Аннотації

ОСОБЛИВОСТІ ВИКОРИСТАННЯ ІНТЕГРАЛІВ, НЕЗАЛЕЖНИХ ВІД КОНТУРУ ІНТЕГРУВАННЯ, В ЗАДАЧАХ МЕХАНІКИ РУЙНУВАННЯ

Автор(и):
Баженов В.А., Вабіщевич М.О., Солодей І.І.
Автор(и) (англ)
Bazhenov Viktor, Vabischevich Maksim, Solodei Ivan
Дата публікації:

10.10.2019

Анотація (укр):

Протягом останніх десятиліть J-інтеграл Черепанова – Райса вважаєтсья основним енергетичним критерієм тріщиностійкості для розв’язання задач механіки руйнування. Цей параметр успішно застосовується при розгляді пружних задач та в межах деформаційної теорії пластичності для стаціонарних тріщин. На жаль, теоретична основа, на якій базується J-інтеграл не дає змогу поширити його використання для розв'язку задач, що потребують врахування неоднорідності матеріалу, наявності температурних впливів, довільної історії навантаження, масових сил, розвитку тріщин тощо.

Анотація (рус):

В течение последних десятилетий J-интеграл Черепанова – Райса считается основным энергетическим критерием трещиностойкости при решении задач механики разрушения. Этот параметр успешно применяется при рассмотрении упругих задач и в пределах деформационной теории пластичности для стационарных трещин. К сожалению, теоретическая основа, на которой базируется J-интеграл не позволяет распространить его использование для решения задач, требующих учета неоднородности материала, наличия температурных воздействий, произвольной истории нагрузки, массовых сил, развития трещин и т. п.

Анотація (англ):

In recent decades, the Cherepanov-Rice J-integral has been considered to be the main energy criterion for fracture toughness in solving the problems of fracture mechanics. This parameter is successfully used in the consideration of elastic problems and within the framework of deformation theory of plasticity for stationary cracks. Unfortunately, the theoretical basis on which the J-integral is based does not allow it to be extended to solve problems requiring material inhomogeneity, the presence of temperature influences, an arbitrary load history, mass forces, crack development, and the like. The purpose of the paper is to review other integrals independent of the contour of integration, from the point of view of their theoretical justification, the possibility of experimentally determined and the ease of calculation. The article considers the J-integral, integrals of Wilson-Yu, Gurtins, Blackburn, Kishimoto, Ainsworth, Atluri.

Література:

  1. Rice, J.R. A Path-Independent Integral and the Approximate Analysis of Strain Concentration by Notches and Cracks // Journal of Applied Mechanics, Vol. 35, 1968, pp 379-386.
  2. Eshelby, J.D. The Continuum Theory of Lattice Defects // Solid State Physics, Vol. III, Academic Press, New York, 1956, pp 79-144.
  3. Sanders, J.L., Jr. On the Griffith-Irwin Fracture Theory // Journal of Applied Mechanics, Vol. 27, 1960, pp 352-353.
  4. Cherepanov, G.P. Crack Propagation in Continuous Media // PMM, Vol. 31, No. 3, 1967, pp 476-488.
  5. Knowles, J.K. On A Class of Conservation Laws in Linearized and Finite Elastostatics / Sternberg, E. // Archive for Rational Mechanics and Analysis, Vol. 44, 1972, pp 187-211.
  6. Green, A.E. On Some General Formulae in Finite Elastostatics // Archive for Rational Mechanics and Analysis, Vol. 50, 1973, pp 73-80.
  7. Chen, F.H.K. Conservation Laws in Elasticity of the J-Integral Type / Shield, R.T. // Journal of Applied Mathematics and Physics, Vol. 28, 1977, pp 1-22.
  8. Smelser, R.E. 0n the J-Integral for Bi-Material Bodies / Gurtin, M.E.// International Journal of Fracture, Vol. 13, 1977, pp 382-284.
  9. McMeeking, R.M. Finite Deformation Analysis of Crack-Tip Opening in Elastic-Plastic Materials and Implications for Fracture // Journal of the Mechanics and Physics of Solids, Vol. 25, 1977, pp 357-381.
  10. Dowling, N.E. Crack Growth During Low Cycle Fatigue of Smooth Axial Specimens, // ASTM STP 637, 1977, 97-121.
  11. Kaisand, L.R. Relationships Between Low-Cycle Fatigue and Fatigue Crack Growth Rate Properties / Mowbray, D.F. // Journal of Testing and Evaluation, Vol. 7, No. 5, 1979, pp 270-280.
  12. Rice, J.R. Mathematical Analysis in the Mechanics of Fracture // Fracture, Vol. 2, Ed. H. Liebowitz, Academic Press, 1971, pp 191-311.
  13. Dowling, N.E. A Fatigue Crack Growth During Gross Plasticity and the J-Integral / Begley, J.A.// Mechanics of Crack Growth, ASTM STP 590, 1976, pp 82-103.
  14. Wilson, W.K. The Use of the J-Integral in Thermal Stress Crack Problems / Yu, I.W. // International Journal of Fracture, Vol. 15, 1979, pp 377-387.
  15. Nguyen, Q.S. A Thermodynamic Description of the Running Crack Problem // Proc. of IUTAM Symposium on Three-Dimensional Constitutive Relations and Ductile Fracture, North-Holland Publishing Company, 1981, pp 315-330.
  16. Germain, P. Continuum Thermodynamics / Nguyen, Q.S., Suquet, P. // Journal of Applied Mechanics, Vol. 50, 1983, PP 1010-1020.
  17. Gurtin, M.E. On a Path-Independent Integral for Thermoelasticity // International Journal of Fracture, Vol. 15, 1979, pp R169 – R170.
  18. Read, D.T. Strain Dependence of the J-Contour Integral in Tensile Panels / McHenry, H.I. // Proc. of the 5th International Conference on Fracture, Cannes, France, 1981, pp 1715-1722.
  19. Ainsworth, R.A. Fracture Behavior in the Presence of Thermal Strains / Neale, B.K., Price, R.H. // Proceedings of Institute of Mechanical Engineers' Conference on Tolerance of Flaws in Pressurized Components, London, 1978, pp 171-178.
  20. Blackburn, W.S. Path-Independent Integrals to Predict Onset of Crack Instability In An Elastic Material // International Journal of Fracture Mechanics, Vol. 8, 1972, pp 343-346.
  21. Blackburn, W.S. An Integral Associated with the State of a Crack Tip in a Non-Elastic Material / Jackson, A.D. // International Journal of Fracture, Vol. 13, 1977, pp 183-200.
  22. Kishimoto, K. 0n the Path-Independent Integral-J / Aoki, S., Sakata, M. // Engineering Fracture Mechanics, Vol. 13, 1980, pp 841-850.
  23. Aoki, S. Elastic-Plastic Analysis of Crack in Thermally-Loaded Structures / Kishimoto, K., Sakata, M. // Engineering Fracture Mechanics, Vol. 16, 1982, pp 405-413.
  24. Atluri, S.N. Path-Independent Integrals in Finite Elasticity and Inelasticity, with Body Forces, Inertia, and Arbitrary Crack – Face Conditions // Engineering Fracture Mechanics, Vol. 16, 1982, pp 341-364.
  25. Atluri, S.N. Incremental Path-Indepen dent Integrals in Inelastic and Dynamic Fracture Mechanics / Nishioka, T., Nakagaki, M. // Georgia Institute of Technology Report GIT-CACM-SNA-83-27, May 1983
  26. Nakagaki, M. On the Path Independent Integral, AT , in Elastic—Plastic Fracture Mechanics / Atluri, S.N., Nishioka, T. // SECTAM XII Conference, Pine Mountain, Georgia, May 1984.

References:

  1. Rice, J.R. (1968). A Path-Independent Integral and the Approximate Analysis of Strain Concentration by Notches and Cracks. Journal of Applied Mechanics, 35, 379-386.
  2. Eshelby, J.D. (1956). The Continuum Theory of Lattice Defects. Solid State Physics, III, 79-144.
  3. Sanders, J.L., Jr. (1960). On the Griffith-Irwin Fracture Theory. Journal of Applied Mechanics, 27, 352-353.
  4. Cherepanov, G.P. (1967). Crack Propagation in Continuous Media. PMM, 31, 3, 476-488.
  5. Knowles, J.K. & Sternberg, E. (1972). On A Class of Conservation Laws in Linearized and Finite Elastostatics. Archive for Rational Mechanics and Analysis, 44, 187-211.
  6. Green, A.E. (1973). On Some General Formulae in Finite Elastostatics. Archive for Rational Mechanics and Analysis, 50, 73-80.
  7. Chen, F.H.K. & Shield, R.T. (1977). Conservation Laws in Elasticity of the J-Integral Type. Journal of Applied Mathematics and Physics, 28, 1-22.
  8. Smelser, R.E. & Gurtin, M.E. (1977). 0n the J—Integral for Bi-Material Bodies. International Journal of Fracture, 13, 382-284.
  9. McMeeking, R.M. (1977). Finite Deformation Analysis of Crack-Tip Opening in Elastic-Plastic Materials and Implications for Fracture. Journal of the Mechanics and Physics of Solids, 25, 357-381.
  10. Dowling, N.E. (1977). Crack Growth During Low Cycle Fatigue of Smooth Axial Specimens. ASTM STP, 637, 97-121.
  11. Kaisand, L.R. & Mowbray, D.F. (1979). Relationships Between Low-Cycle Fatigue and Fatigue Crack Growth Rate Properties. Journal of Testing and Evaluation, 7, 5, 270-280.
  12. Rice, J.R. (1971). Mathematical Analysis in the Mechanics of Fracture. Fracture, 2, 191-311.
  13. Dowling, N.E. & Begley, J.A. (1976). A Fatigue Crack Growth During Gross Plasticity and the J-Integral. Mechanics of Crack Growth. ASTM STP, 590, 82-103.
  14. Wilson, W.K. & Yu, I.W. (1979). The Use of the J-Integral in Thermal Stress Crack Problems. International Journal of Fracture, 15, 377-387.
  15. Nguyen, Q.S. (1981). A Thermodynamic Description of the Running Crack Problem. Proc. of IUTAM Symposium on Three-Dimensional Constitutive Relations and Ductile Fracture, North-Holland Publishing Company, pp 315-330.
  16. Germain, P., Nguyen, Q.S., Suquet, P. (1983). Continuum Thermodynamics. Journal of Applied Mechanics, 50, 1010-1020.
  17. Gurtin, M.E. (1979). On a Path-Independent Integral for Thermoelasticity. International Journal of Fracture, 15, R169—R170.
  18. Read, D.T. & McHenry, H.I. (1981). Strain Dependence of the J-Contour Integral in Tensile Panels. Proc. of the 5th International Conference on Fracture, Cannes, France, pp 1715-1722.
  19. Ainsworth, R.A., Neale, B.K., Price, R.H. (1978). Fracture Behavior in the Presence of Thermal Strains. Proceedings of Institute of Mechanical Engineers' Conference on Tolerance of Flaws in Pressurized Components, London, pp 171-178.
  20. Blackburn, W.S. (1972). Path-Independent Integrals to Predict Onset of Crack Instability In An Elastic Material. International Journal of Fracture Mechanics, 8, 343-346.
  21. Blackburn, W.S. & Jackson, A.D. (1977). An Integral Associated with the State of a Crack Tip in a Non-Elastic Material. International Journal of Fracture, 13, 183-200.
  22. Kishimoto, K., Aoki, S., Sakata, M. (1980). 0n the Path-Independent Integral-J. Engineering Fracture Mechanics, 13, 841-850.
  23. Aoki, S., Kishimoto, K., Sakata, M. (1982). Elastic-Plastic Analysis of Crack in Thermally-Loaded Structures. Engineering Fracture Mechanics, 16, 405-413.
  24. Atluri, S.N. (1982). Path-Independent Integrals in Finite Elasticity and Inelasticity, with Body Forces, Inertia, and Arbitrary Crack—Face Conditions. Engineering Fracture Mechanics, 16, 341-364.
  25. Atluri, S.N., Nishioka, T., Nakagaki, M. (1983). Incremental Path-Indepen dent Integrals in Inelastic and Dynamic Fracture Mechanics. Georgia Institute of Technology Report GIT-CACM-SNA-83-27, May 1983
  26. Nakagaki, M., Atluri, S.N., Nishioka, T. (1984). On the Path Independent Integral, AT, in Elastic—Plastic Fracture Mechanics. SECTAM XII Conference, Pine Mountain, Georgia, May 1984.