## 留言板

 引用本文: 杜景峰, 吴强杰. 平面应力状态断裂强度的椭圆准则分析[J]. 应用数学和力学, 2020, 41(3): 292-301.
DU Jingfeng, WU Qiangjie. Fracture Strength Analysis of the Plane-Stress State by the Ellipse Criterion[J]. Applied Mathematics and Mechanics, 2020, 41(3): 292-301. doi: 10.21656/1000-0887.400155
 Citation: DU Jingfeng, WU Qiangjie. Fracture Strength Analysis of the Plane-Stress State by the Ellipse Criterion[J]. Applied Mathematics and Mechanics, 2020, 41(3): 292-301.

• 中图分类号: O346

## Fracture Strength Analysis of the Plane-Stress State by the Ellipse Criterion

• 摘要: 简要分析了近年来提出的一个断裂准则——椭圆准则的基本特征，导出了它在主应力坐标系下的基本方程.根据所导出的基本方程，获得了平面应力条件下椭圆准则理论断裂强度曲线的完整描述关系，并分析讨论了破坏发生的方位及断裂形式与材料本征力学性质参数之间的联系.与既有理论结果及实验现象的对比解释了椭圆准则在材料相关参数确定方面的局限性.当应力状态相关材料特征参数在拉伸区和压缩区均作为常数时，获得了铸铁和混凝土平面应力状态下的断裂强度曲线.与相关实验数据的对比表明，它们在拉伸区能较好地吻合，但压缩区的差异十分显著，进一步证实了材料特征参数随应力状态变化规律对椭圆准则发展的必要性.
•  [1] ALTENBACH H, BOLCHOUN A, KOLUPAEV V A. Phenomenological Yield and Failure Criteria [M]. Berlin: Springer, 2014. [2] ANDRIANOPOULOS N P, MANOLOPOULOS V M. Can Coulomb criterion be generalized in case of ductile materials? An application to Bridgman experiments[J]. International Journal of Mechanical Sciences,2012,54(1): 241-248. [3] YU M H. Advances in strength theories for materials under complex stress state in the 20th century[J]. Applied Mechanics Reviews,2002,55(3): 169-218. [4] CHRISTENSEN R M. The Theory of Materials Failure [M]. Oxford: Oxford University Press, 2013. [5] ZHANG Z F, ECKERT J. Unified tensile fracture criterion[J]. Physical Review Letters,2005,94(9): 094301. [6] QU R T, ZHANG Z F. A universal fracture criterion for high-strength materials[J]. Scientific Reports,2013,3: 1117. [7] LIU Z Q, QU R T, ZHANG Z F. Elasticity dominates strength and failure in metallic glasses[J]. Journal of Applied Physics,2015,117(1): 014901. [8] QU R T, ZHANG Z J, ZHANG P, et al. Generalized energy failure criterion[J]. Scientific Reports,2016,6: 23359. [9] QU R T, ECKERT J, ZHANG Z F. Tensile fracture criterion of metallic glass[J]. Journal of Applied Physics,2011,109(8): 083544. [10] LIU Z Q, WANG W H, JING M Q, et al. Intrinsic factor controlling the deformation and ductile-to-brittle transition of metallic glasses[J]. Philosophical Magazine Letter s, 2014,94(10): 658-668. [11] YUAN Z, LI F, WANG R, et al. Influence of Poisson’s ratio and stress triaxiality on fracture behavior based on elastic strain energy density[J]. Theoretical and Applied Fracture Mechanics,2014,74: 96-108. [12] DING B, LI X. An eccentric ellipse failure criterion for amorphous materials[J]. Journal of Applied Mechanics,2017,84(8): 081005. [13] CAO J, LI F, MA X, et al. A modified elliptical fracture criterion to predict fracture forming limit diagrams for sheet metals[J]. Journal of Materials Processing Technology,2018,252: 116-127. [14] TIMOSHENKO S P, GOODIER J N. Theory of Elasticity [M]. 3rd ed. New York: McGraw-Hill, 1970. [15] GRIFFITH A A. The phenomena of rupture and flow in solids[J]. Philosophical Transactions of the Royal Society of London(Series A),1921,221: 163-198. [16] OROWAN E. Fracture and strength of solids[J]. Reports on Progress in Physics,1949,12(1): 183-187. [17] 江见鲸, 冯乃谦. 混凝土力学[M]. 北京: 中国铁道出版社, 1991.(JIANG Jianjing, FENG Naiqian. Concrete Mechanics [M]. Beijing: China Railway Publishing House, 1991.(in Chinese)) [18] CORNET I, GRASSI R C. A study of theories of fracture under combined stresses[J]. Journal of Basic Engineering,1961,83(1): 39-44. [19] MAIR W M. Fracture criteria for cast iron under biaxial stresses[J]. Journal of Strain Analysis,1968,3(4): 254-263. [20] 沈聚敏, 王传志, 江见鲸. 钢筋混凝土有限元与板壳极限分析[M]. 北京: 清华大学出版社, 1993.(SHEN Jumin, WANG Chuanzhi, JIANG Jianjing. Finite Element Analysis and Plate Shell Limit Analysis of Reinforced Concrete [M]. Beijing: Tsinghua University Press, 1993.(in Chinese))

##### 计量
• 文章访问数:  742
• HTML全文浏览量:  65
• PDF下载量:  260
• 被引次数: 0
##### 出版历程
• 收稿日期:  2019-05-05
• 修回日期:  2019-12-18
• 刊出日期:  2020-03-01

/

• 分享
• 用微信扫码二维码

分享至好友和朋友圈