Relationship of Modulus to thermal expansion

[joeaccetta]

I'm trying to figure out how to relate expected thermal expansion of a uv cured polymer within a rigid cylinder to a modulus specification. The issue is the expected change in refractive index due to thermal expansion. The expansion coefficients are not available. Anybody have an idea. Do greater specified moduli lead to increased or decreased expansion?

 

[jrmichler]

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.

 

[FEAnalyst]

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: $$\Delta L= \alpha L_{0} \Delta T$$ $$\varepsilon=\frac{\Delta L}{L_{0}}$$ $$E=\frac{\sigma}{\varepsilon}$$ $$\sigma=E \varepsilon=E \alpha \Delta T$$

 

[joeaccetta]

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 was not specified.

 

[joeaccetta]

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.

 

[joeaccetta]

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: $$\Delta L= \alpha L_{0} \Delta T$$ $$\varepsilon=\frac{\Delta L}{L_{0}}$$ $$E=\frac{\sigma}{\varepsilon}$$ $$\sigma=E \varepsilon=E \alpha \Delta T$$

Thank you