamic recrystallization process. The model is based on the consideration of homogeneous elements (grains, subgrains) aggregated into a representative volume (macropoint) under the Voigt hypothesis. In the framework of this statistical approach, there is no mandatory requirement for continuous filling of the computational domain with crystallites; however, the material grain structure cannot be created arbitrarily. Using the Laguerre polyhedra, we develop a method of grain structure simulation coupled with subsequent processing and transferring of the necessary data on the grain structure to the modified statistical model. Our research is of much current interest due to the fact that the mutual arrangement of crystallites, as well as the interfaces between them, has a significant impact on the properties of polycrystals, which are particularly important for physical mechanisms that provide and accompany the processes of inelastic deformation (recrystallization, grain boundary hardening, grain boundary sliding, etc.). The results of the simulations of the high-temperature deformation of a copper polycrystal, including the description of the recrystallization process, are presented.

Impulsive Tsunami and Large Runup Along the Sanriku Coast of Japan Produced by an Inelastic Wedge Deformation Model

AbstractDynamic wedge failure produces short‐wavelength seafloor uplift efficiently with diminishing shallow slip on the plate interface, generating impulsive tsunami. For ria coasts with prevalent small‐wavelength bathymetric and geomorphologic features, such as the Sanriku coast of Japan, impulsive tsunami can be amplified to produce large runup. We model tsunami propagation and runup of the 1896 Sanriku tsunami by using the seafloor deformation from dynamic rupture models of Ma and Nie (2019) for a MW 8 earthquake with inelastic wedge deformation. The nonlinear Boussinesq equation is solved by a nested‐grid finite‐difference method with high‐resolution bathymetry data. We show that an inelastic deformation model with extensive wedge failure produces impulsive tsunami similar to those observed offshore the Sanriku coast in the 2011 Tohoku earthquake and generates large runup remarkably consistent with the 1896 Sanriku tsunami. As an alternative to previous models based solely on fault slip, we suggest that the impulsive tsunami and large runup along the Sanriku coast observed in the 2011 Tohoku earthquake can be explained by inelastic wedge deformation north of 38.5°N.

Inelastic Behavior of Polyoxymethylene for Wide Strain Rate and Temperature Ranges: Constitutive Modeling and Identification.

The aim of this paper is to present experimental data and the constitutive model for the inelastic behavior of polyoxymethylene in wide strain rate and temperature ranges. To capture the non-linearity of the stress responses for both loading and unloading regimes, the composite model of inelastic deformation is utilized and further developed. The equivalent inelastic strain rate is described by the Prandtl–Eyring law, while the temperature dependence is characterized by the modified Arrhenius-type law. Generalized equivalent stress and the flow rule are formulated to capture pressure sensitivity, transverse strain and volumetric strain responses. The results obtained by the constitutive law are compared with experimental data for stress vs. axial strain from standard tension tests as well as with axial and transverse strains measured by digital image correlation. The developed composite model is able to capture the non-linearity of stress–strain curves for complex loading paths within the small strain regime. For higher strains, apart from geometrically non-linear theory, evolution laws for the volume fraction of the constituents should be modified and calibrated. For the small strain regime, the inelastic dilatation is negligible. For higher axial strain values, a decrease in Poisson’s ratio under tension and increase in it under compression are observed. The Drucker–Prager-type equivalent stress and the developed flow rule provide a better description of both the transverse and volumetric strains than that of the classical von Mises–Odqvist flow rules.

Crystal plasticity modeling of non-Schmid yield behavior: from Ni3Al single crystals to Ni-based superalloys

A crystal plasticity finite element (CPFE) framework is proposed for modeling the non-Schmid yield behavior of L12 type Ni3Al crystals and Ni-based superalloys. This framework relies on the estimation of the non-Schmid model parameters directly from the orientation- and temperature-dependent experimental yield stress data. The inelastic deformation model for Ni3Al crystals is extended to the precipitate (γ′) phase of Ni-based superalloys in a homogenized dislocation density based crystal plasticity framework. The framework is used to simulate the orientation- and temperature-dependent yield of Ni3Al crystals and single crystal Ni-based superalloy, CMSX-4, in the temperature range 260–1304 K. Model predictions of the yield stress are in general agreement with experiments. Model predictions are also made regarding the tension–compression asymmetry and the dominant slip mechanism at yield over the standard stereographic triangle at various temperatures for both these materials. These predictions provide valuable insights regarding the underlying (orientation- and temperature-dependent) slip mechanisms at yield. In this regard, the non-Schmid model may also serve as a standalone analytical model for predicting the yield stress, the tension–compression asymmetry and the underlying slip mechanism at yield as a function of orientation and temperature.

The Brittle‐Ductile Transition in Porous Limestone: Failure Mode, Constitutive Modeling of Inelastic Deformation and Strain Localization

AbstractUnderstanding of the mechanics of the brittle‐ductile transition (BDT) in porous limestone is significantly more challenging than for sandstone because of the lack of consistent acoustic emission activity in limestone, meaning that one must rely on alternative techniques. In this paper, we investigate systematically the failure modes in Indiana limestone using X‐ray microComputed Tomography imaging (μCT) and Digital Volume Correlation (DVC). Our new mechanical data show that the envelope for the onset of shear‐enhanced compaction can be well approximated by an elliptical cap. The DVC analysis revealed the development of shear bands through the BDT, but no evidence of compaction bands. The shear band angles were between 29° and 46° with respect to the maximum principal stress. Compiling these new results with published data on Purbeck and Leitha limestones, we showed that inelastic compaction in each of these dual porosity allochemical limestones was in a good agreement with the normality condition, as defined in plasticity theory. Comparison of the observed failure modes with predictions based on bifurcation analysis showed that the shear band angles are consistently smaller than the theoretical predictions.

Модель неупругого деформирования сплавов с памятью формы

Предложен вариант модели фазово-структурного деформирования сплавов с памятью формы, в рамках которого параметром изотропного упрочнения для процесса деформирования по структурному механизму является интенсивность собственной фазово-структурной деформации мартенситной части представительного объема материала. Получено решение задачи об обратном термоупругом фазовом превращении в заневоленном стержне с предварительно заданной растягивающей или сжимающей деформацией. Исследовано влияние на решение значения параметра трансляционного упрочнения.

Объединенная модель фазово-структурного деформирования сплавов с памятью формы

A combined model of inelastic deformation of shape-memory alloys for phase and structural transformations is proposed, taking into account the fundamental difference between these two mechanisms and the influence of the first mechanism on the second. In contrast to the known analogs, the model allows for non-monotonic loading processes to exceed the long arc of phase-structural deformation (an analogue of the Odqvist parameter in the theory of plasticity) of the intensity of crystallographic deformation of the phase transition.

Multi-level model describing phase transformations of polycrystalline materials under thermo-mechanical impacts

The problem of constructing the multilevel physical model of inelastic deformation in steels allowing to take into consideration diffusionless solid-state phase (martensitic) transitions is considered. The model structure includes three scale levels with the closed system of equations offered for them. Explicit internal variables reflecting the evolution of the material structure (both the defect structure and the grain one) are introduced at the lower scale levels of the model. The distinctive feature of the developed model is consideration of the lower scale level in such a way that a homogeneous element of this level completely turns into a new phase at a high speed (relative to the kinematic quasi-static loading), that is close to the speed of sound in the crystal medium. Based on the principles of classical thermodynamics the phase transformation criterion is written. According to this criterion, the choice of a transformational system under the martensitic transition is made. The algorithm of the model is developed and its realization features are described in connection with the high-rate restructuring of the face-centered cubic lattice to the body-centered tetragonal one. The result of this restructuring is a severe change in the physic-mechanical properties of the material.

Comparison of self-consistent and crystal plasticity FE approaches for modelling the high-temperature deformation of 316H austenitic stainless steel

The present article examines the predictive capabilities of a crystal plasticity model for inelastic deformation which captures the evolution of dislocation structure, precipitates and solute atom distributions at the microscale, recently developed by Hu and Cocks (2015) and Hu et al. (2013). The model is implemented within a self-consistent framework and a crystal plasticity finite element (CPFE) scheme. Through direct comparison between the two CP schemes and with an extensive material database for Type 316H stainless steel, the different types of information and the degree to which the models are consistent with experimental observations are assessed. The study demonstrates an agreement between the SCM and the CPFE schemes, providing confidence in the micromechanical deformation model employed. The multi-scale approach also allows the effects of micro-scale deformation processes, related to dislocation-obstacle interactions, on the global deformation response to be captured. Modelling results from this study and their comparison to experimental observations show that deformation of polycrystalline materials, such as 316H stainless steel, is controlled by the evolution of microstructural state of the material and the redistribution of stress between individual grains. The study suggests that the SCM is a feasible tool to simulate and explain the deformation behaviour of complex alloys under industrially-relevant thermo-mechanical operating histories. The CPFE framework captures the effects of the variation in grain geometry and provides more detailed information about the variation of stress and strain within the individual grains, particularly their distribution near grain boundaries and triple points – which are important to understand in the context of damage development and failure. The SCM predicts a “stiffer”, more creep-resistant response than a CPFE model for a given set of material parameters due to the more highly-constrained deformation modes allowed in the model. As a result, material parameters calibrated using one modelling approach are not necessarily suitable for use in another approach – although parameters obtained when fitting the different models should not vary significantly.

Thermo-electro-mechanical modeling, simulation and experiments of field-assisted sintering

Contact growth and temperature behavior in time during a single high-current pulse representing the initial stage of field-assisted/spark plasma sintering (FAST/SPS) have been studied experimentally and numerically. The measured evolution of the electrical resistance and of the neck formation process in two-particle systems is compared to the results obtained from the fully coupled thermo-electro-mechanical finite element simulations. The results of simulations with various models of inelastic deformation show that the viscoelastic/viscoplastic material model provides a realistic contact growth in initial stage of FAST/SPS. The impact of electrical and mechanical loads, material parameters and particle size on temperature, on inelastic strain distribution and on densification has been studied by finite element simulations for copper, stainless steel and nickel particles.

Mesoscale Modeling of Inelastic Deformation and Stress in High Temperature Oxidation of Metals

Metal oxidation mostly involves significant volume change that cannot be accommodated by elastic deformation alone. Consequently, during the growth of oxide there are various elastic/inelastic deformation in the matrix, oxide, and slip along phase boundaries and grain boundaries. Due to the microstructural complexity, it is difficult to model inelasticity in oxidation from the dislocation level. Here we develop a mesoscale phase-field approach, based on Khachaturyan’s close-form solution for microelasticity, to solve the inelastic deformation coupled with mass transport and microstructure evolution. The model incorporates both classical J2 plasticity and crystal plasticity to accommodate inelastic deformation of a polycrystal with interfacial sliding. The model is validated by a series of analytical solutions and by comparing with other numerical simulations. Finite deformation is approached by an incremental realization algorithm. The model is also applied to simulate incoherent interfaces and coherency loss. During internal oxidation, isolated oxide particles are usually coherent when they are small while they gradually lose coherency during the growth.

Experimental characterization of composites to support an orthotropic plasticity material model

Test procedures for characterizing the orthotropic behavior of a unidirectional composite at room temperature and quasi-static loading conditions are developed and discussed. The resulting data consisting of 12 stress–strain curves and associated material parameters are used in a newly developed material model—an orthotropic elasto-plastic constitutive model that is driven by tabulated stress–strain curves and other material properties that allow for the elastic and inelastic deformation model to be combined with damage and failure models. A unidirectional composite—T800/F3900, commonly used in the aerospace industry, is used to illustrate how the experimental procedures are developed and used. The generated data are then used to model a dynamic impact test. Results show that the developed framework implemented into a special version of LS-DYNA yields reasonably accurate predictions of the structural behavior.

Study on Modeling of Inelastic Deformation of Semi-crystalline Polymer based on Kinetics of Molecular Chain

Study on Modeling of Inelastic Deformation of Semi-crystalline Polymer based on Kinetics of Molecular Chain

Two-scale models of polycrystals: Evaluation of validity of Ilyushin’s isotropy postulate at large displacement gradients

This paper discusses multiscale models of inelastic deformation of single- and polycrystals, which are based on crystal plasticity theories, as applied to the verification and justification of Ilyushin’s isotropy postulate (in a special form) at large displacement gradients. Different approaches to motion decomposition on the macroscale into quasi-rigid (described by the motion of a corotational coordinate system) and strain-induced motion (a relatively moving coordinate system) are considered. The strain path is defined in terms of a moving coordinate system. Corresponding kinematic effects are defined in terms of a laboratory coordinate system. In this case, the loading process image is constructed and loading conditions are specified in terms of the moving coordinate system. Calculations are performed for two types of strain paths with different curvature by assuming two different hypotheses about quasi-rigid motion on the macroscale: (i) the spin of the moving coordinate system is equal to an averaged mesoscale spin, and (ii) the spin is equal to the macroscale vortex. It is shown that the isotropy postulate is more valid in the case of assuming the first hypothesis.

Strongly objective numerical implementation and generalization of a unified large inelastic deformation model with a smooth elastic–inelastic transition

In the present work, a general theoretical framework for modeling a smooth elastic inelastic transition for large deformations of rate independent elastic–plastic and rate dependent elastic–viscoplastic materials is proposed. Generally speaking, in classical rate independent elastic–plastic models the transition from the elastic regime to the plastic regime is sharp, while in the present model this transition is smooth and both rate independent and rate dependent models are characterized by overstress. A finite element formulation has been developed for the general plasticity model, which integrates the evolution equations and formulates the tangent stiffness in terms of the state variables and the relative deformation gradient during a time step. In particular, this formulation is independent of a total strain measure and arbitrariness of the specification of a reference configuration. A number of large deformation example problems, which examine and verify the implementation of the developed finite element, show that the integration scheme for the elastic distortional deformation is strongly objective and demonstrate the capability of the formulation in modeling realistic problems like necking of cylindrical bar.