On a Possible Approximation of Changes in Elastic Properties of a Transversely Isotropic Material due to an Arbitrarily Oriented Crack

The present paper addresses an approximate analytical model for contribution of an arbitrarily oriented circular crack into effective elastic compliance of a transversely isotropic material. We numerically examine the bounds of applicability of the hypothesis that change in elastic potential due to an arbitrarily oriented circular crack in a transversely-isotropic material can be approximated by the change calculated for a certain isotropic environment. In particular, we obtained that the error of such an approximation is less than 20% if the extent of anisotropy is moderate – the ratio of Young’s moduli in transverse and in-plane directions is less than 1.87. The obtained result can be used for development of a simple model for microcracked transversely-isotropic materials with mild-to-moderate extent of anisotropy.     

Debonding of a Weak Interface in Front of a Through-Thickness Crack

A through thickness crack traversing a laminate and approaching an interface weakened by the presence of a small debonding defect is analysed in the case when the defect is fully embedded in the K-field of the main crack. Plane approximation estimates of critical interfacial strength for crack deflection are compared with 3D calculations using integral equation and weight function formulations.     

Semi-Infinite Anti-Plane Crack in a Piezoelectric Material

The problem of an impermeable semi-infinite crack in a piezoelectric material is considered. The electroelastic field due to a pair of concentrate forces and free charges applied at the crack surfaces is obtained by using the Mellin transform method, and the intensity factors of the quantities of concern and the mechanical strain energy release rate are given. The obtained results may be used as the fundamental solution, from which some general solutions can be calculated by superposition. The well-known solution for a purely elastic material will be recovered from the present solution if letting the coupling constant vanish.     

Cylindrical Helix Spline Approximation of Spatial Curves

In this paper, we present a new method for approximating spatial curves with a G^1 cylindrical helix spline within a prescribed tolerance. We deduce the general formulation of a cylindrical helix, which has 11 freedoms. This means that it needs 11 restrictions to determine a cylindrical helix. Given a spatial parametric curve segment, including the start point and the end point of this segment, the tangent and the principal normal of the start point, we can always find a cylindrical segment to interpolate the given direction and position vectors. In order to approximate the known parametric curve within the prescribed tolerance, we adopt the trial method step by step. First, we must ensure the helix segment to interpolate the given two end points and match the principal normal and tangent of the start point, and then, we can keep the deviation between the cylindrical helix segment and the known curve segment within the prescribed tolerance everywhere. After the first segment had been formed, we can construct the next segment. Circularly, we can construct the G^1 cylindrical helix spline to approximate the whole spatial parametric curve within the prescribed tolerance. Several examples are also given to show the efficiency of this method.     

Steady-State Crack Velocity in a Viscoelastic Composite Material

The velocity of a semi-infinite crack slowly propagating in aninfinitely long strip made of a viscoelastic composite material isdetermined according to Christensen's fracture criterion. The edges ofthe strip are subjected to uniform opposite displacements normal to thecrack plane. The crack velocity is obtained from an energy balanceequation involving the energy dissipated in the whole strip; the latteris evaluated using an approximate, but sufficiently accurate, expressionof the stress field in the structure obtained by taking into account thestrong anisotropy of the long fibre composite material of interest. Thisnew version of Christensen's criterion compares favourably with theoriginal one and gives crack velocity predictions very close to thoseprovided by Schapery's criterion.     

Crack Front Waves in Dynamic Fracture*

A rapidly moving tensile crack is often idealized as a one-dimensional object moving through an ideal two-dimensional material, where the crack tip is a singular point. When a material is translationally invariant in the direction normal to the crack's propagation direction, this idealization is justified. A real tensile crack, however, is a planar object whose leading edge forms a propagating one-dimensional singular front (a `crack front'). We consider the interaction of a crack front with localized material inhomogeneities (asperities), in otherwise ideal brittle amorphous materials. We review experiments in these materials which indicate that this interaction excites a new type of elastic wave, a front wave, which propagates along the crack front. We will show that front waves (FW) are highly localized nonlinear entities that propagate along the front at approximately the Rayleigh wave speed, relative to the material. We will first review some of their characteristics. We then show that by breaking the translational invariance of the material, FW effectively act as a mechanism by which initially `massless' cracks acquire inertia.     

基于RPIFS模型的曲线分形逼近

E Guérin[1]给出了统一逼近光滑曲线与分形曲线的投影迭代函数系统(PIFS)模型,但该方法在逼近圆锥曲线时不能很好地逼近圆和椭圆线。为了弥补其不足,笔者提出了有理投影迭代函数系统(RPIFS)模型,并进一步给出了模型的几何性质及收敛性定理。RPIFS 不仅可以更好地逼近光滑曲线与分形曲线,还增加了自由度,扩展了表示对象的范围,一定程度上完善和推广了 E Guérin[1]等人的有关结果。本模型的主要用途是曲线造型及形状描述。     

Tabu搜索在平面曲线多边形近似中的应用

为在平面数字曲线的多边近似中克服顶点的检测只依靠局部区域,缺乏全局信息的弱点,把多边形近似问题作为一定的允许误差下寻找最少顶点数的最优化问题来处理。为能够处理点数较多的曲线,采用Ｔａｂｕ搜索来求近似最优解。和一些经典算法的实验比较表明,与只依靠曲线局部特性的一类算法相比,该算法在近似的保真性和效率上有明显的改进,同时又比准确寻优一类的算法如动态规划等有大幅度的时间节省。     

Self-similarity of the Crack Front in Stress Corrosion Fracture

In this letter, a new method was proposed to visualize the crack front in stress corrosion fracture of high strength steel. The fractal characteristic of the crack front was analyzed by measuring its fractal dimension and roughness exponent at the same time. The experimental results show that the irregularity of the crack front was partly self-affine.     

Plane Stress Steady Crack Growth in a Power-Law Hardening Material

The paper reports the results from an asymptotic analysis for a crack growing quasistatically under Mode I, plane stress conditions for a power-law hardening material. The asymptotic stress and deformation velocity fields near the growing crack tip are determined, comparisons to related work are discussed and some numerical results for aluminum are included. This revised version was published online in August 2006 with corrections to the Cover Date.     

Intersonic Crack Propagation in an Orthotropic Material

Intersonic crack propagation is found to exhibit essentially the same features in orthotropic and isotropic materials, provided that the crack propagates along a plane of elastic symmetry. Thus the stress and strain singularity at the crack edge is weaker than the inverse square root singularity in the sub-Rayleigh case, except at one distinct velocity. The energy flux into the process region is determined by using the Barenblatt model. It depends on the crack velocity and on the size of the process region, approaching zero with this size. This revised version was published online in July 2006 with corrections to the Cover Date.     

Damage Field Ahead of a Tensile Crack in an Elastic-Plastic and Viscoplastic Material

This paper investigates the interaction between a macroscopic crack and microscopic damage in an elastic-plastic and viscoplastic material subjected to tensile in-plane loading. The aim is to predict the fracture conditions by accounting for void accumulation in the vicinity of the crack-tip. A power law relates the stress to the strain of the material. The damage, which invokes the growth and coalescence of microvoids, is confined to a small circular zone surrounding the crack-tip. At the onset of crack extension, the applied stress for small-scale and large-scale yielding solutions is found to be proportional to a₀ ^-1/(n+1), where 2a₀is the initial crack length and n is the strain hardening exponent of the material. For small-scale yielding, the conditions required for fatigue crack growth and steady-state creep are determined. In particular, the variations of the normalized crack length with the number of loading cycles and the time required for failure are shown for various strain hardening exponents, applied loading, and material damage parameters. This revised version was published online in July 2006 with corrections to the Cover Date.     

Initiation of a Crack from the Edge of a Notch with Oblique Front in Specimens of Brittle Materials

The possibility of stable initiation and propagation of cracks from the edge of a notch with oblique front is established for specimens made of brittle tool materials. The compliance calibration of compact specimens weakened by notches with oblique front is obtained with the help of approximation of the experimental data by the method of least squares and applied to the evaluation of fracture toughness along the oblique profile in the process of wedging of a compact specimen.     

Plastic Deformation at the Tip of a Tensile Crack in a Non-linear Kinematic Hardening Material

The plastic deformation at the tip of a tensile crack in a non-linear kinematic hardening material under small-scale yielding conditions is investigated, with a view to quantifying the functional dependence of crack-tip plastic blunting size on material's strain hardening parameters. It is shown by dimensional analysis that, for materials being characterised by the Armstrong-Frederick non-linear kinematic hardening rule, the crack-tip blunting parameter depends parametrically on only two non-dimensional parameters; the functional dependence is determined using a parametric finite element analysis.     

Modeling of Ductile Crack Growth in Reactor Pressure-Vessel Steels and Determination of JR Curves

A method is presented for predicting JR curves for reactor pressure-vessel steels. The authors propose a procedure for determining the ductile fracture model parameters from the test results for smooth and notched cylindrical specimens. The stress and strain fields at the tip of a stationary and propagating cracks are studied by the finite-element method. The predicted JR curves are compared to the experimental data obtained for the 2T-CT-type specimens of 15Kh2NMFA-A reactor pressure-vessel steel in the initial and embrittled state.     

基于能量密度确定缓冲材料性能曲线的研究

目的 为了不断提高缓冲结构的综合防护性能,设计一种刚性和柔性模块组合化的一体式托架缓冲防护结构。方法 设计缓冲防护总体结构,分析总体结构的综合性功能,计算理论柔性模块缓冲性能,采用Ansys有限元静态模块分析贮存状态的托架强度,采用动态模块分析跌落状态的产品加速度冲击过载、产品位移量和托架强度。结果 缓冲防护结构强度小于材料抗拉强度,产品在跌落过程中受到的加速度冲击过载满足设计要求。结论 缓冲防护结构设计合理可行,综合防护性能更优,为缓冲防护领域结构设计和分析提供了设计和数据参考。     

后方器材仓库设施设备数量需求模型

针对后方器材仓库设施设备数量配置方法量化不足的实际情况,分析了后方器材仓库设施设备需求数量的主要影响因素,结合后方器材仓库的特点,建立了货架、搬运机械、包装设备以及温(湿)度控制设备等几种典型设施设备数量需求模型,并通过实例说明了模型的有效性和可操作性,所建立的模型可为后方器材仓库合理确定设施设备需求数量提供了科学依据。     

基于多结点样条的自由曲线最小误差逼近及其应用

多结点样条函数具有良好的局部性,而最小二乘法对数据拟合的全局性较好,因此多结点样条函数最小二乘逼近的稳定性及数值精度都能得到有效的保证。该文综合两者的特点,实现了自由曲线离散数据最小逼近误差数学模型的建立。同时应用此数学模型于一些平面及空间(甚至一些带噪音的)自由曲线拟合上和几何造型骨骼化上,测试其对各种自由曲线的拟合效果,结果证明最小逼近效果明显。     

Crack propagation in brittle heterogeneous solids: Material disorder and crack dynamics

Crack propagation in a linear elastic material with weakly inhomogeneous failure properties is analyzed. An equation of motion for the crack is derived in the limit of slow velocity. Predictions of this equation on both the average crack growth velocity and its fluctuations are compared with recent experimental results performed on brittle heterogeneous materials (Ponson in Phys Rev Lett, 103, 055501; Måløy et al. in Phys Rev Lett, 96, 045501). They are found to reproduce quantitatively the main features of crack propagation in disordered systems. This theoretical framework provides new tools to predict life time and fracture energy of materials from their properties at the micro-scale.