Criterion of the incubation time in the problems of pulsed fracture and electric breakdown

The problems of a pulsed strength of continuum media are considered in terms of the structural-time approach that is based on the concept of the incubation fracture time. This approach makes it possible to describe phenomena that arise under high-velocity external effects. A limiting condition that determines the instant of rupture or breakdown is proposed on the basis of the structural-time approach. A way to interpret and to determine the incubation time is proposed. A phenomenological model of an electric breakdown of solid dielectrics is formulated. Examples are considered where the structural-time approach is applied to problems of spall fracture, crack initiation, and a pulsed breakdown of dielectrics. A procedure for describing the time dependence of the electric strength (volt-second characteristic) is described in detail. The results of the calculations are found to be in good agreement with experimental data.     

A three-dimensional Eulerian method for the numerical simulation of high-velocity impact problems

In the present paper, a three-dimensional （3D） Eulerian technique for the 3D numerical simulation of high-velocity impact problems is proposed. In the Eulerian framework, a complete 3D conservation element and solution element scheme for conservative hyperbolic governing equations with source terms is given. A modified ghost fluid method is proposed for the treatment of the boundary conditions. Numerical simulations of the Taylor bar problem and the ricochet phenomenon of a sphere impacting a plate target at an angle of 60~ are carried out. The numerical results are in good agreement with the corresponding experimental observations. It is proved that our computational technique is feasible for analyzing 3D high-velocity impact problems.     

An improved particle correction procedure for the particle level set method

The particle level set method [D. Enright, R. Fedkiw, J. Ferziger, I. Mitchell, A hybrid particle level set method for improved interface capturing, J. Comput. Phys. 183 (2002) 83–116.] can substantially improve the mass conservation property of the level set method by using Lagrangian marker particles to correct the level set function in the under-resolved regions. In this study, the limitations of the particle level set method due to the errors introduced in the particle correction process are analyzed, and an improved particle correction procedure is developed based on a new interface reconstruction scheme. Moreover, the zero level set is “anchored” as the level set functions are reinitialized; hence the additional particle correction after the level set reinitialization is avoided. With this new scheme, a well-defined zero level set can be obtained and the disturbances to the interface are significantly reduced. Consequently, the particle reseeding operation will barely result in the loss of interface characteristics and can be applied as frequently as necessary. To demonstrate the accuracy and robustness of the proposed method, two extreme particle reseeding strategies, one without reseeding and the other with reseeding every time step, are applied in several benchmark advection tests and the results are compared with each other. Three interfacial flow cases, a 2D surface tension driven oscillating droplet, a 2D gas bubble rising in a quiescent liquid, and a 3D drop impact onto a liquid pool are simulated to illustrate the advantages of the current method over the level set and the original particle level set methods with regard to the smoothness of geometric properties and mass conservation in real physical applications.     

钽的层裂实验数值模拟

 采用连续介质力学基唯象模型模拟分析了钽的平板撞击层裂行为。该模型包括了材料的非线性弹性（状态方程）、率相关塑性和孔洞的形核及生长等多种效应,并且采用一种对角隐式Runge-Kutta方法来求解本构率方程组,提高了热粘塑性本构关系计算的稳定性及精度。将数值模拟结果和相关实验数据进行了对比分析,结果表明,对于样品中的拉应力峰值明显高于材料层裂强度的实验（中、高速平板撞击实验）,理论模型具有较好的预估能力,但对于临界层裂问题（低速平板撞击实验）,该模型对材料损伤与失效过程的描述可能不够准确,需要进一步改进。     

A numerical scheme for the Green–Naghdi model

In this paper a hybrid numerical method using a Godunov type scheme is proposed to solve the Green–Naghdi model describing dispersive “shallow water” waves. The corresponding equations are rewritten in terms of new variables adapted for numerical studies. In particular, the numerical scheme preserves the dynamics of solitary waves. Some numerical results are shown and compared to exact and/or experimental ones in different and significant configurations. A dam-break problem and an impact problem where a liquid cylinder is falling to a rigid wall are solved numerically. This last configuration is also compared with experiments leading to a good qualitative agreement.     

脆性动态断裂模型

 本文借鉴于Perzyna的基本思想及Seaman等人的实验结果提出了一个脆性材料动态断裂模型。利用本文的模型对Cochran的实验结果进行了数值模拟，其计算结果比Cochran的计算结果与实验吻合得更好。     

A Crack Driving Force Criterion for the Prediction of Interface Crack Kinking in Thin-Film Composites

Interfacial fracture mechanics is a relatively new field with many issues that have not yet been resolved. One such issue is the ability to accurately predict whether or not a bimaterial interface crack will propagate along the interface, kink into the film or substrate, or not propagate at all. In the present work, a crack driving force criterion is proposed in order to predict the level of applied load required to propagate a pre-existing interface crack in thin-film composites subjected to thermal loading. A primary objective is to predict the critical length of an interface crack at which it kinks into the substrate. The phenomenon of interface cracks kinking into the substrate is frequently observed when the film is under tensile loading and the substrate is brittle. An interface crack that advances into the substrate eventually propagates parallel to the interface at a certain steady-state depth. Ultimately, the portion of the structure that remains above the crack may spall, resulting in catastrophic failure. The crack driving force criterion is applied to a two-dimensional, plane strain interface crack problem, and the results compare favorably with available experimental results.     

Experimental and numerical analysis of Izod impact test of cortical bone tissue

Bones can only sustain loads until a certain limit, beyond which they fail. Usually, the reasons for bone fracture are traumatic falls, sports injuries, and engagement in transport or industrial accidents. A proper treatment of bones and prevention of their fracture can be supported by in-depth understanding of deformation and fracture behavior of this tissue in such dynamic events. In this paper, a combination of experimental and numerical analysis was carried out in order to comprehend the fracture behavior of cortical bone tissue. Experimental tests were performed to study the transient dynamic behavior of cortical bone tissue under impact bending loading. The variability of absorbed energy for different cortex positions and notch depths was studied using Izod impact tests. Also, Extended Finite-Element Method implemented into the commercial finite-element software Abaqus was used to simulate the crack initiation and growth processes in a cantilever beam of cortical bone exposed to impact loading using the Izod loading scheme. The simulation results show a good agreement with the experimental data.     

AF1410钢的层裂断裂特性研究

 利用一级轻气炮作为加载手段,对AF1410钢的层裂特性进行了研究,获得了AF1410钢的Hugoniot关系、塑性应变率、层裂强度以及层裂片厚度等动态力学参数。对回收的AF1410钢样品进行了断口分析和金相分析,从宏、微观角度分析了AF1410钢在不同应变率下的断裂特性。     

动态断裂过程的数值分析及LY-12铝的层裂

 本文从文献[1]中用于分析柱壳动态膨胀断裂过程的损伤度函数出发，将它推广到对一维应变下层裂过程的数值模拟研究。试件材料为LY-12铝，其特性方程取为含粘性的本构方程形式。数值计算结果很好地再现了实测自由面速度u_fs随时间t的变化过程，并表现出层裂强度σ_c及层裂面上的临界损伤度α_c都分别是应变率ε_c'的单调递增函数关系。σ_c~ε_c'的这种变化规律在许多文献中已屡见报道，例如可见文献[2-3]。在10⁵ s^-1~10⁶ s^-1应变率范围内，σ_c~ε_c'关系可以表示为ε_c'exp(-11.4α_c)=2 100 s^-1，这个式子可以作为一种层裂判据使用。数值计算还给出了层裂片的损伤度剖面，其形状特征与Barbee等对回收试件的细观测量结果在定性上一致。     

A Free-Lagrange Augmented Godunov Method for the Simulation of Elastic–Plastic Solids

A Lagrangian finite-volume Godunov scheme is extended to simulate two-dimensional solids in planar geometry. The scheme employs an elastic–perfectly plastic material model, implemented using the method of radial return, and either the ‘stiffened’ gas or Osborne equation of state to describe the material. The problem of mesh entanglement, common to conventional two-dimensional Lagrangian schemes, is avoided by utilising the free-Lagrange Method. The Lagrangian formulation enables features convecting at the local velocity, such as material interfaces, to be resolved with minimal numerical dissipation. The governing equations are split into separate subproblems and solved sequentially in time using a time-operator split procedure. Local Riemann problems are solved using a two-shock approximate Riemann solver, and piecewise-linear data reconstruction is employed using a MUSCL-based approach to improve spatial accuracy. To illustrate the effectiveness of the technique, numerical simulations are presented and compared with results from commercial fixed-connectivity Lagrangian and smooth particle hydrodynamics solvers (AUTODYN-2D). The simulations comprise the low-velocity impact of an aluminium projectile on a semi-infinite target, the collapse of a thick-walled beryllium cylinder, and the high-velocity impact of cylindrical aluminium and steel projectiles on a thin aluminium target. The analytical solution for the collapse of a thick-walled cylinder is also presented for comparison.     

延性材料动态拉伸断裂早期连通过程的逾渗描述

 借鉴逾渗理论,提出了新的应力松弛函数,简称PR函数（Percolation-Release Function）,用以描述断裂发生前由于微孔洞连通而引起的快速应力松弛过程,具有较为明确的物理意义。通过其与损伤度函数模型进行耦合,对无氧铜和45钢平板撞击层裂进行了数值模拟。结果表明：数值计算不仅有效地再现了界面的应力历史和自由面速度历史,而且再现了靶中的损伤分布;新的逾渗松弛函数具有较好的适用性。     

A hybrid scheme for computing incompressible two-phase flows

We propose a hybrid scheme for computations of incompressible two-phase flows. The incompressible constraint has been replaced by a pressure Poisson-like equation and then the pressure is updated by the modified marker and cell method. Meanwhile, the moment equations in the incompressible Navier-Stokes equations are solved by our semidiscrete Hermite central-upwind scheme, and the interface between the two fluids is considered to be continuous and is described implicitly as the 0.5 level set of a smooth function being a smeared out Heaviside function. It is here named the hybrid scheme. Some numerical experiments are successfully carried out, which verify the desired efficiency and accuracy of our hybrid scheme.     

弹性壳结构静力与动力分析的光滑粒子法

本文通过采用移动最小二乘函数作为近似函数 和完全拉格朗日方程作为近似方程来改善光滑粒子法的稳定性和数值精度; 在此基础上, 提出了壳结构静力分析的光滑粒子法, 并完善了壳结构动力分析方法; 最后, 采用国际公认的壳结构的标准测试模型对静力和动力问题分别进行了验证, 所得结果与已有数据吻合良好, 证明了本文数值模型的有效性和可靠性, 为光滑粒子法进一步在裂纹、破碎等非线性壳结构中的应用提供参考. 关键词： 弹性壳 静力与动力分析 光滑粒子法 完备性和稳定性     

Time dependence of the spall strength under nanosecond loading

The problem of spall fracture is considered using an incubation time criterion. Some experimental fracture effects are discussed. The spall strength is found to depend substantially on the pulse parameters, in particular, the rate of decrease of the load. The strain-rate and time dependences of spall strength are shown to be considered as calculated characteristics rather than as functions of a material.     

Rigid finite element model of a cracked rotor

The article introduces a new mathematical model for the cracked rotating shaft. The model is based on the rigid finite element (RFE) method, which has previously been successfully applied for the dynamic analysis of many complicated, mechanical structures. In this article, the RFE method is extended and adopted for the modeling of rotating machines. An original concept of crack modeling utilizing the RFE method is developed. The crack is presented as a set of spring–damping elements of variable stiffness connecting two sections of the shaft. An alternative approach for approximating the breathing mechanism of the crack is introduced. The approach is simple and allows one to intuitively and systematically prepare and analyze the model of a cracked rotor.The proposed method is illustrated with numerical and experimental results. The experiments conducted for the uncracked free–free rotor as well as the numerical results obtained with other software confirm the accuracy of the RFE model. The numerical analysis conducted for a set of cracked rotors has shown that, depending on the eccentricity and its angular location, the breathing behavior of the crack may take different forms. In spite of this, the frequency spectra for different cracks are almost identical.Due to its simplicity and numerous advantages, the proposed approach may be useful for rotor crack detection, especially if methods utilizing the mathematical model of the rotor are applied.     

Crack Tip Opening Angle as a Fracture Resistance Parameter to Describe Ductile Crack Extension and Arrest in Steel Pipes under Service Pressure

The angle between two element sides representing the crack tip is defined as the crack tip opening angle (CTOA). Its critical value is used as a criterion of fracture resistance for characterizing stable tearing in thin metallic materials. Various methods are used for determination of the CTOA. Optical microscopy is one of the most common methods as well as fitting of experimental load-displacement diagrams by the finite element method (DIC). Additionally, analytical analysis using the experimental load-displacement curve method (SSM) derived from the plastic hinge model of deflection in three-point bending of a ductile specimen is applied. This approach assumes a constant rotation centre distance. Values of CTOA for API 5L X65 pipe steel found by three methods—DIC, CNM, and SSM—are given. Values of CTOA given by these three methods are similar and close to 20°. A discussion on the different parameters used to characterize the fracture resistance of running cracks in a pipe under service pressure is presented. The energy of fracture at impact determined by Charpy or drop-weight tear test (DWTT) tests and the critical J energy parameter are considered as well as the yield locus after damage, cohesive zone energy, and CTOA is another approach. One notes that CTOA is assumed to be constant during stable crack extension and decreases linearly with crack length during the instable and primary phase. A numerical technique to describe a ductile running crack using the node release technique and using CTOA as the fracture resistance criterion is presented. This method is compared with three different two-curve methods (TCMs): the Battelle, high strength line pipe (HLP), and HLP-Sumitomo methods. The Batelle TCM, as the oldest method, based on Charpy energy, gives a strongly conservative prediction. Predictions by the CTOA method are close to those obtained by the HLP-Sumitomo one.     

Hybrid method in elastic and elastoplastic fracture mechanics

The utility of the hybrid experimental–numerical method in elastic and elastoplastic fracture mechanics is demonstrated through a fracture process zone analysis and a J-integral computation, respectively. For the former, the crack bridging stresses in the fracture process zones of concrete and alumina fracture specimens were determined through an inverse analysis and the dissipated energies in these zones were quantified. For the latter, J-integral was shown to be highly path dependent with stable crack growth.     

Interrelation between the threshold characteristics of erosion and spall fracture

Threshold diagrams of erosion and spall fracture are constructed based on the concept of incubation time of the fracture. It is shown that in the case of a defectless material, the incubation time can be estimated from the spallation or erosion experimental data. The temperature dependence of the threshold velocities of microparticle impact is considered. The effect of increasing the dynamic yield stress upon an increase in the surface temperature of the target material is obtained for small-size microparticles. The relationship with an analogous effect in the spallation experiments is discussed.     

Linear least squares approach for evaluating crack tip fracture parameters using isochromatic and isoclinic data from digital photoelasticity

In this work, digital photoelasticity technique is used to estimate the crack tip fracture parameters for different crack configurations. Conventionally, only isochromatic data surrounding the crack tip is used for SIF estimation, but with the advent of digital photoelasticity, pixel-wise availability of both isoclinic and isochromatic data could be exploited for SIF estimation in a novel way. A linear least square approach is proposed to estimate the mixed-mode crack tip fracture parameters by solving the multi-parameter stress field equation. The stress intensity factor (SIF) is extracted from those estimated fracture parameters. The isochromatic and isoclinic data around the crack tip is estimated using the ten‐step phase shifting technique. To get the unwrapped data, the adaptive quality guided phase unwrapping algorithm (AQGPU) has been used. The mixed mode fracture parameters, especially SIF are estimated for specimen configurations like single edge notch (SEN), center crack and straight crack ahead of inclusion using the proposed algorithm. The experimental SIF values estimated using the proposed method are compared with analytical/finite element analysis (FEA) results, and are found to be in good agreement.