Viscoplasticity Theory Based On Overstress Model Research Articles

The study on change of mechanical properties of NBR due to deterioration

Rubber is an important industrial material. However, mechanical properties and deformation of the high polymer including rubber are not clear. A method of estimating the mechanical properties which can be used for the deteriorated rubber is demanded to improve the reliability of it. Improved VBO (Viscoplasticity theory based on overstress) model is a constitutive equation. We applied it for the compression stress-strain behavior of deteriorated NBR (acryloNitrile-Butadiene rubber). Furthermore, we proposed a method of estimating the mechanical properties of deteriorated NBR. In this paper, deterioration tests in water and in air were conducted. To confirm the validity of the proposed improved VBO model and estimated mechanical properties, simulations of the stress-strain curves obtained in the tests were conducted.

Cooperative viscoplasticity theory based on the overstress approach for modeling large deformation behavior of amorphous polymers

A micromechanically based formulation of the cooperative model is incorporated into the viscoplasticity theory based on overstress (VBO) model. The plastic shear strain rate given by the cooperative model is used as a flow function which is responsible for rate and temperature dependence in the VBO model. In this way, thermomechanical analysis can be performed under different loading rates and temperatures of amorphous polymers. Introducing strain softening, the temperature- and strain-rate-dependent elasticity moduli are two other modifications of the VBO formulation. The validity of the newly proposed cooperative VBO model is demonstrated by modeling the uniaxial compression behavior of poly(methyl methacrylate) under different temperatures and strain rates. © 2013 Society of Chemical Industry

Modelling effects of degree of crystallinity on mechanical behavior of semicrystalline polymers

Viscoplasticity theory based on overstress (VBO) which is one of the unified state variable theories is extended to account for crystallinity ratio ( ϕ) on mechanical behavior of semicrystalline polymers. The modifications on VBO are done considering the semicrystalline polymeric materials somewhat as a composite material since it consists of amorphous and crystalline phases. Amorphous and crystalline phase resistances are arranged in two different analog models: amorphous stiffness and flow are in parallel and series with crystalline phase. Apart from many existing work in the literature, not only uniaxial loading are modeled but also creep and relaxation behaviors are simulated for a hypothetical material. It is shown that when amorphous and crystalline phase resistances acting in parallel are considered in the model, creep, relaxation and uniaxial loading and unloading behaviors can be simulated well using the modified VBO. In addition, uniaxial compression loading and unloading behavior of highly crosslinked ultra-high molecular weight polyethylene (UHMWPE) and creep behavior of polytetrafluoroethylene (PTFE) with different crystallinity ratios are simulated using the proposed VBO model where amorphous and crystalline phases are parallel. Simulation results are compared to the experimental data by Kurtz et al. (2002) and Sun et al. (2005) [Kurtz, S.M., Villarragaa, M.L., Herra, M.P., Bergström, J.S., Rimnacc, C.M., Edidin, A.A., 2002. Thermomechanical behavior of virgin and highly crosslinked ultra-high molecular weight polyethylene used in total joint replacements. Biomaterials 23, 3681–3697; Sun, H., Cooke, R. S., Bates, W. D., Wynne, K.J., 2005. Supercritical CO 2 processing and annealing of polytetrafluoroethylene (PTFE) and modified PTFE for enhancement of crystallinity and creep resistance. Polymer 46, 8872–8882] respectively and good match with experimental data is obtained.

High density polyethylene (HDPE): Experiments and modeling

The uniaxial tension (loading and unloading), creep and relaxation experiments on high density polyethylene (HDPE) have been carried out at room temperature. The stress–strain behavior of HDPE under different strain rates, creep (relaxation) behavior at different stress (strain) levels have been investigated. These experimental results are used to compare the simulation results of a unified state variable theory, viscoplasticity theory based on overstress (VBO) and a macro-mechanical constitutive model for elasto-viscoplastic deformation of polymeric materials developed by Boyce et al. (Polymer 41:2183–2201, 2000). It is observed that elasto-viscoplasticity model by Boyce et al. (Polymer 41:2183–2201, 2000) is not good enough to simulate stress–strain, creep and relaxation behaviors of HDPE. However, the aforementioned behaviors can be modeled quantitatively by using VBO model.

Modeling of uniaxial and biaxial ratcheting behavior of 1026 Carbon steel using the simplified Viscoplasticity Theory Based on Overstress (VBO)

Hassan and Kyriakides [1], Hassan et al. [2], and Corona et al. [3] performed uniaxial and biaxial ratcheting experiments on heat-treated 1026 Carbon steel. The loading histories performed with uniaxial and tubular specimens were selected to simulate those encountered in nuclear reactor vessels. The stress-strain diagram of 1026 Carbon steel was used to determine the material constants in a simplified version of VBO. Small rate dependence was allowed. The model represents some nonlinear rate dependence, kinematic hardening and cyclically neutral behavior. The set of material constants determined only from uniaxial tests was used throughout the paper. Numerical experiments included are: (i) uniaxial stress-controlled cycling with various mean stresses, (ii) strain-controlled axial tests with tubular specimens under constant and variable internal pressure, and (iii) examination and variation of certain material constants of the VBO model that can influence ratcheting. Very good agreement with the experiments is found for the uniaxial case. However the ratchet strain accumulation during biaxial cycling is over-predicted by VBO and other constitutive models.

Extension of the viscoplasticity theory based on overstress (VBO) to capture non-standard rate dependence in solids

Abstract The viscoplasticity theory based on overstress (VBO) can model unusual loading rate effects. Included are rate-insensitivity and positive and negative rate sensitivity. An augmentation function is required that operates on the dynamic recovery term of the growth law for the equilibrium stress, which is a state variable in VBO. The augmentation function does not affect the initial, quasi-elastic region. Its full effect appears when the long-time, asymptotic solution, which corresponds to the flow stress region is reached in an experiment. The flow stress of the VBO model consists of monotonic, rate-independent hardening affected by the kinematic stress, the viscous, rate-dependent hardening through the overstress and the rate-independent hardening represented by the isotropic stress. With the augmentation function it is possible to have only rate-dependent contributions to the flow stress. Through a proper choice of the augmentation function the rate-dependent and the rate-independent contributions can be apportioned to yield positive, zero and negative rate dependence in a consistent manner. As a demonstration, the stress-strain curves of Copper, a fcc metal, are reproduced. In fcc metals the positive rate dependence increases with deformation. The rate-dependent stress-strain curves of polymethylmethacrylate (PMMA) exhibiting a distinct yield point are also reproduced. Numerical creep tests performed at the same stress level before and after the yield point lead to unlimited creep strain and primary creep, respectively. The modeling of these very different types of material behavior requires only different material constants and augmentation functions within the same general constitutive equation.

Modeling of positive, negative and zero rate sensitivity by using the viscoplasticity theory based on overstress (VBO)

Almost complete rate independence or negative rate sensitivityand an increase in strength with a concurrent decrease in ductilitytogether with jerky flow are reportedly observed when dynamic strainaging occurs in metals and alloys. These phenomena are sometimesreferred to as the ‘Portevin Le Chatelier’ effect. Most engineeringalloys experience dynamic strain aging in some temperature region andnormal behavior (positive rate sensitivity and a decrease in strengthwith an increase in temperature) is observed outside the strain-agingregion. The ‘unified’ viscoplasticity theory based on overstress (VBO),which models positive rate sensitivity, is modified to reproduce thezero and negative rate sensitivity and the increase in strength withtemperature. This is accomplished through the introduction of a singlenew term in the growth law of one state variable. In the initialquasi-elastic region the new term has no influence on the modelpredictions but reaches full influence when the flow stress is reached.During dynamic strain aging, creep and relaxation behaviors arepredicted to be normal. While there are very few experimental resultsavailable, they are all in agreement with these predictions. An analysisof the properties of this new term and numerical experiments illustratethe capability of the extended VBO model.

Modeling of High Homologous Temperature Deformation Behavior Using the Viscoplasticity Theory Based on Overstress (VBO): Part II—Characteristics of the VBO Model

Characteristics of the high homologous temperature VBO model under extreme conditions such as very fast and very slow tensile tests, long-term-creep and relaxation tests are investigated via numerical experiments and analysis. To this end, material constants of Alloy 800H determined from other tests in Part I were utilized for the prediction. Although no experiments are available for the extreme conditions, the predictions are plausible. For cyclic, strain controlled hold-time tests the predictions compare well with sparse experimental data. The results give confidence that VBO can be used to predict the long-term behavior at high homologous temperature once the constants have been determined from regular, short-term tests.

Modeling of High Homologous Temperature Deformation Behavior Using the Viscoplasticity Theory Based on Overstress (VBO): Part I— Creep and Tensile Behavior

The viscoplasticity theory based on overstress (VBO) is a state variable theory without a yield surface and without loading/unloading conditions. It contains two tensor valued state variables, the equilibrium (back) stress and the kinematic stress that is a repository for work hardening (softening). The scalar valued isotropic or time (rate)-independent stress models cyclic hardening (softening). For application to high homologous temperature, the effects of diffusion which counteracts the hardening of inelastic deformation has to be accounted for. Recovery of state terms are introduced in the growth laws for the state variables. A high homologous temperature VBO model is introduced and applied to the creep and tensile tests of Alloy 800 H between 750°C and 1050°C. Primary, secondary and tertiary creep as well as tensile behavior were well reproduced. It is shown that the transition to fluid state can be modeled with VBO.