Crack front waves and the dynamics of a rapidly moving crack

Crack front waves are nonlinear localized waves that propagate along the leading edge of a crack. They are generated by both the interaction of a crack with a localized material inhomogeneity and the intrinsic formation of microbranches. Front waves are shown to transport energy, generate surface structure, and lead to localized velocity fluctuations. Their existence locally imparts inertia, which is not incorporated in current theories of fracture, to initially "massless" cracks. This, coupled to microbranch formation, yields both inhomogeneity and scaling behavior within the fracture surface structure.     

Nonlinear photothermal and photoacoustic processes for crack detection

We show that, using the thermal and mechanical nonlinearities of cracks, it is possible to produce nonlinear effects in the process of thermoelastic laser-generation of sound at the surface of a metallic sample. Two independent laser bursts centered on two different frequencies f₁ and f₂ are focused on the same spot, which can be close or distant form an artificial surface crack. By recording the acoustic response of the sample, frequency spectra obtained at different spot distances from the crack are compared. We observe that the frequency components resulting from the nonlinear process of frequency mixing (f₁+f₂, 2f₁, 2f₂, ...) are detectable for a generation on the crack but are absent out of the crack. Possible future improvements and other opportunities of crack imaging or non destructive testing methods based on these nonlinear processes are discussed.     

顶爆和拱腰侧爆同时作用下锚固洞室的动态响应

基于相似模型试验,采用显式非线性动力分析程序LS-DYNA3D研究了地下锚固洞室在拱顶和拱腰侧两处集中装药爆源同时爆炸作用下应力波传播规律、裂纹形成机理以及洞壁围岩位移分布特征。通过对比分析顶爆试验和计算模型的压应力时程曲线,发现模拟与试验结果吻合,且符合应力波的传播规律,表明数值模拟结果可靠。爆源爆炸后,应力波以圆形向周围岩体传播,两应力波相遇处压应力强度明显大于周围岩体;当应力波传到自由面时,会反射形成拉伸波,在地表下方和洞室上方发生“层裂”现象,在拱顶和拱腰侧爆源中间沿洞室径向有裂纹延伸,由于拉伸波的叠加,在爆源下方出现“八”字形的锥形裂纹面。锚杆能够起到加固岩体的作用,锚固洞室比毛洞裂纹分布少,毛洞迎爆侧裂纹主要为横向裂纹,而锚固洞室则为径向劈裂和横向裂纹。两爆源中点洞室径向处的洞壁围岩位移峰值最大,极易产生破坏。     

Determination of pyrolysis temperature for charring materials

An energy and mass balanced method of determining the pyrolysis temperature is proposed. The concept is to find the pyrolysis temperature that consumes the same amount of energy to produce the same amount of mass when using the pyrolysis front model as when using finite rate kinetics models for the entire charring process. The resulting pyrolysis temperature has the form of pyrolysis rate weighted average temperature. Comparisons between finite rate kinetics and pyrolysis front models for various boundary conditions, geometries, heats of decomposition, kinetic parameters and assumptions used in the literature were made to assess the proposed method. Models using energy and mass balanced pyrolysis temperature show good agreement with finite rate models and the experiments. Extensive numerical studies on various factors influencing the charring material pyrolysis show that heat flux, sample size, heat of decomposition and kinetic parameters are the most important factors for determining an appropriate pyrolysis temperature. Thermal conductivity, specific heat and density have a lesser effect on the pyrolysis temperature. For practical application, a non-dimensional correlation is developed to determine the appropriate pyrolysis temperature without solving the problem by using finite rate models. With this correlation the energy and mass balanced pyrolysis temperature can be determined with a standard deviation of 7.6 K. These predictions are validated by comparison with measurements of wood cylinder pyrolysis. A good agreement suggests that simpler pyrolysis front models yield practically useful and accurate results given an appropriate pyrolysis temperature.     

Estimating the sizes of surface cracks based on Hall element measurements of the leakage magnetic field and a dipole model of a crack

A method is proposed for estimating the sizes of surface cracks in magnetic materials. The method is based on applying a magnetic field, then determining the leakage magnetic field in the vicinity of a crack by moving a Hall element on the surface of the material along one or two scanning lines crossing the crack, and measuring the corresponding Hall voltage distribution. A dipole model of a crack is utilized, in which a surface crack is considered as being full of magnetic dipoles aligned parallel to the applied field, and whose density varies linearly along the depth of the crack. Analytical expressions are derived for the z-component of the intensity of the leakage magnetic field, and for the measured Hall voltage in the vicinity of a crack with an arbitrary cross-section along its long axis when it is perpendicular to the applied field. The crack sizes and the parameters of the distribution of magnetic dipoles along the crack depth are computed by crack inversion, which represents a regression for the Hall voltage distribution. A variable theoretical Hall voltage distribution is fitted to the measured Hall voltage distribution by minimizing the corresponding RMS error, which gives the unknown parameters at the end of the minimization. Hall voltage distributions are measured on ferromagnetic steel samples containing one artificial surface crack. Some crack inversions are performed for estimating the maximum crack depth and the crack width of cracks with rectangular and isosceles triangular cross-sections along the long crack axis. The accuracy of these crack inversions increases by utilizing either Hall voltage distributions measured along only one of the scanning lines, instead of along both scanning lines, or by using more precisely measured Hall voltage distributions. The fast and accurate estimation of the maximum crack depth and the crack width by such crack inversions could be important for pipeline inspection. Other crack inversions are performed for determining the cross-section along the long axis of the investigated cracks with satisfactory results. Received: 2 March 2001 / Accepted: 10 April 2001 / Published online: 25 July 2001     

The interaction and the surface crack of single-crystal silicon induced by a millisecond laser

When the silicon material is irradiated by laser, it absorbs the laser energy leading to the temperature rise and the thermal stress. The damage effect includes melting, vaporation and thermal stress damage. Once the thermal stress exceeds the stress strength the crack will initiate. The silicon surface cracks induced by a millisecond laser are investigated. The experimental results show that three types of cracks are generated including cleavage crack, radial crack and circumferential crack. The cleavage crack is located within the laser spot. The radial crack and circumferential crack are located outside the laser spot. A two-dimensional spatial axisymmetric model of silicon irradiated by a 1064 nm millisecond laser is established. To assess what stresses generate and explain the generation mechanism of the different cracks, the thermal stress fields during laser irradiation and the cooling process are obtained using finite element method. The radial stress and hoop stress within the laser spot are tensile stress after the laser irradiation. The temperature in the center is the highest but the thermal stress in the center is not always highest during the laser irradiation. The cleavage cracks are induced by the tensile stress after the laser irradiation. The radial crack and the circumferential crack are generated during the laser irradiation.     

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.     

光学元件亚表层裂纹成核临界条件研究

基于压痕实验和连续刚度测量法得到了熔石英材料硬度和弹性模量随压入深度的变化曲线, 系统分析了材料由延性到脆性转变的过程, 确定了熔石英晶体在静态/准静态印压和动态刻划时产生裂纹的临界载荷和临界深度。渐变载荷刻划实验结果表明, 划痕过程诱发的裂纹对法向载荷有很强的依赖性, 载荷较小时材料去除方式为延性域去除。随着法向载荷的增加, 首先产生垂直于试件表面的中位裂纹和平行于试件表面方向扩展的侧向裂纹, 而在试件表面上并没有产生明显的特征。载荷进一步增加后, 侧向裂纹扩展并形成了明亮区域, 最终诱发了沿垂直于或近似垂直于压头运动方向扩展的径向裂纹, 实现了材料的脆性去除。     

弱场下熔融织构YBa2Cu3O7-δ样品局域磁通蠕动的实验研究

利用半导体霍尔探头测量法在液氮温度下研究了低场下圆柱状熔融织构YBa₂Cu₃O_7-δ样品的局域磁通蠕动行为.对瞬时加减场样品端面局域磁场的磁弛豫,磁滞回线以及不同扫场速率下局域磁场的变化进行了测量,观察到了对数时间磁弛豫的行为,发现由加场和去场数据所得的激活能U₀有明显的不同.磁滞回线测量中,局域点的磁场随外场几乎同步变化,不同扫场速率下局域磁场随外场变化的差别不大.实验结果表明,外场除对样品侧面外,对端面也有明显的穿 关键词： 局域磁通蠕动 激活能 磁弛豫     

表面垂直裂痕诱发瑞利波散射的数值分析

激光激发的声表面波为材料表面缺陷的检测提供了有力的工具.针对含缺陷材料在模型边界上的复杂性,建立了基于平面应变的有限元模型并选取了相同厚度但含有不同深度的表面裂痕的单层铝板进行了对比计算,得到了声表面波经过不同深度的表面裂痕时产生的反射及透射信号波形的时域特征.进而引入了基于Wigner-Ville分布理论的时-频分析方法计算裂痕前、后散射的瞬态表面波的能量在时间-频率平面内分布的情形.结果显示：声表面波接近中心频率的某一频率成分在经过深度小于其中心波长的表面缺陷时,随着裂痕深度的增加,对应于该频率的反射系数呈现单调递增的趋势;而透射系数呈现递减的特征,这一结果可以为激光超声检测表面缺陷提供一种定量的表征手段.     

Modeling of thermomechanical fracture of functionally graded materials with respect to multiple crack interaction

Different aspects of thermomechanical fracture of functionally graded materials (FGMs) are considered. Among them are the crack interaction problems in a functionally graded coating on a homogeneous substrate (FGM/H). The interaction between systems of edge cracks is investigated, as well as, how this mutual interaction influences the fracture process and the formation of crack patterns. The problem is formulated with respect to singular integral equations which are referred to the boundary equation methods. The FGM properties are modeled by exponential functions. The main fracture characteristics are calculated, namely, the stress intensity factors, the angles of deviation of the cracks from their initial propagation direction and the critical stresses when the crack starts to propagate. The last two characteristics are calculated using an appropriate fracture criterion. The problem contains different parameters, such as the geometry (location and orientation of cracks, their lengths, and the width of the FGM layer) and material parameters, i.e. the inhomogeneity parameters of elastic and thermal coefficients of the functionally graded material. The influence of these parameters on the thermo-mechanical fracture of FGM/H is investigated. As examples the following real material combinations are discussed: TiC/SiC, Al₂O₃/MoSi₂, MoSi₂/SiC, ZrO₂/nickel and ZrO₂/steel.     

激光激发瑞利波检测表面倾斜缺陷的研究

研究激光激发瑞利波检测样品的表面倾斜缺陷。基于频域热弹耦合方程,采用有限元方法建立激光激发瑞利波检测倾斜缺陷的数值模型,研究倾斜缺陷的检测机理。数值计算含不同的长度及倾斜角度缺陷的样品中瞬态位移波形,分析瑞利波在倾斜缺陷处模式转换的过程,研究各种瑞利波的传播路径。在此基础上,研究缺陷宽度与材料黏性对瑞利波传播及缺陷检测的影响。结果表明:瑞利波在缺陷处产生的反射及透射瑞利波的到达观测点的时间可以检测缺陷位置和长度,瑞利波在缺陷的底部发生模式转换产生的切变波可以检测缺陷倾斜角度。数值结果和已有的实验结果一致,从而为表面倾斜缺陷的检测提供有效的理论依据。      

The elastic field of general-shape 3-D cracks

We extend here the Bilby-Eshelby approach of 2-D crack representation with dislocation pileups to treat 3-dimensional cracks of general geometry. Cracks of any specified external bounding 3-D contour under general loading conditions are represented by sets of parametric Somigliana loops that satisfy total (interaction, self, and external) force equilibrium. Loop positions are solved by using a time integration scheme till equilibrium is achieved. The local Burgers vector is suitably adjusted to be proportional to the local applied surface traction on the crack. The developed method is computationally advantageous, since accurate crack stress fields are obtained with very few concentric parametric loops that adjust to the external crack shape and the local force conditions. The method is tested against known elasticity solutions for 3-D cracks and found to be convergent with an increase in the number of pileup dislocation loops. The method is applied to the determination of the stress field around a 3-D Griffith crack under general loading and a grain boundary crack before and after branching.     

Solution of collinear cracks in an electrostrictive solid

A general treatment is presented of the two-dimensional problem of N collinear cracks in an infinite electrostrictive material subjected to remote electric loads based on the complex variable method combined with analytical extension of the complex variable functions. First, for the case of permeable cracks, general solutions for the electric potentials, Maxwell stresses, electroelastic stresses and stress intensity factors are derived. As specific examples, explicit and concise results are obtained for the cases of one crack and two collinear cracks. Then, these results are extended to the cases of impermeable and conducting collinear cracks, respectively. It is found that, in general, the total stresses always have the classical singularity of the r ^{- 1/2} type at the crack tips, whereas the Maxwell stresses have an r ^{- 1} singularity for the above three crack models. Finally, it is concluded that the applied electric field may either enhance or retard crack growth depending on the electric boundary conditions adopted on the crack faces, and the Maxwell stresses on the crack faces and at infinity.     

Non-local theory solution of two collinear mode-I permeable cracks in a magnetoelectroelastic composite material plane

The non-local theory solution of two collinear mode-I permeable cracks in a magnetoelectroelastic composite material plane was investigated using the generalized Almansi's theorem and the Schmidt method. The problem was formulated through Fourier transform into two pairs of dual integral equations, in which the unknown variables are the jumps in displacements across the crack surfaces. To solve the dual integral equations, the displacement jumps across the crack surfaces were directly expanded as a series of Jacobi polynomials. Numerical examples were provided to show the effects of crack length, the distance between two collinear cracks and the lattice parameter on the stress field, the electric displacement field and the magnetic flux field near the crack tips. Unlike the classical elasticity solutions, it is found that no stress, electric displacement or magnetic flux singularities are present at the crack tips in a magnetoelectroelastic composite material plane. The non-local elastic solutions yield a finite hoop stress at the crack tip, thus allowing us to use the maximum stress as a fracture criterion.     

A comparative analysis of reticular crack on ceramic plate driven by thermal shock

Reticular crack is generally found on the surface of ceramic material that has been subjected to a thermal-shock condition. In the present study, a quantitative effect of thermal shock and quench temperature has been studied and investigated. Experimental tests were carried out to characterize the reticular crack that has been found in the Ge Kiln, which is a famous art of the ancient Chinese culture. After comparative analysis between thermal-shock cracks and the glaze crack patterns of the Ge Kiln porcelain, it is found that this study is expected to provide a powerful tool for recurrence of the long-lost firing and cooling process of the Ge Kiln porcelain.     

Modeling the Effect of Thermophysical Properties on Pyrolysis of Intumescent Fire-retardant Materials

Thermophysical properties of intumescent fire-retardant (IFR) materials are important input parameters to simulate the pyrolysis process of IFR materials in fire scenarios. In this article, the effects of the thermophysical properties on pyrolysis of IFR materials are simulated based on a pyrolysis model of IFR materials. The selected thermophysical properties here are the specific heat capacity of the virgin material, thermal conductivity of the virgin material and char layer, heat of decomposition, density of virgin material, intumescent temperature, and surface emissivity of virgin material and char layer. Simulated mass loss rates (MLR) for the IFR materials at an incident heat flux of 50 kW/m² are investigated for the varied thermophysical parameter values. The results show that changes in these property values can affect the pyrolysis behavior of materials profoundly. Comparison with experimental results indicates that the simulations of MLR are in reasonably good agreement with the experiments.     

裂纹或气泡对熔石英损伤修复坑场调制的近场模拟

建立了含有裂纹或气泡的高斯型修复坑的3维模型, 用3维时域有限差分方法研究了熔石英后表面该类缺陷对355 nm入射激光的近场调制. 研究表明, 裂纹的调制明显大于气泡或者高斯坑本身, 因此为了抑制修复元件的初始损伤, 应尽量避免任何未修复的裂纹存在, 尤其是与入射光呈夹角约25°的裂纹, 同时应避免尺寸大于5 λ 的气泡存在. 当裂纹或气泡位于近表面层3 λ 以内且靠近修复坑环边缘时, 对场的调制最明显. 随着侧移的增加, 近表面区缺陷诱导场叠加, 强点总数涨落较大且易形成极大峰值, 特别是含有裂纹的情形; 远表面区强点总数逐渐增大并趋于稳定. 随着嵌深的增加, 强点的数目大体呈减弱趋势, 当嵌深大于3 λ 时, 逐渐趋于平缓振荡. 如果裂纹或气泡位于坑点正下方几个波长内, 激光辐照下其效果相当于延长了高斯坑的深度.     

激光激发声表面波在缺陷板材中散射过程的有限元分析

利用有限元法模拟了金属板材中激光激发的声表面波经过缺陷位置时发生散射的瞬态过程,采用线状激光源作为超声导波的激发源.针对三种不同深度的表面缺陷以及三种亚表面缺陷的模型进行了对比计算,结果显示缺陷的深度及位置对声表面波的时域特征存在显著的影响.表面缺陷深度越深将产生较大幅度的表面反射回波,亚表面缺陷的影响将取决于缺陷上顶面距离板材上表面的距离.因此,数值模拟结果表明通过分析激光产生的表面波形可以判定近表面缺陷的尺寸和所处的位置.     

Pulsed Rayleigh wave scattered at a surface crack

This paper investigates Rayleigh wave interaction with machined slots on flat aluminium blocks to simulate surface breaking cracks. Using a finite element method, Rayleigh wave scattering by narrow slots of varied depth ranging from 0.5 mm to 20 mm is calculated. Pulsed wideband Rayleigh waves with a centre frequency of 590 kHz and -6 dB bandwidth of 520 kHz is considered. Reflection and transmission coefficients are calculated and compare well with the published literature. We and other workers have reported enhancement of the measured amplitude or particle velocity of an apparent Rayleigh wave close to a surface defect. In this paper, it is found that the predicted enhancement of in-plane components of particle velocities close to a crack is significantly higher than that of the out-of-plane components of particle velocities which appears to be mainly due to the mode-converted surface skimming longitudinal wave from the crack that has mainly in-plane components near the sample surface. The enhancement of the in-plane particle velocity will be observed regardless of the type of in-plane sensitive ultrasonic detector used. The explanation of the discrepancy of the reflection and transmission coefficients obtained by pulsed and narrow band or pseudo continuous Rayleigh waves is discussed. The later-arriving Rayleigh waves from reverberation along the inside of the crack surface are observed, as has been previously reported by other workers, and this may also be used to gauge slot depth.