Answer ALL PARTS !! A square of an isotropic metallic material having sides of 2

Question

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.

Explanation / Answer

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

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