循环荷载下岩盐Poyhting-Thomson模型研究

循环荷载下盐岩流变模型,是岩石力学的重要内容之一。利用Poyhting-Thomson模型,根据岩样真实循环加载疲劳过程,推导出初始匀速加载段和正弦循环加载段的应变随时间变化的本构方程。对盐岩进行了循环加载疲劳试验,由于疲劳损伤的原因,平均应变值随时间延长等速增加。据此,对理论本构方程进行了修正,用时间的幂函数来描述应变增量,得到了修正的Poyhting-Thomson疲劳流变本构方程。匀速加载阶段理论模型能较好模拟试验曲线。用修正的流变本构模型对循环加载疲劳阶段的应变曲线的上限线、下限线和中间线进行拟合分析,得到了相应的拟合参数。取参数的平均值,用修正模型对试验疲劳曲线进行了模拟,模拟曲线与试验曲线比较接近,几乎可以代替试验。通过试验和数学验证表明,Poyhting-Thomson模型及其修正的模型,来描述循环载荷作用下盐岩的疲劳应变发展是可行的,能较好的刻画应变随时间变化的规律。     

不同循环上限荷载下泥质石英粉砂岩力学特性试验研究

通过开展循环加卸载转单调加载试验和疲劳破坏试验,揭示循环荷载下泥质石英粉砂岩的变形和力学响应特征。试验与研究结果表明,当循环上限荷载位于疲劳强度前后,试件的轴向和横向累计残余应变由单调递增凸曲线向凹曲线延伸,滞回环间距由“疏-密”向“疏-密-疏”发展,残余应变率和滞回环相对面积由L形向U形转化;弹性模量由初始快速上升、下降、缓慢稳定发展3个阶段向单调递减凹曲线转凸曲线衰减;而横向-轴向应变比则由单调递减凹曲线,转变为单调递增凸曲线,然后向凹曲线延伸;随上限荷载的增加,循环加卸载3000次后泥质石英粉砂岩抗压强度先增大后减小,最大增幅较单轴抗压强度高13.62%,而当上限荷载小于单轴压缩弹性上限时,循环荷载作用后的岩石抗压强度略小于单轴抗压强度;当试件发生疲劳破坏时,疲劳寿命与上限荷载呈幂函数分布,疲劳强度约为单轴抗压强度的80%~89%。试件弹性模量整体随着循环上限荷载先增大后减小,而横向-轴向应变比则随上限荷载的增加而增大;提出了循环荷载的“薄弱结构断裂效应”和“压密嵌固效应”,探讨了循环加卸载过程中多孔弱胶结岩石的强度变化特征和力学参数演化机制。     

复合材料疲劳分层的界面单元模型

提出一种三维黏聚力界面损伤模型,可以描述单调和交变载荷下层合复合材料混合型的分层损伤。损伤用界面所经历过的最大位移间断来定义,交变荷载下一个周期的加、卸载过程均考虑有损伤积累,模型还考虑了单调和疲劳损伤的门槛效应和交变载荷下裂纹的闭合效应。建立了包含该界面损伤模型的初始无厚度八节点等参界面单元,并引入加速损伤的算法,用一次计算循环代替若干次实际循环,提高计算效率。用该单元模型对某复合材料动部件疲劳分层裂纹的形成和扩展进行了模拟,得到了分层裂纹前沿界面局部损伤和结构疲劳分层的发展规律,模型预测的裂纹长度-荷载循环次数对数(a-log N)曲线和结构剩余刚度与试验数据吻合。     

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。     

橡胶材料的非线性黏弹性本构方程

橡胶是一种非线性黏弹性材料,准确描述其非线性黏弹性力学响应的本构方程是橡胶材料及制品设计优化的关键。文中基于超弹性模型和并行流变模型(PRF)描述了橡胶材料的非线性黏弹性响应特征,重点探讨了由实验数据确定PRF本构方程材料参数的方法。首先通过单轴拉伸实验数据拟合得到超弹性模型,将应力松弛实验数据拟合得到表征材料线性黏弹性的模型-Prony级数,再将Prony级数转化为初始的PRF模型,进而不断优化得到PRF模型的准确材料参数,最后进行实验验证。结果表明,PRF模型计算的不同应变下的应力松弛数据与实验数据之间的误差仅为0.067%,PRF能准确地描述橡胶材料非线性响应的应力松弛行为。     

二维编织C/SiC复合材料非线性损伤本构模型与应用

基于二维编织C/SiC复合材料的基本力学性能试验, 建立了该材料的宏观正交各向异性非线性损伤本构模型。模型中以可检测的应变作为变量, 采用形式简单的函数分别描述了单轴拉伸和剪切加载下的材料损伤演变下的应力-应变关系, 以及卸载状态的刚度变化规律。同时, 考虑了材料的单边效应以及拉压应力状态转换时的损伤钝化行为。将此本构模型编写成UMAT子程序并引入ABAQUS有限元软件, 可以完整描述该材料的加载非线性和卸载线性的应力-应变关系特征, 及其加卸载历史。通过对带孔板的拉伸模拟, 孔边应变分布与试验结果吻合较好, 验证了本构模型的有效性。     

混凝土拉-压疲劳损伤模型及其验证

基于连续损伤力学理论,提出了混凝土单轴拉-压疲劳损伤模型。模型中采用了拉和压两个边界面。加载面、边界面方程均以损伤能量释放率表示。在能量释放率空间内,由加载面与初始损伤面、边界面之间的位置描述损伤状态。通过建立累积损伤与相应循环损伤能量释放率阈值之间的关系,确定了疲劳加载中极限断裂面尺寸的变化规律,由此模拟混凝土在循环荷载作用下的刚度退化过程。结合作者完成的疲劳试验结果,确定了理论模型中的计算参数。经比较,理论模型预测的应力-应变数值、疲劳寿命和试验结果吻合较好。     

聚氨酯注浆材料在循环压缩加载下疲劳性能与微观结构演化

应用于基础设施维修加固的聚氨酯注浆材料通常承受反复荷载作用,对聚氨酯注浆材料进行循环压缩加载试验以测试其压缩疲劳性能,全程记录材料的应变响应,并在SEM下观测材料泡孔结构疲劳破坏的微观形貌特征。试验结果表明:材料在循环荷载下的响应分为三个阶段,第一阶段持续数十次,弹性应变递次增大;第二阶段应变值稳定;第三阶段在高应力水平下表现为疲劳破坏,在低应力水平下表现为循环硬化。对于0.3g/cm3的试件,导致疲劳破坏的应力阈值α在0.7~0.8之间;而0.5g/cm3试件的阈值在0.6~0.7之间。发生疲劳破坏时,材料的宏观表现为垂直于荷载方向的鼓出,微观表现为泡壁裂纹扩张和棱边屈曲。此外,提出疲劳损伤参数D表征材料模量在循环荷载下的演化,D可以敏感地捕捉低应力水平下第三阶段材料的循环硬化。     

白垩系冻结砂岩动态统计损伤本构关系研究

为了研究饱和冻结砂岩的本构关系,依托白垩系地层煤矿立井建设中冻结凿井工程,开展室内SHPB冲击试验获取冻结砂岩在不同应变率下的动态应力应变曲线,在分析岩石动力学特性的基础上,建立了基于Weibull统计分布、Drucker-Prager破坏准则及等效应变原理的砂岩强度型动态统计损伤本构关系。结果表明:冻结砂岩动态应力应变曲线分为线弹性、弹塑性及塑形软化3个阶段,动态抗压强度与峰值应变的应变率■强化效应显著;随■的升高,岩石用于内部微缺陷衍生和扩展的能量逐渐变大,参与破坏过程的裂隙增多,宏观上表现出比能量吸收值(SEA)的应变率相关性明显;统计本构关系中,表征岩石初始微缺陷的损伤系数δ能够反映饱和冻结砂岩受冲击时的弹塑性特征,经拟合确定最佳初始损伤系数δ=0.95;理论模型曲线与试验曲线吻合良好,模型能较好地反映冲击载荷下岩石线弹性和弹塑性阶段的强度分布。     

定侧压混凝土双压疲劳损伤模型

基于边界面概念和损伤力学理论,建立了一向定侧压混凝土双轴压各向异性损伤模型。加载面、边界面方程均以损伤能量释放率表示。在能量释放率空间内,由加载面与初始损伤面、边界面之间的位置描述损伤状态。通过建立累积损伤与相应循环损伤能量释放率阈值之间的关系,确定了疲劳加载中极限断裂面尺寸的变化规律,由此模拟混凝土在循环荷载作用下的刚度退化过程。结合已有的试验结果,确定了理论模型中的计算参数。经比较,理论模型预测的应力-应变数值、疲劳寿命和试验结果吻合较好。     

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.     

An improved unified viscoplastic constitutive model for strain-rate sensitivity in high temperature fatigue

An improved unified cyclic viscoplastic material model for high temperature fatigue of P91 steel is presented. The primary enhancement over existing models is in relation to strain-rate independence of parameters, for accurate interpolation and extrapolation across a range of strain-rates and stress regimes, as relevant to flexible operation of high temperature power generation plant. The model combines a hyperbolic sine constitutive equation with anisothermal cyclic evolution of isotropic and kinematic hardening variables. The material model is developed from a thermodynamic framework and is implemented in multi-axial form within a user material subroutine. The user material subroutine is calibrated and validated for P91 steel across a range of cyclic (isothermal fatigue and thermo-mechanical fatigue) and non-cyclic high temperature loading conditions. A novel method for the identification of the cyclic viscoplastic material parameters is also presented.     

The choice of cyclic plasticity models in fatigue life assessment of 304 and 1045 steel alloys based on the critical plane-energy fatigue damage approach

The present study intends to examine various cyclic plasticity models in fatigue assessment of 304 and 1045 steels based on the critical plane-energy damage approach developed earlier. Cyclic plasticity models of linear hardening, nonlinear, multi-surface, and two-surface were chosen to study fatigue damage and life of materials under proportional and non-proportional loading conditions. The effect of additional hardening induced due to non-proportional loading in 1045 steel and particularly in 304 steel was further evaluated as different constitutive models were employed. In the present study, the plasticity models were calibrated by the equivalent cyclic stress–strain curves. The merits of the models were then investigated to assess materials deformation under proportional and non-proportional loading conditions. Under non-proportional loading, the cyclic plasticity models were found to be highly dependent upon the employed hardening rule as well as the materials properties/coefficients.The stress and strain components calculated through constitutive laws were then used as input parameters to evaluate fatigue damage and assess the fatigue life of materials based on the critical plane-energy approach.The calculated values of stress components based on constitutive laws resulted in a good agreement with those of experimentally obtained under various loading paths of proportional and non-proportional conditions in 1045 steels. In 304 steel, the calculated stress components were however found in good agreement when plasticity models were employed for proportional loading conditions. Under non-proportional loading, the application of the multi-surface plasticity model in conjunction with the fatigue damage approach resulted in more reasonable results as compared with other plasticity models. This can be attributed to the motion of the yield surface in deviatoric stress space in the multi-surface model encountering additional hardening effect through estimated higher stress values under non-proportional loading conditions.Predicted fatigue lives based on the critical plane-energy damage approach showed such range of agreements as ±1.05–±3.0 factors in 1045 and 304 steels as compared with experimental life data when various constitutive plasticity models were employed.     

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.     

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。     

循环荷载下大孔隙红砂岩的动力响应及损伤研究

为探究循环荷载下不同孔隙率红砂岩的动力特性和损伤规律,采用SHPB冲击实验系统,选取了2组不同孔隙率的红砂岩进行循环冲击实验,分析大孔隙率红砂岩的动力波形,本构曲线及损伤度,得到不同孔隙率红砂岩的变形模量、峰值应力、峰值应变及损伤度的变化规律。结果表明:不同孔隙率的红砂岩试件在循环荷载下的应力时程基本一致,随着循环次数的增加,岩石经历了孔隙闭合-裂隙开展-应力硬化-应变软化直至破坏的阶段,其变形模量和峰值应变呈现出先减小,再增大,再减小的趋势,峰值应力与速度呈正相关的关系。随着循环次数的递增,孔隙率大的岩石的峰值应力下降趋势大于孔隙率小的岩石,并且损伤累积使岩石在冲击破坏前表现出了较明显的塑性特征,不同孔隙率红砂岩的损伤度变化趋势基本是先增大后减小,孔隙率大的岩石累计损伤度大于孔隙率小的岩石,其损伤裂纹基本都是从透射杆端部开始,随着裂纹的产生扩展直至破坏。     

循环荷载下大孔隙红砂岩的动力响应及损伤研究

为探究循环荷载下不同孔隙率红砂岩的动力特性和损伤规律,采用SHPB冲击实验系统,选取了2组不同孔隙率的红砂岩进行循环冲击实验,分析大孔隙率红砂岩的动力波形,本构曲线及损伤度,得到不同孔隙率红砂岩的变形模量、峰值应力、峰值应变及损伤度的变化规律。结果表明:不同孔隙率的红砂岩试件在循环荷载下的应力时程基本一致,随着循环次数的增加,岩石经历了孔隙闭合-裂隙开展-应力硬化-应变软化直至破坏的阶段,其变形模量和峰值应变呈现出先减小,再增大,再减小的趋势,峰值应力与速度呈正相关的关系。随着循环次数的递增,孔隙率大的岩石的峰值应力下降趋势大于孔隙率小的岩石,并且损伤累积使岩石在冲击破坏前表现出了较明显的塑性特征,不同孔隙率红砂岩的损伤度变化趋势基本是先增大后减小,孔隙率大的岩石累计损伤度大于孔隙率小的岩石,其损伤裂纹基本都是从透射杆端部开始,随着裂纹的产生扩展直至破坏。     

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.     

Fatigue life prediction method of face-centered cubic single-crystal metals under multiaxial nonproportional loading based on structural mechanical model

Based on the characteristics of the sliding surface, sliding direction, and fatigue damage mechanism of metal materials, the mechanical model of a body–bar–plate structure is proposed with consideration to the plastic damage mechanism. The elastoplastic constitutive equations and damage constitutive equations of the face-centered cubic (FCC) structure subjected to multiaxial cyclic loading were derived, and the damage evolution law of the body–bar–plate mechanical model was investigated. Then, the meso-damage evolution equation was established under multiaxial nonproportional loading. Subsequently, the relationship between the fatigue performance and microstructure under multiaxial nonproportional loading was investigated, and a damage mechanics–finite element method (FEM) with consideration to the damage evolution is proposed. The proposed model and method provide a new approach for predicting the fatigue life of metal materials.