Abstract
Polyimides, due to their superior mechanical behavior at high temperatures, are used in a variety of applications that include aerospace, automobile and electronic packaging industries, as matrices for composites, as adhesives etc. In this paper, we extend our previous model in S. Karra and K. Rajagopal (Mech. Mater. 43(1):54–61, 2011), to include thermo-oxidative degradation of these high temperature polyimides. Appropriate forms for the Helmholtz potential and the rate of dissipation are chosen to describe the degradation. The results for a specific boundary value problem, using our model, compares well with the experimental creep data for PMR-15 resin that is aged in air.
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Notes
In general, it is the mapping from the tangent space at a material point in κ p(t) to the tangent space at the same material point in κ t .
The standard method in continuum mechanics to obtain constraints appeals to the notion that the constraint response does not work. It has been shown recently by Rajagopal and Srinivasa (2005) that such an assumption is in general incorrect.
The term dissipation is used to refer to the mechanical working being converted into energy in thermal form, and associated with this dissipation we have entropy production. We shall abuse the use of the term dissipation and refer to other entropy producing mechanism such as degradation as also dissipation.
References
Baek, S., Pence, T.J.: On swelling induced degradation of fiber reinforced polymers. Int. J. Eng. Sci. 47(11–12), 1100–1109 (2009)
Björnbom, P.H.: The independent reactions in calculations of complex chemical equilibria. Ind. Eng. Chem. Fundam. 14(2), 102–106 (1975)
Bowen, R.M.: On the stoichiometry of chemically reacting materials. Arch. Ration. Mech. Anal. 29(2), 114–124 (1968a)
Bowen, R.M.: Thermochemistry of reacting materials. J. Chem. Phys. 49, 1625–1637 (1968b)
Bowles, K.J., Papadopoulos, D.S., Inghram, L.L., McCorkle, L.S., Klan, O.V.: Longtime durability of PMR-15 matrix polymer at 204, 260, 288 and 316°C. Technical report 210602, NASA (2001)
Bowles, K.J., Tsuji, L., Kamvouris, J., Roberts, G.D.: Long-term isothermal aging effects on weight loss, compression properties, and dimensions of T650-35 fabric-reinforced PMR-15 composites–data. Technical report 211870, NASA (2003)
de Donder, T., Van Rysselberghe, P.: Thermodynamic Theory of Affinity. Stanford University Press, Palo Alto (1936)
Falcone, C.M., Ruggles-Wrenn, M.B.: Rate dependence and short-term creep behavior of a thermoset polymer at elevated temperature. J. Press. Vessel Technol. 131(011403), 1–8 (2009)
Fishtik, I., Datta, R.: De Donder relations in mechanistic and kinetic analysis of heterogeneous catalytic reactions. Ind. Eng. Chem. Res. 40(11), 2416–2427 (2001)
Germain, P., Suquet, P., Nguyen, Q.S.: Continuum thermodynamics. J. Appl. Mech. 50(4), 1010–1020 (1983)
Kannan, K., Rajagopal, K.R.: A thermodynamical framework for chemically reacting systems. Z. Angew. Math. Phys. 62(2), 331–363 (2011)
Karra, S.: Diffusion of a fluid through a viscoelastic solid (2010). arXiv:1010.3488
Karra, S., Rajagopal, K.: Modeling the non-linear viscoelastic response of high temperature polyimides. Mech. Mater. 43(1), 54–61 (2011)
Nunziato, J.W., Walsh, E.K.: On ideal multiphase mixtures with chemical reactions and diffusion. Arch. Ration. Mech. Anal. 73(4), 285–311 (1980)
Pekar, M.: Thermodynamics and foundations of mass-action kinetics. Prog. React. Kinet. Mech. 30(1–2), 3–113 (2005)
Pochiraju, K., Tandon, G.P.: Interaction of oxidation and damage in high temperature polymeric matrix composites. Composites, Part A, Appl. Sci. Manuf. 40(12), 1931–1940 (2009)
Prigogine, I.: Introduction to Thermodynamics of Irreversible Processes. Wiley, New York (1967)
Rajagopal, K.R., Srinivasa, A.R.: On the thermomechanics of materials that have multiple natural configurations. Part I. Viscoelasticity and classical plasticity. Z. Angew. Math. Phys. 55(5), 861–893 (2004)
Rajagopal, K.R., Srinivasa, A.R.: On the nature of constraints for continua undergoing dissipative processes. Proc. R. Soc., Math. Phys. Eng. Sci. 461(2061), 2785–2795 (2005)
Rajagopal, K.R., Tao, L.: Mechanics of Mixtures. World Scientific, Singapore (1995)
Rajagopal, K.R., Srinivasa, A.R., Wineman, A.S.: On the shear and bending of a degrading polymer beam. Int. J. Plast. 23(9), 1618–1636 (2007)
Roy, S., Singh, S., Schoeppner, G.A.: Modeling of evolving damage in high temperature polymer matrix composites subjected to thermal oxidation. J. Mater. Sci. 43(20), 6651–6660 (2008)
Ruggles-Wrenn, M.B., Broeckert, J.L.: Effects of prior aging at 288°C in air and in argon environments on creep response of PMR-15 neat resin. J. Appl. Polym. Sci., Appl. Polym. Symp. 111(1), 228–236 (2009)
Samohỳl, I.: Thermodynamics of reacting mixtures of any symmetry with heat conduction, diffusion and viscosity. Arch. Ration. Mech. Anal. 147(1), 1–45 (1999)
Tandon, G.P., Pochiraju, K.V., Schoeppner, G.A.: Modeling of oxidative development in PMR-15 resin. Polym. Degrad. Stab. 91(8), 1861–1869 (2006)
Van Rysselberghe, P.: Reaction rates and affinities. J. Chem. Phys. 29, 640–642 (1958)
Zeleznik, F.J., Gordon, S.: Calculation of complex chemical equilibria. Ind. Eng. Chem. 60(6), 27–57 (1968)
Acknowledgements
The authors thank AFOSR/AFRL for supporting this work. Part of this work was done when Satish Karra was appointed as a lecturer during his Ph.D. by the Department of Mechanical Engineering at Texas A&M University. He appreciates this support by the department.
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Karra, S., Rajagopal, K.R. A model for the thermo-oxidative degradation of polyimides. Mech Time-Depend Mater 16, 329–342 (2012). https://doi.org/10.1007/s11043-011-9165-6
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DOI: https://doi.org/10.1007/s11043-011-9165-6