The discussion revolves around the relationship between the modulus of elasticity (specifically Young's modulus) and the thermal expansion of a UV-cured polymer constrained within a rigid cylinder. Participants explore how the modulus specification may influence the expected thermal expansion and the associated change in refractive index, while noting the absence of specific expansion coefficients.
Participants generally agree on the definitions of thermal expansion and modulus of elasticity, but there is no consensus on how these concepts specifically relate in the context of the constrained polymer. Multiple viewpoints on the implications of modulus specifications remain unresolved.
Limitations include the absence of specific thermal expansion coefficients and the unspecified modulus type, which may affect the analysis. The discussion also highlights the need for clarity in terminology to avoid confusion.
Thanks. Unfortunately, the particular modulus was not specified.jrmichler said:The thermal coefficient of expansion is one property. It describes how much an unconstrained object changes size with temperature change.
The modulus of elasticity, AKA elastic modulus, AKA Young's modulus, describes how much an object changes size with stress change.
You need to use the correct terms to avoid confusion.
If a polymer is constrained inside a rigid cylinder, then there is no thermal expansion. That is a simple problem to solve. Step 1: Calculate thermal expansion from temperature change. Step 2: Calculate stress to force the part back to its original size. Step 3 (optional): Calculate the force to get that stress.
One good way to get a better understanding of the relationships is to do the calculations for one polymer, then repeat for a different polymer with different properties.
Thanks. Unfortunately the particular modulus is not specified but probably Youngs.jrmichler said:The thermal coefficient of expansion is one property. It describes how much an unconstrained object changes size with temperature change.
The modulus of elasticity, AKA elastic modulus, AKA Young's modulus, describes how much an object changes size with stress change.
You need to use the correct terms to avoid confusion.
If a polymer is constrained inside a rigid cylinder, then there is no thermal expansion. That is a simple problem to solve. Step 1: Calculate thermal expansion from temperature change. Step 2: Calculate stress to force the part back to its original size. Step 3 (optional): Calculate the force to get that stress.
One good way to get a better understanding of the relationships is to do the calculations for one polymer, then repeat for a different polymer with different properties.
Thank youFEAnalyst said:You didn’t say which modulus you mean but I’ll also assume that it’s just Young’s modulus and share simple formulas involving thermal expansion coefficient and aforementioned modulus of elasticity: $$\Delta L= \alpha L_{0} \Delta T$$ $$\varepsilon=\frac{\Delta L}{L_{0}}$$ $$E=\frac{\sigma}{\varepsilon}$$ $$\sigma=E \varepsilon=E \alpha \Delta T$$