Meshless simulation of crack propagation in multiphase materials

The material body considered in this work consists of multiphases. Digital imaging data are taken as the input to specify the configuration and composition of the specimen. Meshless method is demonstrated as a superior numerical tool to analyze crack initiation and propagation in multiphase material. A fracture criterion, based on the ratio of the opening stress over the material toughness distributed in front of the crack tip, is proposed to determine the direction of crack propagation of mixed mode fracture problem in multiphase material. Numerical results are presented and discussed.     

三维热权函数法和多虚拟裂纹扩展技术

热权函数法直接利用温度场与热权函数的乘积的积分来求应力强度因子(SIF)的过渡过程，它可以免除对每一时刻进行热弹性力学有限元或边界元应力分析，计算效率大大提高。本文给出了三维热权函数法的基本方程，并提出了求解三维热权函数法基本方程的多虚拟裂纹扩展法(MVCE法)。在MVCE法中，可以引入无穷多个虚拟裂纹扩展模式；虚拟裂纹扩展模式与应力强度因子的插值直接相联系，所得到的方程组的系数矩阵是一个三对角矩阵，具有良好的计算性能。它对于裂纹前缘SIF分布急剧变化的情况，有良好的数值模拟能力。实例计算表明，MVCE法具有权高的计算效率，并具有很高的计算精度。     

Rapid extension of a crack

Summary For a body which is initially in a state of uniform anti-plane shear, the wave motion generated by a rapidly extending crack is analyzed in this paper. It is shown that extension with constant speeds of the crack tips is not consistent with the criterion for brittle fracture, but it is consistent with a fracture criterion related to postulated zones of cohesive tractions near the crack tips.

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Zusammenfassung Anbringen eines Lochs in einem gespannten Körper kann die Entstchung eines rasch sich ausbreitenden Risses veranlassen. In dieser Arbeit wird für einen Körper, der sich ursprünglich in einem Zustand gleichförmiger Schubspannung befand, die durch einen in schneller Ausbreitung begriffenen Riß verursachte Wellenbewegung untersucht. Es wird gezeigt, daß eine Ausbreitung mit konstanten Geschwindigkeiten der Rißenden nicht verträglich ist mit dem Kriterium für Sprödbruch, wohl aber mit einem Bruchkriterium, das mit postulierten Zonen kohäsiver Zugspannungen in der Nähe der Rißenden zusammenhängt.

     

Material force for dynamic crack propagation in multiphase micromorphic materials

Micromorphic theory, which considers material body as a continuous collection of deformable particles of finite size and inner structure; each has nine independent degrees of freedom describing the stretches and rotations of the particle in addition to the three classical translational degrees of freedom of its center, is briefly introduced in this work. The concept of material forces, which may also be referred as Eshelbian mechanics, is extended to micromorphic theory. The balance law of pseudo-momentum is formulated. The detailed expressions of Eshelby stress tensor, pseudo-momentum, and material forces are derived for thermoelastic micromorphic solid. It is found that the material forces are due to (1) body force and body moment, (2) temperature gradient and (3) material inhomogeneities in density, microinertia, and elastic coefficients. The general expression of material forces due to the presence of dynamically propagating crack front has also been derived. It is found that, at the crack front, material force is reduced to the J-integral in a very special and restrictive case.     

Propagation crack problems in interfaces between dissimilar orthotropic media

By the theory of complex functions, the general representation of the solution is derived for crack problems of arbitrary index of self-similarity expanding along the interfaces between dissimilar orthotropic media. The problems of Riemann and Hilbert can be formulated immediately and the analytical solution was obtained with this method. Some problems were analyzed as examples. The analytical solution for the cracked body subjected to an arbitrary load can be obtained with the summary method based on the present solution.     

Physical approach to averaging theorems on phase interfaces in a dispersed multiphase medium

Within the framework of a procedure for scale-changing by averaging a representative elementary volume, theorems are developed to relate the averages of derivatives to the derivatives of averages over a surface, using elementary differential calculus. These theorems form the basis of a general macroscopic balance equation for a given quantity over interfaces of a dispersed multiphase medium. The equations of phase interfaces complement equations related to bulk phases describing transport in dispersed multiphase media.     

Prediction of thermal crack spacing

When the thermally induced stress in a shrinking pavement layer reaches the tensile strength of asphalt, regularly spaced thermal cracks form across the width of the pavement. A one-dimensional analytical solution for the stress distribution in a thermally shrinking elastic pavement layer placed on an elastoplastic, cohesive–frictional base is developed and validated by comparison with a 2D numerical solution. From the analytical model, a prediction of a length parameter that provides bounds on the thermal crack spacing is obtained. Predicted bounds on crack spacing are validated by comparison with field observations. It is demonstrated that the proposed formulation can also be applied to estimate the average crack density observed in thin ceramic films subjected to the application of an axial strain; in the latter system, the crack spacing is six decades smaller than that observed in pavement systems.     

Rapid extension of a penny-shaped crack under torsion

The rapid extension of a penny-shaped crack under torsion is investigated. Both dynamic and quasi-static loading is considered. The wave motion is analyzed through a Green's function technique which leads to an integral equation for the stress field around the crack. Asymptotic expansions for the stress intensity and displacement rate intensity functions which are valid for a small time are obtained for the two types of loading. The propagation of the crack is analyzed through the balance of rates of energy criterion.     

A domain independent integral expression for the crack extension force of a curved crack in three dimensions

An integral expression that is domain independent in curvilinear coordinates and compatible with zero divergence of Eshelby's (Phil. Trans. Roy. Soc. (London) 244 (1951) 87.) energy momentum tensor was obtained from the principle of virtual work. By applying Eshelby's definition of the force on a material defect a general expression of the crack extension force for a curved crack in three dimensions, here called the F-integral, was derived from the domain independent integral expression. The F-integral is given explicitly for a number of curved cracks and found to be in agreement with previously known solutions, when available. The influence of crack surface and crack front curvature upon the various forms of the F-integral is discussed. The F-integral presented in this work is a generalisation of the J-integral (Rice, J. Appl. Mech. 35 (1968) 379.) to curved cracks in orthogonal curvilinear coordinates.     

Effect of local elastic softening on crack extension

Elastic softening materials are brittle materials such that crack extension is associated with a softening zone behind the crack tip, with the material elements within this zone exerting a restraining effect on the crack tip. Crack extension is sometimes characterised in terms of the stress intensity K_F, due to the applied loadings, at the front of the softening zone, i.e. the actual crack tip. This paper is concerned with the determination of the maximum load K_F value for a general positive geometrical configuration, for the case where the softening zone size is small compared with a solid's characteristic dimension. The resulting expression for K_F is compared with the maximum load stress intensity value K_T measured with regard to the initial crack position, i.e. the trailing edge of the softening zone.     

On the penny-shaped crack in inhomogeneous elastic materials under normal extension

The solution of the problem of a penny-shaped crack in an inhomogeneous material with elastic coefficients which are varying continuously along the direction perpendicular to the crack is examined in this paper. We studied the problem for an inhomogeneous material which satisfies the conditions of either torsional deformation and normal extension. A series form solution to the problem is proposed and analytical expressions for the first two terms of the series are obtained by using a Hankel transform technique. In the solution a homogeneous body is chosen as the reference so that inhomogeneous quantities are treated as being perturbed from the zeros reference solutions. Closed form expressions for the relevant stress intensity factors and the crack energy are derived and specific cases of the problem are also considered.     

Application of hypersingular integral equation method to three-dimensional crack in electromagnetothermoelastic multiphase composites

A three-dimensional crack problem in electromagnetothermoelastic multiphase composites (EMTE-MCs) under extended loads is investigated in this paper. Using Green’s functions, the extended general displacement solutions are obtained by the boundary element method. This crack problem is reduced to solving a set of hypersingular integral equations coupled with boundary integral equations, in which the unknown functions are the extended displacement discontinuities. Then, the behavior of the extended displacement discontinuities around the crack front terminating at the interface is analyzed by the main-part analysis method of hypersingular integral equations. Analytical solutions for the extended singular stresses, the extended stress intensity factors (SIFs) and the extended energy release rate near the crack front in EMTE-MCs are provided. Also, a numerical method of the hypersingular integral equations for a rectangular crack subjected to extended loads is put forward with the extended displacement discontinuities approximated by the product of basic density functions and polynomials. In addition, distributions of extended SIFs varying with the shape of the crack are presented. The results show that the present method accurately yields smooth variations of extended SIFs along the crack front.     

Simulation of fatigue crack growth at plastically mismatched bi-material interfaces

The present paper reports the results of a study on fatigue crack growth in a system with an interface between two elastic–plastic solids of different yield strength. Fatigue crack growth analysis is conducted by the use of a cohesive zone model. Irreversibility of material separation processes is introduced through the load history dependent degradation of the cohesive strength. Fatigue crack growth is considered to occur along the direction perpendicular to the interface and along the interface. Crack growth rate acceleration, deceleration or arrest, as well as crack bifurcation at the interface are predicted in dependence of the plastic property mismatch of the two solids and the interface properties. The outcome of the simulations is in very good agreement with trends of published experimental data.     

Notes on plastic reloading zone in the asymptotic analysis of elastic-plastic crack extension

Summary The asymptotic structures of near-tip stress and deformation fields are studied for steady-state crack extension in elastic-plastic solids. The condition for the existence of a plastic reloading zone is formulated. If a plastic reloading zone is to exist in hardening materials, the effective stress must become unbounded as the crack flank is approached. It is shown explicitly in the case of mode III that solutions with logarithmic singularity produce negative plastic dissipation in the plastic reloading sector.

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Über die rückplastizierte Zone bei asymptotischen Lösungen der elastisch-plastischen Rißausbreitung

Übersicht Untersucht wird die asymptotische Form von rißspitzennahen Spannungs- und Verformungsfeldern bei der stationären Rißausbreitung in elastisch-plastischen Körpern. Die Bedingung für die Existenz einer rückplastizierten Zone wird formuliert. Wenn eine solche Zone bei verfestigendem Material vorhanden sein soll, muß die Vergleichsspannung bei Annäherung an die Rißflanke unendlich werden. Es wird gezeigt, daß bei Mode III die Lösungen mit logarithmischer Singularität negative Dissipation in der rückplastizierten Zone bedeuten würden.

     

Near field behavior of in-plane crack extension in nonlinear incompressible material

The nonlinear theory of finite elasticity is applied to obtain the in-plane displacement and stresses in the immediate vicinity of the crack tip. Incompressibility, homogeneity, elasticity and isotropy are assumed for the material while the resultant shear stress and shear strain are assumed to follow a nonlinear hardening/softening behavior. The system of governing differential equations becomes nonelliptical when the strains are sufficiently large.     

Quantitative assessment of the surface crack density in thermal barrier coatings

In this paper, a modified shear-lag model is developed to calculate the surface crack density in thermal barrier coatings（TBCs）. The mechanical properties of TBCs are also measured to quantitatively assess their surface crack density. Acoustic emission（AE） and digital image correlation methods are applied to monitor the surface cracking in TBCs under tensile loading. The results show that the calculated surface crack density from the modified model is in agreement with that obtained from experiments. The surface cracking process of TBCs can be discriminated by their AE characteristics and strain evolution. Based on the correlation of energy released from cracking and its corresponding AE signals, a linear relationship is built up between the surface crack density and AE parameters, with the slope being dependent on the mechanical properties of TBCs.