Fatigue models for glassy polymers

Temperature effects on fatigue crack propagation in glassy polymers can be described by the Chudnovsky and Moet model, which is based on the propagation of microdefects near the crack tip. This was shown by fitting several models to fatigue data for polycarbonate and poly (methyl methacrylate). Statistical regression analysis and a global search method were used in the model fitting.     

Supersonic crack propagation in a class of lattice models of mode III brittle fracture

We study a lattice model for mode III crack propagation in brittle materials in a stripe geometry at constant applied stretching. Stiffening of the material at large deformation produces supersonic crack propagation. For large stretching the propagation is guided by well-developed soliton waves. For low stretching, the crack-tip velocity has a universal dependence on stretching that can be obtained using a simple geometrical argument.     

An extensive 3D dislocation dynamics investigation of stage-I fatigue crack propagation

Stage-I fatigue crack propagation is investigated using 3D discrete dislocation dynamics (DD) simulations. Slip-based propagation mechanisms and the role of the pre-existing slip band on the crack path are emphasized. Stage-I crack growth is found to be compatible with successive decohesion of the persistent slip band/matrix interface rather than a mere effect of plastic irreversibility. Corresponding crack tip slip displacement magnitude and the associated crack growth rate are evaluated quantitatively at various tip distances from the grain boundary. This shows that grain boundaries systematically amplify slip dispersion ahead of the crack tip and consequently, slow down the stage-I crack growth rate. The results help in developing an original crack propagation model, accounting for the boundary effects relevant to polycrystals. The crack growth trend is then evaluated from calculations of the energy changes due to crack length increments. It is shown that the crack necessarily propagates by increments smaller than 10 nm.     

NON-DESTRUCTIVE EVALUATION OF HORIZONTAL CRACK DETECTION IN BEAMS USING TRANSVERSE IMPACT

Numerical and experimental studies for crack detection in beam employing transverse impact are presented. In the numerical study, a beam model of wave propagation is developed to calculate the time history of beam response before, over and after the crack region. It is expected that the resulting wave in the beam will be scattered by the crack and will carry information on the location and geometry of the crack. Experiments using a scanning laser vibrometer on specimens containing simulated crack are then conducted to verify the numerical results. Comparison study between the numerical results and experimental observations are conducted; good correlation between theory and experiment is observed. The beam model of wave propagation and adaptive multilayer perceptron networks (MLP) are then used for inverse identification of crack parameters (i.e., crack location, depth and length) in the beams. Time-domain displacement responses calculated using the present beam model containing predetermined crack parameters are used as training data for the MLP. Once the MLP is trained, the MLP networks are then employed for inverse determination of an unknown crack in a beam using experimental displacement responses measured with a scanning laser vibrometer. Examples show that the procedure performs well for the determination of a wide range of values for the location, depth and length of the crack.     

基于FBG反射谱特征的修补结构裂纹扩展监测

为了提高飞行器壁板裂纹修补结构的安全性,对基于光纤布拉格光栅(FBG)反射谱特征的航空铝合金修补结构疲劳裂纹扩展长度及角度监测方法进行了研究。修补结构在疲劳载荷的作用下,裂纹发生扩展,其尖端附近会产生不均匀应变场,在其作用下FBG传感器反射谱发生变形,通过检测反射谱变形达到监测裂纹扩展的目的。建立了实验样件的模型,使用有限元方法计算得到不同角度下裂纹扩展到不同长度时的应变分布,使用传输矩阵数值计算方法得到相应的FBG反射谱。提取反射谱的主峰偏移、反射谱面积、次峰峰值和三峰峰值等变形特征,建立并训练人工神经网络(ANN),通过ANN建立反射谱变形特征同裂纹扩展情况的关系,实现了对修补结构裂纹扩展的精确监测,监测裂纹长度误差在0.5 mm之内,角度误差在5°之内。解决了修补结构的裂纹扩展精确监测问题,对提高飞行器安全以及节约维护成本有着重要意义。     

Formation and propagation of cracks during cyclic deformation

Summary Starting from observation of the geometric features of formation and propagation of cracks in cycled single crystals of copper a model was developed for fatigue cracking. The only and experimentally well established assumption of the model is that the slip during cyclic deformation tends to be coarse. By the cooperation of stress concentrations at the slip steps and the hardening of slip planes activated locally two slip systems (with different slip planes and Burgers vectors) are activated alternatively so that a crack develops from the slip step. It propagates without monotonically increasing the hardening at the crack tip. The coarse slip produces sharp slip steps at the surface for crack formation and prohibits crack blunting during propagation. In contrast to other models the one described can show how the irreversible process of crack formation and propagation can take place despite completely symmetrical push-pull stresses. The whole crack is formed merely by the motion of dislocations present in the material so that but comparatively small stresses are needed. As, moreover, no thermally activated processes are necessary, fatigue at 4·2°K can be explained too. The strong dependence of fatigue on the state of the surface can also be accounted for since the cracks form at the surface steps. Materials which tend to coarse slip even in unidirectional tests are expected to fatigue easily. This is corroborated experimentally. Finally, many details of crack geometry can be explained in terms of the model.Published in Z. f. Metallkunde58 (1967), 780.     

Crack growth in polyconvex materials

We discuss a model for crack propagation in an elastic body, where the crack path is described a priori. In particular, we develop in the framework of finite-strain elasticity a rate-independent model for crack evolution which is based on the Griffith fracture criterion. Due to the nonuniqueness of minimizing deformations, the energy-release rate is no longer continuous with respect to time and the position of the crack tip. Thus, the model is formulated in terms of the Clarke differential of the energy, generalizing the classical crack evolution models for elasticity with strictly convex energies. We prove the existence of solutions for our model and also the existence of special solutions, where only certain extremal points of the Clarke differential are allowed.     

Baseline-free estimation of residual fatigue life using a third order acoustic nonlinear parameter

Prediction of crack growth and fatigue life estimation of metals using linear/nonlinear acousto-ultrasound methods is an ongoing issue. It is known that by measuring nonlinear parameters, the relative accumulated fatigue damage can be evaluated. However, there is still a need to measure two crack propagation states to assess the absolute residual fatigue life. A procedure based on the measurement of a third-order acoustic nonlinear parameter is presented to assess the residual fatigue life of a metallic component without the need of a baseline. The analytical evaluation of how the cubic nonlinear-parameter evolves during crack propagation is presented by combining the Paris law to the Nazarov-Sutin crack equation. Unlike other developed models, the proposed model assumes a crack surface topology with variable geometrical parameters. Measurements of the cubic nonlinearity parameter on AA2024-T351 specimens demonstrated high sensitivity to crack propagation and excellent agreement with the predicted theoretical behavior. The advantages of using the cubic nonlinearity parameter for fatigue cracks on metals are discussed by comparing the relevant results of a quadratic nonlinear parameter. Then the methodology to estimate crack size and residual fatigue life without the need of a baseline is presented, and advantages and limitations are discussed.     

Dynamic instability in intergranular fracture

A molecular-dynamics model for crack propagation under steady-state conditions is used to study dynamic instabilities along a grain boundary in aluminum that occur when the crack speed approaches 1/3 of the material's Rayleigh wave speed. Instead of crack branching, as is characteristic for a crack propagating in a homogeneous environment, the instability of an intergranular crack results in a periodic series of dislocation bursts. These bursts limit the crack speed and produce velocity oscillations with a large increase in energy dissipation that increases the grain boundary toughness.     

Crack propagation as a free boundary problem

A sharp interface model of crack propagation as a phase transition process is discussed. We develop a multipole expansion technique to solve this free boundary problem numerically. We obtain steady state solutions with a self-consistently selected propagation velocity and shape of the crack, provided that elastodynamic effects are taken into account. Also, we find a saturation of the steady state crack velocity below the Rayleigh speed, tip blunting with increasing driving force, and a tip splitting instability above a critical driving force.     

Real-time quantitative optical method to study temperature dependence of crack propagation process in colloidal photonic crystal film

A real-time quantitative optical method to characterize crack propagation in colloidal photonic crystal film(CPCF)is developed based on particle deformation models and previous real-time crack observations. The crack propagation process and temperature dependence of the crack propagation rate in CPCF are investigated. By this method, the crack propagation rate is found to slow down gradually to zero when cracks become more numerous and dense. Meanwhile, with the temperature increasing, the crack propagation rate constant decreases. The negative temperature dependence of the crack propagation rate is due to the increase of van der Waals attraction, which finally results in the decrease of resultant force. The findings provide new insight into the crack propagation process in CPCF.     

Hot cracks in rubber: origin of the giant toughness of rubberlike materials

We study crack propagation in rubberlike materials and show that the nonuniform temperature distribution which occurs in the vicinity of the crack tip has a profound influence on the crack propagation, and may strongly enhance the crack propagation energy G(v) for high crack velocities v. At very low crack-tip velocities, the heat produced at the crack tip can diffuse away, but already at moderate crack-tip velocities a very large temperature increase occurs close to the crack tip resulting in a "hot-crack" propagation regime. The transition between the low-speed regime and the hot-crack regime is very abrupt and may result in unstable crack motion, e.g., stick-slip motion or catastrophic failure.     

Mean stress effect in fatigue crack propagation

Crack propagation rates in three different grades of mild steel and two types of age hardening aluminium alloys have been measured for different stress ratios. The results show a pronounced stress ratio effect for all these materials. A model of fatigue crack propagation is formulated in terms of the size of the cyclic plastic instability zone at the crack tip rather than the zone of plastic yielding. The micro-plastic instability zone is measured by a parameter involving the ratio of the maximum stress intensity and the stress level at which macro-plastic instability occurs in the $\text{S}\text{N}$ curve of plain fatigue test pieces. Such a parameter provides a means of normalizing crack propagation results obtained for various stress ratios.     

Planar cracks in the fuse model

We simulate the propagation of a planar crack in a quasi-two dimensional fuse model, confining the crack between two horizontal plates. We investigate the effect on the roughness of microcrack nucleation ahead of the main crack and study the structure of the damage zone. The two-dimensional geometry introduces a characteristic length in the problem, limiting the crack roughness. The damage ahead of the crack does not appear to change the scaling properties of the model, which are well described by gradient percolation. Received 29 March 2000     

Finite element analysis of quasistatic crack propagation in brittle media with voids or inclusions

A three-level finite element scheme is proposed for simulation of crack propagation in heterogeneous media including randomly distributed voids or inclusions. To reduce total degrees of freedom in the view of mesh gradation, the entire domain is categorized into three regions of different-level meshes: a region of coarse-level mesh, a region of intermediate-level mesh, and a region of fine-level mesh. The region of coarse-level mesh is chosen to be far from the crack to treat the material inhomogeneities in the sense of coarse-graining through homogenization, while the region near the crack is composed of the intermediate-level mesh to model the presence of inhomogeneities in detail. Furthermore, the region very near the crack tip is refined into the fine-level mesh to capture a steep gradient of elastic field due to the crack tip singularity. Variable-node finite elements are employed to satisfy the nodal connectivity and compatibility between the neighboring different-level meshes. Local remeshing is needed for readjustment of mesh near the crack tip in accordance with crack growth, and this is automatically made according to preset values of parameters determining the propagation step size of crack, and so the entire process is fully automatic. The effectiveness of the proposed scheme is demonstrated through several numerical examples. Meanwhile, the effect of voids and inclusions on the crack propagation is discussed in terms of T-stresses, with the aid of three-level adaptive scheme.     

基于$lt;i$gt;J$lt;/i$gt;积分的颗粒煤岩单轴压缩下裂纹扩展研究

颗粒煤岩是由众多离散的煤岩颗粒组成的固态多层次多结构物质,具有煤岩与颗粒物质的双重性质,其裂纹扩展规律可以从煤岩力学特性和颗粒物质多尺度特性进行研究. 首先,从能量角度对线弹性材料受压破坏,裂纹扩展产生原因进行了阐述,指出线弹性阶段裂纹的扩展动力源自应变能的释放. 然后,通过物理实验和数值试验从宏观和细观两方面对颗粒煤岩受压破裂过程中裂纹扩展做了进一步研究,结果表明:颗粒煤岩完全破裂后,底部会形成一个锥形堆,裂纹的扩展随着煤岩颗粒粒径的减小而减缓,部分裂纹扩展会出现突变点,且裂纹无光滑性;由于煤岩颗粒粒径等引起介质的非均匀性对裂纹扩展有重要的影响,均质度系数越大裂纹起裂时间越晚,声发射能量释放在裂纹扩展的轻度、中度和深度三个不同阶段逐渐变得频繁、剧烈. 研究结果将有利于进一步研究岩土类颗粒材料受压破裂过程的裂纹扩展规律. 关键词： J积分')" href="#">J积分 颗粒煤岩 单轴压缩 裂纹扩展     

边界元法分析二维线弹性裂纹扩展

用边界元法研究裂纹扩展过程.首先将尖端区域Williams渐近展开的特征分析法与边界积分方程结合,解出切口尖端附近应力奇异性区域的各应力场渐近展开项系数,获得平面切口/裂纹结构完整的位移和应力场.再基于考虑非奇异应力项贡献的最大周向应力脆性断裂准则,运用边界元法分析边缘含裂纹半圆形弯曲试样在荷载作用下的启裂方向,对裂纹扩展过程给出自动跟踪方法,通过算例证明边界元法模拟裂纹扩展过程的正确性和有效性.     

韧性材料的微裂纹扩展与分叉的晶体相场模拟

采用晶体相场方法研究韧性单晶材料在双轴拉伸条件下微裂纹扩展与分叉的演化过程,分析应变、温度、初始裂口形状等因素对裂纹扩展和分叉的影响.结果表明:对于简单的单向拉伸,应变需要达到一定的临界值,裂纹扩展才会启动.对于二组相互垂直的双轴拉伸作用,当应变达到临界值后,裂纹扩展过程中会发生分叉现象.温度越高,裂纹扩展越快且分叉越多.裂纹在扩展过程中,体系能量不断降低,当裂纹出现分叉时,体系能量降低得更快.在裂纹扩展过程中,有时是会在裂尖处前方出现微小的空洞,类似在裂纹尖端前方出现位错发射情况,这些微小的空洞逐渐扩大连成裂纹.本文所得结果与相关模拟结果和实验结果符合.     

Laser cutting silicon-glass double layer wafer with laser induced thermal-crack propagation

This study was aimed at introducing the laser induced thermal-crack propagation (LITP) technology to solve the silicon-glass double layer wafer dicing problems in the packaging procedure of silicon-glass device packaged by WLCSP technology, investigating the feasibility of this idea, and studying the crack propagation process of LITP cutting double layer wafer. In this paper, the physical process of the 1064 nm laser beam interact with the double layer wafer during the cutting process was studied theoretically. A mathematical model consists the volumetric heating source and the surface heating source has been established. The temperature and stress distribution was simulated by using finite element method (FEM) analysis software ABAQUS. The extended finite element method (XFEM) was added to the simulation as the supplementary features to simulate the crack propagation process and the crack propagation profile. The silicon-glass double layer wafer cutting verification experiment under typical parameters was conducted by using the 1064 nm semiconductor laser. The crack propagation profile on the fracture surface was examined by optical microscope and explained from the stress distribution and XFEM status. It was concluded that the quality of the finished fracture surface has been greatly improved, and the experiment results were well supported by the numerical simulation results.     

Dynamic caustics and its applications

For the study of elastodynamic problems of propagating cracks it is necessary to evaluate the dynamic stress intensity factor K^d_I which depends on the form of expressions for the stress components existing at the running crack tip at any instant of the propagation of the crack and the corresponding dynamic mechanical and optical properties of the material of the specimen under identical loading conditions. In this paper the distortion of the form of the corresponding reflected caustic from the lateral faces of a dynamically loaded transparent and optically inert specimen containing a transverse crack running under constant velocity was studied on the basis of complex potential elasticity theory and the influence of this form on the value of the dynamic stress intensity factor was given. The method was applied to the study of a propagating Mode I crack in a PMMA specimen under various propagation velocities and the corresponding dynamic stress intensity factor K^d_I evaluated. Also, crack propagation behaviour of notched composites in dynamic loading modes are reviewed and evaluated. A relatively large data base using metal-epoxy particulates, rubber-toughened poly(methyl methacrylate), and Sandwich plates are given. In all cases, a combination of high-speed photography and the optical method of dynamic caustics has been used. Results on the dynamic crack propagation mode, fracture toughness and crack propagation velocities of several rubber-modified composite models are presented. The composite models studied include specimens with one and/or two ‘complex’ two-stage inclusions, i.e. PMMA round inclusions surrounded by concentric rubber rings, one and/or press-fifting inclusions without rubber interface, all under dynamic loading. In all cases both qualitative and quantitative results were obtained. Also, results on crack propagation mode, crack propagation velocity, stress intensity factors and on the influence of the sandwich phases on crack propagation mode are presented.