13th International Conference on Fracture June 16–21, 2013, Beijing, China -10- analysis of specimen A7, A8 and S13, crack growth followed tension mode in most cases until the crack reaches a certain length corresponding to: (1) The mode II component of the maximum equivalent Keq,max in one loading cycle exceeds a threshold value and in the meantime; (2) The ratio of mode II stress intensity factor range to mode I stress intensity factor range in one loading cycle is higher than a corresponding threshold value and; (3) Shear mode crack growth occurs when the latter ratio exceeds a critical value. Considering that no theoretical hypotheses can be applied to confirm the two threshold values to the transition mode at present, further research is needed to explain the crack growth path behavior under non-proportional loading cases. Further investigations especially in the field of micromechanics may provide more indications for this problem and improve the proposal of the present paper. Acknowledgements The authors wish to thank the Senior Research Associate in Cornell Fracture Group, Carter Bruce, for technical advice in FRANC3D operating. References [1] Erdogan, F., Sih, G.C., On the Crack Extension in Plates Under Plane Loading and Transverse Shear. J. Basic Engineering, 85D (1963) 519-527. [2] Sih, G.C., Strain-energy-density factor applied to mixed mode crack problems. Int. J. Fracture, 10 (1974) 305-321. [3] R. J. Nuismer, An energy release rate criterion for mixed mode fracture. Int. J. Fracture, 11 (1975) 245-250. [4] Chambers. A. C., Hyde. T. H., Webster. J. J., Mixed mode fatigue crack growth at 550°C under plane stress conditions in Jethete M152. Engng. Frac. Mech, 39 (1991) 603-619. [5] Hussain, M.A., Pu, S.L., Underwood, J.H., Strain energy release rate for a crack under combined mode I and II. Fracture Analysis, (1974) 2-28. ASTM STP 560, Philadelphia. [6] Highsmith Jr., S., Crack path determination for non-proportional mixed-mode fatigue. PhD Thesis, Georgia Institute of Technology, USA, (2009). [7] M. Vormwald, P. Zerres, Review of fatigue crack growth under non-proportional loading. Proceedngs of the 4th international conference on CRACK PATHS, (2012) 1-14. [8] Y. Yang, M. Vormwald, LEFM-based simulation of fatigue crack growth under non- proportional mixed-mode loading. Proceedngs of the 4th international conference on CRACK PATHS, (2012) 465-472. [9] Brüning, J., Untersuchungen zum Rissfortschrittsverhalten unter nichtproportionaler Belastung bei elastisch-plastischem Materialverhalten-Experimente und Theorie, Instituts für Stahlbau und Werkstoffmechanik der Technischen Universität Darmstadt, report 85 ISBN 978-3-939195-14-6, Germany. (2008) [10] D. Haboussa, T. Elguedj, B. Leblé, A. Combescure, Simulation of the shear-tensile mode transition on dynamic crack propagations. Int. J. Fracture, 178 (2012) 195-213.
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