Stress distribution in front of the crack – analytical solutions vs. numerical. Can the differences be minimized?
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Kielce University of Technology, Faculty of Mechatronics and Mechanical Engineering, Kielce, Poland
Submission date: 2018-07-10
Acceptance date: 2019-03-31
Online publication date: 2019-07-15
Publication date: 2019-07-15
Journal of Theoretical and Applied Mechanics 2019;57(3):713–721
It is shown that it is possible to obtain such parameters as and Q, which, when used in the analytical formulae proposed by O’Dowd and Shih, can lead to stress distributions similar to those obtained numerically. The numerical solution obtained after calibration of the stress-strain uniaxial curve and assuming large strains is expected to be close to the “real” stress distribution. Thus, the analytical solution after correction is also close to the “real” stress distribution. These new values of and Q can now be used in fracture criteria proposed within the scope of classical nonlinear fracture mechanics.
Ainsworth R.A., O'Dowd N.P., 1995, Constraint in the failure assessment diagram approach for fracture assessment, ASME Journal of Pressure Vessels Technology, 117, 260-267.
Bai Y., Wierzbicki T., 2008, A new model plasticity and fracture with pressure and Lode dependence, International Journal of Plasticity, 24, 1071-1096.
Cherepanov G.P., 1967, O racprostranenii treshchin v sploshnoj srede, Prikladnaya Matematika i Mekhanika, PMM, 31, 3, 476-488.
Dugdale D.S., 1960, Yielding of steel sheets containing slits, Journal of the Mechanics and Physics of Solids, 8, 100-104.
Guo W., 1993, Elastoplastic three dimensional crack border field – I. Singular structure of the field, Engineering Fracture Mechanics, 46, 93-104.
Hutchinson J.W., 1968, Singular behaviour at the end of a tensile crack in a hardening material, Journal of the Mechanics and Physics of Solids, 16, 13-31.
Koçak M., Webster S., Janosch J.J., Ainsworth R.A., Koers R., edit., 2008, FITNET: Fitness-for-Service. Fracture-Fatigue-Creep-Corrosion, GKSS Research Centre Geesthacht, ISBN 978-3-940923-00-4.
McClintock F.A., 1971, Plasticity Aspects of Fracture, [In:] Fracture an Advanced Treatise, Edited by H. Liebowitz, Academic Press, New York and London, 3, 47-225.
Neimitz A., Dzioba I., 2015, The influence of the out-of-plane and in-plane constraint on fracture toughness of high strength steel in the ductile to brittle transition temperature range, Engineering Fracture Mechanics, 147, 431-448.
Neimitz A., Gałkiewicz J., Dzioba I., 2018, Calibration of constitutive equations under conditions of large strains and stress triaxiality, Archives of Civil and Mechanical Engineering, 18, 1123-1135.
Neimitz A., Gałkiewicz J., Graba M., Computer program: Name: HRR_par program: Internet address:
Neimitz A., Graba M., 2008, Analytical-numerical hybrid method to determine the stress field in front of the crack in 3D elastic-plastic structural elements, Proceedings of 17th European Conference on Fracture – Multilevel Approach to Fracture of Materials, Components and Structures, Brno, Czech Republic, article on CD, abstract – book of abstracts, p. 85.
Neimitz A., Graba M., Gałkiewicz J., 2007, An alternative formulation of the Ritchie-Knott-Rice local fracture criterion, Engineering Fracture Mechanics, 74, 8, 1308-1322.
O'Dowd N.P., 1995, Applications of two parameter approaches in elastic-plastic fracture mechanics, Engineering Fracture Mechanics, 52, 3, 445-465.
O'Dowd N.P., Shih C.F., 1991, Family of crack-tip fields characterized by a triaxiality parameter – I. Structure of fields, Journal of the Mechanics and Physics of Solids, 39, 8, 989-1015.
Rice J.R., 1968, A path independent integral and the approximate analysis of strain concentration by notches and cracks, Journal of Applied Mechanics, 35, 379-386.
Rice J.R., Rosengren G.F., 1968, Plane strain deformation near a crack tip in a power-law hardening material, Journal of the Mechanics and Physics of Solids, 16, 1-12.
Sherry A.H., Hooton D.G., Beardsmore D.W., Lidbury D.P.G., 2005a, Material constraint parameters for the assessment of shallow defects in structural components – Part II: Constraint – based assessment of shallow cracks, Engineering Fracture Mechanics, 72, 2396-2415.
Sherry A.H., Wilkes M.A., Beardsmore D.W., Lidbury D.P.G., 2005b, Material constraint parameters for the assessment of shallow defects in structural componenets – Part I: Parameter solutions, Engineering Fracture Mechanics, 72, 2373-2395.
Xiang M., Guo W., 2013, Formulation of the stress fields in power law solids ahead of three-dimensional tensile cracks, International Journal of Solids and Structures, 50, 3067-3088.
Yang S., Chao Y.J., Sutton M.A., 1993, Higher order asymptotic crack tip in a power-law hardening material, Engineering Fracture Mechanics, 45, 1, 1-20.