Crack motion in viscoelastic solids: The role of the flash temperature

We present a simple theory of crack propagation in viscoelastic solids. We calculate the energy per unit area, G(v), to propagate a crack, as a function of the crack tip velocity v. Our study includes the non-uniform temperature distribution (flash temperature) in the vicinity of the crack tip, which has a profound influence on G(v). At very low crack tip velocities, the heat produced at the crack tip can diffuse away, resulting in very small temperature increase: in this “low-speed” regime the flash temperature effect is unimportant. However, because of the low heat conductivity of rubber-like materials, already at moderate crack tip velocities a very large temperature increase (of order of 1000 K) can occur close to the crack tip. We show that this will drastically affect the viscoelastic energy dissipation 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, which may result in unstable crack motion, e.g. stick-slip motion or catastrophic failure, as observed in some experiments. In addition, the high crack tip temperature may result in significant thermal decomposition within the heated region, resulting in a liquid-like region in the vicinity of the crack tip. This may explain the change in surface morphology (from rough to smooth surfaces) which is observed as the crack tip velocity is increased above the instability threshold.     

Three-dimensional characterisation and modelling of small fatigue corner cracks in high strength Al-alloys

The growth of fatigue cracks at small length scales is known to be influenced by a variety of factors, including local microstructure, varying stress states and crack shape. High resolution computed tomography allows for sub-micron resolution imaging of failure processes in small test coupons undergoing in situ cyclic loading, providing detailed three-dimensional (3D) assessment of propagation processes across the entire crack front (surface and depth). In this work fatigue crack growth has been examined in an advanced Direct Chill (DC) cast aluminium alloy, along with a fine grained powder-metallurgy alloy. The latter is identified as a model material, offering considerably simpler microscopic crack paths than the DC cast alloy, and hence a means of separating bulk mechanical effects (such as stress state variations across a crack front and plasticity induced closure) from microstructural effects (such as crystallographic deflection and roughness induced crack closure). Crack growth has been studied in both materials under both constant amplitude (CA) and single peak overload (OL) conditions. Experimental results are presented in the present paper, particularly in relation to micromechanical understanding of failure. A modelling approach based on those results, and some typical results, is also presented.     

Atomic scale investigation of grain boundary structure role on intergranular deformation in aluminium

The role that grain boundary (GB) structure plays on the directional asymmetry of an intergranular crack (i.e. cleavage behaviour is favoured along one direction, while ductile behaviour along the other direction of the interface) was investigated using atomistic simulations for aluminium 〈1 1 0〉 symmetric tilt GBs. Middle-tension (M(T)) and Mode-I crack propagation specimens were used to evaluate the predictive capability of the Rice criterion. The stress–strain response of the GBs for the M(T) specimens highlighted the importance of the GB structure. The observed crack tip behaviour for certain GBs (Σ9 (2 2 1), Σ11 (3 3 2) and Σ33 (4 4 1)) with the M(T) specimen displayed an absence of directional asymmetry which is in disagreement with the Rice criterion. Moreover, in these GBs with the M(T) specimen, the dislocation emission from a GB source at a finite distance ahead of the crack tip was observed rather than from the crack tip, as suggested by the Rice criterion. In an attempt to understand discrepancy between the theoretical predictions and atomistic observations, the effect of boundary conditions (M(T), Mode-I and the edge crack) on the crack tip events was examined and it was concluded that the incipient plastic events observed were strongly influenced by the boundary conditions (i.e. activation of dislocation sources along the GB, in contrast to dislocation nucleation directly from the crack tip). In summary, these findings provide new insights into crack growth behaviour along GB interfaces and provide a physical basis for examining the role of the GB character on incipient event ahead of a crack tip and interface properties, as an input to higher scale models.     

Analytical modeling and vibration analysis of internally cracked rectangular plates

This study proposes an analytical model for nonlinear vibrations in a cracked rectangular isotropic plate containing a single and two perpendicular internal cracks located at the center of the plate. The two cracks are in the form of continuous line with each parallel to one of the edges of the plate. The equation of motion for isotropic cracked plate, based on classical plate theory is modified to accommodate the effect of internal cracks using the Line Spring Model. Berger?s formulation for in-plane forces makes the model nonlinear. Galerkin?s method used with three different boundary conditions transforms the equation into time dependent modal functions. The natural frequencies of the cracked plate are calculated for various crack lengths in case of a single crack and for various crack length ratio for the two cracks. The effect of the location of the part through crack(s) along the thickness of the plate on natural frequencies is studied considering appropriate crack compliance coefficients. It is thus deduced that the natural frequencies are maximally affected when the crack(s) are internal crack(s) symmetric about the mid-plane of the plate and are minimally affected when the crack(s) are surface crack(s), for all the three boundary conditions considered. It is also shown that crack parallel to the longer side of the plate affect the vibration characteristics more as compared to crack parallel to the shorter side. Further the application of method of multiple scales gives the nonlinear amplitudes for different aspect ratios of the cracked plate. The analytical results obtained for surface crack(s) are also assessed with FEM results. The FEM formulation is carried out in ANSYS.     

Diversion of energy flow near crack tips of a vibrating plate using the structural intensity technique

The structural intensity (SI) of a vibrating rectangular plate with a crack is computed using the finite element method. The overall behavior of power flow patterns of the cracked plate is investigated. The presence of the crack can be identified by the changes of the directions of SI vectors near the crack. The effects of orientation of the crack and crack length on the energy flow pattern are also investigated. The SI method is then used to explore the positioning of dampers in vibrating thin plates to divert the vibration energy flow away from crack tips. This approach is proposed as a temporary measure to prevent further propagation of the crack before repair of the crack can be done.     

Plastic zone size and crack tip opening displacement of a Dugdale crack interacting with a coated circular inclusion

An analytical investigation on the plastic zone size of a crack near a coated circular inclusion under three different loading conditions of uniaxial tension, uniform tension and pure shear was carried out. Both the crack and coated circular inclusion are embedded in an infinite matrix, with the crack oriented along the radial direction of the inclusion. In the solution procedure, the crack is simulated as a continuous distribution of edge dislocations. With the Dugdale model of small-scale yielding [J. Mech. Phys. Solids 8 (1960) p. 100], two thin strips of yielded plastic zones are introduced at both crack tips. Using the solution for a coated circular inclusion interacting with a single dislocation as the Green's function, the physical problem is formulated into a set of singular integral equations. Using the method of Erdogan and Gupta [Q. J. Appl. Math. 29 (1972) p. 525] and iterative numerical procedures, the singular integral equations are solved numerically for the plastic zone sizes and crack tip opening displacement.     

Atomic simulations of influence of twinning on crack propagation of Al

Molecular dynamics simulation was performed to investigate the influence of twin boundary(TB) spacing on crack propagation of Al.This study reveals the orientation of initial crack may affect the mechanism of crack growth obviously.TB strengthens Al when the crack orientation is parallel with TB because of the hinderance of TB to the emission of the dislocations.The results indicate that there is an optimal TB spacing for mechanical properties of the Al,exhibiting reverse HP(Hall-Petch) and HP effect when the TB spacing is near the critical TB spacing.Furthermore,we find that there is a yield strength hardening effect in nanotwinned Al when the crack orientation is perpendicular to the TB,and the Young’s modulus is smaller in the nanotwinned Al than that of twin free Al.The studies also demonstrate that this distinctive deformation behavior is related to nucleation of dislocations and the repulsive force of TB to the dislocations and crack propagation,as well as the distance between the crack tip and the TB.     

Unstable Fracture Behavior of Rubber Toughened Poly(Styrene-co-Acrylonitrile)

A linear elastic fracture mechanics (LEFM) approach was used to study fracture characteristics of ABS materials. The effects of crack (ligament) length and rubber content on the microscopic deformations taking place at the front of crack tip and in the bulk of the specimens were investigated. The results of fractography studies showed that, in addition to rubber content, the microscopic deformations are influenced by crack length. For some materials this manifests itself as a change in macroscopic response. The ligament length dependent behavior was increased for the samples with higher rubber contents. The results also showed that, although the elastic behavior with unstable crack growth is the dominant micromechanism of deformation, stable crack propagation still occurred in some compositions. All the fracture parameters, including fracture toughness, fracture energy, plastic zone size, and crack tip opening, increased with rubber content. The changes in microscopic and, as a consequence, in the macroscopic deformation behavior of a given specimen with ligament length were attributed to changes in yield stress of the sample and maximum stress on the ligament.     

纳观尺度裂纹扩展微观机理的晶体相场法研究

采用晶体相场方法模拟不同预变形量的样品在单轴拉应变作用下的纳观裂纹扩展行为.观察纳观尺度的裂纹演化过程,结果表明：对于无预变形的样品,在拉应变作用下,由于裂口处应变集中,当应变量达到临界值时,裂口开始起裂并伴随位错出现,随着裂尖的前进位错伴随着裂尖而滑移.对于预变形的样品,在较小的临界应变值裂口起裂,且预变形量越大,裂纹越易起裂和扩展.在裂纹扩展早期阶段呈现出扩展-转向-扩展的长大特征,其本质是裂纹扩展由于裂尖附近的位错滑移受阻引起应变集中,造成主次原子晶面方向的原子键交替断裂,使得裂尖扩展沿[√3,1]和[√3,-1]方向交替改变而前进,裂纹边缘呈锯齿形状.样品的裂纹扩展后期出现显著的类似解理裂纹扩展行为,解理方向沿[√3,1]和[√3,-1]方向,且预变形量大的样品裂纹解理扩展更明显且扩展较快.     

An investigation of cracking in brittle solids under dynamic compression using photoelasticity

Crack initiation in brittle materials was experimentally studied using photoelasticity under dynamic loading conditions with particular attention to the frictional characteristics of the microcracks. Two pieces of Homalite-100 were bonded except central region to prepare plate specimens with an inclined center crack. An edge of the specimen was impacted with and without lateral confinement. In situ photoelastic (isochromatic) fringes were obtained using a high-speed camera. Initial direction and profile of wing crack was the same as in static loading tests. Effect of crack surface roughness and lateral confinement on fringe pattern is discussed. Average speed of wing crack propagation was about 100 m/s and wing cracks from a crack with higher friction coefficient propagated faster than from a smooth crack.     

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.     

Effect of periodic surface cracks on the interfacial fracture of thermal barrier coating system

Periodic surface cracks and interfacial debonding in thermal barrier coating (TBC) system may be induced during cooling process. The objective of this work is to investigate the effect of periodic surface cracks on the interfacial fracture of TBC system. The finite element method (FEM) incorporating cohesive zone model is used in analysis. It is found that surface crack spacing has significant effect on the initiation and propagation of short interface crack. Three different regions are identified for describing the effect of surface crack spacing. In Region I the interface crack driving force is dramatically reduced due to high surface crack density. In this case, the initiation of interfacial delamination can be delayed. Region II applies as the surface crack spacing is moderate. Analysis of this transition zone brings to the definition of normalized critical surface crack spacing. Region III arises for sufficient large surface crack spacing. In this case, the interface crack driving force reaches a steady state, where the effects of adjacent surface cracks are relatively insignificant and can be ignored. It can be concluded that an appropriately high surface crack density can enhance the durability of TBC system.     

Low-cycle fatigue small crack initiation and propagation behaviour of cast magnesium alloys based on in-situ SEM observations

In-situ observations on the initiation and propagation behaviour of low-cycle fatigue small cracks in cast magnesium–aluminium alloys (AM50 and AM60B) were carried out with scanning electron microscopy (SEM) to elucidate the resistance to fatigue cracking and to evaluate the fatigue small crack growth rate accurately and quantitatively. The results indicate that the fatigue small cracks formed preferentially on β-phase (Mg₁₇Al₁₂) boundaries at room temperature. In addition, the effects of the parameters of stress levels in low-cycle fatigue and temperatures as well as microstructure on fatigue small crack propagation behaviour are revealed. The variation of crack open displacement (COD) with stress levels and cycles at elevated temperature shows that it is unsuitable to estimate the fatigue small crack growth rate of cast magnesium alloys using conventional measurement methods such as the plastic-replica technique due to the obvious difference between microscopic cracks in the open and closed states. Stabilized crack propagation behaviour is limited to cases where the physical crack length is less than 1?mm in low-cycle fatigue.     

含随机裂纹网络孔隙材料渗透率的逾渗模型研究

采用逾渗理论对含随机裂纹网络的孔隙材料渗透性进行研究. 开裂孔隙材料渗透率的影响因素包括裂纹网络的几何特征、孔隙材料本体渗透率以及裂纹开度, 本文使用连续区逾渗理论模型建立了渗透率的标度律. 对于裂纹网络的几何特征, 本文基于连续区逾渗理论并考虑裂纹网络的分形特征提出了有限区域内二维随机裂纹网络的连通度定义; 对随机裂纹网络的几何分析表明, 随机裂纹局部团簇效应会降低裂纹网络的整体连通性, 随机裂纹网络的标度指数并非经典逾渗理论给出的固定值, 而是随着网络的分形维数的减小而增大. 本文在网络连通度和主裂纹团的曲折度的基础上, 提出了开裂孔隙材料渗透率标度律的解析表达, K=K₀(K_m,b)(ρ-ρ_c)^μ, 分别考虑了裂纹网络的几何逾渗特征 (ρ-ρ_c)^μ、孔隙材料渗透率K_m 以及裂纹开度比b; 对有限区域含有随机裂纹网络的孔隙材料渗透过程的有限元模拟表明, K₀ 在裂纹逾渗阈值附近与b呈指数关系, 但当裂纹的局部渗透率与K_m比值高于10⁶ 后, 开度比b对渗透率不再有影响.     

α-Fe裂纹的分子动力学研究

通过分子动力学方法，模拟了α-Fe裂纹的单轴拉伸实验中的形变过程.研究了不同晶体取向裂纹的形变特点和断裂机理，观察到各种形变现象，如位错形核和发射，位错运动，堆垛层错或孪晶的形成，纳米空洞的形成与连接等.计算结果表明，裂纹扩展是塑性过程和弹性过程相结合的过程，其中塑性过程表现为由裂尖发射的位错导致的原子切变行为，而弹性过程的发生则是由无位错区中的原子断键所导致.同时还研究了α-Fe裂纹的形变特点和断裂机理与温度场和应力场的依赖关系.     

HF酸刻蚀提升熔石英亚表面划痕抗损伤性能的机理

用HF酸刻蚀熔石英元件,研究刻蚀对元件后表面划痕的形貌结构及损伤性能的影响,探索损伤阈值提升的原因.时域有限差分算法理论计算结果表明:对于含有50nm直径氧化锆颗粒的划痕,对入射光调制引发场增强的最大值是入射光强的6.1倍,且最强点位于划痕内部氧化锆颗粒附近,而结构相同但不含杂质的划痕引发的最大场增强为入射光强的3.6倍,最强区位于划痕外围;HF酸刻蚀能够有效去除划痕中的杂质,改变划痕结构,增加其宽深比值,经刻蚀的划痕对入射光调制引发场增强降低到入射光强的2.2倍.实验结果表明,经过深度刻蚀的划痕初始损伤阈值较刻蚀之前提高一倍多;光热弱吸收测试仪测试刻蚀后划痕对1 064nm激光的吸收最大值仅为230ppm.HF酸刻蚀同时可以提升元件整体损伤阈值,由于元件上无缺陷区域损伤阈值随刻蚀的深入先增加后降低,因此HF酸刻蚀应进行到元件损伤阈值提升到最大值为止.     

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。     

HF酸刻蚀提升熔石英亚表面划痕抗损伤性能的机理

用HF酸刻蚀熔石英元件,研究刻蚀对元件后表面划痕的形貌结构及损伤性能的影响,探索损伤阈值提升的原因.时域有限差分算法理论计算结果表明:对于含有50 nm直径氧化锆颗粒的划痕,对入射光调制引发场增强的最大值是入射光强的6.1倍,且最强点位于划痕内部氧化锆颗粒附近,而结构相同但不含杂质的划痕引发的最大场增强为入射光强的3.6倍,最强区位于划痕外围;HF酸刻蚀能够有效去除划痕中的杂质,改变划痕结构,增加其宽深比值,经刻蚀的划痕对入射光调制引发场增强降低到入射光强的2.2倍.实验结果表明,经过深度刻蚀的划痕初始损伤阈值较刻蚀之前提高一倍多;光热弱吸收测试仪测试刻蚀后划痕对1 064 nm激光的吸收最大值仅为230 ppm.HF酸刻蚀同时可以提升元件整体损伤阈值,由于元件上无缺陷区域损伤阈值随刻蚀的深入先增加后降低,因此HF酸刻蚀应进行到元件损伤阈值提升到最大值为止.     

Response of line focus acoustic microscope to specimen containing a subsurface crack

A numerical model is presented to calculate V(z) and V(x, z) curves for a line focus acoustic microscope and a specimen containing a subsurface crack. In this model, a Gaussian beam which is tracked through the lens into the coupling fluid and into the specimen, interacts with the crack. The numerical approach is based on the solution of singular integral equations by the boundary element method. The system of singular integral equations follows from the conditions at the interface of the coupling fluid and the specimen and on the faces of the crack. An electromechanical reciprocity relation is used to express the voltage at the terminals of the microscope's transducer in terms of the calculated incident and back-scattered fields. V(z) and V(x, z) curves are presented for various locations and orientations of the crack. The characteristic features of the V(z) and particularly the V(x, z) curves, as they relate to crack configuration, are discussed in some detail.