Advertisement

Quasi-Brittle Fracture of Compact Specimens with Sharp Notches and U-Shaped Cuts

  • V. M. Kornev
  • A. G. Demeshkin
Article
  • 12 Downloads

Abstract

A two-parameter (coupled) discrete-integral criterion of fracture is proposed. It can be used to construct fracture diagrams for compact specimens with sharp cracks. Curves separating the stress–crack length plane into three domains are plotted. These domains correspond to the absence of fracture, damage accumulation in the pre-fracture region under repeated loading, and specimen fragmentation under monotonic loading. Constants used for the analytical description of fracture diagrams for quasi-brittle materials with cracks are selected with the use of approximation of the classical stress–strain diagrams for the initial material and the critical stress intensity factor. Predictions of the proposed theory are compared with experimental results on fracture of compact specimens with different radii made of polymethylmethacrylate (PMMA) and solid rubber with crack-type effects in the form of U-shaped cuts.

Keywords

brittle and quasi-brittle fracture small-scale yielding necessary and sufficient criteria of fracture elastoplastic material edge crack U-shaped cut 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    V. V. Panasyuk, A. E. Andreikin, and V. Z. Parton, Fracture Mechanics and Material Strength: Reference Book, Vol. 1: Fundamentals of Material Fracture Mechanics (Naukova Dumka, Kiev, 1988) [in Russian].Google Scholar
  2. 2.
    X.-K. Zhu and J. A. Joyce, “Review of Fracture Toughness (G, K, J, CTOD, CTOA) Testing and Standardization,” Eng. Fracture Mech. 85, 1–46 (2012).CrossRefGoogle Scholar
  3. 3.
    F. Berto and P. Lazzarin, “Recent Developments in Brittle and Quasi-Brittle Failure Assessment of Engineering Materials by Means of Local Approaches,” Mater. Sci. Eng. R 75, 1–48 (2014).CrossRefGoogle Scholar
  4. 4.
    M. Ya. Leonov and V. V. Panasyuk, “Development of the Smallest Cracks in Solids,” Prikl. Mekh. 5 (4), 391–401 (1959).Google Scholar
  5. 5.
    D. S. Dugdale, “Yielding of Steel Sheets Containing Slits,” J. Mech. Phys. Solids 8, 100–104 (1960).ADSCrossRefGoogle Scholar
  6. 6.
    G. Neuber, Kerbspannunglehre: Grunglagen fur Genaue Spannungsrechnung (Springer-Verlag, Berlin, 1937).CrossRefGoogle Scholar
  7. 7.
    V. V. Novozhilov, “On the Necessary and Sufficient Criterion of Brittle Strength,” Prikl. Mat. Mekh. 33 (2), 212–222 (1969).Google Scholar
  8. 8.
    V. D. Kurguzov and V. M. Kornev, “Construction of Quasi-Brittle and Quasi-Ductile Fracture Diagrams Based on Necessary and Sufficient Criteria,” Prikl. Mekh. Tekh. Fiz. 54 (1), 179–195 (2013) [J. Appl. Mech. Tech. Phys. 54 (1), 156–170 (2013)].MATHGoogle Scholar
  9. 9.
    I. M. Kershtein, V. D. Klyushnikov, E. V. Lomakin, and S. A. Shesterikov, Fundamentals of Experimental Fracture Mechanics (Izd. Mosk. Gos. Univ., Moscow, 1989) [in Russian].Google Scholar
  10. 10.
    V. M. Kornev, “Assessment Diagram of Quasi-Brittle Fracture of Bodies with a Hierarchy of Structures. Multiscale Necessary and Sufficient Criteria of Fracture,” Fiz. Mezomekh. 13 (1), 47–59 (2010).Google Scholar
  11. 11.
    V. M. Kornev and A. G. Demeshkin, “Quasi-Brittle Fracture Diagram of Structured Bodies in the Presence of Edge Cracks,” Prikl. Mekh. Tekh. Fiz. 52 (6), 152–164 (2011) [J. Appl. Mech. Tech. Phys. 52 (6), 975–985 (2011)].MATHGoogle Scholar
  12. 12.
    M. P. Savruk, Fracture Mechanics and Material Strength: Reference Book, Vol. 2: Stress Intensity Factors in Cracked Bodies (Naukova Dumka, Kiev, 1988) [in Russian].Google Scholar
  13. 13.
    Stress Intensity Factors Handbook, Ed. by Y. Murakami (Pergamon Press, Oxford, 1986).Google Scholar
  14. 14.
    V. M. Kornev, “Diagrams of Quasi-Brittle Fracture of Bent Structural Elements with Cracks,” Probl. Mashinostr. Nadezh. Mashin, No. 2, 38–46 (2015).Google Scholar
  15. 15.
    S. E. Kovchik and E. M. Morozov, Fracture Mechanics and Material Strength: Reference Book, Vol. 3: Characteristics of Short-Time Fracture Toughness of Materials and Methods of their Determination (Naukova Dumka, Kiev, 1988) [in Russian].Google Scholar
  16. 16.
    V. M. Kornev, “Critical Fracture Curves and Effective Diameter of the Structure of Brittle and Quasi-Brittle Materials,” Fiz. Mezomekh. 16 (5), 25–34 (2013).Google Scholar
  17. 17.
    V. M. Kornev, “Fracture Diagrams for Bodies with Short Microcracks. Embrittlement of the Material during Fatigue Fracture,” Fiz. Mezomekh. 19 (2), 80–99 (2016).Google Scholar
  18. 18.
    M. Eleces, G. V. Guinea, J. Gomez, and J. Planas, “The Cohesive Zone Model: Advantages, Limitations and Challenges,” Eng. Fracture Mech. 69, 137–163 (2002).CrossRefGoogle Scholar
  19. 19.
    G. I. Barenblatt, “Mathematical Theory of Equilibrium Cracks Formed during Brittle Fracture,” Prikl. Mekh. Tekh. Fiz., No. 4, 3–56 (1961).Google Scholar
  20. 20.
    V. Z. Parton and E. M. Morozov, Elastoplastic Fracture Mechanics: Fundamentals of Fracture Mechanics (Izd. LKI, 2008) [in Russian].Google Scholar
  21. 21.
    V. M. Kornev and N. S. Astapov, “Model of Fracture of a Piecewise–HomogeneousMedium during Delamination of Elastoplastic Structured Materials,” Mekh. Kompoz. Mater. Konstr. 16 (3), 347–360 (2010).Google Scholar
  22. 22.
    V. M. Kornev, V. D. Kurguzov, and N. S. Astapov, “Fracture Model of Bimaterial under Delamination of Elasto-Plastic Structured Media,” Appl. Compos. Mater. 20 (2), 129–143 (2013).ADSCrossRefGoogle Scholar
  23. 23.
    A. G. Demeshkin, V. M. Kornev, and N. S. Astapov, “Strength of a Glued Composite with Crack-Type Defects,” Mekh. Kompoz. Mater. Konstr. 19 (3), 445–458 (2013).Google Scholar
  24. 24.
    V. M. Kornev, “Delamination of Bimaterial and Critical Curves of Quasi-Brittle Fracture in the Presence of Edge Cracks,” Adv. Materials Sci. Appl. 3 (4), 164–176 (2014).Google Scholar
  25. 25.
    N. S. Astapov, V. D. Kurguzov, and V.M. Kornev, “Modeling of Bimaterial Delamination Induced by Transverse Shear,” Mekh. Kompoz. Mater. Konstr. 22 (1), 40–53 (2016).Google Scholar
  26. 26.
    N. S. Astapov, V. M. Kornev, and V. D. Kurguzov, “Model of Delamination of a Cracked Bimaterial with Different Moduli,” Fiz. Mezomekh. 19 (4), 49–57 (2016).Google Scholar
  27. 27.
    M. M. Shakirtov, A. P. Shabanov, and V. M. Kornev, “Construction of Fracture Diagrams for Plates with a Crack-Like Cut with the Use of Necessary and Sufficient Criteria,” Prikl. Mekh. Tekh. Fiz. 54 (2), 163–170 (2013) [J. Appl. Mech. Tech. Phys. 54 (2), 308–314 (2013)].MATHGoogle Scholar
  28. 28.
    V. M. Kornev, “Quasi-Brittle Fracture Diagrams due to Fatigue (Two-Frequency Loading),” Fiz. Mezomekh. 15 (6), 45–58 (2012).Google Scholar
  29. 29.
    V. M. Kornev, “Quasi-Brittle Fracture Diagrams under Low-Cycle Fatigue (Variable Amplitude Loadings),” Eng. Failure Anal. 35, 533–544 (2013).CrossRefGoogle Scholar
  30. 30.
    A. Yu. Larichkin, V. M. Kornev, and A. G. Demeshkin, “Changes in Plasticity Regions and Damage Accumulation in the Course of Crack Propagation in Quasi-Brittle Materials under Low-Cycle Loading,” Fiz. Mezomekh. 19 (4), 38–48 (2016).Google Scholar
  31. 31.
    V. M. Kornev, “Diagrams of Quasi-Brittle Fracture ofWelded Joints under Low-Cyclic Fatigue Loading,” Mekh. Kompoz. Mater. Konstr. 19 (4), 568–581 (2013).MathSciNetGoogle Scholar
  32. 32.
    V. M. Kornev, “Damage Accumulation and Fracture of Welded Joints under Low-Cyclic Loading Conditions,” Appl. Mech. Mater. 784, 179–189 (2015).CrossRefGoogle Scholar
  33. 33.
    O. N. Romaniv, S. Ya. Yarema, G. N. Nikiforchin, N. A. Makhutov, and M. M. Stadnik, Fracture Mechanics and Material Strength: Reference Book, Vol. 4: Fatigue and Cyclic Fracture Toughness of Structural Materials (Naukova Dumka, Kiev, 1990) [in Russian].Google Scholar
  34. 34.
    V. V. Bolotin, Mechanics of Fatigue (CRC Press, Boka Raton, London, 1998).Google Scholar

Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  1. 1.Lavrent’ev Institute of Hydrodynamics, Siberian BranchRussian Academy of SciencesNovosibirskRussia

Personalised recommendations