A virtual crack-closure technique for calculating stress intensity factors for cracked three dimensional bodies (original) (raw)
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Cracking Elements Method for Simulating Complex Crack Growth
2019
The cracking elements method (CEM) is a novel numerical approach for simulating fracture of quasi-brittle materials. This method is built in the framework of conventional finite element method (FEM) based on standard Galerkin approximation, which models the cracks with disconnected cracking segments. The orientation of propagating cracks is determined by local criteria and no explicit or implicit representations of the cracks' topology are needed. CEM does not need remeshing technique, cover algorithm, nodal enrichment or specific crack tracking strategies. The crack opening is condensed in local element, greatly reducing the coding efforts and simplifying the numerical procedure. This paper presents numerical simulations with CEM regarding several benchmark tests, the results of which further indicate the capability of CEM in capturing complex crack growths referring propagations of existed cracks as well as initiations of new cracks.
Crack paths and the linear elastic analysis of cracked bodies.PDF
The linear elastic analysis of cracked bodies is a Twentieth Century development, with the first papers appearing in 1907, but it was not until the introduction of the stress intensity factor concept in 1957 that widespread application to practical engineering problems became possible. Linear elastic fracture mechanics (LEFM) developed rapidly in the 1960s, with application to brittle fracture and fatigue crack growth. The first application of finite elements to the calculation of stress intensity factors for two dimensional cases was in 1969. Finite element analysis had a significant influence on the development of LEFM. Corner point singularities were investigated in the late 1970s. It was soon found that the existence of corner point effects made interpretation of calculated stress intensity factors difficult and their validity questionable. In 1998 it was shown that the assumption that crack growth is in mode I leads to geometric constraints on permissible fatigue crack paths. Current open questions are. The need for a new field parameter, probably a singularity, to describe the stresses at surfaces. How best to allow for the influence of corner point singularities in three dimensional numerical predictions of fatigue crack paths. Adequate description of fatigue crack path stability.
The elastic field of general-shape 3-D cracks
Philosophical Magazine, 2006
We extend here the Bilby-Eshelby approach of 2-D crack representation with dislocation pileups to treat 3-dimensional cracks of general geometry. Cracks of any specified external bounding 3-D contour under general loading conditions are represented by sets of parametric Somigliana loops that satisfy total (interaction, self, and external) force equilibrium. Loop positions are solved by using a time integration scheme till equilibrium is achieved. The local Burgers vector is suitably adjusted to be proportional to the local applied surface traction on the crack. The developed method is computationally advantageous, since accurate crack stress fields are obtained with very few concentric parametric loops that adjust to the external crack shape and the local force conditions. The method is tested against known elasticity solutions for 3-D cracks and found to be convergent with an increase in the number of pileup dislocation loops. The method is applied to the determination of the stress field around a 3-D Griffith crack under general loading and a grain boundary crack before and after branching.
Journal of The Brazilian Society of Mechanical Sciences and Engineering, 2016
List of symbols a Crack length B Specimen thickness A n , B m Coefficients of the crack tip asymptotic field E Young's modulus h Half height of the plate K I Stress intensity factors in Mode I K IC Critical stress intensity factor of the first mode L Length of half specimen P Applied load on the specimen P i (r, θ) Locations of virtual strain gages r Radial distance from the crack tip r, θ Polar coordinate components W Specimen width x, y, z Cartesian coordinates components ε xx , ε yy Normal strains in x and y direction ε x'x' , ε y'y' Normal strains in relative to a rotated coordinate system (x', y ') γ xy Shear strain in x-y plane ν Poisson's ratio ρ Mass density µ Shear modulus σ xx , σ yy Normal stresses in x and y directions τ xy Shear stress in x-y plane Abbreviations CTOD Crack tip opening displacement FEM Finite element method HRR Hutchinson-Rice-Rosengren field LEFM Linear elastic fracture mechanics PMMA Poly(methyl methacrylate) (Plexiglas) QPE Quarter point element Abstract A simple method, called the virtual strain gage method, is proposed for an accurate numerical evaluation of the stress intensity factor, the T-stress and the biaxiality parameter β. This method is based on the optimal positions of virtual strain gages located near a crack tip so that the effect of dominant singular strains are canceled. The applicability of the proposed method is examined for quasi-static and low-velocity impact loading conditions on an epoxy three-point bending specimen and PMMA single edge notched specimen. The effects of the loading conditions, the geometry configuration and the length of the crack were presented and discussed. A good agreement has been found between the results of the proposed method and those of the numerical and experimental data previously published. In addition, it is noticed that the proposed method is an alternative and more advantageous then the extrapolation method because of its simplicity and accurate results.
Material Point Method Calculations with Explicit Cracks
Cmes-computer Modeling in Engineering & Sciences, 2003
A new algorithm is described which extends the material point method (MPM) to allow explicit cracks within the model material. Conventional MPM enforces velocity and displacement continuity through its background grid. This approach is incompatible with cracks which are displacement and velocity discontinuities. By allowing multiple velocity fields at special nodes near cracks, the new method (called CRAMP) can model cracks. The results provide an “exact” MPM analysis for cracks. Comparison to finite element analysis and to experiments show it gets good results for crack problems. The intersection of crack surfaces is prevented by implementing a crack contact scheme. Crack contact can be modeled using stick or sliding with friction. All results are two dimensional, but the methods can be extended to three dimensional problems. keyword: Material point method, cracks, fracture, numerical methods, contact
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.
Boundary elements for three-dimensional elastic crack analysis
International Journal for Numerical Methods in Engineering, 1987
In this paper 8-node traction singular boundary clcments are employed to represent displacement and traction variations in the vicinity of the crack front in thrce-dimensional geometries. The numerical procedure suggested for evaluating the singular integrals extending over these special elements is described. The efficiency and accuracy of the special elements and integration procedure are demonstrated by the results obtained in a simple test problem whose analytical solution is known. Theinteraction of two circular coplanar cracks embedded in an infinite medium under uniform tension loading is also analysed. Finally, the stress intensity factor variation computed for a semi-circular inner surface crack in a pressurized cylinder is presented. 0029-59X 1 JX7jl22253-19S0'3.50 1987 by John Wiley & Sons, Ltd.
International Journal for Numerical Methods in Engineering, 2005
We present a new formulation and a numerical procedure for the quasi-static analysis of threedimensional crack propagation in brittle and quasi-brittle solids. The extended finite element method (XFEM) is combined with linear tetrahedral elements. A viscosity-regularized continuum damage constitutive model is used and coupled with the XFEM formulation resulting in a regularized 'crack-band' version of XFEM. The evolving discontinuity surface is discretized through a C 0 surface formed by the union of the triangles and quadrilaterals that separate each cracked element in two. The element's properties allow a closed form integration and a particularly efficient implementation allowing largescale 3D problems to be studied. Several examples of crack propagation are shown, illustrating the good results that can be achieved.