Mode I fracture toughness analysis of a single-layer grapheme sheet

To predict the fracture toughness of a single-layer graphene sheet (SLGS), analytical formulations were devised for the hexagonal honeycomb lattice using a linkage equivalent discrete frame structure. Broken bonds were identified by a sharp increase in the position of the atoms. As crack propagation progressed, the crack tip position and crack path were updated from broken bonds in the molecular dynamics (MD) model. At each step in the simulation, the atomic model was centered on the crack tip to adaptively follow its path. A new formula was derived analytically from the deformation and bending mechanism of solid-state carbon-carbon bonds so as to describe the mode I fracture of SLGS. The fracture toughness of single-layer graphene is governed by a competition between bond breaking and bond rotation at a crack tip. K-field based displacements were applied on the boundary of the micromechanical model, and FEM results were obtained and compared with theoretical findings. The critical stress intensity factor for a graphene sheet was found to be K _IC = 2.63 ~ 3.2MPa \(\sqrt m \) for the case of a zigzag crack.     

Characterisation of crack tip stresses in elastic-perfectly plastic material under mode-I loading

Asymptotic crack tip stress fields are developed for a stationary plane strain crack in incompressible elastic-perfectly plastic material under mode-I loading. Detailed investigations have revealed that in between the two extreme conditions of crack tip constraint, that is, between the fully plastic Prandtl [1] field and the uniform stress field the most general elastic-plastic crack tip fields can be completely described by the 5-sector stress solution proposed in this article. The 3-sector stress field proposed by Li and Hancock [2] and the 4-sector field proposed by Zhu and Chao [3] are subsets of the general elastic-plastic field proposed in this work. This study has revealed that cases arise where the severe loss of crack tip constraint can lead to compressive yielding of crack flank. This particular situation leads to 5-sector stress field. Detailed studies have revealed that, in the most general case of elastic-plastic crack tip fields, the T_π parameter proposed by Zhu and Chao [3] cannot be used as a constraint parameter to represent a unique state of stress at the crack tip. A new constraint-indexing parameter T_CS-2 is proposed, which along with T_p is capable of representing the entire elastic-plastic crack tip stress fields over all angles around a crack tip. Excellent agreement is obtained between the proposed asymptotic crack tip stress field and the full-field finite element results for constraint levels ranging from high to low. It is demonstrated that the proposed constraint parameters are adequate to represent the crack tip constraint arising due to specimen geometry and loading conditions as well as the additional constraint that arises due to weld strength mismatch.     

用弹塑性有限元法对焊接接头裂尖场J积分的研究

采用平面应力弹塑性有限元法研究了中心裂纹板焊接接头裂尖场J积分参量及其应用的可行性，数值分析采用MARC软件的二维弹塑性分析模型，探讨了不同强度匹配（高，等，低匹配）的焊接接头试样在加载过程中裂尖场J积分的变化情况，计算结果表明，靠近焊接接头裂纹尖端的J积分回路明显的路径相关性，而远离裂尖的J积分回路表现出路径无关性，焊接接头强度匹配因子M对裂纹尖端的J积分值有很大的影响，对应于每一个载荷P／P0，J积分的值随M的增大而减小，特别是当P／P0＞1．0时这种情况更明显。     

氢对裂纹尖端塑性变形及裂纹扩展影响的TEM观察

利用透射电镜原位动态拉伸方法观察、分析氢对裂纹尖端塑性变形及裂纹扩展过程的影响。结果表明，氢促进裂纹尖端的局部塑性变形，改变裂纹扩展方式，并使裂纹以“Ｚ”字型的途径扩展。     

基于红外热成像的镁合金疲劳裂纹扩展的研究

采用红外热成像技术监测疲劳裂纹扩展过程中试件表面温度的变化情况,对AZ31B镁合金板材室温下的疲劳裂纹扩展特征进行研究。分析疲劳裂纹尖端温升值与裂纹长度的对应关系,试件表面温度分布差异与裂纹扩展趋势的关系,探索镁合金材料疲劳裂纹扩展的规律。试验结果表明,疲劳裂纹扩展过程中,镁合金表面温度变化经过一个升温、降温的过程,在稳定扩展阶段,温度变化不大,在快速扩展阶段,温度呈明显上升趋势。三组试件最高温升值分别为A试件10.89℃、B试件15.19℃、C试件12.37℃。裂纹尖端及其附近组织观察发现,裂纹尖端发生转向,裂纹总体为穿晶断裂,并伴随少量沿晶断裂,在裂纹附近区域有少量塑性变形。疲劳试件表面的最高温度区域与材料的疲劳损伤机制相关,该区域对应材料的应力集中区,是疲劳微裂纹形成与扩展的部位,温度变化与试件的最终断面相吻合。     

Estimation of fully plastic crack tip stresses from equilibrium of least upper bound circular arcs

This paper presents a simple method to estimate fully plastic crack tip stresses based on the equilibrium condition of the least upper bounds for plane strain deformation fields consisting of rigid-body rotation across a circular arc extending from a crack tip across the remaining ligament. The method is applied to deep, single-edge-cracked specimens under combined bending and tension. For various bending-to-tension ratios, the limit loads and crack tip stresses are estimated from the present method and compared with results from finite element limit analyses. The present method gives impressive results.     

Effect of local yield strength gradients on fatigue crack propagation

A new crack propagation effect is discussed analytically and demonstrated experimentally. It is shown that local one-dimensional variations in yield strength (strength gradients) can effect a major change in the rate of crack growth under conditions of constant amplitude cycled stress intensity at the crack tip as determined by linear elastic fracture mechanics. Rice's path independent integral is combined with certain fracture mechanics arguments to derive a crack propagation law which predicts that crack extension per cycle is modulated by strength gradients if they are present, in proportion to their slope. Experimental data are developed for two aluminum alloys which demonstrate the effect conclusively. The importance of these results as they apply to real engineering components where strength gradients are known to occur because of casting, forging, rolling, joining, etc. is discussed. The strength gradient effect is shown to be discrete and separate from other effects including the influence of local levels of strength.     

A study of spur gear pitting formation and life prediction

In this study, a numerical prediction on pitting formation is carried out in spur gear made from austempered ductile iron. General two-dimensional rolling sliding contact situations are considered for the development of the analytical model. The problem is assumed under linear elastic fracture mechanics and the finite element method is used for numerical solutions. Mixed mode stress intensity factors K_I and K_II for cyclic loading are evaluated and related to crack extension by a Paris-type equation. The maximum tangential stress criterion is used to determine the crack-turn-angle during crack propagation under cyclic loading.A series of experimental study is also carried out to determine the pitting formation life. Test specimens were first austenitized in salt bath at 900 °C for 90 min after which they were quenched in salt bath at 325 and 425 °C, for 60 min. A comparison is carried out between numerical and experimental results.     

压电介质中裂纹与邻近微孔洞的交互作用

基于线性压电理论，文中对裂纹和微孔洞的交互作用进行有限元计算分析。结果表明，(1)电场对裂纹启裂起促进还是抑止作用，与外加电场方向和裂纹面电学边界条件密切相关。(2)电-力载荷比、电学边界条件和微孔洞裂纹之间的韧带长度对裂纹前缘应力场均有一定影响，但无论对于何种裂纹电学边界条件(可导或绝缘)，裂纹前端的微孔洞只有在韧带长度小于2倍微孔洞直径时，才对裂纹前缘应力场有明显的影响。(3)在一定的电-力加载比和一定的韧带长度范围内，微孔洞对裂纹的启裂有屏蔽作用，且微孔洞对导通裂纹的屏蔽作用比绝缘裂纹要明显得多。此外，文中还给出韧带上张开应力的分布。     

高频谐振载荷作用下Ⅰ型疲劳裂纹尖端力学参数变化规律

为研究高频谐振式疲劳裂纹扩展试验中带有Ⅰ型预制裂纹的紧凑拉伸(CT)试件裂纹尖端力学参数的变化规律,利用动态有限元方法,采用ANSYS和MATLAB软件编写程序,计算了CT试件在高频恒幅正弦交变载荷作用下,在一个应力循环及裂纹扩展到不同长度时裂纹尖端区域的位移、应变场及裂纹尖端的应力强度因子,并分析了其变化规律。在计算裂纹尖端应力强度因子时,首先采用静态有限元方法和理论公式验证了有限元建模和计算的正确性,然后采用动态有限元方法研究了裂纹扩展过程中裂纹尖端应力强度因子的变化规律。最后进行了高频谐振式疲劳裂纹扩展试验,采用动态高精度应变仪测量了裂纹扩展到不同阶段时裂纹尖端点的应变,并对有限元计算结果进行了验证。研究结果表明：在稳态裂纹扩展阶段,高频谐振载荷作用下Ⅰ型疲劳裂纹尖端位移、应变及应力强度因子均为与载荷同一形式的交变量;随着裂纹的扩展,Ⅰ型疲劳裂纹尖端的位移、应变及应力强度因子幅不断增大;静态应力强度因子有限元计算值和理论值的误差为2.51%,裂纹尖端点应变有限元计算结果和试验结果最大误差为2.93% 。     

Fatigue crack propagation behavior in STS304 under mixed-mode loading

The use of fracture mechanics has traditionally concentrated on crack growth under an opening mechanism. However, many service failures occur from cracks subjected to mixed-mode loading. Hence, it is necessary to evaluate the fatigue behavior under mixed-mode loading. Under mixed-mode loading, not only the fatigue crack propagation rate is of importance, but also the crack propagation direction. In modified range 0.3≤a/W≤0.5, the stress intensity factors (SIFs) of mode I and mode II for the compact tension shear (CTS) specimen were calculated by using elastic finite element analysis. The propagation behavior of the fatigue cracks of cold rolled stainless steels (STS304) under mixed-mode conditions was evaluated by using K_I and K_II(SIFs of mode I and mode II). The maximum tangential stress (MTS) criterion and stress intensity factor were applied to predict the crack propagation direction and the propagation behavior of fatigue cracks.     

Deformations of a simplified flip chip structure under thermal testing inspected using a real-time Moiré technique

Deformations of a Si-epoxy-FR4 (simplified flip chip) structure under thermal testing were inspected with a real-time Moiré technique. Specimens without cracks and specimens with a crack at the silicon-epoxy interface were prepared. The measurement results showed that the maximum deformation appeared at the edge. When the specimen was cooled to 20 °C, there was residual plastic deformation in the specimen. The creep effect was more dominant in the FR4-epoxy interface. Upon cooling to 20 °C, the specimen experienced partial strain recovery. To characterize the behavior of the interfacial crack, stress intensity factors K_I and K_II, and the strain energy release rate G in the vicinity of the crack tip were calculated using the measured deformations to conduct a quantitative study. It was observed that a sharp strain gradient occurred at the crack tip. K_I and K_II were dependent on temperature, and G was dominated by K_I for the interfacial crack in the specimen.     

Effects of substrate materials on fracture toughness measurement in adhesive joints

To understand the effects of substrate materials on the fracture behavior of adhesive joints, experimental studies and finite element analyses have both been conducted for double-cantilever-beams (DCB) with aluminum and steel substrates at different bond thickness (h). Numerical results show that the region dominated by the crack singularity is much smaller than by the bond thickness. Very small plastic deformation may hence violate the requirements for small-scale yielding where the crack-tip field can be characterized uniquely by the stress intensity factor. Both critical strain energy release rate and J-integral for the joints with steel substrate are lower than those for the joints with aluminum substrate. Compared to the critical strain energy release rate, the critical J-integral is less sensitive to the substrate material if small plastic deformation occurs before cohesive failure takes place through the adhesive layer. For the joints with aluminum substrate, the fracture toughness initially increases and then decreases with bond thickness. Elastic–plastic crack-tip analysis indicates that at the same level of loading, a higher opening stress is observed in the joint with a smaller bond thickness. A self-similar stress field can be obtained by the normalised loading parameter, J/hσ₀.     

Determination of the fracture toughness of polycarbonate using an energy approach

A number of polycarbonate (PC) specimens, having the same compact tension type configuration but with different initial crack lengths, was tested at −12°C under Mode I type loading. The pop-in loads and corresponding displacements at the loading pins were plotted and connected by a common curve. The value of K_IC was determined using the method first proposed by Gurney and Hunt and was in close agreement with values reported by others. It is concluded that the pop-in load versus displacement curve is equivalent to a locus describing crack propagation under plane-strain conditions and suggests a new approach for determining K_IC for ductile solids.     

Hybrid determination of mixed-mode stress intensity factors on discontinuous finite-width plate by finite element and photoelasticity

For isotropic material structure, the stress in the vicinity of crack tip is generally much higher than the stress far away from it. This phenomenon usually leads to stress concentration and fracture of structure. Previous researches and studies show that the stress intensity factor is one of most important parameter for crack growth and propagation. This paper provides a convenient numerical method, which is called hybrid photoelasticity method, to accurately determine the stress field distribution in the vicinity of crack tip and mixed-mode stress intensity factors. The model was simulated by finite element method and isochromatic data along straight lines far away from the crack tip were calculated. By using the isochromatic data obtained from finite element method and a conformal mapping procedure, stress components and photoelastic fringes in the hybrid region were calculated. To easily compare calculated photoelastic fringes with experiment results, the fringe patterns were reconstructed, doubled and sharpened. Good agreement shows that the method presented in this paper is reliable and convenient. This method can then directly be applied to obtain mixed mode stress intensity factors from the experimentally measured isochromatic data along the straight lines.     

加载速率对焊接接头断裂行为的影响

在不同温度、不同加载速率下，对典型建筑结构用钢及其焊缝进行拉伸试验，测试其基本力学性能。采用能综合考虑加载速率及高加载速率下材料温度变化的R参量，确定本构关系。通过断裂力学试验，测试不同温度及加载速率下供试钢材及其焊接接头的断裂韧度值。随加载速率的增大，断裂韧度降低，但存在有较大的分散性。不同加载速率下裂纹尖端应力场数值分析结果表明，裂纹尖端最大主应力随加载速率的增大而升高。最后基于局部法，研究不同加载速率下母材及接头的断裂行为。局部断裂参量－－威布尔应力不受温度、加载速率的影响，可有效地描述材料的断裂行为。     

Toughness and fracture mechanisms of glass fiber/aluminum hybrid laminates under tensile loading

Tensile properties and fracture toughness of monolithic aluminum (Al), glass fiber reinforced plastics (GFRPs) and glass fiber/aluminum hybrid laminates (GFMLs) were examined in relation to the fracture processes of plain coupon and single-edge-notched specimens. Elastic modulus and ultimate tensile strength of GFMLs showed characteristic dependences on the kind of Al, fiber orientation and the Al/fiber layer composition ratio. Fracture toughnesses K_C and G_C of A-GFML-UD were comparable to those of GFRP-UD and were much superior to monolithic Al. However, GFML with a transverse crack parallel to the fiber layer deteriorated largely in toughness. Microscopic observation of the fracture zone in the vicinity of the crack tip revealed various modes of micro-cracks in the respective layers as well as fiber fractures and delamination between fiber/Al layers. Such damage advances in GFMLs dependent on the orientation of the fiber layer and the Al/fiber composition ratio strongly influenced the strength and toughness of GFMLs.     

Experimental investigation on the essential work of mixed-mode fracture of PC/ABS alloy

The mixed-mode fracture of polycarbonate (PC)/acrylonitrile-butadiene-styrene (ABS) alloy is experimentally investigated in this work. The essential work of fracture method is employed to measure the mixed-mode fracture toughness of PC/ABS alloy. Results show that the essential fracture work w _e increases significantly with the decrease in loading angles. Crack initiation angles are measured on the fractured specimens. The deviation of crack growth direction from the initial crack plane also increases with the decrease in loading angles, which corresponds to the increase of shear components. Microfracture processes of PC/ABS alloy with different loading angles are examined in situ by a scanning electron microscope. Crazing structures are clearly seen around the crack tip. The appearance, growth, and coalescence of crazes can be observed in the microfracture processes, and the macrocrack propagation direction is finally determined by the coalesced direction of crazes.     

Micromechanics analysis of progressive failure in cross-ply carbon fiber/epoxy composite under uniaxial loading

Three-dimensional micromechanics models were created for cross-ply carbon fiber/epoxy composite with a layer stacking-sequence arranged in [0/90]_s. Elasto-plastic finite element (FE) analysis was performed to study the effects of thermal residual stress and the stress redistribution as individual fiber fractures. The modified Rice and Tracey (RT) void growth model was used to predict the location of transverse matrix crack. The stress amplification factors (SAF) in intact fibers adjacent to a fractured fiber were calculated and compared with the planar array composite. The FE results show that small defects have already formed in curing process, and ply-delamination is likely to occur near the comer of free-edges. The transverse matrix crack was predicted to occur near the fiber fracture location in the models having little inter-fiber spacing.     

计算平面Ⅰ、Ⅱ型复合应力强度因子的半权函数法

给出计算一般平面裂纹问题应力强度因子的半权函数方法。该方法引入两个满足裂纹面零应力条件、平衡方程以及裂尖位移具有r^-1/2奇异性的虚拟位移与应力函数的解析表达式，即半权函数。从功能互等定理出发，结合从裂纹下缘到上缘绕裂尖任意路径的位移与应力的近似值，得到Ⅰ、Ⅱ复合型应力强度因子KⅠ和KⅡ积分形式的表达式。由于在积分中避开了裂尖的奇异性，因此即使采用较粗糙的模型或方法得到的近似值，也可以得到精度较高的KⅠ、KⅡ。相对于权函数法，本方法的限制条件较少，半权函数易于获得，实用性强；相对于有限元法计算量小，模型建立简便。