Damage and fracture: Classical continuum theories

This paper reports the research results on the continuum theory of damage which goes back to the works of Kachanov, Gurson, and Rabotnov. In these models, internal variables that generally have different mathematical structure are explicitly introduced to constitutive relations. The internal variables describe a non-oriented (using scalar damage parameters) or oriented (using different-order tensors) damage distribution in the material. Then, a fracture criterion is introduced based on mechanical or thermodynamic considerations. Models of this type are still most frequently used in the structural analysis of strength of some materials (e.g., composites). Since damage nucleation and growth are closely related to strain localization, consideration is given to formulations and methods for analyzing the stability of inelastic deformation processes. Much attention is given to the effect of the finite element mesh on simulation results, to solution algorithms for such problems, and to the possibilities of using non-local constitutive models. The studies that use gradient models are also included, because damage formation is associated with sharp spatial variations of kinematic and/or dynamic characteristics which must be described by non-classical constitutive relations (gradient, non-local, micromorphic continuum).     

Dynamic fatigue

Dynamic fatigue differs from quasi-static fatigue in the spall damage nature. A consequence of the spall nature is the alternate appearance of longitudinal cracks, each of which becomes the source of rarefaction. The focusing or interference of rarefaction waves specifies the sites of nucleation and growth of channel and ring cracks; therefore, initially existing surface defects are not operative. Another consequence of the spall damage nature is the determining effect of the orientation of the lateral faces of flyer plates having finite dimensions, since these faces specify the intensity of the appearing lateral rarefaction wave.     

A multiscale coupling method for the modeling of dynamics of solids with application to brittle cracks

We present a multiscale model for numerical simulations of dynamics of crystalline solids. The method combines the continuum nonlinear elasto-dynamics model, which models the stress waves and physical loading conditions, and molecular dynamics model, which provides the nonlinear constitutive relation and resolves the atomic structures near local defects. The coupling of the two models is achieved based on a general framework for multiscale modeling – the heterogeneous multiscale method (HMM). We derive an explicit coupling condition at the atomistic/continuum interface. Application to the dynamics of brittle cracks under various loading conditions is presented as test examples.     

基于八面体理论的岩石循环加-卸载本构模型及修正

探究岩石的受力特点及破坏特性是研究岩石地下工程安全性的关键,诸多学者都期望能在岩石本构模型的研究上取得突破性进展。在此背景下,提出了一种能够描述循环加-卸载条件下岩石的本构模型。首先,假设岩石的微元强度服从八面体剪应力理论并且微元破坏服从Weibull概率公式,将岩石本构中的损伤变量以及岩石微元强度表达式里包含的损伤因子进行本构变换,得到关于应力、应变等其他表现加-卸载下岩石损伤本构模型的参数,表示出岩石微元强度和损伤变量,再将得到的岩石微元强度和损伤变量代入所提出的岩石本构模型中,并进行等式变换得到一个函数表达式。通过将其与实验数据进行拟合对比分析,得出修正后的拟合参数,将其代入函数式中,得到损伤本构模型的修正式。最后将拟合参数进行必要的敏感性分析,得出各拟合参数的实际物理意义。     

Damage and fracture: Review of experimental studies

This paper is a part of a review of recent (last 15 years) publications on experimental and theoretical methods and approaches for studying damage accumulation and fracture in crystalline solids. The first part of the review is devoted to the experimental studies that examine the physical mechanisms of microdamage nucleation and growth under various thermomechanical loads, physical and mechanical properties of materials, and the issues concerning the formation and growth of main cracks and transition to macrofracture. Particular attention is given to the studies of fatigue failure of various metals and alloys, particularly the features of micro- and macrodamage nucleation and growth in structures and specimens at different loading cycle parameters, and the effect of grain size, solid phase inclusions, grain boundaries, twins, etc. on damage evolution. A whole variety of modern approaches to the experimental study (including in situ studies) of specimen structure and stress-strain state is shown. Disadvantages of current experimental studies on damage and fracture are discussed, such as insufficient attention to the scale factor and determination of the representative volume for fracture analysis.     

Cyclic deformation of polycrystalline Cu films

Fatigue impairs the reliability of macroscopic metallic components utilized in a variety of technological applications. However, the fatigue behaviour of thin metal films and small-scale components used in microelectronics and mechanical microdevices has yet to be explored in detail. The fatigue behaviour in submicrometre thin films is likely to differ from that in bulk material, since the volume necessary for the formation of dislocation structures typical of cyclic deformation in bulk material is larger than that available in thin films. The thin-film dimensions and microstructure, therefore, affect the microscopic processes responsible for fatigue. The fatigue behaviour of Cu films 0.4, 0.8 and 3.0 µm thick on polyimide substrates was investigated. The specimens were fatigued at a total strain amplitude of 0.5% using an electromechanical tensile-testing machine. This work focuses on the characterization of fatigue mechanisms and the resulting fatigue damage of thin Cu films. Extrusions similar to those observed in bulk material were found at the film surfaces after cyclic loading. Voids observed beneath the extrusions, close to the film-substrate interface, contributed significantly to thin-film failure. Thinner films were more fatigue resistant and contained fewer and smaller extrusions than thicker films did. A small thickness appears to inhibit void nucleation. This observation is explained in terms of vacancy diffusion and annihilation at free surfaces or grain boundaries. Transmission electron microscopy investigations confirmed that no long-range dislocation structures have developed during fatigue loading of the films investigated.     

Modeling nonlinearities of ultrasonic waves for fatigue damage characterization: Theory,simulation, and experimental validation

A dedicated modeling technique for comprehending nonlinear characteristics of ultrasonic waves traversing in a fatigued medium was developed, based on a retrofitted constitutive relation of the medium by considering the nonlinearities originated from material, fatigue damage, as well as the “breathing” motion of fatigue cracks. Piezoelectric wafers, for exciting and acquiring ultrasonic waves, were integrated in the model. The extracted nonlinearities were calibrated by virtue of an acoustic nonlinearity parameter. The modeling technique was validated experimentally, and the results showed satisfactory consistency in between, both revealing: the developed modeling approach is able to faithfully simulate fatigue crack-incurred nonlinearities manifested in ultrasonic waves; a cumulative growth of the acoustic nonlinearity parameter with increasing wave propagation distance exists; such a parameter acquired via a sensing path is nonlinearly related to the offset distance from the fatigue crack to that sensing path; and neither the incidence angle of the probing wave nor the length of the sensing path impacts on the parameter significantly. This study has yielded a quantitative characterization strategy for fatigue cracks using embeddable piezoelectric sensor networks, facilitating deployment of structural health monitoring which is capable of identifying small-scale damage at an embryo stage and surveilling its growth continuously.     

Critical measurements for validation of constitutive equations under shock and impact loading conditions

Interpretation of the data often requires numerical simulations of the experiments and comparisons with the data. However, determination of an appropriate set of values for parameters in constitutive equations valid under shock and high strain rate loading remains one of the most difficult tasks for material model developers. Most researchers employ experimental data obtained under idealized stress/strain states in the model parameter calibration scheme. Since the dynamic response of materials is very complex, especially the failure response, the generality of the model parameters is highly questionable. For example, the fracturing of ceramic materials involves nucleation, propagation, and coalescence of microcracks under shock and impact. The dynamic deformation processes in ceramics include dynamic pore collapse, dislocation generation, twinning, and microcracking. When shocked above the Hugoniot elastic limit, the ceramic deformation becomes inelastic; therefore, the constitutive model formulation should consider modeling the effects of these various processes on the degradation of strength and stiffness of ceramic. This paper presents a brief summary of diagnostic measurements and modeling techniques associated with validation and verification of ceramic constitutive/damage models under high strain rate, shock, and penetration loading applications.     

Kinetics of defect accumulation and duality of the weller curve in gigacycle fatigue of metals

We propose a model describing the kinetics of accumulation of defects under cyclic loading in metals. Analysis of experimental data on the initial defect distribution and of the role of the free surface of the sample in straining makes it possible to explain the features of generation of fatigue cracks in the bulk, which is typical of the gigacycle fatigue regime at a low stress level. The duality of the Weller curve in the gigacycle fatigue regime is attributed to the emergence of a fine-grain region in the form of a dissipative peaking structure in the defect ensemble.     

An energy-equilibrium model for complex stress effect on fatigue crack initiation

Based on Tanaka and Mura’s fatigue model and Griffith theory for fracture,an energy-equilibrium model was proposed to explain the complex stress effect on fatigue behavior.When the summation of the elastic strain energy release and the stored strain energy of accumulated dislocations reach the surface energy of a crack,the fatigue crack will initiate in materials.According to this model,for multiaxial stress condition,the orientation of the crack initiation and the initiation life can be deduced from the energy equilibrium equation.For the uniaxial fatigue loading with mean stress,the relation between the maximum stress or the minimum stress and the stress amplitude is in agreement with an ellipse equation on the constant life diagram.If the ratio of the mean stress to stress amplitude is less than a critical value-0.17,and the stress amplitude keeps constant,the fatigue crack initiation life will decrease with the increase of the compress mean stress.In this model,the mean stress does not cause damage accumulation with the fatigue cycles in crack initiation.For this reason,the loading sequence of different load levels would induce the cumulative damage to deviate from the Palmgren-Miner cumulative damage rule.The procedure of estimating the damage under random loading is also discussed.     

Experimental and theoretical study of multiscale damage-failure transition in very high cycle fatigue

Multiscale mechanisms of failure of metals (Armco iron, titanium, aluminum) are studied for high cycle and very high cycle fatigue. By correlating with the results of structural studies, a theoretical approach is developed to describe fatigue crack kinetics in damaged material under high cycle and very high cycle fatigue loading conditions. Stages of crack nucleation and propagation are analyzed using the profilometry data from the fracture surface. The scale invariance of fracture surface roughness is established, which allows an explanation of the self-similar nature of fatigue crack kinetics under high cycle and very high cycle fatigue. Variation of elastic-plastic properties of Armco iron under very high cycle fatigue is studied using an acoustic resonance method. It is found that the material density decreases during fatigue damage accumulation, with the minimum of the material density in the bulk of the specimen.     

冲击载荷下混凝土本构模型构建研究

 在对混凝土动态力学性能和现有本构模型综合分析的基础上,构建了一个新的适用于冲击响应问题数值分析的混凝土本构模型。该本构模型全面考虑了压力、应力第三不变量、变形的硬化和软化、应变率强化以及拉伸损伤等各个影响因素。将其加入LTZ-2D程序,确定了本构模型参数,对混凝土靶板的穿透问题进行了数值验证分析。计算得到的弹体剩余速度同实验结果基本一致,同时得到了混凝土靶板破裂的计算图像。计算结果及其分析表明,所构建的本构模型能够较好地反映冲击载荷作用下混凝土动态响应的主要特性。     

基于粘结界面模型的三维裂纹扩展研究

根据界面断裂的特点,将粘结界面模型应用于有限元,采用非线性显式动力学算法,编写粘结-体积单元计算程序.其中体积和粘结单元分别采用四面体和三棱柱单元;粘结单元本构关系选择双线性内聚力-位移曲线,避免了界面完全断裂后发生穿透;以界面相对位移的形式定义线性损伤准则;以Benzeggagh-Kenane模式的扩展准则确定界面失效位移;以Turon模式的初始损伤准则确定界面启裂位移.该程序能够实现混合加载模式下材料界面断裂问题的三维数值模拟.用所编写的程序(CVFEM)分别对Ⅰ,Ⅱ,Ⅲ型裂纹扩展问题进行数值模拟,并且与Abaqus6.7计算结果进行对比.     

Non-local theory solution of two collinear mode-I permeable cracks in a magnetoelectroelastic composite material plane

The non-local theory solution of two collinear mode-I permeable cracks in a magnetoelectroelastic composite material plane was investigated using the generalized Almansi's theorem and the Schmidt method. The problem was formulated through Fourier transform into two pairs of dual integral equations, in which the unknown variables are the jumps in displacements across the crack surfaces. To solve the dual integral equations, the displacement jumps across the crack surfaces were directly expanded as a series of Jacobi polynomials. Numerical examples were provided to show the effects of crack length, the distance between two collinear cracks and the lattice parameter on the stress field, the electric displacement field and the magnetic flux field near the crack tips. Unlike the classical elasticity solutions, it is found that no stress, electric displacement or magnetic flux singularities are present at the crack tips in a magnetoelectroelastic composite material plane. The non-local elastic solutions yield a finite hoop stress at the crack tip, thus allowing us to use the maximum stress as a fracture criterion.     

Nucleation of cracks near the free surface in deformed metallic nanomaterials with a bimodal structure

A theoretical model that effectively describes the nucleation of cracks in stress fields of dislocation pile-ups near the free surface in metallic nanomaterials with a bimodal structure has been developed. The dependences of the critical shear stress τ_c (for the formation of a crack with an equilibrium length of 10 nm on a dislocation pile-up near the surface) on the size d of a grain containing the dislocation pile-up have been calculated for copper with a bimodal structure. Theoretically, it has been found that the critical shear stress τ_c for the nucleation of a crack near the free surface in a nanomaterial with a bimodal structure is approximately 30% higher than that for the crack nucleation within the nanomaterial at a distance from the free surface.     

高应变率下TC4及TC9钛合金的动态断裂

 报导了由短脉冲激光引起的应力波加载及电炮驱动Mylar膜平面飞片碰撞TC4、TC9钛合金靶的实验及数值计算研究结果。由回收靶样品的金相分析表明：在电炮驱动飞片碰撞及由激光引起的应力波加载所造成的应变率分别在10⁶ s^-1左右及10⁷ s^-1以上两种情形下，TC4、TC9钛合金的层裂特性都是以微孔洞的成核、增长、汇合为特征的韧性断裂。运用一维流体弹塑性动力学程序进行数值研究表明：成核增长NAG模型在一定程度上可以用来描述高应变率下TC4、TC9钛合金的损伤破坏特性。     

Plate bending investigations by comparative holographic moiré interferometry. Evaluation by the finite-element method

Bending of clamped defect-containing and defect-free circular plates, subjected to equal uniformly distributed loading is investigated. Using the finite-element method (FEM), a numerical model is produced and the results from the numerical computations are compared with those from a holographic experiment, based on comparative holographic moiré interferometry (CHMI). The theoretical and experimental approach to solving the problem is discussed and the measurement accuracy is analyzed. Good agreement between the numerical and experimental results is observed. The possibility of applying the techniques developed to a wide scope of mechanical problems in non-destructive testing (detection of hidden defects, cracks and debonds, as well as investigations on material fatigue and plastic deformations) is pointed out.