micro mechanism

MİCROMECHANİCS

Micro-mechanics of composites

Micromechanics deals with the study of composite

material behavior in terms of the interaction of its

constituents.

There are two basic approaches of the micromechanics of

composite materials, namely

i. Mechanics of materials

ii. Elasticity

Micromechanics

Determining unknown properties of the composite based on known properties of the fiber and matrix

Micromechanics

Uses of Micromechanics

Predict composite properties from fiber and matrix data

Extrapolate existing composite property data to different

fiber volume fraction or void content

Check experimental data for errors

Determine required fiber and matrix properties to produce

a desired composite material .

Limitations of Micromechanics

Predicted composite properties are only as good as fiber and matrix properties used

Simple theories assume isotropic fibers many fiber reinforcements are orthotropic

Some properties are not predicted well by simple theories more accurate analyses are time consuming and expensive

Predicted strengths are upper bounds

Notations

Subscript f, m, c refer to fiber, matrix, composite respectivelyv volumeV volume fractionw weightW weigth fractionsρ density

Terminology Used in Micromechanics

• Ef, Em – Young’s modulus of fiber and matrix• Gf, Gm – Shear modulus of fiber and matrix• υf, υm – Poisson’s ratio of fiber and matrix• Vf,Vm – Volume fraction of fiber and matrix

Volume Fractions

Fiber Volume Fraction

Matrix Volume Fraction

Mass Fractions

Fiber Mass Fraction

Matrix Mass Fraction

Density

Total composite weight: wc = wf + wm

Substituting for weights in terms of volumes and densities

Dividing through by vc gives,

Density

Whenmore than two constituents enter in the composition of the composite material

where n is the number of constituent.

Void Content

Effects of Voids on Mechanical Properties

Lower stiffness and strength Lower compressive strengths Lower transverse tensile strengths Lower fatigue resistance Lower moisture resistance.

Evaluation of Four Elastic Moduli

There are four elastic moduli of a unidirectional lamina:

Longitudinal Young’s modulus, E1

Transverse Young’s modulus, E2

Major Poisson’s ratio, υ12

In-plane shear modulus, G12

Strength of Materials Approach

Assumptions are made in the strength of materials approach

The bond between fibers and matrix is perfect. The elastic moduli, diameters, and space between fibers are

uniform. The fibers are continuous and parallel. The fiber and matrix follow Hooke’s law (linearly elastic). The fibers possess uniform strength. The composites is free of voids.

Representative Volume Element (RVE)

This is the smallest ply region over which the stresses and strains behave in a macroscopically homogeneous behavior. Microscopically, RVE is of a heterogeneous behavior. Generally, single force is considered in the RVE.

RVE

RVE

fibrematrix

Longitudinal Modulus, E1

Total force is shared by fiber and matrix

Assuming that the fibers, matrix, and composite follow Hooke’s law and that the fibers and the matrix are isotropic, the stress–strain relationship for each component and the composite is

The strains in the composite, fiber, and matrix are equal (εc = εf = εm);

Longitudinal Modulus, E1

Transverse Young’s Modulus, E2

The fiber, the matrix, and composite stresses are equal.

σc = σf = σm

the transverse extension in the composite Δc is the sum of the transverse extension in the fiber Δf , and that is the matrix, Δm.

Δc = Δf + Δm

Δc = tc εc

Δf = tf εf

Δm = tm εm

tc,f,m = thickness of the composite, fiber and matrix, respectively

εc,f,m = normal transverse strain in the composite, fiber, and matrix, respectively


By using Hooke’s law for the fiber, matrix, and composite, the normal strains in the composite, fiber, and matrix are


Major Poisson’s Ratio, ν12

In-Plane Shear Modulus, G12

Apply a pure shear stress τc to a lamina

In-Plane Shear Modulus, G12

Thank you

micro mechanism

Documents