Larson Miller correlations

Overview

This class implements a classical Larson-Miller [LM1952] correlation between stress, temperature, and rupture time. These correlations are developed using a large database of creep test results giving the applied stress, temperature, and the resulting time to rupture for a given material for many different experimental conditions.

The Larson-Miller relation takes the form:

$\log_{10}{\sigma_R} = f\left(\mathrm{LMP}\right)$

where $\sigma_R$ is the time to rupture and $f$ is some generic function (often a polynomial regression or a piecewise polynomial regression) of the Larson-Miller parameter $\mathrm{LMP}$ , defined as

$\mathrm{LMP} = T \left(C + \log_{10}{t_R} \right)$

where $T$ is absolute temperature, $C$ is a constant fit to data, and $t_R$ is the time to rupture.

NEML implements Larson-Miller relations by using a generic interpolate object. That is, the interpolate object provides the function $f$ in the above equation relating the Larson-Miller parameter to the log of the stress to rupture.

Parameters

Parameter	Object type	Description	Default
`function`	`neml::Interpolate`	Generic Larson-Miller relation	No
`lmr`	`double`	Constant C from the Larson-Miller parameter	No
`tol`	`double`	Solver tolerance	`1.0e-6`
`miter`	`int`	Maximum solver iterations	`20`
`verbose`	`bool`	Verbosity flag	`false`

Class description

class LarsonMillerRelation : public neml::NEMLObject, public neml::Solvable 

Classical Larson-Miller relation between stress and rupture time.

Public Functions

LarsonMillerRelation(ParameterSet &params)

void sR(double t, double T, double &s) const: Stress as a function of rupture time (not really used)

void tR(double s, double T, double &t): Rupture time as a function of stress.

void dtR_ds(double s, double T, double &dt): Derivative of rupture time with respect to stress.

virtual size_t nparams() const: Number of solver parameters.

virtual void init_x(double *const x, TrialState *ts): Setup an iteration vector in the solver.

virtual void RJ(const double *const x, TrialState *ts, double *const R, double *const J): Solver function returning the residual and jacobian of the nonlinear system of equations integrating the model

Public Static Functions

static std::string type(): Type for the object system.

static ParameterSet parameters(): Parameters for the object system.

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