Residual Stress and Opening-Mode Fracture Analysis of Multilayered Structures Subjected to Thermal Loading
Publication: Journal of Engineering Mechanics
Volume 145, Issue 3
Abstract
Temperature change after formation commonly results in thermal residual stress in multilayered structures due to the different thermal and mechanical properties of each layer. In this paper, a three-dimensional (3D) elastic model is developed to study the residual stress and opening-mode fractures (OMFs) in a multilayered structure consisting of arbitrary number of layers under temperature change. The general solution of displacement field in the multilayered structure is derived by solving the elastic boundary value problem. In order to verify the proposed model, the elastic field in the advanced polymeric solar reflectors that consist of four layers is solved by applying the present model and compared with the finite-element (FE) simulation. In addition, parametric studies are conducted to investigate the effect of the thickness ratio between each layer on the accuracy of the developed model. Based on the obtained elastic field, the fracture energy release rate (ERR) in the surface layer of the advanced polymeric reflector is obtained and used to study the fracture initiation, infilling, and saturation successfully.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
This study was supported by the US Department of Energy under Contract No. DE-AC36-08-GO28308 with the National Renewable Energy Laboratory through the DOE SETP program and the US National Science Foundation under award No. 1738802 with the Center for Energy Harvesting Materials and Systems through NSF Industry/University Cooperative Research Center Program. The US Government retains, and the publisher, by accepting the article for publication, acknowledges that the US Government retains a nonexclusive, paid-up, irrevocable, worldwide license to publish or reproduce the published form of this study, or allow others to do so, for US Government purposes.
References
Ahmed, F., K. Bayerlein, S. Rosiwal, M. Göken, and K. Durst. 2011. “Stress evolution and cracking of crystalline diamond thin films on ductile titanium substrate: Analysis by micro-Raman spectroscopy and analytical modelling.” Acta Mater. 59 (14): 5422–5433. https://doi.org/10.1016/j.actamat.2011.05.015.
Askarinejad, S., P. Kotowski, S. Youssefian, and N. Rahbar. 2016. “Fracture and mixed-mode resistance curve behavior of bamboo.” Mech. Res. Commun. 78 (12): 79–85. https://doi.org/10.1016/j.mechrescom.2016.02.001.
Bai, T., and D. D. Pollard. 2000. “Spacing of fractures in a multilayer at fracture saturation.” Int. J. Fract. 100 (4): 23–28. https://doi.org/10.1023/A:1018748026019.
Bai, T., D. D. Pollard, and H. Gao. 2000a. “Explanation for fracture spacing in layered materials.” Nature 403 (6771): 753–756. https://doi.org/10.1038/35001550.
Bai, T., D. D. Pollard, and M. R. Gross. 2000b. “Mechanical prediction of fracture aperture in layered rocks.” J. Geophys. Res. Solid Earth 105 (B1): 707–721. https://doi.org/10.1029/1999JB900303.
Berry, B. 1989. “Anelastic relaxation and diffusion in thin-layer materials.” In Diffusion phenomena in thin films and microelectronic materials, 73–145. Yorktown Heights, NY : Noyes Data Corporation.
Beuth, J. 1992. “Cracking of thin bonded films in residual tension.” Int. J. Solids Struct. 29 (13): 1657–1675. https://doi.org/10.1016/0020-7683(92)90015-L.
Beuth, J., and N. Klingbeil. 1996. “Cracking of thin films bonded to elastic-plastic substrates.” J. Mech. Phys. Solids 44 (9): 1411–1428. https://doi.org/10.1016/0022-5096(96)00042-7.
Chai, H. 2011. “Channel cracking in inelastic film/substrate systems.” Int. J. Solids Struct. 48 (7): 1092–1100. https://doi.org/10.1016/j.ijsolstr.2010.12.014.
Chai, H., and J. Fox. 2012. “On delamination growth from channel cracks in thin-film coatings.” Int. J. Solids Struct. 49 (22): 3142–3147. https://doi.org/10.1016/j.ijsolstr.2012.06.012.
Chen, F., X. He, P. Prieto-Munoz, and H. Yin. 2015. “Opening-mode fractures of a brittle coating bonded to an elasto-plastic substrate.” Int. J. Plast. 67 (4): 171–191. https://doi.org/10.1016/j.ijplas.2014.10.007.
Çolak, A. 2001. “Parametric study of factors affecting the pull-out strength of steel rods bonded into precast concrete panels.” Int. J. Adhes. Adhes. 21 (6): 487–493. https://doi.org/10.1016/S0143-7496(01)00028-8.
DeGarmo, E. P., J. T. Black, R. A. Kohser, and B. E. Klamecki. 1997. Materials and process in manufacturing. London: Prentice Hall.
Evans, A., and J. Hutchinson. 1995. “The thermomechanical integrity of thin films and multilayers.” Acta Metall. Mater. 43 (7): 2507–2530. https://doi.org/10.1016/0956-7151(94)00444-M.
Freund, L. B., and S. Suresh. 2004. Thin film materials: Stress, defect formation and surface evolution. Cambridge, UK: Cambridge University Press.
Fu, Y., H. Du, W. Huang, S. Zhang, and M. Hu. 2004. “TiNi-based thin films in MEMS applications: A review.” Sens. Actuators, A 112 (2–3): 395–408. https://doi.org/10.1016/j.sna.2004.02.019.
Guo, C. F., T. Sun, Q. Liu, Z. Suo, and Z. Ren. 2014. “Highly stretchable and transparent nanomesh electrodes made by grain boundary lithography.” Nat. Commun. 5: 3121. https://doi.org/10.1038/ncomms4121.
He, X., F. Chen, and H. Yin. 2017. “Opening-mode micro-cracking in brittle coatings on ductile wires/rods.” Int. J. Damage Mech. 26 (1): 119–146. https://doi.org/10.1177/1056789516659330.
Hsueh, C., and M. Yanaka. 2003. “Multiple film cracking in film/substrate systems with residual stresses and unidirectional loading.” J. Mater. Sci. 38 (8): 1809–1817. https://doi.org/10.1023/A:1023200415364.
Hutchinson, J. W. 1996. Stresses and failure modes in thin films and multilayers. Lyngby, Denmark: Technical Univ. of Denmark.
Jorgensen, G., R. Gee, and M. DiGrazia. 2010. Development and testing of abrasion resistant hard coats for polymer film reflectors. Golden, CO: National Renewable Energy Libratory.
Kennedy, C., K. Terwilliger, and M. Milbourne. 2005. Development and testing of solar reflectors. Golden, CO: National Renewable Energy Libratory.
Li, J., and T.-W. Chou. 1997. “Elastic field of a thin-film/substrate system under an axisymmetric loading.” Int. J. Solids Struct. 34 (35–36): 4463–4478. https://doi.org/10.1016/S0020-7683(97)00053-X.
Ochiai, S., H. Okuda, S. Iwamoto, T. Tomida, T. Nakamura, M. Tanaka, and M. Hojo. 2005. “Multiple-cracking phenomenon of the galvannealed coating layer on steels under thermal and tensile stresses.” Metall. Mater. Trans. A 36 (7): 1807–1816. https://doi.org/10.1007/s11661-005-0044-0.
Ohring, M. 2001. Materials science of thin films. Hoboken, NJ: Academic Press.
Park, J. S., H. Chae, H. K. Chung, and S. I. Lee. 2011. “Thin film encapsulation for flexible AM-OLED: A review.” Semicond. Sci. Technol. 26 (3): 034001.
Roy, U., and C. Ghosh. 2016. “Residual stress analysis in galvannealed coating.” Ironmaking Steelmaking 43 (6): 465–472. https://doi.org/10.1080/03019233.2016.1142055.
Sansom, C., A. Fernández-García, F. Sutter, H. Almond, P. King, and L. Martnez-Arcos. 2016. “Soiling and cleaning of polymer film solar reflectors.” Energies 9 (12): 1006. https://doi.org/10.3390/en9121006.
Schwarzer, N., and F. Richter. 2006. “On the determination of film stress from substrate bending: Stoney’s formula and its limits.” Accessed April 1, 2018. https://monarch.qucosa.de/api/qucosa%3A18453/attachment/ATT-0/.
Stoney, G. G. 1909. “The tension of metallic films deposited by electrolysis.” Proc. R. Soc. London, Ser. A 82 (553): 172–175. https://doi.org/10.1098/rspa.1909.0021.
Suo, Z., and J. W. Hutchinson. 1989. “Steady-state cracking in brittle substrates beneath adherent films.” Int. J. Solids Struct. 25 (11): 1337–1353. https://doi.org/10.1016/0020-7683(89)90096-6.
Sutter, F., S. Ziegler, M. Schmücker, P. Heller, and R. Pitz-Paal. 2012. “Modelling of optical durability of enhanced aluminum solar reflectors.” Sol. Energy Mater. Sol. Cells 107 (11): 37–45. https://doi.org/10.1016/j.solmat.2012.07.027.
Thouless, M., Z. Li, N. Douville, and S. Takayama. 2011. “Periodic cracking of films supported on compliant substrates.” J. Mech. Phys. Solids 59 (9): 1927–1937. https://doi.org/10.1016/j.jmps.2011.04.009.
Timm, D., B. Guzina, and V. Voller. 2003. “Prediction of thermal crack spacing.” Int. J. Solids Struct. 40 (1): 125–142. https://doi.org/10.1016/S0020-7683(02)00496-1.
ToolBox. 2016. “The engineering toolbox.” Accessed April 1, 2018. https://www.engineeringtoolbox.com/.
Wellner, P., O. Kraft, G. Dehm, J. Andersons, and E. Arzt. 2004. “Channel cracking of -NiAl thin films on Si substrates.” Acta Mater. 52 (8): 2325–2336. https://doi.org/10.1016/j.actamat.2004.01.023.
Xia, Z. C., and J. W. Hutchinson. 2000. “Crack patterns in thin films.” J. Mech. Phys. Solids 48 (6): 1107–1131. https://doi.org/10.1016/S0022-5096(99)00081-2.
Ye, T., Z. Suo, and A. Evans. 1992. “Thin film cracking and the roles of substrate and interface.” Int. J. Solids Struct. 29 (21): 2639–2648. https://doi.org/10.1016/0020-7683(92)90227-K.
Yin, H. M. 2010a. “Fracture saturation and critical thickness in layered materials.” Int. J. Solids Struct. 47 (7): 1007–1015. https://doi.org/10.1016/j.ijsolstr.2009.12.016.
Yin, H. M. 2010b. “Opening-mode cracking in asphalt pavements: Crack initiation and saturation.” Road Mater. Pavement Des. 11 (2): 435–457. https://doi.org/10.1080/14680629.2010.9690283.
Yin, H. M., W. Buttlar, and G. H. Paulino. 2007a. “Simplified solution for periodic thermal discontinuities in asphalt overlays bonded to rigid pavements.” J. Transp. Eng. 133 (1): 39–46. https://doi.org/10.1061/(ASCE)0733-947X(2007)133:1(39).
Yin, H. M., G. Paulino, and W. Buttlar. 2008. “An explicit elastic solution for a brittle film with periodic cracks.” Int. J. Fract. 153 (1): 39–52. https://doi.org/10.1007/s10704-008-9286-3.
Yin, H. M., G. Paulino, W. Buttlar, and L. Sun. 2007c. “Micromechanics-based thermoelastic model for functionally graded particulate materials with particle interactions.” J. Mech. Phys. Solids 55 (1): 132–160. https://doi.org/10.1016/j.jmps.2006.05.002.
Yin, H. M., and P. A. Prieto-Muñoz. 2013. “Stress transfer through fully bonded interface of layered materials.” Mech. Mater. 62: 69–79. https://doi.org/10.1016/j.mechmat.2013.03.007.
Zhang, C., F. Chen, M. H. Gray, R. Tirawat, and R. E. Larsen. 2017. “An elasto-plastic solution for channel cracking of brittle coating on polymer substrate.” Int. J. Solids Struct. 120 (11): 125–136. https://doi.org/10.1016/j.ijsolstr.2017.04.033.
Zhang, C., M. H. Gray, R. Tirawat, R. E. Larsen, and F. Chen. 2016. Effects of UV aging on the cracking of titanium oxide layer on poly (ethylene terephthalate) substrate. Golden, CO: National Renewable Energy Laboratory.
Zhang, X., Y. Wu, B. Xu, and H. Wang. 2007. “Residual stresses in coating-based systems. Part I: Mechanisms and analytical modeling.” Front. Mech. Eng. China 2 (1): 1–12. https://doi.org/10.1007/s11465-007-0001-2.
Information & Authors
Information
Published In
Copyright
©2019 American Society of Civil Engineers.
History
Received: Apr 9, 2018
Accepted: Sep 4, 2018
Published online: Jan 14, 2019
Published in print: Mar 1, 2019
Discussion open until: Jun 14, 2019
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.