91Ó°ÊÓ

A three-point bending test is performed on a spinel (MgAl_O_) specimen having a rectangular cross section of height \(d 3.8 \mathrm{mm}\) \((0.15 \text { in. })\) and width \(b 9 \mathrm{mm}(0.35 \text { in. }) ;\) the distance between support points is \(25 \mathrm{mm}\) \((1.0 \text { in. })\) (a) Compute the flexural strength if the load at fracture is \(350 \mathrm{N}\left(80 \mathrm{lb}_{\mathrm{f}}\right)\) (b) The point of maximum deflection \(\Delta y\) occurs at the center of the specimen and is described by $$\Delta y=\frac{F L^{3}}{48 E I}$$ where \(E\) is the modulus of elasticity and \(I\) is the cross-sectional moment of inertia. Compute \(\Delta y\) at a load of \(310 \mathrm{N}\left(70 \mathrm{lb}_{f}\right)\)

A three-point bending test was performed on an aluminum oxide specimen having a circular cross section of radius \(5.0 \mathrm{mm}\) \((0.20 \text { in. }) ;\) the specimen fractured at a load of \(3000 \mathrm{N}\left(675 \mathrm{lb}_{\mathrm{f}}\right)\) when the distance between the support points was \(40 \mathrm{mm}\) (1.6 in.). Another test is to be performed on a specimen of this same material, but one that has a square cross section of \(15 \mathrm{mm}\) ( 0.6 in.) length on each edge. At what load would you expect this specimen to fracture if the support point separation is maintained at \(40 \mathrm{mm}(1.6 \mathrm{in.}) ?\)

Cite one reason why ceramic materials are, in general, harder yet more brittle than metals.