Question

Consider a block of size 30 mm x 20 mm x 10 mm made of two metallic materials, the stronger material for the bottom half of the block and the weaker material for the top half. The displacements of 8 material points of the block have been measured after certain loading and they are given in the Table below.

(a) Determine the distributions of displacements, strains and stresses in the block, in the xyz co-ordinate system. Choose two suitable isotropic materials.

(b) Determine the stresses at the corner points of the plane at the interface of the two materials. Using these values, determine the stress distributions over that plane, and determine the maximum value of all these stresses (and its type and direction of action). Also determine the maximum value of the principal stress on this plane.

(c) Determine the stresses and strains in the directions of any two diagonals of the block, at each of the corner points of the block. Calculate also the changes in the lengths of these two diagonals.

Determine the changes in the maximum shear stress and octahedral shear stress at each of the corner points of the interface plane, and the changes in the lengths of the two diagonals after deformation due to a +10% change in material properties. Which property has more influence on the octahedral shear stress at each corner 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 Mises failure 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

Answer 1