Crack bridging (e.g., from stitches or pins) and friction have profound and potentially very useful effects on delamination crack growth, controlling growth rates (damage levels) and the energy absorbed. However, the implications for structural design principles have remained quite obscure. The difficulty is that no simple analogue of crack toughness, which underpins static structural design, exists for dynamic cases with large-scale bridging effects. The external shape of the structure and the loading configuration dictate stress waves, frictional contact zones, and crack tip stress intensity factors in a way that is very difficult to approach, other than by brute case-specific numerical simulation. The problem is compounded by the common occurrence of multiple cracking, a complexity that is rarely entertained in laboratory fracture specimen design. Physically sound material models for the important structural problem of multiple, nonlinear cracking in laminated structures with large-scale bridging due to friction and reinforcement had previously remained undeveloped, in spite of the technological importance of these systems.
A program of basic research was conducted to develop engineering principles for dealing with dynamic, multiple cracking damage in laminated structures, including large-scale crack bridging due to through-thickness reinforcement and friction. Bridging and friction were treated by materials models at the smallest scales relevant to the mechanisms. By reference to the fundamentals of the dynamic growth of single cracks, which are already largely understood, simple approaches have been formulated for calculating the development of distributed delamination cracks in laminated structures. To treat large-scale bridging effects, structural sub-component models must support dimensions of ~100 mm or more. This approach bridged scales ranging from this characteristic size down to that of micro-mechanisms (friction, fiber bridging) within the process zone of a single crack. Thus, a direct link has been established between structural performance and materials design.
The analyses show the existence of regimes, within the full computed solution space, where crack growth is approximately steady state. A simplified approach to inferring rate effects in the cohesive law can then be taken by restricting the domains of the solutions considered to the steady-state domains. A limited solution domain is conservative with respect to assessing information content, because the full domain must contain more information.
In the steady-state regimes, the local sliding speed in the process zone, which is the parameter that controls rate effects in the cohesive law, is a known function of the crack tip speed and the sliding displacement profile. Both of these quantities could be measured using a digital image correlation system. In addition, the average sliding speed along the process zone when the crack is propagating in steady-state conditions coincides with the local sliding speed if the profile is approximately linear. In this case, numerical solutions obtained for a rate-independent cohesive law would represent general rate-dependent materials since a rate effect would simply imply different but fixed values of the cohesive parameters.
By examining the steady-state domains for different rate-independent cases, behavior for assumed rate-dependent variations can be reconstructed. In the ENF specimen, this can be done if the crack is propagating in small-scale bridging conditions; in other specimens where the load is applied directly onto the crack surfaces, behavior of rate-dependent materials can also be reconstructed for general large-scale bridging conditions using solutions for rate-independent materials.
The research contributes to a systematic method for simplified design of laminated engineering structures, which will impact the design and performance of all lightweight military vehicles and structures. Newly gained understanding points the way to significant improvements in impact and ballistic resistance via materials and structural design.
This work was done by Qingda Yang of Rockwell Scientific Co.; Brian Cox of Teledyne Scientific Co.; Roberta Massabò, Martin Andrews, and Andrea Cavicchi of the University of Genova; Weixing Josh Zhou of the University of Illinois at Urbana Champaign; Christian Lundsgaard-Larsen of the Technical University of Denmark; and Holly Barth of the University of California Berkeley for the Army Research Office. ARL-0109