Modeling and simulation of intersonic crack growth.

*(English)*Zbl 1045.74588Summary: Intersonic crack growth has been studied using an interfacial fracture model in which an additional material phase within a bonding layer is proposed to describe the failure behavior of the interface. In this material phase, a strain gradient based damage model is applied with a built-in cohesive law, which is governed by an material intrinsic length scale that bridges the mechanisms that operate at continuum mechanics scale and at smaller scales. Simulations of the intersonic crack growth experiments [A. J. Rosakis et al., J. Mech. Phys. Solids 47, No. 9, 1983–1916 (1999; Zbl 0963.74050)] have been performed with varying material length scales and other parameters. The study is focused on two subjects: (1) the process of decohesion-induced cracking, explaining fracture process zone initiation and propagation as well as the corresponding contact mechanisms; (2) propagation speed, investigating the effects of length scales and loading parameters.

The simulations reveal that a fracture process zone initiates first and extends with a speed faster than shear wave speed. After initiation, the crack speed exhibits oscillations with an average value between \(c_s\sqrt 2\) and \(c_l\), where \(c_s\) and \(c_l\) refer to shear wave and dilatation wave speeds, respectively. In such a quasi-steady-state propagation, the crack opening profiles exhibit a time-invariant profile, while the fracture process zone size and decohesion energy remain constant. Contact between the crack faces is taken into account in the numerical simulations. A contact zone behind the crack tip has been captured which represents a self-healing-like mechanism. The leading edge of both the fracture process zone and the contact zone may cause strong shocks. When the average crack propagation speed approaches the supersonic region, two stress shocks radiate from the crack tip, corresponding to shear and dilatation wave radiation, respectively. The simulation results demonstrate that length and time scales play vital roles during crack propagation. Here the length scales refer to the bonding layer thickness and the material’s intrinsic length that governs energy dissipation during failure; whereas the time scales refer to the effects of material strain rate dependence, material failure speed, and wave propagation properties. A parameter \(R_s\), expressed as the ratio of material shear strength and the applied stress that is calculated from the remote imposed displacement boundary condition, is proposed to scale crack speed. Intersonic propagation occurs when \(R_s\) is greater than a threshold value. The numerical computations are compared with experiments [A. J. Rosakis et al. (1999)] and with the theoretical solution [Philos. Mag., A, in press], which demonstrates the trend that crack propagation is unstable in the open speed interval between \(c_s\) and \(\kappa_{\text v}c_s (\sqrt 2 \leqslant \kappa_{text v} < c_1/c_s\)) whereas it is stable when the speed lies in the close interval between \(\kappa_{\text v}c_s\) and \(c_l\). The coefficient \(\kappa_{\text v}\) is a function of material length scale, strain rate sensitivity, and boundary conditions. The moving particle finite element method, a newly developed meshfree method, and the pinball contact algorithm are applied in the numerical analysis.

The simulations reveal that a fracture process zone initiates first and extends with a speed faster than shear wave speed. After initiation, the crack speed exhibits oscillations with an average value between \(c_s\sqrt 2\) and \(c_l\), where \(c_s\) and \(c_l\) refer to shear wave and dilatation wave speeds, respectively. In such a quasi-steady-state propagation, the crack opening profiles exhibit a time-invariant profile, while the fracture process zone size and decohesion energy remain constant. Contact between the crack faces is taken into account in the numerical simulations. A contact zone behind the crack tip has been captured which represents a self-healing-like mechanism. The leading edge of both the fracture process zone and the contact zone may cause strong shocks. When the average crack propagation speed approaches the supersonic region, two stress shocks radiate from the crack tip, corresponding to shear and dilatation wave radiation, respectively. The simulation results demonstrate that length and time scales play vital roles during crack propagation. Here the length scales refer to the bonding layer thickness and the material’s intrinsic length that governs energy dissipation during failure; whereas the time scales refer to the effects of material strain rate dependence, material failure speed, and wave propagation properties. A parameter \(R_s\), expressed as the ratio of material shear strength and the applied stress that is calculated from the remote imposed displacement boundary condition, is proposed to scale crack speed. Intersonic propagation occurs when \(R_s\) is greater than a threshold value. The numerical computations are compared with experiments [A. J. Rosakis et al. (1999)] and with the theoretical solution [Philos. Mag., A, in press], which demonstrates the trend that crack propagation is unstable in the open speed interval between \(c_s\) and \(\kappa_{\text v}c_s (\sqrt 2 \leqslant \kappa_{text v} < c_1/c_s\)) whereas it is stable when the speed lies in the close interval between \(\kappa_{\text v}c_s\) and \(c_l\). The coefficient \(\kappa_{\text v}\) is a function of material length scale, strain rate sensitivity, and boundary conditions. The moving particle finite element method, a newly developed meshfree method, and the pinball contact algorithm are applied in the numerical analysis.

##### MSC:

74R15 | High-velocity fracture |

74S05 | Finite element methods applied to problems in solid mechanics |

74M20 | Impact in solid mechanics |