项目来源

湖南省自然科学基金

项目主持人

李显方

项目受资助机构

中南大学

项目编号

2020JJ4106

立项年度

2020

立项时间

未公开

项目级别

省级

研究期限

未知 / 未知

受资助金额

未知

学科

一般工业技术

学科代码

未公开

基金类别

面上项目

关键词

表面效应 ; 纳米裂纹 ; 币型裂纹 ; 应力强度因子 ; 薄板 ; Surface effect ; Nanoscaled crack ; Penny-shaped crack ; Stress intensity factor ; Thin plate

参与者

未公开

参与机构

未公开

项目标书摘要：随着纳米技术的发展，纳米材料和结构的力学性能吸引了广泛的研究。大量实验和仿真表明当结构或材料的尺寸达到纳米甚至微米量级时，其有效力学性能与大尺度宏观材料和结构的力学性能存在较大的差别。考虑到微纳尺度下材料的比表面积增加，材料的表面能和表面弹性影响材料和结构的宏观力学性能。鉴于此，该研究考虑表面效应的三维微纳米材料断裂研究。主要研究1纳米硬币形裂纹表面效应对弹性材料裂纹前沿的奇异性影响,2复合纳米材料界面能和硬币形裂纹表面能对裂纹扩展的影响,3纳米材料三维断裂的数值仿真研究。研究方法以理论分析为主，首先建立相应力学模型，导出偏微分方程组及控制方程，给出具体问题相应的初边值问题，采用严谨的数学求解方法包括Fourier积分变换、Hankel积分变换、Laplace积分变换等将力学模型的初边值问题化为一个相应积分方程，然后，基于积分方程的求解方法给出解析或数值解答，从而解释纳米币形裂纹在拉伸、剪切等外加荷载下的失效机理。结果发现表面弹性影响应力强度因子及其对裂纹前缘周围存在塑性区尺寸，扭转变形下的Dugdale塑性区边界因表面弹性的考虑而增强；基尔霍夫纳米薄板在刚性线夹杂有一个刚体转动情况下尖端附近弯矩和应力分量呈现−3∕2的奇异性，而有效剪切力具有−5∕2奇异性，而贯穿裂纹尖端附近弯矩和应力分量具有传统的平方根奇异性，而有效剪力却具有−3∕2奇异性。成果对微纳米尺度下结构的可靠性、完整性和安全设计有重要的指导意义。

Application Abstract: With the development of nanotechnology,the mechanical properties of nanomaterials and structures have attracted extensive research.A large number of experiments and simulations show that when the size of structures or materials reaches nanometer or micron,its effective mechanical properties are quite different from those of large-scale macroscopic materials and structures.Considering the increase of specific surface area of materials at micro and nano scales,the surface energy and surface elasticity of materials affect the macroscopic mechanical properties of materials and structures.In view of this,the project considers the surface effects of 3D micro-nanomaterials fracture.The main research contains 1the surface effect of nanoscaled penny-shaped crack on the singularity of the crack front,2the influence of composite nanomaterial interfacial energy and penny-shaped crack surface energy on crack propagation,3the numerical simulation of three-dimensional fracture of nanomaterial.The method is mainly theoretical analysis.Firstly,the mechanical model is established,the system of partial differential equations and governing equations are derived,and the corresponding initial-boundary value problem of associated problems is given.Rigorous mathematical solutions including Fourier transform,Hankel transform and Laplace transform,are adopted to transform the initial-boundary value problem of the mechanical model into a corresponding integral equation.Then,analytical or numerical solutions are given based on the solution method of the integral equation.The failure mechanism of nanoscaled cracks under tensile and shear loads is explained.The results show that the surface elasticity affects the SIF and the size of the plastic zone around the crack front.The boundary of the Dugdale plastic zone under torsional deformation is enhanced by the consideration of the surface elasticity.The bending moment and stress component near the tips of a rigid line in a Kirchhoff nanoplate show the singularity of − 3/2,while the effective shear force has the singularity of − 5/2,while the bending moment and stress component near the crack tips have the traditional square-root singularity,but the effective shear force has the singularity of − 3/2.The results have important guiding significance for the reliability,integrity and safety design of structures at micro and nano scales.

项目受资助省

湖南省