Time Hardening model

The Time Hardening creep model is a combination of Norton-Bailey model, describing the primary phase, and Norton Model, describing the secondary phase. With the assumption of a constant temperature the model is defined by five constants: $K_1$ to $K_5.$

The creep strain is the sum of strains of both models and is defined as $\varepsilon_c = K_1\sigma_e^{K_2}t^{K_3}+K_4\sigma_e^{K_5}t\tag{1}\label{1}$ and the creep strain rate as $\dot\varepsilon_c = K_1\sigma_e^{K_2}K_3t^{K_3-1}+K_4\sigma_e^{K_5}.$

Implementation in ANSYS

In ANSYS, this model is denoted $\mathtt{TBOPT}=11.$ The creep strain is defined as $\varepsilon_c = \frac{C_1\sigma_e^{C_2}t^{C_3+1}e^{-C_4/T}}{C_3+1}+C_5\sigma_e^{C_6}te^{C_7/T}.\tag{2}\label{2}$

If we assume a constant temperature, it is $C_4=C_7=0,$ and the equation $\eqref{2}$ has the form $\varepsilon_c = \frac{C_1\sigma_e^{C_2}t^{C_3+1}}{C_3+1}+C_5\sigma_e^{C_6}t.\tag{3}\label{3}$

Comparing $\eqref{1}$ and $\eqref{3}$ we obtain the conversion equations: $\begin{align} K_1 &= C_1/(C_3+1) & C_1 &= K_1K_3\\ K_2 &= C_2 & C_2 &= K_2\\ K_3 &= C_3+1 & C_3 &= K_3-1\\ K_4 &= C_5 & C_4 &= 0\\ K_5 &= C_6 & C_5 &= K_4\\ & & C_6 &= K_5\\ & & C_7 &= 0 \end{align}$

Input quantities

The Time Hardening model is activated by the parameter $\mathtt{KCRP}=4$ in the file name.iP. All materials used must be assigned to the elements using the file name.DAT. The material parameter files have the following structure:

* * Comments * TH MODEL PMD/ANSYS POCET DAT

$N$ DATA

$T_1$

$K_{11}$

$K_{21}$

$K_{31}$

$K_{41}$

$K_{51}$

$\vdots$

$T_N$

$K_{1N}$

$K_{2N}$

$K_{3N}$

$K_{4N}$

$K_{5N}$

The number of initial comment lines is unlimited.
There must be an empty line before each block.
The block TH MODEL contains the keyword either PMD, or ANSYS (see below).
The block POCET DAT contains the number of lines $N$ in the block DATA, $N\le20.$
The block DATA contains $N$ lines of six values $[T,K_1,K_2,K_3,K_4,K_5]$ (for model PMD), or $[T,C_1,C_2,C_3,C_5,C_6]$ (for model ANSYS). Temperatures are specified in $^\circ\text{C}.$

Example

There is only one material used in the creep problem.

name.iP

; KREST NLC NCYC KMOD KCRP KLARG KCNT
IP  1    11   1    0    4    0     0  3*0  11*2
RP 10*0 0 1 100 1000 10000 30000 80000 120000 160000 200000 250000
EN
EN

name.DAT

number 1
thans.dat

thans.dat

************************************************************************
*                                                                      *
*     test example                                                     *
*                                                                      *
*     parameters   description                                         *
*                                                                      *
*     TH MODEL     identification of the Time Hardening model          *
*     PMD/ANSYS    flag specifying which coefficients are present      *
*                     T K1 K2 K3 K4 K5 - PMD                           *
*                     T C1 C2 C3 C5 C6 - ANSYS                         *
*     POCET DAT    the number of data lines (max. 20)                  *
*     DATA         6 parameters on each line                           *
*        T         temperature in deg. Celsius                         *
*        K1 - K5   model parameters                                    *
*                                                                      *
************************************************************************

TH MODEL
ANSYS

POCET DAT
2

DATA
540  1.9907955E-08   1.41564      -0.65744   5.96523E-18   5.494
560  1.9907955E-08   1.41564      -0.65744   5.96523E-18   5.494