Cyclic viscoelastoplasticity and low-cycle fatigue of polymer composites

Observations are reported on a polymer composite (polyamide-6 reinforced with short glass fibers) in tensile relaxation tests with various strains, tensile creep tests with various stresses, and cyclic tests with a stress-controlled program (ratcheting with a fixed maximum stress and various minimum stresses). Constitutive equations are developed in cyclic viscoelastoplasticity of polymer composites. Adjustable parameters in the stress–strain relations are found by fitting observations in relaxation tests and cyclic tests (16 cycles of loading–unloading). It is demonstrated that the model correctly predicts experimental data in creep tests and dependencies of maximum and minimum strains per cycle on number of cycles up to fatigue fracture of specimens. The influence of strain rate and minimum stress on number of cycles to failure is studied numerically.     

Experimental investigation of cyclic and time-dependent deformation of titanium alloy at elevated temperature

A novel cyclic deformation test program was undertaken to characterize macroscopic time dependent deformation of a titanium alloy for use in viscoplastic model development. All tests were conducted at a high homologous temperature, 650 °C, where there are large time dependent and loading rate dependent effects. Uninterrupted constant amplitude tests having zero mean stress or a tensile mean stress were conducted using three different control modes: strain amplitude and strain rate, stress amplitude and stress rate, and a hybrid stress amplitude and strain rate. Strain ratcheting occurred for all cyclic tests having a tensile mean stress and no plastic shakedown was observed. The shape of the strain ratcheting curve as a function of time is analogous to a creep curve having primary, steady state and tertiary regions, but the magnitude of the ratchet strains are higher than creep strains would be for a constant stress equal to the mean stress. Strain cycles interrupted with up to eight 2-h stress relaxation periods around the hysteresis loop, including hold times in each quadrant of the stress–strain diagram, were also conducted. Stress relaxation was path-dependent and in some cases the stress relaxed to zero. The cyclic behavior of these interrupted tests was similar even though each cycle was very complex. These results support constitutive model development by providing exploratory, characterization and validation data.     

Explicit and implicit viscoplastic models for polymeric composite

The viscoplastic behavior of a carbon-fiber/polymer matrix composite was investigated through two different modeling efforts. The first model is phenomenological in nature and utilizes the tensile and stress relaxation experiments to predict the creep strain. The phenomenological model was constructed based on the overstress viscoplastic model. In the second model, the composite viscoplastic behavior is captured via neural networks formulation. The neural networks model was constructed directly from the experimental results obtained via creep tests performed at various stress–temperature conditions. The neural network was trained to predict the creep strain based on the stress–temperature–time values. The performance of the neural model is evaluated through the mean squared error between the neural network prediction and the experimental creep strain results. To minimize this error, several optimization techniques were examined. The minimization of the error when carried out by the Truncated Newton method outperforms the standard back-propagation and the conjugate gradient method in terms of convergence rate and accuracy. Using neural network with truncated Newton training algorithm, the prediction of the creep strain was very satisfactory compared to the phenomenological model.     

Experimental investigation and modeling of non-monotonic creep behavior in polymers

The deformation behavior of two unfilled engineering thermoplastics, ultra high molecular weight polyethylene (UHMWPE) and polycarbonate (PC), has been investigated in creep test conditions. It has been found that a loading history (prior to the creep test) comprising of loading to a maximum stress or strain value followed by partial unloading to arrive at the target stress value can greatly modify the strain-time behavior. Under such a test protocol, while the expected increase in strain during creep (constant tensile load) is observed, at relatively low creep stresses specimens have also demonstrated a monotonic decrease in strain. In an intermediate stress range, specimens have demonstrated time dependent behavior comprising of a transition from decreasing to increasing strain during creep in tension. This paper presents experimental results to delineate these findings and explore the effect of prior strain rate on the qualitative and quantitative changes in the output (strain-time) behavior. Furthermore, modification of the viscoplasticity theory based on overstress (VBO) model into a double element configuration is introduced. These changes confer upon the model the ability to yield non-monotonic behavior in creep, and supporting simulation results have been included. These changes, therefore, allow the model to simulate strain rate sensitivity, creep, relaxation, and recovery behavior, but more importantly address the issue of non-monotonic changes in creep and relaxation when a loading history involves some degree of unloading.     

Stress relaxation,creep and set recovery of elastomers

The stress relaxation, creep and recovery behaviour of a cross-linked unfilled natural rubber has been investigated at moderate stresses in tension. The aim being to extend the idea, initially developed by Alan Gent in his seminal 1962 paper on the relaxation behaviour of rubber, in order to understand and examine the time dependent mechanisms that are present in elastomers under strain. A method based upon the Boltzmann superposition principle was used to compare the creep compliance with a measurement of its recovery after release from a range of constant loads held for different times. The creep behaviour was seen to exhibit the usual linear dependence on the logarithm of time. The recovery data was also seen to reduce onto a single recovery curve for any given applied tensile stress for a range of loading times using the Boltzmann superposition principle. The differences between the relative rates of the creep and the recovery behaviour can in part be attributed to the non-linearity in the stress–strain behaviour exhibited in tension of the elastomer.     

Quasi-static properties of a photoviscoelastic material

This paper describes the results of mechanical and optical measurements in plasticized polyvinyl chloride under conditions of creep and relaxation at room temperature. It covers one task of a broader investigation aimed at developing experimental methods for viscoelastic stress analysis. The moiré method of strain analysis was found well suited for continuous recording of axial and transversal deformation in creep tests. The material exhibits linear viscoelastic behavior, both mechanical and optical. Strain, stress and birefringence measured from creep and relaxation tests gave straightline plots on log-log scale and, thus simple empirical formulas were possible to derive. The theoretical prediction that birefringence in a linear viscoelastic material not exhibiting flow can be expressed as a linear relationship of stress and strain was satisfactorily substantiated.     

螺旋压缩弹簧应力松弛特性试验分析及其应用

本文通过应力松弛试验、理论推导及数值模拟研究了高温下螺旋压缩弹簧的应力松弛规律,并利用加速模型对工况下弹簧应力松弛服役寿命做出预测.首先,根据螺旋压缩弹簧的结构特点搭建了弹簧应力松弛连续动态测试装置,该装置不仅避免了传统测试方法存在的缺陷,而且能够保证试验过程中位移载荷恒定,并实时监测载荷变化.本文以某飞机舱门单锁机构...     

Multi-cycle deformation of silicone elastomer: observations and constitutive modeling with finite strains

Observations are reported on a medical grade of silicone elastomer in uniaxial tensile tests up to breakage of specimens, short-term relaxation tests, and cyclic tests with monotonically increasing maximum elongation ratios. Experimental data in cyclic tests demonstrate the fading memory phenomenon: stress–strain diagrams for two specimens with different deformation histories along the first n?1 cycles and coinciding loading programs for the other cycles become identical starting from the nth cycle. A constitutive model is developed in cyclic viscoplasticity of elastomers with finite strains, and its adjustable parameters are found by fitting the experimental data. Ability of the stress–strain relations to predict the mechanical response in cyclic tests with various deformation programs is confirmed by numerical simulation.     

Viscoplasticity theory based on overstress. The prediction of monotonic and cyclic proportional and nonproportional loading paths of an aluminum alloy

An isotropic formulation of the viscoplasticity theory for small strain and based on overstress with a differential growth law for the equilibrium stress is introduced. The four material constants and the two material functions of the theory are determined from uniaxial tensile tests involving strain-rate changes at room temperature and performed on a 6061 T6 Aluminum Alloy. Subsequently the theory is used to predict the biaxial behavior under axialtorsion loading. All tests are under strain control and involve proportional loading and axial followed by torsional straining (and vice versa). Cyclic histories include in-phase and out-of-phase cycling. The predictions of the theory are very reasonable for this cyclically neutral alloy. For cyclic hardening or softening materials a modification of the theory is necessary and is under development.     

Creep analysis of V-notched metallic plates: boundary element method

Application of the domain boundary element method is made to the creep analysis of two-dimensional viscoplastic structures containing V-notches under plane stress. Stress and strain distributions are obtained for tensile specimens with a single edge notch. The formulation assumes small-strain and small-rotation for a viscoplastic medium. The combined creep-plasticity constitutive model of Hart is used. Numerical examples are solved for different load histories.     

Constitutive relation for rheological processes: Properties of theoretic creep curves and simulation of memory decay

We study the nonlinear stress-strain constitutive relation proposed earlier for describing one-dimensional isothermal rheological processes in the case of monotonous variation of the strain (in particular, viscoplasticity, creep, relaxation, plasticity, and superplasticity). This relation contains integral time operators of the strain and strain rate, which are the norms in the Lebesgue and Sobolev spaces equipped with special weight factors, one material function, and nine material parameters determined by the results of tests of the material for relaxation, creep, long-term strength, and constant-rate strain.We analytically inverse the constitutive relation and study the properties of the inverse operator. We derive the equation of creep curves corresponding to an arbitrary law of loading at the stage of passing from the zero stress to a given constant level. We study their dependence on the material parameters and the loading stage characteristics and find restrictions on the material parameters which ensure that the asymptotic behavior of the creep curves for large times is independent of the length of the loading stage and the specific law of stress variation during this stage, i.e., we find the conditions of the model memory decay in creep. Thus we have proved that the constitutive relation proposed above can adequately model both creep and the effect of the material memory decay.     

Material effects during monotonic-cyclic loading

The effects commonly related with deformation caused by proportional and non-proportional loading types were identified experimentally. In the case of non-proportional cyclic loading along circular strain path the second order effects such as: phase shift between stress and strain signals was observed. An analysis of experimental data from tests under non-proportional cyclic loading along square strain path exhibited a significant reduction of stress independently on direction of deformation.The paper also presents experimental results concerning evaluation of an influence of cyclic loading on stress variations during monotonic deformation carried out on the pure copper and X10CrMoVNb9-1 steel. All strain controlled tests were performed at room temperature using thin-walled tubular specimens. The experimental programme contained selected combinations of monotonic and cyclic loadings, i.e. the torsion-reverse-torsion cycles were superimposed on the monotonic tension. It is shown that such cycles associated with monotonic tension caused essential variations of tensile stress. For both materials, a significant decrease of the axial stress was visible. The effects observed during monotonic and cyclic loading combinations were theoretically described using the Mróz and Maciejewski model.     

Viscoelasticity of brain corpus callosum in biaxial tension

Computational models of the brain rely on accurate constitutive relationships to model the viscoelastic behavior of brain tissue. Current viscoelastic models have been derived from experiments conducted in a single direction at a time and therefore lack information on the effects of multiaxial loading. It is also unclear if the time-dependent behavior of brain tissue is dependent on either strain magnitude or the direction of loading when subjected to tensile stresses. Therefore, biaxial stress relaxation and cyclic experiments were conducted on corpus callosum tissue isolated from fresh ovine brains. Results demonstrated the relaxation behavior to be independent of strain magnitude, and a quasi-linear viscoelastic (QLV) model was able to accurately fit the experimental data. Also, an isotropic reduced relaxation tensor was sufficient to model the stress-relaxation in both the axonal and transverse directions. The QLV model was fitted to the averaged stress relaxation tests at five strain magnitudes while using the measured strain history from the experiments. The resulting model was able to accurately predict the stresses from cyclic tests at two strain magnitudes. In addition to deriving a constitutive model from the averaged experimental data, each specimen was fitted separately and the resulting distributions of the model parameters were reported and used in a probabilistic analysis to determine the probability distribution of model predictions and the sensitivity of the model to the variance of the parameters. These results can be used to improve the viscoelastic constitutive models used in computational studies of the brain.     

Remarks on properties of photoviscoelastic model materials

One of the basic problems of structural-model analysis, model photoelasticity and photoelastic coatings in the problem of mechanical and optical creep, relaxation and related phenomena. It is pointed out that, in spite of creep or relaxation, it is possible to achieve physical similarity between model and object if the model material behaves in a certain range as a linear viscoelastic material. Such a material is called a “momentarily linear material.” Several model materials behave in this way in a certain range of stress and time. Because of creep and relaxation, the common tensile tests are, in general, not quite adequate for evaluation of physical properties of plastics used for models. Also the bending test is not always adequate. It is shown how to obtain sufficiently accurate relations between stress, strain, birefringence and time, using tapered specimens. The problem of biaxial creep of model materials is discussed, and a simple method of evaluating the suitability of a given plastic as a model material is shown. Some conclusions concerning time-dependent factors are formulated, and some possible areas of investigation are shown.     

Rate dependent finite strain constitutive model of polyurea

Continuous loading and unloading experiments are performed at different strain rates to characterize the large deformation behavior of polyurea under compressive loading. In addition, uniaxial compression tests are carried out with multistep strain history profiles. The analysis of the experimental data shows that the concept of equilibrium path may not be applied to polyurea. This finding implies that viscoelastic constitutive models of the Zener type are no suitable for the modeling of the rate dependent behavior of polyurea. A new constitutive model is developed based on a rheological model composed of two Maxwell elements. The soft rubbery response is represented by a Gent spring while nonlinear viscous evolution equations are proposed to describe the time-dependent material response. The eight material model parameters are identified for polyurea and used to predict the experimentally-measured stress-strain curves for various loading and unloading histories. The model provides a good prediction of the response under monotonic loading over wide range of strain rates, while it overestimates the stiffness during unloading. Furthermore, the model predictions of the material relaxation and viscous dissipation during a loading-unloading cycle agree well with the experiments.     

纯铝在单轴应力循环作用下棘轮行为的试验研究

对纯铝进行了单轴应变控制和应力控制下的系统循环试验。对纯铝应变循环下的循环应变幅值、应变幅值历史、平均应变对循环特性的影响进行了揭示，对纯铝在非对称应力循环下的应力幅值、平均应力及其历史对循环蠕变〈即棘轮〉的影响进行了分析，得到了纯铝单轴循环行为的一些有意义的结果。     

Experimental identification and mathematical modeling of viscoplastic material behavior

Uniaxial torsion and biaxial torsion-tension experiments on thin-walled tubes were carried out to investigate the viscoplastic behavior of stainless steel XCrNi18.9. A series of monotonic tests under strain and stress control shows nonlinear rate dependence and suggests the existence of equilibrium states, which are asymptotically approached during relaxation and creep processes. Strain controlled cyclic experiments display various hardening and softening phenomena that depend on strain amplitude and mean strain. All experiments indicate that the equilibrium states within the material depend on the history of the input process, whereas the history-dependence of the relaxation and creep behavior appears less significant. From the experiments the design of a constitutive model of viscoplasticity is motivated: The basic assumption is a decomposition of the total stress into an equilibrium stress and a non-equilibrium overstress: At constant strain, the overstress relaxes to zero, where the relaxation time depends on the overstress in order to account for the nonlinear rate-dependence. The equilibrium stress is assumed to be a rate independent functional of the total strain history. Classical plasticity is utilized with a kinematic hardening rule of the Armstrong-Frederick type. In order to incorporate the amplitude-dependent hardening and softening behavior, a generalized arc length representation is applied [14]. The introduction of an additional kinematic hardening variable facilitates consideration of additional hardening effects resulting from the non-radiality of the input process. Apart from the common yield and loading criterion of classical plasticity, the proposed constitutive model does not contain any further distinction of different cases.The experimental data are sufficient to identify the material parameters of the constitutive model. The results of the identification procedure demonstrate the ability of the model to represent the observed phenomena with satisfactory approximation.     

Study of lattice strains in magnesium alloy AZ31 based on a large strain elastic-viscoplastic self-consistent polycrystal model

The recently developed large strain elastic visco-plastic self-consistent (EVPSC) model, which incorporates both slip and twinning deformation mechanisms, is used to study the lattice strain evolution in extruded magnesium alloy AZ31 under uniaxial tension and compression. The results are compared against in-situ neutron diffraction measurements done on the same alloy. For the first time, the effects of stress relaxation and strain creep on lattice strain measurements in respectively displacement controlled and load controlled in-situ tests are numerically assessed. It is found that the stress relaxation has a significant effect on the lattice strain measurements. It is also observed that although the creep does not significantly affect the trend of the lattice strain evolution, a better agreement with the experiments is found if creep is included in the simulations.     

A new unified constitutive model with short- and long-range back stress for lead-free solders of Sn–3Ag–0.5Cu and Sn–0.7Cu

A series of tensile tests of Sn–3Ag–0.5Cu and Sn–0.7Cu lead-free solders were investigated at various strain rates from 1 × 10⁻⁴ s⁻¹ to 1 × 10⁻² s⁻¹ and over a wide temperature range from 25 ^oC to 150 ^oC. Two-step strain rate jump tests, three-step short term creep tests with stress jump, and uniaxial ratcheting tests were also conducted. Based on the test data, a new constitutive model was proposed with a simple formulation and only eight material constants which can be easily obtained. The model employs two carefully defined back stress components to simulate the loading/unloading asymmetry phenomenon in uniaxial ratcheting tests. Different evolution rules of short-range back stress were given for loading and unloading stage, which provides the model ability to simulate the asymmetry in hysteresis loops. The proposed model presents good simulation of uniaxial tensile tests, strain rate jump tests, short term creep tests with stress jump, and uniaxial ratcheting tests.