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Determination of elastic-plastic stresses and strains from measured surface strain data

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Abstract

A rigorous approach founded in the fundamental principles of plasticity is used to develop an accurate numerical algorithm for the determination of stresses and elastic and plastic strains from total strain data measured on a structure surface. The approach used to develop the algorithm and its relationship to both the flow theory of plasticity and recent advances in tangent stiffness-based numerical solution procedures for elastic-plastic boundary value problems are presented. Verification of the method for plane stress problems is demonstrated. A discussion of how the method can be used with measured surface displacement data is proved.

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References

  1. Kobayashi, A. S., ed., Handbook on Experimental Stress Analysis, SEM Publisher (1993).

  2. Mendelson, A., Plasticity: Theory and Application, Krieger Publishing (1983).

  3. Owen, D.R.J. andHinton, E., Finite Element in Plasticity: Theory and Practice, Pineridge Press, Swansea, England (1980).

    Google Scholar 

  4. Wilkins, M. L., “Calculation of Elastic-Plastic Flow,”Methods of Computational Physics, vol. 3, eds. B. Alder, S. Fernback andM. Roternerg, Academic Press, New York (1964).

    Google Scholar 

  5. Krieg, R. D. and Key, S. W., “Implementation of a Time-Independent Plasticity Theory into Structural Computer Programs,” ASME AMD 20: Constitutive Equations in Viscoelasticity, eds. J. A. Stricklin and K. J. Saczalski, ASME, 125–137 (1976).

  6. Hughes, T.J.R. andShakib, F., “Pseudo-Corner Theory: A Simple Enhancement of J 2 Flow Theory for Applications Involving Non-proportional Loading,”Eng. Comput.,3,116–120 (1986).

    Google Scholar 

  7. Rice, J. R. andTracy, D. M., “Computational Fracture Mechanics,”Numerical and Computer Methods in Structural Mechanics, eds. S. J. Fenves, N. Perrone, A. Robinson andW. C. Schnobrich, Academic Press, New York (1973).

    Google Scholar 

  8. Tracy, D. M., “Finite Element Solutions for Crack-Tip Behavior in Small-Scale Yielding,”J. Eng. Mat. and Technol.,98 (2),146–151 (1976).

    Google Scholar 

  9. Krieg, R. D. andKrieg, D. B., “Accuracies of Numerical Solution Methods for the Elastic-Perfectly Plastic Model,”J. Pressure Vessel Technol.,99 (4),510–515 (1977).

    Google Scholar 

  10. Schreyer, H. L., Kulak, R. F. andKramer, J. M., “Accurate Numerical Solutions for Elastic-Plastic Models,”J. Pressure Vessel Technol.,101,226–234 (1979).

    Google Scholar 

  11. Deng, X., “Dynamic Crack Propagation in Elastic-Plastic Solids,”Ph.D. dissertation, California Institute of Technology, Pasadena (1990).

    Google Scholar 

  12. Marcal, P. V., “A Stiffness Method for Elastic-Plastic Problems,”Int. J. Mech. Sci.,7,220–238 (1965).

    Google Scholar 

  13. Marcal, P. V. andKing, I. P., “Elastic-Plastic Analysis of Two-Dimensional Stress Systems by the Finite Element Method,”Int. J. Mech. Sci.,9,143–155 (1967).

    Article  Google Scholar 

  14. Marques, J.M.M.C., “Stress Computation in Elastoplasticity,”Eng. Comput.,1,42–51 (1984).

    Google Scholar 

  15. Deng, X., “Negative Plastic Flow and Its Prevention in Elasto-Plastic Finite Element Computation,”Finite Elements in Analysis and Design,7,181–191 (1990).

    Article  Google Scholar 

  16. Keil, S. andBenning, O., “On the Evaluation of Elasto-Plastic Strains Measured with Strain Gages,”Exp. Mech.,19 (8),265–270 (1979).

    Article  Google Scholar 

  17. Kang, B.S.J. andKobayashi, A. S., “J-Resistance Curves in Aluminum SEN Specimens Using Moiré Interferometry,”Exp. Mech. 28 (2),159–169 (1988).

    Google Scholar 

  18. Cardenas-Garcia, J. F., Read, D. T. andMoulder, J. C., “Experimental Study of Path Independence of the J-Integral in an Aluminum Tensile Panel,”Exp. Mech.,27 (3),328–332 (1987).

    Google Scholar 

  19. Guery, M. andFrancois, D., “Analyse experimentale des champs de contraintes planes elasto-plastiques par la methode du moire,”Journal de Mecanique theorique et appliquee,4 (1),139–155 (1985).

    Google Scholar 

  20. Sharpe, W. N., “On the Measurement of Elastoplastic Stresses,”Exp. Mech.,32 (1),62–67 (1992).

    Google Scholar 

  21. ABAQUS, Finite Element Program Version 4.9, Hibbett, Karlsson and Sorenson, Providence, RI (1992).

  22. Deng, X., PSOLID: A Finile Element Program for Elastic-Plastic Solids, California Institute of Technology, Pasadena (1988).

    Google Scholar 

  23. Sutton, M. A., Turner, J. L., Bruck, H. A. andChae, T. L., “Full-Field Representation of the Discretely Sampled Surface Deformations for Displacement and Strain Analysis,”Exp. Mech.,31 (2),168–177 (1991).

    Google Scholar 

  24. Post, D., Han, B. T. andIfju, P., High Sensitivity Moiré, Springer-Verlag, New York (1994).

    Google Scholar 

  25. Han, G., Sutton, M. A. andChao, Y. J., “A Study of Stationary Crack-Tip Deformation Fields in Thin Sheets by Computer Vision,”Exp. Mech.,34 (2),125–140 (1994).

    Article  Google Scholar 

  26. Han, G., Sutton, M. A., Chao, Y. J. andLyons, J. S., “A Study of Stable Crack Growth in Thin SEC Specimens of 304 Stainless Steel by Computer Vision,”Eng. Fract. Mech.,52, (3),525–555 (1995).

    Google Scholar 

  27. Dawicke, D. S. andSutton, M. A., “CTOA and Crack-Tunneling Measurements in Thin Sheet 2024-T3 Aluminum Alloy,”Exp. Mech.,34 (4),357–369 (1994).

    Article  Google Scholar 

  28. Sutton, M. A., Bruck, H. A. andMcNeill, S. R., “Determination of Deformations Using Digital Correlation with the Newton-Raphson Method for Partial Differential Corrections,”Exp. Mech.,29 (3),261–267 (1989).

    Google Scholar 

  29. Sutton, M. A. andMcNeill, S. R., “The Effects of Subpixel Image Restoration on Digital Correlation Error Estimates,”Opt. Eng.,27 (3),163–175 (1988).

    Google Scholar 

  30. Dohrmann, C. R. and Busby, H. R., “Spline Function Smoothing and Differentiation of Noisy Data on a Rectangular Grid,” Proc. 6th Int. Conf. on Exp. Mech., 843–849 (1988).

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Sutton, M.A., Deng, X., Liu, J. et al. Determination of elastic-plastic stresses and strains from measured surface strain data. Experimental Mechanics 36, 99–112 (1996). https://doi.org/10.1007/BF02328705

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