短裂纹随机行为与金属疲劳损伤的理论分析

近似求解了微裂纹演化系统随机偏微分方程。结果表明：当裂纹扩展速率的随机偏差正比于其平均速率时，材料损伤不随裂纹随机行为而变化。同时，还讨论了金属疲功损伤随机波动程度的变化趋势。     

一种微裂纹型拉伸损伤模型在混凝土材料中的应用

将包含众多不同规则微裂纹的混凝土材料视为等效微裂纹系统,结合细观微裂纹动力律与波动理论,确定了裂纹演化与应力波传播的内在关系;根据有核长大思想和能量耗散理论,建立了一种便于工程应用的混凝土类准脆性材料拉伸损伤演化方程,并由混凝土单轴拉伸实验确定了相关材料参数;进行了混凝土平板撞击和内爆炸所引起的波传播和层裂问题的数值计算。结果表明:混凝土靶板的自由面速度时程曲线呈现明显周期性震荡,震荡周期与应力波在裂片中往返一次的时间基本相同;混凝土靶板损伤空间分布和损伤云纹图与已有实验结果一致,验证了本文所建立的微裂纹型拉伸损伤模型的科学实用性。     

单轴拉伸条件下脆性岩石微裂纹损伤模型研究

利用断裂力学、损伤力学和均匀化原理,对脆性岩石单轴拉伸条件下的力学特性进行分析,建立了脆性岩石的微裂纹损伤本构模型.首先对岩石内部微裂纹的统计分布规律进行分析,给出了理论分析过程中微裂纹分布的假设条件,在此基础上,参考已有研究成果,得到含细长微裂纹脆性岩石有效弹性参数的计算公式.然后,对岩石内部单一微裂纹进行断裂力学和损伤力学分析,得到了扩展裂纹尖端的应力强度因子计算公式,在一定微裂纹断裂扩展准则和断裂扩展速率的假设基础上,利用积分原理,得到了岩石整体的损伤变量和损伤演化方程,由此建立单轴拉伸条件下脆性岩石的微裂纹损伤本构模型.最后,通过一花岗岩的单轴拉伸试验结果对微裂纹损伤本构模型进行了验证.     

SiCp/ZL101AI复合材料中的层裂微损伤演化行为

对ＳｉＣｐ／ＺＬ１０１Ａｌ复合材料进行了层裂损伤演化实验，得到了试样的层裂损伤演化图像．通过对这些微损伤演化图像的微观观察和对微损伤的统计定量分析，发现在层裂损伤演化过程中，微损伤的形成和发展不仅与应力水平、作用时间相关，而且还与材料中的微结构分布密切相关．通过层裂损伤演化实验，得到了在这种复合材料中，微裂纹在基体中的扩展速度及其与宏观应力水平的关系     

SiCp/ZL101AI复合材料中的层裂微损伤演化行为

对ＳｉＣｐ／ＺＬ１０１Ａｌ复合材料进行了层裂损伤演化实验，得到了试样的层裂损伤演化图像．通过对这些微损伤演化图像的微观观察和对微损伤的统计定量分析，发现在层裂损伤演化过程中，微损伤的形成和发展不仅与应力水平、作用时间相关，而且还与材料中的微结构分布密切相关．通过层裂损伤演化实验，得到了在这种复合材料中，微裂纹在基体中的扩展速度及其与宏观应力水平的关系     

基于局域分析的疲劳短裂纹群体演化随机模型

采用局域裂纹数密度描述金属材料中不同局部区域的疲劳短裂纹群体损伤的发展情况通过考虑在不同局域存在的材料性质的随机涨落及局部损伤对损伤总量发展的影响，建立了局域裂纹数密度演化随机方程对方程数值求解从而模拟了材料的疲劳短裂纹损伤过程结果显示出主裂纹出现的随机性，并讨论了裂纹总数与最大裂纹尺度在统计意义上的演化特征     

含微裂纹材料的损伤理论

本文从含微裂纹材料的变形能出发引出了裂纹的方位张量。在考虑裂纹受压闭合与滑动摩擦的基础上,给出了损伤张量、损伤应变及有效弹性常数。文中给出了损伤机构离散化的方法,并对方位密度给出了演化方程。最后给出一个单向拉压的应力应变关系例子,并揭示了裂纹扩展时的应力突跌现象。     

考虑微裂纹相互作用的的岩石微观力学弹塑性损伤模型研究

本文建立基于微裂纹扩展的岩石弹塑性损伤微观力学模型。用自洽方法考虑裂隙间相互影响，压缩载荷下微裂纹尖端翼裂纹稳定扩展表征岩石的微观损伤，基于应变能密度准则用Newton迭代法求复合型断裂的翼裂纹扩展长度，并采用微裂隙统计的二参数Weibull函数模型反映绝对体积应变对微裂纹分布数目影响，进而用翼裂纹扩展所表征的应力释放体积和微裂纹数目来表示含有微裂隙的岩石损伤演化变量；宏观塑性屈服函数采用Voyiadjis等的等效塑性应变的硬化函数，反映塑性内变量对硬化函数的影响；建立岩石的弹塑性损伤本构关系及其数值算法，并用回映隐式积分算法编制了弹塑性损伤模型的程序。从围压和微裂隙长度等因素分析弹塑性损伤模型的岩石的损伤和宏观塑性特性。     

升温热冲击环境下超高温陶瓷材料抗热震性能的热-损伤模型

在现有的抗热震理论基础上考虑到超高温陶瓷材料热物理性能对温度的敏感性及损伤在其使役历程中随温度的演化,建立了适用于升温服役环境下表征超高温陶瓷材料抗热震性能的热-损伤模型。该模型考虑了微裂纹尺寸、密度、热冲击环境温度等因素对材料抗热震性能的影响。利用此模型研究了超高温陶瓷材料在升温服役环境下损伤以微裂纹形核规律演化时对其抗热震性能的影响。从理论上验证了基于材料微结构设计思想在制备超高温陶瓷材料时,引进一定密度一定尺寸的微裂纹并控制其随温度演化规律以形核方式进行,既可以使材料保持较高的强度又能大幅度提升材料的抗热震性能。     

粉末冶金材料各向异性连续型损伤模型研究

在采用微裂纹扩展区描述脆性材料损伤状态的基础上,通过引入颗粒度大小和微裂纹概率分布密度函数来研究粉末冶金材料特征体积单元的损伤演化.同时结合Hill自洽模型采用空间混合平均的方法,可考虑粉末冶金材料的微结构特征及微裂纹间相互作用的影响,可描述粉末冶金类材料的各向异性连续型损伤.     

Formulation of statistical evolution of microcracks in solids

The paper presents a principal formulation of statistical evolution of microcracks, occurring in solids, subjected to external loading. In particular, the concept of ideal microcracks is elaborated, in order to describe the fundamental features of damage resulting from nucleation and extension of microcracks. Relevant average damage functions are also discussed. The project partially supported by National Natural Science Foundation of China     

Anisotropic damage law of evolution

A formulation for anisotropic damage is established in the framework of the principle of strain equivalence. The damage variable is still related to the surface density of microcracks and microvoids and, as its evolution is governed by the plastic strain, it is represented by a second order tensor and is orthotropic. The coupling of damage with elasticity is written through a tensor on the deviatoric part of the energy and through a scalar taken as its trace on the hydrostatic part. The kinetic law of damage evolution is an extension of the isotropic case. Here, the principal components of the damage rate tensor are proportional to the absolute value of principal components of the plastic strain rate tensor and are a nonlinear function of the effective elastic strain energy. The proposed damage evolution law does not introduce any other material parameter. Several series of experiments on metals give a good validation of this theory. The coupling of damage with plasticity and the quasi-unilateral conditions of partial closure of microcracks naturally derive from the concept of effective stress. Finally, a study of strain localization makes it possible to determine the critical value of the damage at mesocrack initiation.     

Influence of lateral confinement on dynamic damage evolution during uniaxial compressive response of brittle solids

A dynamic damage growth model applicable to brittle solids subjected to biaxial compressive loading is developed. The model incorporates a dynamic fracture criterion based on wing-crack growth model with a damage evolution theory based on a distribution of pre-existing microcracks in a solid. Influences of lateral confinement pressure (dynamic or static) as well as frictional coefficient on the rate dependence of fracture strength of basalt-rock are investigated systematically. It is found that the failure strength, damage accumulation and wing-crack growth rate are strongly influenced by the nature and the magnitude of confinement pressure. It is also verified that the effect of strain rate on fracture strength of brittle solids is independent of confinement pressure in a certain range of strain rate.     

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.     

Analysis of cracked magnetoelectroelastic composites under time-harmonic loading

This paper presents a numerical model for the analysis of cracked magnetoelectroelastic materials subjected to in-plane mechanical, electric and magnetic dynamic time-harmonic loading. A traction boundary integral equation formulation is applied to solve the problem in combination with recently obtained time-harmonic Green’s functions (Rojas-Diaz et al., 2008). The hypersingular boundary integral equations appearing in the formulation are first regularized via a simple change of variables that permits to isolate the singularities. Relevant fracture parameters, namely stress intensity factors, electric displacement intensity factor and magnetic induction intensity factor are directly evaluated as functions of the computed nodal opening displacements and the electric and magnetic potentials jumps across the crack faces. The method is checked by comparing numerical results against existing solutions for piezoelectric solids. Finally, numerical results for scattering of plane waves in a magnetoelectroelastic material by different crack configurations are presented for the first time. The obtained results are analyzed to evaluate the dependence of the fracture parameters on the coupled magnetoelectromechanical load, the crack geometry and the characteristics of the incident wave motion.     

PROGRESSIVE FRACTURE MODELING OF THE FAILURE WAVE IN IMPACTED GLASS

The failure wave has been observed propagating in glass under impact loading since 1991. It is a continuous fracture zone which may be associated with the damage accumulation process during the propagation of shock waves. A progressive fracture model was proposed to describe the failure wave formation and propagation in shocked glass considering its heterogeneous meso-structures. The original and nucleated microcracks will expand along the pores and other defects with concomitant dilation when shock loading is below the Hugoniot Elastic Limit. The governing equation of the failure wave is characterized by inelastic bulk strain with material damage and fracture. And the inelastic bulk strain consists of dilatant strain from nucleation and expansion of microcracks and condensed strain from the collapse of the original pores. Numerical simulation of the free surface velocity was performed and found in good agreement with planar impact experiments on K9 glass at China Academy of Engineering Physics. And the longitudinal, lateral and shear stress histories upon the arrival of the failure wave were predicted, which present the diminished shear strength and lost spall strength in the failed layer.     

Damage and self-similarity in fracture

Consider applications of damage mechanics to material failure. The damage variable introduced in damage mechanics quantifies the deviation of a brittle solid from linear elasticity. An analogy between the metastable behavior of a stressed brittle solid and the metastable behavior of a superheated liquid is established. The nucleation of microcracks is analogous to the nucleation of bubbles in the superheated liquid. In this paper we have applied damage mechanics to four problems. The first is the instantaneous application of a constant stress to a brittle solid. The results are verified by applying them to studies of the rupture of chipboard and fiberglass panels. We then obtain a solution for the evolution of damage after the instantaneous application of a constant strain. It is shown that the subsequent stress relaxation can reproduce the modified Omori’s law for the temporal decay of aftershocks following an earthquake. Obtained also are the solutions for application of constant rates of stress and strain. A fundamental question is the cause of the time delay associated with damage and microcracks. It is argued that the microcracks themselves cause random fluctuations similar to the thermal fluctuations associated with phase changes.     

Fractal analysis of fracture in concrete

Experimental results indicate that propagation paths of cracks in concrete are often irregular, producing rough fracture surfaces which are fractal. Based on dynamic analysis of microcrack coalescence, this paper presents a statistical fractal model to describe the damage evolution of concrete. The model demonstrates that the mechanism of fracture surfaces formed in concrete is closely related to the dynamic processes of the cascade coalescence of microcracks. A unimodal relation between the fractal dimension and the coalescence threshold can qualitatively explain the relation between fractal dimension and fracture energy.     

损伤和断裂的统一

本文讨论了连续损伤力学基础的缺陷,从微裂纹随机演化出发给损伤概念作出新的普适的统计定义,导出了损伤断裂几率的动力学方程,使损伤、断裂、统计、微观机理及宏观特性五者有机地相结合,从而有可能形成一个统一的损伤断裂微观统计理论。