A 20mm square metallic material undergoes an elastic deformation, elongating 0.0038mm along the X-axis and contracting 0.0026mm along the Y-axis, with rotations of 613x10^-6 and 36x10^-6 radians. The normal and shear strains, principal strains, maximum shear strain, and applied stress state for this deformation are calculated using given material properties.

1. Answer ALL PARTS !!
A square of an isotropic metallic material having sides of 20 mm is subjected to an elastic
deformation. The displacements are such that an elongation of 0.0038mm is observed parallel to
the X-axis and a contraction of 0.0026mm is observed parallel to the Y-axis. Additionally, you
are given that alpha x =613 times 10-6 radians and alpha y = 36 times 10-6 radians. Assume E =
200 GPa, G = 77 GPa, and v = 0.3. Neglect rig id body rotations. Are these strains elastic or
plastic? Justify your answer. Calculate the normal and shear strains acting on the 20 times 20
mm square. Calculate the principal strains and the maximum shear strain resulting from the
deformation. Calculate the applied stress state (sigma ij) causing the deformation of the square.
Solution
A) In the case of elastic strain this is observed as a distortion of the crystal lattice, in the case of plastic strain this is
observed by the presence of dislocations