An engineering methodology taking into account the effect of local damage on the global behavior of surface cracked shell structures

• Autorzy: Chiesa, M. , Ostby, E. , Skallerud, B. , Thaulow, Ch.
• Języki publikacji: EN

Abstrakty

EN

The line spring finite element is a versatile numerical tool for performing engineering fracture mechanics analysis of surface cracked shells. An accurate yield surface of plane strain single-cracked (SEC) specimens having shallow, as well as deep, cracks is presented here. The meaning of the J-integral when crack growth occurs is discussed. The J-integral is regarded as a sort of accumulated measure of the global deformation in the ligament. The complete Gurson is used in order to support our observations. Furthermore a crack propagation law relating a local criterion for crack growth to the global deformation field is outlined. A methodology to link micro-mechanically based crack growth simulations with line spring analysis is proposed by suggesting an alternative way to calculate the J-integral from the line spring framework. Some details of the numerical implementation of the backward Euler integration scheme at the integration point of the line spring element in order to account for plasticity are presented here for a bilinear material model. An efficient numerical procedure, based on a proposed crack growth law, is also presented in order to account for ductile crack propagation. A numerical case is considered in order to show that the proposed procedure is suited to the purpose.

Słowa kluczowe

PL

plastyczność; pęknięcie; odkształcenie

EN

line spring; plasticity; yield surface; cracked shells; J integral; elastic predictor; plastic corrector; crack growth

• Czasopismo: International Journal of Applied Mechanics and Engineering
• Rocznik: 2002
• Tom: Vol. 7, no 1
• Strony: 267-291
• Opis fizyczny: Bibliogr. 29 poz., rys., wykr.

Twórcy

autor

Chiesa, M.

• Department of Mechanical Engineering Norwegian University of Technology, Trondheim, Norway,

autor

Ostby, E.

• Department of Mechanical Engineering Norwegian University of Technology, Trondheim, Norway

autor

Skallerud, B.

• Department of Mechanical Engineering Norwegian University of Technology, Trondheim, Norway

autor

Thaulow, Ch.

• Department of Mechanical Engineering Norwegian University of Technology, Trondheim, Norway

Bibliografia

• [1] ABAQUS Manual. - Version 5.2., Hibbit Karlson and Sorenson.
• [2] Chiesa M., Skallerud B. and Gross D. (2000): Closed form line spring yield surfaces for deep and shallow cracks: formulation and numerical performance. - Accepted for publication in Computers and Structures.
• [3] Chiesa M., Skallerud B. and Nyhus B. (2001): Efficient numerical procedures for fracture assessments of surface cracked shells. - Presented at European Conference on Computational Mechanics, June 26-29, Cracow, Poland.
• [4] Crisfield M.A. (1991): Non-linear Finite Element Analysis of Solids and Structures. - vol.1, Chichester, Wiley.
• [5] Crisfield M.A. (1997): Non-linear Finite Element Analysis of Solids and Structures. - vol.2, Chichester, Wiley.
• [6] Green A.P. and Hundy B.B. (1956): Initial plastic yielding in notch bend tests. - Journal of the Mechanics and Physics of Solids, vol. 16, pp. 128-144.
• [7] Hutchinson J.W. (1968,): Singular behavior at the end of a tensile crack in a hardening material. - J. of the Mechanics and Physics of Solids, vol. 16, pp. 13-31.
• [8] Koplik J. and Needleman A. (1990): Void growth and coalescence in porous plastic solids. - Int. J. of Solids and Structures, vol.24, pp.835-853.
• [9] Lee H. and Parks D.M. (1993): Fully plastic analysis of plane strain single edged cracked specimen subjected to combined tension and bending. - International Journal of Fracture, vol.63, pp.329-349.
• [10] Odegaard J. and Zhang Z. (1998): Quantification of Damage Parameters. - Sintef Report No.345526.
• [11] Rice J.R. (1968): A path independent integral and the appropriate analysis of strat concentration by notches and cracks. - J. Applied Mech., vol.35, pp.379-386.
• [12] Rice J.R. (1972): The line spring model for surface flaws, In: The Surface Crack Physical Problems and Computer Solutions (J.L. Sweldow, Ed.). - ASME.
• [13] Rice J.R. and Levy N. (1968): The part through surface crack in an elastic plate. - J. Applied Mech., vol.7, pp. 185-194.
• [14] Rice J.R. and Rosengren G.F. (1968): Plane strain deformation near a creak tip in power-low hardening material. - Journal of the Mechanics and Physics of Solids, vol.16, pp.1-12.
• [15] Simo J.C., Kennedy J.C. and Govindee S. (1988): Non-smooth multisurface plasticity and viscoplasticity. Loading/unloading conditions and numerical algorithms. - International Journal for Numerical Methods in Engineering, vol.26, pp.2161-2186.
• [16] Simo J.C. and Taylor R.L. (1985): Consistent tangent operators for rate-independent elastoplasticity. - Computer Methods in Applied Mechanics and Engineering, vol.48, pp. 101-118.
• [17] Simo J.C. and Taylor R.L. (1986): A return mapping algorithm for plane stress elastoplasticity. - International Journal for Numerical Methods in Engineering, vol.22, pp.649-670.
• [18] Skallerud B. (1999): Numerical analysis of cracked inelastic shells under large deformation or mixed mode loading. - Int. J. of Solids and Structures, vol.56, pp.25-40.
• [19] Skallerud B. and Haugen B. (1999): Collapse of thin shell structures: stress resultant plasticity modelling within a co-rotated ANDES finite element formulation. J International Journal for Numerical Methods in Engineering, vol.46, pp. 1961-1986.
• [20] Thomason P.P. (1985a): A three-dimensional model for ductile fracture by the growth and coalescence of microvoids. - Acta Metall., vol.33, pp. 1087-1095.
• [21] Thomason P.P. (1985b): Three-dimensional models for the plastic limit-loads at incipient failure of the intervoid matrix in ductile porous solids. - Acta Metall,, vol.33, pp.1079-1085.
• [22] Tvergaard V. (1982): Material failure by void coalescence in localized shear bands. - Int. J. of Solids and Structures, vol. 18, pp.659-672.
• [23] Tvergaard V. (1990): Material failure by void growth to coalescence. - Advances in Applied Mechanics, Academic Press, vol. 27, pp.83-151.
• [24] Tvergaard V. and Needleman A. (1992): Effect of crack meandering on dynamic ductile fracture. - Mech. Phys. Solid, vol.40, No.2, pp.447-471.
• [25] USFOS Theory Manual. - Version 7.4., SINTEF, Trondheim Norway, 2000.
• [26] Wang Y.Y. and Parks D.M. (1992): Evaluation of the elastic T-stress in surface cracked plates using the line-spring method. - Int. J. Frac., vol.56, pp.25-40.
• [27] White C.S., Ritchie R.O., and Parks D.M. (1983): Ductile growth of part through surface cracks: experiment and analysis. - In: ASTM STP 803 (C.F. Shih and J.P. Gudas, Eds.). - ASTM.
• [28] Williams M.L. (1957): On the stress distribution at the base of a stationary crack. - J. Applied Mech., vol.24, pp.109-114.
• [29] Zhang Z.L., Thaulow C. and 0degard J. (2000): A complete Gurson model approach for ductile fracture. - Engineering Fracture Mechanics, vol.67, No.2, pp.155-168.