Swelling (TB,SWELL) is a material enlargement (volume expansion) caused by neutron bombardment or other effects (such as moisture). The swelling strain rate is generally nonlinear and is a function of factors such as temperature, time, neutron flux level, stress, and moisture content.
Irradiation-induced swelling and creep apply to metal alloys that are exposed to nuclear radiation. However, the swelling equations and the fluence input may be completely unrelated to nuclear swelling. You can also model other types of swelling behavior, such as moisture-induced volume expansion.
Swelling strain is modeled using additive decomposition of strains, expressed as:
where ε is the total strain, εel is the elastic strain, εpl is the plastic strain, εcr is the creep strain, εth is the thermal strain, and εsw is the swelling strain. The mechanical strain is the total strain minus the thermal and swelling strains. Swelling strain is assumed to be isotropic. You can combine swelling strain with other material models such as plasticity and creep; however, you cannot use swelling with any hyperelasticity or anisotropic hyperelasticity material model.
Irradiation-induced swelling is generally accompanied by irradiation creep for metals and composites, such as silicon carbide (SiC). The irradiation-induced swelling strain rate may depend on temperature, time, fluence (the flux x time), and stress, such as:
where t is time, T is the temperature, Φt is the fluence, and σ is the stress. Temperatures used in the swelling equations should be based on an absolute scale (TOFFST). Specify temperature and fluence values via the BF or BFE command.
The following options for modeling swelling are available:
Linear swelling defines swelling strain rate as a function of fluence rate, expressed as:
where C is the swelling constant, which may depend on temperature.
A user-defined swelling option is available if you wish to create your own swelling function. For more information, see
userswstrainin the Programmer's Reference.
Swelling equations are material-specific and are empirical in nature.
For highly nonlinear swelling strain vs. fluence curves, it is good practice to use a small fluence step for better accuracy and solution stability. If time is changing, a constant flux requires a linearly changing fluence (because the swelling model uses fluence [Φt] rather than flux [Φ]).
Initialize the swelling table (TB,SWELL) with the desired data-table option
(TBOPT), as follows:
Swelling
Model Options (TB,SWELL,,TBOPT) | |||
|---|---|---|---|
Option (TBOPT)
| Constant | Description | Constant Value Input |
| LINE | C1 | Linear swelling | TBDATA,1,C1 |
| EXPT | C1, C2, C3, C4 | Exponential swelling | TBDATA,1,C1,C2,C3,C4 |
| USER | C1, ..., Cn | User-defined | TBDATA,1,C1,C2,… |
Issue the TBDATA command to enter the swelling table constants (up to six per command), as shown in the table.
For a list of the elements that you can use with the swelling model, see Material Model Support for Elements. The swelling model does not support sections (SECTYPE).
For more information about this material model, see Swelling in the Structural Analysis Guide.