Mukherjee creep

Overview

This implements the Mukherjee creep model [BMD1969]

$\dot{\varepsilon}^{cr} = A D_0 e^\frac{Q}{RT} \frac{\mu b}{k T} \left( \frac{\sigma_{eq}}{\mu}\right)^n$

with $A$ , $D_0$ , $Q$ , and $n$ parameters and $R$ the gas constant, $T$ absolute temperature, $\mu$ the temperature dependent shear modulus, $b$ a Burgers vector length, and $k$ the Boltzmann constant.

Parameters

Parameter	Object type	Description	Default
`emodel`	`neml::LinearElasticModel`	Elasticity model (for shear modulus)	No
`A`	`double`	Prefactor	No
`n`	`double`	Stress exponent	No
`D0`	`double`	Zero temperature lattice diffusivity	No
`Q`	`double`	Activation energy for diffusivity	No
`b`	`double`	Burgers vector	No
`k`	`double`	Boltzmann constant	No
`R`	`double`	Gas constant	No

Class description

class MukherjeeCreep : public neml::ScalarCreepRule 

Classical Mukherjee creep.

Public Functions

MukherjeeCreep(ParameterSet &params): Parameters: elastic model (for shear modulus), prefactor, stress exponent, reference lattice diffusivity, activation energy for lattice diffusion, burgers vector, boltzmann constant, gas constant

virtual void g(double seq, double eeq, double t, double T, double &g) const: scalar creep rate = A * D0 * exp(Q / (RT)) * mu * b / (k * T) * (seq / mu)**n

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.

double A() const: Getter for A.

double n() const: Getter for parameter n.

double D0() const: Getter for parameter D0.

double Q() const: Getter for parameter Q.

double b() const: Getter for parameter b.

double k() const: Getter for parameter k.

double R() const: Getter for parameter R.

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 default parameters.