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Fracture assessment of polymethyl methacrylate using sharp notched disc bend specimens under mixed mode I + III loading

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Abstract

Mixed mode I/III behavior of Perspex (polymethyl methacrylate (PMMA)) is studied experimentally and theoretically in this research using a new and simple laboratory test configuration. The specimen is a circular disc containing a sharp V-notch along the diameter that is loaded by the conventional three-point bend fixture. The critical values of notch stress intensity factors (K VI and K VIII ) were obtained for the whole combinations of modes I and III simply by changing the notch inclination angle relative to the loading rollers. The value of notch fracture toughness under pure or dominantly tension loads was greater than its corresponding value under mode III or dominantly torsion loads. The experimental results were also predicted very well by employing the local strain energy density (SED) criterion.

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References

  1. Erdogan, F. and Sih, G.C., On the Crack Extension in Plates under Plane Loading and Transverse Shear, J. Basic. Eng., 1963, vol. 85, no. 4, pp. 519–525.

    Article  Google Scholar 

  2. Maccagno, T.M. and Knott, J.F., The Fracture Behaviour of PMMA in Mixed Modes I and II, Eng. Fract. Mech., 1989, vol. 34, no. 1, pp. 65–86.

    Article  Google Scholar 

  3. Aliha, M.R.M. and Ayatollahi, M.R., Geometry Effects on Fracture Behaviour of Polymethyl Methacrylate, Mater. Sci. Eng. A, 2010, vol. 527, no. 3, pp. 526–530.

    Article  Google Scholar 

  4. Awaji, H., Kato, T., Honda, S., and Nishikawa, T., Criterion for Combined Mode I-II Brittle Fracture, J. Ceramic Soc. Japan, 1999, vol. 107, no. 10, pp. 918–924.

    Article  Google Scholar 

  5. Ayatollahi, M.R., Aliha, M.R.M., and Hassani, M.M., Mixed Mode Brittle Fracture in PMMA—an Experimental Study Using SCB Specimens, Mater Sci. Eng. A, 2006, vol. 417, no. 1, pp. 348–356.

    Article  Google Scholar 

  6. 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 

  7. Saghafi, H., Zucchelli, A., and Minak, G., Evaluating Fracture Behavior of Brittle Polymeric Materials Using an IASCB Specimen, Polym. Test, 2013, vol. 32, no. 1, pp. 133–140.

    Article  Google Scholar 

  8. Aliha, M.R.M., Bahmani, A., and Akhondi, S., Mixed Mode Fracture Toughness Testing of PMMA with Different Three-Point Bend Type Specimens, Eur. J. Mech. A/Solid, 2016, vol. 58, pp. 148–162.

    Article  ADS  Google Scholar 

  9. Ayatollahi, M.R. and Aliha, M.R.M., Analysis of a New Specimen for Mixed Mode Fracture Tests on Brittle Materials, Eng. Fract. Mech., 2009, vol. 76, no. 11, pp. 1563–1573.

    Article  Google Scholar 

  10. Richard, H.A., Some Theoretical and Experimental Aspects of Mixed Mode Fractures, 6 Int. Conf. on Fracture, New Delhi, India, 1984.

    Google Scholar 

  11. Gómez, F.J. and Elices, M., Fracture of Components with V-Shaped Notches, Eng. Fract. Mech., 2003, vol. 70, no. 14, pp. 1913–1927.

    Article  Google Scholar 

  12. Gómez, F.J. and Elices, M., A Fracture Criterion for Sharp V-Notched Samples, Int. J. Fract., 2003, vol. 123, no. 3–4, pp. 163–175.

    Article  MATH  Google Scholar 

  13. Gómez, F.J., Elices, M., and Planas, J., The Cohesive Crack Concept: Application to PMMA at-60°C, Eng. Fract. Mech., 2005, vol. 72, no. 8, pp. 1268–1285.

    Article  Google Scholar 

  14. Gómez, F.J., Elices, M., Berto, F., and Lazzarin, P., Local Strain Energy to Assess the Static Failure of UNotches in Plates under Mixed Mode Loading, Int. J. Fract., 2007, vol. 145, no. 1, pp. 29–45.

    Article  MATH  Google Scholar 

  15. Susmel, L., and Taylor, D., The Theory of Critical Distances to Predict Static Strength ofNotched Brittle Components Subjected to Mixed-Mode Loading, Eng. Fract. Mech., 2008, vol. 75, no. 3, pp. 534–550.

    Article  Google Scholar 

  16. Berto, F., Cendon, D.A., Lazzarin, P., and Elices, M., Fracture Behaviour of Notched Round Bars Made of PMMA Subjected to Torsion at-60°C, Eng. Fract. Mech., 2013, vol. 102, pp. 271–287.

    Article  Google Scholar 

  17. Ahmadi-Moghadam, B. and Taheri, F., An Effective Means for Evaluating Mixed-Mode I/III Stress Intensity Factors Using Single-Edge Notch Beam Specimen, J. Strain Anal. Eng. Des., 2013, vol. 48, no. 4, pp. 245–257.

    Article  Google Scholar 

  18. Liu, S., Chao, Y.J., and Zhu, X., Tensile-Shear Transition in Mixed Mode I/III Fracture, Int. J. Solids Struct., 2004, vol. 41, no. 22, pp. 6147–6172.

    Article  MATH  Google Scholar 

  19. Ayatollahi, M.R. and Saboori, B., A New Fixture for Fracture Tests under Mixed Mode I/III Loading, Eur. J. Mech. A/Solids, 2015, vol. 51, pp. 67–76.

    Article  ADS  Google Scholar 

  20. Richard, H.A., Schramm, B., and Schirmeisen, N.H., Cracks on Mixed Mode Loading—Theories, Experiments, Simulations, Int. J. Fatigue, 2014, vol. 62, pp. 93–103.

    Article  Google Scholar 

  21. Lazzarin, P. and Berto, F., Some Expressions for the Strain Energy in a Finite Volume Surrounding the Root of Blunt V-Notches, Int. J. Fract., 2005, vol. 135, no. 1–4, pp. 161–185.

    Article  MATH  Google Scholar 

  22. 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 

  23. Aliha, M.R.M., Bahmani, A., and Akhondi, S., Numerical Analysis of a New Mixed Mode I/III Fracture Test Specimen, Eng. Fract. Mech., 2015, vol. 134, pp. 95–110.

    Article  Google Scholar 

  24. Aliha, M.R.M., Bahmani, A., and Akhondi, S., Determination of Mode III Fracture Toughness for Different Materials Using a New Designed Test Configuration, Mater. Des., 2015, vol. 86, pp. 863–871.

    Google Scholar 

  25. Williams, M.L., Stress Singularities Resulting from Various Boundary Conditions, J. Appl. Mech., 1952, vol. 19, no. 4, pp. 526–528.

    Google Scholar 

  26. Zappalorto, M., Lazzarin, P., and Berto, F., Elastic Notch Stress Intensity Factors for Sharply V-Notched Rounded Bars under Torsion, Eng. Fract. Mech., 2009, vol. 76, no. 3, pp. 439–453.

    Article  Google Scholar 

  27. Zappalorto, M., Lazzarin, P., and Filippi, S., Stress Field Equations for U-and Blunt V-Shaped Notches in Axisymmetric Shafts under Torsion, Int. J. Fract., 2010, vol. 164, no. 2, pp. 253–269.

    Article  MATH  Google Scholar 

  28. Zappalorto, M., Lazzarin, P., and Yates, J.R., Elastic Stress Distributions for Hyperbolic and Parabolic Notches in Round Shafts under Torsion and Uniform Antiplane Shear Loadings, Int. J. Solids Struct., 2008, vol. 45, no. 18, pp. 4879–4901.

    Article  MATH  Google Scholar 

  29. Qian, J. and Hasebe, N., Property of Eigenvalues and Eigenfunctions for an Interface V-Notch in Antiplane Elasticity, Eng. Fract. Mech., 1997, vol. 56, no. 6, pp. 729–734.

    Article  Google Scholar 

  30. Berto, F., Lazzarin, P., Kotousov, A., and Harding, S., Out-of-Plane Singular Stress Fields in V-Notched Plates and Welded Lap Joints Induced by In-Plane Shear Load Conditions, Fatigue Fract. Eng. Mater. Struct., 2011, vol. 34, no. 4, pp. 291–304.

    Article  Google Scholar 

  31. Berto, F. and Lazzarin, P., Fatigue Strength of Structural Components under Multi-Axial Loading in Terms of Local Energy Density Averaged on a Control Volume, Int. J. Fatigue, 2011, vol. 33, no. 8, pp. 1055–1065.

    Article  Google Scholar 

  32. Gough, H.J. and Pollard, H.V., Properties of Some Materials for Cast Crankshafts, with Special Reference to Combined Stresses, Proc. Inst. Auto. Eng., 1963, vol. 31, no. 1, pp. 821–893.

    Google Scholar 

  33. Lazzarin, P., Sonsino, C.M., and Zambardi, R., A Notch Stress Intensity Approach to Assess the Multiaxial Fatigue Strength of Welded Tube-to-Flange Joints Subjected to Combined Loadings, Fatigue Fract. Eng. Mater. Struct., 2004, vol. 27, no. 2, pp. 127–140.

    Article  Google Scholar 

  34. Lazzarin, P., Berto, F., Elices, M., and Gomez, J., Brittle Failures from U-and V-Notches in Mode I and Mixed, I + II, Mode: A Synthesis Based on the Strain Energy Density Averaged on Finite-Size Volumes, Fatigue Fract. Eng. Mater. Struct., 2009, vol. 32, no. 8, pp. 671–684.

    Article  Google Scholar 

  35. Berto, F. and Lazzarin, P., A Review of the Volume-Based Strain Energy Density Approach Applied to V-Notches and Welded Structures, Theor. Appl. Fract. Mech., 2009, vol. 52, no. 3, pp. 183–194.

    Article  Google Scholar 

  36. 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. Rep., 2014, vol. 75, pp. 1–48.

    Article  Google Scholar 

  37. Berto, F., Campagnolo, A., and Ayatollahi, M.R., Brittle Fracture of Rounded V-Notches in Isostatic Graphite under Static Multiaxial Loading, Phys. Mesomech., 2015, vol. 18, no. 4, pp. 283–297.

    Article  Google Scholar 

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Authors and Affiliations

  1. Welding and Joining Research Center, School of Industrial Engineering, Iran University of Science and Technology, Narmak, Tehran, 16846-13114, Iran

    M. R. M. Aliha, A. Bahmani & Sh. Akhondi

  2. Department of Management and Engineering, University of Padova, Vicenza, 36100, Italy

    F. Berto

  3. Department of Engineering Design and Materials, Norwegian University of Science and Technology, Trondheim, 7491, Norway

    F. Berto & A. Barnoush

Authors
  1. M. R. M. Aliha
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  2. F. Berto
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  3. A. Bahmani
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  4. Sh. Akhondi
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  5. A. Barnoush
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Correspondence to M. R. M. Aliha.

Additional information

Original Text © M.R.M. Aliha, F. Berto, A. Bahmani, Sh. Akhondi, A. Barnoush, 2016, published in Fizicheskaya Mezomekhanika, 2016, Vol. 19, No. 4, pp. 92-100.

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Aliha, M.R.M., Berto, F., Bahmani, A. et al. Fracture assessment of polymethyl methacrylate using sharp notched disc bend specimens under mixed mode I + III loading. Phys Mesomech 19, 355–364 (2016). https://doi.org/10.1134/S1029959916040020

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  • DOI: https://doi.org/10.1134/S1029959916040020

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