闪长岩单轴加载过程中声发射和弹性波速度变化规律的研究

为研究闪长岩在单轴加载过程中的声发射和各向波速变化规律,在单轴阶段加载和循环阶段加载条件下,对闪长岩岩样破裂过程中的声发射累计数、不同应力水平不同方向的波速、切线模量、轴向应变速率进行了研究。实验结果表明:(1)随着应力水平的增高,声发射事件数不断增加,在高应力水平(约80%峰值强度)时,声发射累计数急剧增多,随后切线模量出现震荡变化。(2)在加载过程中,压密程度及裂纹扩展方向对波速产生了巨大的影响,导致不同方向波速在不同的应力水平呈现出不同的变化规律,由此可以推测破裂面位置和破裂模式。在较高应力水平下(约60%峰值强度),平行于加载方向的波速趋于稳定,而垂直于加载方向的波速则持续下降,故用垂直于加载方向传播的波速预测岩石的破坏更具可靠性。(3)随着应力的增加,应变速率有逐渐减小的趋势,但临近岩石破裂时无异常变化出现,说明利用变形观测难以预测此类岩石的破坏。以上研究表明,根据纵波波速、声发射累计数和切线模量的变化可以有效预测岩石的破坏。     

周期荷载作用下煤岩声发射特征的颗粒流模拟

为研究周期荷载应力水平对煤样声发射特征的影响,采用PFC数值软件开展了3种不同应力水平的等幅周期荷载数值模拟试验,分析了周期荷载应力水平对煤样破坏循环次数、声发射计数及损伤演化特征的影响。研究结果表明:周期荷载作用下,煤样破坏过程中的声发射活动呈现初始、相对平静和活跃三阶段演化规律,且在煤样破坏前的周期荷载卸载阶段及低应力水平阶段几乎没有声发射活动;周期荷载上限应力水平的微小提高会加快煤样的破坏过程。提出了声发射比率的概念,当声发射比率大于1时,表明煤样即将发生破坏。声发射比率可作为预测现场工程煤体失稳的重要指标。     

Prediction of forming limit diagrams based on shear failure criterion

Maximum shear stress theory, also called the ‘Third Strength Theory’, is a classical theory used to predict the failure of common metal, but it cannot be used directly to predict sheet metal failure due to anisotropy and the loading path. Therefore, this paper proposes a maximum shear stress calculating method, which has been named “shear failure criterion” for the purpose of this paper. In order to validate the shear failure criterion, a general program was developed, and two typical materials, steel, and aluminum alloy, were used to study the new shear failure criterion in this study. The two materials were modeled by advanced constitutive models, including Hill1948 and Yld2000-2d yield functions and several types of isotropic hardening models. Experimental validation has indicated the accuracy of predicted FLD using shear failure criterion, which is able to provide a new alternative method to numerically predict FLD.     

基于应变能的复杂应力场低周疲劳分析

塑性应变能使材料微观组织结构发生不可逆变化,从而引起等效宏观应力,该应力随循环加载而增大．假定材料疲劳源处破坏是由最大拉应力引起的,最大等效宏观应力与外加应力叠加达到材料本征断裂应力时形成微裂纹．微裂纹引起上述两部分应力变化,继续加载直至宏观裂纹出现,从而得到材料的疲劳寿命．本文所建立的多轴疲劳寿命公式包含材料参数、拉应力以及塑性应变能等,以上数据可通过单轴疲劳数据和有限元方法获得．通过对SM45C材料的计算验证,表明该模型对多轴随机应变加载低周疲劳寿命,具有良好的预测结果．     

反倾层状边坡弯曲折断的应力及挠度判据

以地质分析为基础 ,将反倾层状边坡的任意岩层概化为受复合作用力的板梁模型 ,通过简单的力学解析 ,开展了反倾层状岩石边坡弯曲折断判据的研究。依据岩层折断时和相临岩层的瞬时关系 ,将岩层下部视为瞬时临空状态 ,考虑岩层自重荷载和上部岩层附加荷载 (上部岩层重力荷载、层间摩擦力 )的共同作用 ,基于最大拉应力准则 ,提出了岩层弯曲折断的应力判据 ;依据应力判据 ,得到了岩层弯曲折断的挠度判据 ;利用应力判据及挠度判据 ,可实现反倾层状边坡弯曲折断的现场判定及其控制设计     

Analysis of Damage and Failure in Anisotropic Ductile Metals Based on Biaxial Experiments with the H-Specimen

Background

Dependence of strength and failure behavior of anisotropic ductile metals on loading direction and on stress state has been indicated by many experiments. To realistically predict safety and lifetime of structures these effects must be taken into account in material models and numerical analysis.

Objective

The influence of stress state and loading direction on damage and failure behavior of the anisotropic aluminum alloy EN AW-2017A is investigated.

Methods

New biaxial experiments and numerical simulations have been performed with the H-specimen under different load ratios. Digital image correlation shows evolution of strain fields and scanning electron microscopy is used to visualize failure modes on fracture surfaces. Corresponding numerical studies predict stress states to explain damage and fracture processes on the micro-scale.

Results

The stress state, the load ratio and the loading direction with respect to the principal axes of anisotropy affect the width and orientation of localized strain fields and the formation of damage mechanisms and fracture modes at the micro-level.

Conclusions

The enhanced experimental program with biaxial tests considering different loading directions and load ratios is suggested for characterization of anisotropic metals.

     

Uniaxial ratcheting and fatigue failure of tempered 42CrMo steel: Damage evolution and damage-coupled visco-plastic constitutive model

Uniaxial ratcheting and fatigue failure of tempered 42CrMo steel were observed by the tests under the uniaxial stress-controlled cyclic loading with non-zero mean stress [G.Z. Kang, Y.J. Liu, Mater. Sci. Eng. A 472 (2008) 258–268]. Based on the obtained experimental results, the evolution features of whole-life ratcheting behavior and low-cycle fatigue (LCF) damage of the material were discussed first. Then, in the framework of unified visco-plasticity and continuum damage mechanics, a damage-coupled visco-plastic cyclic constitutive model was proposed to simulate the whole-life ratcheting and predict the fatigue failure life of the material presented in the uniaxial stress cycling with non-zero mean stress. In the proposed model, the damage was divided into two parts, i.e., elastic damage and plastic damage, which were described by the evolution equations with the same form but different constants, since the maximum applied stresses in most of loading cases were lower than the nominal yielding strength of the material. The ratcheting of the material was still described by employing a nonlinear kinematic hardening rule based on the Abdel-Karim–Ohno combined kinematic hardening model [M. Abdel Karim, N. Ohno, Int. J. Plast. 16 (2000) 225–240] but extended by considering the effect of damage. The maximum strain criterion combined with an elastic damage threshold was employed to determine the failure life of the material caused by two different failure modes, i.e., fatigue failure (caused by low-cycle fatigue due to plastic shakedown) and ductile failure (caused by large ratcheting strain). The simulated whole-life ratcheting behavior and predicted failure life of tempered 42CrMo steel are in a fairly good agreement with the experimental ones.     

Predicting variability in the dynamic failure strength of brittle materials considering pre-existing flaws

We perform two-dimensional dynamic fracture simulations of a specimen in biaxial tension, incorporating various distributions of pre-existing microcracks. The simulations consider the spatial distribution of flaws while modeling the discrete failure processes of crack interactions and coalescence, and predict the macroscopic variability in failure strength. The model quantitatively predicts the effect (on the dynamic failure strength) of different shapes of the flaw size distribution function, the random spatial distribution of flaws, and the random local resistance to crack growth (i.e. strength) associated with each flaw. The effect of changing material volumes on the variability in failure strengths is also examined in relation to the flaw size distribution. The effect of loading rate on the variability in failure strengths is presented in a form that will enable improved constitutive modeling using non-local formulations at the continuum scale.     

Computational analysis of stress-based forming limit curves

This article, through computational analyses, examines the validity of using the stress-based and extended stress-based forming limit curves to predict the onset of necking during proportional loading of sheet metal. To this end, a model material consisting of a homogeneous zone and a zone that has voids (material inhomogeneity) is proposed and used to simulate necking under plane strain and uni-axial stress load paths. Results of the in-plane loading computations are used to construct a strain-based formability limit curve for the model material. This limit curve is transformed into principal stress space using the procedure due to Stoughton [Stoughton, T.B., 2000. A general forming limit criterion for sheet metal forming. International Journal of Mechanical Sciences 42, 1–27]. The stress-based limit curve is then transformed into equivalent stress and mean stress space to obtain an Extended Stress-Based Limit Curve (XSFLC). When subjected to three-dimensional loading, the model material is observed to display a variety of responses. From these responses, a criterion for the applicability of the XSFLC to predict the onset of necking in the model material when it is subjected to three-dimensional loading is obtained. In the context of straight tube hydroforming, to provide support for the use of the XSFLC, it is demonstrated that the criterion is satisfied.     

The cumulative stress hazard density as an alternative to the Weibull model

A simple, easily reproduced experiment based on artificial flaws has been proposed which demonstrates that the distribution of the minimum failure load does not necessarily follow a Weibull distribution. The experimental result presented in the paper clearly indicates that the Weibull distribution with its strictly increasing function, is incapable of approximating a constant probability of failure over a loading region.New fundamental concepts have been introduced referred to as ‘hazard stress density’ and ‘cumulative hazard stress density’. These concepts helped derive an equation giving the probability of failure without making use of the notions ‘flaws’ and ‘locally initiated failure by flaws’. As a result, the derived equation is more general than earlier models. The cumulative hazard stress density is an important fingerprint of materials and can be used for determining the reliability of loaded components. It leaves materials to ‘speak for themselves’ by not imposing a power law dependence on the variation of the critical flaws which is always the case if the Weibull model is used.An important link with earlier models has also been established. We show that the cumulative hazard stress density is numerically equal to the product of the number density of the flaws with a potential to cause failure and the probability that a flaw will be critical at the specified loading stress.We show that, predictions of the probability of failure from tests related to a small gauge length to a large gauge length are associated with large errors which increase in proportion with the ratio of the gauge lengths. Large gauge length ratios amplify the inevitable errors in the probability of failure associated with the small gauge length to a level which renders the predicted probability for failure of the large gauge length meaningless.Finally, a general integral has been derived, giving the reliability associated with time interval and random loading of a material with flaws. The integral has been validated by a Monte Carlo simulation.     

Numerical simulation study on particle breakage behavior of granular materials in confined compression tests

In order to study the fragmentation law, the confined compression experiment of granular assemblies has been conducted to explore the particle breakage characteristic by DEM approach in this work. It is shown that contact and contact force during the loading process gradually transform from anisotropy to isotropy. Meanwhile, two particle failure modes caused by different contact force states are analyzed, which are single-through-crack failure and multi-short-crack failure. Considering the vertical distribution of the number of cracks and the four characteristic stress distributions (the stress related to the maximum contact force, the major principal stress, the deviatoric stress and the mean stress), it is pointed out that the stress based on the maximum contact force and the major principal stress can reflect the distribution of cracks accurately. In addition, the size effect of particle crushing indicates that small size particles are prone to break. The lateral pressure coefficient of four size particles during the loading process is analyzed to explain the reason for the size effect of particle breakage.     

SMT solder joint's semi-experimental fatigue model

The low-cycle fatigue induced by thermal cycling is the major concern in the reliability of surface mounted technology (SMT) for electronic packaging; however, dynamic loading effects to solder joint fatigue life have not been thoroughly investigated. In fact, the high-cycling fatigue induced by vibration can also contribute a significant effect. In certain circumstances it can become the dominant failure case when semiconductor devices are used in a vibration environment. In this paper, according to random vibration theory, a random fatigue semi-experimental model of SMT solder joint in random vibration condition is created and a series of vibration fatigue experimental vehicles including PBGA256 assembly were conducted. Compared with random vibration test results, its results are good enough to predict solder joints' fatigue.     

Multiaxial cyclic deformation and non-proportional hardening employing discriminating load paths

Some novel discriminating multiaxial cyclic strain paths with incremental and random sequences were used to investigate cyclic deformation behavior of materials with low and high sensitivity to non-proportional loadings. Tubular specimens made of 1050 QT steel with no non-proportional hardening and 304L stainless steel with significant non-proportional hardening were used. 1050 QT steel was found to exhibit very similar behavior under various multiaxial loading paths, whereas significant effects of loading sequence were observed for 304L stainless steel. In-phase cycles with a random sequence of axial-torsion cycles on an equivalent strain circle were found to cause cyclic hardening levels similar to 90° out-of-phase loading of 304L stainless steel. In contrast, straining with a small increment of axial-torsion on an equivalent strain circle results in higher stress than for in-phase loading of 304L stainless steel, but the level of hardening is lower than for 90° out-of-phase loading. Tanaka’s non-proportionality parameter coupled with a Armstrong–Fredrick incremental plasticity model, and Kanazawa et al.’s empirical formulation as a representative of such empirical models were used to predict the stabilized stress response of the two materials under variable amplitude axial-torsion strain paths. Consistent results between experimental observations and predictions were obtained by employing the Tanaka’s non-proportionality parameter. In contrast, the empirical model resulted in significant over-prediction of stresses for 304L stainless steel.     

PREDICTIVE APPROACH TO FAILURE OF COMPOSITE LAMINATES WITH EQUIVALENT CONSTRAINT MODEL

<正>This work established a new analytical model based upon the equivalent constraint model(ECM)to constitute an available predictive approach for analyzing the ultimate strength and simulating the stress/strain response of general symmetric laminates subjected to combined loading,by taking into account the effect of matrix cracking.The ECM was adopted to mainly predict the in-plane stiffness reduction of the damaged laminate.Basic consideration that progressive matrix cracking provokes a re-distribution of the stress fields on each lamina within laminates, which greatly deteriorates the stress distributed in the primary load-bearing lamina and leads to the final failure of the laminates,is introduced for the construction of the failure criterion. The effects of lamina properties,lay-up configurations and loading conditions on the behaviors of the laminates were examined in this paper.A comparison of numerical results obtained from the established model and other existed models and published experimental data was presented for different material systems.The theory predictions demonstrated great match with the experimental observations investigated in this study.     

RHEOLOGICAL FRACTURE ANALYSIS OF CABLE BY CONSIDERING THE SECOND ORDER EFFECTS OF RANDOM SLACK

In this paper,we consider the cable as a bundle consisting of n sub-bundles,with mparallel tension members per sub-bundle,and the tension members themselves are polymeric yarns im-pregnated with a resin matrix.The nonfailed members at any instant must share an applied system loadaccording to some rule,since there is a clearly expressed dependence of the fracture on the durationand character of the loading.So then,the fracture of cable is a process of nonlinear dynamic evolu-tion,which accommodates to the non-equilibrium thermodynamics of irreversible processes by itself.Let us assume that the polymeric yarns are as viscoelastic solid,under certain probabilistic assump-tions,according to the principles of theology of bodies with defects,the relationship between the singlemember loading and failure and the bundle loading are investigated.It can be shown that the bundlefailure time is asymptotically normally distributed as the number of members grows large.After astudy of the second order effects of random slack,it is known that the asymptotic mean and varianceare functions of the parameters of loading and single member rhcological behavior.Hence the loss inthe asymptotic bundle strength mean brought about by random member and sub-bundle slack,L.,andthe loss in the asymptotic bundle strength variance caused by random member slack,Δ_(?),are deter-mined.And finally,it is known that the asymptotic time of failure can make up a considerable part ofthe fracture of cable,and the fracture of cable is a time-dependent process of rheological fracture.     

Nonlinear granular micromechanics model for multi-axial rate-dependent behavior

Constitutive equations for class of materials that possess granular microstructure can be effectively derived using granular micromechanics approach. The stress–strain behavior of such materials depends upon the underlying grain scale mechanisms that are modeled by using appropriate rate-dependent inter-granular force–displacement relationships. These force–displacement functions are nonlinear and implicit evolutions equations. The numerical solution of such equation under applied overall stress or strain loading can entail significant computational expense. To address the computations issue, an efficient explicit time-integration scheme has been derived. The developed model is then utilized to predict primary, secondary and tertiary creep as well as rate-dependent response under tensile and compressive loads for hot mix asphalt. Further, the capability of the derived model to describe multi-axial behavior is demonstrated through generations of biaxial time-to-creep failure envelopes and rate-dependent failure envelopes under monotonic biaxial and triaxial loading. The advantage of the approach presented here is that we can predict the multi-axial effects without resorting to complex phenomenological modeling.     

Influence of reinforcement arrangement on the local reinforcement stresses in composite materials

The state of stress in and around reinforcements governs a number of physical processes in composite (multi-phase) materials, including the initiation of damage by either reinforcement cracking or interfacial decohesion. The stresses in the reinforcements have been observed to depend on the spatial distribution of the reinforcements, although the exact correlation is unclear. The present work determines the reinforcement stress for different reinforcement arrangements, ranging from a linear array of three uniformly spaced particles, to random and clustered microstructures. The stress calculations for elastic matrices were undertaken using a computationally efficient iterative technique. The technique was validated by comparing the results to finite element models, and the range of validity was determined. For the three-particle arrangements, the maximum reinforcement stress was observed when the particles were close to each other along the line of loading (a vertical arrangement). On the other hand, when the particle arrangement made a large angle with the loading direction, the reinforcement stress was low. Similar observations were recorded for the random and clustered arrangements where the location of the maximum reinforcement stress coincided with a vertical arrangement. The present work also develops a scheme for determining ‘representative volume elements’ for composite micromechanical models, based on the length scales of stress field interactions. These observations can be used to rationalize damage evolution mechanisms in commercial composites, and aid the development of physically based failure models for such materials.     

悬臂梁振动可靠性分析的研究

本文把悬臂梁的固有频率、激振力频率、平均应力、应力幅和疲劳极限处理为随机变量，提出了悬臂梁在强迫振动时不发生共振和疲劳损坏的可靠性分析方法。     

Is Weibull distribution the correct model for predicting probability of failure initiated by non-interacting flaws?

The utility of the Weibull distribution has been traditionally justified with the belief that it is the mathematical expression of the weakest-link concept in the case of flaws locally initiating failure in a stressed volume. This paper challenges the Weibull distribution as a mathematical formulation of the weakest-link concept and its suitability for predicting probability of failure locally initiated by flaws. The paper shows that the Weibull distribution predicts correctly the probability of failure locally initiated by flaws if and only if the probability that a flaw will be critical is a power law or can be approximated by a power law of the applied stress.Contrary to the common belief, on the basis of a theoretical analysis and Monte Carlo simulations we show that in general, for non-interacting flaws randomly located in a stressed volume, the distribution of the minimum failure stress is not necessarily a Weibull distribution. For the simple cases of a single group of identical flaws or two flaw size groups each of which contains identical flaws, for example, the Weibull distribution fails to predict correctly the probability of failure. Furthermore, if in a particular load range, no new critical flaws are created by increasing the applied stress, the Weibull distribution also fails to predict correctly the probability of failure of the component. In all these cases however, the probability of failure is correctly predicted by the suggested alternative equation. This equation is the correct mathematical formulation of the weakest-link concept related to random flaws in a stressed volume. The equation does not require any assumption concerning the physical nature of the flaws and the physical mechanism of failure and can be applied in cases of locally initiated failure by non-interacting entities.     

A stochastic theory of cumulative fatigue damage

A stochastic theory for the cumulative fatigue damage of structural components with random fatigue strength under random loading is proposed on the basis of Stratonovich-Khasminskii theorem. The analytical solutions for the probability densities of the cumulative fatigue damage and fatigue life and for the reliability function are given for steel and reinforced concrete components with constant fatigue strength subject to a narrow band stationary Gaussian stress process with zero mean. The results agree very well with those of digital simulation. It is noted that the theory can be applied, in principle, to both metallic and non-metallic materials, narrow band and wide band stress process, and adapted to a sequence ofn, stationary stress processes or quasi-stationary stress process. The scatter and degradation of fatigue strength and the inspection maintenance can also be incorporated into the theory.