On acquiring data for large-scale crack bridging at high strain rates

Abstract

Numerical simulations are used to design test geometries and loading histories that are suitable for probing the large-scale bridging effects of through-thickness reinforcement that is shearing at high strain rates. The bridging effects are represented by a cohesive law and tests are sought that will determine any rate dependence in its parameters. The end-notched flexure test is studied, because it allows easy application of time-dependent loading and has proven to be an information-rich test in the quasi-static case. However, dynamic conditions greatly complicate fracture behavior, with possible regimes of hammering and multiple cracking, which should be avoided when maximum information is sought. Information content is addressed by focusing on regimes within the full computed solution space where crack growth is approximately steady state and the information content of experiments can be most easily assessed. Numerical results show that the hypothetical rate dependence in the cohesive law causes strong and measurable changes in the regime of steady-state behavior, if the tests are properly selected to vary the crack sliding speed. The estimates of information content are conservative, because the information available from all possible tests of specimens designed by analysis of the steady-state regime will necessarily exceed the information deduced by analyzing the steady-state regime alone.

Mode II dominant fracture of layered composite beams and wide-plates: a homogenized structural approach

“…uses the Finite Element Method and cohesive interface elements [1][2][3][4][5][6][7]. Damage within the layers may be accounted for using continuum damage approaches which modify the elastic constants of the layers when damage progresses.…”

“…There the concentrated load generates a compression region which typically arrests the cracks in quasi static laboratory experiments. Here the solution is presented also for aL  , which now defines a stable propagation approaching the limiting solution (dash-dot line) of two separated layers free to slide along each other (see also [7]).…”

Assessment and correction of theories for multilayered plates with imperfect interfaces

“…The interfacial traction laws in Eqs. (2) and (3) assume no coupling between in-plane and outof-plane interface tractions, namely K k 13 ¼ K k 23 ¼ 0 and K k 33 ¼ K k N , as it is normally assumed in the literature on cohesive cracks [1][2][3][4][5][6][7][8].…”

“…(3), using Eqs. (7) and (8). After lengthy algebraic manipulations, as suggested in [17], the resulting displacement jumps are defined in terms of the global displacement variables:…”

“…The response and final failure of these systems is controlled by progressive interfacial and intra-layer damage and is accurately studied using models based on a discrete-layer approximation of the system, as an assemblage of layers and cohesive interfaces, Fig. 1, and nonlinear fracture mechanics concepts [1][2][3][4][5][6][7][8]. The number of unknown displacement functions in these models depends on the numbers of layers used to discretize the systems and this strongly restricts the range of problems that can be treated semi-analytically and makes the computational solutions very expensive.…”