Determination of the dynamic stress intensity factorsK I d andK II d,for a mixed-mode propagating crack

In this paper, the dynamic propagation problem of a mixed-mode crack was studied by means of the experimental method of caustics. The initial curve and caustic equations were derived under the mixed-mode dynamic condition. A multi-point measurement method for determining the dynamic stress intensity factors,K _I ^d , andK _II ^d , and the position of the crack tip was developed. Several other methods were adopted to check this method, and showed that it has a good precision. Finally, the dynamic propagating process of a mixed-mode crack in the three-point bending beam specimen was investigated with our method.     

Semiclassics around a phase space caustic: An illustration using the Nelson Hamiltonian

The semiclassical formula for the coherent-state propagator is written in terms of complex classical trajectories of an equivalent classical system. Depending on the parameters involved, more than one trajectory may contribute to the calculation. Eventually, however, two contributing trajectories coalesce, characterizing what is called phase space caustic. In this case, the usual semiclassical formula for the propagator diverges, so that a uniform approximation is required to avoid this singularity. In this Letter, we present a non-trivial numerical application illustrating this scenario, showing the accuracy of the uniform formula that we have previously derived.     

反射焦散线实验中斜入射光对应力强度因子测试精度的影响

本文用空间解析几何方法,推导了在一般非平行斜入射光条件下,裂纹体表面所形成的反射焦散线和初始曲线的方程.分析了倾斜入射光造成的焦散线畸变,给出了这种畸变造成的裂端应力强度因子测量误差的解析表达式.     

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)     

焦散线法对双折射材料断裂性能的研究

提出了双折射材料Ⅰ-Ⅱ混合型裂纹问题焦散线的形成原理,讨论了μ(=K_I/K_I)及光学各向异性系数ξ对焦散线形状及其几个特征量的影响,得到了双折射材料应力强度因子K_Ⅰ、K_Ⅱ的求法.以聚碳酸脂、环氧树脂为例,确定了它们在不同裂纹及不同载荷条件下的应力强度因子K_Ⅰ、K_Ⅱ.     

Internal waves around a disturbance in a fluid with arbitrary stratification and background shear flow

A three-dimensional ray theory is presented for calculating the phase configuration of internal waves around a moving disturbance in a flow with arbitrary stratification and background shear. The theory is applied to two-dimensional stratified shear flows which have been produced in the laboratory and good agreement is shown between the theoretical and experimental phase configurations. Good agreement is also shown when caustics and critical levels are present. This paper includes the wave systems arising from a combined translation and oscillatory motion of a source and it shows how distinct systems of waves arise from each, type of motion under different background conditions. This paper shows that for two-dimensional steady wave systems the critical level is at a well defined height which is independent of wavenumber but in three dimensions the critical height can in general vary with wavenumber.     

Local Smooth Transformations of Differential Equations Preserving Linear Automorphisms

This paper deals with problems related to local smooth transformations of ordinary differential equations preserving linear automorphisms of these equations.     

Effects of the curvature radius of a cylindrical shell on the stress intensity factors of surface cracks

The effects of the curvature radius of a cylindrical shell on stress intensity factors are investigated in circumferential (inner and outer) semielliptical surface cracks in a cylindrical shell. What is new in this paper is to have given: (1) The stress intensity factors for surface cracks in a cylindircal shell are determined by photoelastic technique. (2) By a special method photoelastic slices are handled for obtaining a clear caustic curve, and the stress intensity factors for surface cracks in a cylindrical shell are determined by the caustic method. (3) An approximate equation of curvature correction factor F_c is proposed. (4) Effects of the curvature radius R of a cylindrical shell on the stress intensity factors of surface cracks are obtained. The results of this paper are in fair agreement with already existing analytical results. The approximate equation of curvature correction factor F_c can be widely used for engineering purposes.