SHANG Xin-chun, ZHANG Rui, REN Hui-lan. Analysis for Cavitation Problem of Elastic Composite Ball Heated[J]. Applied Mathematics and Mechanics, 2011, 32(5): 556-562. doi: 10.3879/j.issn.1000-0887.2011.05.005
Citation: SHANG Xin-chun, ZHANG Rui, REN Hui-lan. Analysis for Cavitation Problem of Elastic Composite Ball Heated[J]. Applied Mathematics and Mechanics, 2011, 32(5): 556-562. doi: 10.3879/j.issn.1000-0887.2011.05.005

Analysis for Cavitation Problem of Elastic Composite Ball Heated

doi: 10.3879/j.issn.1000-0887.2011.05.005
  • Received Date: 2011-01-04
  • Rev Recd Date: 2011-03-04
  • Publish Date: 2011-05-15
  • The cavitation problem of composite ball, composed by two elastic solid materials and in uniformtemperature, was investigated. The nonlinear mathematical model of the problem was established by using finite logarithmic strain measure for geometric large deformation and by employing Hooke law for elastic solid. Analytic solutions in the form of parameter were derived for thermal dilatation of the composite ball with large elastic deformation. Solution curves were given to describe variations of the critical temperature in cavitation with the geometric and material parameters. Bifurcation curve was also given to reveal cavity growth after void nucleation. The numeric results for a computational example indicated that radius of cavity would rapidly enlarge over critical temperature, and the loop stress would become infinite with void nucleation. This means the materials near the cavity would produce plastic deformation which leads to local failure and fracture if the material of internal ball is elastoplastic. In addition, the cavitation for the composite ball could appear in a low temperature if elastic property for the material of internal ball is close to be uncompressible.
  • loading
  • [1]
    Tvergaard V. Material failure by void growth to coalescence[J].Advances in Applied Mechanics.1990, 27: 83-151.
    [2]
    McClinitock F A. A criterion for ductile fracture by growth of holes [J]. J Appl Mech, 1968, 35: 363-371. doi: 10.1115/1.3601204
    [3]
    Rice J R, Tracey D M. On the ductile enlargement of voids in triaxial stress fields[J]. J Mech Phys Solids, 1969, 17(3): 201-217. doi: 10.1016/0022-5096(69)90033-7
    [4]
    Ball J M. Discontinuous equilibrium solutions and cavitation in nonlinear elasticity[J]. Phil Trans R Soc London, A, 1982, 306(1496): 557-610. doi: 10.1098/rsta.1982.0095
    [5]
    Horgan C O, Abeyaratne R. A bifurcation problem for a compressible nonlinearly elastic medium: growth of a micro-void [J]. J Elasticity, 1986, 16(2): 189-200. doi: 10.1007/BF00043585
    [6]
    Horgan C O, Polignone D A. Cavitation in nonlinearly elastic solid: a review[J]. ASME Appl Mech Rev, 1995, 48(6): 471-485. doi: 10.1115/1.3005108
    [7]
    尚新春,程昌钧. 超弹性材料中的球形空穴分岔[J]. 力学学报, 1996, 28(6):751-755.(SHANG Xin-chun, CHENG Chang-jun. The spherical cavitation bifurcation in hyperelstic materials[J]. Acta Mech Sinica, 1996, 28(6):751-755.(in Chinese))
    [8]
    SHANG Xin-chun, CHENG Chang-jun. Exact solution for cavitated bifurcation for compressible hyperelastic material[J]. Int J Eng Sci , 2001, 39(10):1101-1117. doi: 10.1016/S0020-7225(00)00090-2
    [9]
    金明,黄克服,武际可.Hooke材料的微孔形空穴分岔[J]. 固体力学学报, 2001, 22(3): 281-286. (JIN Ming, HUANG Ke-fu, WU Ji-ke. A study of the catastrophe and the cavitation for a spherical cavity in Hooke’s material with 1/2 Poisson’s ratio [J]. Acta Mechnica Solida Sinica, 2001, 22(3):281-286. (in Chinese))
    [10]
    SHANG Xin-chun, CHENG Chang-jun. Cavitation in Hookean elastic membranes[J]. Acta Mech Solida, 2002, 15(1):126-129.
    [11]
    尚新春,程昌钧. 弹性固体材料中的空穴萌生于增长[J]. 北京科技大学学报, 2002, 24(3): 380-382. (SHANG Xin-chun, CHENG Chang-jun. Void nucleation and growth for elastic solid materials[J]. J University of Science and Technology Beijing, 2002, 24(3): 380-382. (in Chinese))
    [12]
    SHANG Xin-chun, CHENG Chang-jun, HU Yin-yan. Cavitated bifurcation in Hookean elastic and elastic-plastic materials[C]CHIEN Wei-zang.Proceeding of 4th International Conference on Nonlinear Mechanical. Shanghai: Shanghai University Press, 2002: 315-319.
    [13]
    宁建国, 李伟, 郝玖锋, 刘海燕, 黄筑平. 平面应变条件下孔洞化不稳定性问题的研究. 固体力学学报, 2003, 24(3): 259-263.(NING Jian-guo, LI Wei, HAO Jiu-feng, LIU Hai-yan, HUANG Zhu-ping. Influence of the temperature on the cavitation instability under plane strain condition[J]. Acta Mech Solida Sinica, 2003, 24(3): 259-263. (in Chinese))
    [14]
    任九生,程昌钧. 热超弹性材料中的空穴生成问题[J]. 固体力学学报,2004, 25(3):275-278.(REN Jiu-sheng, CHENG Chang-jun. Cavitation problem for thermohyperelastic materials[J]. Acta Mech Solida Sinica, 2004, 25(3): 275-278 (in Chinese))
  • 加载中

Catalog

    通讯作者: 陈斌, bchen63@163.com
    • 1. 

      沈阳化工大学材料科学与工程学院 沈阳 110142

    1. 本站搜索
    2. 百度学术搜索
    3. 万方数据库搜索
    4. CNKI搜索

    Article Metrics

    Article views (1290) PDF downloads(817) Cited by()
    Proportional views
    Related

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return