Elastic-viscoplastic Theory Research Articles

A corrosion cracking mechanism-based model with molten salt corrosion damage coupling the effect of chloride impurity and plastic deformation

The corrosion kinetic models, incorporating the effects of chloride impurity and plastic deformation were proposed. Molten salt corrosion (MSC) damage was quantitatively described using the corrosion kinetic and the distance of materials points from the corrosion surface. By employing the elastic-viscoplastic theory with a hyperbolic-sine flow rule and the proposed damage model, a corrosion cracking mechanism-based model was developed and implemented using finite element (FE) analysis method. The corrosion-assisted cracking ahead of crack tips in accordance with the corrosion cracking mechanism was simulated. Furthermore, the predicted corrosion depth, corrosion morphologies, and multi-site corrosion cracking behaviors showed good agreement with the experimental results.

Influence of creep on preload relaxation of bolted composite joints: Modeling and numerical simulation

Preload relaxation can greatly influence the durability of bolted composite joints. This paper focuses on the effects of material creep and contact creep between rough surfaces on preload relaxation. An efficient finite element model is proposed to predict bolt preload relaxation in ABAQUS. First, a creep constitutive model of the composite based on elastic-viscoplastic theory was established and the contact stiffness of uneven interfaces of the joints, featuring multi-asperity contact at the micro perspective, were derived using fractal contact theory. Then, fractal contact theory was extended to address the time-dependent elastic-viscoplastic contact problem. The models were implemented within ABAQUS software using the UMAT and UINTER subroutines. Finally, a comparison of the numerical and experimental results showed that calculation error decreased from 1.4–2.0% to 0.1–0.5% after 35 h when effects of rough surface contact were considered, thereby significantly improving model accuracy. Furthermore, the results suggest that thicker jointing materials could effectively reduce preload relaxation. In addition, according to surface fractal parameters D and G, rougher surfaces facilitate contact creep and preload relaxation. Thus, controlling surface topography could be an effective way to improve surface contact properties in practical applications.

Continuum thermomechanics of nonlinear micromorphic, strain and stress gradient media.

A comprehensive constitutive theory for the thermo-mechanical behaviour of generalized continua is established within the framework of continuum thermodynamics of irreversible processes. It represents an extension of the class of generalized standard materials to higher order and higher grade continuum theories. It reconciles most existing frameworks and proposes some new extensions for micromorphic and strain gradient media. The special case of strain gradient plasticity is also included as a contribution to the current debate on the consideration of energetic and dissipative mechanisms. Finally, the stress gradient continuum theory emerges as a new research field for which an elastic-viscoplastic theory at finite deformations is provided for the first time. This article is part of the theme issue 'Fundamental aspects of nonequilibrium thermodynamics'.

On crystal shear, lattice rotation and constraint stress in (1 1 0) channel die compression: rate-independent and viscoplastic analyses and predictions compared

Rate-independent crystal plasticity theory and a classic viscoplastic power-law are investigated, contrasted and compared for finite deformation analysis of fcc crystals in channel die compression, including full consideration of lattice straining. Both experiment-based anisotropic and isotropic (Taylor) hardenings are evaluated in rate-independent theory; and an unlimited range of power-law exponent n is considered in viscoplasticity. The focus is on predictions of lateral constraint stress, lattice rotation and crystal shear, and their comparison with experiment. General elastic-plastic equations (for both theories) are given for the range of unstable lattice orientations in (1 1 0) compression (‘range I’) and evaluated before and after a finite rotation of the lattice about the load axis. Equations also are given and evaluated for the ‘Brass’ orientation. It is shown that the theories can be in close agreement at the onset of finite deformation in range I, but that viscoplasticity gives results (for any n) after finite rotation that are in sharp contrast to rate-independent theory. The latter’s predictions for crystal shear and lattice rotation are in good to very good agreement with finite deformation experiments on aluminium and copper. The inclusion of lattice elasticity is found to have a negligible effect in range I. In contrast, for finite deformation in the stable Brass orientation, elastic-viscoplastic theory can be made to agree very closely with rate-independent theory and with experiment.

Evaluation of the viscous behaviour of clay using generalised overstress viscoplastic theory

In this paper, generalised elastic-viscoplastic (EVP) theory combined with a power law is used to derive simplified equations relating undrained shear strength and preconsolidation pressure to strain rate. An additional equation is derived relating the strain-rate parameter in EVP theory to the secondary compression index. The derived equations are used to evaluate the rate-sensitive and drained creep response of 20 clays reported in the literature. The evaluation shows strong evidence that the rate-sensitivity and time-dependency of clay in compression can be described simultaneously using the generalised EVP theory and power law. In addition, the constitutive parameter governing rate-sensitivity in EVP theory appears to be unique for constant rate-of-strain tests such as undrained triaxial compression and drained oedometer compression as well as stress controlled tests such as drained oedometer creep. To conclude, an approach to select the viscous parameters for clay is provided.

Analysis of Asphalt Pavement Rut Based on Elastic-viscoplastic Theory

The elastic-viscoplastic theory was applied to research the permanent deformation of asphalt mixture, and a creep model was adopted for its good agreement with actual result. ABAQUS, the finite element modeling technique, were employed to simulate and investi- gate rut of the asphalt pavements with flexible base, and then the results were validated according to the circular track test. It is indicated that, rut increases fast in the early stage, but slow in later stage; pavement rut consists chiefly of absolute rut, and lateral upheaval only ac- counts for 15% -30% ; deformation rate increases as the depth increases and achieves the largest value at the depth of 8 cm then it de- creases gradually; pavement absolute rut is composed primarily of rut of the layer within the depths of 4 cm and 20 cm, especially within the depths of 4 cm and 12 cm.In addition,pavement ruts were simulated under different loads,and the axle load conversion indices were obtained by the rut equivalent method.For the adopted structures,the index is 5.9.

Integrated Micro/Macro Approach for Laminate Composite Analysis: Applications to Turbine Blades

An integrated micro/macro mechanical procedure for structural analysis of unidirectional metal matrix composites is proposed. The micromechanical analysis is performed with the composite cylinder assemblage model or the representative volume element approach. The macroscopic stress-strain relation is based on a modification of the vanishing fiber diameter theory and the concept of a smeared finite element. The fibers are considered to be linear elastic, and the matrix viscoplastic behavior is described by the Bodner and Partom model (Bodner, S. R., Review of Unified Elastic-Viscoplastic Theory, Unified Constitutive Equations for Plastic Deformation and Creep of Engineering Alloys, edited by A. Miller, Elsevier Science, New York, 1987, pp. 77-106). The overall composite behavior is assumed to be elastic-viscoplastic. Two types of material systems are used: SCS-6/Ti-15-3 and SCS-6/Tiβ21-S. Both sets of material systems exhibit isotropic and/or kinematic hardening under specific conditions of temperature and loading. The proposed methodology is validated with experimental and analytical results available in the literature. After the validation process, this methodology is applied to a three-dimensional finite element model of a [0/90] 2s SCS-6/Tiβ21-S turbine blade tip. Aerodynamic and centrifugal loading are considered to be acting at the same time. The turbine blade tip inelastic strain field is presented.

One-Dimensional Theory of Uni-Axial Shear Elastic-Plastic-Viscoplastic Stress Waves of Solids.

An uni-axial shear elastic-plastic-viscoplastic constitutive equation has been derived from the generalized constitutive equation. The constitutive equation is in which the understress in introduced to the shear strain and the overstress is employed in the shear viscoplastic strain rate. Using the constitutive equation, an analysis is done on the one-dimensional uni-axial shear elastic-plastic-viscoplastic stress wave propagation. And the equations describing the wave propagation speed and the relation of any physical quantities are derived. The derived equation for describing the shear wave propagation speed expresses the experimental results qualitatively. Also, from the developped theory of the shear elastic-plastic-viscoplastic wave propagation, the theories of a shear elastic-plastic, elastic-viscoplastic and elastic wave propagation are derived. The wave propagation speed of the elastic-viscoplastic theory can't express that of the experimental results at all except the precursor.

On the treatment of elastic deformation in finite elastic-viscoplastic theory

Abstract This paper lists a number of physical attributes which have been formulated and incorporated into a new microstructural model for finite deformations of elastic-viscoplastic materials (Rubin (“Plasticity Theory Formulated In Terms of Physically Based Microstructural Variables — Parts I & II,” Int. J. Solids Struct. , 31 , 2615–2652)). With particular reference to one of these attributes, it appears that other theories do not completely separate the notion of elastic deformation of the atomic lattice from deformation of macroscopic material line elements. Consequently, the comparison presented here of the new model with other models attempts to clarify consequences of this conceptual subtlety.

An incremental elastic-viscoplastic theory indicating a reduced modulus for non-proportional buckling

The small deformation elastic-viscoplastic constitutive equations of Bodner-Partom are modified to model strong non-proportional loading paths such as experienced in corner turning tests and certain cases of inelastic buckling. An essential generalization is made to the flow rule, causing the magnitude and direction of plastic strain rate to become an explicit function of deviatoric total strain rate as well as of stress and hardening variables. With this and other modifications, the equations indicate some of the important characteristics of the response to abrupt changes in the loading direction. These are: (a) a reduced effective shear modulus; (b) a transient drop in the effective stress; and (c) a transient non-coaxiality of the plastic strain rate relative to the deviatoric stress. Predictions of the modified theory compare reasonably well with experimental values for inelastic torsional buckling of axially compressed cruciform columns and for corner turning tests.

Inelastic Deformation Under Nonisothermal Loading

The objective of this paper is to evaluate, both experimentally and analytically, the appropriate forms of the hardening evolution equations in unified constitutive models for conditions involving nonisothermal loading. Critical experiments were performed for a cast nickel-base superalloy by using variable temperature tensile, creep, and cyclic tests in the 538°C–982°C temperature range. These experimental results were compared with both isothermal data and predictions of the Bodner-Partom elastic-viscoplastic theory to assess the effects of thermal history on constitutive behavior. The results indicate that the hardening evolution equations based on isothermal data are applicable for nonisothermal loading of these precipitation strengthened alloys. Additional thermal history effect terms in the hardening evolution equations were not required beyond those accounting for the variation of material constants with temperature. Using material constants determined solely from isothermal data, the inelastic deformation behavior of B1900 + Hf subject to thermomechanical loading were adequately predicted by the Bodner-Partom model.

A Large Deformation Elastic-Viscoplastic Analysis of a Thick-Walled Spherical Shell

A large deformation elastic-viscoplastic theory is formulated which considers both elastic and inelastic deformations to be present at all stages of loading and unloading. The theory does not require the assumption of a yield criterion or the prior determination of whether the material is loading or unloading. The theory is based on relating the essential parameters to state variables; the particular constitutive relations are motivated by the equations of “dislocation dynamics.” In the present formulation, thermal effects and properties representing the worked state of the material such as strain hardening are not considered. A numerical scheme for calculating deformations is developed and applied to a thick-walled spherical shell under internal pressure. Various numerical examples are presented.