A finite element method for crack growth without remeshing

An improvement of a new technique for modelling cracks in the finite element framework is presented. A standard displacement‐based approximation is enriched near a crack by incorporating both discontinuous fields and the near tip asymptotic fields through a partition of unity method. A methodology that constructs the enriched approximation from the interaction of the crack geometry with the mesh is developed. This technique allows the entire crack to be represented independently of the mesh, and so remeshing is not necessary to model crack growth. Numerical experiments are provided to demonstrate the utility and robustness of the proposed technique. Copyright © 1999 John Wiley & Sons, Ltd.     

Elastic crack growth in finite elements with minimal remeshing

A minimal remeshing finite element method for crack growth is presented. Discontinuous enrichment functions are added to the finite element approximation to account for the presence of the crack. This method allows the crack to be arbitrarily aligned within the mesh. For severely curved cracks, remeshing may be needed but only away from the crack tip where remeshing is much easier. Results are presented for a wide range of two‐dimensional crack problems showing excellent accuracy. Copyright © 1999 John Wiley & Sons, Ltd.     

A three-dimensional (3D) numerical study of fatigue crack growth using remeshing techniques

Numerical analyses based on the finite element (FE) method and remeshing techniques have been employed in order to develop a damage tolerance approach to be used for the design of aeroengines shaft components. Preliminary experimental tests have permitted the calculation of fatigue crack growth parameters for the high strength alloy steel adopted in this research. Then, a robust numerical study have been carried out to understand the influence of various factors (such as: crack shape, crack closure) on non-planar crack evolution in solid and hollow shafts under mixed-mode loading. The FE analyses have displayed a satisfactory agreement compared to experimental data on compact specimens (CT) and solid shafts.     

Distributed cracks and kinked cracks in bonded dissimilar half planes with an interface crack

This paper is concerned with the interactions between an interface crack and other arbitrarily distributed cracks in two bonded dissimilar half planes. Special emphasis is placed on the cracks kinked at a tip of the interface crack, which remain unsolved as far as the authors are concerned. For the present, we pay attention to the stress intensity factors at the tips of the kinks or the distributed cracks, and not to those at the tips of the interface crack. The analysis is based on continuous distributions of the body forces along the cracks, and their densities are determined with a new procedure in order to get highly accurate results. The present analysis for distributed line cracks applies to kinked cracks, branched cracks and those piercing the interface just by joining some of the line cracks. Numerical calculations are performed for various important problems, and the effects of geometric and mechanical parameters on the stress intensity factors are examined.     

Numerical simulation of multiple crack growth in brittle materials with adaptive remeshing

In this paper, an automated adaptive remeshing procedure is presented for simulation of arbitrary shape crack growth in multiple cracked bodies. The Zienkiewicz–Zhu error estimator is employed in conjunction with the modified superconvergent patch recovery (SPR) technique to obtain more accurate estimation of error. A stability analysis is performed to determine active cracks from a set of competitive cracks. Various crack growth criteria together with the respective crack trajectory prediction are compared. Several numerical examples are illustrated to demonstrate the efficiency, robustness and accuracy of computational algorithm in the simulation of multiple crack growth. Copyright © 2010 John Wiley & Sons, Ltd.     

A finite element algorithm for creep crack growth

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.     

A mesh-independent method for planar three-dimensional crack growth in finite domains

The discrete crack mechanics (DCM) method is a dislocation-based crack modeling technique where cracks are constructed using Volterra dislocation loops. The method allows for the natural introduction of displacement discontinuities, avoiding numerically expensive techniques. Mesh dependence in existing computational modeling of crack growth is eliminated by utilizing a superposition procedure. The elastic field of cracks in finite bodies is separated into two parts: the infinite-medium solution of discrete dislocations and an finite element method solution of a correction problem that satisfies external boundary conditions. In the DCM, a crack is represented by a dislocation array with a fixed outer loop determining the crack tip position encompassing additional concentric loops free to expand or contract. Solving for the equilibrium positions of the inner loops gives the crack shape and stress field. The equation of motion governing the crack tip is developed for quasi-static growth problems. Convergence and accuracy of the DCM method are verified with two- and three-dimensional problems with well-known solutions. Crack growth is simulated under load and displacement (rotation) control. In the latter case, a semicircular surface crack in a bent prismatic beam is shown to change shape as it propagates inward, stopping as the imposed rotation is accommodated.     

Fatigue crack growth in reinforced panels with initial corner cracks

Fatigue crack growth test results are presented for 42 structural sheet-stringer specimens with 0.050 in. initial corner cracks at fastener holes. The method of combining known stress intensity factor and stress concentration factor solutions is used to predict the sequences of growth, arrest and reinitiation of cracks leading to failure of these panels. The reliability of this commonly-used predict:ion approach is assessed by comparisons between predictions and the test data.     

A fatigue crack growth model for interacting cracks in a plate of arbitrary thickness

Fatigue and fracture assessment of structures weakened by multiple site damage, such as two or more interacting cracks, represents a very challenging problem. A proper analysis of this problem often requires advanced modelling approaches. The objective of this paper is to develop a general theoretical approach and investigate the fatigue behaviour of two interacting cracks. The developed approach is based on the classical strip yield model and plasticity induced crack closure concept. It also utilises the 3D fundamental solution for an edge dislocation. The crack advance scheme adopts the cycle‐by‐cycle calculations of the effective stress intensity factors and crack increments. The modelling results were validated against experimental data available in the literature. Further, the nonlinear effects of the crack interaction and plate thickness on the crack opening stresses and crack growth rates were studied with the new approach for the problem geometry. It was demonstrated that the both effects could have a significant influence on fatigue life and cannot be disregarded in life and integrity assessments of structural components with multiple site damage.     

An analysis of the energy release rate for non-coplanar crack growth in fiber reinforced composite materials

In view of the fact that non-coplaner crack growth is a common characteristic of crack propagation in fiber reinforced composite materials, an attempt is made to derive the equation of the energy release rateG for non-coplaner crack extension in orthotropic linear elastic solids. Combining the idea developed in our previous paper and the analysis by Sihet al., the equation ofG is obtained for the cases of plane symmetric loading, plane skew-symmetric loading, antiplane shear loading, and a combination of these. The result will serve as a basic tool for developing a fracture mechanics approach to composites.     

Estimating the statistical properties of crack growth for small cracks

A series of statistical studies were conducted on two sets of fatigue crack growth data which were generated under variable amplitude loading from cracks that initiated in 7475-T7351 Aluminum down in the bore of typical aircraft quality prepared holes. The study considered fatigue crack growth (life) behavior and fatigue crack growth rate behavior. Generally, the study showed that small crack growth behavior was similar to that observed for larger cracks and that a stress intensity factor parameter could be used to describe the mean trend of the fatigue crack growth rate behavior via a power law relationship.     

Experimental investigation of crack growth direction in multiple cracks

In this paper, the interaction between multiple cracks in crack growth direction is studied in an aluminium alloy under static and fatigue loading. Self similar as well as non‐self‐similar crack growth has been observed which depends on the relative crack positions defined by crack offset distance and crack tip distance. On the basis of experimental observations, the criterion for crack coalescence and crack growth direction are expressed in terms of the crack positions defined by crack offset and crack tip distances. The criterion presented in this study can be used to determine the limiting value of crack tip and crack offset distance and to determine the mode in which cracks coalesce during their growth process. Experimental results and crack interaction criterion presented under various crack positions and size conditions could be used to derive a new evaluation method of crack growth in multiple crack geometry.     

Threshold crack growth behavior of shear and tensile cracks

Crack-face interference-free mode I and mode II crack-growth data was combined with smooth axial (λ = ε_xy/ε_xx = 0) and torsional (λ = ∞) endurance limit data to develop unified crack growth models that incorporate both shear and tensile cracking. The crack growth models incorporated growth from a slip band (including short crack behavior) size crack until the final failure of a long crack, and the ability to switch between crack growth on shear planes to growth on tensile planes. The models successfully predicted smooth specimen crack-face interference-free fatigue lives and gave reasonable estimates of the smooth specimen endurance limits of crack-face interference free tubular tests run at intermediate strain ratios (λ = 3/4, 3/2, and 3). The series of Kitigawa–Takahashi (threshold fatigue) diagrams developed from the models help illustrate the competition between shear and tensile cracking at the fatigue limit under crack-face interference-free crack growth.     

Discussions of three-dimensional models for mixed-mode fatigue crack growth

This technical note discusses several three-dimensional models for mixed-mode fatigue crack growth that were developed recently by Bian and coauthors [1], [2], [3], [4] and [5]. However, these models are found being formulated from a generally incorrect three-dimensional crack-front stress field for embedded elastic elliptical cracks. The corresponding correct crack-front stress field for the elliptical cracks is thus presented, and then the three-dimensional fatigue crack growth models are corrected and expressed in much simpler functions.     

On the implications for LEFM of the three-dimensional aspects in some crack/surface intersection problems

Several elastic configurations containing cracks under transverse tension which intersect a free surface are investigated. In order to ensure reliable results two independent numerical methods are employed on a comparison problem, each method being tuned to handle the special features involved. The comparison provides confidence in other results which focus on the key quantity in linear elastic fracture mechanics, the energy release rate. These findings may be summarized as follows: that the decays in the energy release rates found as the free surface is approached in the various problems treated are probably not significant from a fracture toughness testing point of view and not of major consequence in cyclic life calculations, although there are some indications that this may not be the case if near-surface residual stress fields are present; and that these variations in energy release rate can be compensated for by relatively minor perturbations in crack-front profiles.

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Résumé On étudie diverses configurations élastiques comportant des fissures coupant une surface libre et soumises à tension transversale. Deux méthodes numériques indépendantes sont utilisées à titre comparatif sur un problème en vue d'obtenir des résultats fiables, chaque méthode étant adaptée en vue de tenir compte des caractéristiques spécifiques au problème.Cette comparaison donne confiance dans d'autres résultats qui se basent sur un paramètre clé de la mécanique de rupture linéaire et élastique, le taux de relaxation de l'énergie. On peut résumer les conclusions de l'étude comme suit. Le fait que l'on trouve une atténuation du taux de relaxation de l'énergie au für et à mesure qu'on se rapproche d'une surface libre n'a probablement pas, dans les divers problèmes traités, de signification du point de vue de l'essai de ténacité à la rupture, et n'a pas d'influence majeure sur le calcul de la vie en fatigue, bien que certaines indications laissent appréhender que ce n'est pas le cas si sont présents au voisinage de la surface des champs de contrainte résiduelle. En outre, ces variations dans le taux de relaxation de l'énergie peuvent être compensées par des perturbations relativement mineures dans le profil du front de fissure.

     

Discrete crack growth analysis methodology for through cracks in pressurized fuselage structures

A methodology for simulating the growth of long through cracks in the skin of pressurized aircraft fuselage structures is described. Crack trajectories are allowed to be arbitrary and are computed as part of the simulation. The interaction between the mechanical loads acting on the superstructure and the local structural response near the crack tips is accounted for by employing a hierarchical modelling strategy. The structural response for each cracked configuration is obtained using a geometrically non-linear shell finite element analysis procedure. Four stress intensity factors, two for membrane behaviour and two for bending using Kirchhoff plate theory, are computed using an extension of the modified crack closure integral method. Crack trajectories are determined by applying the maximum tangential stress criterion. Crack growth results in localized mesh deletion, and the deletion regions are remeshed automatically using a newly developed all-quadrilateral meshing algorithm. The effectiveness of the methodology, and its applicability to performing practical analyses of realistic structures, is demonstrated by simulating curvilinear crack growth in a fuselage panel that is representative of a typical narrow-body aircraft. The predicted crack trajectory and fatigue life compare well with measurements of these same quantities from a full-scale pressurized panel test.