A micromechanical damage theory for brittle materials with small cracks

For brittle solids containing numerous small cracks, a micromechanical damage theory is presented which accounts for the interactions between different small cracks and the effect of the boundary of a finite solid, and includes growth of the pre-existing small cracks. The analysis is based on a superposition scheme and series expansions of the complex potentials. The small crack evolution process is simulated through the use of fracture mechanics incorporating appropriate failure criteria. The stress-strain relations are obtained from the micromechanics analysis. Typical examples are given to illustrate the potential capability of the proposed theory. These results show that the present method provides a direct and efficient approach to deal with brittle finite solids containing multiple small cracks. The stress-strain relation curves are evaluated for a rectangular plate containing small cracks.

The elasto-damage theory of the components assembling model

The potential energy in materials is well approximated by pair functional which is composed of pair potentials and embedding energy. During calculating material potential energy, the orientational component and the volumetric component are derived respectively from pair potentials and embedding energy. The sum of energy of all these two kinds of components is the material potential. No matter how microstructures change, damage or fracture, at the most level, they are all the changing and breaking atomic bonds. As an abstract of atomic bonds, these components change their stiffness during damaging. Material constitutive equations have been formulated by means of assembling all components' response functions. This material model is called the component assembling model. Theoretical analysis and numerical computing indicate that the proposed model has the capacity of reproducing some results satisfactorily, with the advantages of great conceptual simplicity, physical explicitness, and intrinsic induced anisotropy, etc.

微裂纹细观损伤理论

材料的宏细观破坏理论是当前固体力学和材料科学研究的一个重要课题。本文在对连续损伤理论和细观损伤理论进行评述的基础上，着重研究了脆性材料中微裂纹细观损伤问题。本文建立了一套完整的细观损伤理论来分析二维多裂纹体问题。该理论的基本方法是基本解叠加法，此方法直接考虑了微裂纹之间的相互作用以及有限边界的影响。通过叠加原理，使在裂纹面和外边界满足边界条件，用边界配置法化控制方程组为线性方程组，进行数值求解。本文以裂纹密度为参量，针对微裂纹随机分布和平行分布两种情况，计算了无限大体中代表性体元（VRVE）和多裂纹有限体的有效弹性模量。数值计算结果表明，本文所用方法具有统一与直能的优点，采用此法所得模量与试验结果吻合，在处理多裂纹体问题时计算效率高、精度好，对求解多裂纹问题非常有效。此外，通过建立微裂纹晶内扩展准则和穿晶扩展准则，分析了微裂纹扩展连接直至裂纹形成、扩展这一全过程的细观力学行为，对微裂纹的损伤演化过程进行了直接模拟，计算了含微裂纹矩形板的宏观应国变关系曲线。本文进一步提出了三维微裂纹相互作用的数学分析方法 — 扁球坐标和位移函数法，并采用边界配置法或裂纹面面力平均化方法进行求解。数值结果表明，扁球坐标和位移函数法分析三维微裂纹的相互作用问题是有效可行的。最后，本文提出了埋入基体的镶嵌体胞模型，建立了计算非均质体有效弹性模量的解析表达式。该式从理论上讲是严格的，且具有形式简单、内涵丰富及有效弹性模量能显式表达等优点。针对球体含球形夹杂、裂纹及旋转扁球体含球形夹杂、裂纹等不同体胞结构计算了其有效弹性模量，并与其他细观力学方法所得结果进行了比较。本文还将埋入基体的镶嵌体胞模型进行了发展，研究了二相颗粒复合材料的弹塑性本构关系（基体为弹性而颗粒为塑性材料），计算了球体含球形颗粒用旋转扁球体含扁球状颗粒两种体胞结构的宏观应力 - 应变曲线。

The development of an inhomogeneous damage field in an elastic-plastic model

By making use of the evolution equation of the damage field as derived from the statistical mesoscopic damage theory, we have preliminarily examined the inhomogeneous damage field in an elastic-plastic model under constant-velocity tension. Three types of deformation and damage field evolution are presented. The influence of the plastic matrix is examined. It seems that matrix plasticity may defer the failure due to damage evolution. A criterion for damage localization is consistent with the numerical results.

三峡库区巴东组泥灰岩溶蚀作用与岩体力学性质弱化研究

Abstract The karsrt erosion engineering geology became a highlight problem in recent years, in particularly, the karst erosion of marlite of Badong formation made the rock mechanics weaken in Three Gorges Reservoir area, which reduces the safety of slope. During the immigrant construction, many high slopes have been formed, whose instabilities problems pose serious threats to the safety of the people and properties. The accidents of the slope failure take place now and then. By testing, it has been found that the karst erosion pattern and dissolution rate of marlite are not weaker than that of the pure limestone. Furthermore, owning to the weathering and unloading, the karst erosion of the marlite will reach certain depth of the slope, which is named infiltrated karst erosion. The karst erosion made the rock mass quality of slope or foundation worse in a large scale. The karst erosion geological disasters, taken place or not, has become the main restrictive factors to the social stability and economic development. Thus the karst erosion process and mechanism of marlite of Badong formation are studied as the main content of this dissertation. The weakening characteristic of rock mass mechanics parameters are studied along with the rock mass structure deformation and failure processes in the course of the karst erosion. At first, the conditions and influencing factors of the karst erosion are analyzed in the investigative region, on the basis of different karst erosion phenomenon of the marlite and different failure modes of slope. Then via indoor the karst erosion tests, it is analyzed that the karst erosion will change the rock mass composition and its structure. Through test, the different karst erosion phenomena between micro and macro have been observed, and the karst erosion mechanism of the marlite has been summarized. Damage theory is introduced to explain the feature of dissolution pore and the law of crack propagation in the marlite. By microscope and the references data, it can be concluded that the karst erosion process can be divided into rock minerals damage and rock structural damage. And the percent of karst erosion volume is named damage factor, which can be used to describe the quantify karst erosion degree of marlite. Through test, the rock mechanical properties in the different period of karst erosion are studied. Based on the damage mechanics theory and the test result, the relation between the karst erosion degree of marlite and weakening degree of mechanical properties is summarized. By numerical simulations, the karst erosive rock mass mechanics is verified. The conclusion is drawn as below: to the rock mass of marlite, the karst erosion damage made mechanics parameters variation, the deformation modulus, cohesion, and inter friction angle reduce as the negative exponent with the increasing of the karst erosion volume, however, the Poisson ratio increases as the positive exponent with the karst erosion volume increasing. It should be noticed that the deduced formulations are limited to the test data and certain conditions. It is suitable to the rock mass parametric weakening process after the karst erosion of marlite in Three Gorges Reservoir area. Based on the failure types of marlite slope in the field, the karst erosion and weathering process of rock mass are analyzed. And the evolution law of deformation and failure of the marlite mass is studied. The main failure feature of the marlite slope is the karst erosive structure subsidence mode in Three Gorges Reservoir area. The karst erosive structure subsidence mode is explained as follows: the rock mass undergoes the synthetic influence, such as weathering, unloading, corrosion, and so on, many pores and cavities have been formed in the rock mass interior, the rock mass quality is worsen and the rock mass structure is changed, and then the inherent structure of rock mass is collapsed under its gravity, therefore, the failure mode of compaction and subsidence take place. Finally, two examples are used to verify the rock mass parameters in Three Gorges Reservoir area, and the relationship between the marlite slope stability and the time of karst erosion is proposed.

3D Anisotropic Elastoplastic-Damage Model and its Application in Simulating the Behavior of Rock Materials

A 3D anisotropic elastoplastic-damage model was presented based on continuum damage mechanics theory. In this model, the tensor decomposition technique is employed. Combined with the plastic yield rule and damage evolution, the stress tensor in incremental format is obtained. The derivate eigenmodes in the proposed model are assumed to be related with the uniaxial behavior of the rock material. Each eigenmode has a corresponding damage variable due to the fact that damage is a function of the magnitude of the eigenstrain. Within an eigenmodes, different damage evolution can be used for tensile and compressive loadings. This model was also developed into finite element code in explicit format, and the code was integrated into the well-known computational environment ABAQUS using the ABAQUS/Explicit Solver. Numerical simulation of an uniaxial compressive test for a rock sample is used to examine the performance of the proposed model, and the progressive failure process of the rock sample is unveiled.

An incremental micromechanical scheme for nonlinear particulate composites

A general incremental micromechanical scheme for the nonlinear behavior of particulate composites is presented in this paper. The advantage of this scheme is that it can reflect partly the effects of the third invariant of the stress on the overall mechanical behavior of nonlinear composites. The difficulty involved is the determination of the effective compliance tensors of the anisotropic multiphase composites. This is completed by making use of the generalized self-consistent Mori-Tanaka method which was recently developed by Dai et al. (Polymer Composites 19(1998) 506-513; Acta Mechanica Solida 18 (1998) 199-208). Comparison with existing theoretical and numerical results demonstrates that the present incremental scheme is quite satisfactory. Based on this incremental scheme, the overall mechanical behavior of a hard-particle reinforced metal matrix composite with progressive particle debonding damage is investigated.

The ultrafast excitation processes in femtosecond laser-induced damage in dielectric omnidirectional reflectors

A pump and probe system is developed, where the probe pulse duration tau is less than 60 fs while the pump pulse is stretched up to 150-670 fs. The time-resolved excitation processes and damage mechanisms in the omnidirectional reflectors SiO2/TiO2 and ZnS/MgF2 are studied. It is found that as the pump pulse energy is higher than the threshold value, the reflectivity of the probe pulse decreases rapidly during the former half, rather than around the peak of the pump pulse. A coupled dynamic model based on the avalanche ionization (AI) theory is used to study the excitation processes in the sample and its inverse influences on the pump pulse. The results indicate that as pulse duration is longer than 150 fs, photoionization (PI) and AI both play important roles in the generation of conduction band electrons (CBEs); the CBE density generated via AI is higher than that via PI by a factor of 10(2)-10(4). The theory explains well the experimental results about the ultrafast excitation processes and the threshold fluences. (c) 2006 American Institute of Physics.

Ultraviolet-infrared femtosecond laser-induced damage in fused silica and CaF2 crystals

The damage in fused silica and CaF2 crystals induced by wavelength tunable femtosecond lasers is studied. The threshold fluence is observed to increase rapidly with laser wavelength lambda in the region of 250-800 nm, while it is nearly a constant for 800 damage in dielectrics irradiated by the visible and near ultraviolet femtosecond lasers. Our theory explains well the experiments.

A New theory for evaluating the number density of inclusions in films

A new formulation derived from thermal characters of inclusions and host films for estimating laser induced damage threshold has been deduced. This formulation is applicable for dielectric films when they are irradiated by laser beam with pulse width longer than tens picoseconds. This formulation can interpret the relationship between pulse-width and damage threshold energy density of laser pulse obtained experimentally. Using this formulation, we can analyze which kind of inclusion is the most harmful inclusion. Combining it with fractal distribution of inclusions, we have obtained an equation which describes relationship between number density of inclusions and damage probability. Using this equation, according to damage probability and corresponding laser energy density, we can evaluate the number density and distribution in size dimension of the most harmful inclusions. (c) 2005 Elsevier B.V. All rights reserved.

Thermodynamic damage mechanism of transparent films caused by a low-power laser

A new model for analyzing the laser-induced damage process is provided. In many damage pits, the melted residue can been found. This is evidence of the phase change of materials. Therefore the phase change of materials is incorporated into the mechanical damage mechanism of films. Three sequential stages are discussed: no phase change, liquid phase change, and gas phase change. To study the damage mechanism and process, two kinds of stress have been considered: thermal stress and deformation stress. The former is caused by the temperature gradient and the latter is caused by high-pressure drive deformation. The theory described can determine the size of the damage pit. (c) 2006 Optical Society of America.

Influence of substoichiometer on the laser-induced damage characters of HfO2 thin films

HfO2 is one of the most important high refractive index materials for depositing high power optical mirrors. In this research, HfO2 thin films were prepared by dual-ion beam reactive sputtering method, and the laser-induced damage thresholds (LIDT) of the sample were measured in 1-on-1 mode for laser with 1064 nm wavelength. The results indicate that the LIDT of the as-grown sample is only 3.96 J/cm(2), but it is increased to 8.98 J/cm(2) after annealing under temperature of 200 degrees C in atmosphere. By measuring the laser weak absorption and SIMS of the samples, we deduced that substoichiometer is the main reason for the low LIDT of the as-grown sample, and the experiment results were well explained with the theory of electronic-avalanche ionization. (C) 2008 Elsevier B.V. All rights reserved.

Relationship between load/unload response ratio and damage variable and its application

The physics-based parameter: load/unload response ratio (LURR) was proposed to measure the proximity of a strong earthquake, which achieved good results in earthquake prediction. As LURR can be used to describe the damage degree of the focal media qualitatively, there must be a relationship between LURR and damage variable (D) which describes damaged materials quantitatively in damage mechanics. Hence, based on damage mechanics and LURR theory, taking Weibull distribution as the probability distribution function, the relationship between LURR and D is set up and analyzed. This relationship directs LURR applied in damage analysis of materials quantitatively from being qualitative earlier, which not only provides the LURR method with a more solid basis in physics, but may also give a new approach to the damage evaluation of big scale structures and prediction of engineering catastrophic failure. Copyright (c) 2009 John Wiley & Sons, Ltd.

Relationship between load/unload response ratio and damage variable and its application

The physics-based parameter: load/unload response ratio (LURR) was proposed to measure the proximity of a strong earthquake, which achieved good results in earthquake prediction. As LURR can be used to describe the damage degree of the focal media qualitatively, there must be a relationship between LURR and damage variable (D) which describes damaged materials quantitatively in damage mechanics. Hence, based on damage mechanics and LURR theory, taking Weibull distribution as the probability distribution function, the relationship between LURR and D is set up and analyzed. This relationship directs LURR applied in damage analysis of materials quantitatively from being qualitative earlier, which not only provides the LURR method with a more solid basis in physics, but may also give a new approach to the damage evaluation of big scale structures and prediction of engineering catastrophic failure. Copyright (c) 2009 John Wiley & Sons, Ltd.