Dimensional Crack Problems Research Articles

An Improved Damage Mechanics Method for Solving Three Dimensional Crack Problems of Concrete

In this paper, a damage mechanical model is improved to simulate the three-dimensional (3D) mixed mode cracking process of quasi-brittle material such as concrete. The cracking and crack propagating in an element is reflected in the model by controlling the degraded stiffness matrix and the dissipated energy. The local tracking algorithm (LTA) is employed to preselect the element that will belong to the crack path to be damaged. The local tracking algorithm is extended to 3D by analyzing and overcoming defects in the previous 3D LTAs. The present LTA has very low computational cost and this fact is proved by comparison with well-known global tracking algorithm. The numerical results from the novel damage model added 3D local tracking algorithm show good agreement with the results of the previous researches, demonstrating the superior performance of the approach in predicting crack propagation and fracture strength.

Simulation of 3-D Thermo-elastic Fracture Problems Using Coupled FE-EFG Approach

The present work deals with formulation and implementation of coupled FE-EFG approach to solve three dimensional crack problems in thermal loading environment. Geometrical discontinuity across crack surface is modelled by extrinsically enriched EFGM and remaining part of the domain is approximated by standard FEM. In interface/transition region, ramp function based interpolation scheme has been implemented. This coupled approach combines the advantages of both EFGM and FEM. Thermo- elastic problems are decoupled into thermal and elastic problems. At first, unknown temperature field has been obtained by solving steady-state heat conduction equation, and it is used as load input in elastic problem to get displacement and stress field. To check accuracy of proposed technique, one 3-D benchmark crack domain is solved for mechanical loading and obtained results are compared with available reference results. Further, a penny shape crack embedded in cuboid domain is simulated under three different thermo-elastic loading conditions namely thermal shock, adiabatic and isothermal loads to reveal the sturdiness and versatility of the coupled approach.

111 XFEMによる弾塑性き裂解析におけるHRR解の適用(OS9 オーガナイズドセッション《計算力学と数値シミュレーション》)

A complex geometry of components and/or flaws requires a very high cost in preparing analysis models for FEM (Finite Element Method) calculations. XFEM (extended Finite Element Method) is one of solutions of this difficulty. Cracks are modeled independently from element subdivisions by XFEM formulation. XFEM uses enrichment functions for discontinuity of displacement and stress singularity around the crack tip. Because the enrichment functions are usually based on elastic analytical solutions around the crack, elastic crack problems are analyzed precisely. Many efforts have been made to calculate elasto-plastic problems by using XFEM. But an allowable answer may not be obtained yet. Here the discussion is focused to the effect of choice of enrichment functions on accuracy of elasto-plastic solutions of two dimensional crack problems.

Evaluation of Fracture Toughness of Ceramic-Metal Functionally Graded Materials

The main objective of this study is to examine the two dimensional surface crack problems in a system with an interface between two elastic-plastic solids of different yield strength subjected to mode I mechanical loading. The surface cracks growth is considered to occure along the interface direction of bimaterials which is perfectly bonded to each others. A two dimensional finite elementmethod is used to solve the structural problem. Solid 183-node elements are utilized to simulate the strain singularity around the crack front. The crack surface is subjected to a compressive load by three point bending. The stress intesity factors are computed by using the displacement correlation technique. The primary goal is to develop a model crack tip stresses and strains in a manner that is useful for crack growth initiation and propagation in a FGM.

Structure of Near-Tip Stress Field and Variation of Stress Intensity Factor for a Crack in a Transversely Graded Material

The existing studies on the behavior of cracks in continuously graded materials assume the elastic properties to vary in the plane of the crack. In the case of a plate graded along the thickness and having a crack in its plane, the elastic properties will vary along the crack front. The present study aims at investigating the effect of elastic gradients along the crack front on the structure of the near-tip stress fields in such transversely graded materials. The first four terms in the expansion of the stress field are obtained by the eigenfunction expansion approach (Hartranft and Sih, 1969, “The Use of Eigen Function Expansion in the General Solution of Three Dimensional Crack Problems,” J. Math. Mech., 19(2), pp. 123–138) assuming an exponential variation of the elastic modulus. The results of this part of the study indicated that for an opening mode crack, the angular structure of the first three terms in the stress field expansion corresponding to r(−1∕2), r0, and r1∕2 are identical to that given by Williams’s solution for homogeneous material (Williams, 1957, “On the Stress Distribution at the Base of a Stationary Crack,” ASME J. Appl. Mech., 24, pp. 109–114). Transversely graded plates having exponential gradation of elastic modulus were prepared, and the stress intensity factor (SIF) on the compliant and stiffer face of the material was determined using strain gauges for an edge crack subjected to pure bending. The experimental results indicated that the SIF can vary as much as two times across the thickness for the gradation and loading considered in this study.

Analysis of cracked plates using an iterative hybrid technique of boundary element method and distributed dislocation method

An iterative hybrid technique of boundary element method (BEM) and distributed dislocation method (DDM) is introduced for solving two dimensional crack problems. The technique decomposes the problem into ( n + 1) subsidiary problems where n is the number of crack branches. The required solution will be the sum of these ( n + 1) solutions. The first subsidiary problem is to find the stress distribution induced in the plate in the absence of the crack using BEM. All of the remaining subsidiary problems, are stress disturbance ones that will be solved using DDM. The results will be added and compared with the boundary conditions of the original problem. Iteration will be performed between the plate boundaries and crack faces until all of the boundary conditions are satisfied.

Boundary integral equation method for conductive cracks in two and three-dimensional transversely isotropic piezoelectric media

Using the fundamental solutions and the Somigliana identity of piezoelectric medium, the boundary integral equations are obtained for a conductive planar crack of arbitrary shape in three-dimensional transversely isotropic piezoelectric medium. The singular behaviors near the crack edge are studied by boundary integral equation approach, and the intensity factors are derived in terms of the displacement discontinuity and the electric displacement boundary value sum near the crack edge on crack faces. The boundary integral equations for two dimensional crack problems are deduced as a special case of infinite strip planar crack. Based on the analogy of the obtained boundary integral equations and those for cracks in conventional isotropic elastic material and for contact problem of half-space under the action of a rigid punch, an analysis method is proposed. As an example, the solution to conductive Griffith crack is derived.

Critical Conditions for Dislocation Nucleation from Surface Steps

AbstractThe critical conditions for dislocation nucleation from the surface steps of various geometries are analyzed based on the Peierls-Nabarro dislocation model. By modeling a surface step as part of a three- dimensional crack surface, the half space problem is transferred into an equivalent three dimensional crack problem in an infinite medium. The profiles of embryonic dislocations, corresponding to the relative displacements between the two adjacent atomic layers along slip planes, are then rigorously solved through the variational boundary integral method. The critical conditions for dislocation nucleation are determined by solving the stress dependent activation energies required to activate embryonic dislocations from their stable to unstable saddle point configurations. For a given slip plane, the effects of step geometry such as the step height and inclined angle on dislocation nucleation are analyzed in detail. The results show that the atomic scale steps may reduce the critical stress required for dislocation nucleation from the surface by several factors. Compared to previous analyses of this type of problem based on continuum elastic dislocation theory, the presented analysis eliminates the uncertain core cutoff parameter by allowing for the existence of an extended dislocation core as the embryonic dislocation evolves. Because of the serious limitation of direct atomic simulation for this type of problem, the presented methodology of incorporating atomic information into continuum approach appears to be particularly noteworthy for providing insights of energetics of the atomic processes involved in dislocation nucleation.

The Prediction Modelling on the Stress Intensity Factor of Two Dimensional Elastic Crack Emanating from the Hole Using Neural Network and Boundary element Method

Recently the boundary element method has been developed swiftly. The boundary element method is an efficient and accurate means for analysis of two dimensional elastic crack problems. This paper is concerned with the evaluation and the prediction of the stress intensity factor(SIF) for the crack emanating from the circular hole using boundary element method-neural network. The SIF of the crack emanating from the hole was calculated by using boundary element method. Neural network is used to evaluate and to predict SIF from the results of boundary element method. The organized neural network system (structure of four processing element) was learned with the accuracy 99%. The learned neural network system could be evaluated and predicted with the accuracy of 83.3% and 71.4% (in cases of SIF and virtual SIF). Thus the proposed boundary element method-neural network is very useful to estimate the SIF.

Determination of Highly Accurate Values of Stress Intensity Factor in a Plate of Arbitrary Form by FEM.

FEM is useful for stress analysis and used widely in general. However, it is still not necessarily easy to obtain the highly accurate values of stress intensity factors by FEM. Recently, a method for calculating the highly accurate values of mode I stress intensity factors is proposed by Nisitani, based on the usefulness of the stress values at a crack tip calculated by FEM. Although the stress value at a crack tip by FEM is finite, it is very effective as a measure of the singular stress field of the crack tip. In this study, an extension of this method to general two dimensional crack problems was made. The extended method was applied to the problems of the inclined crack, the interference of two cracks in a strip and the micro-crack in a finite plate. As the results, it was confirmed that the present method has the sufficient accuracy in all these problems.

Dynamic Stress Intensity Factor Analysis of Interface Crack Using Line-Spring Model.

In this study, a method for calculating the dynamic stress intensity factor of a bimaterial bending specimen with an interface crack is proposed for the first time by making use of a line-spring model. A precracked bending specimen is modeled by one-dimensional beam finite elements and a line-spring representing the stiffness or compliance of a cracked part. The present method enables the one-dimensional analysis of a two -dimensional crack problem ; thus the time variation of dynamic stress intensity factors of a bimaterial bending specimen with an interface crack can be obtained by making use of a personal computer within a few minutes. The results obtained from the present method agree reasonably well with those obtained from the two-dimensional finite element method, although a slight difference in period can be found. The present method enables rapid evaluation of dynamic stress intensity factors. Thus a rapid evaluation system of dynamic fracture toughness of a bimaterial with an interface crack can be achieved by combining an impact test apparatus with a computer program based on the present method which runs on a personal computer.

Frictional contact problems of kinked cracks modelled by a boundary integral method

AbstractA numerical method is presented for the solution of two dimensional crack problems including the effects of crack kinks and frictional contact between crack faces. The metod is based on an integral equation for the resultant forces along a crack. Coulomb friction between contacting crack surfaces is taken into account. The numerical implementation is demonstrated by considerations of surface and sub‐surface piece‐wise straight line cracks in a half‐plane. Numerical results are presented to illustrate the efficiency and the reliability of the presented method.

Numerical Calculation of Singularities at Reentrant Edges and Corners for Three Dimensional Crack Problems

Numerical Calculation of Singularities at Reentrant Edges and Corners for Three Dimensional Crack Problems

Weight function method for three dimensional crack problems—I. Basic formulation and application to an embedded elliptical crack in finite plates

A weight function technique for analyses of three dimensional crack problems has been developed based on the general expressions of weight functions for two dimensional crack problems and the slice synthesis technique. The weight function method is then used to determine stress intensity factors for an embedded elliptical crack in a finite plate under symmetric loadings. The results, where possible, are compared with other solutions available in the literature. The versatility, efficiency and accuracy of this method are demonstrated.

Weight function method for three dimensional crack problems—II. Application to surface cracks at a hole in finite thickness plates under stress gradients

The weight function method developed in part I is used to determine stress intensity factors for half-elliptical surface cracks at a hole in finite thickness plates under polynomial crack face loading. Superpositions of these results allow determination of stress intensity factors for this crack configuration under general stress distributions. The approach is demonstrated by obtaining stress intensity factors for a variety of load cases including biaxial tension (compression), wedge loading in the hole and simulated pin loading. Both single and double crack configurations are considered and their difference in stress intensity factors is investigated. These results are compared, where possible, with other solutions available in the literature. Very good agreement is obtained.

Application of boundary element method with singular and isoparametric elements in three dimensional crack problems

In the paper, an investigation into the stress intensity factors of mixed-mode three dimensional crack problem is studied. In the method presented in the paper, the number of elements and nodes can be decreased greatly while computational accuracy and efficiency increase, the continuous functions of stress intensity factors along the front of crack can be obtained easily. For an elliptical crack, the parametric equation of an ellipse is introduced, so that the contour of the crack can be represented exactly. There are two examples to test the efficiency of the method. Finally, a cross-shaped pipe-junction with surface cracks is investigated, which is used in offshore engineering.

A boundary element procedure for estimating the residual fatigue life of three dimensional crack problem under cyclic loadings with varying amplitudes

In this paper, a method for estimating the residual fatigue life of three dimensional crack body under cycle loadings with varying amplitude is provided. The boundary element method is employed to calculate the weighted function. The residual fatigue life of the steam turbine rotor under cycle loading with constant amplitude is investigated. The estimated result of fatigue life is on the safe side comparing with the result in other literature.

New method of analysis of three dimensional dimensional crack problems : Isida, M; Tsuru, H; Noguchi, H Mem Fac Engng Kyushu UnivV43, N4, Dec 1983, P317–334

New method of analysis of three dimensional dimensional crack problems : Isida, M; Tsuru, H; Noguchi, H Mem Fac Engng Kyushu UnivV43, N4, Dec 1983, P317–334

Statistical Treatment of Transverse Crack Propagation in Aligned Composites

This paper theoretically examines the failure process of unidirectiona lly reinforced fiber composites with a transverse notch under a tensile load. The fiber stress distribution around the crack tip and the fiber stress redistribution during the initial failure steps have been obtained based upon the explicit solutions of two- dimensional crack problems by the shear-lag method. Failure sequence analysis is conducted to study the effect of variability in fiber strength on the failure process of the composite. Numerical results show that the failure steps ahead of the first intact fiber are not negligible when the Weibull shape parameter of fiber strength distribution is less than four. HE tensile failure of a unidirectionally reinforced fiber composite is a complex process that involves an accumulation of microstructur al damage. In such a material, fibers are relatively weakly coupled by the matrix so that failure of one fiber does not generally precipitate immediate failure of the composite as a whole. Due to this redundancy of the composite's structure, its failure has been considered as a statistical process in which strength is expressed as some measure of the probability of failure such as the mean or median stress. Zweben and Rosen1'2 first analyzed the tensile failure of a fiber reinforced composite in terms of crack instability. However, due to the complexity of the problem, they were unable to arrive at a general failure criterion and proposed a conservative approximation of the failure load. Recently, Harlow and Phoenix outlined the complexity of the problem3 and have obtained exact expressions4 for the probability of failure of small bundles of fibers under the simplified assumption of stress distribution around fiber fractures. Approximate solutions have also been obtained for larger bundles.5'11 In this paper we examine the failure process of uni- directionally reinforced fiber composites with a transverse slit notch, precisely considering the stress field around the crack tips. Based upon the explicit solution12 of two-dimension al crack problems by the shear-lag method,13'14 we obtain the fiber stress around the crack and fiber stress redistribution after several fibers ahead of the crack tip have failed. The knowledge of the fiber stress distribution is incorporated into the failure sequence analysis. In the present analysis, we assume the elastic behavior of the matrix material. However, discussion based upon the inelastic analysis15 will be reported in a future publication. The primary purpose of the study is to provide some insight into the mechanism of failure of notched composites.

Stress concentration around a crack in a granular solid

Two dimensional crack problems are examined in Weiskopf's theory of granular solids using Fourier transform methods. Stress concentrations around cracks as well as the shapes of the cracks are compared with their classical values.