On shear-rate dependent relaxation spectra in superposition rheometry: a basis for quantitative comparison/interconversion of orthogonal and parallel superposition moduli
| Autor: | A.R. Davies, D. J. Curtis |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: |
Physics
010304 chemical physics Rheometry Deformation (mechanics) Plane (geometry) Applied Mathematics Mechanical Engineering General Chemical Engineering Mathematical analysis Condensed Matter Physics 01 natural sciences 010305 fluids & plasmas Moduli Shear rate Nonlinear system Superposition principle 0103 physical sciences Relaxation (physics) General Materials Science |
| Popis: | In 1971, in a seminal paper, Yamamoto derived integral relationships between dynamic moduli and rate-dependent relaxation spectra, H ( τ , γ ˙ 2 ) , in parallel superposition of oscillatory shear on steady shear flow, where both the flows and deformation gradients exist in the same plane. These integral relationships are more complicated than their counterparts for orthogonal superposition (where the oscillatory and unidirectional flow fields occur in orthogonal planes), since they involve not only the spectrum, but also its derivative with respect to unidirectional shear-rate. Herein we derive (i) expressions for determining rate-dependent relaxation spectra directly from parallel superposition rheometry data and (ii) expressions to convert from parallel to orthogonal dynamic moduli in a stable manner. These results facilitate the physical interpretation of parallel superposition dynamic moduli, and direct model-based comparison of parallel and orthogonal superposition moduli in the study of weak nonlinear response. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|