Phenomenological Viscoplastic Model Research Articles

Numerical analysis of a caprock integrity during oil production by steam-assisted gravity drainage method

The work is devoted to the investigation of a caprock integrity during oil production by steam-assisted gravity drainage method. An originally proposed thermo-hydro-mechanical model was used for the evaluation of mechanical loading acting on the over-burden. The model includes mass conservation laws, the energy conservation law and the linear momentum balance. Filtration of each phase of the three-phase flow (steam, oil and water) is described by Darcy’s law. Inelastic deformations are described by the phenomenological viscoplastic model based on Drucker-Prager yield criterion. The effect of the porosity evolution induced by the propagation of the steam chamber within the reservoir on the oil production rate and the caprock integrity is studied. It has been shown that the oil production rate is strongly depend on the prevailing physical mechanism of the porosity evolution. Reservoirs characterized by the volumetric strain mechanism of the porosity evolution produce slightly higher values of the mechanical loadings acting on the over-burden.

A thermodynamically-consistent phenomenological viscoplastic model for hydrogels

Today, hydrogels have a plethora of biomedical and biotechnological applications such as controlled drug delivery, tissue engineering and wound dressing. These materials possess high stretchability and are able to undergo large deformation. Hydrogels deform nonlinearly under the influence of external loads because of their nonlinear elasticity, plasticity and viscosity, which are manifestations of the interactions between the solvent and the cross-linked polymeric chains at different length and time scales. This paper attempts to model the mechanical behavior of hydrogels through a thermodynamically-consistent phenomenologically-motivated viscoplastic approach. Uniaxial compressive tests are conducted on cross-linked polyvinyl alcohol hydrogels with varying amounts of a chemical cross-linker (Gluteraldehyde) to check the validity of the model developed. Creep tests are carried out to understand the time-dependent mechanical response of the hydrogels. The results obtained from the theoretical model are found to be in close agreement with experimental observations.

Tensile Creep Behavior of Quasi-Unidirectional E-Glass Fabric Reinforced Polypropylene Composite.

The present work addressed the creep behavior of quasi-unidirectional E-glass fabric reinforced polypropylene composites under off-axis tensile loading. A series of creep tests were performed on the composite at three different loading stress levels. The creep response of off-axis samples of quasi-unidirectional composites under a constant loading level can be clearly observed. A phenomenological viscoplasticity model was built for describing the creep behavior of the composite. To improve the accuracy of prediction, cyclic loading-unloading tests were adopted to determine the material constants in the model. The predicted results in terms of the strains after a load over a period of time were found to be satisfactory, compared with the experimental results. In addition, same failure mechanism was found in off-axis samples under quasi-static and creep loading cases.

Analyzing time- and temperature dependent responses of NARloy-Z

In this study, we investigate the mechanical responses of copper based alloy, NARloy-Z, under cyclic loadings at different strain rates and strain amplitudes, and also creep at different levels of stresses. We examine the effect of temperature changes, as a result of energy dissipation during loading, on the overall cyclic and creep responses of NARloy-Z. A phenomenological viscoplastic model, developed by Freed et al. (1994), is adopted and modified in order to incorporate the effect of energy dissipation on the viscoplastic response of NARloy-Z. An adiabatic process is assumed to convert the dissipated energy into temperature increase, and the resulting temperature changes alter the elastic modulus and plastic flow of NARloy-Z during loading. A numerical method is also presented in order to implement the above nonlinear constitutive model. Experimental data reported by Conway et al. (1975) for cyclic loading and Ellis and Michal (1996) for creep loading are used to examine the viscoplastic responses of NARloy-Z. From the analyses, it is concluded that the amount of energy dissipation is much more pronounced under cyclic loading, especially for long-term duration of cyclic loading, while it is negligible under creep loading. Higher strain rates result in higher energy dissipation, which is expected as higher strain rates accumulate more hysteretic cycles at the same loading duration. Large amount of energy dissipation leads to a pronounced stress softening behavior due to significant increases in temperatures. The stress softening is one of the sources for material failures. It is also seen that the energy dissipation, and its corresponding temperature increase, is an important component in determining fatigue failure of NARloy-Z.

Micro-Macro Analysis and Phenomenological Modelling of Salt Viscous Damage and Application to Salt Caverns

This paper aims to gain fundamental understanding of the microscopic mechanisms that control the transition between secondary and tertiary creep around salt caverns in typical geological storage conditions. We use a self-consistent inclusion-matrix model to homogenize the viscoplastic deformation of halite polycrystals and predict the number of broken grains in a Representative Elementary Volume of salt. We use this micro-macro modeling framework to simulate creep tests under various axial stresses, which gives us the critical viscoplastic strain at which grain breakage (i.e., tertiary creep) is expected to occur. The comparison of simulation results for short-term and long-term creep indicates that the initiation of tertiary creep depends on the stress and the viscoplastic strain. We use the critical viscoplastic deformation as a yield criterion to control the transition between secondary and tertiary creep in a phenomenological viscoplastic model, which we implement into the Finite Element Method program POROFIS. We model a 850-m-deep salt cavern of irregular shape, in axis-symmetric conditions. Simulations of cavern depressurization indicate that a strain-dependent damage evolution law is more suitable than a stress-dependent damage evolution law, because it avoids high damage concentrations and allows capturing the formation of a damaged zone around the cavity. The modeling framework explained in this paper is expected to provide new insights to link grain breakage to phenomenological damage variables used in Continuum Damage Mechanics.

Effects of pre-strain and bake-hardening on the crash properties of a top-hat section

The effects of pre-strain on the crushing properties of a crash-box structure are reported for two Advanced High Strength Steels produced by ArcelorMittal (Dual-Phase DP600 and Transformation Induced by Plasticity TRIP780 steels). In addition, the effect of a bake-hardening treatment is studied on the TRIP780 steel. The material's behaviors have been determined in tensile loading in a wide range of strain-rates ( 8 × 10 − 3 s − 1 ≤ ε ˙ ≤ 10 3 s − 1 ) including strain-rate jump tests from quasi-static to dynamic loading. These interrupted tests allow us to characterize the effect of the (quasi-static) forming process on the subsequent dynamic behavior associated to the crash event. A phenomenological visco-plastic model, based on the evolution of an internal variable, has been implemented in PAMCRASH using a user-defined subroutine in order to simulate the crushing of the crash-boxes. A simple approach is proposed to account for the bake-hardening treatment in numerical simulations. A good correlation between experimental and predicted mean crush forces is obtained.

一方向ＣＦＲＰの高温における非主軸引張・圧縮非線形挙動のひずみ速度依存性と粘塑性モデルの定式化

Off-axis compressive deformation behavior of a unidirectional CFRP laminate at high temperature and its strain-rate dependence in a quasi-static range are examined for various fiber orientations. By comparing the off-axis tensile and compressive behaviors at an equal loading rate, the effect of loading direction on the flow stress level, nonlinearity and rate-dependence of off-axis deformation is elucidated. The experimental results show that the compressive flow stresses for relatively larger off-axis angles 30, 45, 90° have about 50 percent larger values than in tension for the same fiber orientations, respectively. The off-axis flow stresses in tension and compression significantly depend on the rate of loading, while they exhibit similar features in fiber orientation dependence and tension-compression asymmetry of off-axis nonlinear behavior regardless of the rate of loading. Then, formulation of a phenomenological viscoplasticity model that can describe the nonlinear rate-dependent behavior as well as its tension-compression asymmetry of unidirectional composites under off-axis loading in a unified manner is attempted. It is demonstrated that the proposed viscoplasticity model succeeds in adequately predicting the fiber orientation dependence of off-axis non-linear behavior, deformation asymmetry in off-axis tension and compression, and the strain rate dependence.

Formulation of a Viscoplasticity Model for Unidirectional Carbon Fiber-Reinforced Composites with Differences in Off-Axis Tensile and Compressive Behaviors

Formulation of a phenomenological viscoplasticity model that accounts for differences in tensile and compressive nonlinear rate-dependent behaviors of unidirectional carbon fiber-reinforced composites in a given off-axis direction is attempted. Effective stress and effective viscoplastic strain for transversely isotropic materials are derived from a three-dimensional pressure-modified Hill's anisotropic yield criterion, and they are reduced to the forms for plane state of stress. A plane-stress viscoplasticity model furnished with a capability to predict the phenomena raised above is formulated on the basis of the concept of overstress and the irreversible thermodynamics with internal variables. A shear constraint parameter, in which the influence of the compressive transverse stress on the shear flow resistance is reflected, is taken into account in defining a modified form of effective viscoplastic strain rate to enhance the predictive capability of the viscoplasticity model. The viscoplasticity model discussed in the present study is designed so as to be reduced to the viscoplasticity model of the Gates-Sun type developed in the previous study, which allows easy identification of material constants. Validity of the proposed viscoplasticity model is evaluated by comparing with results of off-axis tension and compression tests on a unidirectional carbon/epoxy composite at different strain rates.

Creep behavior of unidirectional and angle-ply T800H/3631 laminates at high temperature and simulations using a phenomenological viscoplasticity model

High-temperature creep behavior of symmetric angle-ply laminates made of unidirectional T800H/3631 carbon/epoxy composite is examined at relatively high stress levels. Constant-stress creep tests in tension are performed at 100 °C for 5 h on plain coupon specimens of three types of angle-ply laminates [±30] 3S, [±45] 3S and [±60] 3S under load control conditions. For each angle-ply laminate, creep tests are carried out at three different stress levels. Creep strain recovery following the 5-h creep is also observed for 5 h at the same temperature, after completely removing the creep stress. Creep responses are clearly observed in all kinds of angle-ply laminates. The creep strain rate in the angle-ply laminates tends to rapidly disappear as the creep strain increases. The transient creep is thus dominant in the angle-ply laminates, regardless of the fiber orientations. The prior creep strain does not completely recover with time after removing the creep stress, which indicates certain inelastic mechanisms have operated with creep. Similar features are also observed for the off-axis creep behavior of the unidirectional laminates of the same composite system. A whole history consisting of the prior instantaneous elastoviscoplastic behavior at a constant strain rate and the subsequent creep response at a constant stress level is simulated using the classical laminated plate theory and a phenomenological viscoplasticity model for individual plies. Material constants involved by the ply viscoplasticity model are identified on the basis of the off-axis creep behavior for unidirectional laminates. It is demonstrated that excellent agreements between the predicted and observed results are obtained by additionally taking into account the fiber rotation induced by deformation.

Application of a phenomenological viscoplasticity model to the stress relaxation behavior of unidirectional and angle-ply CFRP laminates at high temperature

Abstract High-temperature stress relaxation behavior of symmetric angle-ply laminates made of unidirectional T800H/3631 carbon/epoxy composite is examined at relatively high strain levels. Stress relaxation tests are performed at 100 °C for 5 h on plain coupon specimens of three types of angle-ply laminates [±30] 3S , [±45] 3S and [±60] 3S under displacement controlled conditions. For each ply orientation, the stress relaxation tests are carried out at three different strain levels. Stress relaxation phenomena clearly appear in all kinds of angle-ply laminate. The average stress in the angle-ply laminates rapidly relaxes to approach a steady-state value associated with the strain sustained. The rate of stress relaxation in the angle-ply laminates substantially diminishes in the tested time range. Stress relaxation simulation of the angle-ply laminates is performed using the classical laminated plate theory and a phenomenological viscoplasticity model for individual plies. Material constants involved in the ply viscoplasticity model are identified on the basis of the off-axis creep behavior for a unidirectional laminate based on the same kind of carbon/epoxy prepregs. Excellent agreements between the predicted and observed results are obtained by taking into account a local recovery of total strain in the gauge-length part of specimens as well as a fiber rotation induced by deformation. The successful application of the ply viscoplasticity model confirms that the stress relaxation behavior is consistent with the creep behavior in the same composite system.

Stress Relaxation Behavior of Unidirectional Carbon/Epoxy Composites at Elevated Temperature and Analysis Using Viscoplasticity Model

Off-axis stress relaxation behavior of unidirectional T800H/3631 carbon/epoxy composite exposed to high temperature is examined at relatively high tensile strain levels, and a phenomenological viscoplasticity model is tested on the capability to describe the time-dependent response observed. First, stress relaxation tests are performed at 100°C on plain coupon specimens with different fiber orientations, θ=0, 10, 30, 45, and 90°. For each of the fiber orientations, in principle, stress relaxation tests are carried out at three different strain levels. The relaxation of axial stress in the unidirectional composite is clearly observed, regardless of the fiber orientation. Just after the total strain hold, the axial stress quickly relaxes with time in a short period. The stress relaxation rate of the composite tends to become zero, irrespective of the fiber orientation. The associated relaxation modulus depends on the level of strain. The entire process of the prior instantaneous tensile response and the subsequent off-axis stress relaxation behavior is simulated using a macromechanical viscoplasticity model based on an overstress concept. It is demonstrated that the model succeeds in adequately reproducing the off-axis stress relaxation behavior of the unidirectional composite laminate.

Multiaxial constitutive model accounting for the strength-differential in Inconel 718

The nickel-base alloy Inconel 718 exhibits a strength-differential, that is, a different plastic flow behavior in uniaxial tension and uniaxial compression. A phenomenological viscoplastic model founded on thermodynamics has been extended for material behavior that deviates from classical metal plasticity by including all three stress invariants in the threshold function. The model can predict plastic flow in isotropic materials with or without a flow stress asymmetry as well as with or without pressure dependence. Viscoplastic material parameters have been fit to pure shear, uniaxial tension, and uniaxial compression experimental results at 650°°C. Threshold function material parameters have been fit to the strength-differential. Four classes of threshold functions have been considered and nonproportional loading of hollow tubes, such as shear strain followed by axial strain, has been used to select the most applicable class of threshold function for the multiaxial model as applied to Inconel 718 at 650 °C. These nonproportional load paths containing corners provide a rigorous test of a plasticity model, whether it is time-dependent or not. A J 2 J 3 class model, where J 2 and J 3 are the second and third effective deviatoric stress invariants, was found to agree the best with the experimental results.

Stress Relaxation Behavior of Symmetric Angle-ply Laminates of CFRP at High Temperature and Numerical Simulation

Stress relaxation behavior of symmetric angle-ply laminates of T800H/3631 at large strain and high temperature has been examined. Stress relaxation tests are performed at 100°C on plain coupon specimens of three types of angle-ply laminates: [±30]s, [±45]s, [±60]s. For each ply orientation, the stress relaxation tests are carried out at three different tensile strain levels. Stress relaxation phenomenon clearly appears in all kinds of angle-ply laminate. Just after the total strain is kept constant, the stress rapidly relaxes with time in a short period. The stress relaxation rate of the angle-ply laminates tends to almost vanish. Simulation of the stress relaxation behavior of the angle-ply laminates is performed using the classic laminated plate theory with a phenomenological viscoplasticity model for elementary plies. Good agreements between the predicted and observed results on the angle-ply laminates are obtained by taking account of the local strain recovery measured with strain gauges. It is also demonstrated that the stress relaxation response is consistent with the creep response of the same material system.

On the Constitutive Response of 63/37 Sn/Pb Eutectic Solder

The constitutive response of 63/37 Sn/Pb eutectic solder is studied under uniaxial tension. Stress-strain tests were performed under a wide range of applied strain rate, and creep tests were performed at several levels of applied load. Temperature dependence was ascertained by running the stress-strain and creep tests at various temperatures. With the goal of providing a constitutive description of the eutectic suitable for use in electronics packaging engineering finite element analyses, the material parameters of the phenomenological viscoplasticity model of Bodner and Partom were fit to these experiments as functions of temperature. The experiments described herein also yield important information concerning how many microstructural units must be present in a sample in order for repeatable, isotropic response to be obtained.

The effect of mechanical constraint on the flow and fracture of 63/37 Sn/Pb eutectic alloy

Copper compact tension specimens containing joints of 63/37 Sn/Pb eutectic solder alloy are used to study experimentally the flow and fracture behavior of eutectic solder under conditions of monotonic loading and mechanical constraint. Such constraint arises naturally due to the presence of the specimens' copper/solder interfaces, and various levels of constraint are achieved by employing joints of various sizes. Concomitant finite element analyses of the compact tension experiments are performed in which the solder is characterized by the phenomenological viscoplasticity model of Bodner and Partom. These experimental and analytical results, along with electron microscopy of the failure surfaces, clearly demonstrate the interplay between plastic flow, mechanical constraint, and microscopic characteristics of copper,/solder interfaces, in the overall response of, and failure initiation in, these composite specimens.

Modeling very large plastic flows at very large strain rates for large-scale computation

There are many important technological problems where accurate modeling of very large plastic deformations at very high strain rates is essential for effective and reliable design and manufacture of metal components. Examples are crashworthy vehicles, automated manufacturing, and automated metal forming and cutting. Another example is the understanding of the deformation field at the tip of a fast-running crack, where strain rates can easily exceed 10 5s −1 with local strains of several hundred percent. This paper summarizes some of the recent efforts by the authors and coworkers at the University of California, San Diego to develop physically-based constitutive models for mono- and polycrystalline solids, and to implement these models in large-scale finite element codes in the form of constitutive modules with efficient and robust computer algorithms. In the case of single crystal viscoplasticity, the constitutive integration is complicated by the fact that the essential set of ordinary differential equations is highly stiff for realistic levels of instantaneous rate-sensitivity. The algorithm that was developed for the integration of these equations in an explicit finite element environment is presented. Two example finite element solutions are given to demonstrate features of the overall finite element code. Also, a phenomenological viscoplasticity model that includes noncoaxiality between the stress and the plastic deformation rate is presented. This model is thought to be appropriate for high-strain-rate problems involving polycrystalline metals. Since the essential equation in this model is a single ordinary differential equation, numerical stiffness is not a factor; however, the integration is still complicated by an abrupt transition from the elastic regime to the plastic flow regime. A simple, robust “predictor-corrector” algorithm for the integration of this equation is presented.