Materials Science and Engineering 4T03

Mid term exam 1th March 2012 - solution

Problem 1:

You are a member of Reinforcement Inc., a producer of fibre for the composite industry. You are partnering with Matrix ltd on a joint venture to develop a solid rod in composite material for an application which leads to variable tensile stresses between 100 and 150 MPa.

To do so you have identified a reinforcement candidate with the following properties:

E = 400 GPa, σy = 800 MPa, and ν = 0.21.

The engineers at Matrix ltd are indecisive and contemplate using 3 matrices:

Matrix / A / B / C
E (GPa) / 0.5 / 5 / 25
σy (MPa) / 1 / 10 / 50
ν / 0.39 / 0.39 / 0.39
  1. What methodology would you use to design this composite material? (5 pts.)

We can use for example an Oshikawa diagram (or fish bone diagram) in order to capture all the parameters to take into account during the design of the composite.

  1. Are there simple models to describe the mechanical properties that you could use and what are key elements of each one? (5 pts.)

Slab model in axial tension: isostrain case

  1. In the case of long fibres, what parameter is required in order to control the mechanical properties of the composite and why? (5 pts.)

Volume fraction of long fiber reinforcement

  1. Calculate for each matrix what should be the compositions of the composites (write down the major steps of the calculation). (10 pts.)

Apply rule of mixtures in Isostrain condition:

Hence calculate f. We can do this in 2 ways: either calculate for σa = 100MPa and 150MPa, or for σa = 125MPa ±25

Case A: f is from 0.12 to 0.19

Case B: f is from0.11 to 0.18

Case C: f is from 0.07 to 0.13

  1. If cost was the same for the 3 matrices, which one would you choose and why? (5 pts.)

Since cost is the same for the 3 matrices, and we have only 1 type of reinforcement, cost will be minimized by considering the lowest volume fraction of reinforcement Case C.

  1. Consider your matrix of choice. Your long fibre manufacturing process uses extrusion dies which can have either a square of hexagonal arrangement. If the average distance between fibres is 20 microns, calculate the range of diameters the fibres would have in both arrangement. (10 pts.)

Case C & h=20 micron:

r=3.72 to 6.22micron r=4.11 to 7.01 micron

  1. What would be the Young’s modulus of the composite in this case? (5pts.)

We apply again the rule of mixtures (isostrain case): E=50 to 75MPa

2