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Mode I Fracture Analysis of Polymethylmetacrylate Using Modified Energy-Based Models

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Abstract

The paper presents two energy-based approaches to predict the fracture trajectory and the fracture load in components containing a mode I crack. The fracture behavior of polymethylmetacrylate (PMMA) samples was investigated experimentally and theoretically for compact tension and double cantilever beam test specimens. The crack growth trajectories and the values of apparent fracture resistance in these two specimens were considerably different although both were under pure mode I loading. Two energy-based methods, i.e., the strain energy density and the averaged strain energy density criteria were modified to estimate the fracture trajectory and the fracture load in brittle materials respectively by considering the T-stress effects. The difference between the crack trajectories and the fracture resistances of different cracked specimens of the same material (PMMA) was found to be related to the magnitude and the sign of T-stress.

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References

  1. Larsson, S.G. and Carlsson, A.J., Influence of Non-Singular Stress and Specimen Geometry on Small-Scale Yielding at Each Tip in Elastic-Plastic Materials, J. Mech. Phys. Solids, 1973, vol. 21, no. 4, pp. 263–277.

    Article  ADS  Google Scholar 

  2. Rice, J.R., Limitations to the Small Scale Yielding Approximation for Crack-Tip Plasticity, J. Mech. Phys. Solids, 1974, vol. 22, no. 1, pp. 17–26.

    Article  ADS  Google Scholar 

  3. Betegon, C. and Hancock, J.W., Two-Parameter Characterization of Elastic-Plastic Crack-Tip Fields, J. Appl. Mech., 1991, vol. 58, no. 1, pp. 104–110.

    Article  ADS  Google Scholar 

  4. Du, Z.Z. and Hancock, J.W., The Effect of Non-Singular Stresses on Crack Tip Constraint, J. Mech. Phys. Solids, 1991, vol. 39, no. 4, pp. 555–567.

    Article  ADS  Google Scholar 

  5. Ayatollahi, M.R. and Sedighiani, K., Crack Tip Plastic Zone under Mode I, Mode II and Mixed Mode (I + II) Conditions, Struct. Eng. Mech., 2010, vol. 36, pp. 575–598.

    Article  Google Scholar 

  6. Ayatollahi, M.R. and Sedighiani, K., Mode I Fracture Initiation in Limestone by Strain Energy Density Criterion, Theor. Appl. Fract. Mech., 2012, vol. 57, no. 1, pp. 14–18.

    Article  Google Scholar 

  7. Smith, D.J., Ayatollahi, M.R., and Pavier, M.J., The Role of T-Stress in Brittle Fracture for Linear Elastic Materials under Mixed-Mode Loading, Fatigue Fract. Engng. Mater. Struct., 2001, vol. 24, no. 2, pp. 137–150.

    Article  Google Scholar 

  8. Aliha, M.R.M., Ayatollahi, M.R., Smith, D.J., and Pavier, M.J., Geometry and Size Effects on Fracture Trajectory in a Limestone Rock under Mixed Mode Loading, Eng. Fract. Mech., 2010, vol. 77, no. 11, pp. 2200–2212.

    Article  Google Scholar 

  9. Aliha, M.R.M. and Ayatollahi, M.R., Geometry Effects on Fracture Behavior of Polymethylmethacrylate, Mater. Sci. Eng., 2010, vol. 527, no. 3, pp. 526–530.

    Article  Google Scholar 

  10. Ayatollahi, M.R. and Aliha, M.R.M., Mixed-Mode Fracture in Soda-Lime Glass Analyzed by Using the Generalized MTS Criterion, Int. J. Solids Struct., 2009, vol. 46, no. 2, pp. 311–321.

    Article  MATH  Google Scholar 

  11. Kumar, B., Chitsiriphanit, S., and Sun, C.T., Significance of K-Dominance Zone Size and Nonsingular Stress Field in Brittle Fracture, Eng. Fract. Mech., 2011, vol. 78, no. 9, pp. 2042–2051.

    Article  Google Scholar 

  12. Sun, C.T. and Qian, H., Brittle Fracture Beyond the Stress Intensity Factor, J. Mech. Mater. Struct., 2009, vol. 4, no. 4, pp. 743–753.

    Article  Google Scholar 

  13. Liu, S. and Chao, Y.J., Variation of Fracture Toughness with Constraint, Int. J. Fract., 2003, vol. 124, no. 3, pp. 113–117.

    Article  Google Scholar 

  14. Chao, Y.J., Liu, S., and Broviak, B.J., Brittle Fracture: Variation of Fracture Toughness with Constraint and Crack Curving under Mode I Conditions, Exp. Mech., 2001, vol. 41, no. 3, pp. 232–241.

    Article  Google Scholar 

  15. Davenport, J.C.W. and Smith, D.J., A Study of Superimposed Modes I, II and III on PMMA, Fatigue Fract. Engng. Mater. Struct., 1993, vol. 16, no. 10, pp. 1125–1133.

    Article  Google Scholar 

  16. Khan, K. and Al-Shayea, N.A., Effect of Specimen Geometry and Testing Method on Mixed Mode I-II Fracture Toughness of a Limestone Rock from Saudi Arabia, Rock Mech. Rock Eng., 2000, vol. 33, no. 3, pp. 179–206.

    Article  Google Scholar 

  17. Lazzarin, P. and Zambardi, R., A Finite-Volume-Energy Based Approach to Predict the Static and Fatigue Behavior of Components with Sharp V-Shaped Notches, Int. J. Fract., 2001, vol. 112, no. 3, pp. 275–298.

    Article  Google Scholar 

  18. Lazzarin, P., Berto, F., Elices, M., and Gomez, J., Brittle Failure from U- and V-Notches in Mode I and Mixed, I + I, tMode: A Synthesis Based on the Strain Energy Density Averaged on Finite- ize VolumesI, {iFatigue Fract. Engng. Mater. Struct.}, 2009, vol. 32, no. 8, pp. 671–684.

    Article  Google Scholar 

  19. Berto, F., Lazzarin, P., and Marangon, C., Brittle Fracture of U-Notched Graphite Plates under Mixed Mode Loading, Mater. Des., 2012, vol. 41, pp. 421–432.

    Article  Google Scholar 

  20. Lazzarin, P., Berto, F., and Ayatollahi, M.R., Brittle Failure of Inclined Key-Hole Notches in Isostatic Graphite under In-Plane Mixed Mode Loading, Fatigue Fract. Engng. Mater. Struct., 2013, vol. 36, no. 9, pp. 942–955.

    Article  Google Scholar 

  21. Berto, F. and Lazzarin, P., Recent Developments in Brittle and Quasi-Brittle Failure Assessment of Engineering Materials by Means of Local Approaches, Mater. Sci. Eng. R, 2014, vol. 75, pp. 1–48.

    Article  Google Scholar 

  22. Lazzarin, P., Campagnolo, A., and Berto, F., A Comparison Among Some Recent Energy- and Stress-Based Criteria for the Fracture Assessment of Sharp V-Notched Components under Mode I Loading, Theor. Appl. Fract. Mech., 2014, vol. 71, pp. 21–30.

    Article  Google Scholar 

  23. Ayatollahi, M.R., Berto, F., and Lazzarin, P., Mixed Mode Brittle Fracture of Sharp and Blunt V-Notches in Polycrystalline graphite // Carbon. - 2011. - V. 49. - P. 24652474.

  24. Ayatollahi, M.R., Aliha, M.R.M., and Saghafi, H., An Improved Semi-Circular Bend Specimen for Investigating Mixed Mode Brittle Fracture, Eng. Fract. Mech., 2011, vol. 78, no. 1, pp. 110–123.

    Article  Google Scholar 

  25. Sih, G.C., Strain-Energy-Density Factor Applied to Mixed Mode Crack Problems, Int. J. Fract., 1974, vol. 10, no. 3, pp. 305–321.

    Article  Google Scholar 

  26. Sih, G.C., Some Basic Problems in Fracture Mechanics and New Concepts, Eng. Fract. Mech., 1973, vol. 5, no. 2, pp. 365–377.

    Article  MathSciNet  Google Scholar 

  27. Beltrami, E., Sulle Condizioni di Resistenza dei Corpi Elastici, Rend. R. 1st. Lombardo di Scienze, Lettere e Arti., 1885, vol. 18, no. 1, pp. 145–155.

    MATH  Google Scholar 

  28. Simulia Inc. ABAQUS 6.10 Manual. Providence, RI 02909, 2010.

  29. Schmidt, R.A., A Microcrack Model and Its Significance to Hydraulic Fracturing and Fracture Toughness Testing, in Proc. 21st US Symp. Rock Mechanics, 1980, pp. 581–590.

    Google Scholar 

  30. Maiti, S.K.M. and Prasad, K.S.R., A Study on the Theories of Unstable Crack Extension for the Prediction of Crack Trajectories, Int. J. Solids Struct., 1980, vol. 16, no. 6, pp. 563–574.

    Article  Google Scholar 

  31. Sumi, Y., Computational Crack Path Prediction, Theor. Appl. Fract. Mech., 1985, vol. 4, no. 2, pp. 149–156.

    Article  MathSciNet  Google Scholar 

  32. Aliha, M.R.M., Hosseinpour, Gh.R., and Ayatollahi, M.R., Application of Cracked Triangular Specimen Subjected to Three-Point Bending for Investigating Fracture Behavior of Rock Materials, Rock Mech. Rock Eng., 2012, vol. 46, no. 5, pp. 1023–1034.

    Article  ADS  Google Scholar 

  33. Ayatollahi, M.R., Razavi, N., and Chamani, H.R., A Numerical Study on the Effect of Symmetric Crack Flank Holes on Fatigue Life Extension of a SENT Specimen, Fatigue Fract. Engng. Mater. Struct., 2014, vol. 37, no. 10, pp. 1153–1164.

    Article  Google Scholar 

  34. Ayatollahi, M.R., Razavi, N., and Chamani, H.R., Fatigue Life Extension by Crack Repair Using Stop-Hole Technique under Pure Mode I and Pure Mode II Loading Conditions, Proc. Eng., 2014, vol. 74, pp. 18–21.

    Article  Google Scholar 

  35. Ayatollahi, M.R., Razavi, N., and Yahya, M.Y., Mixed Mode Fatigue Crack Initiation and Growth in a CT Specimen Repaired by Stop Hole Technique, Eng. Fract. Mech., 2015 (in press).

    Google Scholar 

  36. ASTM D5045, Standard Test Methods for Plane-Strain Fracture Toughness and Strain Energy Release Rate of Plastic Materials. Annual Book of ASTM Standards, Vol. 08.03.

  37. ASTM E399, Standard Test Methods for Plane-Strain Fracture Toughness of Metallic Materials, Annual Book of ASTM Standards, Vol. 03.01.

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Authors and Affiliations

  1. Fatigue and Fracture Research Laboratory, Center of Excellence in Experimental Solid Mechanics and Dynamics, School of Mechanical Engineering, Iran University of Science and Technology, Narmak, Tehran, 16846, Iran

    M. R. Ayatollahi, N. Razavi & M. Rashidi Moghaddam

  2. University of Padova, Vicenza, 36100, Italy

    F. Berto

Authors
  1. M. R. Ayatollahi
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  2. N. Razavi
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  3. M. Rashidi Moghaddam
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  4. F. Berto
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Correspondence to M. R. Ayatollahi.

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Original Text © M.R. Ayatollahi, N. Razavi, M. Rashidi Moghaddam, F. Berto, 2015, published in Fizicheskaya Mezomekhanika, 2015, Vol. 18, No. 5, pp. 53-62.

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Ayatollahi, M.R., Razavi, N., Rashidi Moghaddam, M. et al. Mode I Fracture Analysis of Polymethylmetacrylate Using Modified Energy-Based Models. Phys Mesomech 18, 326–336 (2015). https://doi.org/10.1134/S1029959915040050

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