Crack Growth Algorithm Research Articles

Modelling of cohesive crack growth in concrete structures with the extended finite element method

In this paper, the extended finite element method (XFEM) is used for a discrete crack simulation of concrete using an adaptive crack growth algorithm. Different criteria for predicting the direction of the extension of a cohesive crack are investigated in the context of the XFEM. The robustness of these criteria is analyzed with reference to three examples and the results are compared to experiments. Furthermore, the efficient application of the quadtree data structure for an iterative mesh refinement in combination with the XFEM is shown considerably to reduce the computational effort.

The advanced simulation of fatigue crack growth in complex 3D structures

An advanced incremental crack growth algorithm for the three-dimensional (3D) simulation of fatigue crack growth in complex 3D structures with linear elastic material behavior is presented. To perform the crack growth simulation as effectively as possible an accurate stress analysis is done by the boundary-element method (BEM) in terms of the 3D dual BEM. The question concerning a reliable 3D crack growth criterion is answered based on experimental observations. All criteria under consideration are numerically realized by a predictor–corrector procedure. The agreement between numerically determined and experimentally observed crack fronts will be shown on both fracture specimens and an industrial application.

Experiments and stochastic model for propagation lifetime of railway axles

Abstract Inspection intervals of critical safety components should be calculated on the basis of sophisticated crack growth algorithms able to describe crack propagation under service loads. The present paper deals with a probabilistic application of the NASGRO crack growth algorithm to estimate the propagation lifetime of railway axles. The analysis of experimental crack growth and threshold data of an A1N steel has enabled us to propose two random variable models for the estimation of propagation lifetimes, discussing their statistical properties and their implications for lifetime estimates.

Efficient simulation of 3D fatigue crack growth based on boundary elements

AbstractThe three‐dimensional simulation of fatigue crack growth under the consideration of 3D effects is presented to follow complex crack paths as realistic as possible from the macroscopic point of view. This aim is mainly based on two aspects. Firstly, an accurate stress analysis is performed by the boundary element method in terms of the 3D Dual BEM. Secondly, a suitable 3D crack growth criterion based on experimental observations is utilized. Due to the non‐linearity of crack growth the whole procedure is embedded in an advanced incremental crack growth algorithm. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Simulation of Fatigue Crack Propagation in Railway Axles

Abstract The need for optimizing inspection intervals of wheelsets has led to increasing attention to those of railway axles. This paper addresses this issue by comparing predictions obtained by an EPFM model and two widely used fatigue crack growth softwares (namely AFGROW and NASGRO) with a set of propagation data derived from small and full-scale specimens made of 30NiCrMoV12, a high strength steel used for railway axles. Comparisons, made under constant amplitude and block loading, support the application of the considered fatigue crack growth algorithms to the estimation of inspection intervals.

A predictor–corrector scheme for the optimization of 3D crack front shapes

ABSTRACTA predictor–corrector scheme is presented to improve the shape of 3D crack fronts within the 3D simulation of fatigue crack growth. This concept is fully functional for mode‐I, and an extension for mixed‐mode problems is presented. The whole procedure is embedded in an automatic incremental crack growth algorithm for arbitrary 3D problems with linear elastic material behaviour. The numerical simulation is based on the 3D dual boundary element method (Dual BEM) and on an optimized evaluation of very accurate stress intensity factors (SIFs) and T‐stresses. As part of the proposed predictor–corrector scheme, 3D singularities along the crack front especially in the vicinity of the intersection of the crack front and the boundary are considered. The knowledge of these singularities allows the specification of crack front shapes with bounded energy release rate. Numerical examples with complex cross‐sections are presented to show the efficiency of the proposed crack growth algorithm. The obtained results are in good agreement with recent experimental results.

Application of fatigue crack growth algorithms to railway axles and comparison of two steel grades

The reduction of the total life cycle cost of the whole wheelset requires an optimization of inspection intervals for axles. Such components can, in most European countries, endure more than 30 years of service life. During this time, they are subjected to frequent non-destructive testing (NDT) inspections. It is therefore important to assess the influence of design options, such as hollow versus solid axles or mild versus high strength steel, on the prospective crack propagation life of an axle. In the present paper two dedicated crack propagation algorithms (namely AFGROW and NASGRO) will be applied to the estimation of inspection intervals of railway axles by comparing the properties of two widely used steels.

Equivalent initial flaw size testing and analysis of transport aircraft skin splices

ABSTRACTThe equivalent initial flaw size (EIFS) concept was developed nearly 30 years ago in an attempt to account for the initial quality, both manufacturing and material properties, of a structural detail prone to fatigue cracking. Widespread use of this concept has been limited due to the large amount of test data required to develop a reliable EIFS distribution. In this effort, an EIFS distribution was determined for four types of flat, production like transport aircraft fuselage skin joints loaded by remote tension. Two crack growth prediction codes, AFGROW and FASTRAN, were used to not only develop the EIFS but also to compare the crack growth algorithms in each code. The EIFS calculations are prone to compounding errors in the crack growth analysis due to the changing stress intensity factor solutions and stress fields as the crack gets longer. Thus, only including EIFS calculations for mechanically small cracks, crack lengths less than 1.27 mm, results in a mean EIFS of 18.0 μm with a standard deviation of 3.78 μm.

A remeshing algorithm for three-dimensional crack growth and intersection with surfaces or cracks in non-coplanar planes

Abstract A recent procedure developed for crack growth in which three-dimensional stress intensity factors are calculated by boundary integral equations is used to compute fatigue crack growth as cracks grow in accordance with Paris’ law and also intersect each other or other surfaces. This paper concentrates on describing the remeshing algorithms needed as the cracks grow and when they intersect each other or other surfaces. The algorithms produced treat crack growth; prior to intersections, after intersection with a free surface, after intersection of a crack edge with a crack surface away from its edge, and after intersection of coplanar cracks. The method is applied here to the growth of an initially circular crack at the centre of a block under uniform tensile traction on the faces parallel to the crack. The crack grows to intersect either a free surface of the block or the centre of a square crack in an orthogonal plane.

Statistical Properties of Fatigue Life Simulated for Notched Components under Combined Loading.

Failure lives of notched components in multiaxial fatigue were statistically estimated by Monte Carlo simulations for materials with different microstructures using a proposed crack growth model. An analytical algorithm for crack growth in a microstructure, which was modeled as an aggregate of hexagons, was based on competition between two possible growth modes. In simulations, various microstructure configurations, which resulted in distinct failure lives, were randomly generated for a material under consideration. Ranges of simulated life almost coincided with experimental results observed in four kinds of materials. The coefficient of variation and the shape parameter in the fitted two-parameter Weibull distribution function for the simulated life distribution were investigated to clarify statistical properties of the failure life in multiaxial fatigue. The life dispersion was found to be larger under a loading mode with a higher proportion of shear stress component and/or in a material with coarser grains.

LIFE PREDICTION BY SIMULATION OF CRACK GROWTH IN NOTCHED COMPONENTS WITH DIFFERENT MICROSTRUCTURES AND UNDER MULTIAXIAL FATIGUE

A modelling procedure was developed which is applicable to crack growth in notched components subjected to multiaxial fatigue for materials with different microstructures. An algorithm for crack growth, in a microstructure that was modelled as hexagons, was established as a competition between growth by crack linkages during the crack initiation and propagation stages and the propagation of a dominant crack as a single crack. Analytical results simulated by using the developed model were compared with experimental results from fatigue tests which had been conducted using notched specimens of pure copper, carbon steel and two kinds of titanium alloy. Cracking morphology, which was experimentally observed to depend on the microstructure and the loading mode, was well simulated using the present model. The fatigue failure life of a notched specimen was statistically estimated by a Monte Carlo procedure based on the model. The simulated life with a statistical scatter‐band almost coincided with the experimental data.

An efficient variable amplitude loading scheme for three-dimensional fatigue crack

The finite element alternating method (FEAM) is an extremely useful and efficient scheme for the accurate calculation of stress intensity factors in complex three dimensional structures. This approach involves the combination of an analytical solution for a crack in an infinite body with a finite element solution for the uncracked component. Previously a three-dimensional fatigue crack growth algorithm has been incorporated into the alternating method for the case of constant amplitude loading. The major accomplishment outlined in this paper is the implementation of an additional numerical scheme for the more difficult case of variable amplitude loading. Test cases, with an emphasis on components taken from the aerospace industry, are used to validate the revised alternating method computer program. Results reveal excellent levels of correlation with existing packages and highlight the suitability of the finite element alternating method for fatigue crack growth analyses in a wide variety of components such as aircraft components, pipelines, offshore structures, pressure vessels, ships, etc.

Computational strategies for fatigue crack growth in three dimensions with application to aircraft components

Abstract The finite element alternating method, which has proved to be an extremely efficient scheme for the accurate calculation of stress intensity factors, is augmented here by an algorithm to calculate the fatigue life, under cyclic loading, of three-dimensional structural components. The alternating method involves the combination of an analytical infinite body solution with a numerical solution for the uncracked physical structure. The advantage here is that mesh generation and computational time are considerably reduced since this finite element approach only entails an analysis of the uncracked body. These simplifications make it possible to implement a three-dimensional fatigue crack growth algorithm into the alternating method. This approach has been applied here to various fatigue problems in complex aircraft components. Solutions were initially developed for constant amplitude loading and then extended to the more difficult case of variable amplitude loading.

Elastoplastic simulation of fatigue crack growth Dual boundary element formulation

Abstract In this paper an algorithm is proposed for the analysis of cracks growin in a stable manner in ductile materials. This algorithm uses a recently presented formulation of the elastoplastic dual boundary element method (EPDBEM) by Leitao et al. , which allows for crack problems to be modelled within a single-region formulation. The elastoplastic behaviour is modelled through the use of an approximation for the plastic component of the strain tensor on the region expected to yield. This region is discretized with internal quadratic, quadrilateral and/or triangular cells. This new algorithm for stable crack growth is based on the release of pairs of elements, which are assumed to be in contact prior to the formation of the crack. Crack-face contact is simulated by directly enforcing compatibility and equilibrium conditions between the surfaces of the crack. Elastoplastic fracture parameters, namely J -type integrals, can be calculated at all stages of the fatigue crack growth process. An example of the application of this technique is presented.

Finite element crack growth algorithm for dynamic fracture

A new finite element crack growth algorithm has been developed to simulate dynamic fracture. In this algorithm, pseudo elements with very high initial density are placed below the crack plane and the density is reduced to zero in a gradual manner as the crack passes the element. A number of linear elastic and elasto-viscoplastic problems have been carried out to test the new algorithm. The results are compared with some of the existing crack growth models.

A Computational investigation of local material strength and toughness on crack growth

Abstract Computational simulation of stable crack growth is an important aspect of structural integrity prediction. Modern alloy strength and ductility increase local material fracture toughness but simultaneously complicate stable crack growth predictions. Material modeling, material parameter identification, fracture criterion and numerical crack growth algorithms are issues which must be addressed for robust crack growth prediction. In this investigation, a series of finite element simulations were undertaken to investigate two-dimensional mode I crack growth in a modified compact tension specimen geometry. Two different crack lengths were considered. HY-100 steel parameters, previously characterized for large strain deformation, were utilized. Additional material responses, based on the HY-100 nonlinear response but with different yield strengths and ductilities, were also considered to assess parametrically material effects on crack growth. A debonding algorithm was employed to produce crack growth by nodal release when local material conditions, satisfying a specified local fracture criterion, were met. Material fracture and crack growth were treated as dependent variables of the analysis, generating crack growth in discrete increments. The results of this parametric computational study demonstrated crack growth of up to 67% of the initial crack length over the total number of load increments allowed for each combination of geometry, material strength and material toughness. The current crack tip energy density histories exhibited piecewise smooth behavior, consistent with the changing crack tip position produced by discrete crack growth across finite elements. The relative loads and crack growth sustained by each specimen were observed to depend on the elastic stress and strain response of the material in addition to the local fracture toughness of the material.

A finite element algorithm for creep crack growth

Abstract A finite element algorithm involving the “Breakable element” concept is proposed for the prediction of the growth of a crack in a solid subject to combined thennoelastic-plastio-creep load. The unique advantage of this algorithm is its ability to provide detail stress and strain distributions, the kinematics of the inelastic zones, as well as the profiles of the growing crack. A numerical example with three assigned effective rupture strains as fracture criteria, is included to illustrate these special features.