Dynamic fracture by focusing flexural waves: Modeling and experimental implementation

Abstract

For the design of crashworthy structures, it is essential to understand the failure mechanisms of materials and structural elements at high strain rates. This has led to the development of tests where materials are loaded at high rates to produce dynamic fracture. Not only is the fracture process itself of interest, but also the elastic waves that are generated during fracture. These so-called acoustic emissions propagate through the structure and can be detected at another, easily accessible location. From the acoustic-emission measurements, information is gathered about the presence, location, and development of cracks in the structure, which is helpful for the assessment of the structural integrity. In this thesis, we present a method for the generation of precisely controlled dynamic fracture by focusing flexural waves. We investigate the dynamic fracture process, and model the resulting acoustic emissions. In our dynamic fracture experiments, flexural waves are generated at one end of a glass tube and focused at an arbitrarily chosen location along the tube. At the focal point, a strong bending-moment pulse is generated that is more than 20 times larger in amplitude than the initially generated flexural waves. Moreover, the bending-moment pulse is larger than the bending strength of the glass tube and thus induces dynamic fracture. Both the location and the shape of the bending-moment pulse are tuned precisely with the wave-focusing process. Therefore, the dynamic fracture process is highly controlled and repeatable acoustic emissions are generated. Our wave-focusing method relies on the time-reversal symmetry and the dispersion of flexural waves, as well as the superposition of multiple reflections. We simulate the dispersion of the focused bending-moment pulse in a spectral-element simulation, where the glass tube is modeled with Timoshenko beam theory. We compute the loading produced by the dispersed bending-moment pulse at the ends of the beam. From the simulated bending moment at the end of the beam, we obtain the excitation signals by reversing the direction of time. Thus, slow frequencies are excited first and fast frequencies are excited at the end of the signal. We compute the excitation signals for multiple wavelets that focus at the focal point after having undergone up to 30 reflections. Thereby, the active time of the transducer is increased and more energy is pumped into the beam. The excitations signals of the individual wavelets are superimposed optimally with a linear-programming algorithm so that the bending moment at the focal point is maximized. We study the dynamic fracture process with a high-speed-video recording and distinguish two phases. In the first phase, the crack traverses 85% of the cross section at relatively high speed. In the second phase, the crack slows down considerably and traverses the remainder of the cross section. In contrast to fracture tests under quasi-static bending, no arrest of the fracture process is observed. We attribute this difference in crack dynamics to our more dynamic and load-controlled configuration. Lastly, we investigate the acoustic-emission generation during the dynamic fracture process under bending. We simulate the interaction of the propagating flexural waves with a gradually growing crack in the glass tube. The scattering of the incident flexural waves at the tractionfree crack surface is computed analytically and the propagation of the resulting flexural and longitudinal waves is simulated with spectral elements. We observe mode conversion of flexural waves to longitudinal waves during the fracture process with very good agreement between our measurements and simulations.