Re-evaluation of the strain concentration factor through elasto-plastic analyses
Keywords:
digital image correlation, elasto-plastic strain variation, finite elements, effective strain concentration factor, V-notchesAbstract
Digital image correlation and three-dimensional finite element investigations are done for analyzing strain concentration for a semicircular notch and two V-notches with different radii. Along the notch bisector normalized true opening strains are represented as a function of the normalized distance from the notch root. In the linear elastic domain a comparison to an analytical solution is also done. Strain variations in the elasto-plastic domain show that the experimental normalized strains are greater than the numerical ones, both close to the notch root and over the whole ligament. The calculation of an effective strain concentration factor for V-notches is done and its variation based on experimental results proves to be much closer to real phenomena of strain distribution in the elasto-plastic domain.
References
WESTERGAARD, H.M., Bearing pressures and cracks, Journal of Applied Mechanics, 6, A49–53, 1939.
IRWIN, G.R., Analysis of stresses and strain near the end of a crack transversing a plate, Journal of Applied Mechanics, 24, pp. 361–364, 1957
WILLIAMS, M.L., Stress singularities resulting from various boundary conditions in angular corners of plates in tension, Journal of Applied Mechanics, 19, pp. 526–528, 1952.
CREAGER, M., PARIS, P.C., Elastic field equations for blunt cracks with reference to stress corrosion cracking, International Journal of Fracture Mechanics, 3, pp. 247–252, 1967.
GLINKA, G., Calculation of inelastic notch-tip strain-stress histories under cyclic loading, Engineering Fracture Mechanics, 22, pp. 839–854, 1985.
LAZZARIN, P., TOVO, R., A unified approach to the evaluation of linear elastic fields in the neighborhood of cracks and notches, International Journal of Fracture, 78, pp. 3–19, 1996.
LAZZARIN, P., TOVO, R., FILIPPI, S., Stress distribution in finite size plates with edge notches, International Journal of Fracture, 91, pp. 69–282, 1998.
GLINKA, G., NEWPORT, A., Universal features of elastic notch-tip stress fields, International Journal of Fatigue, 9, pp. 143–150, 1987.
XU, R.X., THOMPSON, J.C. AND TOPPER, T.H., Practical stress expressions for stress concentration regions, Fatigue and Fracture of Engineering Materials and Structures, 18, pp. 885–895, 1995.
KUJAWSKI, D., SHIN, C.S., On the elastic longitudinal stress estimation in the neighbourhood of notches, Engineering Fracture Mechanics, 56, pp. 137–138, 1997.
FILIPPI, S., LAZZARIN, P., TOVO, R., Developments of some explicit formulas useful to describe elastic stress fields ahead of notches in plates, International Journal of Solids and Structures, 39, pp. 4543–4565, 2002.
BERTO, F., LAZZARIN, P., RADAJ D., Fictitious notch rounding concept applied to sharp Vnotches: Evaluation of the microstructural support factor for different failure hypotheses. Part I: Basic stress equations, Engineering Fracture Mechanics, 75, pp. 3060–3072, 2008.
NEUBER, H., Theory of Notch Stresses, Springer-Verlag, Berlin, 1958.
NEUBER H., Theory of stress concentration for shear-strained prismatical bodies with arbitrary nonlinear stress strain law, Journal of Applied Mechanics, 26, pp. 544–550, 1961.
LI, Z., GUO, W., KUANG, Z., Three-dimensional elastic stress fields near notches in finite thick plates, International Journal of Solids and Structures, 37, pp. 7617–7631, 2000.
LI, Z., GUO, W., Three-dimensional elastic stress fields ahead of blunt V-notches in finite thickness plates, International Journal of Fracture, 107, pp. 53–71, 2001.
KOTOUSOV, A., WANG, C.H., Three dimensional stress constraint in an elastic plate with a notch, International Journal of Solids and Structures, 39, pp. 4311–4326, 2002.
HUTCHINSON, J.W., Singular behavior at the end of a tensile crack in a hardening material, Journal of the Mechanics and Physics of Solids, 16, pp. 13–31, 1968.
RICE, J.R., ROSENGREN G.F., Plane strain deformation near a crack tip in a power-law hardening material, Journal of the Mechanics and Physics of Solids, 16, pp. 1–12, 1968.
LAZZARIN, P., ZAMBARDI, R., LIVIERI, P., Plastic notch stress intensity factors for large Vshaped notches under mixed load conditions, International Journal of Fracture, 107, pp. 361– 377, 2001.
GROSS, R., MENDELSON, A., Plane elastostatic analysis of V-notched plates, International Journal of Fracture Mechanics, 8, pp. 267–27, 1972.
MOLSKI, K., GLINKA, G., A method of elastic–plastic stress and strain calculation at a notch root, Material Science Engineering, 50, pp. 93-100, 1981.
LAZZARIN, P., ZAMBARDI, R., The equivalent strain energy density approach re-formulated and applied to sharp V-shaped notches under localized and generalized plasticity, Fatigue and Fracture of Engineering Materials and Structures, 25, pp. 917–928, 2002.
SETHURAMAN, R., VISWANADHA, S., Evaluation of notch root elasto-plastic stress–strain state for general loadings using an elastic solution, International Journal of Pressure Vessels and Piping, 81, pp. 313–325, 2004.
SINGH, M.N.K., GLINKA, G., DUBEY, R.N., Elastic–plastic stress–strain calculation in notched bodies subjected to non-proportional loading, International Journal of Fracture, 76, pp. 39–60, 1996.
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