Regime switching Kocks-Mecking creep¶

Overview¶

This model implements a creep law based on the Kocks-Mecking normalized activation energy [KM2003]. The basic creep rate law is

$F = -\frac{\mu b^3}{kT} \dot{\varepsilon}^{cr} = \dot{\varepsilon}_0 \exp\left( B F \right) \left(\frac{\sigma_{eq}}{\mu} \right)^{A F}.$

Here $\dot{\varepsilon}_0$ , $A$ , $B$ are parameters, $\mu$ is the temperature dependent shear modulus, $k$ is the Boltzmann constant, and $b$ is a Burgers vector length. The model constants can be fit using a Kocks-Mecking diagram.

The formulation can switch between different Kocks-Mecking models as a function of normalized stress $s = \frac{\sigma_{eq}}{\mu}$ . The model first computes the normalized stress. It then consults a table of $n$ normalized stress cutoffs, $c_i$ . If $s \le c_1$ then the model applies the strain rate equation above using constants $A_1$ and $B_1$ . If $c_i < s \le c_{i+1}$ then the model uses constants $A_{i+1}$ and $B_{i+1}$ . If $s > c_n$ then the model uses $A_n$ and $B_n$ .

Parameters¶

Parameter	Object type	Description	Default
`cuts`	`std::vector<double>`	Normalized stress cutoffs	No
`A`	`std::vector<neml::Interpolate>`	Corresponding A constants	No
`B`	`std::vector<neml::Interpolate>`	Corresponding B constants	No
`kboltz`	`double`	Boltzmann constant	No
`b`	`double`	Burgers vector	No
`eps0`	`double`	Reference strain rate	No
`emodel`	`neml::LinearElasticModel`	Elastic model (for shear modulus)	No

Class description¶

class RegionKMCreep : public neml::ScalarCreepRule ¶

A power law type model that uses KM concepts to switch between mechanisms.

Public Functions

RegionKMCreep(ParameterSet &params)¶: Inputs: cuts in normalized activation energy, prefactors for each region exponents for each region, boltzmann constant, burgers vector, reference strain rate, elastic model, to compute mu

virtual void g(double seq, double eeq, double t, double T, double &g) const¶: See documentation for details of the creep rate.

virtual void dg_ds(double seq, double eeq, double t, double T, double &dg) const¶: Derivative of creep rate wrt effective stress.

virtual void dg_de(double seq, double eeq, double t, double T, double &dg) const¶: Derivative of creep rate wrt effective strain.

Public Static Functions

static std::string type()¶: String type for the object system.

static std::unique_ptr<NEMLObject> initialize(ParameterSet &params)¶: Setup from a parameter set.

static ParameterSet parameters()¶: Return the default parameters.