Elasticity is a material property which should be fairly constant irrespective of the processing conditions or test conditions, but I have come across a paper [*] which reports different values of elasticity for monotonic loading and cyclic loading. The difference in the reported values is quite large (119 GPa for monotonic and 106 GPa for cyclic) so I am not sure what can be the reason. 

* http://www.sciencedirect.com/science/article/pii/S0921509315307152

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