13th International Conference on Fracture June 16–21, 2013, Beijing, China -10- 5. Conclusions The present work discovers the most fundamental fracture modes – the two sets of orthogonal pure modes. A mixed-fracture mode can be superimposed or partitioned by these most fundamental pure modes. The two sets co-exist in classical laminated composite beams and plates and coincide in shear deformable beams and plates for rigid interfaces. When non-rigid interfaces considered the two sets coincide in both classical and shear deformable theories. By using these two sets of pure modes, a mixed-mode can also be partitioned based on 2D elasticity theory. The novel methodology is rooted in the mechanics of material and operated by a powerful mathematical method. It is capable of studying delamination in curved laminated composite beams and shells as well. It is also capable of studying general and buckling driven delamination consisting of all opening, shearing and tearing modes. References [1] J.G. Williams, On the calculation of energy release rates for cracked laminates. Int J Fract Mech, 36 (1988) 101–119. [2] R.A. Schapery, B.D. Davidson, Prediction of energy release rate for mixed-mode delamination using classical plate theory. Appl Mech Rev, 43 (1990) S281–S287. [3] J.W. Hutchinson, Z. Suo, Mixed mode cracking in layered materials. Adv Appl Mech, 29 (1992) 63–191. [4] M. Charalambides, A.J. Kinloch, Y. Wang, J.G. Williams, On the analysis of mixed-mode failure. Int J Fracture, 54 (1992) 269–291. [5] Z. Zou, S.R. Reid, P.D. Soden, S. Li, Mode separation of energy release rate for delamination in composite laminates using sublaminates. Int J Solids Struct, 38 (2001) 2597–2613. [6] D. Bruno, F. Greco, Mixed mode delamination in plates: a refined approach. Int J Solids Struct, 38 (2001) 9149–9177. [7] Q. Luo, L. Tong, Calculation of energy release rates for cohesive and interlaminar delamination based on the classical beam-adhesive model. J Compos Mater, 43 (2009) 331–348. [8] S. Wang, C.M. Harvey, A theory of one-dimensional fracture. Compos Struct, 94 (2012) 758–767. Also a plenary lecture at the 16th international conference on composite structures (ICCS-16), 28–30th June 2011, Porto, Portugal. [9] C.M. Harvey, S. Wang, Experimental assessment of mixed-mode partition theories. Compos Struct, 94 (2012) 2057–2067. [10] S. Wang, C.M. Harvey, Mixed mode partition theories for one dimensional fracture. Eng Fract Mech, 79 (2012) 329–352. Also a plenary lecture at the 8th international conference on fracture and strength of solids (FEOFS 2010), 7-9th June 2010, Kuala Lumpur, Malaysia. [11] C.M. Harvey, S. Wang, Mixed-mode partition theories for one-dimensional delamination in laminated composite beams. Eng Fract Mech, 96 (2012) 737–759. [12]S. Wang, C.M. Harvey, Partition of mixed modes in double cantilever beams with non-rigid elastic interfaces. Eng Fract Mech (under review). [13]C.M. Harvey, Mixed-Mode Partition Theories for One-Dimensional Fracture. PhD Thesis. March 2012, Loughborough University, UK.
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