WANG Zhiqiang, YANG Hongsheng, ZHOU Fenghua. Bending waves excited by bending fractures of brittle beams[J]. Explosion And Shock Waves, 2024, 44(9): 091424. doi: 10.11883/bzycj-2024-0046
Citation:
WANG Zhiqiang, YANG Hongsheng, ZHOU Fenghua. Bending waves excited by bending fractures of brittle beams[J]. Explosion And Shock Waves, 2024, 44(9): 091424. doi: 10.11883/bzycj-2024-0046
WANG Zhiqiang, YANG Hongsheng, ZHOU Fenghua. Bending waves excited by bending fractures of brittle beams[J]. Explosion And Shock Waves, 2024, 44(9): 091424. doi: 10.11883/bzycj-2024-0046
Citation:
WANG Zhiqiang, YANG Hongsheng, ZHOU Fenghua. Bending waves excited by bending fractures of brittle beams[J]. Explosion And Shock Waves, 2024, 44(9): 091424. doi: 10.11883/bzycj-2024-0046
Under pure bending, a brittle slender beam may undergo sudden fracture, leading to the occurrence of secondary fractures near the initial fracture point. Studies suggest that the secondary fractures are induced by the unloading bending wave released from the initial fracture. Unloading causes an overshoot of the bending moment near the location of the initial fracture. Traditional Euler-Bernoulli beam theory cannot describe the wave propagation phenomena resulting from sudden loading or unloading. In this paper, the bending fracture problem is analyzed based on Timoshenko beam theory. In this theory, the bending wave velocity is finite, and it possesses an intrinsic characteristic time. Utilizing Timoshenko beam theory and incorporating a brittle cohesive bending fracture model containing fracture energy, an initial-boundary value problem is established for the one-dimensional propagation of bending waves. The problem with three boundary conditions is solved using the characteristic line method: (1) the beam is suddenly applied with a boundary transverse velocity; (2) the beam is suddenly applied with a boundary bending moment; (3) the beam initially bears a constant moment, which is released according to a cohesive bending fracture law. Through numerical calculations, the dynamic responses of the beam under these three conditions are presented. Initially, the problems (1) and (2) are calculated using the characteristic line method, validating the feasibility of this approach. Subsequently, by calculating problem (3), the impact of fracture energy on fracture time and peak moment is analyzed. The study reveals that once a beam in a pure bending state undergoes instantaneous fracture, the shortest distance between the point of secondary fracture and the point of primary fracture is 5 times characteristic length. When the non-dimensional fracture energy is 1.4×10−4, the location at 17.7 characteristic lengths from the initial fracture point exhibits a peak moment with an amplitude of 1.67, making it the most likely position for secondary fracture. Larger fracture energy prolongs the fracture time, resulting in a more distant peak moment position and a corresponding reduction in peak load.
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