Extended finite element modeling of fatigue crack growth microstructural mechanisms in alloys with secondary/reinforcing
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ORIGINAL PAPER
Extended finite element modeling of fatigue crack growth microstructural mechanisms in alloys with secondary/reinforcing phases: model development and validation Anthony G. Spangenberger1 · Diana A. Lados1 Received: 10 January 2020 / Accepted: 31 August 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract Light structural metals have been extensively applied throughout the transportation sector in recent years with greater impetus to reduce vehicle weight and enhance energy efficiency. However, their use is restricted by the engineering challenge of fatigue crack growth and the need to understand, simulate, and predict crack propagation mechanisms with respect to materials’ microstructure. To address this need, a comprehensive computational methodology has been developed using the extended finite element method to predict fatigue crack interaction mechanisms with characteristic microstructural features. Mathematical formulations and algorithmic development are rigorously addressed, with specific emphasis on the incorporation of relevant physical phenomena of plasticity and particle debonding/fracture. This approach is validated by comparison with analytical models and experiments on cast aluminum–silicon alloys using digital image correlation. The proposed methodology constitutes a framework for the successful development, application, and advancement of computational design of materials. Ultimately, this contributes to material/process selection and design for structural integrity by enabling rapid assessment of fatigue crack growth resistance without prior testing, thereby reducing of the extent of costly experimental investigations. Keywords Extended finite element method · Fatigue crack growth · Digital image correlation · Microstructure
List of symbols A A a¯ B B˜ b C Cep C C RO da dg dK dN
B 1
Domain of the interaction integral Matrix operator of spatial derivatives Sign function enriched degrees of freedom Strain–displacement matrix with small strain (linear) approximation Strain-displacement matrix for finite strains Body force loads Elastic stiffness tensor Elasto-plastic stiffness tensor Paris law constant Ramberg-Osgood parameter Crack growth increment Incremental plastic consistency parameter Mixed mode crack driving force Crack cycle number increment
Anthony G. Spangenberger [email protected] Integrative Materials Design Center, Worcester Polytechnic Institute, 100 Institute Rd, Worcester, MA 01609, USA
EG E f e-j, p, s, t f trial G G G, H I2x2 I (1) , I (2) J J K K I , K II KT L l1 , l2 MS m
Green strain tensor Elastic modulus Global force vector Iteration indices Trial function for radial return algorithm Shape function derivative matrix Yield function The set of Gaussian quadrature points Two-by-two identity matrix Interaction integral for calculation of the Jintegral Jacobian matrix The set of enriched nodes Global stiffness matrix Mode I and II stress intensity factors Global tangent stiffness matrix for simulations with non-linear constitutive beh
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