SUMMARYA novel approach to simulate crack growth within an extended finite element framework is presented. The introduced approach combines the material force concept and the extended finite element method (xFEM) that is not straight forward and faces the major problem that a crack tip node, which is required for the evaluation of the material force, is not available within an xFEM framework.The introduced concept enables an efficient single step evaluation of the crack state and the crack growth direction based on a continuum mechanics approach and represents an alternative to the common procedure of using the stress intensity factor solution within a stress or energy-based empirical formulation for the determination of the crack growth direction. Two different approaches are introduced that evaluate the crack tip material force within the xFEM based on a domain or contour approach, both providing equivalent results. After an evaluation of the method, a major focus is set on crack growth investigations with increased complexity, including mixed mode loading and crack interaction with other discontinuities. The influence of different evaluation parameters is studied by comparing the results with empirical, experimental and alternative numerical solutions and confirms the applicability and capability of the proposed combination of both concepts.
In industrial practice, innovative structural aircraft design is, on the one hand, driven by several design criteria like static stress, damage tolerance, and stability, and, on the other hand, by new manufacturing methods and materials, which promise beneficial effects on manufacturing costs and weight. Published optimization approaches are mostly based on pure static stress criteria, albeit the important influence of stability and damage tolerance is neglected. This assumption is perilous but significantly simplifies the investigation. The investigation of unconventional designs under consideration of the preceding criteria is challenging because no analytical or handbook solutions are available. This paper introduces an optimization approach based on an evolution strategy, which incorporates multiple criteria by using nonlinear finite-element analyses for stability and a set of linear analyses for damage-tolerance evaluation. To demonstrate the approach, one design investigation is presented for the window area of a generic aircraft fuselage. The definition of dimensions and the choice of an ideal topology define the optimization problem. The chosen fuselage structure uses an integral design with an innovative combination of window and circumferential frame and is investigated with regard to three load cases that represent relevant in-flight conditions derived from global finite-element analyses. NomenclatureA, B, k, C f , n f , K c = Forman coefficients a = crack length a m , b m , m = shape coefficients of the mass mapping function a u , b u = shape coefficients of the deflection mapping function a SIF , b SIF = shape coefficients of the fatigue-response mapping function C feas , D feas = coefficients of the failure mapping function, feasible state C limit , D limit = coefficients of the failure mapping function, limit state d i = design response i E = Young's modulus G I = energy release rate, mode I G II = energy release rate, mode II g = gravitational acceleration K = stress intensity factor K th = stress intensity factor, threshold value N = load cycle n = load factor p = pressure R = stress ratio t = thickness u = longitudinal displacements at the crack surface v = normal displacements at the crack surface w i = weight factor i X i = longitudinal force at the crack tip Y i = normal force at the crack tip d = exponent of the deflection mapping function SIF = exponent of the fatigue-response mapping function = life span = offspring per generation = population size = Poisson's ratio = density
This work presents the enhancement of a pseudo-numerical tool for fatigue crack growth investigations on integrally stiffened metallic panels. The model is based on an analytical approach that demands compatibility of displacement between skin sheet and stiffener. Since the basis model was presented before, the focus of the present work is on the incorporation of residual stress effects in order to improve simulation results of welded panel configurations that are manufactured by laser beam welding or friction stir welding and exhibit a significant amount of residual stresses. The necessary input parameters for the developed residual stress module are determined from experimental residual stress field measurements. Simulation results using the presented approach are compared with results from finite element simulations on a two stringer panel which show the good accordance of the base model as well as the capability of the tool enhancements to account for the crack retarding effect caused by residual stresses.
The fatigue crack growth behavior in integrally stiffened, welded panels is influenced by residual stresses caused by the welding process. The paper presents a semi-numerical method for the determination of stress intensity factors, taking into account the residual stresses in such a way that the relaxation of the residual stresses during the crack propagation phase is covered. This approach is different from the one presented in .
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