{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

HW1-solution

# HW1-solution - Homework 1 Anirban Chaudhuri 1 Using the...

This preview shows pages 1–3. Sign up to view the full content.

Homework 1 Anirban Chaudhuri 1. Using the stiffness representation models discussed in Section 1.2.2, show that the transverse stiffness, E 2 , of a fiber-reinforced composite material is given by Eq. (1.2.6). Solution: Eq. 1.2.6 is 2 1 f m f m V V E E E = + where, V f and V m are the volume fractions and E f and E m are Young’s Moduli of fiber and matrix material respectively. Fig 1: Rule of mixtures model of a transverse stiffness of a composite layer (Fig 1.5 in the book) In this case the stress on the fiber and matrix material is the same which gives us f m f m P P P A A A = = …(1) where, P is the total force and A is the cross sectional area. The indices f and m represent the respective quantities for fiber and matrix respectively. If each constituent is assumed to be an axial bar then force displacement relation gives PL AE δ = . In this case the length is proportional to the volume fractions. , f f m m L V L L V L = = …(2) It can also be seen from the figure 1 that f m δ δ δ = + . or, 2 f f m m f f m m P L P L PL AE A E A E = +

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
2 f m f m L L L E E E = + [from (1)] 2 f m f m V L V L L E E E = + [from (2)] or, 2 1 f m f m V V E E E = + which is the same as equation 1.2.6. 2. Assuming the packing of the fibers to be represented by the unit volume shown in Fig. 1.8, plot the longitudinal and transverse specific stiffness, E 1 / ρ and E 2 / ρ , and the weight density of the composite, ρ , as a function of the fiber radius (0.0 r f r f max ) for a unidirectional fiber- reinforced Graphite/Epoxy composite. Solution: Graphite properties: E f = 230GPa, ρ f = 17.2 kN/m 3 Epoxy properties: E m = 3.45GPa, ρ m = 12.0 kN/m 3 Fig. 2: Unit volume r f is the fiber radius. Fiber volume fraction, 2 2 f f f A V r A π = = ...(1)
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 8

HW1-solution - Homework 1 Anirban Chaudhuri 1 Using the...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online