Simplified Stress Gradient Method for Stress-Intensity Factor Determination

Authors: Jeries J. Abou-Hanna

Abstract:

Several techniques exist for determining stress-intensity factors in linear elastic fracture mechanics analysis. These techniques are based on analytical, numerical, and empirical approaches that have been well documented in literature and engineering handbooks. However, not all techniques share the same merit. In addition to overly-conservative results, the numerical methods that require extensive computational effort, and those requiring copious user parameters hinder practicing engineers from efficiently evaluating stress-intensity factors. This paper investigates the prospects of reducing the complexity and required variables to determine stress-intensity factors through the utilization of the stress gradient and a weighting function. The heart of this work resides in the understanding that fracture emanating from stress concentration locations cannot be explained by a single maximum stress value approach, but requires use of a critical volume in which the crack exists. In order to understand the effectiveness of this technique, this study investigated components of different notch geometry and varying levels of stress gradients. Two forms of weighting functions were employed to determine stress-intensity factors and results were compared to analytical exact methods. The results indicated that the “exponential” weighting function was superior to the “absolute” weighting function. An error band +/- 10% was met for cases ranging from a steep stress gradient in a sharp v-notch to the less severe stress transitions of a large circular notch. The incorporation of the proposed method has shown to be a worthwhile consideration.

Keywords: Fracture mechanics, finite element method, stress intensity factor, stress gradient.

Digital Object Identifier (DOI): doi.org/10.6084/m9.figshare.12489788

References:

[1] G. Pluvinage and M. Gjonaj (eds), Notch Effects in Fatigue and Fracture, 1-22. Kluwer Academic Publishers, Netherlands, 2001.
[2] G. Qylafku, Z, Azari, M. Gjonaj, G. Pluvinage, On the Fatigue Failures and Life Prediction for Notched Specimens. Materials Science, Vol. 34, No. 5, 1998.
[3] Y. Weixing. Stress field intensity approach for predicting fatigue life. Int. J Fatigue 15 No 3 (1992), 243-245.
[4] Y. Weixing, Xia Kaiquan and Gu Yi. On the fatigue notch factor, Kf. Int. J. Fatigue Vol. 17, No. 4 (1995), 245-251.
[5] G. R. Irwin, Trans. ASME, J. Appl mech. 24, 361. (1957).
[6] Y. Murakami. Stress Intensity Factors Handbook. Soc. Materials Sci., Japan, Vol. 4, 2001.
[7] G. Glinka, Calculation of Inelastic Notch-Tip Strain-Stress Histories under Cyclic Loading, Engineering Fracture Mechanics Vol. 22, No. 5, 839-854. Pergamon Press, 1985.
[8] Y. Murakami: Metal Fatigue: Effects of Small defects and Nonmetallic Inclusions. Elsevier Science Ltd., Oxford, UK, 2002.
[9] Y. Murakami and M. Endo, Quantitative Evaluation of Fatigue Strength of Metals Containing Various Small Defects or Cracks. Engng Fract. Mech. 17, 1-15. 1983.
[10] Y. Murakami and M. Endo, Effects of Hardness and Crack Geometries on ΔKth of Small Cracks Emanating from Small Defects. The Behavior of Short Fatigue Cracks. Mechanical Engineering Publication, London, 275-293. 1986.
[11] Y. Murakami and M. Endo, Prediction Equation for ΔKth of Various Metals Containing Small Defects in Terms of the Vickers Hardness (HV) and Square Root of the Projected Area of Defects. Current Japanese Material Research, Vol. 8: Fracture Mechanics. Society of Materials Science, Japan, 105-124. 1991.
[12] H. Nisitani, Bull. JSME, 11, 14, 1968.
[13] H. Nisitani and Y. Murakami, Stress Intensity Factors of an Elliptical Crack or a Semi-Elliptical Crack Subject to Tension. Int. Journ. of Fracture, Vol. 10, No. 3 353-368. 1974.
[14] R. Perez et al, Interpolative Estimates of Stress Intensity Factors for Fatigue Crack Growth Predictions. Engineering Fracture Mechanics Vol. 24, No. 4, 629-633. 1986.
[15] Y. Lui and S. Manadevan, Fatigue Limit Prediction of Notched Components Using Short Crack Growth Theory and an Asymptotic Interpolation Method. Engineering Fracture Mechanics, 2008, doi:10.1016/j.engfracmech.2008.06.006
[16] G. Chell. Engng Fracture Mech. 7, 137. 1975.
[17] G. Chell. The Stress Intensity Factors for Part through Thickness Embedded and Surface Flaws Subject to a Stress Gradient. Engng Fracture Mech. Vol. 8, 331-340. 1976.
[18] ASME Nonmandatory Appendix A, Article A-3000, Method for KI Determination.
[19] J. Bloom. Determination of the Stress Intensity Factor for Gradient Stress Fields. Journal of Pressure Vessel Technology, Vol. 99, Issue 3, 477-484. 1977.
[20] H. Bueckner. A Novel Principal for the Computing of Stress Intensity Factors. Zeitschrift fur angewandte Mathematik und Mechanik 50, 529-545. 1997
[21] J. Rice. Some Remarks on Elastic Crack-Tip Stress Field. Int. J. Solids Structures, 8, 751-758. 1972.
[22] Y. Liu et al. Numerical Methods for Determination of Stress Intensity Factors of Singular Stress Field. Engineering Fracture mechanics. 75, 4793-4803. 2008.
[23] S. Ju and H. Chung. Accuracy and Limit of a Least-Squares Method to Calculate 3D Notch SIFs. International Journal of Fracture, 148, 169-183. 2007.
[24] J. Xu et al. Numerical Methods for the Determination of Multiple Stress Singularities and Related Stress Intensity Coefficients. Engineering Fracture Mechanics, 63, 775-790. 1999.
[25] D. Taylor, Theory of Critical Distances, Elsevier Ltd. 2007.
[26] D. Bellett et al, The fatigue behavior of three-dimensional stress concentrations. International Journal of Fatigue 27 (2005), 207-221.
[27] R. Adib, et al, Application of Volumetric Method to the Assessment of Damage Induced by Action of Foreign Objects on Gas Pipes. Strength of Materials, Vol. 38, No. 4, 409-416. 2006.
[28] H. Adib-Ramezani and J. Jeong. Advanced Volumetric Method for Fatigue Life Prediction Using Stress Gradient Effects at Notch Roots. Computational Materials Science 39, 649-663. 2007.
[29] H. Tada, P. Paris, and G. Irwin, The Stress Analysis of Cracks Handbook, 3rd edition, ASME, New York, NY, 2000.