纤维增强复合材料轴对称界面端的奇异应力场

提出了一种分析横观各向同性纤维增强复合材料轴对称界面端的奇异应力场的特征值法。基于横观各向同性弹性材料空间轴对称问题的基本方程和一阶近似假设,利用分离变量形式的位移函数和无网格算法,导出了关于应力奇异性指数和应力角函数的奇异性特征方程。对于纤维/基体轴对称界面端模型,特征值法给出的应力奇异性指数、相应的位移和应力角函数,与通过有限元分析得到的结果非常吻合。利用有限元计算得到的奇异应力场,结合特征值法给出的应力奇异性指数和应力角函数,通过线性外插得到了相应的应力强度系数。特征值法结合有限元分析,可以完全确定横观各向同性纤维增强复合材料轴对称界面端的奇异应力场。     

双材料界面端应力奇异性的数字光弹性分析

在双材料界面端奇异性应力场方程的基础上,采用数字相移光弹性方法分析了具有实数应力奇异性的界面端应力强度因子。实验选择铝合金/环氧树脂双材料形成135°和90°界面端切口进行四点弯曲测试,利用数字相移光弹性法得到界面端全场等色线级数作为原始数据。将应力光学定律和界面端奇异性应力场方程相结合,分别得到条纹级数距离界面端成线...     

压电与导体双材料界面端的奇异性研究

提出了一种求解平面应变条件下横观各向同性压电与导体双材料界面端的应力及电位移奇异性的特征值法。基于横观各向同性压电材料的基本方程和一阶近似假设,利用分离变量形式的位移函数和电势函数,导出了关于应力和电位移奇异性指数的奇异性特征方程。求解由无网格法离散的特征方程,即可得到应力和电位移的各阶奇异性指数,同时还可得到相应的应力和电位移角函数。数值计算结果与文献中给出的结果非常吻合,表明该方法具有很高的精度和效率。     

双材料界面端附近奇异应力场消除几何条件研究

基于 Bogy 特征值方程,分析了消除界面端奇异应力场的几何条件,给出了平面应力和平面应变条件下的接合角组合曲线。应用有限单元法对上述结果进行了验证,并对消除应力奇异性后的界面应力进行了分析与讨论;结果表明:采用刚好使奇异性消失的接合角会获得最均匀的界面应力分布。     

压电材料切口奇性指数计算

利用一种数值方法分析压电材料切口尖端包括奇异应力场和奇异电位移场在内的双重奇异性。基于切口尖端的位移场按幂级数渐近展开假设, 从应力平衡方程和Maxwell方程出发, 推导出关于压电材料切口奇性指数的特征方程组, 同时将切口的力学和电学边界条件转化为奇性指数和特征函数的组合表达, 从而将压电材料双重奇性分析问题转化为在相应边界条件下微分方程组的特征值求解问题, 采用插值矩阵法, 可以一次性地计算出压电材料切口的各阶奇性指数。裂纹作为切口的特例, 其尖端的电弹性奇性指数亦可以根据本法求出。     

压电材料切口奇性指数计算

利用一种数值方法分析压电材料切口尖端包括奇异应力场和奇异电位移场在内的双重奇异性.基于切口尖端的位移场按幂级数渐近展开假设,从应力平衡方程和Maxwell方程出发,推导出关于压电材料切口奇性指数的特征方程组,同时将切口的力学和电学边界条件转化为奇性指数和特征函数的组合表达,从而将压电材料双重奇性分析问题转化为在相应边界条件下微分方程组的特征值求解问题,采用插值矩阵法,可以一次性地计算出压电材料切口的各阶奇性指数.裂纹作为切口的特例,其尖端的电弹性奇性指数亦可以根据本法求出.     

无应力奇异性条件下的界面应力集中问题研究

应用有限元分析技术,对无应力奇异性条件下的双材料粘接接头的应力集中问题进行了数值研究。首先,根据特征方程分析求解出消除接头界面端和界面角奇异应力场的材料组合和几何条件;据此提出了几种无应力奇异性影响并且为宏观等截面的双材料粘接接头几何模型。然后在轴对称假设条件下,对上述模型理想粘接界面上的应力分布进行了分析,着重讨论了材料组合和界面几何形状对这些应力大小的影响。结果表明:由于材料性能错配,界面上的应力集中现象不可避免,其大小依赖于材料组合和界面几何形状。这些分析结果对于指导界面几何形状优化设计,最终提高界面强度具有一定的参考价值。     

各向异性复合材料尖劈的应力奇异性次数研究

为了确定各向异性复合材料尖劈的应力奇异性次数,提出了一种确定广义平面应变情况下各向异性弹性接合材料界面端应力奇异性次数的一维特殊有限元法。该方法基于最小势能原理,通过坐标变换和变量分离消除径向坐标,把应力奇异性次数的求解降阶为仅与环向坐标相关的一维问题。采用三节点一维等参数二次单元,对该一维线性领域做网格划分。数值计算结果与理论解比较,表明该方法具有很高的精度和效率。     

残余应力对固体氧化物燃料电池弹塑性性能的影响

半电池结构NiO-YSZ/YSZ由于弹性模量不同和热膨胀系数不匹配,导致烧结过程中产生残余应力. 残余应力对于燃料电池的性能和使用带来一定的影响, 本文把残余应力引入到计算薄膜性能的逆向分析模型中, 建立了考虑残余应力影响的薄膜的纳米压痕分析模型. 利用纳米压痕方法测试了离双层材料界面不同距离处的载荷-位移曲线和相应的材料性能, 用本文建立的模型计算了不同点的性能的变化, 发现离界面越远, 电解质YSZ薄膜的硬度越大. 将热力分析得到的残余应力场作为压痕模拟的初始应力场, 计算三棱锥压头下压痕载荷-位移曲线, 结果显示考虑残余应力时的载荷-位移曲线更接近实验曲线, 并给出了残余应力下压痕形貌图, 发现有残余应力时的压痕形貌更深更大.     

基于钉杆变形均匀性的锥形半圆头铆钉优化设计研究

目的 针对铆接过程中铆钉钉杆发生镦粗变形,其变形的均匀性影响连接接头力学性能的问题,提出一种钉杆带有锥度的变径铆钉,以改善钉杆变形的均匀性.方法 基于三维有限元仿真方法,对准静态铆接过程进行仿真,获取锥形与常规半圆头铆钉在铆接后钉杆变形情况,同时对比分析板材残余应力变化情况.最后建立由钉杆变形均匀度与铆钉尺寸以及镦头高...     

Stress singularities in bimaterial bodies of revolution

An eigenfunction expansion solution is first developed for determining the stress singularities of bimaterial bodies of revolution by directly solving the equilibrium equations of three-dimensional elasticity in terms of displacement functions. The characteristic equations are explicitly given for determining the stress singularities in the vicinity of the interface corner of two intersecting bodies of revolution having a sharp corner with free boundary conditions along the corner. The characteristic equations are found to be equivalent to a combination of the characteristic equations for plane elasticity problems and St. Venant torsion problems. The strength of stress singularities varying with the interface angles is also investigated. The first known asymptotic solutions for the displacement and stress fields are also explicitly shown for some interface angles. The present results will be useful not only for understanding the singularity behaviors of stresses in the vicinity of a revolution interface corner, but also for developing accurate numerical solutions with fast convergence for stress or vibration analysis of a body of revolution having an interface corner.     

Singularities of an inclined crack terminating at the bi-material interface in a Reissner plate

On the basis of Reissner’s plate theory, the stress singularities at the tip of an arbitrarily inclined semiinfinite crack terminating at the interface of two dissimilar materials are investigated in the present paper. Using the eigenfunction expansion method, the eigenequation of the corresponding problem is derived explicitly by directly solving the governing equations of Reissner’s plate theory in terms of three generalized displacement components. In this paper, the focus is on the calculation of the singularity order as a fundamental quantity in fracture mechanics. The singularity orders of the moments and shear force at the crack tip are determined by the dominant eigenvalues whose real parts lie between 0 and 1. The influences of the bi-material parameters and the crack inclination angle on the moment and shear force singularity orders are discussed in detail. Specifically, the variations of the shear force singularity order with the bi-material parameter and the crack inclination angle are examined in detail. It is proved that the shear force singularity order is a completely monotonic function of the bi-material parameter and the inclination angle. Some numerical results are given in order to prove the validity of the present study.     

Evaluation of multiple stress singularity orders of a V-notch by the boundary element method

A new technique concerning the evaluation of multiple stress singularity orders of a V-notch with the boundary element method is proposed. For linear elastic material, the asymptotic displacement field in a V-notch tip region is expressed as a series expansion with respect to the radial coordinate from the V-notch tip. The series expansion of the asymptotic field is then substituted into the boundary integral equation established on the V-notch. By boundary element discretization, the boundary integral equation is transformed into an eigen-equation with respect to the stress singularity orders. Hence the eigen-values, which are the singularity orders, can be obtained simultaneously by solving the eigen-equation. An evident feature of the present method is that the real and complex singularity orders together with the non-singularity ones can be obtained at the same time.     

Singularity analysis near the vertex of the V‐notch in Reissner's plate by coupling the asymptotic expansion technique with the interpolating matrix method

A new numerical method for calculating the singularity orders of V‐notches in Reissner's plate is proposed in this paper. By introducing the asymptotic expansion of the generalised displacement field at the notch tip into the equilibrium equations of a plate, a set of characteristic ordinary differential equations with respect to the singularity order are established. In addition, by adopting the variable substitution technique, the obtained non‐linear characteristic equations are transformed into linear ones, which are solved by the interpolating matrix method. The singularity orders of moments and shear forces can be obtained simultaneously and can be distinguished from the corresponding characteristic angular functions conveniently. Four types of boundary conditions are proposed to investigate the influence of boundary conditions on the singularity order values. The effect of the Poisson's ratio on the singularity orders of the V‐notch in Reissner's plate is discussed. The present method is versatile for the singularity analysis of single material V‐notches and bi‐material V‐notches, and can be easily extended to multi‐material V‐notches.     

Three-dimensional asymptotic stress fields at the front of a trimaterial junction

A recently developed eigenfunction expansion method is employed for obtaining three-dimensional asymptotic displacement and stress fields in the vicinity of the junction corner front of an infinite pie-shaped trimaterial wedge, of finite thickness, formed as a result of bimaterial (matrix plus reaction product or contaminant) deposit over a substrate or reinforcement. The wedge is subjected to extension/bending (mode I), inplane shear/twisting (mode II) and antiplane shear (mode III) far field loading. Each material is isotropic and elastic, but with different material properties. The material 2 (substrate) is always taken to be a half-space, while the wedge aperture angle of the material 1 is varied to represent varying composition of the bimaterial deposit. Numerical results pertaining to the variation of the mode I, II, III eigenvalues (or stress singularities) with various moduli ratios as well as the wedge aperture angle of the material 1 (reaction product/contaminant), are also presented. Hitherto unavailable results, pertaining to the through-thickness variations of stress intensity factors for symmetric exponentially decaying distributed load and its skew-symmetric counterpart that also satisfy the boundary conditions on the top and bottom surfaces of the trimaterial plates under investigation, bridge a longstanding gap in the stress singularity/interfacial fracture mechanics literature.     

碳纤维增强环氧树脂复合材料层合板结构及间隙尺寸对铆接性能的影响

通过对不同纺织结构的碳纤维增强树脂基复合材料（CFRP）层合板与铝合金（AlMg3）异质材料连接结构进行单剪切拉伸研究,分析间隙尺寸对不同纺织结构CFRP层合板与AlMg3连接结构性能的影响。试验结果表明,当CFRP层合板铺层数目相同时,对于纺织结构不同、间隙配合尺寸相同的CFRP-AlMg3单铆钉单剪切连接结构,编织结构碳纤维增强树脂基复合材料（WO-CFRP）层合板所受挤压应力比非编织结构碳纤维增强复合材料（UD-CFRP）层合板所受挤压应力大25%左右;对于纺织结构相同、间隙配合尺寸不同的CFRP-AlMg3单铆钉单剪切连接结构,其各自铆钉所受剪切应力和连接CFRP层合板所受挤压应力相差不大。同时对相同间隙尺寸、不同纺织结构的CFRP-AlMg3单铆钉单剪切连接结构各个阶段挤压应力分析得知：其他条件一定,各个阶段中WO-CFRP的挤压应力比UD-CFRP的挤压应力高20%左右。最后研究间隙尺寸对CFRP-AlMg3单铆钉单剪切连接结构性能的影响,发现铆钉与孔壁间隙尺寸对位移为铆钉直径大小的4%时的CFRP层合板受到的挤压应力影响较大,铆钉与孔壁间隙大小增加0.1 mm,位移为铆钉直径大小的4%时的CFRP层合板受到的挤压应力降低约17%,而对CFRP层合板的初始损伤应力和破坏应力几乎没有影响,对铆钉所受剪切作用力和AlMg3板材所受挤压应力也几乎没有影响。     

On the stress singularity of dissimilar anisotropic wedges and junctions in antiplane shear

In this paper, r^λ−1 type antiplane stress singularities in dissimilar anisotropic wedges and junctions are studied. For some special wedge angles, the eigenequations derived are a function of fiber orientations and the elastic constants in the principal material coordinates. The boundary surfaces of the wedges can be subjected to combinations of free and clamped boundary conditions. The repeated occurrence of stress singularity orders is examined. By properly selecting the fiber orientations, the degree of the stress singularities can be diminished or even disappeared. The singularities of the materials reduced to isotropic are discussed as well.