Equation of State for Viscoelasticity of Polymethyl Methacrylate

This paper presents our results on the creep of polymethyl methacrylate (PMMA) in the temperature range from 0 to +30°C at strain rates from 0.02 to 2%/min and stresses from 48 to 72 MPa during holding for up to 100 h. We consider viscoelastic behavior of PMMA under normal service conditions, before the onset of damage to the material. For such conditions, we obtain a single power-law dependence of the creep strain on time during the whole period of holding, without dividing the process into transient and steady-state creep stages. Formulas are proposed for fitting isothermal test results obtained at a constant strain rate and during holding under constant load. We derive dependences of fitting parameters on strain rate, stress level, and temperature in tests of PMMA. Comparison of creep strain diagrams obtained at the same stress during holding after deformation at various strain rates shows that, after displacement along the time axis, the diagrams fall on a single curve. This suggests the feasibility of describing the experimental data set we obtained by a single equation of state relating the creep rate to stress and temperature. Differentiation of fitting relations allows us to find general trends in the variation of the creep rate during tests, and second differentiation makes it possible to obtain an equation for creep acceleration at a constant strain rate and eliminate the time variable from it. In this form, these two equations can be regarded as particular cases of the equation of state of a viscoelastic material whose behavior is independent of the loading history. Creep during continuous deformation can be thought of as a combination of two processes: creep acceleration as a consequence of stress growth and creep deceleration over time. Based on this, we formulate a single equation of state of a viscoelastic material for a process with an arbitrary strain and stress growth law. The parameters of the equation of state are temperature, creep rate, creep acceleration, stress, and the rate of its variation, without accumulated creep strain. Applicability of this equation under more complex conditions, such as nonmonotonic thermal power loading, requires additional experimental substantiation and identification of its parameters.