斜入射透射焦散线测量误差的数值分析

本文根据程函理论，用空间解析几何方法，推导了在ｘ－ｚ或ｙ－ｚ平面内斜入射的平行光线在含Ⅰ型裂纹透明材料中传播的方程，并通过数值解对其形成的焦散线的畸变进行了分析，给出了几种典型透射材料中由于斜入射造成的焦散线直径的偏差曲线     

声焦散线及其与应力强度因子的关系

 根据焦散线的形成原理，以及含I型裂纹试件受力前后光程差与 声程差表达式的相似性，提出了声焦散线的概念，得到了声焦散线沿 横向最大尺寸与应力强度因子的关系，为通过声焦散线法确定应力强 度因子打下了基础.     

爆炸载荷下非透明介质断裂的焦散线实验方法

首次把焦散线实验方法应用于非透明介质在爆炸载荷作用下的断裂问题的研究.在采用DDGS-Ⅱ型多火花式高速摄影和反射式焦散线光路系统基础上,改进了镜面移植的试件加工方法,实现了较大面积的镜面移植;设计了可多角度调节的爆炸加载架,引进切槽控制爆破技术,满足了爆生裂纹穿过镜面区的要求和摄影记录测量要求.并应用该实验方法,进行了两种非透明介质(人造石和PVC)爆炸致裂的焦散线实验,得到爆生裂纹在人造石和PVC试件扩展过程中不同时刻的焦散线照片,分析了人造石试件中爆生裂纹的运动学和力学行为特征.爆炸加载反射式焦散线实验方法拓展了焦散线实验的应用范畴,为研究非透明介质的爆炸动态断裂问题提供了方法.     

焦散线法在断裂力学中的应用(应力强度因子K_1的测定)

本文介绍了一种测量应变奇异性的新方法-焦散线法。阐述了焦散线的基本理论和试验技术。得到了清晰的焦散线照相。材料的应力光学系数通过透射焦散线和反射焦散线的两尺寸比值来确定。通过试验,测定了单边裂纹板受拉时的应力强度因子,与计算结果附合良好。     

Ⅰ型焦散线图象的微机自动处理

根据焦散线的原理,分析了Ⅰ型焦散线实验图象的特点,提出确定图像中焦散线位置的准则。基于此准则的微机图象处理,可自动精确测量Ⅰ型焦散线的最大直径。     

焦散线法及其与应力“解冻”相结合的应用

详细地阐述了焦散线法原理，对焦散线的形成作了说明，简述了焦散线法在平面问题中的应用，结合笔者研究工作介绍了将焦散线法拓广应用于三维问题的关键技术和实例。     

用焦散线方法测量集中载荷的误差分析

在实验应力应变分析中，焦散线方法是研究奇异应力场的有效方法．本文以半无限平面受边界压缩载荷作用的问题为例，对集中力作用下的焦散线与分布力作用下的焦散线作了比较，分析了由分布载荷得到的焦散线而计算得到的载荷与施加到试件上的实际载荷之间的误差，并提出了减小误差的措施．     

I型焦散线图象的微机自动处理

根据焦散线的原理，分析了Ｉ型焦散线实验图象的特点，提出确定图像中焦散线位置的准则，基于此准则的微机图象处理，可自动精确测量Ｉ型焦散线的最大直径。     

线性规律功能梯度材料断裂行为实验研究

焦散线方法与高速摄影技术结合,对线性规律功能梯度材料的I型静、动态断裂特性进行实验研究,并利用有限元软件进行数值模拟. 首先推导了线性规律功能梯度材料静、动态裂尖的焦散线初始曲线方程和参数方程,提出通过迭代方法根据功能梯度材料的复杂焦散线方程求解应力强度因子. 为对比材料梯度对断裂行为的影响,利用重力沉降法制备了3种梯度变化规律的试件. 然后对功能梯度材料试件进行三点弯曲实验,通过CCD和高速摄影装置采集试件焦散线图像,提取各种静、动态断裂参数. 最后通过与有限元模拟结果进行对比,证明在功能梯度材料断裂实验中焦散线方法的有效性,并详细分析了不同梯度变化规律对材料静、动态断裂性能的影响.      

用焦散线法测定材料的断裂韧性

用焦散线法测定材料的断裂韧性.     

A study on caustic method in cracked plate under symmetric bending

Based on Chun-Tu Liu's result for Reissner's plate, an equation of caustics in cracked plate under symmetric bending was obtained. The shape and the distribution of light intensity of the caustic curve were discussed in detail. The relation between the stress intensity factor (SIF) and the size of the caustic curve was found by numerical method, and a simple and accurate experimental method for evaluating SIF in plate under bending was proposed.     

Stress singularities at concentrated loads

The stress singularity created by a concentrated load applied at the boundary of a half-plane was studied by transforming it into an optical singularity by the optical method of caustics. The half-plane was considered to be elastic, isotropic and under generalized plane-stress conditions. According to the method of caustics, the light rays impinging normally at the thin plate are partly reflected from either the front or the rear faces of the plate. The reflected rays are deviated because of the important constraint of the plate at the vicinity of the applied load and the significant variation of the refractive index there. The deviated light rays, when projected on a reference screen, are concentrated along a singular curve which is, therefore, strongly illuminated and forms a caustic. It is shown that the shape and size of the caustic depends on the stress singularity at the point of application of the load. Thus, by measuring the dimensions of this singular curve, one can evaluate the state of stress at the singularity. The characteristic properties of the caustic created by such a singularity were studied in relation with the loading mode of the plate.     

爆炸载荷下板条边界斜裂纹的动态扩展行为

为了研究爆炸应力波作用下板条边界斜裂纹的动态扩展行为,首先分析了爆炸应力波在含边界斜裂纹板条中的传播,其次采用动态焦散线实验方法,进行了爆炸载荷下板条边界斜裂纹扩展规律的实验研究.研究结果表明,爆炸应力波作用下,板条试件边界斜裂纹的扩展过程中,裂纹扩展速度、扩展加速度和裂尖动态应力强度因子随时间波动变化,扩展速度最大值...     

Spatial motion of a chemically active medium near a caustic

A study is made of the three-dimensional problem of determining the parameters of motion of a gaseous chemically active medium near a caustic, the envelope curve of the rays of the wave fronts in the geometrical acoustics approximation. Two limiting processes whereby perturbations propagate [1] can be distinguished, depending on the ratio of the reaction time of the chemical reaction to a macroscopic time: a quasifrozen process and a quasiequilibrium process. The problem is considered in a linear formulation in [2-6] in the absence of viscosity, thermal conductivity, and chemical reactions. Nonlinear equations are derived in [7–10] for an arbitrary nondissipative medium near a caustic. In the present paper Ryzhov's method [1] is used to derive the nonlinear equations of motion of the medium for both types of process. The pressure distributions near and on the caustic itself are found for an incident step wave. The effect of the chemical reaction on how the flow parameters are distributed in the vicinity of the caustic is ascertained. Equations are derived for an inhomogeneous initially moving fluid near a caustic. A nonlinear equation containing a highest derivative of third order is obtained in the vicinity of the caustic for the case of special media in which the limiting velocities of sound in the mixture at rest are close in value. It is shown that the solution of the corresponding linear equation is expressed in the form of a quadrature from the solution for a chemically inert medium and contains oscillations near the wave fronts.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 81–91, March–April, 1977.     

A study of dynamic caustics around running interface crack tip

Based on the first invariant of stress singular field in the vicinity of running tip of an interface crack, mapping equations of the caustic curve on the reference plane and the initial curve on the specimen plane are developed. The dynamic caustics are analyzed for the crack propagating along the interface between two bonded dissimilar materials. The variation of the caustic configurations is shown with the velocity change of the running crack and the ratio change of the stress intensity factors. Two characteristic dimensions are proposed that are not only practically measurable from optical caustic contours but also suitable to represent the behavior of transient caustics. The project supported by the National Natural Science Foundation of China and the Scientific Commission of Yunnan Province of China     

The warping functions of regular prismatic bars under torsion evaluated by caustics

Reflection of a bundle of coherent light on the warped cross section of a prismatic bar submitted to torsion forms a caustic on a receiver plane. From the mathematical expression of this curve and the theory of reflected caustics, it is possible to evaluate accurately the warping function of the cross section. Using this idea, it was possible to study the torsion problem in prismatic bars with sections which were equilateral triangles and squares. It was observed that the shape of the caustic is an hypocycloid curve with three or four cusps respectively. By evaluating the warping function by using elements from the respective caustics it was possible to find out that, for the triangular cross section, the expression for the warping function coincided exactly with the expression given by the exact solution of the problem. For the square cross section, a closed-form solution for its warping function was readily derived, to which the series approximation solution differed only by a few percent at maximum for the shear stresses. Since the method can be readily extended to any canonical polygonic cross section, it constitutes a general solution for the torsion of prismatic bars, which approximates their exact deformations better than the solutions based on the Saint-Vénant assumptions.     

Propagating Behavior of Stress Pulses in Large Diameter Hopkinson Tube

A large diameter Hopkinson tube has been developed to measure the dynamic fracture toughness of materials. The stress wave propagation behavior in the Hopkinson tube under different impact conditions were studied both experimentally and numerically. Both the experimental and simulated results indicated that the characteristics of the incident stress pulse critically depended on the impact alignment conditions. When the striker tube impacts the incident tube in an axial, normal alignment condition, the incident pulse shows an obvious dispersive effect. While under an oblique impact condition, a smooth incident pulse with a long rise time is achieved. Therefore, an oblique impact pulse shaping technique is proposed in this study.     

焦散线法确定应力强度因子的条件

基于焦散线的形成原理及含裂纹受力试件在裂尖附近区域的应力分布,得到了焦散线法确定应力强度因子的条件：初始曲线半径与试件厚度之比大于0．5。当满足该条件时,对光学各向同性材料及光学各向异性材料前表面反射的情形,只需测量焦散线沿横向的最大尺寸便可较精确地确定应力强度因子;而对于光学各向异性材料的透射或后表面反射情形,只有在忽略远场非奇异应力的影响后,才可借助焦散线的横向尺寸近似确定应力强度因子。     

Inter-contact force analysis of impacted disk assembly by dynamic caustics

The caustic method was utilized to study the contact force transmission in disk assemblies under impact load. The mapping equations were obtained based on the first invariant of the stress components in the disk subject to a normal concentrated force, and a characteristic dimension of the maximum size in the caustic curve was proposed to evaluate the contact force between the disks. Transient patterns of the caustic shadows were recorded by means of a high-speed camera of off-focus imaging, then the histories of the inter-contact forces among the disks were obtained with respect to the conditions of different masses and heights of the falling hammers. The influence of the impact loading and impulsive velocity was analyzed with respect to the force responses of the disk assembly, the double-peak phenomenon with comparison to the initial masses, and the energy dissipation of the systems under impact of different momentums. The project supported by the National Natural Science Foundation of China (10125211)     

Sensitivity analysis for fixed-grid shape optimization by using oblique boundary curve approximation

The remesh-free property is the most attractive feature of the various versions of fixed-grid-based shape optimization methods. When the design boundary curves do not pass through the predetermined analysis grids, however, the element stiffness as well as the stress along the curves may be computed inaccurately. Even with the popular area-fraction-based stiffness evaluation approach, the whole optimization process may become quite inefficient in such a case. As an efficient alternative approach, we considered a stiffness matrix evaluation method based on the boundary curve approximation by piecewise oblique curves which can cross several elements. The main contribution of this work is the analytic derivation of the shape sensitivity for the discretized system by the fixed-grid method. Since the force term in the sensitivity equation is associated only with the elements crossed by the design boundary curve, we only need the design velocities of the intersecting points between the curve and the fixed mesh. The present results obtained for two-dimensional elasticity and Poisson’s problems are valid for both the single-scale standard fixed-grid method and the multiscale fictitious domain-based interpolation wavelet-Galerkin method.