Table of Contents
Bina model
The total creep strain in percent in time $t$ for the specified stress $\sigma$ and temperature $T$ is expressed as $$\varepsilon_\text{tot}(t|\sigma,T) = \varepsilon_0\left(\frac{\varepsilon_m}{\varepsilon_0}\right)^{g(\pi)},$$ where $\varepsilon_0$ is the initial strain, $\varepsilon_m$ is the limit strain, and $g(\pi)$ is the hardening function.
The value of the initial strain depends on the material and is given as
- type 2a) \begin{align} \varepsilon_0 &= 100\frac{\sigma}{E(T)}\\ E(T) &= E_1+E_2\exp\left(-\frac{E_3}{T}\right) \end{align}
- type 2b) \begin{align} \varepsilon_0 &= 100\frac{\sigma}{E(T)}\left[A\tanh(B\sigma)\exp\left(\frac{Q}{T^n}\right)\right]\\ E(T) &= E_1+E_2\exp\left(-\frac{E_3}{T}\right) \end{align}
- type 2c) \begin{align} \varepsilon_0 &= 100\frac{\sigma}{E(T)}\left[A\left(\frac{\sigma}{\sigma_m(T)}\right)^{m(T)}\exp\left(\frac{Q}{T^n}\right)\right]\\ E(T) &= E_1+E_2\exp\left(-\frac{E_3}{T}\right)\\ \sigma_m(T) &= B_1+B_2\exp\left(\frac{B_3}{T}\right)\\ m(T) &= N_1+N_2T+N_3T^2+N_4T^3+N_5T^4 \end{align}
The limit strain is defined as $$\varepsilon_m = \exp\left\{M_1+M_2\tanh\left[\frac{\ln(t_r)-M_3-M_4T}{M_5}\right]\right\}+100\frac{\sigma}{E(T)}.$$
The time to fracture $t_r$ is determined from $$\log(t_r) = A_1+A_2\log\left|\frac{1}{T}-\frac{1}{A_5}\right|+A_3\log\left|\frac{1}{T}-\frac{1}{A_5}\right|\log\left[\sinh(A_6\sigma T)\right]+A_4\log\left[\sinh(A_6\sigma T)\right].$$
The hardening function $g(\pi)$ is then defined as $$g(\pi) = \pi^N\left[\frac{1+\exp\left(-2\pi^{K(T)}\right)}{1+\exp(-2)}\right]^M,$$ where $\pi$ is the damage $\pi=t/t_r,$ $N$ a $M$ are material constants, and parameter $K$ is defined using constants $K_1$ and $K_2$ as $$K(T)=\exp\left(K_1+\frac{K_2}{T}\right).$$
The material constants $E_1$ to $E_3,$ $A,$ $B,$ $Q,$ $n,$ $B_1$ to $B_3,$ $N_1$ to $N_5,$ $A_1$ to $A_6,$ $M_1$ to $M_5,$ $N,$ $M,$ $K_1,$ and $K_2$ are specified in separate input files, see below.
Input quantities
The Bina model is activated by the parameter $\mathtt{KCRP}=pqr$ in the file name.iP
, where:
- the first digit $p=2$
- the second digit $q\in\{1,2,3\}$ specifies the calculation of initial strain
- type 2a)
- type 2b)
- type 2c)
- the third digit $r\in\{1,2,3,4\}$ specifies the transition between creep curves
- “Strain Hardening” theory
- “Time Hardening” theory
- “Life Fraction Rule” theory
- “Strain Fraction Rule” theory
All materials used must be assigned to the elements using the file name.DAT
.
The material parameter files have the following structure:
* * Comments *
POCATECNI DEFORMACE $E_1$ $E_2$ $E_3$
PEVNOST PRI TECENI $A_1$ $A_2$ $A_3$ $A_4$ $A_5$ $A_6$
2B) $A$ $Q$ $B$ $n$
2C) $A$ $Q$ $n$ $B_1$ $B_2$ $B_3$ $N_1$ $N_2$ $N_3$ $N_4$ $N_5$
MEZNA DEFORMACE $M_1$ $M_2$ $M_3$ $M_4$ $M_5$
FUNKCE ZPEVNENI $N$ $M$ $K_1$ $K_2$
- The number of initial comment lines is unlimited.
- There must be an empty line before each block.
- The block
POCATECNI DEFORMACE
contains the constants for the calculation of the initial strain. - The block
2B)
contains further constants for the calculation of the initial strain; if $k_B\in\{1,3\},$ this block must be omitted. - The block
2C)
contains further constants for the calculation of the initial strain; if $k_B\in\{1,2\},$ this block must be omitted. - The block
PEVNOST PRI TECENI
contains the constants for the calculation of the time to fracture. - The block
MEZNA DEFORMACE
contains the constants for the calculation of the limit strain. - The block
FUNKCE ZPEVNENI
contains the constants for the calculation of the damage function.
The program checks, according to the specified values of $k_B,$ if each material parameter file contains — or does not contain — the blocks 2B)
and 2C)
. This prevents a possible error in the parameter $\mathtt{KCRP}$ in the file name.iP
or on the material
line in the file name.DAT
.
Example
There is only one material $k_B=1$ used in the creep problem.
- name.iP
; KREST NLC NCYC KMOD KCRP KLARG KCNT IP 1 11 1 0 213 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 mat.dat
Example
There are three materials used in the creep problem. Let for the material number 1 be $k_B=3,$ for the material number 2 be $k_B=2,$ and the material number 3 be $k_B=1.$
- name.iP
; KREST NLC NCYC KMOD KCRP KLARG KCNT IP 1 11 1 0 233 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 3 mat1.dat mat2.dat mat3.dat material 2 2 8 10 13 14:15 17:20 material 3 1 37 12 21:30 35:60
Example
The sample material parameter file for a single material $k_B=1.$
- 15128_5.dat
************************************************************************ * * 15128.5 Z-89-6013 CSN 1.3.1979, (470-900/2.5E5) * * * QUANTITY UNIT * ---------------------------------------------- * Temperature [K] * Stress [MPa] * Initial strain, Limit s., Creep s. [%] * Time to fracture [h] * Creep strain rate [%/h] * * POCATECNI DEFORMACE parameters E(1) - E(3) * DOBA DO LOMU parameters A(1) - A(6) * MEZNA DEFORMACE parameters M(1) - M(5) * FUNKCE ZPEVNENI parameters N, M, K(1), K(2) * ************************************************************************ POCATECNI DEFORMACE 0.21425035E+6 -0.45038419E+6 0.19371094E+4 PEVNOST PRI TECENI -0.1840487E+2 -0.5906108E+1 0.7682633E+1 0.2298323E+2 0.6730000E+3 0.4000000E-5 MEZNA DEFORMACE 0.144927e+1 0.0E+0 0.0E+0 0.0E+0 1.0E+0 FUNKCE ZPEVNENI 0.26069593E+0 -0.80546546E+0 -0.51082559E+0 0.0