I performed stress relaxation test, resulting in collecting time, stress, strain. I fitted these data to a 3-decay exponential decay model strain(t)=A0+Ai*exp(-t/ti), with i=1,2,3 and got my parameters A0, Ai and ti. Thus, I calculated modulus of elasticity of the samples.
The fact that in a stress/strain graph the curve given by data of relaxation phase doesn’t coincide with the loading, does not imply with certainty that deformation is plastic, since in the long run it can recover the shape, or am I assuming it wrong?
Is it possible to determine the type of deformation maybe starting from the time constants "ti" - or eventually from other collected data?
The stress relaxation experiments are generally used to quantify plasticity and elasticity of the samples. Please see the reference below:
Qian Zhao, Weike Zou, Yingwu Luo, and Tao Xie. Shape memory polymer network with thermally distinct elasticity and plasticity. Sci Adv. 2016 Jan; 2(1): e1501297.
If you need to know the 'type of deformation' you have to perform a full cycle in order to assesss if strains can be fully recovered (elastic or viscoelastic behaviour) or not (elasto-plastic or viscous behaviour).
Being initially loaded, your material is immediately deformed with a certain strain. Usually, the applied loading's value is chosen so that the immediately arisen strain will be elastic. Then, throughout a time, the initial strain grows while the stress relaxation occurs. This is, actually, a creep of material. Usually, three creep stages are distinguished: primary (decreasing strain rate vs time dependence), secondary (constant strain rate vs time dependence) and third (increasing strain rate vs time dependence). The secondary and the third stages are sure irreversible ("plastic"), while only initial stage of the primary creep i reversible ("elastic"). Actually, a creep is accompanied by dislocation movement, so it principally irreversible ("plastic") process. The only short-time continuing "elastic" stage is really an exception.
It is possible to determine if materials deform elastically or plastically. In materials science, stress relaxation is the observed decrease in stress in response to strain generated in the structure. It is a time dependent decrease in stress under constant strain. The characteristics behavior of polymer studies by applying a fixed amount of deformation to a specimen and measuring the load required to maintain it as a function of time. Since relaxation relieves the state of stress, it has the effect of also relieving the equipment reactions. Thus, relaxation has the same effect as cold springing, except it occurs over a longer period of time. The amount of relaxation which takes place is a function of time, temperature and stress level, thus the actual effect it has on the system is not precisely known, but can be bounded. Stress relaxation data has been used in many practical applications.
At low temperatures, amorphous polymers deform elastically, like glass, at small elongation. At high temperatures the behavior is viscous, like liquids. At intermediate temperatures, the behavior, like a rubbery solid, is termed viscoelastic.
Viscoelasticity is characterized by the viscoelastic relaxation modulus
Er = s(t)/e0.
If the material is strained to a value e0.it is found that the stress needs to be reduced with time to maintain this constant value of strain.
In viscoelastic creep, the stress is kept constant at s0 and the change of deformation with time e(t) is measured. The time-dependent creep modulus is given by
Ec = s0/e(t).
Stress relaxation describes how polymers relieve stress under constant strain. Because they are viscoelastic, polymers behave in a nonlinear, non-Hook fashion. This nonlinearity is described by both stress relaxation and a phenomenon known as creep, which describes how polymers strain under constant stress. That means it can deform elastically and plastically. It can be measured experimentally. The time dependent creep modulus is a suitable example of stress relaxation.
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