Energy-based equivalence between damage and fracture in concrete under fatigue

Damage in concrete members, occur in a distributed manner due to the formation and coalescence of micro-cracks, and this can easily be described through a local damage approach. During subsequent loading cycles, this distributed zone of micro-cracks get transformed into a major crack, introducing a discrete discontinuity in the member. At this stage, concepts of fracture mechanics could be used to describe the behavior of the structural member. In this work, an approach is developed to correlate fracture and damage mechanics through energy equivalence concepts and to predict the damage scenario in concrete under fatigue loading. The objective is to smoothly move from fracture mechanics theory to damage mechanics theory or vice versa in order to characterize damage. The analytical methods developed here have been exemplified with some already available data in the literature. The strength and stiffness reduction due to progressive cracking or increase in damage distribution, has been characterized using the available indices such as the strength reduction and stiffness reduction factors. It is seen through numerical examples, that the strength and stiffness drop indices using fracture and damage mechanics theory agree well with each other. Hence, it is concluded, that through the energy approach a discrete crack may be modeled as an equivalent damage zone, wherein both correspond to the same energy loss. Finally, it is shown that by knowing the critical damage zone dimension, the critical fracture property such as the fracture energy can be obtained.     

Experimental evaluation of the strength distribution of E-glass fibres at high strain rates

A bimodal Weibull distribution function was applied to analyse the strength distribution of glass fibre bundles under tensile impact. The simulation was performed using a one-dimensional damage constitutive model. The results show that there were two concurrent flaw populations in the fracture process. The regression analysis using the bimodal Weibull distribution function was in good agreement with experiment.     

Statistical investigation of the fracture behaviour of inhomogeneous materials in tension and three-point bending

Development of damage in heterogeneous materials submitted to tensile tests and flexural tests is analysed using finite element analysis and considering statistical distribution of material strength. Materials are assumed to have a brittle local behaviour and fracture stresses are distributed randomly through test specimens. Also, the analysis considers that it exists a dimension which is characteristic of damage growing, depending on the fracture processes induced. A simulation procedure for evaluating damage development through test specimens is next implemented and the influence of the scattering width of the fracture stress distributions is analysed.     

Modelling the effect of temperature and damage on the fracture strength of ultra-high temperature ceramics

A fracture strength theoretical model for ultra-high temperature ceramics is proposed in which both high temperature dependency and damage dependency are considered. The model accounts for the effects of temperature, crack size and damage accumulation on fracture strength. Predictions are presented for TiC and compared with experimental results obtained at different temperatures. The dependency of fracture strength on several parameters is discussed. The sensitivity of fracture strength to crack size declines rapidly as temperature rises, while its sensitivity to Young??s modulus increases rapidly as temperature rises.     

The structural strength of glass: hidden damage

We discuss “hidden damage” of glass by the rolling process, which results in heterogeneous distribution of microcracks on the edge surface of glass element, which are the fracture source deteriorating glass element strength. It is shown that removal of this damage on the edges of glass elements increases the engineering strength of float glass significantly. Using the “hidden damage” approach, we provide strength determination for the weakest specimens that is statistically relevant and is based on a reliable engineering parameter.     

Numerical simulation of the damage behavior of bidirectionally reinforced ceramic cross-ply laminates

The behavior of bidirectionally reinforced SiC/SiC cross-ply laminates is studied with the help of numerical simulations based on the finite element method (FEM). Within the presented model the composite is regarded on the layer scale considering each layer as homogeneous with `layer properties'. Brittle cracking as well as damage effects can appear within each layer, which is why both a damage and a fracture model for the plies is derived. The damage model is based on damage variables depending on the strain state. Fracture is checked using a fracture criterion, a crack and a post-failure model. In this way fracture can be considered for multiaxial stress states and the statistical distribution of strength values as well as load transfer effects after crack initiation can be taken into account. By subjecting the structure to a cooling down process before mechanical loading in one of the fiber directions the residual thermal stresses within the layers can also be regarded. The purpose of the simulations is to indicate the influence of important parameters on the composite behavior.     

Anisotropic dynamic damage and fragmentation of rock materials under explosive loading

This paper describes the development of a constitutive model for predicting dynamic anisotropic damage and fragmentation of rock materials under blast loading. In order to take account of the anisotropy of damage, a second rank symmetric damage tensor is introduced in the present model. Based on the mechanics of microcrack nucleation, growth and coalescence, the evolution of damage is formulated. The model provides a quantitative method to estimate the fragment distribution and fragment size generated by crack coalescence in the dynamic fragmentation process. It takes account of the experimental facts that a brittle rock material does not fail if the applied stress is lower than its static strength and certain time duration is needed for fracture to take place when it is subjected to a stress higher than its static strength. Numerical results are compared with those from independent field tests.     

Analysis of Local Fracture Strain and Damage Limit of Advanced High Strength Steels using Measured Displacement Fields and FEM

The local mechanical behaviors of advanced high strength steels undergoing a very large strain from uniform plastic deformation to fracture were investigated with the aid of a measured displacement field and a measurement based FEM. As a measurement method, a digital image grid method (DIGM) was developed and the three-direction transient displacement field on uniaxial tensile test pieces was measured. Combining the measured transient displacement field with the finite element method, a measurement based FEM (M-FEM) was developed for the computation of distribution of the local strains, local stresses and ductile damage accumulation in a tensile test piece. Furthermore, the local fracture strain and damage limit of several advanced high strength steel sheets (980MPa/t1.2mm, 980MPa/t1.6mm, 1180MPa/t1.6mm) were identified by uniaxial tensile tests and the measurement based FEM. The identified damage limit of materials agreed very well compared with that measured by a conventional press test, and the validity of the measuring method and measurement based FEM was verified.     

单丝复合体系渐进损伤过程模拟及组分性能对损伤过程的影响

为研究单丝复合体系在单向加载过程中的应力传递及损伤演化规律,基于剪滞模型建立了渐进损伤过程的三维数值分析模型。单丝复合体系的渐进损伤过程曲线和临界状态下的纤维段数、应变载荷及纤维轴向应力分布均与文献试验结果非常吻合,表明本文所提出的单丝复合体系渐进损伤模型能够有效模拟单丝断裂过程中的损伤起始、损伤演化和断裂临界状态。研究了模型中组分材料的模量和强度对损伤过程的影响。结果表明：保持组分材料强度不变,增加纤维的模量能够加快损伤过程,基体模量和界面模量的增加对单丝复合体系渐进损伤过程影响不大;在组分材料模量及界面强度不变的情况下,随着纤维强度的增加,单丝复合体系渐进损伤过程的起始应变载荷和临界应变载荷均增加,临界状态下的纤维断点数减少。     

The influence of backgrinding on the fracture strength of 100 mm diameter (1 1 1) p-type silicon wafers

The influence of grinding geometry and damage depth on the fracture strength of 100 mm diameter (1 1 1) p-type silicon wafers has been studied. The fracture strengths were measured in a biaxial flexure test after the wafers were ground to 0.36 mm from 0.53 mm thick, in a grinding apparatus that produces a swath of swirls on the silicon wafer surfaces. Analysis of orientations of the swirl geometries and fracture probability was used to deduce the fracture strength relative to the crystallographic orientation of the wafers. Optical and scanning electron microscopy of bevelled, and cleaved and etched samples was used to measure the damage depths from selected locations on the wafers. The depth of damage and fracture strengths were correlated to the geometry of the backgrind swirl pattern and the relative position of the orientation flat. The damage depth was smaller when the swirl path was parallel or at 45° to the orientation flat as compared to the swirl paths at 90° and 135° orientations. As a result, the wafers ground in the former orientations had a higher fracture strength than those of the latter orientations (136 and 124 MPa versus 100 and 103 MPa, for the four orientations, respectively). This revised version was published online in November 2006 with corrections to the Cover Date.     

Fracture of fatigue-loaded composite laminates

While the quasi-static fracture load of many composite laminates can be estimated with engineering accuracy, the fracture event itself has not been clearly characterized and is incompletely understood. When cyclic loading is present, the pre-fracture damage state is altered significantly, so that estimating strength (or residual strength) is greatly complicated. The present paper examines this complexity and attempts to assess the manner in which pre-fracture fatigue damage affects residual strength and the fracture event. It is found that the large strength reductions observed prior to failure at low load levels can be accounted for by internal stress redistribution and material degradation events. A careful chain of physical evidence in support of this approach is presented.     

Tensile fracture of soft and hard PZT

Power applications generate high stresses which can damage piezoceramic components. In this study tensile fracture of several types of PZT (hard/soft) is investigated. After validation of the specimen geometry by means of numerical simulation, samples are led to failure using a specific device. Weibull law parameters enable the characterisation of the tensile strength distribution and highlight clear differences between soft and hard ceramics. A fractographic approach emphasises the specificities of the fracture mode and the fracture origin for each type of samples.     

基于内聚力行为和扩展有限元的砂/树脂复合材料拉伸失效行为的数值计算

基于砂/树脂断裂与砂树脂界面脱粘失效行为的砂/树脂三维微细观单胞模型被构建,用于研究砂/树脂在拉伸载荷作用下的微观应力特征、树脂粘结桥的损伤破坏模式及微观结构（树脂含量、砂粒粒径、砂粒级配及粘结桥有效横截面积比）对其宏观拉伸强度的影响。该三维微细观单胞模型采用内聚力行为方法刻画粘结砂/树脂界面的失效,采用扩展有限元方法（Extented finite element,XFEM）捕捉树脂基体损伤和裂纹扩展。计算结果表明:所构建的三维微细观单胞模型能够显式刻画砂/树脂微细观结构断裂过程,解释微细观结构断裂机制,能够有效地提供树脂含量、砂粒粒径、砂粒级配、粘结桥有效横截面积比等微细观结构对砂/树脂宏观拉伸强度（S_t）影响的信息,可为砂/树脂优化设计提供理论指导。      

Comparative Analysis of Fracture Strength of Slurry and Diamond Wire Sawn Multicrystalline Silicon Solar Wafers

This paper presents an analysis of fracture strength of multicrystalline silicon (mc‐Si) solar wafers produced by slurry and diamond wire sawing. The wafers were bent in two orthogonal orientations relative to the saw marks. The fracture strength of slurry sawn wafers increases gradually from wire entry to wire exit whereas the strength variation in the wire feed direction is small. The fracture strength of diamond wire sawn wafers is bi‐directional, with a higher strength if bent perpendicular to the saw marks and a lower strength if bent parallel to the saw marks. The fracture strength variation is related to the microcracks generated in the vicinity of grit‐induced surface damage.     

Fracture strength distribution of porous ceramics under quasi-static load

The purpose of this paper is to estimate the fracture strength distribution of porous ceramics under quasi-static load. Four-point bending test was performed for SiC-porous ceramics at room temperature under quasi-static load. Fracture strength distributions obtained in the above test were estimated with the aid of a conventional probabilistic time-dependent fracture model on the basis of the slow crack growth concept in conjunction with two-parameter Weibull distribution. The results showed that the estimated fracture strength distribution curves were not in good agreement with the experimental data at stress rates. Porous ceramics have damage-tolerable property due to failure of a lot of grain boundaries. Therefore, this is because the dispersion of applied stress was not considered in the conventional model. A new probabilistic time-dependent fracture model considered the dispersion of applied stress was proposed based on Markov process in conjunction with local load sharing rule. The fracture strength distribution curves estimated the aid of the new model were in reasonably good agreement.     

考虑纤维随机分布的复合材料热残余应力分析及其对横向力学性能的影响

建立了考虑纤维随机分布并包含界面的复合材料微观力学数值模型,模拟玻璃纤维/环氧复合材料固化过程中的热残余应力。通过与纤维周期性分布模型的计算结果进行对比,发现纤维分布形式会对复合材料的热残余应力产生重要影响,纤维随机分布情况下的最大热残余应力明显大于纤维周期性分布的情况下。研究了含热残余应力的复合材料在横向拉伸与压缩载荷下的损伤和破坏过程,结果表明:热残余应力的存在显著影响了复合材料的损伤起始位置和扩展路径,削弱了复合材料的横向拉伸和压缩强度。在横向拉伸载荷下,考虑热残余应力后,复合材料的强度有所下降,断裂应变显著降低;在横向压缩载荷下,考虑热残余应力后,复合材料的强度略有下降,但失效应变基本保持不变。由于热残余应力的影响,复合材料的横向拉伸和压缩强度分别下降了10.5%和5.2%。      

Analysis and design of dual-phase steel microstructure for enhanced ductile fracture resistance

The goal of this paper is to predict how the properties of the constituent phases and microstructure of dual phase steels (consisting of ferrite and martensite) influence their fracture resistance. We focus on two commercial low-carbon dual-phase (DP) steels with different ferrite/martensite phase volume fractions and properties. These steels exhibit similar flow behavior and tensile strength but different ductility. Our experimental observations show that the mechanism of ductile fracture in these two DP steels involves nucleation, growth and coalescence of micron scale voids. We thus employ microstructure-based finite element simulations to analyze the ductile fracture of these dual-phase steels. In the microstructure-based simulations, the individual phases of the DP steels are discretely modeled using elastic-viscoplastic constitutive relations for progressively cavitating solids. The flow behavior of the individual phases in both the steels are determined by homogenizing the microscale calibrated crystal plasticity constitutive relations from a previous study (Chen et al. in Acta Mater 65:133–149, 2014) while the damage parameters are determined by void cell model calculations. We then determine microstructural effects on ductile fracture of these steels by analyzing a series of representative volume elements with varying volume fractions, flow and damage behaviors of the constituent phases. Our simulations predict qualitative features of the ductile fracture process in good agreement with experimental observations for both DP steels. A ‘virtual’ DP microstructure, constructed by varying the microstructural parameters in the commercial steels, is predicted to have strength and ductile fracture resistance that is superior to the two commercial DP steels. Our simulations provide guidelines for improving the ductile fracture resistance of DP steels.     

FRP-混凝土三点受弯梁损伤粘结模型有限元分析

该文采用双线形损伤粘结模型研究带切口FRP-混凝土三点受弯梁(3PBB)I型加载下的界面断裂性能。通过有限元参数分析,详细讨论了界面粘结强度、界面粘结能、混凝土抗拉强度、混凝土断裂能对3PBB受力性能的影响。数值模拟表明,FRP-混凝土界面有两种破坏形式,包括FRP-混凝土界面的损伤脱粘和界面混凝土的损伤脱粘破坏,与实验所观察到的现象一致。两种破坏形式尽管在宏观上均表现为界面脱粘,但破坏机制却不同。FRP-混凝土界面的损伤粘结模型与混凝土的拉伸塑性损伤模型相结合,不但再现了3PBB的宏观力学性能,数值分析得到的荷载-位移曲线接近实验结果,而且还能详细展示FRP-混凝土界面的损伤、断裂破坏过程以及损伤在FRP-混凝土界面和界面混凝土之间的转移,能够预测构件的承载力,有助于界面优化设计,这是单纯以能量判据预测裂纹发展的经典断裂力学方法所无法做到的。     

Damage prediction of clamped circular plates subjected to contact underwater explosion

Contact explosion damage prediction of circular steel plates is of interest to the naval architects and warship designers. During contact explosion, a fraction of the explosive energy goes for plastic deformation and fracture of the plate. Experiments were conducted on air backed circular high strength low alloy (HSLA) steel plates to establish this fraction. There was a large amount of plastic deformation preceding fracture in the contact exploded plates. The deformation contour was found to be spherical showing maximum absorption of energy for the depth of bulge attained. The radius of penetration of the test plate was obtained by applying the terminal strain to fracture and the non-uniform strain distribution in the target plate. A case history is presented where the current predictions are compared with the existing empirical methodology and experimental data.     

Kinetic genesis of some statistic regularities of fracture

The statistics of strength and longevity of solids has been the subject of investigation for many years. Some common regularities in fracture statistics have been experimentally revealed. These are Jhurkov's exponential and power-type longevity equations, Weibull's statistics of strength, and different types of size effect. However, the present notions on the nature of the observed statistic regularities are far from being complete. Here the object is to examine fracture statistics on the basis of a previously suggested kinetic approach. We consider the evolution of the statistical ensemble of cracks under static and steady-rate loading of a solid. The growth of an individual crack is therewith treated as a spasmodic stochastic process and presented by a time-dependent distribution density of a crack size. That function is used to construct the conditional longevity distribution with respect to the growth of an individual crack with the prescribed initial size. The final longevity distribution is found as the distribution of a minimum of conditional longevities. That procedure has been realized for both brittle and quasi-brittle cases. The obtained longevity and strength distributions were found to be in qualitative agreement with the observed statistic regularities. However, the conventional `weak link concept' and proposals for the statistics of dangerous defects are in conflict with the obtained results. It is moreover shown that, within the limits of the wide-spread concept, Jhurkov's longevity equation and Weibull's statistics of strength are mutually exclusive. Although the results were obtained from simple models, there is a good probability of kinetic origin for the basic statistic regularities of fracture.