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The separation of the fracture energy in metallic materials

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Abstract

The total plastic strain energy which is consumed during fracture of a plain-sided CT specimen is separated into several components. These are the energies required for deforming the specimen until the point of fracture initiation, for forming the flat-fracture surfaces, for forming the shear-lip fracture surfaces, and for the lateral contraction and the blunting at the side-surfaces, W lat. Characteristic crack growth resistance terms, R flat and R slant, are determined describing the energies dissipated in a unit area of flat-fracture and slant-fracture surface, respectively. R flat is further subdivided into the term R surf, to form the micro-ductile fracture surface, and into the subsurface term, R sub, which produces the global crack opening angle. Two different approaches are used to determine the fracture energy components. The first approach is a single-specimen technique for recording the total crack growth resistance (also called energy dissipation rate). Plain-sided and side-grooved specimens are tested. The second approach rests on the fact that the local plastic deformation energy can be evaluated from the shape of the fracture surfaces. A digital image analysis system is used to generate height models from stereophotograms of corresponding fracture surface regions on the two specimen halves. Two materials are investigated: a solution annealed maraging steel V 720 and a nitrogen alloyed ferritic-austenitic duplex steel A 905. For the steel V 720 the following values are measured: J i=65 kJ/m2, R surf=20 kJ/m2, R flat=280 kJ/m2, R slant=1000 kJ/m2, W lat=30 J. For the steel A 905 which has no shear lips, the measured values are: J i=190 kJ/m2, R flat=1000 kJ/m2, and W lat=45 J. Apart from materials characterization, these values could be useful for predicting the influence of specimen geometry and size on the crack growth resistance curves.

Key words: Elastic-plastic fracture mechanics, fracture energy, energy dissipation rate, fracture surface analysis.

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References

  • ASTM E 1152-87 (1993). Standard Test Method for Determining J-R Curves. Annual Book of ASTM Standards, Vol.03.01. pp. 1129–1145.

  • Atkins, A.G. and Mai, Y.W. (1986). Residual strain energy in elastoplastic adhesive and cohesive fracture. International Journal of Fracture 30, 203–221.

    Google Scholar 

  • Atkins, A.G. (1995). Toughness given by accumulated work in LEFTM: possible implications for elastoplastic JRresistance curves. Fatigue and Fracture of Engineering Materials and Structures 181007–1017.

    Google Scholar 

  • Bauer, B. and Haller, A. (1981). Determining the three dimensional geometry of fracture surfaces. Practical Metallography 18, 327–341.

    Google Scholar 

  • Braga, L. and Turner, C.E. (1993). Energy dissipation rate and crack opening angle analyses of fully plastic tearing. ASTM STP 1171, 158–175.

    Google Scholar 

  • Brocks, W. and Schmitt, W. (1995). The second parameter in J Rcurves: constraint or triaxiality. ASTM STP 1244, 209–231.

    Google Scholar 

  • Bryant, D. (1986). Semi-automated topographic mapping of fracture surfaces through stereo-photogrammetry. Micron Microscopy Acta 17, 3365–3372.

    Google Scholar 

  • Budiansky B., Hutchinson, J.W. and Evans, A.G. (1986). Matrix fracture in fibre-reinforced ceramics. Journal of Mechanics and Physics of Solids 34, 167–189. 344

    Google Scholar 

  • Cotterell, B. and Reddel, J.K. (1977). The essential work of plane stress ductile fracture. International Journal of Fracture 13, 267–277.

    Google Scholar 

  • Cotterell, B. and Atkins, A.G. (1996). A review of the Jand Iintegrals and their implications for crack growth resistance and toughness in ductile fracture. International Journal of Fracture 81, 357–372.

    Google Scholar 

  • Dawicke, D.S., Piascik, R.S. and Newman, Jr. J.C. (1997). Analysis of stable tearing in a 7.6mm thick aluminum plate alloy. ASTM STP 1321, 309–324.

    Google Scholar 

  • ESIS P2-92 (1992) ESIS Procedure for Determining the Fracture Behaviour of Materials.European Structural Integrity Society, Delft, The Netherlands.

    Google Scholar 

  • Evans, A.G. (1989). The new high toughness ceramics. ASTM STP 907, 267–291.

    Google Scholar 

  • Exner, H.E. and Fripan, M. (1985). Quantitative assessment of three-dimensional roughness, anisotropy and angular distributions of fracture surfaces by stereometry. Journal of Microscopy 139, 161–178.

    Google Scholar 

  • Gerberich, W.W. and Kurman, E. (1985). New contributions to the effective surface energy of cleavage. Scripta Metallurgica 19, 295–298.

    Google Scholar 

  • Griffith, A.A. (1920). The phenomena of rupture and flow in solids. Philosophical Transactions of the Royal Society London A221, 163–198.

    Google Scholar 

  • Gruber, M. and Kolednik, O. (1992). A contribution to the photogrammetric determination of the critical crack tip opening displacement. In: International Archives of Photogrammetry and Remote Sensing, Proc. of ISPRS XVII(Edited by L.W. Fritz and J.R. Lucas). Vol. 29, Part B5, Commission V, pp. 305–310.

  • Gruber, M. and Walcher, W. (1994). Spatial information from digital photogrammetry and computer vision. In: International Archives of Photogrammetry and Remote Sensing, Proc. of ISPRS XVIII. Vol. 30, Part 3/1, pp. 311–315.

    Google Scholar 

  • Gurney, C. (1994). Continuum mechanics and thermodynamics in the theory of cracking. Philosophical Magazine 69, 33–43.

    Google Scholar 

  • Hancock, J.W., Reuter, W.G. and Parks, D.M. (1993). Constraint and toughness parameterised by T. ASTM STP 1171, 21–40.

    Google Scholar 

  • Hutchinson, J.W. (1987). Crack tip shielding by micro cracking in brittle solids. Acta metallurgica 35, 1605–1619.

    Google Scholar 

  • Irwin, G.R. (1949). Fracture dynamics. In American Society of Metals Seminar Fracture of Metalspp. 147–166.

  • John, S. and Turner, C.E. (1991). Alternative representations for scaled R-curves in a titanium alloy. In Defect Assessment in Components; Fundamentals and Applications, ESIS/EGF Pub. 9(Edited by J. G. Blauel and K.-H. Schwalbe). MEP, London, pp. 299–318.

    Google Scholar 

  • Kobayashi, T. and Giovanola, J.H. (1989). Crack opening profile observations for dynamic cleavage crack propagation and arrest. Journal of Mechanics and Physics of Solids 37, 759–777.

    Google Scholar 

  • Kobayashi, T. and Shockey, D.A. (1987). A fractographic investigation of thermal embrittlement in cast duplex stainless steel. Metallurgical Transactions 18A, 1941–1949.

    Google Scholar 

  • Kolednik, O. (1981). A contribution to stereophotogrammetry with the Scanning Electron Microscopy. Practical Metallography 18, 562–573.

    Google Scholar 

  • Kolednik, O. (1991). On the physical meaning of the J-1a-curves. Engineering Fracture Mechanics 38, 403–412.

    Google Scholar 

  • Kolednik, O. (1993). A simple model to explain the geometry dependence of the J-1a-curves. International Journal of Fracture 63, 263–274.

    Google Scholar 

  • Kolednik, O. and Kutleša, P. (1989). On the influence of specimen geometry on the critical crack-tip-opening displacement. Engineering Fracture Mechanics 33, 215–223.

    Google Scholar 

  • Kolednik, O. and Stüwe, H.P. (1982). Abschätzung der Rißzähigkeit eines duktilen Werkstoffes aus der Gestalt der Bruchfläche. Zeitschrift für Metallkunde 73, 219–223.

    Google Scholar 

  • Kolednik, O. and Stüwe, H.P. (1985). The stereophotogrammetric determination of the critical crack tip opening displacement. Engineering Fracture Mechanics 21, 145–155.

    Google Scholar 

  • Kolednik, O. and Stüwe, H.P. (1987). A proposal for estimating the slope of the bluning line. International Journal of Fracture 33, R63–R66.

    Google Scholar 

  • Kolednik, O., Albrecht, M., Berchthaler, M., Germ, H., Pippan, R., Riemelmoser, F., Stampfl, J. and Wei, J. (1996). The fracture resistance of a ferritic-austenitic duplex steel. Acta Metallurgica et Materialia 44, 3307–3319.

    Google Scholar 

  • Kolednik, O., Shan, G.X. and Fischer, F.D. (1997). The energy dissipation rate – a new tool to interpret geometry and size effects. In: ASTM STP 1296, 126–151.

    Google Scholar 

  • Krasowsky, A.J. and Stepanenko, V.A. (1979). A quantitative stereoscopic fractographic study of the mechanism of fatigue crack propagation in steel. International Journal of Fracture 15, 203–215.

    Google Scholar 

  • Leevers, P.S. and Radon, J.C. (1982). Inherent stress biaxiality in various fracture specimen geometries. International Journal of Fracture 19, 311.

    Google Scholar 

  • Mao, X. and Shoji, T. (1993). Recrystallization-etch approach to study the plastic energy absorption at crack initiation and extension of pressure-vessel steel. Journal of Materials Science 28, 927–930.

    Google Scholar 

  • Marchal, Y. and Delannay, E. (1996). Influence of test parameters on the measurement of the essential work of fracture of zinc sheets. International Journal of Fracture 80, 295–310.

    Google Scholar 

  • Mecklenburg, M.F., Joyce, J.A. and Albrecht, P. (1989). Separation of energies in elastic-plastic fracture. ASTM STP 995, 594–612.

    Google Scholar 

  • O'Dowd, N.P. and Shih, C.F. (1991). Family of crack-tip fields characterized by a triaxiality parameter – I: structure of fields. Journal of Mechanics and Physics of Solids 39, 989–1015.

    Google Scholar 

  • O'Dowd, N.P. and Shih, C.F. (1994). Two-parameter fracture mechanics: theory and applications. ASTM STP 1207, 21–47.

    Google Scholar 

  • Orowan, E. (1945). Notch brittleness and the strength of metals. Transactions of the Institute of Engineers and Shipbuilders Scotland 89, 165–215.

    Google Scholar 

  • Scherer S., Stampfl, J., Gruber, M. and Kolednik, O. (1996). Automatische 3-D Oberflächenrekonstruktion aus steroskopischen Rasterelektronenmikrosko-paufnahmen. In: '95, 1. Tagung des DVMArbeitskreises Mikrosystemtechnik(Edited by B. Michel and T. Winkler). DVM, Berlin, pp. 671–676.

    Google Scholar 

  • Shan, G.X., Kolednik, O., Fischer, F.D. and Stüwe, H.P. (1993). A 2-D model for the numerical investigations of the stable crack growth in thick smooth fracture mechanics specimens. Engineering Fracture Mechanics 45, 99–106.

    Google Scholar 

  • Shoji, T. (1981). Determination of crack tip energy dissipation and elastic-plastic fracture toughness parameter with ductile crack extension. Journal of Testing and Evaluation 9, 324–334.

    Google Scholar 

  • Stampfl J., Scherer, S., Gruber, M. and Kolednik, O. (1996). Reconstruction of surface topographies by scanning electron microscopy for application in fracture research. Applied Physics A 63, 341–346.

    Google Scholar 

  • Stampfl, J. (1996). Lokale Bruchzähigkeit Metallischer Werkstoffe. PhD thesis, University of Mining and Metallurgy, Leoben.

    Google Scholar 

  • Stampfl, J., Scherer, S., Stüwe, H.P. and Kolednik, O. (1996a). The stereophotogrammetric determination of the plastic work for ductile fracture. In: Mechanisms and Mechanics of Damage and Failure, Proc. of ECF 11(Edited by J. Petit). EMAS, UK, Vol. 3, pp. 1271–1276.

    Google Scholar 

  • Stampfl J., Scherer, S., Berchthaler, M., Gruber, M. and Kolednik, O. (1996b). Determination of the fracture toughness by automatic image processing. International Journal of Fracture 78, 35–44.

    Google Scholar 

  • Stüwe, H.P. (1981). The plastic work spent in ductile fracture. In: Three-dimensional Constitutive Relations and Ductile Fracture(Edited by S. Nemat-Nasser). North-Holland, Amsterdam, pp. 213–221.

    Google Scholar 

  • Stüwe, H.P. (1990). The work necessary to form a ductile fracture surface. Engineering Fracture Mechanics 13, 231–236.

    Google Scholar 

  • Turner, C.E. (1990). A re-assessment of the ductile tearing resistance, Paris I and II. In Fracture Behavior and Design of Materials and Structures, Proc. ECF8(Edited by D. Firrao), Vol. II, pp. 933–949 and pp. 951–968. EMAS, UK.

    Google Scholar 

  • Turner, C.E. and Kolednik, O. (1994). A micro and macro approch to the energy dissipation rate model of stable ductile crack growth. Fatigue and Fracture of Engineering Materials and Structures 17, 1089–1107.

    Google Scholar 

  • Turner, C.E. and Kolednik, O. (1997). A simple test method for exergy dissipation rate and CTOA for large amounts of growth and the study of size and transferability effects. Fatigue and Fracture of Engineering Materials and Structures 20, 1507–1528.

    Google Scholar 

  • Wnuk, M.P. and Read, D.T. (1986). Essential work of fracture weversus energy dissipation rate J cin plane stress ductile fracture. International Journal of Fracture 31, 161–171.

    Google Scholar 

  • Yan, W.-Y., Shan, G.X., Kolednik, O. and Fischer F.D. (1998). A numerical simulation of the crack growth in a smooth CT specmen. Key Engineering Materials 145–149, 179–184.

    Google Scholar 

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Authors and Affiliations

  1. Erich Schmid Institut of Materials Science, Austrian Academy of Sciences, Austria

    Jürgen Stampfl & Otmar Kolednik

  2. Institute of Metal Physics, University of Leoben, Jahnstrasse 12, A-8700, Leoben, Austria

    Jürgen Stampfl & Otmar Kolednik

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  1. Jürgen Stampfl
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  2. Otmar Kolednik
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Stampfl, J., Kolednik, O. The separation of the fracture energy in metallic materials. International Journal of Fracture 101, 321–345 (2000). https://doi.org/10.1023/A:1007500325074

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