Micromechanical Analysis of Lamina Ultimate Strengths in Composite Materials
Explore the micromechanical analysis of the ultimate strengths of a unidirectional lamina in composite materials. Derive formulas for transverse tensile and compressive strengths, and calculate the ultimate transverse compressive strength for a Glass/Epoxy lamina with 70% fiber volume fraction. Discover the stress-strain curve for a graphite/epoxy laminate under transverse compressive load and determine the ultimate shear strength for a Glass/Epoxy lamina with fiber volume fraction.
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Chapter 3 Micromechanical Analysis of a Lamina Ultimate Strengths of a Unidirectional Lamina Part 2 Dr. Autar Kaw Department of Mechanical Engineering University of South Florida, Tampa, FL 33620 Courtesy of the Textbook Mechanics of Composite Materials by Kaw
Remember for the transverse tensile strength formula derivation T 2 T 2 ( ( E = ) ) 2 ult ult d d E m T 2 T m ( ( = + - 1 ) ) ult ult s s E f Following same logic C 2 C 2 ( ( where , E = ult ) ) 2 ult E d d + C 2 C m ( 1 ( m = ) ) ult ult s E s f
Find the ultimate transverse compressive strength of a Glass/Epoxy lamina with 70% fiber volume fraction. Use the properties of glass and epoxy from Table 3.1 and Table 3.2, respectively. Assume the fibers are circular and are packed in a square array. , GPa 85 = E f d 0.9441 = s , = 3.4 GPa Em , = 10.37 GPa E2 C m ( , = ult 102 MPa ) 102 and 6 10 C m ( = ult ) 9 3.4 10 0.0300 =
E d d + C 2 C m ( 1 ( m = ) ) ult ult s E s f 9 3.4 10 C 2 ( 0.9441 - 1 ( ) 0.03 ( ) = ult 0.9441 + ) 9 85 10 2 - 0.2810 = 10 C 2 C 2 ( ( where , E = ult ) ) 2 ult C 2 9 -2 ( 10.37 ( 0.2810 )( = ) = ult ) 29.14 MPa 10 10
FIGURE 3.35 Stress strain curve for a [90]40 graphite/epoxy laminate under a transverse compressive load perpendicular to the fibers.
c = f + m where : ( = c s , ) 12 c ( and , d = f ) 12 f ( )( m = d - s ) 12 m
d d ( ( ( c = f + - 1 ) ) ) 12 12 12 m s s ( ( G m = m G ) ) f 12 12 f d d G m ( ( c = + - 1 ) ) 12 12 m s s G f d d G m ( ( = + - 1 ) ) G 12 12 ult m ult s s G ( f ( = ) ) 12 12 12 ult ult d d G m ( = + - 1 ) G 12 12 ult m s s G f
Find the ultimate shear strength for a Glass/Epoxy lamina with 70% fiber volume fraction. Use properties for glass and epoxy from Tables 3.1 and 3.2, respectively. Assume the fibers are circular and are arranged in a square array. GPa 35.42 = Gf GPa 1.308 = Gm 12 G = ( ( = ) ) G 12 12 12 ult ult d d G m ( + - 1 ) 4.014 10 12 ult m s s G 10 f 9 1.308 = 4.014 GPa G12 9 1 - ( ( ) 0.9441 - 1 ( ) 0.2599 ( ) = ult ) 0.9441 + 9 10 12 35.42 10 d 9.469 = MPa 0.9441 = s = ult m 12 ) ( 6 34 10 9 1.308 10 1 - 0.2599 = 10
x ( ) x ( and , ult = ult ) 45o 12 2 45o ( ( ( | = | | + | ) ) ) x y 12 ult ult ult x 45o Strain-Gage Rosette 45o 1 2 3 Schematic of a [ 45]2S laminate shear test.
= 5.566 GPa, G12 ( and = ult 87.57 MPa, ) 12 ( 2.619% = ult 12) Shear stress shear strain curve obtained from a [ 45]2S graphite/epoxy laminate under a tensile load.
