Consider a block of size 30 mm x 20 mm x 10 mm made of twometallic materials, the stronger material for the bottom half ofthe block and the weaker material for the top half. Thedisplacements of 8 material points of the block have been measuredafter certain loading and they are given in the Table below.
(a) Determine the distributions of displacements, strains andstresses in the block, in the xyz co-ordinate system. Choose twosuitable isotropic materials.
(b) Determine the stresses at the corner points of the plane atthe interface of the two materials. Using these values, determinethe stress distributions over that plane, and determine the maximumvalue of all these stresses (and its type and direction of action).Also determine the maximum value of the principal stress on thisplane.
(c) Determine the stresses and strains in the directions of anytwo diagonals of the block, at each of the corner points of theblock. Calculate also the changes in the lengths of these twodiagonals.
Determine the changes in the maximum shear stress and octahedralshear stress at each of the corner points of the interface plane,and the changes in the lengths of the two diagonals afterdeformation due to a +10% change in material properties. Whichproperty has more influence on the octahedral shear stress at eachcorner point of the interface?
Point | Co-ordinates Before loading | Co-ordinates After loading |
A | 0,0,20 | 0.001, 0.002, 20 |
B | 30, 0, 20 | 30.001, 0.0, 20.004 |
C | 30, 10, 20 | 29.997, 10.003, 19.996 |
D | 0, 10, 20 | 0.004, 10.009, 19.995 |
E | 0, 0, 0 | 0, 0, 0.0 |
F | 30, 0, 0 | 30.009, 0.001, 0.0026 |
G | 30,10,0 | 29.996, 10.0033, 0 |
H | 0, 10, 0 | 0.0011, 9.996, 0.0021 |
Check whether the interface will fail using Tresca and von Misesfailure criteria.
The elasticity of the top material is 105 GPa, G = 39 GPa,v=0.346. Bottom material E = 195 GPa, G = 77 GPa, v = 0.27
