Abstract
A critical examination of measured and computed three-dimensional deformations in the vicinity of a crack in an elastic/plastic plate subjected to three-point-bending are presented in a series of three papers. The aim is to apply interferometric measurement methods to the large plastic deformation at the tip of a crack in a ductile steel, and to assess the current ability to model that deformation numerically. Comparison between the precise interferometric measurements and the finite element model, which has been closely matched to the physical specimen, including internal tunneling of the crack, indicates good agreement up to 75 percent of the ultimate failure load; above that level, discrepancies increase to levels on the order of 25 percent. It also develops that out-of-plane measurements are less than optimal for deducing in-plane stress and deformation states. This finding implies consequences for working with caustics and similar methods when applied to cracks in plastically deforming solids. This first paper presents a description and assessment of the experimental methods and outlines the fracture experiment itself. The second paper describes the material characterization to closely match the finite element model to the physical fracture specimen, as well as a description of the finite element model itself. The third paper presents the results of the comparison between experiment and model, as well as some additional results from the numerical model alone.
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References
Biegen, J.F. (1989). Calibration requirements for Mirau and Linnik microscope interferometers. Applied Optics 28, 1972–1974.
Born, M. and Wolf, E. (1980). Principles of Optics, Sixth Edition, Pergamon Press, Oxford.
Creath, K. (1988). Phase-measurement interferometry techniques. Progress in Optics (Edited by E. Wolf), North-Holland, Amsterdam 26, 349–393.
Creath, K. (1989). Calibration of numerical aperture effects in interferometric microscope objectives. Applied Optics 28, 3333–3338.
Duley, W.W. (1992). Lasers, gas. Encyclopedia of Physical Science and Technology, Second Edition, Academic Press, Inc., San Diego 8, 545–554.
Han, B. (1992). Higher sensitivity moiré interferometry for micromechanics studies. Optical Engineering 31, 1517–1526.
Hutchinson, J.W. (1968a). Singular behaviour at the end of a tensile crack in a hardening material. Journal of Mechanics and Physics of Solids 16, 13–31.
Hutchinson, J.W. (1968b). Plastic stresses and strain fields at a crack tip. Journal of Mechanics and Physics of Solids 16, 337–347.
Knauss, W.G. and Losi, G.U. (1993). Crack propagation in a nonlinearly viscoelastic solid with relevance to adhesive bond failure. Journal of Applied Mechanics 60, 793–801.
KODAK Pamphlet P-110 (1976). KODAK Materials for Holography, Eastman Kodak Company, Rochester, New York.
KODAK Pamphlet P-255 (1985). KODAK Technical Pan Film 2415/6415, Eastman Kodak Company, Rochester, New York.
Livnat, A. and Post, D. (1985). The governing equations of moiré interferometry and their identity to equations of geometrical moiré. Experimental Mechanics 25(4), 360–366.
Narasimhan, R. and Rosakis, A.J. (1990). Three-dimensional effects near a crack tip in a ductile three-point bend specimen, Part I: A numerical investigation. Journal of Applied Mechanics 57, 607–617.
Narasimhan, R., Rosakis, A.J. and Moran, B. (1992). A three-dimensional numerical investigation of fracture initiation by ductile failure mechanisms in a 4340 steel. International Journal of Fracture 56, 1–24.
Parvin, M. and Knauss, W.G. (1990). Damage induced constitutive response of a thermoplastic related to composites and adhesive bonding. International Journal of Fracture 42, 57–72.
Post, D. (1980). Optical interference for deformation measurements - classical, holographic and moiré interferometry. Mechanics of Nondestructive Testing (Edited by W.W. Stinchcomb), Plenum Press, New York.
Post, D. (1993). Moiré interferometry. Handbook on Experimental Mechanics, Second Revised Edition (Edited by A.S. Kobayashi), Society for Experimental Mechanics, Inc., Prentice-Hall, Inc., Englewood Cliffs, New Jersey, 297–364.
Post, D., Han, B. and Ifju, P. (1994). High Sensitivity Moiré, Experimental Analysis for Mechanics and Materials, Springer-Verlag, New York.
Reynolds, G.O., DeVelis, J.B., Parrent Jr., G.B. and Thompson, B.J. (1989). The New Physical Optics Notebook: Tutorials in Fourier Optics, SPIE Optical Engineering Press, Bellingham.
Rice, J.R. and Rosengren, G.F. (1968). Plane strain deformation near a crack tip in a power-law hardening material. Journal of Mechanics and Physics of Solids 16, 1–12.
Schultheisz, C.R. and Knauss, W.G. (1994). The governing equations of moiré interferometry I. The effect of out-of-plane displacement gradients for application to crack-tip fields. Optics and Lasers in Engineering 20, 259–282.
Schulz, G. (1990). Calibration requirements for Mirau and Linnik microscope interferometers: comment. Applied Optics 29, 2838.
Shield, T.W. and Kim, K.-S. (1991). Diffraction theory of optical interference moiré and a device for production of variable virtual reference gratings: A moiré microscope. Experimental Mechanics 31, 126–134.
Stroke, G.W. (1992). Light. McGraw-Hill Encyclopedia of Science and Technology, Seventh Edition, McGraw-Hill, Inc., New York 10, 49–57.
Taylor, J.R. (1982). An Introduction to Error Analysis, University Science Books, Oxford University Press.
Tvergaard, V. and Needleman, A. (1992). Effect of crack meandering on dynamic, ductile fracture. Journal of the Mechanics and Physics of Solids 40, 447–471.
Tvergaard, V. and Needleman, A. (1993). An analysis of the brittle-ductile transition in dynamic crack growth. International Journal of Fracture 59, 53–67.
Walker, C.A. and McKelvie, J. (1978). A practical multiplied moiré method. Experimental Mechanica 18(8), 316–320.
Williams, M.L. (1957). On the stress distribution at the base of a stationary crack. Journal of Applied Mechanics 24, 109–114.
Zehnder, A.T. (1987). Dynamic Fracture Initiation and Propagation in Metals: Experimental Results and Techniques, Doctoral Thesis, California Institute of Technology.
Zehnder, A.T. and Rosakis, A.J. (1990). Three-dimensional effects near a crack tip in a ductile three-point bend specimen, Part II: An experimental investigation using interferometry and caustics. Journal of Applied Mechanics 57, 618–626.
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Schultheisz, C., Pfaff, R. & Knauss, W. An experimental/analytical comparison of three-dimensional deformations at the tip of a crack in a plastically deforming plate I: Optical interferometry and experimental preliminaries. International Journal of Fracture 90, 1–25 (1998). https://doi.org/10.1023/A:1007499604086
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DOI: https://doi.org/10.1023/A:1007499604086