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Research Papers

# Scaling Analysis and a Critical Thickness Criterion for Thermosetting Composites

[+] Author and Article Information
Thomas W. Secord

Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139

Susan C. Mantell, Kim A. Stelson

Department of Mechanical Engineering, University of Minnesota, Minneapolis, MN 55455

J. Manuf. Sci. Eng 133(1), 011005 (Jan 24, 2011) (6 pages) doi:10.1115/1.4003338 History: Received June 22, 2010; Revised November 26, 2010; Published January 24, 2011; Online January 24, 2011

## Abstract

In thermosetting composite manufacturing, part thickness, mold temperature, pressure, and resin kinetics can affect the uniformity of cure in the finished part. If the interaction of these parameters is not accounted for, then unwanted overshoot of the processing temperature can occur within a part during cure. In this paper, the relationship between processing and material parameters was considered to establish a critical thickness separating parts having large overshoots from parts having small overshoots. The one-dimensional heat equation with an autocatalytic relation for curing was used to model the process. The equations were placed in dimensionless form using a scaling analysis. A finite difference model was also created to calculate part temperatures during cure as a function of the key dimensionless groups. For experimental validation, composite plates of varying thickness were fabricated from a glass fiber prepreg material, and the processing conditions were varied according to thickness. The scaling analysis identified five dimensionless groups. Two of these groups were found to affect the overshoot of the temperature: the modified Damköhler number $Da∗$, which includes the heat generated during the reaction, and the dimensionless temperature ramp rate $t¯rise$, which describes the tooling temperature ramp rate relative to the natural time scale of the heat transfer. There was good agreement between the numerical model prediction of temperature overshoot and the experimental data. The results also confirm that the behavior of thin and thick parts, as defined by the relative temperature overshoot, can be well defined and predicted by the two proposed dimensionless groups: $Da∗$ and $t¯rise$.

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## Figures

Figure 1

Assumed processing cycle for model development

Figure 2

Composite centerline temperature compared with the tooling temperature

Figure 3

Comparison of theoretical and measured overshoots in composite

Figure 4

Contours of θ as a function of Da∗ and t¯rise

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