Simulation of thin films delamination under compression
DOI:
https://doi.org/10.7242/1999-6691/2014.7.10Keywords:
thin films, delamination, elastic foundation, buckling, nonlinear strainsAbstract
Processes of elastic deformation of thin films under mechanical loading conditions are considered. A film is modeled as a longitudinally compressed beam with a small-area of initial delamination of the film from the initial film carrier. The compressive buckling problem of a beam partially fixed on the elastic foundation is solved. Bending strains of the beam are considered to be small; therefore the approximate differential equation of the bending line of a beam is used. The gluing conditions for the solution of both the delaminated beam and the beam on the elastic foundation have been defined. The post-buckling behavior of the “beam - foundation” system has been studied. The forms of beam buckling within the constant factor have been derived when exceeding the Euler critical loading by a compressive force takes place. Comparison of the proposed deformation model of a beam partially glued on the elastic foundation with the numerical solution of the buckling problem of a thin plate fixed on the elastic foundation obtained in the geometrically nonlinear statement by the finite element method shows the qualitative agreement between these solutions. The computer simulation shows a possibility for progressive delamination of a thin film from the film carrier when exceeding a critical loading. In contrast to the currently available approaches, the proposed one takes into consideration the elastic strain of a film carrier that provides the relationship of critical bending stress versus foundation stiffness.
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Feldman L., Majer D. Osnovy analiza poverhnosti i tonkih plenok. - M.: Mir, 1989. - 344 s.
2. Freund L.B., Suresh S. Thin film materials: stress, defect formation and surface evolution. - Cambridge: Cambridge University Press, 2003. - 750 p.
3. Janssen G.C.A.M., Dammers A.J., Sivel V.G.M., Wang W.R. Tensile stress in hard metal films // Appl. Phys. Lett. - 2003. - Vol. 83, No. 16. - P. 3287-3289. DOI
4. Panin A.V., Sugurov A.R., Srajber U., Oskomov K.V. Osobennosti plasticeskoj deformacii i razrusenia tonkih metalliceskih plenok pri termiceskom i mehaniceskom nagruzenii // Fiz. mezomeh. - 2004. - T. 7, No S1-1. - S. 142-145.
5. Panin A.V., Sugurov A.R., Oskomov K.V., Sidorenko A.I. Mezomehanika povedenia tonkih plenok Cu na podlozke pri odnoosnom rastazenii i termiceskom otzige. Mnogourovnevyj podhod // Fiz. mezomeh. - 2005. - T. 8, No 4. - S. 27-35.
6. Panin V.E., Panin A.V., Sergeev V.P., Sugurov A.R. Effekty skejlinga v strukturno-fazovoj samoorganizacii na interfejse <> // Fiz. mezomeh. - 2007. - T. 10, No 3. - S. 9-21.
7. Nix W.D. Mechanical properties of thin films // Metall. Trans. A. - 1989. - Vsd. 20, No. 11. - P. 2217-2245. DOI
8. Smith U., Kristensen N., Ericson F., Schweitz J.-A. Local stress relaxation phenomena in thin aluminum films // J. Vac. Sci. Technol. A. - 1991. - Vol. 9, No. 4. - P. 2527-2535. DOI
9. Cherepanov G.P. On the theory of thermal stresses in a thin bonding layer // J. Appl. Phys. - 1995. - Vol. 78. - P. 6826-6832. DOI
10. Vinci R.P., Zielinski E.M., Bravman J.C. Thermal strain and stress in copper thin films // Thin Solid Films. - 1995. - Vol. 262, No. 1-2. - P. 142-153. DOI
11. Vol’mir A.S. Ustojcivost’ deformiruemyh sistem. - M.: Nauka, 1967. - 984 s.
12. Sugurov A.R., Panin A.V. Mehanizmy periodiceskoj deformacii sistemy <> pod dejstviem szimausih naprazenij // Fiz. mezomeh. - 2009. - T. 12, No 3. - S. 23-32.
13. Wang E.Z., Shrive N.G. Brittle fracture in compression: Mechanisms, models and criteria // Eng. Fract. Mech. - 1995. - Vol. 52, No. 6. - P. 1107-1126. DOI
14. Asinskij F.S. O soprotivlenii prodol’nomu izgibu / F.S. Asinskij. Izbrannye raboty po ustojcivosti szatyh sterznej. - M.-L.: Gostehizdat, 1952. - S. 11-137.
15. Asinskij F.S. Opyt razvitia teorii prodol’nogo izgiba / F.S. Asinskij. Izbrannye raboty po ustojcivosti szatyh sterznej. - M.-L.: Gostehizdat, 1952. - S. 138-194.
16. Vlasov V.Z., Leont’ev N.N. Balki, plity i obolocki na uprugom osnovanii. - M.: Fizmatgiz, 1960. - 492 s.
17. Astapov I.S., Astapov N.S., Vasil’eva E.L. Kvadraticnaa approksimacia bol’sih peremesenij gibkogo szatogo sterzna // MTT. - 2003. - No 1. - S. 164-171.
18. Aleksandrov V.M. Ustojcivost’ sistemy pokrytie-podlozka pri prodol’nom szatii pokrytia // MTT. - 2001. - No 4. - S. 76-79.
19. Aleksandrov V.M., Zarubov D.I. Ustojcivost’ beskonecnoj plity pri prodol’nom szatii na neszimaemom prednaprazennom silami tazesti uprugom poluprostranstve // MTT. - 2006. - No 6. - S. 61-70.
20. Tvergaard V., Needleman A. On the localization of buckling patterns // J. Appl. Mech. - 1980. - Vol. 47, No. 3. - P. 613-619. DOI
21. Astapov N.S., Demeskin A.G., Kornev V.M. Vypucivanie sterzna, lezasego na uprugom osnovanii // PMTF. - 1994. - T. 35, No 5. - S. 106-112. DOI
22. Astapov N.S., Kornev V.M. Vypucivanie ekscentricno szatogo uprugogo sterzna // PMTF. - 1996. - T. 37, No 2. - S. 162-169. DOI
23. Panayotounakos D.E. Non-linear and buckling analysis of bars lying on an elastic foundation // Int. J. Nonlinear Mech. - 1989. - Vol. 24, No. 4. - P. 295-307. DOI
24. Waas A.M. Initial postbuckling behavior of beams on non-linear elastic foundations // Mech. Res. Commun. - 1990. - Vol. 17, No. 4. - P. 239-248. DOI
25. Vallabhan C.V.G., Das Y.C. A refined model for beams on elastic foundations // Int. J. Solids Struct. - 1991. - Vol. 27, No. 5. - P. 629-637. DOI
26. Astapov N.S., Kornev V.M. Zakriticeskoe povedenie ideal’nogo sterzna na uprugom osnovanii // PMTF. - 1994. - T. 35, No 2. - S. 130-142. DOI
27. Astapov N.S. Priblizennoe predstavlenie formy szatogo gibkogo sterzna // PMTF. - 1999. - T. 40, No 3. - S. 200-203. DOI
28. Korobejnikov S.N. Nelinejnoe deformirovanie tverdyh tel. - Novosibirsk: Izd-vo SO RAN, 2000. - 262 s.
29. MARC Users Guide. Vol. A: Theory and Users Information. - Santa Ana (CA): MSC.Software Corporation, 2012. - 813 p.
30. Cotterell B., Chen Z. Buckling and cracking of thin films on compliant substrates under compression // Int. J. Fracture. - 2000. - Vol. 104, No. 2. - P. 169-179. DOI
31. Yu H.-H., Hutchinson J.W. Influence of substrate compliance on buckling delamination of thin films // Int. J. Fracture. - 2002. - Vol. 113, No. 1. - P. 39-55. DOI
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