Pendahuluan Material Komposit BAB 3 Micromechanical Analysis of a Lamina Modulus Elastis Qomarul Hadi, ST,MT Teknik Mesin Universitas Sriwijaya Sumber Bacaan Mechanics of Composite Materials by Kaw

Strength of Materials Approach

Strength of Materials Approach

Strength of Materials Approach Gambar 3.3 Representative volume element of a unidirectional lamina.

Strength of Materials Approach Gambar 3.4 A longitudinal stress applied to the representative volume element to calculate the longitudinal Young’s modulus for a unidirectional lamina.

Longitudinal Young’s Modulus

Longitudinal Young’s Modulus

Longitudinal Young’s Modulus

Longitudinal Young’s Modulus Gambar 3.5 Fraction of load of composite carried by fibers as a function of fiber volume fraction for constant fiber to matrix moduli ratio.

Example Example 3.3 Find the longitudinal elastic modulus of a unidirectional Glass/Epoxy lamina with a 70% fiber volume fraction. Use the properties of glass and epoxy from Tables 3.1 and 3.2, respectively. Also, find the ratio of the load taken by the fibers to that of the composite.

Example Example 3.3 Ef = 85 Gpa Em = 3.4 GPa

Example Example 3.3 Gambar 3.6 Longitudinal Young’s modulus as function of fiber volume fraction and comparison with experimental data points for a typical glass/polyester lamina.

Example Example 3.3

Transverse Young’s Modulus Gambar 3.7 A transverse stress applied to a representative volume element used to calculate transverse Young’s modulus of a unidirectional lamina.

Transverse Young’s Modulus

Transverse Young’s Modulus

Example Example 3.4 Find the transverse Young's modulus of a Glass/Epoxy lamina with a fiber volume fraction of 70%. Use the properties of glass and epoxy from Tables 3.1 and 3.2, respectively.

Example Example 3.4 = 85 GPa Em = 3.4 GPa

Transverse Young’s Modulus Gambar 3.8 Transverse Young’s modulus as a function of fiber volume fraction for constant fiber to matrix moduli ratio.

Transverse Young’s Modulus

Transverse Young’s Modulus Gambar 3.9 Fiber to fiber spacing in (a) square packing geometry and (b) hexagonal packing geometry.

Transverse Young’s Modulus Gambar 3.10 Theoretical values of transverse Young’s modulus as a function of fiber volume fraction for a boron/epoxy unidirectional lamina (Ef = 414 GPa, vf = 0.2, Em = 4.14 GPa, vm = 0.35) and comparison with experimental values. Gambar (b) zooms Gambar (a) for fiber volume fraction between 0.45 and 0.75. (Experimental data from Hashin, Z., NASA tech. rep. contract no. NAS1-8818, November 1970.)

Transverse Young’s Modulus Gambar 3.11 A longitudinal stress applied to a representative volume element to calculate Poisson’s ratio of unidirectional lamina.

Major Poisson’s Ratio

Major Poisson’s Ratio

Major Poisson’s Ratio

Example Example 3.5 Find the Major and Minor Poisson's ratio of a Glass/Epoxy lamina with a 70% fiber volume fraction. Use the properties of glass and epoxy from Tables 3.1 and 3.2, respectively.

Example Example 3.5

Example Example 3.5 E1 = 60.52 Gpa E2 = 10.37 GPa

Example Example 3.5

In-Plane Shear Modulus Gambar 3.12 An in-plane shear stress applied to a representative volume element for finding in-plane shear modulus of a unidirectional lamina.

In-Plane Shear Modulus

In-Plane Shear Modulus

In-Plane Shear Modulus

Example Example 3.6 Find the in-plane shear modulus of a Glass/Epoxy lamina with a 70% fiber volume fraction. Use properties of glass and epoxy from Tables 3.1 and 3.2, respectively.

Example Example 3.6

Example Example 3.6

Example Example 3.6

In-Plane Shear Modulus Gambar 3.13 Theoretical values of in-plane shear modulus as a function of fiber volume fraction and comparison with experimental values for a unidirectional glass/epoxy lamina (Gf = 30.19 GPa, Gm = 1.83 GPa). Gambar (b) zooms Gambar (a) for fiber volume fraction between 0.45 and 0.75. (Experimental data from Hashin, Z., NASA tech. rep. contract no. NAS1-8818, November 1970.)

Longitudinal Young’s Modulus

Example Example 3.7 Find the transverse Young's modulus for a Glass/Epoxy lamina with a 70% fiber volume fraction. Use the properties for glass and epoxy from Tables 3.1 and 3.2, respectively. Use Halphin-Tsai equations for a circular fiber in a square array packing geometry.

Example Example 3.7 Gambar 3.14 Concept of direction of loading for calculation of transverse Young’s modulus by Halphin–Tsai equations.

Example Example 3.7 Ef = 85 GPa Em = 3.4 GPa

Example Example 3.7

Transverse Young’s Modulus Gambar 3.15 Theoretical values of transverse Young’s modulus as a function of fiber volume fraction and comparison with experimental values for boron/epoxy unidirectional lamina (Ef = 414 GPa, νf = 0.2, Em = 4.14 GPa, νm = 0.35). Gambar (b) zooms Gambar (a) for fiber volume fraction between 0.45 and 0.75. (Experimental data from Hashin, Z., NASA tech. rep. contract no. NAS1-8818, November 1970.)

Transverse Young’s Modulus Ef/Em = 1 implies = 0, (homogeneous medium) Ef/Em implies = 1, (rigid inclusions) Ef/Em implies (voids)

Transverse Young’s Modulus Gambar 3.16 Concept of direction of loading to calculate in-plane shear modulus by Halphin–Tsai equations.

Transverse Young’s Modulus

Example Example 3.8 Using Halphin-Tsai equations, find the shear modulus of a Glass/Epoxy composite with a 70% fiber volume fraction. Use the properties of glass and epoxy from Tables 3.1 and 3.2, respectively. Assume the fibers are circular and are packed in a square array. Also get the value of the shear modulus by using Hewitt and Malherbe’s8 formula for the reinforcing factor.

Example Example 3.8

Example Example 3.8

Example Example 3.8

Example Example 3.8

Example Example 3.8

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Pendahuluan Material Komposit BAB 3 Micromechanical Analysis of a Lamina Coefficients of Thermal Expansion Qomarul Hadi, ST,MT Teknik Mesin Universitas Sriwijaya Sumber Bacaan Mechanics of Composite Materials by Kaw

Coefficients of Thermal Expansion

Longitudinal Thermal Expansion Coefficient

Longitudinal Thermal Expansion Coefficient

Longitudinal Thermal Expansion Coefficient

Transverse Thermal Expansion Coefficient

Transverse Thermal Expansion Coefficient

Transverse Thermal Expansion Coefficient

Example Example 3.18 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.

Example Example 3.18

Example Example 3.18

Example Example 3.18 Gambar 3.38 Longitudinal and transverse coefficients of thermal expansion as a function of fiber volume fraction for a glass/epoxy unidirectional lamina.

Example Example 3.18 Gambar 3.39 Unidirectional graphite/epoxy specimen with strain gages and temperature sensors for finding coefficients of thermal expansion.

Example Example 3.18

Example Example 3.18 Gambar 3.40 Induced strain as a function of temperature to find the coefficients of thermal expansion of a unidirectional graphite/epoxy laminate.

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Pendahuluan Material Komposit BAB 3 Micromechanical Analysis of a Lamina Coefficients of Moisture Expansion Qomarul Hadi, ST,MT Teknik Mesin Universitas Sriwijaya Sumber Bacaan Mechanics of Composite Materials by Kaw

Coefficients of Moisture Expansion

Coefficients of Moisture Expansion

Coefficients of Moisture Expansion

Coefficients of Moisture Expansion

Example Example 3.19 Find the two coefficients of moisture expansion 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 glass does not absorb moisture.

Example = 2500 kg/m3 = 0.3 = 1200 kg/m3 = 2110 kg/m3 = 0.33 m/m/kg/kg = 60.52 GPa = 3.4 GPa = 0.230

Example Example 3.19

Example Example 3.19

Pendahuluan Material Komposit BAB 4 Macromechanical Analysis of a Laminate Objectives and Laminate Code Qomarul Hadi, ST,MT Teknik Mesin Universitas Sriwijaya Sumber Bacaan Mechanics of Composite Materials by Kaw

Laminate Stacking Sequence Gambar 4.1 Schematic of a lamina

BAB Objectives Understand the code for laminate stacking sequence Develop relationships of mechanical and hygrothermal loads applied to a laminate to strains and stresses in each lamina Find the elastic stiffnesses of laminate based on the Modulus Elastis of individual laminas and the stacking sequence Find the coefficients of thermal and moisture expansion of a laminate based on Modulus Elastis, coefficients of thermal and moisture expansion of individual laminas, and stacking sequence

Laminate Code   -45 90 60 30

Laminate Code   -45 90 60

Laminate Code   -45 60

Laminate Code   -45 60

Laminate Code   Graphite/Epoxy Boron/Epoxy 45 -45

Special Types of Laminates Symmetric Laminate: For every ply above the laminate midplane, there is an identical ply (material and orientation) an equal distance below the midplane. Balanced Laminate: For every ply at a +θ orientation, there is another ply at the – θ orientation somewhere in the laminate.

Special Types of Laminates Cross-ply Laminate: Composted of plies of either 0° or 90° (no other ply orientation). Quasi-isotropic Laminate: Produced using at least three different ply orientations, all with equal angles between them. Exhibits isotropic extensional stiffness properties.

Laminate Behavior The Stacking Position Thickness Modulus Elastis The Stacking Position Thickness Angles of Orientation Coefficients of Thermal Expansion Coefficients of Moisture Expansion

Strains in a beam (4.1) Gambar 4.2 A beam under (a) axial load, (b) bending moment, and (c) combined axial and bending moment.

Types of loads allowed in CLT analysis Nx = normal force resultant in the x direction (per unit length) Ny = normal force resultant in the y direction (per unit length) Nxy = shear force resultant (per unit length) Gambar 4.3 Resultant forces and moments on a laminate.

Types of loads allowed in CLT analysis Mx = bending moment resultant in the yz plane (per unit length) My = bending moment resultant in the xz plane (per unit length) Mxy = twisting moment resultant (per unit length)

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