结构破坏的尺度律

文中综述了结构破坏的尺度律和尺寸效应的研究进展,尤其将重点放在准脆性材料的分析上,因为它们的尺寸效应是重要和复杂的．在回顾了尺寸效应研究的悠远发展史以后。着重讨论了三种主要类型的尺寸效应,即由于强度随机性引起的统计尺寸效应、能量释放的尺寸效应和由于微裂纹或断裂的分形特性可能引起的尺寸效应．得出了这些理论应用的明确结论．之后讨论了如何运用已知的尺寸效应律来测量材料的断裂特性,并采用内聚裂纹模型（cohesivecrackmodel）、非局域化有限元模型和离散元模型等对尺寸效应进行模化．文中还进而分析了尺寸效应在压缩失效和车相关材料行为下的有关问题,并讨论了在断裂扩展区描述含微裂纹材料所需的损伤本构关系．最后也讨论了尺寸效应对准脆性材料的多种应用,这些材料包括,如混凝土、海冰、纤维复合材料、岩石和陶瓷等．本文包含了参考文献377篇     

基于细观力学的混凝土弹塑脆性损伤研究

将混凝土假定为一种由硬化水泥砂浆、粗骨料、界面粘结带所组成的三相复合材料,在满足骨料级配曲线算法的基础上,采用细观单元的弹塑脆性损伤本构关系,考虑材料的非均质特性,建立了基于细观力学的混凝土弹塑脆性损伤数值模型;分别研究了单轴受拉预置裂纹试样和单轴受压混凝土试样的细观弹塑脆性损伤破坏行为,并揭示了混凝土的宏观表征强度存在明显的尺寸效应,通过将计算结果与 Bazant 尺寸效应公式、单轴受压物理实验曲线进行对比,验证了模型的正确性。数值试验表明：该模型可以清晰地模拟混凝土细观塑性屈服和失效裂纹的萌生和扩展。骨料与水泥砂浆间的界面粘结带相对薄弱,在混凝土试件形成宏观损伤局部化带前,试件的屈服和破坏首先发生在骨料边缘处的界面位置,并沿着界面粘结带扩展、贯通;同时,导致宏观裂纹形成和发展的因素仍以细观单元的拉伸破坏为主。     

基于近场动力学理论的准脆性材料的本构力函数的构建

近场动力学理论(PD)是基于非局部思想的连续介质力学新理论,用于研究材料破坏问题。根据准脆性材料破坏的线性和非线性的力学行为,在初始微观弹脆性材料(PMB)的本构力函数中引入了键的损伤模型,将键的断裂过程分成了线性的弹性变形阶段和非线性的损伤变形阶段,以此构建了准脆性材料的本构力函数的基本形式。以典型的准脆性材料为例构建了其本构力函数,通过在压缩载荷下对含预制不同角度单裂纹缺陷的类岩材料的裂纹扩展进行PD数值模拟仿真,裂纹起裂位置和扩展方向与试样试验结果在一定程度上保持了一致,证明了该基于近场动力学理论的典型准脆性材料的本构力函数可用于该类材料的破坏分析。     

化学腐蚀后砂岩三轴压缩力学特性及其能量机制的试验研究

为研究不同化学溶液对砂岩力学性质及能量特征的影响,采用不同的水化学溶液对砂岩试样进行腐蚀,利用WDT-1500多功能材料试验机对化学腐蚀后饱和状态与自然状态的试样进行常规三轴压缩试验。试验结果表明:化学腐蚀后砂岩试样的强度及其抗变形能力呈现不同程度的劣化;化学腐蚀后砂岩试样的峰值应变小于相同围压下自然状态试样的峰值应变,与单轴压缩条件下不同,这可能是由于围压和化学溶液共同作用的结果;砂岩试样的似软化系数与围压之间呈现负相关性,同时,其降低速率随着围压的增加而降低。砂岩试样峰值前吸收的能量绝大部分是以可释放弹性应变能Ue形式储存下来的,而化学腐蚀后砂岩试样以Ue形式储存下来的能量占其总吸收应变能的百分比却有所下降;同时,围压与试样的可释放应变能/应变能比值之间呈负相关性,而与耗散能/应变能比值存在正相关性;岩石脆性指标修正值呈现不同程度的增加,试样的脆性减弱延性增强,即塑性变形增加,塑性变形与耗散能之间具有很好的线性特征。溶液的pH值、浓度和化学成分对砂岩试样峰值处各部分应变能的影响显著。     

飞机风挡无机玻璃在不同应变率下的力学行为

利用电子万能试验机和改进的分离式Hopkinson压杆测试了飞机风挡无机玻璃在2种准静态应变率(4×10-4、4×10-3 s-1)和2种动态应变率(200、400 s-1)下的单轴压缩力学行为,并利用高速摄像机记录试样破坏过程。实验结果表明:玻璃破坏时表现为典型的脆性材料,随着应变率的提高,材料的压缩强度显著提高。通过观察试样变形过程及变形后的形貌可知,玻璃在压缩载荷下的破坏模式为横向张应力引起的裂纹成核、沿轴向扩展与联结交错导致的失效破坏,并从微裂纹成核扩展和能量耗散的角度对材料的应变率效应做出了合理的解释。     

考虑损伤的内变量黏弹--黏塑性本构方程

基于Rice不可逆内变量热力学框架,在约束构型空间中讨论材料的蠕变损伤问题.通过给定具体的余能密度函数和内变量演化方程推导出考虑损伤的内变量黏弹--黏塑性本构方程.通过模型相似材料单轴蠕变加卸载试验对一维情况下的本构方程进行参数辨识和模型验证,本构方程能很好地描述黏弹性变形和各蠕变阶段.不同的蠕变阶段具有不同的能量耗散特点.受应力扰动后,不考虑损伤的材料系统能自发趋于热力学平衡态或稳定态.在考虑损伤的整个蠕变过程中,材料系统先趋于平衡态再背离平衡态发展.能量耗散率可作为材料系统热力学状态偏离平衡态的测度;能量耗散率的时间导数可用于表征系统的演化趋势;两者的域内积分值可作为结构长期稳定性的评价指标.     

考虑损伤的内变量黏弹-黏塑性本构方程

基于Rice 不可逆内变量热力学框架,在约束构型空间中讨论材料的蠕变损伤问题. 通过给定具体的余能密度函数和内变量演化方程推导出考虑损伤的内变量黏弹-黏塑性本构方程. 通过模型相似材料单轴蠕变加卸载试验对一维情况下的本构方程进行参数辨识和模型验证,本构方程能很好地描述黏弹性变形和各蠕变阶段.不同的蠕变阶段具有不同的能量耗散特点. 受应力扰动后,不考虑损伤的材料系统能自发趋于热力学平衡态或稳定态. 在考虑损伤的整个蠕变过程中,材料系统先趋于平衡态再背离平衡态发展. 能量耗散率可作为材料系统热力学状态偏离平衡态的测度;能量耗散率的时间导数可用于表征系统的演化趋势;两者的域内积分值可作为结构长期稳定性的评价指标.      

SBFEM与非局部宏微观损伤模型相结合的准脆性材料开裂模拟

混凝土是一种被广泛应用于土木和水利工程中的准脆性材料, 在各种内外部因素的作用下, 开裂是混凝土结构最为普遍的破坏形式, 准确模拟结构的开裂过程, 对于结构的安全评估至关重要. 将比例边界有限元与非局部宏微观损伤模型相结合提出一种准脆性材料开裂模拟新方法. 以比例边界有限元子域的比例中心作为物质点, 通过两比例中心(物质点对)之间的物质键的正伸长率来定义微细观损伤, 将某点影响域内物质键的微细观损伤加权平均得到该点的宏观拓扑损伤. 再引入能量退化函数, 将宏观拓扑损伤嵌入到比例边界有限元的基本框架中. 充分利用比例边界有限元网格允许存在悬挂节点的优势, 采用四叉树网格离散技术进行快速、高质量的多级网格划分与过渡. 通过一个I型开裂与一个混合型开裂的两个典型算例, 验证了该方法可捕获结构裂纹扩展路径与荷载变形曲线. 与现有的方法相比, 本文的损伤模型可得到更准确的局部开裂损伤带, 结果更为合理, 且具有更高的计算精度和计算效率. 当损伤过程区网格尺寸小于影响域半径的1/5时, 计算结果不存在网格敏感性问题.      

基于固有耗散的材料疲劳性能快速评估方法

材料疲劳损伤的累积过程是一个伴随着温度变化的能量耗散过程. 相比于疲劳过程中试件的局部温升,固有耗散是材料能量变化的直接反映,与材料微观结构演化联系也更为紧密,因此以材料的固有耗散作为疲劳损伤指标具有更加明确的物理意义. 基于对试件表面温升的一维双指数回归,构建了一种材料固有耗散的计算模型,并在此基础上提出了一种快速评估材料疲劳性能的能量方法. 利用该能量方法,对FV520B 钢的疲劳性能进行了实验研究,并对实验结果进行了分析与对比,从而证明了该能量方法及计算模型的可行性和有效性.      

AN ENERGY APPROACH TO RAPIDLY ESTIMATE FATIGUE BEHAVIOR BASED ON INTRINSIC DISSIPATION

材料疲劳损伤的累积过程是一个伴随着温度变化的能量耗散过程. 相比于疲劳过程中试件的局部温升,固有耗散是材料能量变化的直接反映,与材料微观结构演化联系也更为紧密,因此以材料的固有耗散作为疲劳损伤指标具有更加明确的物理意义. 基于对试件表面温升的一维双指数回归,构建了一种材料固有耗散的计算模型,并在此基础上提出了一种快速评估材料疲劳性能的能量方法. 利用该能量方法,对FV520B 钢的疲劳性能进行了实验研究,并对实验结果进行了分析与对比,从而证明了该能量方法及计算模型的可行性和有效性.     

Tensile failure of two-dimensional quasi-brittle foams

Stress redistribution caused by damage onset and the subsequent local softening plays an important role in determining the ultimate tensile strength of a cellular structure. The formation of damage process zones with struts dissipating a finite amount of fracture energy will require the macroscopic stress to be increased in order to continue structural damage. The goal of this paper is to investigate the influence of the fracture energy of the solid on the tensile fracture strength and the strain to fracture in quasi-brittle two-dimensional foams using a microstructural model. We analyze the mesoscopic damage and failure mechanisms in uniaxial tension. Relative density, strut cross-sectional profile, solid’s fracture strain, and fracture energy are varied systematically. The effect of the specific fracture energy on the peak behavior has been shown to be captured by the ratio of the fracture energy to the stored elastic energy. We have also explored the net section strength variation in the presence of a central crack at two different fracture energies. Comparison is made between two structurally identical quasi-brittle and ductile strain hardening foams to identify the differences in the damage mechanisms.     

MICROMECHANICAL MODELLING OF STRAIN SOFTENING IN MICROCRACK-WEAKENED QUASI-BRITTLE MATERIALS

By using the concept of domain of microcrack growth(DMG),themicromechanisms of damage in quasi-brittle materials subjected to triaxial either tensileor compressive loading are investigated and the complete strew-strain relation includingfour stages is obtained from micromechanical analysis.The regime of pre-peaknonlinear hardening corresponds to the distributed damage,i.e.the stable propagationof microcracks.After the attainment of the ultimate strength of load-bearing capacity,some microcracks experience the second unstable growth and the distributed damage istransmitted to the localization of damage.These analyses improve our understanding ofthe hardening and softening behaviors of quasi-brittle materials.     

A first-order strain gradient damage model for simulating quasi-brittle failure in porous elastic solids

In order to simulate quasi-brittle failure in porous elastic solids, a continuum damage model has been developed within the framework of strain gradient elasticity. An essential ingredient of the continuum damage model is the local strain energy density for pure elastic response as a function of the void volume fraction, the local strains and the strain gradients, respectively. The model adopts Griffith’s approach, widely used in linear elastic fracture mechanics, for predicting the onset and the evolution of damage due to evolving micro-cracks. The effect of those micro-cracks on the local material stiffness is taken into account by defining an effective void volume fraction. Thermodynamic considerations are used to specify the evolution of the latter. The principal features of the model are demonstrated by means of a one-dimensional example. Key aspects are discussed using analytical results and numerical simulations. Contrary to other continuum damage models with similar objectives, the model proposed here includes the effect of the internal length parameter on the onset of damage evolution. Furthermore, it is able to account for boundary layer effects.     

Micromechanical concept for the analysis of damage evolution in thermo-viscoelastic and quasi-brittle materials

The aim of this paper is to develop a thermodynamically consistent micromechanical concept for the damage analysis of viscoelastic and quasi-brittle materials. As kinematical damage variables a set of scalar-, vector-, and tensor-valued functions is chosen to describe isotropic and anisotropic damage. Since the process of material degradation is governed by physical mechanisms on levels with different length scale, the macro- and mesolevel, where on the mesolevel microdefects evolve due to microforces, we formulate in this paper the dynamical balance laws for macro- and microforces and the first and second law of thermodynamics for macro- and mesolevel.Assuming a general form of the constitutive equations for thermo-viscoelastic and quasi-brittle materials, it is shown that according to the restrictions imposed by the Clausius–Duhem inequality macro- and microforces consist of two parts, a non-dissipative and a dissipative part, where on the mesolevel the latter can be regarded as driving forces on moving microdefects. It is shown that the non-dissipative forces can be derived from a free energy potential and the dissipative forces from a dissipation pseudo-potential, if its existence can be assured.The micromechanical damage theory presented in this paper can be considered as a framework which enables the formulation of various weakly nonlocal and gradient, respectively, damage models. This is outlined in detail for isotropic and anisotropic damage.     

Short-Term Microdamageability of Fibrous Composites with Transversally Isotropic Fibers and a Microdamaged Binder

The theory of microdamageability of fibrous composites with transversally isotropic fibers and a microdamaged isotropic porous matrix is proposed. Microdamages in the matrix are simulated by pores filled with particles of the destroyed material that resist compression. The criterion of damage in the matrix microvolume is taken in the Schleicher–Nadai form. It accounts for the difference between the ultimate tensile and compressive loads. The ultimate strength is a random function of coordinates with Weibull distribution. The stress–strain state and effective properties of the material are determined from the stochastic equations of the elastic theory for a fibrous composite with porous components. The equations of deformation and microdamage are closed by the equations of porosity balance in the matrix. Nonlinear diagrams of the concurrent processes of deformation of fibrous materials and microdamage of the matrix are plotted. The effect of the physical and geometrical parameters on them is studied     

考虑应变率效应的混凝土随机损伤本构模型研究

混凝土材料组分复杂且具有随机分布的特点, 其受力力学行为不可避免地存在非线性和随机性. 同时, 在动力荷载作用下, 混凝土材料具有不可忽视的率敏感性. 为了综合反映混凝土受力力学行为中的非线性、随机性与率敏感性, 本文从对材料的纳-微观裂纹扩展分析入手, 引入速率过程理论描述纳观裂纹的扩展速率, 并研究了对应的能量耗散过程. 在此基础上通过裂纹层级模型将纳观分析推演到微观尺度, 建立了微观能量耗散的基本表达式. 进而与微-细观随机断裂模型相结合, 形成了混凝土纳-微-细观随机损伤本构模型. 同时, 基于速率相关势垒的分析, 揭示了动力强度的提高源自加载速率和原子键断裂速率的竞争机制. 据此, 假定微裂纹间相互作用与应变率比值的相关关系以建立微弹簧能量耗散速率与应变率的联系, 实现了从静力本构模型向动力本构模型的扩展. 数值算例表明, 建议模型能够同时反映混凝土材料力学行为中的非线性、随机性和率敏感性. 最后通过与相关试验结果的对比, 验证了建议模型的正确性.      

A damage model with evolving nonlocal interactions

We present a damage model for softening materials with evolving nonlocal interactions. The thermodynamic implications and the material stability issue are addressed. The proposed nonlocal averaging scheme provides the obtained constitutive models with an evolving nonlocal interaction which is activated only when damage occurs. In the analysis of structures made of quasi-brittle materials, this feature helps not only to overcome some issues with the incorrect initiation of damage but also to better control the evolving size of the active fracture process zone. This is an essential feature that is usually not considered in depth in many existing nonlocal approaches to the continuum modelling of quasi-brittle fracture. Numerical examples are given to demonstrate features of the proposed modelling approach.     

Tensile fracture behavior of heterogeneous materials based on fractal geometry

Many of heterogeneous structural materials, like concrete, have different behavior under tensile stresses in comparison to their behavior under compressive stresses. The aim of this paper is to interpret behavior of such materials subjected to tensile stresses, by using newly introduced concept of fractal geometry. In the first part of this paper, tensile behavior of granular composites has been studied by using fractal geometry. It is shown that the fractality of the cross section in this kind of composites can be used to interpret the size effect on tensile strength. In fact, this work is a modification with innovations on the previous studies on fractal based size effect.This hypothesis that the fracture surfaces of quasi-brittle materials are fractals has been verified by several investigations. Accordingly, in the other part of this paper, softening process in heterogeneous materials is studied. Resulting from presented approach, a new softening curve for quasi-brittle materials is proposed. This new softening curve is denominated “Quasi-fractal softening curve” and is consisted of two parts, a linear portion in beginning part and an exponential portion in rest of the curve. This makes it very compatible to the pre-existing softening curves.