bridging law and the proportional bridging law. For instance, when the bridging ligaments obey the Dugdale bridging law, steady state crack propagation with small scale bridging is provided max 0A A£ , where max A is given by: 0 D ( Sin( (1 2Aˆ ) ) Sin( Aˆ ) ) D ( Sin( Aˆ ) Sin( ) ) 2 D Aˆ ( Cos( (1 Aˆ ) ) 1 ) Cos( (1 Aˆ ) ) ) 2 ( Cos( ) max max max max max max = - + + - + - - + - - - l l l l l l l l l (15) and where L l=b , º l D d/ , and Aˆ A / L max max º . Regions of steady state stable crack growth under small scale bridging condition can thus be deduced as a function of the material properties of the through thickness reinforcement, the size of the DCB specimen and the velocity of the wedge. CONCLUSIONS The dynamic delamination cracking behavior and the energetics of crack growth in through thickness double cantilever beam (DCB) specimens has been analyzed. The role of bridging by stitches or rods in dynamic crack growth was computed by solving the bridged crack problem within the framework of beam theory. For steady state crack growth conditions, different regimes of the solution behavior have been identified which would correspond to different crack propagation characteristics. Regions of steady state crack growth under small scale bridging condition can be deduced as a function of the material properties of the through thickness reinforcement, the size of the DCB specimen and the velocity of the wedge. This provides guidelines for design of experiments to probe the efficacy of bridging on improving the dynamic fracture toughness of through thickness reinforced structures. ACKNOWLEDGMENTS: All four authors are grateful for support from the U.S. Army Research Office through contract number DAAD19-99-C-0042, administered by Dr. David Stepp. IJB is grateful for support from U.S. Dept. Of Energy through contract W-7405-ENG-36 and RM for support from the Italian Department for the University and for Scientific and Technological Research REFERENCES: 1. Cartié, D. D. R., and Partridge, I. K., "Z-Pinned Composite Laminates: Improvements in Delamination Resistance", Proc. DFC5 Conference, I. Mech. E., March, 1999. 2. Jain, L.K., Mai, Y-W. (1994), “Analysis of stitched laminated ENF specimens for interlaminar mode-II fracture toughness”, Int. Journal of Fracture 68(3), 219-244. 3. M. He and B. N. Cox, "Crack Bridging by Through-Thickness Reinforcement in Delaminating Curved Structures", Composites A, 29[4] 377-93 (1998). 4. R. Massabò and B. N. Cox, "Concepts for Bridged Mode II Delamination Cracks," J. Mech. Phys. Solids, 47, 1265-1300 (1999). 5. B. N. Cox, "Constitutive Model for a Fiber Tow Bridging a Delamination Crack", Mechanics of Composite Materials and Structures, in press. 6. R. Massabò and B. N. Cox, "Unusual Characteristics of mixed mode delamination fracture in the presence of large scale bridging", Mech. Comp. Mater. Structures, in press 7. N.Sridhar, I.J.Beyerlein, B.N.Cox and R. Massabò, "Delamination mechanics in ThroughThickness Reinforced Structures under dynamic crack growth conditions", in prepn. 8. L.B.Freund, "Dynamic Fracture Mechanics", Cambridge University Press, New York (1993)
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