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Research Papers

# Some Analytical Solutions of the Kamal Equation for Isothermal Curing With Applications to Composite Patch Repair

[+] Author and Article Information
G. J. Tsamasphyros

Department of Theoretical and Applied Mechanics, School of Applied Mathematics and Physical Sciences, National Technical University of Athens, 9 Iroon Polytechniou Street, Zografou Campus, 15773 Athens, Greecetsamasph@central.ntua.gr

Th. K. Papathanassiou1

Department of Theoretical and Applied Mechanics, School of Applied Mathematics and Physical Sciences, National Technical University of Athens, 9 Iroon Polytechniou Street, Zografou Campus, 15773 Athens, Greecethpapath@lycos.com

S. I. Markolefas

Department of Theoretical and Applied Mechanics, School of Applied Mathematics and Physical Sciences, National Technical University of Athens, 9 Iroon Polytechniou Street, Zografou Campus, 15773 Athens, Greecemarkos34@gmail.com

1

Corresponding author.

J. Eng. Mater. Technol 131(1), 011008 (Dec 17, 2008) (7 pages) doi:10.1115/1.3026550 History: Received February 11, 2008; Revised September 05, 2008; Published December 17, 2008

## Abstract

In this paper, we derive some analytical solutions of the Kamal cure rate differential equation. The Kamal model is a first order quasilinear ordinary differential equation, describing the progress of the curing reaction of several thermosetting polymers. All the examined cases refer to isothermal curing processes. The solutions obtained in this paper are all of implicit form. The derived solutions are applied to a repair technique based on the adhesive bonding of polymer matrix composite patches onto damaged or corroded areas. Critical duration times of realistic cure cycles corresponding to composite patch repair are estimated. The practical importance of the proposed analytic solutions is demonstrated through the presented engineering application.

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## Figures

Figure 3

Comparison of the exact solution with a fourth order Runge–Kutta scheme for m=0.5, n=1.5, and k1=k2=0.01

Figure 4

Comparison of exact and numerical solutions for m=0.5, n=1.5 (fourth order RK, Δt=0.02)

Figure 5

Comparison of exact and numerical solutions for m=0.5, n=1.5, and k1=k2=6.4314

Figure 1

Typical curing cycle for CPR

Figure 2

Plateau time needed for 95% cure with respect to k variance

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