Micromechanical Analysis of Lamina Coefficients of Thermal Expansion
This chapter delves into the micromechanical analysis of lamina coefficients of thermal expansion in composite materials, specifically focusing on the Glass/Epoxy lamina with calculations and properties provided by Dr. Autar Kaw. The equations and diagrams presented offer insights into understanding thermal expansion behaviors within the composite lamina.
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Chapter 3 Micromechanical Analysis of a Lamina Coefficients of Thermal Expansion Dr. Autar Kaw Department of Mechanical Engineering University of South Florida, Tampa, FL 33620 Courtesy of the Textbook Mechanics of Composite Materials by Kaw
1 ( ) = 1 E f V f + f E m V m m E 1 2 = + (1 ) f V f + + (1 ) m V m - 1 f m 12
= 1 V f = 0 = A c V + f + f 0 = m F A A m 1 f m m where f : T ( and ) , E = f f f T ( ) E = m m m m V + E V E f f m f m m = f T E + f V V E E f m m = 1 T 1 V + E V f f m f m m = 1 E + f V V E f m m
V + E V E f f m f m m = 1 E + f V V E f m m 1 ( ) = 1 E f V + E m V m m f f E 1 E E V f E f V = + m E m 1 f m 1 1
?1= ? 1=1 ( ) ( ( )1 ( ) ( )1 f ( 1 = = E = = E m m m 1 f f 1 ) T ) m 1 ) T ) f ( m E E E 1 m m f f ( E ( ( ) ) = T f = 1 T m m 2 f f 2 m f ( ) ( ) = + V V ) 2 f f m m 2 2 ( E T 1 f f f = T V 2 f f E f ( ) E T + 1 m m m E T V m m m
2 = T 2 = + [ ( )] [ ( )] V V 2 1 1 f f f f m m m m = + V V 12 f f m m ( 1 ) ( ) = + + + 1 1 V V 2 12 f f f m m m
Find the coefficients of thermal expansion for a Glass/Epoxy lamina with 70% fiber volume fraction. Use the properties of glass and epoxy from Tables 3.1 and 3.2, respectively. GPa 85 = E f = m 0.3 -6 = m 63 m/m/ C = f 0.2 10 60.52 = E1 GPa. 10 6 0 5 = f m/m C / 0 = 12 0.230 = 3.4 GPa Em
1 ( ) = 1 E f V f + f E m V m m E 1 2 = + (1 ) f V f + + (1 ) m V m - 1 f m 12 6 6 6 + 1 ( ( ) ( ) + ) + 1 ( ( ) ( ) ) ( ( ) ) = 2 0.2 5.0 0.7 0.3 63 0.3 5.978 0.23 10 10 10 6 0 = 27.40 m/m C 10 /
Longitudinal and transverse coefficients of thermal expansion as a function of fiber volume fraction for a glass/epoxy unidirectional lamina.
FIGURE 3.39 Unidirectional graphite/epoxy specimen with strain gages and temperature sensors for finding coefficients of thermal expansion.
10 -6 0 and C, - = 1 1.3 m/m / 10 -6 0 = 2 33.9 m/m C / Induced strain as a function of temperature to find the coefficients of thermal expansion of a unidirectional graphite/epoxy laminate.
