Conditions for Cracking and Debond Development at Partially Bonded Bimaterial Half-Planes

Fracture phenomena at the debond tip of partially bonded bimaterial half-planes subjected to concentrated normal forces, couples, and uniform tension are considered. The crack initiation conditions are described by the stress distribution before the initiation and the energy release rate of the crack immediately after the initiation. The debond development conditions are described by the stress distribution and the energy release rate of the debond before its initiation. When both the crack and the debond have chances to occur, or when cracks can arise in both the materials, the fracture phenomena are predicted by comparing the ratio of energy release rates and the ratio of fracture toughnesses.     

Simulation of crack–propagation using embedded discontinuities

The transition from microscale damage phenomena to crack initiation and growth at the macroscale is an important mechanism which constrains the lifetime of concrete structures. Analysing crack growth using the finite element method without enhancement of the shape functions is possible only by continuously updating the corresponding meshes, which constitutes a significant computational effort. But even then the results can be substantially mesh–dependent and hard to interpret. The extended Finite Element Method (XFEM) uses additional discontinuous shape–functions and is one possibility to overcome these problems. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Algorithms to Find Exact Inclusion Probabilities for Conditional Poisson Sampling and Pareto πps Sampling Designs

Conditional Poisson Sampling Design as developed by Haje´k may be defined as a Poisson sampling conditioned by the requirement that the sample has fixed size. In this paper, an algorithm is implemented to calculate the conditional inclusion probabilities given the inclusion probabilities under Poisson Sampling. A simple algorithm is also given for second order inclusion probabilities in Conditional Poisson Sampling. Furthermore a numerical method is introduced to compute the unconditional inclusion probabilities when the conditional inclusion probabilities are predetermined. Simultaneously, we study the Pareto ps sampling design. This method, introduced by Rose´n, belongs to a class of sampling schemes called Order Sampling with Fixed Distribution Shape. Methods are provided to compute the first and second order inclusion probabilities numerically also in this case, as well as two procedures to adjust the parameters to get predetermined inclusion probabilities.     

A fast algorithm for balanced sampling

Summary  The cube method (Deville & Tillé 2004) is a large family of algorithms that allows selecting balanced samples with equal or unequal inclusion probabilities. In this paper, we propose a very fast implementation of the cube method. The execution time does not depend on the square of the population size anymore, but only on the population size. Balanced samples can thus be selected in very large populations of several hundreds of thousands of units.     

A coupled stress and energy failure model for crack initiation in arbitrarily shaped adhesive lap joints

In this work, crack initiation in adhesive lap joints of arbitrary joint configuration is studied by means of a finite fracture mechanics approach. The analysis is based on a general stress solution for adhesive joints combined with a coupled stress and energy criterion. The instantaneous formation of a crack of finite size is predicted if a stress and energy criterion are satisfied simultaneously. The closed-form analytical solution of the stress field allows for an efficient evaluation of the crack initiation load and corresponding finite crack length. A comparison to experimental results from literature and to numerical results obtained with a cohesive zone model approach shows a good agreement. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Simulation of Hertzian cone cracks using a phase field description for fracture

The present contribution focuses on fracture caused by indentation loading on the surface of a brittle solid. Its theoretical prediction is a challenging task due to the fact that crack nucleation is not geometrically induced, but is caused by the stress concentration in the contact near-field. The application of the phase field model requires constitutive assumptions to ensure a tension-compression asymmetric material response and prevent damage in compressed regions. This is achieved at the cost of giving up the variational concept of brittle fracture. We simulate the indentation of a cylindrical flat-ended punch on brittle materials like silicate glass. In order to reduce the numerical effort, we exploit axisymmetric conditions for the finite element formulation. After crack initiation stable propagation of a cone crack can be observed in good agreement with experiments. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

An accurate and efficient algorithm for the simulation of fatigue crack growth based on XFEM and combined approximations

This study aims to reduce the computational cost in the simulation of fatigue crack growth process. Extended finite element method and combined approximations (CA) are integrated to form an efficient algorithm for such analysis. In the CA approach, binomial series are used as high quality basis vectors for the reduced basis expression and then crack propagation path can be predicted without solving the complete set of system equations. The validity of presented algorithm is fully investigated through several numerical examples. From these results, it is shown that the presented algorithm is very accurate and can save huge amounts of computational effort.     

PROCRACK-A Software Tool for Finite Element Simulation of Three-Dimensional Fatigue Crack Growth

The lifetime of structural components is limited by fatigue cracks. After initiation from an existing defect the crack grows subcritically until it reaches a critical size. At this point it becomes unstable and the structural component fails. PROCRACK is a powerful tool that enables the commercial finite element software Abaqus to calculate the crack propagation in pre-cracked components. The complete capability of Abaqus can be used to simulate nearly arbitrary geometries. Abaqus/CAE is used for the three-dimensional modeling of the initial crack at a geometrical level by means of points, lines and triangles. The numerical analysis is performed by Abaqus/Standard. PROCRACK automatically generates a tube-shaped submodel around the crack front to calculate the stress intensity factors with high accuracy. The Paris law or the NASGRO equation can be used to calculate the incremental crack growth. The shape of the crack and the finite element mesh are updated in every crack growth step. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Mode I,mode II,and mixed-mode I/II interlaminar fracture toughness of GFRP influenced by fiber surface treatment

The interlaminar fracture behavior of unidirectional glass fiber reinforced composites with fiber surface treatment has been investigated in modes I and II and for fixed mode I to mode II ratio of 1.33. The data obtained from these tests have been analyzed by using different analytical approaches. The present investigation is focused on the influence of the glass fiber surface treatment on the interlaminar fracture toughness of unidirectional laminates. Glass fibers with two different fiber surface treatments have been investigated. fiber surface treatment was carried out by using a polyethylene or silane coupling agent in combination with modifying agents. The glass fibers were embedded in the brittle epoxy matrix. Mode I, mode II, and mixed-mode I/II tests were performed in order to determine critical strain energy release rates. Double cantilever beam (DCB), end-notched flexure (ENF), and mixed-mode flexure (MMF) specimens were used. For both types of fiber surface treatment about the same values of mode I initiation fracture toughness G_IC ^init were obtained. It was observed that in mode I interlaminar crack growth in the DCB test for the composite sized by polyethylene, the crack propagation is accompanied by extensive fiber bridging. For both fiber surface treatments interlaminar fracture toughness increases considerably with increasing of crack length. For the fiber surface treatment with the silane coupling agent, the value of mode II initiation fracture toughness G_IIC ^init was about 2.5-times higher in comparison with that of a composite sized by polyethylene. For both types of fiber surface treatments the mixed-mode I/II test has shown a similar behavior to the mode I DCB test.     

The problem of an inclusion in a three-dimensional elastic wedge

Fundamental solutions for a three-dimensional wedge are used to investigate problems of a thin, rigid, elliptic inclusion in a wedge. A regular asymptotic form is employed which has previously been used in contact problems for a wedge [1] and in problems of a crack in a wedge [2] in the case of an elliptic shape of the contact region or crack. The method is effective in the case of an inclusion which is sufficiently distant from an edge of the wedge when the known exact solution for the space [3] can be taken as the zeroth approximation. A numerical analysis and comparison of different characteristics of wedge problems is carried out.     

夹杂和裂纹的相互作用及端点相交的奇性性态分析

利用单根裂纹和单根夹杂的基本解,通过弹性力学的线性叠加原理,将平面裂纹和夹杂相互作用的问题归结为解一组带有柯西型奇异积分的积分方程组,计算了裂纹和夹杂端点的应力强度因子,给出了一些数值例子,并对夹杂和裂纹水平接触时的情形作了奇性分析,结果可作为研究夹杂尖端引起的裂纹及其扩展的工程分析的计算模型。     

A contact problem for a smooth rigid disc inclusion in a penny-shaped crack

The present paper examines the problem of the complete indentation of the surface of a penny-shaped crack by a smooth rigid disc inclusion. The integral equation governing the problem is solved numerically to evaluate the axial stiffness of the rigid inclusion and the stress intensity factors at the tip of the penny-shaped crack.     

On bending an elastic plate with a delaminated thin rigid inclusion

Under study is the problem of bending an elastic plate with a thin rigid inclusion which may delaminate and form a crack. We find a system of boundary conditions valid on the faces of the crack and prove the existence of a solution. The problem of bending a plate with a volume rigid inclusion is also considered. We establish the convergence of solutions of this problem to a solution to the original problem as the size of the volume rigid inclusion tends to zero.     

On the assessment of cracks within the interface of thin layers on a substrate

Although bimaterial wedge or notch configurations are identified as potential weak locations, the assessment of the degree of criticality of cracks in such regions is still a demanding problem. The singular character of the stress field at cracks or at bimaterial notches can be calculated analytically or numerically. The angle of the direction of potential crack initiation may also be determined, but the decisive question is whether a hypothetical crack will be initiated or not. An essential question in the context of crack assessment is to find a criterion for crack nucleation. For that aim, the hypothesis of Leguillon is modified. Herein, the crack is assumed to be critical when and only when both the released energy and the local stress reach critical values along a hypothetical crack of finite length. This concept can be transferred to a bimaterial interface configuration of a thin layer on a substrate. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Scenario-based portfolio selection of investment projects with incomplete probability and utility information

In the selection of investment projects, it is important to account for exogenous uncertainties (such as macroeconomic developments) which may impact the performance of projects. These uncertainties can be addressed by examining how the projects perform across several scenarios; but it may be difficult to assign well-founded probabilities to such scenarios, or to characterize the decision makers’ risk preferences through a uniquely defined utility function. Motivated by these considerations, we develop a portfolio selection framework which (i) uses set inclusion to capture incomplete information about scenario probabilities and utility functions, (ii) identifies all the non-dominated project portfolios in view of this information, and (iii) offers decision support for rejection and selection of projects. The proposed framework enables interactive decision support processes where the implications of additional probability and utility information or further risk constraints are shown in terms of corresponding decision recommendations.     

基于TNT当量法的储罐内爆压力简化计算与应力分析

以立式拱顶储罐为研究对象,综合考虑储罐内气体容积与几何结构的影响:依据TNT当量法推导了内爆载荷下储罐超压计算公式并计算得到了储罐内不同起爆点下的超压分布曲线.当起爆点在储罐中轴线时,罐顶或罐底压力约为相反侧的6倍;当起爆点在靠近罐壁一侧时,靠近爆炸点一侧的罐顶或罐底压力约为相反侧的30倍.最后,通过储罐内爆载荷下的动力学仿真计算,对储罐在不同起爆点和不同液位的破坏情况进行了评定.有限元计算结果表明:储罐在操作过程中应控制其液位在半罐以上,可保证在任意起爆点位置罐顶均先与罐底发生破坏.     

裂纹面分布加载裂尖SIFs分析的广义参数Williams单元北大核心CSCD

带裂缝服役是工程结构的常态,由于流体侵入到裂缝内部,裂纹面直接受荷,使得裂缝进一步扩展,甚者影响结构的安全性.广义参数Williams单元(简记W单元)在分析断裂问题中,利用Williams级数建立裂尖奇异区的位移场,通过求解广义刚度方程可直接获得应力强度因子(stress intensity factors,SIFs),具有高精高效性;但W单元需满足奇异区内裂纹面自由的边界条件,故在分析裂纹面加载的问题中受限.该文基于SIFs互等,在等效奇异区范围中,将裂纹面的荷载等效为奇异区外围边界裂纹面上的集中力,避免奇异区内裂纹面受荷,故采用W单元即可简便计算.算例分析表明:等效奇异区尺寸取裂纹长度的1/20,等效荷载系数P建议取2.0,W单元计算精度均满足1%的误差限,证明该文在奇异区裂纹面受荷等效处理方法上具有合理性、通用性,克服了W单元在分析裂纹面加载问题的局限性.     

Computation of crack propagation in 3-dimensional anisotropic solids

This contribution presents ideas, how crack propagation in three-dimensional solids composed of anisotropic materials can be predicted using the Griffith energy principle. Since the work of Irwin the change of potential energy caused by a straight elongation of a crack in an isotropic two-dimensional homogeneous structure can be expressed in quadratic terms of the stress intensities at the crack tip. This result was generalized in the last decades using methods of asymptotic analysis by many authors [1] to more complicated geometries, to anisotropic and inhomogeneous materials. With the energy release rate at hand, quasi-static scenarios of crack propagation can be simulated for plane problems [2], but this is still a complicated task for three-dimensional problems [3]. We show an idea how the change of energy caused by propagation of a crack surface in a fully three-dimensional solid of nearly arbitrary shape can be computed in anisotropic materials. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

反平面裂纹在裂纹自由表面附近的弹塑性分析

裂纹自由面附近的弹塑性场和弹塑性边界是裂纹弹塑性分析的重要内容,但现有的方法难以对其进行有效描述．该文发展了裂纹线场分析方法的研究思路,将裂纹面视为裂纹线的拓展部分,对理想弹塑性Ⅲ型裂纹进行了裂纹面附近弹塑性场的分析,得出了裂纹面附近弹塑性应力场、塑性区长度和弹塑性边界的单位法向量．分析结果表明,可放弃传统的小范围屈服条件．