3D structures such as crystals often experience a volumetric change when elastic

Question

3D structures such as crystals often experience a volumetric change when elastically loaded with stresses below the proportional limit due to the resulting elastic strains. Would we expect the volume to increase or decrease? Why and under what condition(s)? Using values from the following table, estimate the magnitude of this change for two cubic metals, nickel and iron, and one cubic ceramic, NaCl, loaded in tension. Comment on how the magnitudes of the elastic constants effect the change in volume of the crystal.

Explanation / Answer

volume can be incresed or decereased for the crystal depending upon applied stress.

when applied stress in all direction are compresson then volume will decrease.

when applied stress in all direction are tension then volume will increase.

when applied stress in one direction in compression & in other direction is tension then volume will decrease or increase depending on conditions.

Nickel Volumetric strain = 2*(1 - u)*Stress / E = [2*(1-0.310)*60*10^6] / (213.7*10^9) = 0.3875 * 10^(-3)

Iron Volumetric strain = 2*(1 - u)*Stress / E = [2*(1-0.290)*140*10^6] / (208.2*10^9) = 0.61 * 10^(-3)

NaCl Volumetric strain = 2*(1 - u)*Stress / E = [2*(1-0.252)*29*10^6] / (39.98*10^9) = 1.085 * 10^(-3)

magnitide of elastic constact inversaly affect change in volume of crystal.

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