Norton-Bailey model

The Norton-Bailey creep model describes the primary phase. With the assumption of a constant temperature the model is defined by three constants: $K,$ $n,$ and $m.$

The creep strain is defined as $$\varepsilon_c = K\sigma_e^nt^m\tag{1}\label{1}$$ and the creep strain rate as $$\dot\varepsilon_c = K\sigma_e^nmt^{m-1}.\tag{2}\label{2}$$

Implementation in ANSYS

In ANSYS, this model is denoted $\mathtt{TBOPT}=2$ (“time hardening”) or $\mathtt{TBOPT}=6$ (“modified time hardening”). For the former, the creep strain rate is defined as $$\dot\varepsilon_c = C_1\sigma_e^{C_2}t^{C_3}e^{-C_4/T}\tag{3}\label{3}$$ and for the latter, the creep strain is defined as $$\varepsilon_c = \frac{C_1\sigma_e^{C_2}t^{C_3+1}e^{-C_4/T}}{C_3+1}.\tag{4}\label{4}$$ The constants $C_1$ to $C_4$ in both equations are the same.

If we assume a constant temperature, it is $C_4=0$ and the equations \eqref{3} and \eqref{4} have the form $$\dot\varepsilon_c = C_1\sigma_e^{C_2}t^{C_3} \quad\text{and}\quad \varepsilon_c = \frac{C_1\sigma_e^{C_2}t^{C_3+1}}{C_3+1}.\tag{5}\label{5}$$ Comparing \eqref{1} and \eqref{2} to \eqref{5} we obtain the conversion relations: \begin{align} K &= C_1/(C_3+1) & C_1 &= Km\\ n &= C_2 & C_2 &= n\\ m &= C_3+1 & C_3 &= m-1\\ & & C_4 &= 0 \end{align}

Input quantitites

The Norton-Bailey model is activated by the parameter $\mathtt{KCRP}=3$ 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 *

NB MODEL PMD/ANSYS

POCET DAT $N$

DATA - T K N M $T_1$ $K_1$ $n_1$ $m_1$ $\vdots$ $T_N$ $K_N$ $n_N$ $m_N$

The number of initial comment lines is unlimited.
There must be an empty line before each block.
The block NB MODEL contains the keyword either PMD, or ANSYS (see below).
The block POCET DAT contains the number of lines $N$ in the block DATA, $N\le30.$
The block DATA - T K N M contains $N$ lines of four values $[T,K,n,m]$ (for model PMD), or $[T,C_1,C_2,C_3]$ (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    3    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
nbpmd.dat

nbpmd.dat

************************************************************************
*                                                                      *
*     test example                                                     *
*                                                                      *
*     parameters   description                                         *
*                                                                      *
*     NB MODEL     identification of the Norton-Bailey model           *
*     PMD/ANSYS    flag specifying which coefficients are present      *
*                     T K N M    - PMD                                 *
*                     T C1 C2 C3 - ANSYS                               *
*     POCET DAT    the number of data lines (max. 30)                  *
*     DATA         4 parameters on each line                           *
*        T         temperature in deg. Celsius                         *
*        K         model parameter                                     *
*        N         model parameter                                     *
*        M         model parameter                                     *
*                                                                      *
************************************************************************

NB MODEL
PMD

POCET DAT
5

DATA
570 3.02676E-13 4.3128 0.3633
580 6.2959E-14  4.5927 0.4204
590 9.45498E-15 4.9251 0.4922
600 7.00039E-16 5.3745 0.5907
610 2.168E-17   5.9644 0.7260