脆性梁弯曲断裂所激发的弯曲波  

Bending waves excited by bending fractures of brittle beams

作　　者：王志强 杨洪升 周风华[1] WANG Zhiqiang;YANG Hongsheng;ZHOU Fenghua(Key Laboratory of Impact and Safety Engineering,Ministry of Education,Ningbo University,Ningbo 315211,Zhejiang,China)

机构地区：[1]宁波大学冲击与安全工程教育部重点实验室,浙江宁波315211

出　　处：《爆炸与冲击》2024年第9期75-88,共14页Explosion and Shock Waves

基　　金：国家自然科学基金(12302474)。

摘　　要：脆性细长结构在弯曲载荷作用下突然断裂,可能导致断裂点附近出现二次断裂。传统的Euler-Bernoulli梁理论难以描述突加载荷或突卸载荷所导致的波动现象,而Timoshenko梁中的弯曲波速度为有限值,具有一个内禀特征时间,因此基于Timoshenko梁理论来分析弹性梁的弯曲断裂问题。使用Timoshenko梁理论,结合一个包含断裂能的脆性内聚力弯曲断裂模型,建立一维弯曲波传播问题的初边值问题,采用特征线方法求解3种边界条件下半无限长梁中卸载弯曲波的传播问题;进一步分析了断裂能对断裂时间以及峰值弯矩的影响,然后通过数值计算给出这3种情况下梁的动力学响应过程。研究结果表明:处于纯弯曲状态的梁一旦发生瞬时断裂,二次断裂发生点距离初次断裂点的最短距离为梁截面回转半径的5倍,因为该距离以内的弯矩不会出现过冲;最有可能发生二次断裂的位置与无量纲断裂能和无量纲开裂角度有关,在距离初始断裂点17.7个特征长度的位置会产生幅值达到1.67倍初始弯矩的峰值弯矩;较大的断裂能将延长断裂时间,导致弯矩峰值点位置偏远,相应的峰值载荷也降低。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.Larg

关 键 词：TIMOSHENKO梁 内聚力弯曲断裂 卸载弯曲波 峰值弯矩 二次断裂 断裂韧性 

分 类 号：O347[理学—固体力学]