Top

Continuum Mechanics and Thermodynamics

Published in:

22-06-2021 | Original Article

Evaluation of stress intensity factors under thermal effect employing domain integral method and ordinary state based peridynamic theory

Authors: Hanlin Wang, Satoyuki Tanaka, Selda Oterkus, Erkan Oterkus

Published in: Continuum Mechanics and Thermodynamics | Issue 3/2023

Activate our intelligent search to find suitable subject content or patents.

search-config

AI-assisted search

Off

Abstract

In this article, several thermoelastic benchmark cases are studied within the framework of ordinary state based peridynamic theory (OSPD). By using OSPD, the limitations of geometrical discontinuity in fracture analysis can be overcome. Meanwhile, double nodes can also be avoided during crack definition. A domain integral method with thermal effect is applied in calculating the thermal stress intensity factors (TSIFs). Meanwhile, peridynamic differential operators are utilized to rewrite the spatial derivatives in the domain integral. Numerical investigations of TSIFs in the single and mixed-mode crack scenarios are provided respectively, and verified by the reference solutions. Good agreements between OSPD and the reference solutions show high performance and capability of the proposed method in thermoelastic fracture analysis.

previous article Civil engineering applications of the Asymptotic Expansion Load Decomposition beam model: an overview

next article Coupled phase field and nonlocal integral elasticity analysis of stress-induced martensitic transformations at the nanoscale: boundary effects, limitations and contradictions

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 390 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Maschinenbau + Werkstoffe

Jetzt Wissensvorsprung sichern!

inform now

Irwin, G.R.: Analysis of stress and strains near the end of a crack traversing a plate. ASME J. Appl. Mech. 24(3), 361–364 (1957)ADS

Rice, J.R.: A path independent integral and the approximate analysis of strain concentration by notches and cracks. ASME J. Appl. Mech. 35, 379–386 (1968)ADS

Chen, Y.M.: Numerical computation of dynamic stress intensity factors by a Lagrangian finite-difference method (the HEMP code). Eng. Fract. Mech. 7(4), 653–660 (1975)

Stern, M., Becker, E.B., Dunham, R.S.: A contour integral computation of mixed-mode stress intensity factors. Int. J. Fract. 12(3), 359–368 (1976)

Yau, J.F., Wang, S.S., Corten, H.T.: A mixed-mode crack analysis of isotropic solids using conservation laws of elasticity. ASME J. Appl. Mech. 47, 335–341 (1980)ADSMATH

Yu, H., Wu, L., Guo, L., Du, S., He, Q.: Investigation of mixed-mode stress intensity factors for nonhomogeneous materials using an interaction integral method. Int. J. Solids Struct. 46(20), 3710–3724 (1980)MATH

Song, S.H., Paulino, G.H.: Dynamic stress intensity factors for homogeneous and smoothly heterogeneous materials using the interaction integral method. Int. J. Solids Struct. 43(12), 4830–4866 (1980)MATH

Kim, J.H., Paulino, G.H.: Consistent formulations of the interaction integral method for fracture of functionally graded materials. ASME J. Appl. Mech. 72(3), 351–364 (2005)ADSMATH

Zamani, A., Eslami, M.R.: Implementation of the extended finite element method for dynamic thermoelastic fracture initiation. Int. J. Solids Struct. 47(6), 1392–1404 (2010)MATH

10.

Duflot, M.: The extended finite element method in thermoelastic fracture mechanics. Int. J. Numer. Methods Eng. 74(5), 827–847 (2008)MathSciNetMATH

11.

Nguyen, M.N., Bui, T.Q., Nguyen, N.T., Truong, T.T.: Simulation of dynamic and static thermoelastic fracture problems by extended nodal gradient finite elements. Int. J. Mech. Sci. 134, 370–386 (2017)

12.

Hosseini-Tehrani, P., Hosseini-Godarzi, A.R., Tavangar, M.: Boundary element analysis of stress intensity factor K\(_{\rm I}\) in some two-dimensional dynamic thermoelastic problems. Eng. Anal. Bound. Elem. 29(3), 232–240 (2005)MATH

13.

Reddy, J.N.: An Introduction to Continuum Mechanics. Cambridge University Press, Cambridge (2013)

14.

Hellan, K.: Introduction to Fracture Mechanics. McGraw-Hill, New York (1984)

15.

Hillerborg, A., Modéer, M., Petersson, P.E.: Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements. Cem. Concr. Res. 6(6), 773–781 (1976)

16.

Xu, X.P., Needleman, A.: Numerical simulations of fast crack growth in brittle solids. J. Mech. Phys. Solids 42(5), 1397–1434 (1994)ADSMATH

17.

Nguyen, T.T., Yvonnet, J., Bornert, M., Chateau, C., Sab, K., Romani, R., Le Roy, R.: On the choice of parameters in the phase field method for simulating crack initiation with experimental validation. Int. J. Fract. 197(2), 213–226 (2016)

18.

Gomez, H., van der Zee, K.G.: Computational Phase-field Modeling. Encyclopedia of Computational Mechanics, 2nd edn, pp. 1–35 (2018)

19.

Tanaka, S., Suzuki, H., Sadamoto, S., Sannomaru, S., Yu, T., Bui, T.Q.: J-integral evaluation for 2D mixed-mode crack problems employing a meshfree stabilized conforming nodal integration method. Comput. Mech. 58, 185–198 (2016)MathSciNetMATH

20.

Tanaka, S., Suzuki, H., Sadamoto, S., Imachi, M., Bui, T.Q.: Analysis of cracked shear deformable plates by an effective meshfree plate formulation. Eng. Fract. Mech. 144, 142–157 (2015)

21.

Tanaka, S., Suzuki, H., Sadamoto, S., Okazawa, S., Yu, T.T., Bui, T.Q.: Accurate evaluation of mixed-mode intensity factors of cracked shear-deformable plates by an enriched meshfree Galerkin formulation. Arch. Appl. Mech. 87(2), 279–298 (2017)ADS

22.

Pant, M., Singh, I.V., Mishra, B.K.: Numerical simulation of thermo-elastic fracture problems using element free Galerkin method. Int. J. Mech. Sci. 52(8), 1745–1755 (2010)

23.

Dell’Isola, F., Andreaus, U., Placidi, L.: At the origins and in the vanguard of peridynamics, non-local and higher-gradient continuum mechanics: an underestimated and still topical contribution of Gabrio Piola. Math. Mech. Solids 20(4), 887–928 (2015)MathSciNetMATH

24.

Silling, S.A.: Reformulation of elasticity theory for discontinuities and long-range forces. J. Mech. Phys. Solids 48(1), 175–209 (2000)MathSciNetADSMATH

25.

Imachi, M., Tanaka, S., Bui, T.Q.: Mixed-mode dynamic stress intensity factors evaluation using ordinary state-based peridynamics. Theor. Appl. Fract. Mech. 93, 97–104 (2018)

26.

Dai, M.J., Tanaka, S., Oterkus, S., Oterkus, E.: Mixed-mode stress intensity factors evaluation of flat shells under in-plane loading employing ordinary state-based peridynamics. Theor. Appl. Fract. Mech. 102841 (2020)

27.

Dai, M.J., Tanaka, S., Bui, T.Q., Oterkus, S., Oterkus, E.: Fracture parameter analysis of flat shells under out-of-plane loading using ordinary state-based peridynamics. Eng. Fract. Mech. 244, 107560 (2021)

28.

Oterkus, S., Madenci, E., Agwai, A.: Fully coupled peridynamic thermomechanics. J. Mech. Phys. Solids 64, 1–23 (2014)MathSciNetADSMATH

29.

Madenci, E., Oterkus, S.: Ordinary state-based peridynamics for thermoviscoelastic deformation. Eng. Fract. Mech. 175, 31–45 (2017)

30.

Nguyen, C.T., Oterkus, S.: Peridynamics for the thermomechanical behavior of shell structures. Eng. Fract. Mech. 219, 106623 (2019)

31.

Ren, H., Zhuang, X., Rabczuk, T.: Dual-horizon peridynamics: a stable solution to varying horizons. Comput. Methods Appl. Mech. Eng. 318, 762–782 (2017)MathSciNetADSMATH

32.

Dorduncu, M., Borut, A., Madenci, E.: Ordinary-state based peridynamic truss element. In: 56th AIAA/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, 0465 (2015)

33.

Silling, S.A., Epton, M., Weckner, O., Xu, J., Askari, E.: Peridynamic states and constitutive modeling. J. Elast. 88(2), 151–184 (2007)MathSciNetMATH

34.

Madenci, E., Oterkus, E.: Peridynamic Theory. Peridynamic Theory and Its Applications. Springer, New York (2014)MATH

35.

Solín, P.: Partial Differential Equations and the Finite Element Method. Wiley, New York

36.

Causon, D.M., Mingham, C.G.: Introductory Finite Difference Methods for PDEs. Bookboon (2010)

37.

Coleman, C.J., Tullock, D.L., Phan-Thien, N.: An effective boundary element method for inhomogeneous partial differential equations. Z. Angew. Math. Phys. ZAMP 42(5), 730–745 (1991)MathSciNetMATH

38.

Cho, H.A., Golberg, M.A., Muleshkov, A.S., Li, X.: Trefftz methods for time dependent partial differential equations. CMC Comput. Mater. Continua 1, 1–38 (2004)

39.

Madenci, E., Barut, A., Futch, M.: Peridynamic differential operator and its applications. Comput. Methods Appl. Mech. Eng. 304, 408–451 (2016)MathSciNetADSMATH

40.

Madenci, E., Dorduncu, M., Barut, A., Futch, M.: Numerical solution of linear and nonlinear partial differential equations using the peridynamic differential operator. Numer. Methods Partial Differ. Equ. 33(5), 1726–1753 (2017)MathSciNetMATH

41.

Madenci, E., Barut, A., Dorduncu, M.: Peridynamic Differential Operator for Numerical Analysis. Springer, Berlin (2019)MATH

42.

Wang, H.: Fracture Analysis in Marine Batteries by Peridynamic Theory. Doctoral dissertation, University of Strathclyde (2018)

43.

Wang, H., Oterkus, E., Oterkus, S.: Three-dimensional peridynamic model for predicting fracture evolution during the lithiation process. Energies 11(6), 1461 (2018)

44.

Wilson, W.K., Yu, I.W.: The use of the J-integral in thermal stress crack problems. Int. J. Fract. 15(4), 377–387 (1979)

45.

Fung, Y.C.: Foundations of Solid Mechanics. Prentice-Hall Inc, New Jersey (1965)

46.

Anderson, T.L.: Fracture Mechanics: Fundamentals and Applications. CRC Press, Boca Raton (2017)MATH

47.

Silling, S.A., Lehoucq, R.B.: Peridynamic theory of solid mechanics. Adv. Appl. Mech. 44, 73–168 (2010)

48.

Narasimhan, T.N.: Fourier’s heat conduction equation: history, influence, and connections. Rev. Geophys. 37(1), 151–172 (1999)ADS

49.

Underwood, P.: Dynamic Relaxation Computational Methods for Transient Analysis, vol. 1, 245–265. Elsevier Science Publishers B.V. (1983)

50.

Kilic, B., Madenci, E.: An adaptive dynamic relaxation method for quasi-static simulations using the peridynamic theory. Theor. Appl. Fract. Mech. 53(3), 194–204 (2010)

51.

Chen, H., Wang, Q., Liu, G.R., Wang, Y., Sun, J.: Simulation of thermoelastic crack problems using singular edge-based smoothed finite element method. Int. J. Mech. Sci. 115, 123–134 (2016)

52.

Prasad, N.N.V., Aliabadi, M.H., Rooke, D.P.: The dual boundary element method for thermoelastic crack problems. Int. J. Fract. 66(3), 255–272 (1994)ADS

53.

Zhou, Z., Leung, A.Y.T., Xu, X., Luo, X.: Mixed-mode thermal stress intensity factors from the finite element discretized symplectic method. Int. J. Solids Struct. 51(21–22), 3798–3806 (2014)

54.

Murkami, Y.: Stress Intensity Factor Handbook. Pergamon Press, New York (1987)

Title: Evaluation of stress intensity factors under thermal effect employing domain integral method and ordinary state based peridynamic theory
Authors: Hanlin Wang
Satoyuki Tanaka
Selda Oterkus
Erkan Oterkus
Publication date: 22-06-2021
Publisher: Springer Berlin Heidelberg
Published in: Continuum Mechanics and Thermodynamics / Issue 3/2023
Print ISSN: 0935-1175
Electronic ISSN: 1432-0959
DOI: https://doi.org/10.1007/s00161-021-01033-z

Springer Professional

Abstract

Please log in to get access to your license.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Springer Professional "Technik"

Other articles of this Issue 3/2023

Derivation of dual-horizon state-based peridynamics formulation based on Euler–Lagrange equation

Thermomechanics of Cosserat medium: modeling adiabatic shear bands in metals

Explicit nonlinear finite element approach to the Lagrangian-based coupled phase field and elasticity equations for nanoscale thermal- and stress-induced martensitic transformations

The distances measurement problem for an underwater robotic swarm: a semi-experimental trial, using power LEDs, in unknown sea water conditions

A comparative study of 1D nonlocal integral Timoshenko beam and 2D nonlocal integral elasticity theories for bending of nanoscale beams

A criterion for dynamic ductile fracture initiation of tensile mode

Premium Partners