A model for the Mullins effect during multicyclic equibiaxial loading

In this paper, we derive a model to describe the cyclic stress softening of a carbon-filled rubber vulcanizate through multiple stress–strain cycles with increasing values of the maximum strain, specializing to equibiaxial loading. Since the carbon-filled rubber vulcanizate is initially isotropic, we can show that following initial equibiaxial loading the material becomes transversely isotropic with preferred direction orthogonal to the plane defined by the equibiaxial loading. This is an example of strain-induced anisotropy. Accordingly, we derive nonlinear transversely isotropic models for the elastic response, stress relaxation, residual strain and creep of residual strain in order to model accurately the inelastic features associated with cyclic stress softening. These ideas are then combined with a transversely isotropic version of the Arruda–Boyce eight-chain model to develop a constitutive relation for the cyclic stress softening of a carbon-filled rubber vulcanizate. The model developed includes the effects of hysteresis, stress relaxation, residual strain and creep of residual strain. The model is found to compare extremely well with experimental data.     

Annealing model of elasto-plastic solids

The paper develops a model of elasto-plastic solids in which the effect of strain hardening is undergoing relaxation or annealing. A system of constitutive equations of this model is formulated and discussed. It is shown that the existence of annealing implies the existence of creep under constant stress and stress relaxation under constant strain.     

Branching of strain histories for nonlinear viscoelastic solids with a strain clock

Summary An important class of constitutive equations for nonlinear viscoelastic response utilizes the concept of a strain clock. The clock takes the form of a material time variable which is defined in terms of the strain history and which increases faster than physical time. Important consequences of the strain clock are that stress relaxation and creep occur faster as strain increases, and the stress may not increase monotonically with time. In this work, we discuss whether this non-monotonic response implies that strain histories may branch into multiple histories.     

A relationship between non-exponential stress relaxation and delayed elasticity in the viscoelastic process in amorphous solids: Illustration on a chalcogenide glass

Inorganic glasses are viscoelastic materials since they exhibit, below as well as above their glass transition temperature, a viscoelastic deformation under stress, which can be decomposed into a sum of an elastic part, an inelastic (or viscous) part and a delayed elastic part. The delayed elastic part is responsible for the non-linear primary creep stage observed during creep tests. During a stress relaxation test, the strain, imposed, is initially fully elastic, but is transformed, as the stress relaxes, into an inelastic and a delayed elastic strains. For linear viscoelastic materials, if the stress relaxation function can be fitted by a stretched exponential function, the evolution of each part of the strain can be predicted using the Boltzmann superposition principle. We develop here the equations of these evolutions, and we illustrate their accuracy by comparing them with experimental evolutions measured on GeSe₉ glass fibers. We illustrate also, by simple equations, the relationship between any kind of relaxation function based on additive contribution of different relaxation processes and the delayed elastic contribution to stress relaxation: the delayed elasticity is directly correlated to the dispersion of relaxations times of the processes involved during relaxation.     

Application of Nonlinear Superposition to Creep and Relaxation of Commercial Die-Casting Aluminum Alloys

Die-cast aluminum alloys are heavily used in small engines, where they are subjected to long-term stresses at elevated temperatures. The resulting time-dependent material responses can result in inefficient engine operation and failure. A method to analytically determine the stress relaxation response directly from creep tests and to accurately interpolate between experimental time-history curves would be of great value. Constant strain, stress relaxation tests and constant load, creep tests were conducted on aluminum die-casting alloys: B-390, eutectic Al–Si and a 17% Si–Al alloy. A nonlinear superposition integral was used to (i) interpolate between empirical primary inelastic creep-strain and stress-relaxation time histories and (ii) to determine the stress relaxation response from corresponding creep data. Using isochronal stress-strain curves, prediction of the creep response at an intermediate stress level from empirical creep curves at higher and lower stresses resulted in a correlation (R) of 0.98. Similarly for relaxation, correlations of 0.98 were obtained for the prediction of an intermediate strain level curve from higher and lower empirical relaxation curves. The theoretical prediction of stress relaxation from empirical creep curves fell within 10% of experimental data.This paper has not been submitted elsewhere in identical or similar form, nor will it be during the first three months after its submission to Mechanics of Time-Dependent Materials     

Modeling of creep and stress relaxation of the nickel‐base alloy NiCr20TiAl at isothermal and non‐isothermal loading conditions

The design and dimensioning of new as well as the assessment of operating high‐temperature components in service require a precise prediction of creep and stress relaxation. The increasing share of renewable energies forces fossil‐fired power plants for increasing numbers of start‐ups and shut‐downs. Consequently, transient loading conditions need to be taken into account. In order to meet this demand, non‐isothermal creep equations are necessary, which enables a consistent prediction of creep strain and stress relaxation in a wide range of temperatures and stresses. In this paper, an approach for the visco‐plastic modeling of creep and stress relaxation for non‐isothermal loading conditions is presented. The strain portions creep, “negative creep” and initial plasticity, occurring at elevated temperatures are described by temperature‐dependent phenomenological equations. Within this paper, the adjustment of the parameters is based on a wide database of hot tensile tests, creep and annealing experiments. The nickel‐base alloy NiCr20TiAl has been examined in a temperature range from 450 °C to 650 °C. The developed material models have been successfully validated with isothermal and non‐isothermal relaxation experiments. Further, the recalculation of a staged relaxation test demonstrates the capability of the defined material laws in a wide stress range under isothermal and non‐isothermal loading conditions.     

Constitutive equations for ligament and other soft tissue: evaluation by experiment

Ligaments, tendons and other soft tissues are nonlinearly viscoelastic. To discriminate among various constitutive equations which may be used to describe the tissue, appropriate experimental modalities are requisite. Ideally, testing should span physiologic ranges for load (or strain), load history (recovery and reloading), and load onset and duration, and a robust model will fit all data. Methods to expand the experimental window of time for relaxation and creep are presented and evaluated. The role of ramp, relaxation and recovery protocols is studied in the context of viscoelasticity describable by linear, quasi-linear, nonlinear superposition, Schapery, and multiple integral formulations. The advantages associated with testing protocols that expand the time windows for creep or relaxation are presented.     

Effect of interface diffusion on the strain and stress stability of particulate reinforced electrostrictive materials

This paper presents an analytical method to solve the creep rate and stress relaxation behaviors of particle reinforced electrostrictive composites induced by the interface diffusion between particle and electrostrictive matrix, subjected to external electric fields. Based on the microstructures evolution theory and electroelastic theory of electrostrictive materials, the thermodynamic equations of creep rate and stress relaxation induced by the interface diffusion are, respectively, deduced and solved. The investigation results show that the strain and stress stabilities of particle reinforced electrostrictive materials can be enhanced by optimizing the shape, stiffness and volume fraction of reinforced particles.     

Theoretical calculation of creep and relaxation of polycrystals,and stress redistribution among constituent grains

Taking into account both transient and steady creep of slip systems in the grain, a theoretical method is developed to determine the overall creep and relaxation behaviour of polycrystals and, by which, the accompanying stress and strain distribution among the constituent grains can also be evaluated. This method extends the incremental self-consistent relation for grain interactions to the total form, and is further complemented with an iterative computational process. It is primarily intended for the calculation of creep under a constant stress, relaxation under a constant strain, and a combination of both. While maintaining almost the same degree of accuracy, this new method, as compared to the incremental one, is far more effective. Its theoretical predictions on the creep and relaxation of a 2618-T61 aluminium are shown to be in good accord with experiments. The heterogeneous nature of creep deformation and stress distribution among the constituent grains are also displayed for several selected grain orientations. Finally some implications and limitations of the model are assessed.     

Fully coupled heat conduction and deformation analyses of nonlinear viscoelastic composites

This study presents an integrated micromechanical model-finite element framework for analyzing coupled heat conduction and deformations of particle-reinforced composite structures. A simplified micromechanical model consisting of four sub-cells, i.e., one particle and three matrix sub-cells is formulated to obtain the effective thermomechanical properties and micro–macro field variables due to coupled heat conduction and nonlinear thermoviscoelastic deformation of a particulate composite that takes into account the dissipation of energy from the viscoelastic constituents. A time integration algorithm for simultaneously solving the equations that govern heat conduction and thermoviscoelastic deformations of isotropic homogeneous materials is developed. The algorithm is then integrated to the proposed micromechanical model. A significant temperature generation due to the dissipation effect in the viscoelastic matrix was observed when the composite body is subjected to cyclic mechanical loadings. Heat conduction due to the dissipation of the energy cannot be ignored in predicting the factual temperature and deformation fields within the composite structure, subjected to cyclic loading for a long period. A higher creep resistant matrix material or adding elastic particles can lower the temperature generation. Our analyses suggest that using particulate composites and functionally graded materials can reduce the heat generation due to energy dissipation.     

印刷纸Z向力学特性研究

应用Laplace变换得出印刷纸z向力学模型的本构方程,并应用该方程分析徐变、回复及应力松弛特性,得到应力时间和应变时间的解析表达式.分析结果表明印刷纸z向的应力应变具有非线性关系,属于材料非线性问题.研究结果为进一步研究印刷纸动态力学特性提供了理论依据.     

A unified model of stress relaxation and creep applied to oriented polyethylene

The stress relaxation behaviour of high-modulus oriented polyethylene fibre has been studied with regard to the response to successive small strain increments imposed on an initial relatively large strain deformation. For isotropic polymers, the results of such experiments have previously been interpreted in terms of a single thermally activated process modified by strain hardening. It has been found that, although this approach can describe satisfactorily some of the stress relaxation experiments on the oriented polyethylene fibres, it is unsatisfactory once the strain increments have exceeded a certain size, and that it is at variance with stress recovery experiments. It is shown that both the present stress relaxation and stress recovery experiments can be interpreted in terms of a model comprising two thermally activated processes acting in parallel. Furthermore, the parameters obtained for the stress relaxation data are consistent with those required to fit creep data obtained in a comparable stress range. The essential feature of the mechanical behaviour which was previously attributed to strain hardening can now be seen to arise from the transfer of stress between the two thermally activated processes in the two-process model.     

沥青砂粘弹塑蠕变损伤本构模型实验研究

针对沥青砂的非线性材料特性,结合连续损伤力学理论,对传统Burgers模型进行改造,提出了粘弹塑蠕变损伤本构模型,通过对不同实验条件下沥青砂单轴蠕变试验结果的非线性拟合,获得模型参数,然后利用模型进行预测分析,得到了不同应力水平与环境温度下的蠕变曲线和损伤演化曲线,通过比较发现该文模型能够更合理地反映沥青砂加速蠕变的非线性特征,而且蠕变过程中损伤演化的速度受蠕变时间、应力水平与环境温度的影响很大。     

Experimental Study and Numerical Modelling of Creep and Stress Relaxation of Dielectric Elastomers

Dielectric elastomers (DEs) are gaining acceptance as potential actuator materials because of their exhibition of a large amount of deformation when stimulated by electrostatic forces. However, time‐dependent behaviour such as creep and stress relaxation still pose a great challenge for the design, modelling and control of the DE‐based actuators. In this work, attempts are made for experimental estimation and modelling of creep and relaxation properties of one of the most widely used dielectric acrylic elastomers, VHB 4910. Experimental investigation shows that the material possesses strong time‐dependent creep and stress relaxation. It has been shown that creep and stress relaxation characteristics vary with the holding stress and holding strain respectively. Creep and stress relaxation properties are also shown to depend on the number of cycles in the case of cyclic loading. Results also show that Findley's power law can successfully model the creep and stress relaxation behaviour of the VHB 4910 elastomer.     

Experimental and numerical analyses of mean stress relaxation in cold expanded plate of Al‐alloy 2024‐T3 in double shear lap joints

In this paper, the mean stress relaxation behavior of simple Al‐alloy 2024‐T3 specimens and also the mean stress relaxation around the hole of cold expanded specimen are studied. The analyses are performed through the combination of the nonlinear isotropic hardening and Chaboche nonlinear kinematic hardening model accompanied by the results of experimental tests. The strain‐controlled axial tests are performed at two different strain amplitudes, while the stress‐controlled tests of cold expanded specimens are performed for three different imposed load amplitudes. The constitutive equations of the hardening model are coded as a UMAT subroutine in FORTRAN programming language and implemented in the commercial finite element code of ABAQUS. The accuracy of the hardening model has been proved in two steps: first by simulations of mean stress relaxation during the uniaxial strain‐controlled cyclic tests and second by simulation of strain ratcheting during the stress‐controlled cyclic loading. The stress and strain distributions after cold expansion process are examined as well as the mean stress relaxation due to cyclic loading. The results show the influences of imposed stress amplitude on increasing mean stress relaxation and also the effect of cold expansion level on reducing the mean stress relaxation.     

Uniaxial nonlinear viscoelastic viscoplastic modeling of polypropylene

This paper presents the application of the Schapery viscoelastic and the Perzyna viscoplastic models to strain recovery data of polypropylene. In a previous study, the recovery of strain after monotonic uniaxial tensile loading was measured to gather information on the viscoelasticity and viscoplasticity. The viscoplastic strains from several load histories were determined and are used to calibrate the viscoplastic model. The parameters of the one-dimensional Schapery model are then found by nonlinear optimization using the strain recovery history. The prediction of stress relaxation and creep behavior is investigated.     

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.     

Applicability of Anisotropic Viscoelasticity of Paper at Small Deformations

In this paper the applicability of two-dimensional phenomenlogical linear viscoelastic modelling aimed at printing applications is presented. An iterative algorithm is used to find model parameters evaluated from dynamic mechanical testing at stationary conditions. Experiments are performed in the time domain with different load stimuli in either displacement or force control. The experiments are compared to model predictions.The results show that only small deviations were found on model parameters from the algorithm used on either the loss or the storage properties of paper. This was illustrated by converting line spectra from storage compliances to loss compliances within the frequency domain. The harmonic properties were obtained at conditions with nonlinear material behaviour. Despite this, the two-dimensional linear viscoelastic model described well the behaviour of paper at different states of stress and strain at levels adequate for web-fed printing. The usefulness of the relation between retardances and relaxances was examined by comparing model predictions with different driving stimuli resulting in either creep or relaxation. The time-dependent transverse strain of machine-made paper due to either longitudinal stress relaxation or creep was demonstrated. Finally, extensions of the present model including inelastic material behaviour were discussed.     

Viscoplastic–plastic modelling of IN792

At high temperatures metallic materials behave in a viscous manner exemplified by strain rate dependence, stress relaxation and creep deformation. At low temperatures however, these effects are extremely small, and the behaviour is strain rate independent and shows no or very small relaxation effects. Finally there exists an intermediate region, in which the material behaviour is close to strain rate independent for high strain rates but at the same time shows time dependent inelastic effects, such as stress relaxation and creep. For IN792 this occurs at temperatures around 650 °C. The article describes the extension of a power-law viscoplastic model describing the behaviour of IN792 at 850 °C, also to describe the behaviour at 650 °C, by bounding the elastic–viscoplastic stress-space by a plastic yield surface. The model parameters have been estimated using data from creep test and tailored step relaxation tests, and the model fits well to both the step relaxation data aimed at resembling relevant component conditions and long term creep data.