Prediction scheme for the catastrophic failure of highly loaded brittle materials or rocks

Due to broadly distributed heterogeneities, the multistep character of the development of random damage in brittle materials or rocks, reflecting the discrete nature of the fracturing process, enables us to compare the diffusion of damages with the percolation phenomenon. Based on a discrete scale hierarchy, the fracturing process leading to material failure is then identified with a second-order phase transition, enabling prediction. In this connection, this paper presents a prediction scheme for the catastrophic failure or the lifetime of highly loaded materials or rocks. An experimental measurement method and a modelling of bi-phase materials or rocks are proposed. Although this scheme is introduced in the context of materials science, it also works in rock for the prediction of large natural earthquakes and some artificially induced earthquakes and rock bursts due to damming and mining. Results with strong forecasting potential explain for the first time the origin of complex critical exponents through a structural parameter.     

连续损伤力学基临界奇异指数与破坏时间预测

响应量在临近破坏时呈现出临界幂律奇异性加速特征,是一种被广泛证实的灾变破坏前兆,并被火山、滑坡和岩石破坏实验等后验预测结果证实为一种对破坏时间进行短临期预测的可行方法.但是,奇异性指数测量值的较大分散性导致了对其具体取值的争议和预测效果的不确定性.因此,理解奇异性指数取值特征及其内在物理控制因素,成为了一个核心问题.本文基于连续介质损伤力学和材料时间相关失效特征,构建了刻画损伤加速发展通向破坏过程的力学模型.导出了恒名义应力蠕变加载和控制名义应力随时间线性增大两种典型加载方式下,损伤和应变率加速发展通向破坏的临界幂律奇异性前兆特征.阐明了临界幂律奇异性指数取值依赖于材料损伤与承受真应力之间的非线性关系这一内在物理根源,表明了实际测量中奇异性指数的分散性不完全归结于测量数据误差,而是有着内在物理控制因素.针对破坏前奇异性指数的不确定性,建议了在未知奇异性指数条件下预测破坏时间的方法,并基于花岗岩脆性蠕变破坏实验进行了验证和说明.      

固体结构损伤破坏统一相场理论、算法和应用

固体开裂引起的损伤和断裂是工程材料和结构最为普遍的破坏形式.为了防止这种破坏,结构设计首先必须了解裂缝在固体内如何萌生、扩展、分叉、汇聚甚至破碎;更重要的是,还需要准确量化这些裂缝演化过程对于结构完整性和安全性降低的不利影响.针对上述固体结构损伤破坏问题,本工作系统地介绍了笔者提出的统一相场理论、算法及其应用.作为一种...     

非均质脆性材料灾变性破坏的一种敏感前兆

非均质脆性材料的失效可能有两种模式:渐进式破坏与灾变性破坏. 灾变性破坏具有更大的危险性,灾变预测是一个有重要意义的难题. 基于统计细观损伤力学分析了两种破坏模式的差异,发现在每一加载步中系统卸载所释放的弹性能与损伤所耗散的能量之比值可为灾变破坏提供一种敏感的前兆. 研究发现在灾变性破坏和非灾变性的渐进式破坏两种失效模式中,虽然系统中卸载所贡献的弹性能增量与损伤消耗和释放的能量增量的比值都有趋向于1的趋势,但是两者的趋近方式不同:灾变性破坏时表征能量比随控制变量变化特征的响应函数R有一个上升段,在灾变破坏点$R$趋向于无穷大,而非灾变性破坏中$R$始终是减小的.      

Damage evaluation and damage localization of rock

Knowledge of damage accumulation and corresponding failure evolution are prerequisite for effective maintenance of civil engineering so as to avoid disaster. Based on statistical mesoscopic damage mechanics, it was revealed that there are three stages in the process of deformation, damage and failure of multiscale heterogeneous elastic–brittle medium. These are uniformly distributed damage, localized damage and catastrophic failure. In order to identify the transitions from scattering damage to macroscopically localized one, a condition for damage localization was given. The experiments of rock under uniaxial compression with the aid of observations of acoustic emission and speckle correlation do support the concept of localization. This provides a potential approach to properly evaluate damage accumulation in practice. In addition, it is found in the experiments that catastrophic failure displays critical sensitivity. This gives a helpful clue to the prediction of catastrophic failure.     

Failure resistance of intermetallic matrix reinforced by wires

Composite materials with brittle matrices such as ceramics and intermetallic compounds have gained increased importance in application. Ceramics and intermetallic compounds possess unique heat-resistance at high temperatures. They are, however, vulnerable to brittle fracture. This problem can be overcome by reinforcing the intermetallic compounds with wires. NiAl-tungsten composite wire was manufactured by hot diffusion welding of alternate layers of the matrix and wires. These specimens were subjected to a three-point bending in the temperature range from 20° to 1000°C. Temperature dependence of the bending strength exhibited brittle to ductile transition behavior. At room temperature, unstable failure by bending is terminated in a stable fashion. Brittle fracture of the matrix and wire were observed. For text temperatures of 300°, 500° and 700°C, subcritical crack growth occurred where the matrix and wire showed brittle and ductile fracture, respectively. A pronounced necking of the specimen was observed as the temperature is increased. Substantial plastic deformation occurred when the test is performed at 1000°C. The critical stress intensity factor K_1c and specific work of fracture were measured and found to be two to three times larger than the intermetallic compounds without wire reinforcement.     

Mixed-mode crack initiation at a v-notch in presence of an adhesive joint

The failure criterion for v-notched specimens developed for mixed-mode loadings by Yosibash et al. [Yosibash, Z., Priel, E., Leguillon, D., 2006. A failure criterion for brittle elastic materials under mixed mode loading. Int. J. Fract. 141(1), 289–310.] is generalised in order to consider the influence of the shear stresses and the mode-dependence of the toughness. This is demonstrated to be important in some cases with adhesive joints under complex loadings for instance. The original criterion assumes that an abrupt onset of a crack with a finite extension occurs when two conditions are fulfilled simultaneously: first the normal traction all along the presupposed crack path reaches a critical value, and second the onset is energetically allowed. The influence of the shear stresses is now considered through a mixed law involving critical shear and tensile stresses as well as the mode-dependent toughness introducing a new equivalent SIF. This extended criterion is applied to the simulation of an Arcan test on v-notched compact tension shear (CTS) specimens made of two parts bonded together along the geometric plane of symmetry of the specimen. The competition between two modes of failure is studied: crack initiation along the weak joint which may constitute a privileged fracture surface and initiation in the homogeneous material at an optimum angle that minimizes the critical load to failure.     

Estimation of Fracture Toughness of Metallic Materials Using Instrumented Indentation: Critical Indentation Stress and Strain Model

We propose a generalized approach based on fracture mechanics and contact mechanics to estimate the fracture toughness in metallic materials from instrumented indentation testing. Models were developed for brittle and ductile fracture. Different criteria were applied to each model to determine the critical fracture point during indentation. For brittle fracture, the critical fracture point was defined in terms of the critical mean pressure; for ductile fracture, the critical fracture point was derived from fracture strain and critical plastic zone size. Each fracture criterion was used to determine the indentation fracture energy corresponding to the fracture energy required for crack extension. The fracture toughness was estimated for various metallic materials using each model and compared with standard fracture toughness tests.     

Breakage mechanics—Part II: Modelling granular materials

The compression of granular materials has been traditionally modelled with the limitations of classical elasto-plasticity. The energy was implicitly assumed to dissipate from the frictional interaction of particles. However, the fact that brittle granular materials crush suggests that energy must also be dissipated from the fracturing of the grains, as in fracture mechanics. The concept of breakage as a thermomechanical internal variable was introduced in Part I [Einav, I., 2006. Breakage mechanics—Part I: theory. J. Mech. Phys. Solids 00,000-000] to describe the fracturing mechanisms. The theory allows to treat ideal theoretical materials that undergo dissipation purely from breakage with no other mechanism allowed for the energy consumption. However, as accounted for in elasto-plasticity, dissipation must also occur from the frictional rearrangement of grains. The combination of the two dissipative mechanisms of breakage and plasticity must therefore be investigated, as we do in this paper. Those two mechanisms are generally coupled, in the sense that one inevitably appears when the other develops. Plastic dissipation emerges as a by-product of breakage dissipation because after grains crush, local rearrangement must occur. This scenario may be termed an ‘active breakage mechanism’, and typifies compression deformations. In shear the plastic dissipation is dominant but breakage appears inevitably from grains abrasion. This scenario may be called a ‘passive breakage mechanism’. Based on the coupling assumption, models are developed for granular materials. In particular, we show that in compression isotropic hardening of sands may appear without involving plastic strains, i.e., independent of frictional dissipation. This interpretation of hardening is different from the one used in classical critical state soil mechanics. However, frictional dissipation leads to plastic straining that are necessary for the models to be predictive in unloading.     

Periodic cracking of films supported on compliant substrates

When a tensile strain is applied to a film supported on a compliant substrate, a pattern of parallel cracks can channel through both the film and substrate. A linear-elastic fracture-mechanics model for the phenomenon is presented to extend earlier analyses in which cracking was limited to the film. It is shown how failure of the substrate reduces the critical strain required to initiate fracture of the film. This effect is more pronounced for relatively tough films. However, there is a critical ratio of the film to substrate toughness above which stable cracks do not form in response to an applied load. Instead, catastrophic failure of the substrate occurs simultaneously with the propagation of a single channel crack. This critical toughness ratio increases with the modulus mismatch between the film and the substrate, so that periodic crack patterns are more likely to be observed with relatively stiff films. With relatively low values of modulus mismatch, even a film that is more brittle than the substrate can cause catastrophic failure of the substrate. Below the critical toughness ratio, there is a regime in which stable crack arrays can be formed in the film and substrate. The depth of these arrays increases, while the spacing decreases, as the strain is increased. Eventually, the crack array can become deep enough to cause substrate failure.     

A theory for brittle fracture in compression

A symmetric cylindrical body composed of brittle material, if compressed along its generators may collapse progressively, firstly through catastrophic loss of material adjacent to its lateral surface(s). With increase of the compressive load the reduced cylinder, unable to resist, sunders. The first stage of this type of failure can be explained by the assumed existence of latent interior cracks which open abruptly on a curved, symmetric interior surface when the total energy of the body reaches a critical value determined by the geometry of the initial fracture surface.     

The Mori–Tanaka method for composite materials with nonlinear interface debonding

We have used the Mori–Tanaka method to study the effect of nonlinear interface debonding on the constitutive behavior of composite material with high particle volume fraction. The interface debonding is characterized by a nonlinear cohesive law determined from the fracture test of the high explosive PBX 9501. Using the example of the composite material with spherical particles subject to hydrostatic tension, we show that the particle size has an important effect on the behavior of the composite material, namely hardening for small particles and softening for large particles. The critical particle size that separates the hardening and softening behavior of the composite material is determined. For the composite material with large particles, the particle/matrix interface may undergo catastrophic debonding, i.e., sudden, dynamic debonding even under static load. The energy release during catastrophic debonding can be very large, thus may trigger the reaction or detonation of high explosives. For the high explosive PBX 9501, the energy release due to catastrophic debonding of coarse (large) particles is equivalent to the free drop of the high explosive from a height of 110 m. This value become much higher, 455 m, once the debonding of fine (small) particle is accounted for.     

Fracture-mode map of brittle coatings: Theoretical development and experimental verification

Brittle coatings, upon sufficiently high indentation load, tend to fracture through either ring cracking or radial cracking. In this paper, we systematically study the factors determining the fracture modes of bilayer material under indentation. By analyzing the stress field developed in a coating/substrate bilayer under indentation in combination with the application of the maximum-tensile-stress fracture criterion, we show that the fracture mode of brittle coatings due to indentation is determined synergistically by two dimensionless parameters being functions of the mechanical properties of coating and substrate, coating thickness and indenter tip radius. Such dependence can be graphically depicted by a diagram called ‘fracture-mode map’, whereby the fracture modes can be directly predicated based on these two dimensionless parameters. Experimental verification of the fracture-mode map is carried out by examining the fracture modes of fused quartz/cement bilayer materials under indentation. The experimental observation exhibits good agreement with the prediction by the fracture-mode map. Our finding in this paper may not only shed light on the mechanics accounting for the fracture modes of brittle coatings in bilayer structures but also pave a new avenue to combating catastrophic damage through fracture mode control.     

Micromechanics of a model heterogeneous material system under compressive loading

Compressive loading is often encountered in mining and mineral processes during the comminution of ore bearing minerals, or alternatively, in the wear-resistant materials used in the comminution circuit. A common thread joining many of the engineered materials used predominantly under compressive loading is the presence of a high modulus secondary phase, either fiber or particulate, embedded within a lower modulus matrix phase (i.e., a brittle heterogeneous material). To improve their toughness, an imperfect or a less-than-coherent interface is often strived for in the manufacture of many heterogeneous materials. To better understand the complex behavior of these materials, a model heterogeneous material system was developed by the U.S. Bureau of Mines and the Idaho National Engineering Laboratory. In this work, moiré interferometry was used to map the micromechanical displacements on the surface of the model system. Uniaxial and biaxial compressive loading was applied to a model system consisting of a PMMA (polymethylmethacrylate) plate having a precision ground steel rod as the cylindrical reinforcement. Moiré patterns revealed that two dominant phenomena occur along the interface: (1) frictional slip/stick and (2) a form of semi-cohesive bonding or mechanical locking. These observations were subsequently confirmed by nonlinear finite-element simulations of the model heterogeneous system. Experimental and numerical results show that the imperfect interface plays an important role in the micromechanical behavior of these model systems.     

Failure probability assessment of parallel redundant structures

Considered in the analysis are complex systems with parallel redundancy. The failure probability of such a system is assessed by the strength probabilistic properties of the structural elements. There is a finite number of parallel structural elements that provides the maximum possible reliability of the system. Parallel systems may fail by instantaneous growth of failed elements. The tendency to catastrophic failure depends on the element strength probability and overload. Calculated is the critical stress corresponding to the beginning of catastrophic failure of the parallel system. Weibull probability distribution is used for describing the structural element strength. The critical stress ranges from 50% to 95% of the mean single element strength; depends on the overload and probability distribution.     

航天器火工冲击模拟试验及响应预示方法研究综述

航天器火工冲击力学环境是由星箭分离、部组件展开等工作过程中的火工品起爆引起的作用于结构上的高频、高加速度量级的瞬态冲击响应,能对航天器上含有晶振、脆性材料等的精密电子设备造成致命损伤,是航天器需要经历的最苛刻的力学环境之一。本文中,对国内外航天器火工冲击地面试验方法和环境预示方法做了全面、详细的介绍,总结了这两个方面的研究进展,分析了我国在这两个方面与航天强国的差距。最后,从我国航天工程实际需求出发,提出了今后航天器火工冲击领域应重点开展的研究方向。     

Balancing strength and toughness of calcium-silicate-hydrate via random nanovoids and particle inclusions: Atomistic modeling and statistical analysis

As the most widely used manufactured material on Earth, concrete poses serious societal and environmental concerns which call for innovative strategies to develop greener concrete with improved strength and toughness, properties that are exclusive in man-made materials. Herein, we focus on calcium silicate hydrate (C-S-H), the major binding phase of all Portland cement concretes, and study how engineering its nanovoids and portlandite particle inclusions can impart a balance of strength, toughness and stiffness. By performing an extensive +600 molecular dynamics simulations coupled with statistical analysis tools, our results provide new evidence of ductile fracture mechanisms in C-S-H – reminiscent of crystalline alloys and ductile metals – decoding the interplay between the crack growth, nanovoid/particle inclusions, and stoichiometry, which dictates the crystalline versus amorphous nature of the underlying matrix. We found that introduction of voids and portlandite particles can significantly increase toughness and ductility, specially in C-S-H with more amorphous matrices, mainly owing to competing mechanisms of crack deflection, voids coalescence, internal necking, accommodation, and geometry alteration of individual voids/particles, which together regulate toughness versus strength. Furthermore, utilizing a comprehensive global sensitivity analysis on random configuration-property relations, we show that the mean diameter of voids/particles is the most critical statistical parameter influencing the mechanical properties of C-S-H, irrespective of stoichiometry or crystalline or amorphous nature of the matrix. This study provides new fundamental insights, design guidelines, and de novo strategies to turn the brittle C-S-H into a ductile material, impacting modern engineering of strong and tough concrete infrastructures and potentially other complex brittle materials.     

Tensile-shear transition in mixed mode I/III fracture

The propensity of the transition of fracture type in either brittle or ductile cracked solid under mixed-mode I and III loading conditions is investigated. A fracture criterion based on the competition of the maximum normal stress and maximum shear stress is utilized. The prediction of the fracture type is determined by comparing τ_max/σ_max at a critical distance from the crack tip to the material strength ratio τ_C/σ_C, i.e., (τ_max/σ_max)<(τ_C/σ_C) for tensile fracture and (τ_max/σ_max)>(τ_C/σ_C) for shear fracture, where σ_C (τ_C) is the fracture strength of materials in tension (shear). Mixed mode I/III fracture tests were performed using circumferentially notched cylindrical bars made of PMMA and 7050 aluminum alloy. Fracture surface morphology of the specimens reveals that: (1) for the brittle material, PMMA, only tensile type of fracture occurs, and (2) for the ductile material, 7050 aluminum alloy, either tensile or shear type of fracture occurs depending on the mode mixity. The transition (in ductile material) or non-transition (in brittle material) of the fracture type and the fracture path observed in experiments were properly predicted by the theory. Additional test data from open literature are also included to validate the proposed theory.     

脆性材料在双向应力下的断裂实验与理论分析

研究了脆性材料在双向应力下的断裂特性和失效机理，特别是在平行于裂纹的应力对临界断裂参数的影响方面进行了实验上和理论上的研究．采用玻璃、陶瓷等脆性材料进行了平面双向拉伸和单向拉伸试验，并对实验结果进行比较．观测直通裂纹的启裂和扩展过程，证明了双向应力对裂纹驱动力有明显影响，讨论了裂纹扩展的应变准则．