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

1. 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}
2. 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}
3. 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.

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
  1. type 2a)
  2. type 2b)
  3. type 2c)
• the third digit $r\in\{1,2,3,4\}$ specifies the transition between creep curves
  1. “Strain Hardening” theory
  2. “Time Hardening” theory
  3. “Life Fraction Rule” theory
  4. “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:

• 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.