The elastic modulus for hydroxyapatite [Ca5(PO4)3(OH)] is 98.3 GPa, which possesses a 10 vol% porosity. Calculate the following:

a. Elastic modulus E0 for the nonporous ceramic material.
b. The elastic modulus for the same sample with 50 vol% porosity. With a larger porosity, will you expect Young's modulus to increase or decrease? Why?

Eo =  120.02 GPa

Eo = 357.454 GPa

Explanation:

given data

elastic modulus E = 98.3 GPa

porosity P =  10 %  = 0.1

solution

we know that young modulus of porous material that is express as

young modulus of porous material = Eo ( 1 - 1.9 P + 0.9 P² )   1

here  Eo is young modulus of non porous material and P is porosity so we get here Eo

98.3 = Eo  ( 1 - 1.9 × (0.1) + 0.9 × (0.1)² )

Eo =  120.02 GPa

and

now for P is 0.5 for the this same material

put value in equation 1

98.3 =   Eo  ( 1 - 1.9 × (0.5) + 0.9 × (0.5)² )  

Eo = 357.454 GPa

so here young modulus increase will porosity.

but in generally elastic modulus of material will decrease

so here P is 0.1 an P is 0.5 consider same classic modulus 98.3 GPa

so value will increase