拉-拉循环荷载作用下的界面脱粘研究

应用弹性力学和断裂力学基本理论，基于剪滞模型，研究了纤维增强复合材料中纤维与基体界面在拉-拉循环荷载作用下的疲劳脱粘特性。建立了描述疲劳裂纹扩展的等效Paris公式，得到了界面疲劳脱粘扩展速率、脱粘应力以及脱粘界面的摩擦系数与循环加载次数的关系式。通过数值模拟计算，进一步分析了界面疲劳脱粘的力学机理。本文分析，考虑了疲劳加载引起的脱粘界面的损伤及损伤分布的不均匀性。同时还考虑了材料泊松比的影响。     

CTS试件中复合型疲劳裂纹扩展

针对复合型循环载荷作用下的金属构件中的裂纹扩展问题进行了实验分析和理论建模. 首先 采用紧凑拉剪试件(CTS)和 Richard研制的复合型载荷加载装置，对承受复合型循环载荷的裂纹进行了实验研究. 实验选择了两种金属材料试件，分别承受3种形式的复合型循环载荷的作用，在裂纹尖端具 有相同的初始应力场强度的条件下考察复合型循环载荷对裂纹扩展规律的影响. 实验结果表明，疲劳裂纹的扩展速率与加载角度有关. 对于同样金属材料的试件，当裂尖处 初始应力场强度相等时，载荷越接近于II型，裂纹增长速率越快. 采用等效应力强度 因子(I型和II型应力强度因子的组合)、裂纹扩展速率及复合强度等参数，以实验数据为 基础，建立了一个疲劳裂纹扩展模型，用来预测裂纹在不同模式疲劳载荷作用下的扩展速率. 为验证其有效性，该模型被应用于钢制试件的数值模拟计算中. 实验结果与模拟计算曲线保 持一致，表明该模型可以用来估算带裂纹金属构件的寿命.     

拉压循环载荷下正交异性钢桥面板肋-面板焊缝裂纹扩展分析

采用四步法计算了考虑循环载荷中压应力影响的正交异性钢桥面板的肋-面板焊缝表面裂纹扩展。第一步是基于正交异性钢桥面板的疲劳分析模型,计算肋-面板焊缝处的应力,第二步是通过肋-面板焊缝的三维局部模型,用Schwartz-Neumann交替法计算焊缝表面裂纹的应力强度因子分布,第三步是用二维断裂力学模型和增量塑性损伤模型,计算循环载荷中的压应力对裂纹扩展的影响,第四步是用第二步中的三维裂纹分析结果和第三步中的二维断裂力学模型得到的裂纹扩展公式,计算钢桥面板的肋-面板焊缝表面裂纹扩展。计算结果表明,对应于正交异性钢桥面板肋-面板焊缝处的循环应力,本文所用模型的裂纹尖端反向塑性区导致裂纹扩展率增加50%以上。研究结果为正交异性钢桥面板肋-面板焊缝裂纹的疲劳寿命分析提供了研究基础。     

Cohesive zone laws for fatigue crack growth: Numerical field projection of the micromechanical damage process in an elasto-plastic medium

Cohesive zone failure models are widely used to simulate fatigue crack propagation under cyclic loading, but the model parameters are phenomenological and are not closely tied to the underlying micromechanics of the problem. In this paper, we will inversely extract the cohesive zone laws for fatigue crack growth in an elasto-plastic ductile solid using a field projection method (FPM), which projects the equivalent tractions and separations at the cohesive crack-tip from field information outside the process zone. In our small-scale yielding model, a single row of discrete voids is deployed directly ahead of a crack in an elasto-plastic medium subjected to cyclic mode I K-field loading. Damage accumulation under cyclic loading is captured by the growth of voids within the micro-voiding zone ahead of the crack, while the evolution of the cohesive zone law representing the micro-voiding zone is inversely extracted via the FPM. We show that the field-projected cohesive zone law captures the essential micromechanisms of fatigue crack growth in the ductile medium: from loading and unloading hysteresis caused by void growth and plastic hardening, to the softening damage locus associated with crack propagation via a void by void growth mechanism. The results demonstrate the effectiveness of the FPM in obtaining a micromechanics-based cohesive zone law in-place of phenomenological models, which opens the way for a unified treatment of fatigue crack problems.     

Integrated numerical–experimental analysis of interfacial fatigue fracture in SnAgCu solder joints

In ball grid array (BGA) packages, solder balls are exposed to cyclic thermo-mechanical strains arising from the thermal mismatch between package components. Thermo-mechanical fatigue crack propagation in solder balls is almost always observed at the chip side of the bump/pad junction. The objective of the experimental part of this study is to characterize the bump/pad interface under fatigue loading. Fatigue specimens are prepared by reflowing Sn3.8Ag0.5Cu lead-free solder alloy on Ni/Au substrates. Obtained results show that fatigue damage evolution strongly depends on the microstructure. Applied strain and solder volume both have an influence on the fatigue damage mechanism. In the numerical part of the study, fatigue experiments are modeled using the finite element technique. A cohesive zone approach is used to predict the fatigue damage evolution in soldered connections. Crack propagation is simulated by an irreversible linear traction–separation cohesive zone law accompanied by a non-linear damage parameter. Cohesive zone elements are placed where failure is experimentally observed. Damage evolution parameters for normal and tangential interaction are scrutinized through dedicated fatigue tests in pure tensile and shear directions. The proposed cohesive zone model is quantitatively capable of describing fatigue failure in soldered joints, which can be further extended to a numerical life-time prediction tool in microelectronic packages.     

A coupled interface-multilayer approach for mixed mode delamination and contact analysis in laminated composites

An accurate laminate model developed by using multilayer shear deformable plate modeling and interface elements, based on fracture mechanics and contact mechanics, is proposed to analyze mixed mode delamination in composite laminates. Perfect adhesion along the undelaminated portion of the delamination plane is simulated by treating interface stiffnesses as penalty parameters, whereas to enforce interface displacement continuity between plate elements constituting each sub-laminate above or below the delamination plane, the Lagrange multiplier method is used. The governing differential equations are derived through a variational procedure by using a modified total potential energy functional. Results are obtained by numerical integration of the non-linear three-point boundary value problem modeling mixed-mode delamination of the laminate plate subjected to end loading, which accounts also for the frictionless contact condition.The coupling of a penalty procedure with the Lagrange multiplier method, results in an accurate and direct energy release rate evaluation. Comparisons with results available from the literature obtained with a local continuum approach, show that mode partition may be performed to the desired accuracy by refining multilayer plate models for each sub-laminate. In addition, original analytical formulas for mode partition are obtained by coupling the interface approach and fracture mechanics concepts, evidencing the effectiveness of the proposed approach and gaining a better insight into the influence of shear effects on mode decomposition. Numerical computations for practical problems, evidence both the relative simplicity and the efficiency of the proposed model to represent mixed mode interlaminar fracturing as well as crack–face interaction.     

Experimental Investigation and Finite Element Analysis of Fatigue Crack Growth in Pipes Containing a Circumferential Semi-elliptical Crack Subjected to Bending

In this paper, a circumferential external surface flaw in a metallic round pipe under cyclic bending loading is considered. Because of very rapid changes in the geometrical parameters around the crack front region, the mesh generation of this region must be done with great care. This may lead to an increase in the run time which makes it difficult to reach valid results and conclusions. Because of the advantages of the sub-modeling technique in problems which need very high mesh density, this method is used. Stress intensity factors in mode I condition are determined using three-dimensional finite element modeling with 20 node iso-parametric brick elements in the ANSYS 9.0 standard code and the singular form of these finite elements at the crack front. In order to estimate the analysis error, the structural parameter error in energy norm criterion was used. Because of the advantages of non-dimensional analysis, this method is employed, and the stress intensity factors are normalized. For the analysis of the fatigue crack growth, the Paris law is used. The propagation path of the surface flaw is obtained from the diagram of aspect ratio versus relative crack depth. The fatigue crack growth analysis (the relative crack depth against loading cycles diagram) of different initial crack aspect ratio under cyclic loading is also considered. Fatigue shape development of initially semi-elliptical external surface defects is illustrated. The effect of the Paris exponent (material constant) on fatigue crack propagation is shown as well. Moreover, the fatigue crack growth of several specimens is assessed experimentally using a manually-constructed experimental set up. Finally, the experimental results obtained by cyclic bending loading tests are compared with the numerical results. The experimental results show good conformity with the finite element results.     

Influence of the Matrix Type on the Mode I Fracture of Carbon-Epoxy Composites Under Dynamic Delamination

The delamination energy and fracture behaviour under static and dynamic mode I loading of two composites, made of the same unidirectional carbon reinforcement embedded in two different matrices, one tough and the other brittle, was investigated with the aim of analyzing the influence of the employed resin on the fatigue delamination behaviour of both composites. In the case of dynamic loading, the number of cycles necessary for the onset of delamination was determined for a given elastic energy release rate and crack growth rate for different critical energy rates. The double cantilever beam (DCB) test was found to be suitable for promoting the initial delamination. The experimental results confirm the enhanced performance of the tough resin both in terms of crack initiation and growth rate.     

巴西圆盘试样中心斜裂纹疲劳扩展轨迹的边界元模拟

提出了一个平面弹性体多裂纹疲劳扩展模型. 它主要涉及到复合型加载情况下多裂纹尖端疲劳扩展的数学模型及杂交位移不连续法(一种边界元法). 在数值模拟中, 对每一裂纹扩展增量分析时,在其先前的边界上增添裂纹扩展增量, 且只对新增添的裂纹扩展增量划分单元, 同时, 按照这种边界元法的实施方法对一些单元特征进行调整, 就可以方便地模拟裂纹扩展. 用这种数值方法模拟了巴西圆盘试样中心斜裂纹疲劳扩展轨迹,数值结果说明了预报模型的有效性, 揭示了裂纹体几何对疲劳扩展的影响.      

复合加载下疲劳裂纹扩展速率研究

本文提出了一种计算曲折裂纹尖端应力强度因子的简单方法。对一种油井钻杆材料在不同Ⅰ－Ⅱ复合比加载下的疲劳裂纹扩展行为的研究表明，Ⅱ型成分成对裂纹扩展速率有两种趋势相反的影响作用，并得到了一个计算复合型裂纹扩展速率的Ｐａｒｉｓ形式的公式。     

Modelling of progressive interface failure under combined normal compression and shear stress

The present work is concerned with an analysis of progressive interface failure under normal compressive stress and varying shear stress using the cohesive crack model. The softening model is assumed and frictional linear stress at contact is accounted for. A monotonic loading in anti-plane shear of an elastic plate bonded to a rigid substrate is considered. An analytical solution is obtained by neglecting the effect of minor shear stress component in the plate. The elastic and plate interface compliances are included into the analysis. Three types of solutions are distinguished in the progressive delamination analysis, namely short, medium and long plate solutions. The analysis of quasi-static progressive delamination process clarifies the character of critical points and post-critical response of the plate. The analytical solution provides a reference benchmark for numerical algorithms of analysis of progressive interface delamination. The case of a rigid–softening interface was treated in a companion paper, where also cyclic loading was considered.     

INTERACTION OF THREE PARALLEL CRACKS IN RECTANGULAR PLATE UNDER CYCLIC LOADS

This paper presents a numerical approach for modeling the interaction between multiple cracks in a rectangular plate under cyclic loads. It involves the formulation of fatigue growth of multiple crack tips under ruixed-mode loading and an extension of a hybrid displacement discontinuity method （a boundary element method） to fatigue crack growth analyses. Because of an intrinsic feature of the boundary element method, a general growth problem of multiple cracks can be solved in a single-region formulation. In the numerical simulation, remeshing of existing boundaries is not necessary for each increment of crack extension. Crack extension is conveniently modeled by adding new boundary elements on the incremental crack extension to the previous crack boundaries. As an example, the numerical approach is used to analyze the fatigue growth of three parallel cracks in a rectangular plate. The numerical results illustrate the validation of the numerical approach and can reveal the effect of the geometry of the cracked plate on the fatigue growth.     

Elastic-viscoplastic field at mixed-mode interface crack-tip under compression and shear

For a compression-shear mixed mode interface crack, it is difficult to solve the stress and strain fields considering the material viscosity, the crack-tip singularity, the frictional effect, and the mixed loading level. In this paper, a mechanical model of the dynamic propagation interface crack for the compression-shear mixed mode is proposed using an elastic-viscoplastic constitutive model. The governing equations of propagation crack interface at the crack-tip are given. The numerical analysis is performed for the interface crack of the compression-shear mixed mode by introducing a displacement function and some boundary conditions. The distributed regularities of stress field of the interface crack-tip are discussed with several special parameters. The final results show that the viscosity effect and the frictional contact effect on the crack surface and the mixed-load parameter are important factors in studying the mixed mode interface crack- tip fields. These fields are controlled by the viscosity coefficient, the Mach number, and the singularity exponent.     

An analytical delamination model for laminated plates including bridging effects

A penalised interface model, whose strain energy is the penalty functional related to interface adhesion constraint, is introduced in conjunction with a damageable interface whose local constitutive law, in turn, represents bridging stress effects, in order to analyse delamination and bridging phenomena in laminated plates. The laminate is modelled by means of first-order shear deformable layer-wise kinematics and the governing equations are formulated in the form of a non-linear differential system with moving intermediate boundary conditions related to opportune delamination and bridging growth conditions. The problem is solved through an analytical approach. The model leads to an accurate and self-consistent evaluation of the energy release rate and its mode components due to the inclusion of significant contributions arising from coupling between in-plane and transverse shear stresses, and to an asymptotic estimate of interlaminar stresses. The salient features of the proposed model are investigated in the context of an energy balance approach and of a J-integral formulation, thus providing simple results useful to model delamination growth and bridging behaviour when mixed mode loading is involved. The accuracy of the proposed model is substantiated through comparisons with results from continuum analysis obtained by a finite element (FE) procedure. The effectiveness of the proposed model is highlighted by showing the solution of a two-layered plate scheme subjected to pure and mixed mode loading conditions and to fibre bridging stresses. The results point out that the present model, despite its low computational cost in comparison with more complex FE analyses, is an efficient tool to predict delamination and bridging evolution.     

Dynamic fracture of concrete compact tension specimen: Experimental and numerical study

Compared to quasi-static loading concrete loaded by higher loading rates acts in a different way. There is an influence of strain-rate and inertia on resistance, failure mode and crack pattern. With increase of loading rate failure mode changes from mode-I to mixed mode. Moreover, theoretical and numerical investigations indicate that after the crack reaches critical velocity there is progressive increase of resistance and crack branching. These phenomena have recently been demonstrated and discussed by O?bolt et al. (2011) on numerical study of compact tension specimen (CTS) loaded by different loading rates. The aim of the present paper is to experimentally verify the results obtained numerically. Therefore, the tests and additional numerical studies on CTS are carried out. The experiments fully confirm the results of numerical prediction discussed in O?bolt et al. (2011). The same as in the numerical study it is shown that for strain rates lower than approximately 50/s the structural response is controlled by the rate dependent constitutive law, however, for higher strain rates crack branching and progressive increase of resistance is observed. This is attributed to structural inertia and not the rate dependent strength of concrete. Maximum crack velocity of approximately 800 m/s is measured before initiation of crack branching. The comparison between numerical and experimental results shows that relatively simple modeling approach based on continuum mechanics, rate dependent microplane model and standard finite elements is capable to realistically predict complex phenomena related to dynamic fracture of concrete.     

A NEW CYCLIC J-INTEGRAL FOR LOW-CYCLE FATIGUE CRACK GROWTH

The constitutive equation under the low-cycle fatigue (LCF) was discussed, and a two-dimensional (2-D) model for simulating fatigue crack extension was put forward in order to propose a new cyclic J-integral. The definition, primary characteristics, physical interpretations and numerical evaluation of the new parameter were investigated in detail. Moreover, the new cyclic J-integral for LCF behaviors was validated by the compact tension (CT) specimens. Results show that the calculated values of the new parameter can correlate well with LCF crack growth rate, during constant-amplitude loading. In addition, the phenomenon of fatigue retardation was explained through the viewpoint of energy based on the concept of the new parameter.     

Strain energy density prediction of fatigue crack growth from hole of aging aircraft structures

Fatigue crack growth rate depends not only on the load amplitude, but also on the morphology of crack path. The strain energy density theory has the ability to analyze crack growth rate. A strain energy density crack growth model is proposed. It can predict the lifetime of fatigue crack growth for mixed mode cracks while an equation for mode I crack is also obtained. The validity of the model is established with two cases: a center-crack panel and cracks emanating from the edge of a hole. The stress intensity factor expression for the former case is analytical while that of the latter is calculated numerically using finite elements. The results are compared with the testing data. Good agreement shows that the proposed model is useful.