Crack Tip Creep Deformation Behavior in Transversely Isotropic Materials

횡방향으로 등방성인 재료에서 균열선단 크리프 변형 거동

  • Published : 2009.12.01


Theoretical mechanics analysis and finite element simulation were performed to investigate creep deformation behavior at the crack tip of transversely isotropic materials under small scale creep (SCC) conditions. Mechanical behavior of material was assumed as an elastic-$2^{nd}$ creep, which elastic modulus ( E ), Poisson's ratio ( ${\nu}$ ) and creep stress exponent ( n ) were isotropic and creep coefficient was only transversely isotropic. Based on the mechanics analysis for material behavior, a constitutive equation for transversely isotropic creep behavior was formulated and an equivalent creep coefficient was proposed under plain strain conditions. Creep deformation behavior at the crack tip was investigated through the finite element analysis. The results of the finite element analysis showed that creep deformation in transversely isotropic materials is dominant at the rear of the crack-tip. This result was more obvious when a load was applied to principal axis of anisotropy. Based on the results of the mechanics analysis and the finite element simulation, a corrected estimation scheme of the creep zone size was proposed in order to evaluate the creep deformation behavior at the crack tip of transversely isotropic creeping materials.


Creep;Creep Anisotropy;Creep Zone Size;Crack;Small Scale Creep;Transverse Isotropy


  1. Landes, J. D. and Begley, J. A., 1976, "A Fracture Mechanics Approach to Creep Crack Growth," ASTM STP 590, In Mechanic of Crack Growth, pp.128~148
  2. Nikbin, K. M., Webster, G. A. and Turner, C. E., 1976, "Relevance of Nonlinear Fracture Mechanics to Creep Cracking," ASTM STP 601, In Cracks and Fracture, pp.47~62
  3. Saxena, A., 1986, "Creep Crack Growth under Nonsteady-State Conditions," ASTM STP 905, Fracture Mechanics: 17th Volume, pp.185~201
  4. Ma, Y. W., Baek, U. B. and Yoon, K. B., 2002, "Evaluation of Creep Fatigue Crack Growth Behavior of 9Cr Steel Employing Creep Reversal Parameter," Transaction of the KSME (A), Vol.26, No.7, pp.1453~1460
  5. Yoon, K. B., Saxena, A. and McDowell, D. L., 1992, "Influence of Crack Tip Cyclic Plasticity on Creep- Fatigue Crack Growth," ASTM STP 1131, pp.367~392
  6. Adefris, N., 1993, "Creep-Fatigue Crack Growth Behavior of 1Cr-1Mo-1/4V Rotor Steel," Doctoral Thesis, School of Materials Science and Engineering, Georgia Institute of Technology, Atlanta, GA
  7. Saxena, A., 1981, "A Model for Prediction the Effect of Frequency on Fatigue Crack Growth Behavior at Elevated Temperature," Fatigue of Engineering Materials and Structures, Vol.3, pp.247~255
  8. Yoon, K. B., Saxena, A. and Liaw, P. K., 1993, "Characterization of Creep-Fatigue Crack Growth Behavior under Trapezoidal Waveshape Using Ct-Parameter," International journal of Fracture, Vol.59, pp.95~114
  9. Bassani, J. L., Hawk, D. E. and Saxena, A., 1989, "Evaluation of the Ct Parameter for Characterizing Creep Crack Growth Rate in the Transient Regime," ASTM STP 995, pp.7~26
  10. Ibanez, A. R., 2003, "Modeling Creep Behavior in a Directionally Solidified Nickel Base Superalloy," Doctoral Thesis, School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA
  11. Gardner, B., Saxena, A. and Qu, J., 2001, "Creep Crack Growth Parameters for Directionally Solidified Superallys," Proc. 10th International Conference on Fracture (ICF10)
  12. Gordon, A. P., Shenoy, M. M. and McDowell, D. L., 2005, "Simulation on Creep Crack Growth of a Directionally-Solidified Ni-Base Superalloy," Proc. 11th International Conference on Fracture (ICF11)
  13. Schubert, F., Fleury, G. and Steinhaus, T., 2000, "Modelling of The Mechanical Behavior of the Single-Crystal Turbine Alloy CMSX-4 During Thermomechanical Loading," Modelling and Simulation in Materials Science and Engineering, Vol.8, pp.947~957
  14. Voyiadjis, G. Z. and Zolochevsky, A., 1988, "Modeling of Secondary Creep Behavior for Anisotropic Materials with Different Properties in Tension and Compression," International Journal of Plasticity, Vol.14, No.10-11, pp.1059~1083
  15. Bhatnagar, N. S. and Gupta, R. P., 1967, "On the Constitutive Equations of the Orthotropic Theory of Creep," Wood Science and Technology, Vol.1, pp.142~148
  16. Betten, J., 1981, "Creep Theory of Anisotropic Solids," Journal of Rheology, Vol.25, No.6, pp.565~581
  17. Matan, N., Cox, D. C., Carter, P., Rist, M. A., Rae, C. M. F. and Reed, R. C., 1999, "Creep of CMSX-4 Superalloy Single Crystals: Effects of Misorientation and Temperature," Acta Mater., Vol.47, No.5, pp.1549~1563
  18. Gunturi, S. S. K., Maclachlan, D. W. and Knowles, D. M., 2000, "Anisotropic Creep in CMSX-4 in Orientations Distant from <001>," Mater. Sci. Eng. A, Vol.289, pp.289
  19. Riedel, H. and Rice, J. R., 1986, "Tensile Cracks in Creeping Solids," ASTM STP 700, pp.112~130
  20. Ma, Y. W. and Yoon, K. B., 2009, "Criteria for Small Scale Creep Testing Condition and Correction of Ct Evaluation Scheme," Journal of Testing and Evaluation. (submitted)
  21. Hill, R., 1950, "The Mathematical Theory of Plasticity," Clarendon Press, Oxford, Oxford Engineering Science Series
  22. Saxena, A., 1998, "Nonlinear Fracture Mechanics for Engineers," CRC Press
  23. Shih, C. F., 1983, "Tables of Hutchinson-Rice- Rosengren Singular Field Quantities," MRL E-147, Brown University
  24. Pan, J. and Shih, C. F., 1986, "Plane Strain Crack Tip Fields for Power-Law Hardening Orthotropic Materials," Mechanics of Materials, Vol.5, pp.299~316
  25. Hibbitt, Karlsson & Sorensen, Inc., 2005, ABAQUS Version 6.5