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。     

考虑时效损伤劣化的变参数非线性蠕变损伤模型

应力长期作用下岩体内部损伤不断累积、扩展,导致部分承载单元丧失承载能力,使得岩体内部真实应力强度大于表观应力。该文以流变学理论为基础,将损伤因子引入弹性元件及黏性元件中,给出弹性损伤元件及黏性损伤元件的蠕变特征方程,用以描述持荷过程中由于损伤累积而呈现出蠕变与时间相关的非线性变形特征;然后以弹性损伤元件及黏性损伤元件的蠕变特征方程为基础,给出考虑损伤效应的经典组合模型的蠕变状态方程,并依据稳定蠕变过程中蠕变变形的组成特征,构建了用于描述软岩稳定蠕变的五元件变参数非线性蠕变损伤模型,同时给出了蠕变损伤组合模型的蠕变变形特征方程;最后以江西东乡铜矿砂质页岩稳定蠕变阶段实验数据为基础,分析并验证了蠕变损伤模型在描述软岩非线性蠕变特征方面的准确性及适用性,拟合结果表明:引入损伤因子的蠕变模型元件,能够很好的描述蠕变的时效-非线性特征。     

岩石非定常Burgers蠕变模型及其参数识别

针对岩石蠕变的非线性特征,提出了一种非线性黏壶元件,并分别替换Burgers模型中的两个线性黏壶元件,从而建立了一种非定常参数Burgers模型。推导了非定常Burgers模型的一维蠕变方程,分析模型参数λ₁与λ₂取值范围对蠕变方程的影响,从理论上确定了非定常模型能够描述蠕变的3个阶段。在此基础上,将非定常Burgers模型的蠕变方程推广至三维应力状态下,并基于Levenberg-Marquardt算法对向家坝岩石的三轴压缩蠕变试验曲线进行拟合及参数识别。通过对比定常与非定常Burgers模型的拟合曲线与相关系数,可以发现非定常Burgers模型拟合效果更好,且能够准确描述包括加速蠕变在内的岩石三阶段蠕变特性,验证了所构建非线性模型的适用性与合理性。     

裂隙岩体非线性流变性态与裂隙损伤扩展过程关系研究

本文研究了裂隙岩体非线性流变性态与裂隙损伤扩展过程的相互关系。文中通过裂隙损伤的流变断裂过程分析，推求具损伤演化耦合效应的岩体非线性流变状态方程，并与宏观唯象流变状态方程相比较，以寻求岩体非线性流变参数与裂隙损伤演化率的关系。最后，用某地下厂房原位试验洞的实测位移作了检验。     

Research on visco-elastic-plastic creep model of artificially frozen soil under high confining pressures

The triaxial creep experiment of artificially frozen soil in deep alluvium was performed by a self-developed machine of triaxial creep frozen soil. After analyzing the experiment results, applying parabolic yield criterion for improved viscoplasticity in the Nishihara model, a new creep constitutive model was established for describing frozen-soil's creep characteristics under high confining pressures. The secondary development tools and data interface had been used to add the visco-elastic-plastic creep constitutive model to standard ADINA FEM. Numerical simulation of the shaft well excavation process and field measurement displacements of frozen wall were performed in the mine; and the results showed that the visco-elastic-plastic creep constitutive model was suitable and reasonable. This constitutive model could be significance for the frozen soil structure long-term stability analysing and the displacement forecasting.     

Multi-axial thermo-mechanical analysis of power plant components from 9–12% Cr steels at high temperature

The aim of this paper is to analyze local changes of stress and strain states in a power plant component under a transient thermal environment. A robust constitutive model is developed to describe inelastic behavior of advanced 9–12% Cr heat-resistant steels at high temperature and in a multi-axial stress state. The model includes the constitutive equation for the inelastic strain rate tensor, the evolution equation for a tensor-valued state variable to reflect hardening/recovery processes and two evolution equations for two scalar-valued variables that characterize softening and damage states. The model is calibrated against experimental creep curves and verified for inelastic responses under different isothermal and non-isothermal loading paths. Steam temperature and loading profiles that correspond to an idealized start-up, holding and shut-down sequence of a power plant component are assumed. To estimate the thermal fields, transient heat transfer analysis is performed. The results are applied in the subsequent structural analysis using the developed inelastic constitutive model. The outcome is a multi-axial thermo-mechanical fatigue loop which can be used for damage assessment.     

Mathematical modelling of creep/environment interactions

Physically-based creep Continuum Damage Mechanics (CDM) is briefly reviewed to introduce the formalism necessary for mathematical modelling of creep and fracture in the presence of a chemically-interacting fluid environment. A recently developed theory of creep in precipitation-hardened alloys is presented in the form of a constitutive equation and two important creep/environment interactions are discussed in detail. Spallation of oxide scales during creep of a low-alloy ferritic steel is one and is modelled using the new creep constitutive equation which incorporates particle-ageing as the principal intrinsic damage mechanism. Lack of experimental data has meant that only qualitative support for the model predictions could be given. Carbon dioxide gas bubble formation along grain boundaries in nickel alloys is the other form of environmental attack considered; a new kinetic model based upon oxyen diffusion-control is described and shown to be in quantitative agreement with a large experimental dataset.     

VPF粘性介质粘弹性本构关系研究

为研究粘性介质的力学性能对板材变形的影响,通过剪切蠕变-回复和松弛试验分析了甲基乙烯基粘性介质的流变性能.实验结果表明粘性介质可以简化为线性粘弹性材料.建立了粘性介质的积分型粘弹性本构方程,并结合剪切蠕变-回复过程的有限元分析确定了方程中的材料参数.利用该本构方程对粘性介质压力胀形过程进行了有限元分析,模拟结果与试验结果对比表明,所建立的本构方程可以较好的预测板材的变形过程.     

中低应变率加载下弱胶结软岩动力学特性

我国西部侏罗系煤层上覆巨厚白垩系富水软岩,为了解此类软岩在冲击荷载作用下的力学本构关系及损伤演化规律,利用Hopkinson压杆装置对干燥、饱和红砂软岩进行中低应变率下的冲击试验,结果表明:红砂软岩峰值应力、峰值应变均表现出明显的应变率效应,其中峰值应力与应变率呈指数关系;相同应变率下,干燥红砂软岩的强度大于饱和状态,对冲击荷载表现出更强的抵抗能力,但饱和红砂软岩的宏观破坏强度大于干燥状态;低应变率加载下,干燥红砂软岩出现负损伤;结合微观机理分析,低应变率下,水对红砂软岩的弱化作用占据主导地位,随着应变率的增大,在惯性效应和水的Stefan效应共同作用下,饱和红砂软岩的动态强度得到强化;基于Z-W-T模型和应变等效原理,建立了服从Weibull分布的损伤本构方程,经验证能很好的反映红砂软岩的动态本构关系,具有一定的工程实际意义。     

Creep and recovery of nonlinear viscoelastic materials of the differential type

In this work, the creep and recovery properties of rubberlike viscoelastic materials in simple shear are studied by two special constitutive equations for isotropic, nonlinear incompressible viscoelastic material of the differential type. The creep and recovery processes are of significant importance to both the mechanics analysis and engineering applications. The constitutive equations introduced in this work generalize the Voigt-Kelvin solid and the 3-parameter model of classical linear viscoelasticity. They describe the uncoupled non-Newtonian viscous and nonlinear elastic response of an isotropic, incompressible material. The creep and recovery processes are treated for simple shear deformation superimposed on a longitudinal static stretch. Closed form solutions are provided and both processes are described effectively by the exponential function.     

A nonlinear constitutive relationship for asphalt binders

A nonlinear constitutive relationship was developed for asphalt binders. Two binders, one polymer modified and one unmodified, were tested in shear using creep and recovery loading. Five different stress levels and four loading times were considered, to capture the response of the binders in the linear and nonlinear viscoelastic range. The creep response of the binders was successfully modeled with a nonlinear power law function. The modified superposition principle was unable to predict the recovery phase of the testing data. A nonlinear constitutive relationship composed of a nonlinear viscous part plus a linear viscoelastic part was developed. The constitutive relationships successfully predicted the binders’ response in creep and recovery. The predictions of the constitutive relationships matched accurately the response of the binders subjected to the Multiple Stress Creep and Recovery loading pattern.     

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。     

Steady-state creep of a pressurized thick cylinder in both the linear and the power law ranges

Summary The classical solution of the steady-state creep problem for a pressurized thick-walled cylinder is based on the power law constitutive equation. Several heat resistant steels show, however, the linear dependence of the creep rate on the applied stress within a certain stress range. In this paper we apply an extended constitutive equation which includes both the linear and the power law stress dependencies. The material constants are identified for the 9Cr1MoVNb steel at 600 °C. We recall the boundary value problem of steady-state creep for the thick cylinder under the plane strain condition. We present an approximate solution illustrating the stress redistributions as a result of the creep process. The analysis shows that for the certain range of the internal pressure both the linear and the power law creep must be taken into account. In this case the results according to the extended constitutive model essentially differ from the classical ones. The obtained solution is also applied to verify the developed user-defined creep material subroutine inside a commercial finite element code. Dedicated to Professor Franz Ziegler on the occasion of his 70th birthday     

Viscoplastic response and creep failure time prediction of polymers based on the transient network model

The nonlinear viscoelastic/viscoplastic response of polymeric materials is described by a new model based on previous works in terms of monotonic loading, stress–relaxation, and creep. In the proposed analysis, following a constitutive equation of viscoelasticity, based on the transient network theory, essential modifications are introduced, which account for the nonlinearity and viscoplasticity at small elastic and finite plastic strain regime. In addition, viscoplastic response is successfully analyzed by a proper kinematic formulation, which is combined with a functional form of the rate of plastic deformation. A three-dimensional constitutive equation is then derived for an isotropic incompressible medium. This analysis is capable of capturing the main aspects of inelastic response and the instability stage taking place at the tertiary creep, related to the creep failure. Model simulations described successfully the experimental data of polypropylene, which were performed elsewhere.     

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。     

Combined plasticity and creep analysis in 2D by means of the boundary element method

This work presents a formulation to make a combined analysis of plasticity and creep in two-dimensional (2D) using the Boundary Element Method. This new approach is developed to combine the constitutive equation for time hardening creep and the constitutive equation for plasticity, the latter based on the Von Misses criterion and the Prandtl–Reuss flow. The implementation of creep strain in the formulation is achieved through domain integrals. The creep phenomenon takes place in the domain which is discretized into quadratic quadrilateral continuous and discontinuous cells. The creep analysis is applied to metals with a power law creep for the secondary creep stage. The results, obtained with reference to three models, show a good agreement when compared to those published in the literature. This finding shows that the Boundary Element Method is a suitable tool to deal with combined nonlinear problems.     

Stress Relaxation of Nonlinear Thermoviscoelastic Materials Predicted from Known Creep

A method to predict the stress relaxation response of nonlinear thermoviscoelastic materials from known creep data is presented. For given nonlinear creep properties, and creep compliance represented by the Prony series, it is shown that the Schapery creep model can be transformed into a set of first order nonlinear differential equations. By solving these equations the nonlinear stress relaxation curves for different strain and temperature levels are established. The strain/temperature-dependent constitutive equation can then be constructed for any nonlinear thermoviscoelastic model, as needed for engineering applications. This revised version was published online in July 2006 with corrections to the Cover Date.     

复合固体推进剂黏弹性微裂纹损伤本构模型

为建立复合固体推进剂的损伤本构模型,在介观尺度上视其为微裂纹损伤,选取微裂纹密度为损伤内变量。在Abdel-Tawab本构方程的基础上,基于微裂纹均匀化理论,推导了损伤映射张量的一般形式。该张量通常具有非完全对称性,其物理意义是将真实应力空间中各向异性材料的多轴加载映射为等效应力空间中各向同性材料的更为复杂的多轴加载。其次,基于黏弹性动态裂纹扩展模型和裂纹扩展阻力曲线的概念,建立了损伤内变量的演化方程。该演化方程仅含4个物理意义明确的细观参数,并且参数的取值规律与宏观应力曲线的变化规律相一致。数值结果表明,建立的模型能够有效反映材料损伤的应变率、温度依赖性及各向异性特征,并且具有一定的蠕变损伤预测能力。