# Design of the internal fixation plate composite material

Task: Bioengineer needs to design a plate for the internal fixation of fractures using the Voigt's model. The plate should be made out of composite material containing carbon fibres and PMMA (Poly(methyl methacrylate)). The engineer has tabulated data about material properties (Young's modulus E, mass density ρ and ultimate tensile strength σ) shown below.

Material E (GPa) ρ (g/cm3) σ (MPa)

Carbon fibres 250 1.95 5000

PMMA 3 1.20 70

(a) What volume fraction of carbon fibres is required to make a plate having Young's modulus (Ec) of 100 GPa? Assume that all carbon fibres are aligned with the axis of the test load.

(b) How many carbon fibres are required to make the same plate design as in (a), if a single fibre has 10 μm diameter and the cross-sectional area of the plate is 1 cm^2.

(c) What is the maximum mechanical stress which the composite can withstand in the direction of carbon fibre?

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#### Solution Preview

(a) Using the Voigt's model for fibrous composites, the volume fraction of carbon fibres can be obtained from the simple rule of mixtures.

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Sum of the volume fractions is Vp + Vf = 1. ...

#### Solution Summary

Solution covers the step-by-step explanation of composite material design intended for the internal fracture fixation plate. Design is simplified with the usage of the Voigt's fibrous model.