Chapter4 Curvilinear Fatigue Crack Growth Under Out-of-Phase Loading Conditions Xiaomin Deng, Xiaodan Ke, Michael A. Sutton, Haywood S. Watts, and Hubert W. Schreier Abstract Methods for predictive modeling and simulation of crack branching and curvilinear crack paths under cyclic out-of-phase loading conditions have been developed and implemented in a custom finite element code CRACK3D. 3D mixed-mode stress intensity factors (SIFs) for fatigue crack growth simulations with curved crack paths and curved crack fronts are determined using the 3D virtual crack closure technique (3D VCCT) and a locally structured re-meshing approach in which the local region immediately surrounding a moving crack front is automatically re-meshed with a structured mesh pattern to facilitate the 3D VCCT and maintain its accuracy. The prediction of the crack growth direction is achieved using the maximum circumferential stress criterion. Fatigue crack growth events under out-of-phase loading conditions in cruciform aluminum specimens with a central hole and an edge crack at the hole are simulated. Simulation predictions of crack branching angles and the curvilinear paths of the branched cracks agree well with experimental measurements. Keywords Fatigue crack growth • Out-of-phase • Mixed mode • Curved crack path • Local remeshing 4.1 Introduction Fatigue crack growth in metals has been studied mostly under in-phase loading conditions, in which all loadings have the same cyclic time dependence. However, fatigue crack growth in critical structures often occur under out-of-phase loading conditions, such as under biaxial loading conditions in which two sets of biaxial cyclic loads have the same frequency but with a phase difference. Studies of fatigue crack growth under out-of-phase loading conditions have been limited in the literature. Most available studies have been focused on experimental investigations under biaxial loading conditions. As shown in Fig. 4.1, there are two common specimens for fatigue crack growth tests under multi-axial and out-of-phase loading conditions (e.g. [1]): (a) cruciform specimen with biaxial normal loading, and (b) thin-walled tube specimen with axial tension and torsion loading. In particular, the cruciform specimen has been the most common specimen in the literature [2–8]. For the cruciform specimen, as shown in Fig. 4.1, the cyclic biaxial loading can be expressed in terms of the applied nominal stresses in the vertical direction (along y) and horizontal direction (along x), respectively: Sx D xmC xa sin!t Sy D ym C ya sin.!t C / (4.1) where xm and ym are the mean values, xa and ya are the amplitudes, ¨is the frequency, t is time and¥is the phase angle (phase difference). When ¥D0 the loading is in-phase andwhen ¥¤0 the loading is out-of-phase.Often ¥D D180ı is X. Deng ( ) • M.A. Sutton • H.S. Watts Department of Mechanical Engineering, University of South Carolina, Columbia, SC 29208, USA e-mail: deng@cec.sc.edu X. Ke • H.W. Schreier Correlated Solutions, Inc., 121 Dutchman Blvd., Columbia, SC 29063, USA J. Carroll and S. Daly (eds.), Fracture, Fatigue, Failure, and Damage Evolution, Volume 5: Proceedings of the 2014 Annual Conference on Experimental and Applied Mechanics, Conference Proceedings of the Society for Experimental Mechanics Series, DOI 10.1007/978-3-319-06977-7__4, © The Society for Experimental Mechanics, Inc. 2015 27
RkJQdWJsaXNoZXIy MTMzNzEzMQ==