Skip to main content
SpringerLink
Log in

Refined Engineering Theory of Fracture with a Two-Parameter Strength Criterion

  • Published:
Physical Mesomechanics Aims and scope Submit manuscript

Abstract

We present a refined engineering theory of cracks based on a two-parameter strength criterion. Unlike the basic theory, the refined approach utilizes an improved algorithm for the regular stress component computation. This improvement allows extending the engineering theory to longer cracks. The two-parameter Leonov–Panasyuk–Dugdale fracture criterion serves as a basis. A coupled fracture criterion includes a strain-based criterion, which is formulated at the tip of the true crack, as well as a stress-based criterion, formulated at the tip of the fictitious crack. Based on the refined criterion, quasi-brittle fracture curves are constructed for a compact specimen, a strip with an edge crack, and a four-point bending beam. To validate the new refined fracture criterion, we present simulation results of quasi-brittle fracture for structures made from various virtual materials. The corresponding virtual materials are modeled using a nonlocal damage theory accounting for the average size of the aggregate state of the material. Additionally, various classes of damage accumulation hypotheses are considered. Analysis of various types of virtual materials provides insights into the impact of hypotheses behind the engineering theory. For each type of material, the influence of the microstructural length scale on the overall structural strength is investigated. The analysis shows that the refined engineering theory has a wider range of applicability as compared to the basic theory based on two-parameter strength criteria.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1.
Fig. 2.
Fig. 3.
Fig. 4.
Fig. 5.
Fig. 6.
Fig. 7.
Fig. 8.
Fig. 9.
Fig. 10.
Fig. 11.
Fig. 12.

Similar content being viewed by others

REFERENCES

  1. 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. https://doi.org/10.1016/j.mser.2013.11.001

    Article  Google Scholar 

  2. Newman, J.C., James, M.A., and Zerbst, U., A Review of the CTOA/CTOD Fracture Criterion, Eng. Fract. Mech., 2003, vol. 70, pp. 371–385. https://doi.org/10.1016/S0013-7944(02)00125-X

    Article  Google Scholar 

  3. Zhu, X.K. and Joyce, J.A., Review of Fracture Toughness (G, K, J, CTOD, CTOA) Testing and Standardization, Eng. Fract. Mech., 2012, vol. 85, pp. 1–46. https://doi.org/10.1016/j.engfracmech.2012.02.001

  4. Leguillon, D., Strength or Toughness? A Criterion for Crack Onset at a Notch, Eur. J. Mech. A. Solids, 2002, vol. 21, no. 1, pp. 61–72. https://doi.org/10.1016/S0997-7538(01)01184-6

    Article  ADS  Google Scholar 

  5. Weissgraeber, P., Leguillon, D., and Becker, W., A Review of Finite Fracture Mechanics: Crack Initiation at Singular and Non-Singular Stress Raisers, Arch. Appl. Mech., 2016, vol. 86, no. 1, pp. 375–401. https://doi.org/10.1007/s00419-015-1091-7

    Article  ADS  Google Scholar 

  6. Zhu, X.K. and Chao, Y.J., Specimen Size Requirements for Two-Parameter Fracture Toughness Testing, Int. J. Fract., 2005, vol. 135, no. 1, pp. 117–136. https://doi.org/10.1007/s10704-005-3946-3

    Article  Google Scholar 

  7. Meliani, M.H., Matvienko, Y.G., and Pluvinage, G., Two-Parameter Fracture Criterion (K, ρ, cTef, c) Based on Notch Fracture Mechanics, Int. J. Fract., 2011, vol. 167, no. 2, pp. 173–182. https://doi.org/10.1007/s10704-010-9542-1

  8. Newman, J.C.Jr. and Newman III, J.C., Validation of the Two-Parameter Fracture Criterion Using Finite-Element Analyses with the Critical CTOA Fracture Criterion, Eng. Fract. Mech., 2015, vol. 136, pp. 131–141. https://doi.org/10.1016/j.engfracmech.2015.01.021

    Article  Google Scholar 

  9. Warren, J.M., Lacy, T., and Newman, J.C.Jr., Validation of the Two-Parameter Fracture Criterion Using 3D Finite-Element Analyses with the Critical CTOA Fracture Criterion, Eng. Fract. Mech., 2016, vol. 151, pp. 130–137. https://doi.org/10.1016/j.engfracmech.2015.11.007

    Article  Google Scholar 

  10. Kornev, V.M., Evaluation Diagram for Quasibrittle Fracture of Solids with Structural Hierarchy. Necessary and Sufficient Multiscale Fracture Criteria, Fiz. Mezomekh., 2010, vol. 13, no. 1, pp. 47–59.

    Google Scholar 

  11. Kornev, V.M. and Demeshkin, A.G., Quasi-Brittle Fracture Diagram of Structured Bodies in the Presence of Edge Cracks, J. Appl. Mech. Tech. Phys., 2011, vol. 52, pp. 975–985. https://doi.org/10.1134/S0021894411060162

    Article  ADS  Google Scholar 

  12. Kornev, V.M., Critical Fracture Curves and Effective Structure Diameter for Brittle and Quasibrittle Materials, Fiz. Mezomekh., 2013, vol. 16, no. 5, pp. 25–34. https://doi.org/10.24411/1683-805X-2013-00050

    Article  Google Scholar 

  13. Leonov, M.Ya. and Panasyuk, V.V., Propagation of Tiny Cracks in a Solid, Prikl. Mekh., 1959, vol. 5, no. 4, pp. 391–401.

    Google Scholar 

  14. Dugdale, D.S., Yielding of Steel Sheets Containing Slits, J. Mech. Phys. Solids, 1960, vol. 8, no. 2, pp. 100–104. https://doi.org/10.1016/0022-5096(60)90013-2

    Article  ADS  Google Scholar 

  15. Neuber, G., Kerbspannunglehre: Grunglagen fur Genaue Spannungsrechnung, Berlin: Springer-Verlag, 1937.

  16. Novozhilov, V.V., On a Necessary and Sufficient Criterion for Brittle Strength, PMM, 1969, vol. 33, no. 2, pp. 212–222. https://doi.org/10.1016/0021-8928(69)90025-2

    Article  Google Scholar 

  17. Gurson, A.L., Continuum Theory of Ductile Rupture by Void Nucleation and Growth: Part I—Yield Criteria and Flow Rules for Porous Ductile Media, J. Eng Mater. Technol., 1977, vol. 99, no. 1, pp. 2–15. https://doi.org/10.1115/1.3443401

    Article  Google Scholar 

  18. Tvergaard, V. and Needleman, A., Analysis of the Cup-Cone Fracture in a Round Tensile Bar, Acta Metallurg., 1984, vol. 32, no. 1, pp. 157–169. https://doi.org/10.1016/0001-6160(84)90213-X

    Article  Google Scholar 

  19. Shutov, A.V., Silbermann, C.B., and Ihlemann, J., Ductile Damage Model for Metal Forming Simulations Including Refined Description of Void Nucleation, Int. J. Plasticity, 2015, vol. 71, pp. 195–217. https://doi.org/10.1016/0001-6160(84)90213-X

    Article  Google Scholar 

  20. Bazant, Z.P. and Jirasek, M., Nonlocal Integral Formulations of Plasticity and Damage: Survey of Progress, J. Eng. Mech., 2002, vol. 128, no. 11, pp. 1119–1149. https://doi.org/10.1061/(ASCE)0733-9399(2002)128:11(111

    Article  Google Scholar 

  21. Shutov, A.V. and Klyuchantsev, V.S., Large Strain Integral-Based Nonlocal Simulation of Ductile Damage with Application to Mode-I Fracture, Int. J. Plasticity, 2021, vol. 144, p. 103061. https://doi.org/10.1016/j.ijplas.2021.103061

    Article  Google Scholar 

  22. Klyuchancev, V.S. and Shutov, A.V., Nonlocal FEM Simulations of Ductile Damage with Regularized Crack Path Predictions, IOP J. Phys. Conf. Ser., 2021, vol. 1945, no. 1, p. 012018. https://doi.org/10.1088/1742-6596/1945/1/012018

    Article  Google Scholar 

  23. Shutov, A.V. and Klyuchantsev, V.S., Integral-Based Averaging with Spatial Symmetries for Nonlocal Damage Modelling, ZAMM, 2023, vol. 103, no. 1, p. e202100434. https://doi.org/10.1002/zamm.202100434

  24. Kurguzov, V.D. and Kornev, V.M., Construction of Quasi-Brittle and Quasi-Ductile Fracture Diagrams Based on Necessary and Sufficient Criteria, J. Appl. Mech. Tech. Phys., 2013, vol. 54, pp. 156–169. https://doi.org/10.1134/S0021894413010197

    Article  ADS  Google Scholar 

  25. Stress Intensity Factors Handbook, vol. 1, Murakami, Y., Ed., Oxford: Pergamon Press, 1987.

  26. Rice, J.R., Mathematical Analysis in the Mechanics of Fracture, Fracture: An Advanced Treatise, vol. 2, in Mathematical Fundamentals, Liebowitz, H., Ed., New York: Academic Press, 1968, pp. 191–311.

  27. Shutov, A.V. and Klyuchantsev, V.S., Geometrically Exact Integral-Based Nonlocal Model of Ductile Damage: Numerical Treatment and Validation, in 16th International Conference on Computational Plasticity: Fundamentals and Applications, COMPLAS 2021, 2021.

  28. Andrade, F.X.C., César de Sá, J.M.A., and Andrade Pires, F.M., A Ductile Damage Nonlocal Model of Integral-Type at Finite Strains: Formulation and Numerical Issues, Int. J. Damage Mech., 2011, vol. 20, no. 4, pp. 515–557. https://doi.org/10.1177/1056789510386850

    Article  Google Scholar 

  29. Eringen, A.C., Speziale, C.G., and Kim, B.S., Crack-Tip Problem in Non-Local Elasticity, J. Mech. Phys. Solids, 1977, vol. 25, no. 5, pp. 339–355. https://doi.org/10.1016/0022-5096(77)90002-3

    Article  MathSciNet  ADS  Google Scholar 

  30. Shlyannikov, V.N., Tumanov, A.V., and Khamidullin, R.M., Strain Gradient Effects at the Crack Tip under Plane Strain and Plane Stress Conditions, Phys. Mesomech., 2021, vol. 24, no. 3, pp. 257–268. https://doi.org/10.1134/S1029959921030048

    Article  Google Scholar 

  31. Deryugin, E.E., Crack Model with Plastic Strain Gradients, Phys. Mesomech., 2022, vol. 25, no. 3, pp. 227–247. https://doi.org/10.1134/S1029959922030043

  32. Wriggers, P., Nonlinear Finite Element Methods, Springer, 2008.

  33. Klyuchantsev, V.S. and Shutov, A.V. Comparative Analysis of Two Approaches to Nonlocal Modeling of Damage Accumulation, J. Eng. Phys. Thermophys., 2022, vol. 95, pp. 1634–1646. https://doi.org/10.1007/s10891-022-02632-6

    Article  Google Scholar 

  34. Lagarias, J.C., Reeds, J.A., Wright, M.N., and Wright, P.E., Convergence Properties of the Nelder–Mead Simplex Method in Low Dimensions, SIAM J. Optimization, 1998, vol. 9, no. 1, pp. 112–147. https://doi.org/10.1137/S105262349630347

    Article  Google Scholar 

  35. Kornev, V.M. and Kurguzov, V.D., Multiparameter Sufficient Criterion of Quasi-Brittle Strength under Complex Stress, Fiz. Mezomekh., 2006, vol. 9, no. 5, pp. 43–52.

    Google Scholar 

  36. Kurguzov, V.D., Kornev, V.M., and Astapov, N.S., Fracture Model of Bi-Material under Exfoliation. Numerical Experiment, Mekh. Komp. Mat. Struct., 2011, vol. 17, no. 4, pp. 462–473. https://doi.org/10.1007/s10443-012-9259-6

    Article  Google Scholar 

  37. Mirza, M.S., Barton, D.C., and Church, P., The Effect of Stress Triaxiality and Strain-Rate on the Fracture Characteristics of Ductile Metals, J. Mater. Sci., 1996, vol. 31, no. 2, pp. 453–461. https://doi.org/10.1007/BF01139164

    Article  ADS  Google Scholar 

  38. Mirone, G. and Corallo, D., A Local Viewpoint for Evaluating the Influence of Stress Triaxiality and Lode Angle on Ductile Failure and Hardening, Int. J. Plasticity, 2010, vol. 26, no. 3, pp. 348–371. https://doi.org/10.1016/j.ijplas.2009.07.006

    Article  Google Scholar 

  39. Huang, J., Guo, Ya., Qin, D., Zhou, Zh., Li, D., and Li, Yu., Influence of Stress Triaxiality on the Failure Behavior of Ti-6Al-4V Alloy under a Broad Range of Strain Rates, Theor. Appl. Fract. Mech., 2018, vol. 97, pp. 48–61. https://doi.org/10.1016/j.tafmec.2018.07.008

    Article  Google Scholar 

  40. Suknev, S.V., Nonlocal and Gradient Fracture Criteria for Quasi-Brittle Materials under Compression, Phys. Mesomech., 2019, vol. 22, no. 6, pp. 504–513. https://doi.org/10.1134/S1029959919060079

    Article  Google Scholar 

  41. Cooper, A.J., Tuck, O.C.G., Burnett, T.L., and Sherry, A.H., A Statistical Assessment of Ductile Damage in 304L Stainless Steel Resolved Using X-Ray Computed Tomography, Mater. Sci. Eng. A, 2018, vol. 728, pp. 218–230. https://doi.org/10.1016/j.msea.2018.05.036

    Article  Google Scholar 

  42. Croom, B.P., Jin, H., Noell, Ph.J., Boyce, B.L., and Li, X., Collaborative Ductile Rupture Mechanisms of High-Purity Copper Identified by In Situ X-Ray Computed Tomography, Acta Mater., 2019, vol. 181, pp. 377–384. https://doi.org/10.1016/j.actamat.2019.10.005

    Article  ADS  Google Scholar 

  43. Kornev, V.M., Kurguzov, V.D., and Astapov, N.S., Fracture Model of Bimaterial under Delamination of Elasto-Plastic Structured Media, Appl. Composite Mater., 2013, vol. 20, no. 2, pp. 129–143. https://doi.org/10.1007/s10443-012-9259-6

    Article  ADS  Google Scholar 

  44. Bazant, Z.P. and Lin, F.B., Non-Local Yield Limit Degradation, Int. J. Numer. Meth. Eng., 1988, vol. 26, no. 8, pp. 1805–1823. https://doi.org/10.1002/nme.1620260809

    Article  Google Scholar 

Download references

Funding

The work was granted by the Ministry of Science and Higher Education of the Russian Federation, Project No. 075-15-2020-781.

Author information

Authors and Affiliations

  1. Lavrentyev Institute of Hydrodynamics, Siberian Branch, Russian Academy of Sciences, 630090, Novosibirsk, Russia

    V. S. Klyuchantsev, V. D. Kurguzov & A. V. Shutov

Authors
  1. V. S. Klyuchantsev
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. V. D. Kurguzov
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. A. V. Shutov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. V. Shutov.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Klyuchantsev, V.S., Kurguzov, V.D. & Shutov, A.V. Refined Engineering Theory of Fracture with a Two-Parameter Strength Criterion. Phys Mesomech 26, 542–556 (2023). https://doi.org/10.1134/S1029959923050077

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1029959923050077

Keywords:

Search

Navigation