Cracking process of a granite specimen that contains multiple pre‐existing holes under uniaxial compression

The pre‐existence of openings, which play an important role in the mechanical properties and cracking behaviours of rock, is prevalent in rock mass. The interaction among pre‐existing openings (or holes) complicates the instability problems when rock contains multiple holes. Studying the strength failure behaviour of rock that contains multiple pre‐existing holes contributes to the fundamental knowledge of the excavation and stability of underground rock engineering. In this study, first, a series of uniaxial compression tests were performed on granite specimens that contain multiple small holes to investigate the effect of the geometry of pre‐existing holes on the strength and fracture behaviours of rock. The crack initiation, propagation and coalescence process, and acoustic emission (AE) characteristics were investigated using photographic and AE monitoring. Three failure modes were identified, ie, splitting failure, stepped path failure, and planar failure modes. Second, a set of micromechanical parameters in the PFC3D model were calibrated by comparison with the experimental results of an intact granite specimen. The numerically simulated peak strength, peak strain, and failure mode of preholed specimens were consistent with the experimental results. In accordance with the numerical results, the failure modes of the preholed specimens were dependent on the bridge angle and number of holes. Last, the internal fracture characteristics of numerical specimens were revealed by analyzing the horizontal and vertical cross sections at different positions.     

Failure mode of laser welds in lap‐shear specimens of high strength low alloy (HSLA) steel sheets

In this paper, the failure mode of laser welds in lap‐shear specimens of non‐galvanized SAE J2340 300Y high strength low alloy steel sheets under quasi‐static loading conditions is examined based on experimental observations and finite element analyses. Laser welded lap‐shear specimens with reduced cross sections were made. Optical micrographs of the cross sections of the welds in the specimens before and after tests are examined to understand the microstructure and failure mode of the welds. Micro‐hardness tests were also conducted to provide an assessment of the mechanical properties in the base metal, heat‐affected and fusion zones. The micrographs indicate that the weld failure appears to be initiated from the base metal near the boundary of the base metal and the heat‐affected zone at a distance away from the pre‐existing crack tip, and the specimens fail due to the necking/shear of the lower left load carrying sheets. Finite element analyses based on non‐homogenous multi‐zone material models were conducted to model the ductile necking/shear failure and to obtain the J integral solutions for the pre‐existing cracks. The results of the finite element analyses are used to explain the ductile failure initiation sites and the necking/shear of the lower left load carrying sheets. The J integral solutions obtained from the finite element analyses based on the 3‐zone finite element model indicate that the J integral for the pre‐existing cracks at the failure loads are low compared to the fracture toughness and the specimens should fail in a plastic collapse or necking/shear mode. The effects of the sheet thickness on the failure mode were then investigated for laser welds with a fixed ratio of the weld width to the thickness. For the given non‐homogenous material model, the J integral solutions appear to be scaled by the sheet thickness. With consideration of the plastic collapse failure mode and fracture initiation failure mode, a critical thickness can be obtained for the transition of the plastic collapse or necking/shear failure mode to the fracture initiation failure mode. Finally, the failure load is expressed as a function of the sheet thickness according to the governing equations based on the two failure modes. The results demonstrate that the failure mode of welds of thin sheets depends on the sheet thickness, ductility of the base metal and fracture toughness of the heat‐affected zone. Therefore, failure criteria based on either the plastic collapse failure mode or the fracture initiation failure mode should be used cautiously for welds of thin sheets.     

Mapping function to failure mode during component development

When designing aerospace systems, it is essential to provide crucial failure information for failure prevention. Failure modes and effects types of analyses and prior engineering knowledge and experience are commonly used to determine the potential modes of failures a product might encounter during its lifetime. When new products are being considered and designed, this knowledge and information is expanded upon to help designers extrapolate based on their similarity with existing products and the potential design tradeoffs. In this work, we aim to enhance this process by providing design-aid tools which derive similarities between functionality and failure modes. Specifically, this paper presents the theoretical foundations of a matrix-based approach to derive similarities that exist between different failure modes, by mapping observed failure modes to the functionality of each component, and applies it to a simple design example. The function–failure mode method is proposed to design new products or redesign existing ones with solutions for functions that eliminate or reduce the potential of a failure mode. Electronic Publication     

Mode II delamination failure mechanisms of polymer matrix composites

The failure process of mode II delamination fracture is studied on the basis of the microscopic matrix failure modes (microcracks and hackles) as well as fracture mechanics principles. The crack tip matrix stresses leading to delamination is analysed by examining an adhesive bond with a crack analogous to a delamination crack in the resin layer of a composite. Such crack tip stresses induce matrix microcracks involving two major events: (a) single microcrack initiation and (b) development of multiple microcracks with regular spacing. The microcrack initiation shear stress τ* is found by the use of fracture mechanics to be related to certain resin properties (shear modulus G and mode I fracture toughness GIC) and microcrack length of the order of the resin layer thickness t (related to resin content). The more or less regular microcrack spacing S deduced from shear lag considerations can be related to resin properties GIC, G, τy (resin yield strength) and t. The multiple microcracks reduce the effective resin modulus and strongly affect the subsequent microcrack coalescence process. As a result of the detailed analysis of the failure process, mode II laminate fracture toughness GIIC can be quantitatively expressed as a function of resin GIC and (τ2y/G). The failure process modelled is used to interpret the mode II delamination behaviour of several carbon/epoxy systems studied here and that reported in the literature. This study reveals the critical importance of resin fracture (GIC related) and deformation (yielding) mechanisms in controlling mode II delamination resistance of laminated composites. This revised version was published online in November 2006 with corrections to the Cover Date.     

A linguistic risk prioritization approach for failure mode and effects analysis: A case study of medical product development

Failure mode and effects analysis (FMEA) is a widely used risk management technique for identifying the potential failures from a system, design, or process and determining the most serious ones for risk reduction. Nonetheless, the traditional FMEA method has been criticized for having many deficiencies. Further, in the real world, FMEA team members are usually bounded rationality, and thus, their psychological behaviors should be considered. In response, this study presents a novel risk priority model for FMEA by using interval two‐tuple linguistic variables and an integrated multicriteria decision‐making (MCDM) method. The interval two‐tuple linguistic variables are used to capture FMEA team members' diverse assessments on the risk of failure modes and the weights of risk factors. An integrated MCDM method based on regret theory and TODIM (an acronym in Portuguese for interactive MCDM) is developed to prioritize failure modes taking experts' psychological behaviors into account. Finally, an illustrative example regarding medical product development is included to verify the feasibility and effectiveness of the proposed FMEA. By comparing with other existing methods, the proposed linguistic FMEA approach is shown to be more advantageous in ranking failure modes under the uncertain and complex environment.     

复合材料夹芯梁屈曲破坏模式及极限承载

为研究复合材料夹芯梁在轴压作用下的屈曲、后屈曲特性及承载能力,进行了试验研究与有限元仿真。首先,开展了系列复合材料夹芯梁屈曲特性试验,研究了铺层比例、梁长度、表层厚度及芯层厚度等因素对其屈曲、后屈曲破坏模式及极限承载的影响;然后,基于非线性屈曲理论,采用三维内聚力界面单元模拟面芯脱粘,并引入初始预变形及材料损伤准则对复合材料夹芯梁在轴压下的屈曲特性及极限承载进行仿真研究。结果显示:界面脱粘是屈曲破坏的重要模式;仿真计算的极限承载与试验结果相比,误差控制在10%以内。所得结论表明该方法可有效预报复合材料夹芯梁的后屈曲路径、破坏模式及极限承载。      

A new testing method to obtain mode II fatigue crack growth characteristics of hard materials

Flaking type failure in rolling‐contact processes is usually attributed to fatigue‐induced subsurface shearing stress caused by the contact loading. Assuming such crack growth is due to mode II loading and that mode I growth is suppressed due to the compressive stress field arising from the contact stress, we developed a new testing apparatus for mode II fatigue crack growth. Although the apparatus is, as a former apparatus was, based on the principle that the static K_I mode and the compressive stress parallel to the pre‐crack are superimposed on the mode II loading system, we employ direct loading in the new apparatus. Instead of the simple four‐point‐shear‐loading system used in the former apparatus, a new device for the application of a compressive stress parallel to the pre‐crack has been developed. Due to these alterations, mode II cyclic loading tests for hard steels have become possible for arbitrary stress ratios, including fully reversed loading (R=?1); which is the case of rolling‐contact fatigue. The test results obtained using the newly developed apparatus on specimens made from bearing steel SUJ2 and also a 0.75% carbon steel, are shown.     

Bridging micromechanisms of Z-pin in mixed mode delamination

A numerical model for analyzing the bridging mechanisms of Z-pining in composite laminates is presented. Main failure modes of the Z-pin are: debonding between the Z-pin and matrix, split and rupture of the Z-pin material; these have been taken into account here. The cohesive zone model was utilized to simulate splitting and rupturing within the Z-pin. The interfacial contact between the Z-pin and matrix was assumed to be initially bonded, followed by debonding and frictional sliding. The present model is validated by mode I experiments; the mode II simulation is verified by similar Z-pin shear tests. It is observed that the shear bridging force component increases with the mode II ratio, while the mode I bridging response decreases slightly with the mode II ratio. An enhanced frictional zone is located near the delamination surface. The mode II bridging force in cross-ply laminates is higher than that in UD laminates, while the Z-pin is more likely to rupture in cross-ply laminates when the mode II ratio is relatively high. The presented model can be used to evaluate the Z-pin bridging response. The calculated bridging force is suitable for analyzing the mechanical performance of Z-pinned structures.     

Failure mode and effects analysis based on D numbers and TOPSIS

Failure mode and effects analysis (FMEA) is a widely used technique for assessing the risk of potential failure modes in designs, products, processes, system, and services. One of the main problems with FMEA is the need to address a variety of assessments given by FMEA team members and the sequence of the failure modes according to the degree of risk factors. Many different methods have been proposed to improve the traditional FMEA, which is impractical when the risk assessments given by multiple experts to one failure mode are imprecise, incomplete, or inconsistent. However, the existing methods cannot adequately handle these types of uncertainties. In this paper, a new risk priority model based on D numbers and technique for the order of preference by similarity to ideal solution (TOPSIS) is proposed to evaluate the risk in FMEA. In the proposed model, the assessments given by the FMEA team members are represented by D numbers, where a new feasible and effective method can effectively represent the uncertain information. The TOPSIS method, a multicriteria decision‐making method is presented to rank the preference of failure modes with respect to risk factors. Finally, an application of the failure modes of the rotor blades of an aircraft turbine is provided to illustrate the efficiency of the proposed method.     

Study on Failure Characteristic of Rock‐Like Materials With an Open‐Hole Under Uniaxial Compression

Abstract: The failure strength model of brittle materials with a pre‐existing open‐hole defect is proposed in this paper. A modified Sammis–Ashby model is deduced, in which it can be used to calculate the peak strength of brittle materials. It shows the law between peak strength σ_p and independent variable μ, which is the ratio of open‐hole radius (a) to half‐width of the specimen (t). Moreover, numerical and experimental investigations on failure process of rock‐like materials with an open‐hole imperfection were carried out. In the experiments, 3D‐digital image correlation method, an optical technique which utilises the full‐field and non‐contact measurement, was employed. A progressive elastic damage method realistic failure process analysis (RFPA) was used in the numerical investigation to inspect and verify the modified model and simulate the failure process. The investigation finds that there are good correlations between the experimental, numerical and theoretical results. Moreover, because of the influences of boundary conditions, shear failure type was obtained both experimentally and numerically.     

Fracture initiation at sharp notches under mode I, mode II, and mild mixed mode loading

In the context of linear elasticity, a stress singularity of the type Kⁿr^δ(δ<0) may exist at sharp re-entrant corners, with an intensity Kⁿ. In general the order of the stress singularity δ and the stress intensity differ for symmetric (mode I) and antisymmetric (mode II) loading. Under general mixed-mode loadings, the magnitudes of the mode I and II intensities fully characterize the stress state in the region of the corner. A failure criterion based on critical values of these intensities may be appropriate in situations where the region around the corner dominated by the singular fields is large compared to intrinsic flaw sizes, inelastic zones, and fracture process zone sizes. We determined the mode I and II stress intensities for notched mode I tensile specimens and notched mode II flexure specimens using a combination of the Williams (1952) asymptotic method, dimensional considerations, and detailed finite element analysis. We carried out a companion experimental study to extract critical values of the mode I and II stress intensities for a series of notched polymethyl methacrylate (PMMA) tensile and flexure specimens with notch angles of 90-. The data show that excellent failure correlation is obtained, in both mode I and II loading, through the use of a single parameter, the critical stress intensity. We then analyzed and tested a series of T-shaped structures containing 90- corners. The applied tensile loading results in mixed-mode loading of the 90- corners. Failure of the specimens is brittle and can be well-correlated with a critical mode I stress intensity criterion using the results of the notched mode I tensile tests. This is attributed to large difference in the strength of the stress singularities in modes I and II: δ= -0.4555 and -0.0915 for modes I and II for a 90- notch. As a result, the mode I loading dominates the failure process for the 90- corner in the T-structure. This revised version was published online in August 2006 with corrections to the Cover Date.     

Fracture and fatigue study of unidirectional glass/epoxy laminate under different mode of loading

Interlaminar fracture is the dominant failure mechanism in most advanced composite materials. The delaminating behaviour of materials is quantified in terms of the strain energy release rate G. In this paper, the experimental measurements of the fatigue delaminating growth for some combinations of energy release rate mode ratio have been carried out on unidirectional glass/epoxy laminates. On this base the constants in the Paris equation have been determined for each G_II/G_T considered modal ratio. The fatigue threshold strain energy release rate Δ G_Tth , below which delaminating doesn't occur, were measured. Three type specimens were tested, namely: double cantilever beam (DCB), end‐loaded split (ELS) and mixed‐mode bending (MMB) under mode I, mode II and mixed‐mode (I + II) loading, respectively. Scanning electron microscopy techniques were used to identify the fatigue delamination growth mechanisms and to define the differences between the various modes of fracture.     

A new risk prioritization model for failure mode and effects analysis

Failure modes and effects analysis is a framework that has been widely used to improve reliability by prioritizing failures modes using the so‐called risk priority number. However, the risk priority number has some problems frequently pointed out in literature, namely its non‐injectivity, non‐surjectivity, and the impossibility to give weights to risk variables. Despite these disadvantages, the risk priority number continues to be widely used due to its higher simplicity when compared with other alternatives found in literature. In this paper, we propose a novel risk prioritization model to overcome the major drawbacks of the risk priority number. The model contains 2 functions, the risk isosurface function that prioritizes 3 risk variables considering their order of importance in a given risk scenario, and the risk prioritization index function which prioritizes 3 risk variables considering their weights. The novelty of the proposed model is its injectivity, surjectivity, and ease of use in failure modes prioritization. The performance of the proposed model was analyzed using some examples typically used to discuss the conventional risk priority number shortcomings. The model was applied to a case study and its performance correlated with other risk prioritization models. Results show that the failure modes prioritization reached with the proposed model agrees with the expectations made for the risk scenario.     

Unified triaxiality at the crack tip subjected to plane strain condition under mixed‐mode (I + II) fracture

The new model of stress triaxiality, subjected to plane strain condition under mixed‐mode (I + II) loading, at the yield loci of the crack tip, has been formulated using unified strength theory. It evaluates critical values of triaxiality for various convex and non‐convex failure criteria, unlike the existing model. It shows the effects of Poisson's ratio and intermediate principal stress for materials whose strength in tension and compression is either equal or unequal. Further, on this basis, the crack initiation angles are predicted for various crack inclinations and compared with those obtained from other fracture criteria. The plastic zone shapes supplement the results. Critical yield stress factor, a significant parameter at the crack tip got lowered as the difference among the three principal stresses reduced to a minimum. The crack initiation angles obtained from the model showed good agreement with those obtained from G‐, S‐, and T‐criterion.     

Fatigue crack growth analysis of different adhesive systems: Effects of mode mixity and load level

The aim of this paper is to investigate the fatigue fracture behavior of three different adhesive systems (epoxy‐based, acrylic, and a rubber‐like adhesive). To achieve this, double cantilever beam specimens were manufactured with different adhesives and tested under several mode mixities and different load levels. Fatigue crack growth rate was evaluated through a Paris law equation. For postprocessing, the compliance‐based beam method was used. Results showed that the variation of the threshold energy with load level is more pronounced for the epoxy‐based adhesive. The crack propagation life is higher for the acrylic adhesive. Although, for pure mode I conditions, the normalized threshold of the rubber‐like adhesive is lower, for pure mode II, it was higher than the epoxy‐based adhesive. Due to the normalization by the static fracture energy, the slope of the Paris law was approximately constant for all the adhesive systems.     

Optimal Bayesian maintenance policy for a gearbox subject to two dependent failure modes

Most maintenance optimization models of gear systems have considered single failure mode. There have been very few papers dealing with multiple failure modes, considering mostly independent failure modes. In this paper, we present an optimal Bayesian control scheme for early fault detection of the gear system with dependent competing risks. The system failures include degradation failure and catastrophic failure. A three‐state continuous‐time–homogeneous hidden Markov model (HMM), namely the model with unobservable healthy and unhealthy states, and an observable failure state, describes the deterioration process of the gear system. The condition monitoring information as well as the age of the system are considered in the proposed optimal Bayesian maintenance policy. The objective is to maximize the long‐run expected average system availability per unit time. The maintenance optimization model is formulated and solved in a semi‐Markov decision process (SMDP) framework. The posterior probability that the system is in the warning state is used for the residual life estimation and Bayesian control chart development. The prediction results show that the mean residual lives obtained in this paper are much closer to the actual values than previously published results. A comparison with the Bayesian control chart based on the previously published HMM and the age‐based replacement policy is given to illustrate the superiority of the proposed approach. The results demonstrate that the Bayesian control scheme with two dependent failure modes can detect the gear fault earlier and improve the availability of the system.     

Coupled multi‐scale cohesive modeling of failure in heterogeneous adhesives

A multi‐scale cohesive numerical framework is proposed to simulate the failure of heterogeneous adhesively bonded systems. This multi‐scale scheme is based on Hill's variational principle of energy equivalence between the higher and lower level scales. It provides an easy way to obtain accurate homogenized macroscopic properties while capturing the physics of failure processes at the micro‐scale in sufficient detail. We use an isotropic rate‐dependent damage model to mimic the failure response of the constituents of heterogeneous adhesives. The finite element method is used to solve the equilibrium equation at each scale. A nested iterative scheme inspired by the return mapping algorithm used in computational inelasticity is implemented. We propose a computationally attractive technique to couple the macro‐ and micro‐scales for rate‐dependent constitutive laws. We introduce an adhesive patch test to study the numerical performance, including spatial and temporal convergence of the multi‐scale scheme. We compare the solution of the multi‐scale cohesive scheme with a direct numerical simulation. Finally, we solve mode I and mode II fracture problems to demonstrate failure at the macro‐scale. Copyright © 2010 John Wiley & Sons, Ltd.     

Strain-rate dependence in spot welds: Non-linear behaviour and failure in pure and combined modes I/II

When modelling assemblies for structural crashworthiness computations, fasteners are usually only characterised by their tension and shear strengths. However, for large deformations potentially leading to the failure of the assembly, joints are often loaded in combined modes, and the usual macro models fail to predict the assemblies' non-linear behaviour and rupture. In this paper, an advanced experimental procedure is proposed for testing and modelling spot-welded plates in pure and combined modes I/II under quasi-static and dynamic loading conditions. Obtained using a hydraulic jack and the Split Hopkinson Pressure Bar technique, the experimental results make it possible to analyse the mechanical strength (and the displacement rate dependence) of spot-welded plates. The non-linear behaviour and failure of experimental spot welds were proved to be strain-rate dependent in pure and combined mode I/II loading conditions. Our analysis showed that ultimate strengths in pure modes I and II would be particularly strain-rate dependent. Based on these results, a strain-rate dependent model was developed for ultimate loads in pure opening mode (tensile load) and presented in this paper. A computational approach for building a model for ultimate loads in pure shear mode is also discussed.     

CFRP加固钢板的粘结界面剥离破坏

II型界面破坏是碳纤维增强树脂复合材料(CFRP)加固钢板常见的破坏方式之一。为揭示CFRP加固钢板粘结界面破坏的力学机制,开展了单剪试验和双剪试验分别研究了CFRP-钢板界面力学性能及破坏过程,并采用数字图像相关技术(DIC)对CFRP的轴向应变分布进行监测。对比两个试验的破坏模式发现,双剪试件的粘结界面主要发生II型破坏,界面破坏的主要力学原因是剪应力;而存在偏心加载的单剪试件,粘结界面上的剪应力和偏心加载引起的弯矩共同作用,使粘结界面发生I/II型混合模式失效。在II型破坏模式下,不同粘结长度的极限荷载及粘结滑移值随着粘结长度的增大而增大,但当粘结长度超过有效粘结长度后,极限荷载及极限滑移值基本保持不变。而在所讨论的偏心加载引起的界面I/II型混合破坏模式下,不同粘结长度的极限荷载基本不变。基于试验数据得到的双线性粘结-滑移关系建立了有限元模型,对CFRP加固钢板的II型界面粘结破坏行为进行分析,数值模拟结果与试验结果吻合较好。      

Localizing gradient damage model with decreasing interactions

Nonlocal integral and/or gradient enhancements are widely used to resolve the mesh dependency issue with standard continuum damage models. However, it is reported that whereas the structural response is mesh independent, a spurious damage growth is observed. Accordingly, a class of modified nonlocal enhancements is developed in literature, where the interaction domain increases with damage. In this contribution, we adopt a contrary view that the interaction domain decreases with damage. This is motivated by the fact that the fracture of quasi‐brittle materials typically starts as a diffuse network of microcracks, before localizing into a macroscopic crack. To ensure thermodynamics consistency, the micromorphic theory is adopted in the model development. The ensuing microforce balance resembles closely the Helmholtz expression in a conventional gradient damage model. The superior performance of the localizing gradient damage model is demonstrated through a one‐dimensional problem, as well as mode I and II failure in plane deformation. For all three cases, a localized deformation band at material failure is obtained. Copyright © 2016 John Wiley & Sons, Ltd.