Estimation of Fracture path in the Structures and the Influences of Non-singular term on crack propagation (original) (raw)
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Extended Finite Element Method for Two-dimensional Crack Modeling
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Non‐planar 3D crack growth by the extended finite element and level setsPart I: Mechanical model
International Journal for …, 2002
A methodology for solving three-dimensional crack problems with geometries that are independent of the mesh is described. The method is based on the extended ÿnite element method, in which the crack discontinuity is introduced as a Heaviside step function via a partition of unity. In addition, branch functions are introduced for all elements containing the crack front. The branch functions include asymptotic near-tip ÿelds that improve the accuracy of the method. The crack geometry is described by two signed distance functions, which in turn can be deÿned by nodal values. Consequently, no explicit representation of the crack is needed. Examples for three-dimensional elastostatic problems are given and compared to analytic and benchmark solutions. The method is readily extendable to inelastic fracture problems. This paper and a companion paper present further developments of the extended ÿnite element method (X-FEM) for modelling cracks and crack growth. The extended ÿnite element method alleviates much of the burden associated with mesh generation for objects with cracks by not requiring the ÿnite elements to conform to the crack surface. Moreover, it provides a convenient way for incorporating near-tip asymptotic ÿelds, so that good accuracy can be obtained for elastic fracture with relatively coarse meshes around the crack.
Applied and Computational Mechanics, 2019
In the present work, the effect of various discontinuities like voids, soft inclusions and hard inclusions of the mixed-mode stress intensity factor (MMSIF), crack growth and energy release rate (ERR) of an edge crack isotropic plate under different loading like tensile, shear, combine and exponential by various numerical examples is investigated. The basic formulation is based on the extended finite element method (XFEM) through the M interaction approach using the level set method. The effect of single and multi voids and inclusions with position variation on MMSIF and crack growth are also investigated. The presented results would be applicable to enhancing the better fracture resistance of cracked structures and various loading conditions.
Modelling crack growth by level sets in the extended finite element method
… Journal for Numerical …, 2001
An algorithm which couples the level set method (LSM) with the extended ÿnite element method (X-FEM) to model crack growth is described. The level set method is used to represent the crack location, including the location of crack tips. The extended ÿnite element method is used to compute the stress and displacement ÿelds necessary for determining the rate of crack growth. This combined method requires no remeshing as the crack progresses, making the algorithm very e cient. The combination of these methods has a tremendous potential for a wide range of applications. Numerical examples are presented to demonstrate the accuracy of the combined methods.
X-FEM simulation of 2-D fracture mechanics problem
2011
In this paper, edge crack problems under mechanical loads have been analysed using extended finite element method (XFEM) as it has proved to be a competent method for handling problems with discontinuities. The XFEM provides a versatile technique to model discontinuities in the solution domain without re-meshing or conformal mesh. The stress intensity factors (SIF) have been calculated by domain based interaction integral method. The effect of crack orientation and interaction under mechanical loading has been studied. Analytical solutions, which are available for two dimensional displacement fields in linear elastic fracture mechanics, have been used for crack tip enrichment. From the present analysis, it has been observed that there is monotonous decrease in the SIF-1 value with the increase in inclination, while SIF-II values first increases then it also decreases. Next study was performed for first edge crack in the presence of second crack on opposite edge. The results were obt...
Fracture analysis in plane structures with the two-scale G/XFEM method
International Journal of Solids and Structures, 2018
Generalized or extended finite element method (G/XFEM) uses enrichment functions that holds a priori knowledge about the problem solution. These enrichment functions are mostly limited to two-dimensional problems. A well-established solution for problems without any specific types of analytically derived enrichment functions is to use numerically-build functions in which they are called global-local enrichment functions. These functions are extracted from the solution of boundary value problems defined around the region of interest discretized by a fine mesh. Such solution is used to enrich the global solution space through the partition of unity framework of the G/XFEM. Here it is presented a two-scale/global-local G/XFEM approach to model crack propagation in plane stress/strain and Reissner-Mindlin plate problems. Discontinuous functions along with the asymptotic crack-tip displacement fields are used to represent the crack without explicitly represent its geometries. Under the linear elastic fracture mechanics approach, the stress intensity factor (obtained from a domain-based interaction energy integral) can be used to either determine the crack propagation direction or propagation status, i.e., the crack can start to propagate or not. The proposed approach is presented in detail and validated by solving several linear elastic fracture mechanics problems for both plane stress/strain and Reissner-Mindlin plate cases to demonstrate its the robustness and accuracy.
Engineering, Technology & Applied Science Research
When the loading or the geometry of a structure is not symmetrical about the crack axis, rupture occurs in mixed mode loading and the crack does not propagate in a straight line. It is then necessary to use kinking criteria to determine the new direction of crack propagation. The aim of this work is to present a numerical modeling of crack propagation under mixed mode loading conditions. This work is based on the implementation of the displacement extrapolation method in a FE code and the strain energy density theory in a finite element code. At each crack increment length, the kinking angle is evaluated as a function of stress intensity factors. In this paper, we analyzed the mechanical behavior of inclined cracks by evaluating the stress intensity factors. Then, we presented the examples of crack propagation in structures containing inclusions and cavities.