New robust self-consistent homogenization schemes of elasto-viscoplastic polycrystals
Not Available
36 MATERIALS SCIENCE↗
SEARCH · Search NASA
Results for “viscoplasticity”
Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.
Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.
On the viscoplastic response of a composite wafer
In the present treatment of a viscoplastic composite wafer formed from a viscoplastic matrix that is reinforced by elastic or viscoplastic fibers attached to its plane surfaces, one constitutive equation is established by considering the viscoplastic behavior of the matrix as determined by an integral-type constitutive law whose intrinsic time-measure is pertinent to endochronic viscoplasticity. Attention is given to asymptotic cases where fiber stiffnesses and the hydrostatic modulus of the wafer are much larger than the latter's shear modulus. An explicit calculation is used when the stress field is uniaxial.
Valanis, K. C.↗
Characterization of elastic-viscoplastic properties of an AS4/PEEK thermoplastic composite
The elastic-viscoplastic properties of an AS4/PEEK (APC-2) thermoplastic composite were characterized at 24 C (75 F) and 121 C (250 F) by using a one-parameter viscoplasticity model. To determine the strain-rate effects, uniaxial tension tests were performed on unidirectional off-axis coupon specimens with different monotonic strain rates. A modified Bodner and Partom's model was also used to describe the viscoplasticity of the thermoplastic composite. The experimental results showed that viscoplastic behavior can be characterized quite well using the one-parameter overstress viscoplasticity model.
Yoon, K. J.↗
An anisotropic viscoplasticity model for shale based on layered microstructure homogenization
Viscoplastic deformation of shale is frequently observed in many subsurface applications. Many studies have suggested that this viscoplastic behavior is anisotropic—specifically, transversely isotropic—and closely linked to the layered composite structure at the microscale. In this work, we develop a two-scale constitutive model for shale in which anisotropic viscoplastic behavior naturally emerges from semianalytical homogenization of a bilayer microstructure. The microstructure is modeled as a composite of soft layers, representing a ductile matrix formed by clay and organics, and hard layers, corresponding to a brittle matrix composed of stiff minerals. This layered microstructure renders the macroscopic behavior anisotropic, even when the individual layers are modeled with isotropic constitutive laws. Using a common correlation between clay and organic content and magnitude of creep, we apply a viscoplastic modified Cam-Clay plasticity model to the soft layers, while treating the hard layers as a linear elastic material to minimize the number of calibration parameters. We then describe the implementation of the proposed model in a standard material update subroutine. The model is validated with laboratory creep data on samples from three gas shale formations. We also demonstrate the computational behavior of the proposed model through simulation of time-dependent borehole closure in a shale formation with different bedding plane directions.
58 GEOSCIENCES↗
Strain localization criteria for viscoplastic geomaterials
This report presents a viscoplastic localization criterion to detect quasi-instantaneous (i.e., load-induced) and delayed (creep-induced) strain localization in rate-dependent solids. The study is based on the theory of controllability and a viscoplastic description of the mechanical response. Analytical precursors of unstable states are defined through systems of ordinary differential equations (OEDs). The use of the proposed criteria is illustrated at the material point level through a set of strain localization analyses simulating active strain localization of a porous rock. In addition, full-field finite element simulations of compression tests conducted under various pressures are reported to demonstrate the role of local unstable viscoplasticity in the spontaneous propagation of deformation bands under stationary boundary conditions. The study shows that the viscoplastic localization criterion maintains a negative sign as long as the behavior is unstable, that is, the rate of deformation is accelerating. The sign switch coincides with the transition to decelerating deformation. The analyses revealed that pulses of overstress always emerge in correspondence with the growth of unstable behavior, and the peak matches the transition to stable behavior. The local responses recovered from full-field analyses were consistent with those observed in analyses at material point level and the predictions of the presented theory.
36 MATERIALS SCIENCE↗
Variational Asymptotic Homogenization of Finitely Deformed Viscoelastic-Viscoplastic Composites
The objective of this paper is to develop a constitutive model for finitely deformed viscoelastic-viscoplastic materials and a micromechanics approach to homogenizing composites consisting of such materials. The development of the constitutive model involves establishing a thermodynamic framework based on finite strain theory, developing a viscoelasticity and a viscoplasticity model based on the thermodynamic framework, developing a radial return algorithm based on a classic framework, and deriving a closed-from incremental constitutive relation in the spatial configuration. The development of the micromechanics approach involves pulling-back the above constitutive relation to the material configuration, formulating a variational statement with the resulting constitutive relation, discretizing variational statement in a finite-dimensional space, and solving the discretized variational statement using an Euler–Newton predictor–corrector method. The constitutive model is calibrated via monotonic uniaxial compression tests on a polymer, and the calibrated model is validated by comparing its predictions with the cyclic test data. It is shown capable of characterizing viscoelasticity, viscoplasticity, and complex loading paths. The micromechanics approach’s capabilities are demonstrated through homogenizing a unidirectional fiber-reinforced composite, subjected to uniaxial, biaxial, and shear loading, at different strain rates. It is demonstrated to be capable of handling rate dependence and complex loading paths. The present framework can be further improved by implementing more sophisticated viscoelasticity and viscoplasticity models in future work.
Finite element analysis↗
Refinements in a viscoplastic model
A thermodynamically admissible theory of viscoplasticity with two internal variables (a back stress and a drag strength) is presented. Six material functions characterize a specific viscoplastic model. In the pursuit of compromise between accuracy and simplicity, a model is developed that is a hybrid of two existing viscoplastic models. A limited number of applications of the model to Al, Cu, and Ni are presented. A novel implicit integration method is also discussed. Applications are made to obtain solutions using this viscoplastic model.
Freed, A. D.↗
Finite element analysis of structural components using viscoplastic models with application to a cowl lip problem
The viability of advanced viscoplastic models for nonlinear finite element analyses of structural components is investigated. Several uniaxial and a multiaxial problem are analyzed using the finite element implementation of Freed's viscoplastic model. Good agreement between the experimental and calculated uniaxial results validates the finite element implementation and gives confidence to apply it to more complex multiaxial problems. A comparison of results for a sample structural component (the cowl lip of a hypersonic engine inlet) with the earlier elastic, elastic-plastic, and elastic-plastic-creep analyses available in the literature shows that the elastic-viscoplastic analyses yield more reasonable stress and strain distributions. Finally, the versatility of the finite-element-based solution technology presented herein is demonstrated by applying it to another viscoplastic model.
Arya, V. K.↗
Efficient and Accurate Explicit Integration Algorithms with Application to Viscoplastic Models
Several explicit integration algorithms with self-adative time integration strategies are developed and investigated for efficiency and accuracy. These algorithms involve the Runge-Kutta second order, the lower Runge-Kutta method of orders one and two, and the exponential integration method. The algorithms are applied to viscoplastic models put forth by Freed and Verrilli and Bodner and Partom for thermal/mechanical loadings (including tensile, relaxation, and cyclic loadings). The large amount of computations performed showed that, for comparable accuracy, the efficiency of an integration algorithm depends significantly on the type of application (loading). However, in general, for the aforementioned loadings and viscoplastic models, the exponential integration algorithm with the proposed self-adaptive time integration strategy worked more (or comparably) efficiently and accurately than the other integration algorithms. Using this strategy for integrating viscoplastic models may lead to considerable savings in computer time (better efficiency) without adversely affecting the accuracy of the results. This conclusion should encourage the utilization of viscoplastic models in the stress analysis and design of structural components.
Arya, Vinod K.↗
Robust integration schemes for generalized viscoplasticity with internal-state variables. Part 1: Theoretical developments and applications
This two-part report is concerned with the development of a general framework for the implicit time-stepping integrators for the flow and evolution equations in generalized viscoplastic models. The primary goal is to present a complete theoretical formulation, and to address in detail the algorithmic and numerical analysis aspects involved in its finite element implementation, as well as to critically assess the numerical performance of the developed schemes in a comprehensive set of test cases. On the theoretical side, the general framework is developed on the basis of the unconditionally-stable, backward-Euler difference scheme as a starting point. Its mathematical structure is of sufficient generality to allow a unified treatment of different classes of viscoplastic models with internal variables. In particular, two specific models of this type, which are representative of the present start-of-art in metal viscoplasticity, are considered in applications reported here; i.e., fully associative (GVIPS) and non-associative (NAV) models. The matrix forms developed for both these models are directly applicable for both initially isotropic and anisotropic materials, in general (three-dimensional) situations as well as subspace applications (i.e., plane stress/strain, axisymmetric, generalized plane stress in shells). On the computational side, issues related to efficiency and robustness are emphasized in developing the (local) interative algorithm. In particular, closed-form expressions for residual vectors and (consistent) material tangent stiffness arrays are given explicitly for both GVIPS and NAV models, with their maximum sizes 'optimized' to depend only on the number of independent stress components (but independent of the number of viscoplastic internal state parameters). Significant robustness of the local iterative solution is provided by complementing the basic Newton-Raphson scheme with a line-search strategy for convergence. In the present first part of the report, we focus on the theoretical developments, and discussions of the results of numerical-performance studies using the integration schemes for GVIPS and NAV models.
Saleeb, Atef F.↗
Robust integration schemes for generalized viscoplasticity with internal-state variables. Part 2: Algorithmic developments and implementation
This two-part report is concerned with the development of a general framework for the implicit time-stepping integrators for the flow and evolution equations in generalized viscoplastic models. The primary goal is to present a complete theoretical formulation, and to address in detail the algorithmic and numerical analysis aspects involved in its finite element implementation, as well as to critically assess the numerical performance of the developed schemes in a comprehensive set of test cases. On the theoretical side, the general framework is developed on the basis of the unconditionally-stable, backward-Euler difference scheme as a starting point. Its mathematical structure is of sufficient generality to allow a unified treatment of different classes of viscoplastic models with internal variables. In particular, two specific models of this type, which are representative of the present start-of-art in metal viscoplasticity, are considered in applications reported here; i.e., fully associative (GVIPS) and non-associative (NAV) models. The matrix forms developed for both these models are directly applicable for both initially isotropic and anisotropic materials, in general (three-dimensional) situations as well as subspace applications (i.e., plane stress/strain, axisymmetric, generalized plane stress in shells). On the computational side, issues related to efficiency and robustness are emphasized in developing the (local) interative algorithm. In particular, closed-form expressions for residual vectors and (consistent) material tangent stiffness arrays are given explicitly for both GVIPS and NAV models, with their maximum sizes 'optimized' to depend only on the number of independent stress components (but independent of the number of viscoplastic internal state parameters). Significant robustness of the local iterative solution is provided by complementing the basic Newton-Raphson scheme with a line-search strategy for convergence. In the present second part of the report, we focus on the specific details of the numerical schemes, and associated computer algorithms, for the finite-element implementation of GVIPS and NAV models.
Li, Wei↗
A comparison of surrogate constitutive models for viscoplastic creep simulation of HT-9 steel
Mechanistic microstructure-informed constitutive models for the mechanical response of polycrystals are a cornerstone of computational materials science. However, as these models become increasingly more complex – often involving coupled differential equations describing the effect of specific deformation modes – their associated computational costs can become prohibitive, particularly in optimization or uncertainty quantification tasks that require numerous model evaluations. To address this challenge, surrogate constitutive models that balance accuracy and computational efficiency are highly desirable. Data-driven surrogate models, that learn the constitutive relation directly from data, have emerged as a promising solution. In this work, we develop two local surrogate models for the viscoplastic response of a steel: a piecewise response surface method and a mixture of experts model. These surrogates are designed to adapt to complex material behavior, which may vary with material parameters or operating conditions. The surrogate constitutive models are applied to creep simulations of HT-9 steel, an alloy of considerable interest to the nuclear energy sector due to its high tolerance to radiation damage, using training data generated from viscoplastic self-consistent (VPSC) simulations. In conclusion, we define a set of test metrics to numerically assess the accuracy of our surrogate models for predicting viscoplastic material behavior, and show that the mixture of experts model outperforms the piecewise response surface method in terms of accuracy.
36 MATERIALS SCIENCE↗
Advanced Newton methods for geodynamical models of Stokes flow with viscoplastic rheologies
Strain localization and resulting plasticity and failure play an important role in the evolution of the lithosphere. These phenomena are commonly modeled by Stokes flows with viscoplastic rheologies. The nonlinearities of these rheologies make the numerical solution of the resulting systems challenging, and iterative methods often converge slowly or not at all. Yet accurate solutions are critical for representing the physics. Moreover, for some rheology laws, aspects of solvability are still unknown. We study a basic but representative viscoplastic rheology law. The law involves a yield stress that is independent of the dynamic pressure, referred to as von Mises yield criterion. Two commonly used variants, perfect/ideal and composite viscoplasticity, are compared. We derive both variants from energy minimization principles, and we use this perspective to argue when solutions are unique. We propose a new stress-velocity Newton solution algorithm that treats the stress as an independent variable during the Newton linearization but requires solution only of Stokes systems that are of the usual velocity-pressure form. To study different solution algorithms, we implement 2-D and 3-D finite element discretizations, and we generate Stokes problems with up to 7 orders of magnitude viscosity contrasts, in which compression or tension results in significant nonlinear localization effects. Comparing the performance of the proposed Newton method with the standard Newton method and the Picard fixed-point method, we observe a significant reduction in the number of iterations and improved stability with respect to problem nonlinearity, mesh refinement, and the polynomial order of the discretization.
Rudi, Johann↗
On numerical integration and computer implementation of viscoplastic models
Due to the stringent design requirement for aerospace or nuclear structural components, considerable research interests have been generated on the development of constitutive models for representing the inelastic behavior of metals at elevated temperatures. In particular, a class of unified theories (or viscoplastic constitutive models) have been proposed to simulate material responses such as cyclic plasticity, rate sensitivity, creep deformations, strain hardening or softening, etc. This approach differs from the conventional creep and plasticity theory in that both the creep and plastic deformations are treated as unified time-dependent quantities. Although most of viscoplastic models give better material behavior representation, the associated constitutive differential equations have stiff regimes which present numerical difficulties in time-dependent analysis. In this connection, appropriate solution algorithm must be developed for viscoplastic analysis via finite element method.
Chang, T. Y.↗
Modeling the viscoplastic behavior of Inconel 718 at 1200 F
A large number of tests, including tensile, creep, fatigue, and creep-fatigue were performed to characterize the mechanical properties of Inconel 718 (a nickel based superalloy) at 1200 F, the operating temperature for turbine blades. In addition, a few attempts were made to model the behavior of Inconel 718 at 1200 F using viscoplastic theories. The Chaboche theory of viscoplasticity can model a wide variety of mechanical behavior, including monotonic, sustained, and cyclic responses of homogeneous, initially-isotropic, strain hardening (or softening) materials. It is shown how the Chaboche theory can be used to model the viscoplastic behavior of Inconel 718 at 1200 F. First, an algorithm was developed to systematically determine the material parameters of the Chaboche theory from uniaxial tensile, creep, and cyclic data. The algorithm is general and can be used in conjunction with similar high temperature materials. A sensitivity study was then performed and an optimal set of Chaboche's parameters were obtained. This study has also indicated the role of each parameter in modeling the response to different loading conditions.
Abdel-Kader, M. S.↗
Analytical and finite element solutions of some problems using a viscoplastic model
The feasibility of using a viscoplastic model developed by Robinson to perform a nonlinear structural analysis was investigated. The paper presents analytical solutions for three classical problems: (1) a pressurized thick-walled cylinder, (2) a thin rotating disk, and (3) a pressurized thick-walled sphere. The analytical expressions derived for the stress and the strain rates for these components are general in nature as they consider both the mechanical and thermal loadings to be time-dependent. A computer program VISTAN (VIscoplastic STructural ANalyzer) was developed to obtain the stress and strain distributions. The finite element solutions for these problems are also presented. The numerical results pertaining to isothermal loading conditions are provided. The results obtained demonstrate the feasibility of using the viscoplastic model developed by Robinson to perform nonlinear structural analyses.
Arya, V. K.↗
Finite element thermo-viscoplastic analysis of aerospace structures
The time-dependent thermo-viscoplastic response of aerospace structures subjected to intense aerothermal loads is predicted using the finite-element method. The finite-element analysis uses the Bodner-Partom unified viscoplastic constitutive relations to determine rate-dependent nonlinear material behavior. The methodology is verified by comparison with experimental data and other numerical results for a uniaxially-loaded bar. The method is then used (1) to predict the structural response of a rectangular plate subjected to line heating along a centerline, and (2) to predict the thermal-structural response of a convectively-cooled engine cowl leading edge subjected to aerodynamic shock-shock interference heating. Compared to linear elastic analysis, the viscoplastic analysis results in lower peak stresses and regions of plastic deformations.
Pandey, Ajay K.↗
Nonlinear structural analysis of cylindrical thrust chambers using viscoplastic models
The results are presented of a viscoplastic stress-strain analysis of a cylindrical thrust chamber used in experiments that were designed to simulate the SSME operating conditions. The inelastic strain was calculated by using a viscoplastic model, and a quasi-three-dimensional structural analysis was performed by using a finite element program MARC. The temperatures and pressures were calculated by using the loading cycles of experiments, and these temperatures and pressures were used in the computations. The deformed shape of the component was predicted after the end of each loading cycle. The predicted shape qualitatively replicated the deformed shape of the component as observed in experiments. The results indicate that the use of viscoplastic models for structural analysis may lead to more realistic life assessments of experimental thrust chambers.
Arya, Vinod K.↗