Wang Hua, Li Xianfang, Tang Guojin, Shen Zhibin
College of Aerospace Science and Engineering, National University of Defense Technology Changsha 410073, China.
J Nanosci Nanotechnol. 2013 Jan;13(1):477-82. doi: 10.1166/jnn.2013.6737.
This paper studies the influence of surface elasticity on crack growth for a nanoscale crack advance. A crack is modeled as a double cantilever beam with consideration of surface stress. Using the Euler-Bernoulli beam theory incorporating with surface effects, a governing equation of static bending is derived and bending solution of a cantilever nanowire is obtained for a concentrated force at the free end. Based on the viewpoint of energy balance, the elastic strain energy is given and energy release rate is determined. The influences of the Surface stress and the surface elasticity on crack growth are discussed. Obtained results indicate that consideration of the surface effects decreases stress intensity factors or energy release rates. The residual surface tension impedes propagation of a nanoscale crack and apparent fracture toughness of nanoscale materials is effectively enhanced.
本文研究了表面弹性对纳米级裂纹扩展的影响。将裂纹建模为考虑表面应力的双悬臂梁。利用考虑表面效应的欧拉 - 伯努利梁理论，推导了静弯曲控制方程，并得到了自由端受集中力作用的悬臂纳米线的弯曲解。基于能量平衡观点，给出了弹性应变能并确定了能量释放率。讨论了表面应力和表面弹性对裂纹扩展的影响。所得结果表明，考虑表面效应会降低应力强度因子或能量释放率。残余表面张力阻碍纳米级裂纹的扩展，并有效提高了纳米级材料的表观断裂韧性。
