Question

A three-point bend test is performed on a block of ZrO2 that is 8 in. long, 0.50 in. wide, and 0.25 in. thick and is resting on two supports 4 in. apart. When a force of 400 lb is applied, the specimen deflects 0.037 in. and breaks. Calculate (a) the flexural strength; and (b) the flexural modulus, assuming that no plastic deformation occurs.

Answer 1

Answer:

a) 76,800 Psi

b) 22.14 × 10⁶ Psi

Explanation:

Data provided in the question:

Length of the block, w = 8 in

Width of the block, h = 0.25  

Distance between the supports, L = 4 in

Applied force, F = 400 lb      

Deflection at the time of failure, δ = 0.037 in

Now,

a) Flexural strength = $\frac{3FL}{2wh^2}$

= $\frac{3\times400\times4}{2\times0.5\times0.25^2}$

= 76,800 Psi

b) Flexural modulus =  $\frac{FL^3}{4wh^3\delta}$

= $\frac{400\times4^3}{4\times0.5\times0.25^3\times0.037}$

= 22.14 × 10⁶ Psi