若干先进电磁材料结构的断裂与稳定性等力学特性的理论研究
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摘要
力-电-磁多场耦合的电磁材料由于其特殊的性质具有广泛应用于工程领域的潜在背景,其断裂与稳定性等力学特性研究已成为电磁材料应用设计中关注的基础性课题。本学位论文主要针对超导材料、电场活化聚合物、压电压磁和功能梯度材料等当前关注的先进电磁材料,在考虑其力-电-磁耦合的基础上,从理论上研究了这些材料应用中所关注的断裂与稳定性等的力学特性。
首先,分析了超导材料中的应力、磁致伸缩和裂纹问题。根据弹性理论,讨论了超导体中磁通钉扎产生的应力和超导体中的非超导态夹杂问题,讨论了超导体内的应力分布和弹性模量以及体积分数对超导复合材料中磁致伸缩的影响。另外,基于简单的小裂纹模型,忽略了裂纹对屏蔽电流和磁场的扰动和影响。利用非理想第Ⅱ类超导体中的Bean和Kim临界态模型,并通过断裂力学中的求解方法,分别讨论了矩形和圆柱超导体中的裂纹问题。分析了场冷却和零场冷却两种超导体磁化过程中裂纹尖端应力强度因子的变化规律。在不同的磁场下降过程中,应力强度因子随磁场的变化是不同的。而Bean模型中应力强度因子的变化与Kim模型中也存在着区别。
其次,研究了电场活化聚合物中的稳定性和粘弹性问题。采用简单的Maxwell应力模型,讨论电场活化聚合物气球受到电场作用的膨胀过程中出现的稳定性问题。气球的失效模式与材料性质及电场的加载方式有关。基于摄动法,分析了小扰动情况下电场活化聚合物中的稳定性问题,得到了不同电场作用下的临界拉伸值。电场活化聚合物中力电耦合的参数不同时,材料稳定性的变化规律也是不同的。同时,基于张量分析和有限元的方法,讨论了电场作用下聚合物中的粘弹性行为,所得数值结果与理论解一致。结果中给出了恒定电场作用下的蠕变行为和周期电场作用下的变形规律。
最后,讨论了功能梯度材料和电磁弹性材料中的裂纹问题。通过Fourier变换的方法,得到了功能梯度材料中静态裂纹问题的奇异积分方程,并进行数值求解。分析了非均匀常数、几何参数和厚度比等对Ⅲ型裂纹应力强度因子的影响。对于电磁弹性材料中的动态裂纹问题,采用Laplace变换和反演计算,得到了不可渗透裂纹问题的奇异积分方程。结果给出了相对载荷参数κD和κB及裂纹构型对电磁弹性条中裂纹动态行为的影响。对于不可渗透裂纹,电场和磁场的冲击对动态应力强度因子和动态能量释放率有重要的影响。
Due to their unique properties and potential background of applications in engineering, the fracture behavior, instability and other mechanical properties of the electromagnetic materials have become the basic problems in applications and design. This thesis mainly aims at the advanced materials which arouse worldwide attentions recently, such as superconductor, dielectric elastomer, magnetoelectroelastic and functionally graded materials. Based on the Magneto-Electro-Elastic coupling properties, the fracture behavior, instability and other mechanical behavior in electromagnetic materials are investigated.
Firstly, the stress distribution, the magnetostriction and the crack problem in the superconductor are analyzed. Accroding to the elasticity theory, the stress induced by the flux pinning and the non-superconducting inclusions in the bulk superconductors are analyzed. The stress distribution in the superconductor and the effects of elastic moduli and volume fraction on the magnetostriction in the superconducting composite are discussed. In addition, based on a simple assumption in which the effect and disturbance of the crack on the shielding current and the magnetic field are neglected. The Bean and Kim model are adopted. Using the basic knowledge of the fracture mechanics, the crack problems in the rectangular and cylindrical superconductors are discussed, respectively. The variations of the stress intensity factors are considered in the magnetization process of zero-field cooling (ZFC) and field cooling (FC). When the magnetic field reduction process is different, the variations of the stress intensity factors are different, and there are differences between the results obtained from the Bean model and the Kim model.
Secondly, the instability and viscoelastic problems in the dielectric elastomer have been taken into account. During the process of inflation of the balloon which subject to the electric field, the Maxwell stress model is used to discuss the instability problem in the dielectric elastomer balloon. The results show that the failure-modes in the dielectric balloon are related to the material properties and the loading history. In addition, using the linear perturbation analysis, the instability problem is discussed in the dielectric elastomer, and the critical stretch values are obtained at different electrical field. It is found that the instability in the dielectric elastomer are dependent of the material parameter. Based on the tensor analysis and the finite element method, the viscoelastic behavior subject to the electric field is obtained in the dielectric elastomer. The numerical resuts agree well with the theoretical results. We further show the creep of the dielectric elastomer subject to a constant electrical field and the strain history of the dielectric elastomer subjected to a cyclic electrical load.
Finally, the crack problems in the functionally graded materials and the magnetoelectroelastic materials are discussed. Using the Fourier transform method, a singular integral equation for a static crack in the functionally graded materials is obtained, and the equation can be solved numerically. The results obtained show the effects of nonhomogeneity constant, relative crack length and thickness ratio on the stress intensity factor. For the transient crack problem in the magnetoelectroelastic materials, the Laplace transform and inversion are employed to reduce the problem to singular integral equations for the impermeable crack. Numerical results are shown graphically to illustrate the effects of relative loading parametersκD andκB, and the crack configuration on the dynamic behavior of the crack in the magnetoelectroelastic strip. The results indicate that the electric and magnetic impact play a great role in the transient fracture behavior.
首先,分析了超导材料中的应力、磁致伸缩和裂纹问题。根据弹性理论,讨论了超导体中磁通钉扎产生的应力和超导体中的非超导态夹杂问题,讨论了超导体内的应力分布和弹性模量以及体积分数对超导复合材料中磁致伸缩的影响。另外,基于简单的小裂纹模型,忽略了裂纹对屏蔽电流和磁场的扰动和影响。利用非理想第Ⅱ类超导体中的Bean和Kim临界态模型,并通过断裂力学中的求解方法,分别讨论了矩形和圆柱超导体中的裂纹问题。分析了场冷却和零场冷却两种超导体磁化过程中裂纹尖端应力强度因子的变化规律。在不同的磁场下降过程中,应力强度因子随磁场的变化是不同的。而Bean模型中应力强度因子的变化与Kim模型中也存在着区别。
其次,研究了电场活化聚合物中的稳定性和粘弹性问题。采用简单的Maxwell应力模型,讨论电场活化聚合物气球受到电场作用的膨胀过程中出现的稳定性问题。气球的失效模式与材料性质及电场的加载方式有关。基于摄动法,分析了小扰动情况下电场活化聚合物中的稳定性问题,得到了不同电场作用下的临界拉伸值。电场活化聚合物中力电耦合的参数不同时,材料稳定性的变化规律也是不同的。同时,基于张量分析和有限元的方法,讨论了电场作用下聚合物中的粘弹性行为,所得数值结果与理论解一致。结果中给出了恒定电场作用下的蠕变行为和周期电场作用下的变形规律。
最后,讨论了功能梯度材料和电磁弹性材料中的裂纹问题。通过Fourier变换的方法,得到了功能梯度材料中静态裂纹问题的奇异积分方程,并进行数值求解。分析了非均匀常数、几何参数和厚度比等对Ⅲ型裂纹应力强度因子的影响。对于电磁弹性材料中的动态裂纹问题,采用Laplace变换和反演计算,得到了不可渗透裂纹问题的奇异积分方程。结果给出了相对载荷参数κD和κB及裂纹构型对电磁弹性条中裂纹动态行为的影响。对于不可渗透裂纹,电场和磁场的冲击对动态应力强度因子和动态能量释放率有重要的影响。
Due to their unique properties and potential background of applications in engineering, the fracture behavior, instability and other mechanical properties of the electromagnetic materials have become the basic problems in applications and design. This thesis mainly aims at the advanced materials which arouse worldwide attentions recently, such as superconductor, dielectric elastomer, magnetoelectroelastic and functionally graded materials. Based on the Magneto-Electro-Elastic coupling properties, the fracture behavior, instability and other mechanical behavior in electromagnetic materials are investigated.
Firstly, the stress distribution, the magnetostriction and the crack problem in the superconductor are analyzed. Accroding to the elasticity theory, the stress induced by the flux pinning and the non-superconducting inclusions in the bulk superconductors are analyzed. The stress distribution in the superconductor and the effects of elastic moduli and volume fraction on the magnetostriction in the superconducting composite are discussed. In addition, based on a simple assumption in which the effect and disturbance of the crack on the shielding current and the magnetic field are neglected. The Bean and Kim model are adopted. Using the basic knowledge of the fracture mechanics, the crack problems in the rectangular and cylindrical superconductors are discussed, respectively. The variations of the stress intensity factors are considered in the magnetization process of zero-field cooling (ZFC) and field cooling (FC). When the magnetic field reduction process is different, the variations of the stress intensity factors are different, and there are differences between the results obtained from the Bean model and the Kim model.
Secondly, the instability and viscoelastic problems in the dielectric elastomer have been taken into account. During the process of inflation of the balloon which subject to the electric field, the Maxwell stress model is used to discuss the instability problem in the dielectric elastomer balloon. The results show that the failure-modes in the dielectric balloon are related to the material properties and the loading history. In addition, using the linear perturbation analysis, the instability problem is discussed in the dielectric elastomer, and the critical stretch values are obtained at different electrical field. It is found that the instability in the dielectric elastomer are dependent of the material parameter. Based on the tensor analysis and the finite element method, the viscoelastic behavior subject to the electric field is obtained in the dielectric elastomer. The numerical resuts agree well with the theoretical results. We further show the creep of the dielectric elastomer subject to a constant electrical field and the strain history of the dielectric elastomer subjected to a cyclic electrical load.
Finally, the crack problems in the functionally graded materials and the magnetoelectroelastic materials are discussed. Using the Fourier transform method, a singular integral equation for a static crack in the functionally graded materials is obtained, and the equation can be solved numerically. The results obtained show the effects of nonhomogeneity constant, relative crack length and thickness ratio on the stress intensity factor. For the transient crack problem in the magnetoelectroelastic materials, the Laplace transform and inversion are employed to reduce the problem to singular integral equations for the impermeable crack. Numerical results are shown graphically to illustrate the effects of relative loading parametersκD andκB, and the crack configuration on the dynamic behavior of the crack in the magnetoelectroelastic strip. The results indicate that the electric and magnetic impact play a great role in the transient fracture behavior.
引文
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