Brittle material failure under static loading
1. A rod made out of a brittle material with a diameter, d=14 mm. The principal stresses were calculated
from the applied loadings and found to be:
$\sigma_1$=6 MPa,
$\sigma_2$=0 MPa,
$\sigma_3$=14 MPa
If the brittle material has the following properties:
$S_{ut}$=20 MPa, $S_{uc}$=60 MPa
Check if this design is safe according to MNST, CMT and MMT and find the factor of safety, N, and
suggest a change in dimension ($d_{new}$) to make the material withstand the load with factor of safety of 1.
Plot the case on the grid below, locate the load point, A, draw the load line, locate points of failure for
each theory, $A_{fi}$, $A_r$, $A_s$, and use $S_{ut}$ and $S_{uc}$ to determine the safe zone.
$N = \frac{OA_{fi}}{OA}$
$R = \frac{OA - OA_{fi}}{OA}$
$d_{new} = (1+R)d
Theory
MNST
Safe/Not safe
OA
$OA_{fi}$
N
R
dnew
CMT
MMT
1/6