Difference between revisions of "First Order Phase Transition Material"
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<math>\Delta H_f = \int_{T_i}^{T_f} \Delta C\ | <math>\Delta H_f = \int_{T_i}^{T_f} \Delta C\ dT</math> | ||
where ΔC is the excess heat capacity during the transition compared to the heat capacity of the material in the absence of a transition. For numerical modeling of heat of fusion, you enter the total heat of fusion and a transition temperature range ΔT, such that T<sub>i</sub> = T<sub>melt</sub>-ΔT and T<sub>f</sub> = T<sub>melt</sub>+ΔT. In the numerical implementation, the excess heat capacity is is spread out over the temperature range as a hat function with the peak value equal to: | where ΔC is the excess heat capacity during the transition compared to the heat capacity of the material in the absence of a transition. For numerical modeling of heat of fusion, you enter the total heat of fusion and a transition temperature range ΔT, such that T<sub>i</sub> = T<sub>melt</sub>-ΔT and T<sub>f</sub> = T<sub>melt</sub>+ΔT. In the numerical implementation, the excess heat capacity is is spread out over the temperature range as a hat function with the peak value equal to: | ||
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<math>\Delta C_{max}= | <math>\Delta C_{max}= {\Delta H_f\over\Delta T}</math> | ||
=== Volume of Fusion === | === Volume of Fusion === | ||
Revision as of 14:06, 21 January 2016
First Order Phase Transition
This exploratory MPM material models a first order phase transition between two materials (it is currently only available in OSParticulas). It has no material responses itself. Instead, it acts as a "parent" material to two "child" materials, where one child is a "solid phase" and the other is a "liquid" phase. The properties of this material control transition from the solid to liquid phase, where solid is the low-temperature phase, and the liquid is the high temperature phase.
A first order phase transition occurs at a melting temperature, Tmelt. The meaning of a first order transition is that thermodynamic energy functions (e.g., Gibbs free energy) are continuous at Tmelt, one the phase which is the lowest energy changes. Although free energy is constant, the first derivatives of free energy undergo a discrete change (hence the origin of the term first-order transition). Namely, there is a change in enthalpy (ΔHf), entropy (ΔSf), and volume (ΔVf), where subscript "f" means fusion. Because free energies of the two phase are equal at Tmelt, the first two are related by
[math]\displaystyle{ \Delta S_f = {\Delta H_f\over T_m} }[/math]
Enthalpy of Fusion
Most materials do not have a sharp transition, but rather undergo a transition over a range of temperatures, such as from Ti to Tf. The enthalpy of fusions is experimentally related to the heat capacity during this transition by:
[math]\displaystyle{ \Delta H_f = \int_{T_i}^{T_f} \Delta C\ dT }[/math]
where ΔC is the excess heat capacity during the transition compared to the heat capacity of the material in the absence of a transition. For numerical modeling of heat of fusion, you enter the total heat of fusion and a transition temperature range ΔT, such that Ti = Tmelt-ΔT and Tf = Tmelt+ΔT. In the numerical implementation, the excess heat capacity is is spread out over the temperature range as a hat function with the peak value equal to:
[math]\displaystyle{ \Delta C_{max}= {\Delta H_f\over\Delta T} }[/math]
Volume of Fusion
Material Properties
The unusual task for this material is to use multiple Gk and tauk properties (all with the same property name) to enter a material with multiple relaxation times.
| Property | Description | Units | Default |
|---|---|---|---|
| pressureLaw | Picks the constitutive law use for time independent pressure. The options are 0 to linear elastic law and 1 to use MGEOS equation of state. | none | 0 |
The total number of Gk and tauk properies must be equal. In XML files, that total number must match the supplied ntaus property.
History Variables
This material tracks internal history variables (one for each relaxation time and each component of stress) for implementation of linear viscoelastic properties, but currently none of these internal variables are available for archiving.
This material also tracks J (total relative volume change) and Jres (volume change of free expansion state) as history variables 1 and 2. Note that Jres is only needed, and therefore only tracked, when using MGEOS for pressure constitutive law (when pressureLaw is 1). If not tracked, it is always 1.