Abstract
Low-density foams have to possess a sufficient resistance to cracking in order to ensure the mechanical integrity of foam materials in service, even when not intended for load-bearing applications. In this study, mode I fracture toughness in the foam rise direction has been experimentally characterized for anisotropic rigid commercial polyurethane foams as well as for polyisocyanurate foams produced using polyols derived from rapeseed oil and filled with a montmorillonite nanoclay. Rectangular parallelepiped unit-cell based scaling relations expressing foam toughness via its relative density, cell dimensions, geometrical anisotropy, and the ultimate tensile stress of the base polymer have been employed for prediction of foam toughness. Assuming a brittle fracture of foam struts, a conservative estimate of toughness is obtained. It is demonstrated that considering the yielding of foam struts at the crack front as the criterion of crack extension provides a closer estimate of foam toughness.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Andersons J, Spārniņš E, Cābulis U, Stirna U (2013) Fracture toughness of PIR foams produced from renewable resources. Key Eng Mater 525–526:29–32
Andersons J, Kirpluks M, Stiebra L, Cabulis U (2016) Anisotropy of the stiffness and strength of rigid low-density closed-cell PIR foams. Mater Des 92:836–845
Arakere NK, Knudsen EC, Wells D, McGill P, Swanson GR (2008) Determination of mixed-mode stress intensity factors, fracture toughness, and crack turning angle for anisotropic foam material. Int J Solids Struct 45:4936–4951
Bednarcyk BA, Aboudi J, Arnold SM, Sullivan RM (2008) Analysis of space shuttle external tank spray-on foam insulation with internal pore pressure. J Eng Mater-T ASME 130:041005
Beverte I (2014) Determination of highly porous plastic foam structural characteristics by processing light microscopy images data. J Appl Polym Sci 131:39477
Cabulis U, Sevastyanova I, Andersons J, Beverte I (2014) Rapeseed oil-based rigid polyisocyanurate foams modified with nanoparticles of various type. Polimery 59:207–212
Dawson JR, Shortall JB (1982) The microstructure of rigid polyurethane foams. J Mater Sci 17:220–224
Ganpatye AS, Kinra VK (2006) Fracture toughness of space shuttle external tank insulation foam. In: 47th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, Newport, Rhode Island. doi:10.2514/6.2006-2020
Gibson LJ, Ashby MF (1997) Cellular solids: structure and properties. Cambridge University Press, Cambridge
Huber AT, Gibson LJ (1988) Anisotropy of foams. J Mater Sci 23:3031–3040
Kim HS, Chun MS, Lee JM, Kim MH (2013) A comparative evaluation of fatigue and fracture characteristics of structural components of liquefied natural gas carrier insulation system. J Press Vess -T ASME 135:021405
Kirpluks M, Cābulis U, Kurańska M, Prociak A (2013) Three different approaches for polyol synthesis from rapeseed oil. Key Eng Mater 559:69–74
Kraus B, Das R, Banrjee B (2014) Characterization of an anisotropic low-density closed-cell polyurethane foam. Parresia Research Limited Report #20151007CI.01. doi:10.13140/RG.2.1.2971.2088
Lee J-R, Dhital D (2013) Review of flaws and damages in space launch vehicle: structures. J Intel Mater Syst Struct 24:4–20
Linul E, Marsavina L (2011) Prediction of fracture toughness for open cell polyurethane foams by finite-element micromechanical analysis. Iran Polym J 20:735–746
Maiti SK, Ashby MF, Gibson LJ (1984) Fracture toughness of brittle cellular solids. Scr Metall 18:213–217
Marsavina L, Linul E, Sadowski T, Constantinescu DM, Knec M, Apostol D (2012) On fracture toughness of polyurethane foams. In: Proc. of the 19th European Conf. on Fracture, Kazan, Russia
Pardo-Alonso S, Solórzano E, Estravís S, Rodríguez-Perez MA, de Saja JA (2012) In situ evidence of the nanoparticle nucleating effect in polyurethane-nanoclay foamed systems. Soft Matter 8:11262–11270
Petrović ZS (2008) Polyurethanes from vegetable oils. Polym Rev 4:109–155
Saenz EE, Carlsson LA, Karlsson AM (2011) In situ analysis of crack propagation in polymer foams. J Mater Sci 46:5487–5494
Stirna U, Beverte I, Yakushin V, Cabulis U (2013) Polyurethane and polyisocyanurate foams in external tank cryogenic insulation. In: Kalia S, Fu S-Y (eds) Polymers at cryogenic temperatures. Springer, Berlin, pp 203–244
Sullivan RM, Ghosn LJ, Lercht BA (2009) Application of an elongated Kelvin model to space shuttle foams. J Spacecr Rocket 46:411–418
Szycher M (1999) Szycher’s handbook of polyurethanes. CRC Press, Boca Raton
Workman GL, Davis J, Farrington S, Spalding C, Walker JL (2007) Development of natural flaw samples for evaluating nondestructive testing methods for foam thermal protection systems. In: IV Conferencia Panamericana de END, Buenos Aires, Argentina, 22–26 Oct 2007
Yu YH, Kim BG, Lee DG (2013) Cryogenic reliability of the sandwich insulation board for LNG ship. Compos Struct 95:547–556
Zieleniewska M, Leszczyński MK, Kurańska M, Prociak A, Szczepkowski L, Krzyżowska M, Ryszkowska J (2015) Preparation and characterisation of rigid polyurethane foams using a rapeseed oil-based polyol. Ind Crop Prod 74:887–897
Acknowledgements
The research has been funded, in part, by the EU Commission through FP7 Project EVOLUTION-314744 and the ERDF via project 2010/0290/2DP/2.1.1.1.0/10/APIA/VIAA/053.
Author information
Authors and Affiliations
Corresponding author
Electronic supplementary material
Below is the link to the electronic supplementary material.
Rights and permissions
About this article
Cite this article
Andersons, J., Cābulis, U., Stiebra, L. et al. Modeling the mode I fracture toughness of anisotropic low-density rigid PUR and PIR foams. Int J Fract 205, 111–118 (2017). https://doi.org/10.1007/s10704-017-0194-2
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10704-017-0194-2