Comparison of finite element techniques for 2D and 3D crack analysis under impact loading

For several technical applications the dynamic aspect in fracture mechanics cannot be neglected. When the reliability of components with macroscopic cracks has to be assessed, the consideration of dynamic effects may lead to much higher stress intensity factors than under static conditions. In this paper three different methods to calculate the dynamic stress intensity factor for the mode-I loading of stationary cracks are compared. Based on two- and three-dimensional finite element simulations, the dynamic stress intensity factor is computed with the dynamic J-integral, the modified crack closure integral and the displacement interpretation method. The theoretical fundamentals of all three methods are summarized in the paper and the numerical implementation is explained briefly. Results for different models are shown and compared to findings in the literature.     

Prediction of fatigue crack growth life under variable-amplitude loading using finite element analysis

This article presents an elastic-plastic study aiming at predicting the fatigue crack growth (FCG) of 2024-T3 aluminum alloys under variable-amplitude loading. The proposed analysis needs the estimation of the residual stress distribution ahead of the crack tip during propagation. An elastic-plastic FE analysis has been implemented for modeling FCG using Chaboche's model. The FE study has been carried out through consideration of the loading history effect using the memory rules. Three different loading spectra have been applied in this work. The obtained results have been compared to the experimental ones and it has been proved that the suggested model has a better prediction of the FCG lives of cracked 2024-T3 aluminum alloy structures subjected to variable-amplitude loading.     

广义扩展有限元法及其在裂纹扩展分析中的应用

结合广义有限元法(GFEM)和扩展有限元法(XFEM)的特点,提出了一种新的数值方法——广义扩展有限元法(GXFEM)。阐述了广义扩展有限元法的基本原理,对相关公式进行推导,探讨数值实施中需注意的重要问题,给出利用广义扩展有限元法进行断裂分析时应力强度因子的计算方法,编写了广义扩展有限元法程序。通过算例进行了应力强度因子的计算,模拟了结构裂纹的扩展过程。算例结果表明,利用广义扩展有限元法计算裂纹扩展问题,不需要进行过密的网格划分,且网格在裂纹扩展后无需重新剖分,具有相当高的计算精度。     

Shear crack propagation in the residual stress field

The problem of propagation of a longitudinal shear crack in a medium with a random field of internal stresses is considered and solved with the use of the theory of quasi-brittle failure. Local criterion of crack propagation under cyclic loading is derived, and its application as a model of fatigue crack propagation is investigated.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, Vol. 11, No. 3, pp. 117–119, May–June, 1970.     

表面裂纹准静态扩展的有限元模拟计算

由于现有断裂准则未能考虑表面裂纹前沿各点实际断裂阻力的变化，所作的表面裂纹准静态扩展模拟计算不能很好地预测几何形貌的真实变化规律。本文提出了一个考虑应力状态不同对实际断裂阻力影响的变阻力断裂准则；并以该准则作为表面裂纹前沿局部断裂扩展的判据，通过三维有限元法进行了表面裂纹准静态扩展的模拟计算；还将模拟预测值与用多试件法测得的实验值进行比较，验证了变阻力断裂准则作为裂纹稳态扩展判据的有效性     

A precise singular finite element for crack analysis

The multi-variable finite element algorithm based on the generalized Galerkin’smethod is more flexible to establish a finite element model in the continuum mechanies.Byusing this algorithm and numerical tests a new singular finite element for elasto-plasticfracture analysis has been formulated.The results of numerical tests show that the newelement possesses high accuracy and good performance.Some rules for formulating amulti-variable singular finite element are also discussed in this paper.     

用边界元方法分析复合材料中的裂纹问题

利用层状材料的广义Klevin基本解，建立了计算三维层状材料中的裂纹边界元方法。采用边界元方法中的多区域方法和能反映均匀介质中裂纹尖端应力场和位移场特征的面力奇异单元。裂纹的应力强度因子由裂纹面上的位移经插值计算得到。算例分析表明，本文建议的方法可以获得较高的计算精度。     

扩展有限元裂尖场精度研究

论述了扩展有限元方法和基本原理,研究了单元类型(四边形单元和三角形单元、线性单元和二次单元)、网格密度、J积分区域半径等因素对裂尖局部应力场(应力强度因子)计算精度的影响。研究发现,上述因素对裂尖应力强度因子计算的收敛速度与稳定性影响不大,证实了XFEM可以用较少的节点获得较高的裂尖场精度,并提出了通过固定裂尖附加区半径可以进一步改善XFEM的收敛速度。     

Two-dimensional fractal-like finite element method for thermoelastic crack analysis

The fractal-like finite element method has been proved to be very efficient and accurate in two-dimensional static and dynamic crack problems. In this paper, we extend our previous study to include the thermal effect for two-dimensional isotropic thermal crack problems. Both the temperature intensity factor and thermal stress intensity factor can be calculated directly. The temperature distribution is first found, which is imposed thereafter as a thermal load in the elastic problem. The transformation function used in the study has been found analytically. The effects of different thermal loading on the thermal stress intensity factor are presented. The numerical examples are compared with the results from other methods and find to be in good agreement.     

Dynamic crack growth under stress wave loading

The crack growth process has been analysed on the basis of a fracture criterion of a dynamic stress intensity factor when a crack in an infinite plate was subjected to a pulse type of stress wave. The crack velocity and the amount of crack extension were related to the constant amplitude and the duration of the stress pulse. The calculated amount of crack extension was well in agreement with the experimental one for the polymer material Acrylite (which is similar to polymethylmethacrylate) found by the authors, thus indicating the validity of the present approach.     

三维板料成形过程的显式有限元分析

本文采用基于随动坐标系的假定应变域壳单元及显式有限元格式求解三维板料成形问题。板材料服从Ｈｉｌ各向异性弹塑性准则，板料与模具之间的接触界面由主仆面接触搜寻法处理，接触力由罚参数法计算。文中给出了几个三维成形过程的计算实例。数值算例表明，本文方法具有较高的计算精度和计算效率，可在微机上分析中等复杂程度的成形过程     

改进的Z~2应力恢复过程与h型自适应有限元分析

建议了一种较为精确的边界应力求解方法，并用于改进Ｚｉｅｎｋｉｅｗｉｃｚ－Ｚｈｕ（Ｚ２）应力恢复过程。改进过程增加的计算量不大，但可有效地改善后验误差估计精度。ｈ型自适应有限元分析结果表明，改进过程更有利于最优网格寻求工作     

A finite element analysis for the mixed mode crack growth in a viscoelastic and orthotropic medium

This paper deals with a finite element algorithm for the creep crack growth process in a viscoelastic medium. The main developments focus on the coupling between the M-integral and an incremental formulation for the viscoelastic behavior. In this context, mixed mode configurations are simulated for orthotropic symmetries. An algorithm uncoupling viscoelastic incremental formulation and the fracture procedure is resolved with finite element software. The global approach is validated in terms of the evolution of energy release rate versus time and the advance of cracks. Numerical simulations are based on a Constant Tension Shear model. The insensitivity of the M-integral to the integration domain is shown from creep crack growth simulations for mixed mode configurations.     

Simulations of 2D and 3D thermocapillary flows by a least-squares finite element method

Numerical results for time-dependent 2D and 3D thermocapillary flows are presented in this work. The numerical algorithm is based on the Crank–Nicolson scheme for time integration, Newton's method for linearization, and a least-squares finite element method, together with a matrix-free Jacobi conjugate gradient technique. The main objective in this work is to demonstrate how the least-squares finite element method, together with an iterative procedure, deals with the capillary-traction boundary conditions at the free surface, which involves the coupling of velocity and temperature gradients. Mesh refinement studies were also carried out to validate the numerical results. © 1998 John Wiley & Sons, Ltd.     

Elastoplastic finite element analysis of three-dimensional fatigue crack growth in aluminum shafts subjected to axial loading

We have developed a three-dimensional cohesive element and a class of irreversible cohesive laws which enable the accurate and efficient tracking of three-dimensional fatigue crack fronts and the calculation of the attendant fatigue life curves. The cohesive element governs the separation of the crack flanks in accordance with an irreversible cohesive law, eventually leading to the formation of free surfaces, and is compatible with a conventional finite element discretization of the bulk material. The versatility and predictive ability of the method is demonstrated through the simulation of the axial fatigue tests of aluminum shafts of Thompson and Sheppard, 1992a, Thompson and Sheppard, 1992b, Thompson and Sheppard, 1992c . The ability of the method to reproduce the experimentally observed progression of beachmarks and fatigue life curves is particularly noteworthy.     

The stress field near a blunting crack tip under mixed modes 1 and 2

The distribution of stress near a crack tip deforming in plane strain under mixed Modes 1 and 2 loads is calculated using slip-line field theory. Large geometry change effects are taken into account. The results are compared and contrasted both with known Mode 1 large-deformation solutions and with previous mixed-mode solutions for a sharp crack. The results are then combined with stress-based fracture criteria to discuss mixed-mode fracture on the lower shelf.     

An efficient 3D stochastic finite element method

Real life structural systems are characterized by their inherent or externally induced uncertainties in the design parameters. This study proposes a stochastic finite element tool efficient to take account of these uncertainties. Here uncertain structural parameter is modeled as homogeneous Gaussian stochastic field and commonly used two-dimensional (2D) local averaging technique is extended and generalized for 3D random field. This is followed by Cholesky decomposition of respective covariance matrix for digital simulation. By expanding uncertain stiffness matrix about its reference value, the Neumann expansion method is introduced blended with direct Monte Carlo simulation. This approach involves decomposition of stiffness matrix only once for the entire simulated structure. Thus substantial saving of CPU time and also the scope of tackling several stochastic fields simultaneously are the basic advantages of the proposed algorithm. Accuracy and efficiency of this method with reference to example problem is also studied here and numerical results validate its superiority over direct simulation method or first-order perturbation approach.     

应力三轴度的有限元计算修正

对某高强度钢制成的光滑圆棒和缺口圆棒进行了系列准静态拉伸实验,采用ABAQUS对每个试 件进行了数值模拟,得到了该材料的真实应力应变曲线,拟合出了J-C本构模型和失效模型的部分材料常数。 最后,对该高强度钢制成的平板进行了撞击实验,并用得到的J-C模型对平板撞击实验进行了数值模拟,计算 结果与实验结果吻合很好,证明利用数值模拟并修正应力三轴度的方法是可行的。