基于不可逆内变量热力学的岩石材料粘弹-粘塑性本构方程

岩石材料的粘弹性和粘塑性变形是与时间相关的能量耗散行为。在Rice不可逆内变量热力学框架下,引入两组内变量分别用来描述在粘弹性和粘塑性变形过程中材料的内部结构调整。通过给定比余能的具体形式和内变量的演化方程,推导出内变量粘弹-粘塑性本构方程。粘弹性本构方程具有普遍性,能涵盖Kelvin-Voigt和Poynting-Thomson在内的经典粘弹性模型的本构方程。并指出热力学力与应力呈线性关系是组合元件模型为线性模型的根本原因。粘塑性本构方程能较好地刻画岩石材料在粘塑性变形过程中的硬化现象。对模拟岩石的模型相似材料进行单轴加卸载蠕变试验,将蠕变过程中的粘弹性和粘塑性变形分离并根据试验数据对本构方程的材料参数进行辨识。试验数据和理论曲线对比结果表明该文提出的本构方程能很好地模拟材料的蠕变行为。该类型的本构方程能为岩石工程的长期稳定性的预测、评价以及加固分析提供基础。     

循环荷载作用下粉砂岩疲劳流变损伤模型研究

针对现有流变模型难以有效描述循环荷载作用下岩石变形及疲劳损伤演化特征等问题,开展了粉砂岩循环加卸载试验,分析了不同上限荷载下岩石的流变规律与疲劳特性。基于Kachanov蠕变损伤理论建立损伤变量,引入一个带应变触发和应力阈值的黏塑性元件,与Burgers模型串联构建循环荷载作用下岩石疲劳流变损伤模型;将正弦波应力函数替换流变微分本构方程中的恒定应力,推导岩石在循环荷载下的一维、三维微分型损伤本构方程,再根据叠加原理得到模型的黏弹塑性流变损伤方程。适用性验证表明,新建模型不仅可以精确地反映循环加卸载过程中粉砂岩的衰减、稳态流变阶段,还可以有效地描述上限荷载高于疲劳强度时的加速流变阶段。通过粉砂岩疲劳损伤流变全过程定量化分析,提出加速流变阶段的临界损伤阈值和破坏失稳判据,并给出加速流变阶段的启始时间、持续时间及疲劳寿命预测方法,模型对岩体工程长期稳定性评价具有一定的理论指导意义。     

A meso-scale damage evolution model for cyclic fatigue of viscoplastic materials

This study presents an approach to predict the degree of material degradation and the resulting changes in elastic, plastic and creep constitutive properties of viscoplastic materials, during cyclic loading in micro-scale applications. The objective of the study is to address the initiation and growth of homogeneous meso-scale damage, in the form of distributions of micro-cracks and micro-voids, due to cyclic, plastic (rate-independent inelastic) and creep (rate-dependent inelastic) deformations in viscoplastic materials and to evaluate the resulting changes in the effective meso-scale elastic, plastic and creep constitutive properties. An energy partitioning damage evolution (EPDE) model is proposed to describe the viscoplastic damage evolution. Development of the EPDE model constants is then demonstrated for a Pb-free solder, based on cyclic fatigue test data. Application of the EPDE model is demonstrated for solder joint fatigue during thermal cycling of a ball grid array (BGA) electronic assembly. A 3D viscoplastic finite element analysis is conducted, and damage evolution is modeled using a successive initiation (SI) technique reported earlier by the authors. In this approach, the local (meso-scale) material properties are progressively degraded and highly damaged sections of the macro-scale structure are ultimately eliminated, using the EPDE model. Prediction of damage initiation and propagation is presented both with and without property updating, for comparison purposes. The analysis shows that the EPDE model can realistically capture the softening observed during cyclic loading.     

One damage law for different mechanisms

We consider here a general three-dimensional kinetic damage law. It uses the thermodynamic of irreversible processes formalism and the phenomenological aspects of isotropic damage. It gives the damage rate as a function of its associated variable, the strain energy density release rate and the accumulated plastic strain rate. Associated with different plastic constitutive equations, this damage law takes into account brittle damage, ductile damage, low and high cycle fatigue and creep damage. In this paper we mainly focus on creep-fatigue interaction and high cycle fatigue. Associated to a viscoplastic constitutive equation having kinematic hardening, the damage law gives the non linear creep-fatigue interaction. The agreement with experiments is good. Associated to plastic constitutive equations also having kinematic hardening but introduced in a micromechanical two scale model based on the self-consistent scheme, it models the non linear accumulation of damage induced by a succession of sequences of different amplitudes as well as the effect of the mean stress and the influence of non proportional loading.     

A theoretical description of large viscoplastic shear deformation in metals

In this work, a new 3-dimensional viscoplastic model based on a previous plasticity theory is presented. The proposed constitutive model anticipates the contribution of the main features of plastic behavior, such as yielding, rate effect, isotropic and kinematic hardening, through a new approximation of the constitutive equation with a viscoplastic term, as well as a new consideration of the functional form of the rate of plastic deformation. A high accuracy simulation of shear experimental data at various rates and temperatures for a variety of materials, as well as the sign inversion of normal stress has been postulated.     

沥青砂混合料粘弹塑力学特性研究

在0.1MPa、0.15MPa、0.2MPa、0.25MPa和0.3MPa下进行了沥青砂试样单轴压缩和蠕变实验,分析了其压缩和蠕变性质,根据变形机理提出了粘弹塑本构模型可由粘弹性和粘塑性的两个子模型串联构成,通过对粘塑性子模型中粘性系数进行改进,理论推导了模型蠕变本构方程,确定了模型参数,并求得模型参数与加载应力函数关系。进行模型预测与实验结果对比,结果表明:该模型能够描述沥青砂试样在不同应力下蠕变变形的3个阶段,反映了沥青砂混合料粘弹塑变形特点。     

Phenomenological formulation of viscoplastic constitutive equation for polyethylene by taking into account strain recovery during unloading

A viscoplastic constitutive equation for polyethylene that properly describes significant strain recovery during unloading was proposed. The constitutive equation was formulated by combining the kinematic hardening creep theory of Malinin and Khadjinsky with the nonlinear kinematic hardening rule of Armstrong and Frederick. In order to describe the strain recovery, the nonlinear kinematic hardening rule was modified. First, a loading surface was defined in a viscoplastic strain space. A loading–unloading criterion was then introduced using the loading surface. Moreover, a new parameter was defined by the relationship between the loading surface and the current state of the viscoplastic strain, and the evolution equation of back stress was modified using this parameter, which has some value only during unloading. Experimental results for polyethylene were simulated by using the modified constitutive equations, and cyclic inelastic deformation in both uniaxial and biaxial states of stress was predicted. Finally, the validity of the above-described modification was verified, and the features of the constitutive equation and the deformation were discussed.     

A mean-field micromechanical formulation of a nonlinear constitutive equation of a two-phase composite

In this paper, a mean-field micromechanical approach has been employed to formulate a nonlinear constitutive equation and yield conditions of a two-phase composite considering plastic and creep deformation of constituent phases. The derived constitutive equation is expressed in a piecewise linear-rate form, so it can be easily combined with common structural analyses such as a finite element analysis as well as lamination theories for typical continuous fiber-reinforced composite structures. The model has taken into account the threshold creep of constituent phases and diffusional mass transfer at the inclusion/matrix interface, which play a significant role in high-temperature deformation of short-fiber-reinforced metal matrix composites. A numerical study on anisotropy in Bauschinger effect and thermal-cycling creep of SiC whisker/Al matrix composites has been made based on the developed model.     

Viscoplastic analysis of structural polymer composites using stress relaxation and creep data

A structural carbon based composite material has been investigated for its high temperature viscoplastic properties using a model based on an overbearing stress concept and using the data obtained from load relaxation and creep. The time dependent viscoplastic properties were obtained at several load and temperature levels. An elastic–viscoplastic constitutive model (proposed by Gates) was used for the modeling efforts. The model is based on an overstress concept appropriate to inelastic properties of composites. The materials parameters for the model are obtained from a set of load relaxation experiments. The model predictions have been compared to the results of creep tests. The results show that the model is capable of predicting the creep behavior at shorter time periods and lower temperatures. As the temperature is increased or as the creep is prolonged the model predictions deviate from the experimental results.     

复合材料蠕变本构关系及实验测定Ⅰ.本构关系

蠕变是复合材料最重要的力学性能之一,实验表明:复合材料在蠕变条件下的变形可以分为弹性变形、粘弹性变形和粘塑性变形.应用不可逆过程的热力学和广义变量的概念可以分析材料的蠕变变形.本文首先回顾了热力学的基本方程;基于Schapery本构关系的假设和思路推导了蠕变本构关系的一般形式,其中包括弹性变形、粘弹性变形和粘塑性变形;考虑到广义力选取的不唯一性,本文提出了广义力选取的原则以使得到的本构关系尽可能地简单;由此本文给出了复合材料的一维蠕变,各向同性复合材料的二维蠕变和纤维增强复合材料平面内的蠕变的本构关系.     

Micromechanically Established Constitutive Equations for Multiphase Materials with Viscoelastic–Viscoplastic Phases

A model for viscoelastic–viscoplastic solids is incorporated in a micromechanical analysis of composites with periodic microstructures in order to establish closed-form coupled constitutive relations for viscoelastic–viscoplastic multiphase materials. This is achieved by employing the homogenization technique for the establishment of concentration tensors that relate the local elastic and inelastic fields to the externally applied loading. The resulting constitutive equations are sufficiently general such that viscoelastic, viscoplastic and perfectly elastic phases are obtained as special cases by a proper selection of the material parameters the phase. Results show that the viscoelastic and viscoplastic mechanisms have significant effect on the global stress-strain, relaxation and creep behavior of the composite, and that its response is strongly rate-dependent in the reversible and irreversible regimes.     

A numerical study of hypoelastic and hyperelastic large strain viscoplastic Perzyna type models

For the case of metals with large viscoplastic strains, it is necessary to define appropriate constitutive models in order to obtain reliable results from the simulations. In this paper, two large strain viscoplastic Perzyna type models are considered. The first constitutive model has been proposed by Ponthot, and the elastic response is based on hypoelasticity. In this case, the kinematics of the constitutive model is based on the additive decomposition of the rate deformation tensor. The second constitutive model has been proposed by García Garino et al., and the elasticresponse is based on hyperelasticity. In this case, the kinematics of the constitutive model is based on the multiplicativedecomposition of the deformation gradient tensor. In both cases, the resultant numerical models have been implemented in updated Lagrangian formulation. In this work, global and local numerical results of the mechanical response of both constitutive models are analyzed and discussed. To this end, numerical experiments are performed and different parameters of the constitutive models are tested in order to study the sensitivity of the resultantalgorithms. In particular, the evolution of the reaction forces, the effective plastic strain, the deformed shapes and the sensitivity of the numerical results to the finite element mesh discretization have been compared and analyzed. The obtained results show that both models have a very good agreement and represent very well the characteristic of the viscoplastic constitutive model.     

Nonlinear constitutive equations for transient creep of viscoelastic polymers including the effect of hydrostatic pressure

The behaviour of polymers is known to be significantly influenced by the hydrostatic pressure in creep deformation or elastic-plastic deformation. The effect of the third stress invariant on the nonlinear viscoelastic deformation is much smaller than that of the hydrostatic pressure. In this paper, a constitutive equation for transient creep is proposed, which includes the effect of the hydrostatic pressure on the yield function. The creep and plastic strains or the creep strain rate converge to zero with increasing hydrostatic pressure. The proposed constitutive equation is in good agreement with the actual creep data of cellulose nitrate and cellulose acetate, under various combinations of superimposed tensile and hydrostatic loadings.     

Creep failure time prediction of polymers and polymer composites

A theoretical approach for the prediction of creep rupture time of polymers and polymer composites is analyzed in the present work. This analysis takes into account the viscoelastic path at small strains and the viscoplastic path at higher stresses. The calculation of the rate of creep strain is based on a thermally activated rate process, while the emergence and growth of plastic strain, with increasing creep time, is also taken into account. When the accumulated strain attains values, high enough to lead to failure, its slope versus time exhibits an abrupt change. At this specific time, the creep rate function in respect to time appears a minimum. The creep failure time is defined as the time where the creep rate takes its minimum value. The model has been tested for various types of polymeric materials, as well as for polymer composites. Once the model parameters are estimated from short time creep strain data, then it was proved to successfully predict the creep failure time at a variety of stress levels, for all material types examined.     

Topology optimization of finite strain viscoplastic systems under transient loads

A transient finite strain viscoplastic model is implemented in a gradient‐based topology optimization framework to design impact mitigating structures. The model's kinematics relies on the multiplicative split of the deformation gradient, and the constitutive response is based on isotropic hardening viscoplasticity. To solve the mechanical balance laws, the implicit Newmark‐beta method is used together with a total Lagrangian finite element formulation. The optimization problem is regularized using a partial differential equation filter and solved using the method of moving asymptotes. Sensitivities required to solve the optimization problem are derived using the adjoint method. To demonstrate the capability of the algorithm, several protective systems are designed, in which the absorbed viscoplastic energy is maximized. The numerical examples demonstrate that transient finite strain viscoplastic effects can successfully be combined with topology optimization.     

考虑塑性徐变的高混凝土坝实测应变转换应力探讨

将应变计组实测应变转换为应力与混凝土的应力状态有关。针对高混凝土坝应力作用水平较高,当混凝土的应力超过一定的限度,混凝土将进入塑性徐变阶段,如果仍基于弹性徐变体的应力-应变关系进行实测应变的应力转换,获得的应力与实际情况不符。该文假设混凝土在高应力作用下将产生塑性流动,根据P.Perzyna假设计算黏塑性应变率,首先推导了最大拉应力屈服准则和Hsieh-Ting-Chen屈服准则的黏塑性应变率计算公式,接着推导了考虑塑性徐变的实测应变转换应力的计算公式,进而探讨了考虑塑性徐变的高混凝土坝实测应变转换为应力。实例分析表明:由于将实测应变转换为应力采用增量法进行计算,在转换过程中,某阶段的应力失真,必然导致后续转换应力的真实性,而考虑塑性徐变的实测应变转换的应力更符合实际情况。     

On the creep crack growth prediction by a local approach

Classical methods to predict crack growth in structures are generally based on fracture mechanics concepts. For high-temperature applications, where creep (monotonic or cyclic) or thermal stresses are present, such classical approaches lead to large difficulties. An alternative method is to calculate as accurately as possible the actual local behaviour including viscoplasticity and creep damage effects. The different levels of the possible “local approaches” are briefly reviewed and discussed; the case of creep crack growth is then studied in detail, through the use of viscoplastic constitutive equations including creep damage effect. Both the creep damage and the hardening of the metal are supposed to be isotropic, characterized respectively by the following scalar internal variables: the Kachanov's damage variable D and the cumulated viscoplastic strain p. The evolution equation of creep damage is a differential non-linear one with non-linear cumulative effect. The local states of different mechanical fields ((σ, , D) and their redistribution, due to damage effect, are accurately investigated and illustrated by various numerical examples. Finally the approach is applied to the creep of initially cracked CT specimen.     

Plastic limit load of Grade 91 steel pipe containing local wall thinning defect at high temperature

This paper aims to predict the plastic limit load of Grade 91 pipe at high temperature by experimental and numerical analysis methods. The elastic–plastic constitutive relation of P91 considering creep damage at high temperature is proposed and the effectiveness is verified by high-temperature instantaneous tensile test after creep of P91 sample. Then, using the elastic–plastic constitutive relation considering creep damage, the plastic limit loads of P91 pipe containing local wall thinning (LWT) defect at high temperature have been calculated by finite element (FE) method and the accuracy is checked by high-temperature burst experiment after creep of T91 pipe containing LWT. Finally, the fracture analysis and metallographic analysis of Grade 91 sample and pipe containing LWT defect are performed. The results show that the elastic–plastic constitutive relation of P91 considering creep damage proposed by this paper can well describe the elastic–plastic behavior of P91 under creep condition and is useful to calculate the plastic limit load of P91 pipe containing LWT. The failures of P91 tensile samples and T91 pipes containing LWT defect are both plastic fracture. This research would provide an optional method for structure integrity analysis of the pipe containing LWT defect at high temperature.