This study computationally and experimentally examines the mechanisms of crack penetration, deflection and the transition between penetration and deflection. The finite element analysis based computational modeling work used strength-and-energy based cohesive-zone approach to study the effect of dimensionless parameters (e.g., interfacial incident angle, fracture-length scale, and normalized toughness) on penetration/deflection behavior for mode-I loading (tensile load normal to crack plane). The first modeling work examines the effect of incident angle between crack plane and interface for a crack incident on an interface. As expected, results exhibit that small incident angles cause deflection whereas penetration is more likely at large incident angles. The transition between penetration and deflection becomes more strength-ratio dependent as incident angle decreases. It appears that, facture-length scale is an influential parameter in crack deflection criterion and chances of deflection reduces as fracture-length-scale decreases. Finally, the analysis looked at the effect of normalized-toughness and found that the normalized-toughness has a small effect on deflection criteria.
The second modeling work investigated the transition mechanism between deflection and penetration. The situation when both mode-I and mode-II works simultaneously is called mixed-mode, which is presented by the parameter phase angle. Phase angle 0° represents pure mode-I, 90° represents pure mode-II (shear load parallel to crack plane), and any phase angle in-between 0° and 90° represents mixed-mode. Results have shown the presence of smaller phase angle in the crack-tip at transition than deflection, while the applied load is elevated at transition due to providing the required energy for both the penetration and deflection. The difference of phase angles between transition and deflection becomes low as fracture-length-scale decreases. The results of cohesive-zone model meet Linear Elastic Fracture Mechanics (LEFM) results for the case of small fracture-length scales. This work analyzed interfacial phase angle during transition, between penetration and deflection, not only for homogeneous materials system but also for modulus mismatch. It was found that stiffer first-phase materials tend to create higher phase angle at the crack tip interfaces; the cases for low modulus mismatches are more sensitive than high modulus mismatches.
A systematic experimental study was performed to compare results with the cohesive-zone method, LEFM, and strength-based method results. A brittle polymer Polymethyl methacrylate (PMMA) was used as substrate material, and two different kind of solvent adhesives Weld-On 4 and Weld-On 16 were used as interfaces that have similar elastic modulus as PMMA. The interfaces created by Weld-On 4 are weaker while Weld-On 16 creates stronger interfaces; however, they have similar toughness. Crack incident angle varied from 75° to 90° with 5° increment. Critical incident angle at transition between penetration and deflection was investigated for each type of interfaces. The results showed that cohesive-zone method can predict crack deflection better than energy-based LEFM; material-to-interface toughness-ratio and strength-ratio both have influence on the transition event.