含硬币型裂纹电磁弹性柱断裂特性研究

发布时间：2018-03-10 22:38

  本文选题：电磁弹性柱　切入点：硬币型裂纹　出处：《哈尔滨工业大学》2017年博士论文　论文类型：学位论文

【摘要】：电磁弹性材料作为一种新型智能材料,因其独特的磁电耦合效应,在智能驱动器、换能器、传感器、致动器等的制作领域具有广泛的应用前景。由于该类材料在制造和使用过程中常含有裂纹,故关于该类材料断裂问题的研究已经成为许多力学工作者的热点研究方向。目前,虽然电磁弹性材料断裂力学问题已经取得了许多研究成果,但这些工作主要关注的是反平面和平面断裂问题,对于更接近真实情况的三维断裂问题,随着材料参数和控制方程个数的增多,加大了数学求解上的困难,故研究成果相对较少。本文将考虑三维断裂问题中的一种特殊情况—硬币型裂纹问题,对含有硬币型裂纹的电磁弹性柱的断裂问题进行研究,揭示其断裂规律,为设计和制造具有柱体形状的电磁元器件提供理论参考。首先,研究了含电磁穿透硬币型裂纹的径向尺寸有限的电磁弹性柱在力-电-磁载荷作用下的断裂问题。考虑两种电磁弹性柱侧面边界条件,利用势函数理论和Hankel积分变换技术,将混合边值问题化为求解一对对偶积分方程,并进一步转化为求解第二类Fredholm积分方程。利用高斯积分进行数值计算,获得了裂纹尖端各种场强度因子的表达式。数值分析结果表明:结构几何尺寸、侧面边界条件对断裂特性有显著影响;考虑电磁穿透模型,电磁载荷是促进还是抑制裂纹扩展取决于远场施加的机械载荷为应力或应变。其次,研究了含电磁半穿透硬币型裂纹的电磁弹性柱在力-电-磁载荷作用下的断裂问题。通过引入三个辅助函数,最终将所研究的混合边值问题转化为求解三个耦合的非线性Fredholm积分方程组,获得了各种场强度因子的表达式,给出了结构几何尺寸、电磁载荷、裂纹内介质的电容率和磁导率对裂纹张开位移强度因子的影响规律。数值分析结果表明:裂纹面电磁边界条件对裂纹扩展有重要影响;电磁弹性材料的断裂韧性与施加的电磁场的方向有关;电磁穿透和电磁不穿透模型可看作是本问题的两种特殊情况。再次,研究了含硬币型裂纹的电磁弹性柱在热冲击载荷作用下的瞬态断裂问题。采用电磁半穿透裂纹面边界条件,假设电磁弹性柱的外表面为自由表面,首先给出无裂纹的电磁弹性柱在瞬时热冲击载荷作用下的温度场,进而根据叠加原理,将温度场在裂纹面处产生的热应力、电位移和磁感应强度反向加在含硬币型裂纹的电磁弹性柱的裂纹面上,从而形成了力-电-磁耦合的混合边值问题。经过复杂的数学推导,最终给出了各种场强度因子的表达式,并讨论了热冲击时间、结构几何尺寸、裂纹面电磁边界条件对应力强度因子的影响规律。数值分析结果表明:给定电磁弹性柱尺寸,裂纹半径越大裂纹越容易扩展;在裂纹最不稳定的时刻,考虑相同的裂纹半径与电磁弹性柱半径的比值,电磁穿透型裂纹最容易扩展;最后,研究了含Dugdale塑性区硬币型裂纹的电磁弹性柱在力-电-磁载荷作用下的断裂问题。采用电磁穿透的裂纹面边界条件,问题最终转化为求解一个分段的第二类Fredholm积分方程,借助于逐次逼近的数值计算方法,获得了影响塑性区宽度的因素,同时给出了力-电-磁载荷、裂纹尺寸等对裂纹张开位移的影响。数值分析结果表明:远场施加的力-电-磁载荷、结构几何尺寸对塑性区宽度有明显影响;远场施加相同的机械载荷,负的电磁载荷更易引起裂纹的扩展。
[Abstract]:The electromagnetic elastic material as a new type of smart materials because of its unique magnetoelectric coupling effect in intelligent driver, transducer, sensor, actuator field has broad application prospects and other production. Because of this kind of materials often contain cracks in the manufacture and use of the process, so the research on the material fracture problem has become a hot research topic the direction of many mechanical workers. At present, although the fracture mechanics problems in magnetoelectroelastic materials has made great achievements, but the work is mainly about the plane and anti plane fracture problems for 3D fracture problems, closer to the real situation, with the increase of the number of material parameters and control equations, increasing the difficulty in solving mathematics therefore, little research results. This paper will consider a penny shaped crack in a special case, 3D fracture problems, with a penny shaped crack Research on the fracture problem of electromagnetic elastic column, reveal the fracture rules and provide a theoretical reference for the design and manufacture of electromagnetic components have a column shape. First, studied with the electromagnetic penetration of a penny shaped crack in the radial dimension of the electromagnetic force in finite elastic cylinder electro magnetic load fracture problem under consideration two. Electromagnetic elastic column lateral boundary conditions, using the theory of potential function and Hankel integral transform technique, the mixed boundary value problem is solved on the dual integral equations, and further transformed into solving Fredholm integral equations of the second kind. The integral calculated by Gauss formula, a variety of crack tip field intensity factor was obtained. The numerical analysis the results show that the geometry of the structure, the side boundary conditions have significant influence on the fracture characteristics; consider the electromagnetic penetration model, electromagnetic load to facilitate or inhibit crack propagation depends on the far The mechanical load applied to the field of stress or strain. Secondly, study the electromagnetic elastic column containing electromagnetic semi penetrating penny shaped crack in force - electric - magnetic fracture loads. By introducing three auxiliary functions, will eventually be mixed on the boundary value problem into nonlinear Fredholm integral equations of the three groups a coupling, received a variety of field intensity factor expressions, the geometry of the structure, gives the electromagnetic load, influence of crack medium permittivity and magnetic permeability of the crack opening displacement intensity factor. The numerical results show that the crack surface electromagnetic boundary conditions have an important influence on the crack propagation; the fracture toughness of magnetoelectroelastic materials with the direction of the applied electromagnetic field; electromagnetic penetration and penetration of electromagnetic model can be regarded as two special cases of the problem. Thirdly, study with a penny shaped crack in electromagnetic elastic column 鐑�鍐插嚮杞借嵎浣滅敤涓嬬殑鐬�鎬佹柇瑁傞棶棰，

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