基于扰动状态概念的软岩蠕变本构模型与试验验证

软岩材料的蠕变过程从初始加载阶段开始即容易产生塑性变形,这与硬岩存在较大差异,而传统的元件模型仅在应力超过某一阈值后才开始描述其粘塑性行为。通过分析岩石加卸载时效变形过程中弹塑性状态的演变规律,以扰动状态理论为基础,确定了以塑性变形为变量的扰动因子函数,并通过塑性变形随时间的变化特征进一步建立了以时间为自变量的蠕变扰动因子演化方程。在此基础上,针对泥质页岩的蠕变变形过程,选取Burgers和Bingham模型分别描述扰动状态理论中的相对完整状态和完全调整状态,并选取蠕变扰动因子为权重函数建立了基于扰动状态理论的蠕变本构模型。通过泥质页岩的室内蠕变特性试验对模型进行有效性检验表明,理论曲线与实测曲线的逼近程度较高,蠕变扰动函数能随时间的发展持续调整相对完整状态向完全调整状态转换的过程,较高应力状态下软岩进入完全调整状态的速率较快,相对传统模型该模型具有更好的非线性及阶段协调性,可较好地描述软岩的初始、稳定和加速蠕变阶段。     

Damage-induced nonassociated inelastic flow in rock salt

The multimechanism deformation coupled fracture model recently developed by Chanet al. [1992], for describing time-dependent, pressure-sensitive inelastic flow and damage evolution in crystalline solids was evaluated against triaxial creep experiments on rock salt. Guided by experimental observations, the kinetic equation and the flow law for damage-induced inelastic flow in the model were modified to account for the development of damage and inelastic dillation in the transient creep regime. The revised model was then utilized to obtain the creep response and damage evolution in rock salt as a function of confining pressure and stress difference. Comparison between model calculation and experiment revealed that damage-induced inelastic flow is nonassociated, dilational, and contributes significantly to the macroscopic strain rate observed in rock salt deformed at low confining pressures. The inelastic strain rate and volumetric strain due to damage decrease with increasing confining pressures, and all are suppressed at sufficiently high confining pressures.     

Uniaxial extensional flow for a viscoelastic model that displays thixotropic yield stress behavior

Homogeneous uniaxial extensional flow of a viscoelastic fluid, namely, the partially extending strand convection model combined with a Newtonian solvent, is investigated for large relaxation time. Initial value problems are addressed, for prescribed constant tensile stress. The limit of large relaxation time introduces a slow time scale of evolution, in addition to a fast time scale for flow. Numerical solutions of the original equations show distinct stages of evolution, which are mathematically analyzed with asymptotic analyses for multiple time scales. We discuss the stages of evolution from equilibrium, as well as unloading the applied stress from a yielded solution. The overall picture which emerges captures a number of features which are usually associated with thixotropic yield stress fluids, such as delayed yielding, and hysteresis for up and down stress ramping. Even at large applied tensile stress, there is persistence of an interval of parameters where the deformation rate increases quickly, only after a delayed response.     

Creep analysis with a stress range dependent constitutive model

Many materials exhibit the stress range dependent creep behavior. The power law creep observed for a certain stress range changes to the viscous type creep as the stress value decreases. Recently published experimental data for advanced heat resistant steels indicate that the high creep exponent (in the range 7–12) may decrease to the low value of approximately unity within the stress range relevant for engineering structures. The aim of this paper is to analyze the influence of the stress range dependent power-law-viscous creep transition on the behavior of structures at elevated temperature. A constitutive model for the minimum creep rate is introduced to describe both the linear and the power law creep depending upon the stress level. To demonstrate basic features of the stress range dependent creep modeling, several elementary examples from structural mechanics are presented. They include a stress relaxation problem, a beam subjected to pure bending and a pressurized thick-walled cylinder. Based on the uni-axial transition stress the transition value of the external load is estimated such that above this value the power law can be applied. For the loading levels below this value the character of the stress distribution as well as the stress values are essentially influenced by the viscous creep.     

A new yield function and a hydrostatic stress-controlled void nucleation model for porous solids with pressure-sensitive matrices

A macroscopic yield function for porous solids with pressure-sensitive matrices modeled by Coulomb's yield function was obtained by generalizing Gurson's yield function with consideration of the hydrostatic yield stress of a spherical thick-walled shell and by fitting the finite element results of the yield stresses of a voided cube. The macroscopic yield function is valid for the negative hydrostatic stress as well as for the positive hydrostatic stress. From the yield function, a plastic potential function for the porous solids was derived either for plastic normality flow or for plastic non-normality flow of the pressure-sensitive matrices. In addition, void nucleation was modeled by a normal distribution function with the macroscopic hydrostatic stress regarded as a controlling stress. This set of constitutive relations was implemented into a finite element code abaqus as a user material subroutine to analyze the cavitation and the deformation behavior of a rubber-modified epoxy around a crack tip under the Mode I plane strain conditions. By comparing the cavitation zone and the plastic zone obtained in the analysis with those observed in an experiment, the mean stress and the standard deviation for the void nucleation model could be determined. The cavitation and the deformation behavior of the rubber-modified epoxy were also analyzed around notches under four-point bending. The size and shape of the cavitation zone and the plastic zone were shown to be in good agreement with those observed in an experiment.     

Analysis of creep deformation and creep damage in thin-walled branched shells from materials with different behavior in tension and compression

A constitutive model for describing the creep and creep damage in initially isotropic materials with different properties in tension and compression has been applied to the modeling of creep deformation and creep damage growth in thin-walled shells of revolution with the branched meridian. The approach of establishing the basic equations for axisymmetrically loaded branched shells under creep deformation and creep damage conditions has been introduced. To solve the initial/boundary-value problem, the fourth-order Runge–Kutta–Merson’s method of time integration with the combination of the numerically stable Godunov’s method of discrete orthogonalization is used. The solution of the boundary value problem for the branched shell at each time instant is reduced to integration of the series of systems of ordinary differential equations describing the deformation of each branch and the shell with basic meridian. Some numerical examples are considered, and the processes of creep deformation and creep damage growth in a shell with non-branched meridian as well as in a branched shell are analyzed. The influence of the tension–compression asymmetry on the stress–strain state and damage evolution in a shell with non-branched meridian as well as in a branched shell with time are discussed.     

Superplastic characteristics of high purity yttria-stabilized zirconia polycrystals

The mechanical characteristics of superplastic yttria-stabilized zirconia polycrystals have been analyzed as a function of stress, temperature and grain size. The evolution of the stress exponent n with stress found in high purity materials is similar to that observed in superplastic metals. True creep parameters can be ascribed to the deformation mechanism at high stresses. By contrast, the creep parameters exhibit a continuous evolution with stress, temperature and grain size at low stresses. The threshold stress formalism used in conventional and high strain rate superplastic metals accounts for the mechanical characteristics observed in fine-grained zirconia polycrystals.     

家兔肌腱的蠕变变形行为的实验研究

研究了家兔肌腱的蠕变规律，测定了稳定蠕变速率等力学参量，通过对试验结果的分析，建立了肌腱的蠕变本构关系，结果表明，蠕变应变与瞬时应力和时间有关，在一定的瞬时应力作用下，稳定蠕变速率近似为常数，稳定蠕变速率与瞬时应力近似成指数关系。     

Experimental study on yield behavior of Daqing crude oil

The yield behavior of Daqing crude oil was studied by means of multi-mode controlled-stress tests with a high-precision stress controlled rheometer. Two experiments of creep and constant stress loading rate were performed. The yield stress of gelled crude oil was dependent on the test conditions such as the stress loading time and the stress loading rate, but the yield strain did not change with test conditions. The yield strain did exist objectively and it can be used as the criterion for the yielding of the structure of gelled crude oil. The yield strain of gelled oil was studied through experiments of creep, constant stress loading rate, oscillatory shear stress increase, and constant shear rate. The yield strain of gelled crude oil decreased with the increasing gel strength. The experiment of constant speed increase of stress showed the strain softening phenomena for low gel strength oil.     

The total creep of viscoelastic composites under hydrostatic or antiplane loading

The problem of bounding the total creep (or total stress relaxation) of a composite made of two linear viscoelastic materials and subjected to a constant hydrostatic or antiplane loading is considered. It is done by coupling the immediate and the relaxed responses of the composite, which are pure elastic. The coupled bounds provide the possible range of the total deformation at infinite time as a function of the initial deformation of the composite. For antiplane shear existing bounds for coupled two-dimensional conductivity yield the required coupled bounds, and these are attained by doubly coated cylinder assemblages. The translation method is used to couple the effective bulk moduli of a viscoelastic composite at zero and infinite time. A number of microgeometries are found to attain the bulk modulus bounds. It is shown that the Hashin's composite sphere assemblage does not necessarily correspond to the maximum or minimum overall creep, although it necessarily attains the bounds for effective bulk moduli. For instance, there are cases when the doubly coated sphere microstructure or some special polycrystal arrangements attain the bounds on the total creep.     

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.     

Finite deformation of a polymer: experiments and modeling

The response of a polymer (polytetrafluoroethylene) to quasi-static and dynamic loading is determined and modeled. The polytetrafluoroethylene is extremely ductile and highly nonlinear in elastic as well as plastic behaviors including elastic unloading. Constitutive model developed earlier by Khan, Huang and Liang (KHL) is extended to include the responses of polymeric materials. The strain rate hardening, creep, and relaxation behaviors of polytetrafluoroethylene were determined through extensive experimental study. Based on the observation that both viscoelastic and viscoplastic deformation of polytetrafluoroethylene are time dependent and nonlinear, a phenomenalogical viscoelasto–plastic constitutive model is presented by a series connection of a viscoelastic deformation module (represented by three elements standard solid spring dashpot model), and a viscoplastic deformation module represented by KHL model. The KHL module is affected only when the stress exceeds the initial yield stress. The comparison between the predictions from the extended model and experimental data for uniaxial static and dynamic compression, creep and relaxation demonstrate that the proposed constitutive model is able to represent the observed time dependent mechanical behavior of polytetrafluoroethylene polytetrafluoroethylene qualitatively and quantitatively.     

The growth of unstable thermoplastic shear with application to steady-wave shock compression in solids*

The catastrophic growth of unstable thermoplastic shear following the transition from homogeneous deformation to heterogeneous localized deformation through distributed shear banding is studied through approximate analytic and computational methods. The calculations provide expressions for shear band widths, spacing, catastrophic growth times and the rate of stress communication between shear bands. The optimum shear band width and spacing are found to be consistent with a minimum work principle. The model predicts that the product of the energy dissipated and the localization time in the shear localization process is invariant with respect to changes in the driving strain rate. Such behavior has been noted in the steady-wave shock compression of a number of solids. The calculations are applied to heterogeneous shear localization observed in the shock compression of aluminum.     

Power-law creep and residual stresses in a carbopol gel

We report on the interplay between creep and residual stresses in a carbopol microgel. When a constant shear stress σ is applied below the yield stress σ _y, the strain is shown to increase as a power law of time, γ(t) = γ ₀ + (t/τ) ^α , with an exponent α = 0.39 ± 0.04 that is strongly reminiscent of Andrade creep in hard solids. For applied shear stresses lower than some typical value σ _c ? 0.2σ _y, the microgel experiences a more complex, anomalous creep behavior, characterized by an initial decrease of the strain, that we attribute to the existence of residual stresses of the order of σ _c that persist after a rest time under a zero shear rate following preshear. The influence of gel concentration on creep and residual stresses are investigated as well as possible aging effects. We discuss our results in light of previous works on colloidal glasses and other soft glassy systems.     

Prediction of the creep behaviour of polyethylene and molybdenum from stress relaxation experiments

In many applications it is useful to be able to convert observed creep data of a material to corresponding stress relaxation data or vice versa. If the material exhibits non-linear viscoelasticity such a conversion can be rather difficult. In this paper two semi-empirical flow equations, the power law and the exponential law, are used to convert stress relaxation data into corresponding creep behaviour data. These two flow equations are often used to describe non-linear viscoelastic behaviour. The procedure adopted here is based on the assumption that the creep data during the experiment decrease due to an increase in the internal stress level, thus decreasing the effective stress for flow. The conversion method is applied to high density polyethylene and polycrystalline molybdenum at room temperature. In general predictions using the power law are in better agreement with the experimental results than predictions using the exponential formula. The concepts of secondary and ceasing creep are discussed in terms of build-up of internal stress during the creep process.     

Time–aging time–stress superposition in soft glass under tensile deformation field

We have studied the tensile deformation behaviour of thin films of aging aqueous suspension of Laponite, a model soft glassy material, when subjected to a creep flow field generated by a constant engineering normal stress. Aqueous suspension of Laponite demonstrates aging behaviour wherein it undergoes time-dependent enhancement of its elastic modulus as well as its characteristic relaxation time. However, under application of the normal stress, the rate of aging decreases and in the limit of high stress, the aging stops with the suspension now undergoing a plastic deformation. Overall, it is observed that the aging that occurs over short creep times at small normal stresses is the same as the aging that occurs over long creep times at large normal stresses. This observation allows us to suggest an aging time–process time–normal stress superposition principle, which can predict rheological behaviour at longer times by carrying out short time tests.     

Model of plastic anisotropy evolution with texture-dependent yield surface

Model of evolution of plastic anisotropy due to crystallographic texture development, in metals subjected to large deformation processes, is presented. The model of single grain with the regularized Schmid law proposed by Gambin is used. Evolution of crystallographic texture during drawing, rolling and pure shear is calculated. Phenomenological texture-dependent yield surface for polycrystalline sheets is proposed. Evolution of this yield surface is compared with evolution of phenomenological higher order yield surfaces proposed by Hill and Barlat with Lian for drawing, rolling and pure shear processes. The change of the Hill yield surface and the Barlat–Lian yield surface is obtained by replacing material parameters present in these conditions by texture-dependent functions.     

Modelling creep tests in HMPE fibres used in ultra-deep-sea mooring ropes

Due to its low density and high strength, HMPE (high modulus polyethylene) fibres are being increasingly used in synthetic ropes for offshore mooring. Nevertheless, the occurrence of creep at sea temperature can be a shortcoming for its practical use. Creep tests performed at different load levels in a sub-system of the HMPE rope (yarn) are frequently used as a first step to obtain some information about the susceptibility to creep deformation at a given temperature. The present paper is concerned with the phenomenological modelling of creep tests in HMPE yarns. In this macroscopic approach, besides the classical variables (stress, total strain), an additional scalar variable related with the damage induced by creep process is introduced. An evolution law is proposed for this damage variable. The predicted lifetimes and elongations of HMPE specimens in creep tests at different load levels and room temperature are compared with experimental results showing a good agreement.     

Forming simulation of aluminum sheets using an anisotropic yield function coupled with crystal plasticity theory

This paper describes the application of a coupled crystal plasticity based microstructural model with an anisotropic yield criterion to compute a 3D yield surface of a textured aluminum sheet (continuous cast AA5754 aluminum sheet). Both the in-plane and out-of-plane deformation characteristics of the sheet material have been generated from the measured initial texture and the uniaxial tensile curve along the rolling direction of the sheet by employing a rate-dependent crystal plasticity model. It is shown that the stress–strain curves and R-value distribution in all orientations of the sheet surface can be modeled accurately by crystal plasticity if a “finite element per grain” unit cell model is used that accounts for non-uniform deformation as well as grain interactions. In particular, the polycrystal calculation using the Bassani and Wu (1991) single crystal hardening law and experimental electron backscatter data as input has been shown to be accurate enough to substitute experimental data by crystal plasticity data for calibration of macroscopic yield functions. The macroscopic anisotropic yield criterion CPB06ex2 (Plunkett et al., 2008) has been calibrated using the results of the polycrystal calculations and the experimental data from mechanical tests. The coupled model is validated by comparing its predictions with the anisotropy in the experimental yield stress ratio and strain ratios at 15% tensile deformation. The biaxial section of the 3D yield surface calculated directly by crystal plasticity model and that predicted by the phenomenological model calibrated with experimental and crystal plasticity data are also compared. The good agreement shows the strength of the approach. Although in this paper, the Plunkett et al. (2008) yield function is used, the proposed methodology is general and can be applied to any yield function. The results presented here represent a robust demonstration of implementing microscale crystal plasticity simulation with measured texture data and hardening laws in macroscale yield criterion simulations in an accurate manner.     

An empirical methodlogy to estimate a local yield stress in work-hardened surface layers

A methodology is proposed for estimating the local yield stress in work-hardened surface layers. It is based on the concept of in-depth normalized variation of hardness and x-ray diffraction peak width, both of which measure the strain-hardening attained by the materials' surface-treated layers due to, for example, shot-peening. Its principle is directly founded on the classical hardness theory. To study the evolution of those values with plastic deformation, specimens of five steels with different mechanical properties were subjected to interrupted tensile tests. The tests were performed at successive increments of plastic strain, until fracture occurred. The specimens were loaded and unloaded in increments of about 2% true strain. After each plastic strain increment, hardness and diffraction peak width were measured. It was observed that the variations of diffraction peak width and hardness are related to the material's strain-hardening, and their normalized variations can be considered proportional to the normalized variation of the material's yield stress. Thus, where the yield stress of the bulk material, its hardness or a characteristic diffraction peak width value, and their relative variations along the hardened layers, are known, an empirical expression could be used to estimate the local yield stress as a function of the treated depth.