Acta Mechanica Solida Sinica

, Volume 20, Issue 1, pp 41–49 | Cite as

Study on dynamic stress intensity factors of disk with a radial edge crack subjected to external impulsive pressure

  • Aijun Chen


A dynamic weight function method is presented for dynamic stress intensity factors of circular disk with a radial edge crack under external impulsive pressure. The dynamic stresses in a circular disk are solved under abrupt step external pressure using the eigenfunction method. The solution consists of a quasi-static solution satisfying inhomogeneous boundary conditions and a dynamic solution satisfying homogeneous boundary conditions. By making use of Fourier-Bessel series expansion, the history and distribution of dynamic stresses in the circular disk are derived. Furthermore, the equation for stress intensity factors under uniform pressure is used as the reference case, the weight function equation for the circular disk containing an edge crack is worked out, and the dynamic stress intensity factor equation for the circular disk containing a radial edge crack can be given. The results indicate that the stress intensity factors under sudden step external pressure vary periodically with time, and the ratio of the maximum value of dynamic stress intensity factors to the corresponding static value is about 2.0.

Key words

circular disk cracks dynamic stress intensity factors dynamic weight function Fourier-Bessel series 


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  1. [1]
    Wang Y.B., Sun Y.Z., A new boundary integral equation method for cracked 2-D anisotropic bodies. Engineering Fracture Mechanics, 2005, 72(13): 2128–2143.CrossRefGoogle Scholar
  2. [2]
    Chen Y.Z., Lin X.Y., Wang Z.X., Solution of periodic group crack problems by using the Fredholm integral equation approach. Acta Mechanica, 2005, 178(1): 41–51.CrossRefGoogle Scholar
  3. [3]
    Fan T.Y., Foundation of Fracture Theory. Beijing: Science Press, 2003: 235–271 (in Chinese).Google Scholar
  4. [4]
    Rubio-Gonzalez C, Mason J.J., Dynamic stress intensity factor due to concentrated loads on a propagating semi-infinite crack in orthotropic materials. International Journal of Fracture, 2002, 118(1): 77–96.CrossRefGoogle Scholar
  5. [5]
    Wang Baolin, Han Jiecai, Du Shanyi, Dynamic response for functionally graded materials with penny-shaped cracks. Acta Mechanica Solida Sinica, 1999, 20(3): 219–225 (in Chinese).Google Scholar
  6. [6]
    Lu Jianfei, Chen Zhangyao, Dynamic response of a broken crack to SH waves. Acta Mechanica Solida Sinica, 2004, 25(2): 315–319 (in Chinese).Google Scholar
  7. [7]
    Guo R.P., Liu G.T., Fan T.Y., Semi-elliptic surface crack in an elastic solid with finite size under impact loading. Acta Mechanica Solida Sinica, 2006, 19(2): 122–127.CrossRefGoogle Scholar
  8. [8]
    Dai Feng, Wang Qizhi, Superposition integral method for deriving stress intensity factor under impact loading. Journal of Vibration and Shock, 2005, 24(3): 89–95 (in Chinese).Google Scholar
  9. [9]
    Zhong Ming, Zhang Yongyuan, The analysis of dynamic stress intensity factor for semi-circular surface crack using time-domain BEM formulation. Applied Mathematics and Mechanics-English Edition, 2001, 22(11): 1344–1351.CrossRefGoogle Scholar
  10. [10]
    Wen P.H., Aliabadi M.H., Young A., Boundary element method for dynamic plate bending problems. International Journal of Solids and Structures, 2000, 37(37): 5177–5188.CrossRefGoogle Scholar
  11. [11]
    Lin Z.S., Dynamic analysis of thick cylinders subjected to internal impulsive pressure. Acta Armamenta II, 1986, 8(1): 57–64 (in Chinese).Google Scholar
  12. [12]
    Wang X., Gong Y.N., A theoretical solution for axially symmetric problems in elastodynamics. Acta Mechanica Sinica, 1991, 7(3): 275–282.CrossRefGoogle Scholar
  13. [13]
    Liang K.M., Equations of Mathematical Physics. Beijing: Higher Education Press, 1990: 364–372 (in Chinese).Google Scholar
  14. [14]
    Yin X.C., Yue Z.Q., Transient plane-strain response of multilayered elastic cylinders to axisymmetric impulse. Journal of Applied Mechanics, 2002, 69(6): 825–835.CrossRefGoogle Scholar
  15. [15]
    Wu Xueren, Weight function and stress intensity factors for an internal axial crack in a hollow cylinder. Acta Mechanica Solida Sinica, 1990, 11(2): 175–180 (in Chinese).Google Scholar
  16. [16]
    Bueckner H.F., A novel principle for the computation of stress intensity factors. Z Angew Math Mech, 1970, 50(9): 529–546.MathSciNetzbMATHGoogle Scholar
  17. [17]
    Rice J.R., Some Remarks on Elastic Crack-tip Stress Fields. International Journal of Solids and Structures, 1972, 8(6): 751–758.CrossRefGoogle Scholar
  18. [18]
    Chen A.J., Zeng W.J., Weight function for stress intensity factors in rotating thick-walled cylinder. Applied Mathematics and Mechanics-English Edition, 2006, 27(1): 29–35.MathSciNetCrossRefGoogle Scholar
  19. [19]
    Kiciak A., Glinka G., Burns D.J., Calculation of stress intensity factors and crack opening displacements for cracks subjected to complex stress fields. Journal of Pressure Vessel Technology, 2003, 125(4): 260–266.CrossRefGoogle Scholar
  20. [20]
    Gregory R.D., A circular disc containing a radial edge crack opened by a constant internal pressure. Math Proc Camb Phil Soc, 1977, 81(5): 497–500.MathSciNetCrossRefGoogle Scholar
  21. [21]
    Petroski H.J., Achenbach J.D., Computation of the weight function from a stress intensity factor. Engineering Fracture Mechanics, 1978, 10(2): 257–266.CrossRefGoogle Scholar

Copyright information

© The Chinese Society of Theoretical and Applied Mechanics and Technology 2007

Authors and Affiliations

  • Aijun Chen
    • 1
  1. 1.School of ScienceNanjing University of Science and TechnologyNanjingChina

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