5.1.1 Tresca or Von Mises

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Subsections

5.1.1 Tresca or Von Mises

(syntax)

$\begin{figure}\centering \begin{tabbing} \texttt{'MATERI'} \\ [-1.0ex] \rule{14... ...\:{]}\\ \>\>\>\texttt{WORK}\\ \>\>\>\texttt{STRAIN} \end{tabbing} \end{figure}$

YIELD

specifies the criterion to be used: TRESCA for Tresca [§17.1.1] or VMISES for Von Mises [§17.1.2].

YLDVAL

sy is the yield stress $\sigma_{{\mathrm{y}}}^{}$ .

HARDIA

specifies a hardening diagram: sy1 to syn ( n $\leq$ 100 )are the yield stresses $\sigma_{{\mathrm{y}}}^{}$ and k1 to kn the corresponding equivalent plastic strains $\kappa$ [Fig.17.3c,d].

NADAI

invokes the hardening function according to the Nadai relation:

$\displaystyle \sigma_{{\mathrm{y}}}^{}$ = $\displaystyle \sigma_{{0}}^{}$ + C $\displaystyle \left(\vphantom{ \varepsilon ^{p0} + \kappa }\right.$ $\displaystyle \varepsilon^{{p0}}_{}$ + $\displaystyle \kappa$ $\displaystyle \left.\vphantom{ \varepsilon ^{p0} + \kappa }\right)^{{{n}}}_{{}}$

(5.1)

Value sig0 is the stress shift factor $\sigma_{{0}}^{}$ , c is the hardening constant C , n is the hardening exponent n and eps0 is the strain shift factor $\varepsilon^{{p0}}_{}$ .

VOCE

invokes the hardening function according to the Voce relation:

$\displaystyle \sigma_{{\mathrm{y}}}^{}$ = $\begin{displaymath}\begin{cases} \sigma _{0} + C \left( 1 - e^{- \tfrac{\kappa ... ... \qquad &\text{if} \quad \kappa < \varepsilon ^{p1} \end{cases}\end{displaymath}$

(5.2)

Value sig0 is the initial yield stress $\sigma_{{0}}^{}$ , c is the hardening constant C , eps0 is the hardening exponent $\varepsilon^{{p0}}_{}$ and eps1 is the yield plateau $\varepsilon^{{p1}}_{}$ .

HARDEN

specifies the hardening hypothesis: WORK for work hardening or STRAIN for strain hardening. [STRAIN]

Hardening plasticity (file.dat)

'MATERI'
   1  YOUNG  200000.
      POISON 0.3
      YIELD  VMISES
      HARDEN WORK
      HARDIA 200. 0.  300. 0.0015  400. 0.006  400. 100.

This example shows the input of a metal with a hardening diagram as shown in Figure 17.3b. Note that the last (horizontal) branch of the diagram must also be specified (400. 100.).

5.1.1.1 Ambient Influence

The yield stress for the Tresca or Von Mises criterion may be specified depending on ambient values for temperature, concentration or maturity. In this case the criterion name as indicated in the previous sections must be specified together with the data records in this section. It is not necessary to specify the constant values.

No hardening (syntax)

$\begin{figure}\centering \begin{tabbing} \texttt{'MATERI'} \\ [-1.0ex] \rule{14... ...extit{mvz}}$_{r}\,$ \texttt{\textit{syz}}$_{r}\,$ \end{tabbing} \end{figure}$

: Values sya to syz are the yield stresses $\sigma_{{\mathrm{y}a}}^{}$ to $\sigma_{{\mathrm{y}z}}^{}$ , respectively valid for the corresponding z ambient values. (z $\leq$ 30 )
TEMYLD: specifies temperature influence, values tea to tez are temperatures T .
CONYLD: specifies concentration influence, values coa to coz are concentrations C .
MATYLD: specifies maturity influence, values mva to mvz are maturity variables M .

(file.dat)

'MATERI'
  1   YIELD     VMISES
      CONYLD    0.0  500.0
                1.0  400.0

Hardening (syntax)

$\begin{figure}\centering \begin{tabbing} \texttt{'MATERI'} \\ [-1.0ex] \rule{14... ...2}}$_{r}\,$ \ldots \texttt{\textit{syzn}}$_{r}\,$ \end{tabbing} \end{figure}$

Ambient dependent hardening needs the specification of hardening diagrams for the z ambient values. (z $\leq$ 30 )

KAPPA: k1 to kn are the equivalent plastic strains $\kappa$ (n $\leq$ 30 )for which points in the diagrams are specified.
: Values sya1 to syan are the yield stresses $\sigma_{{\mathrm{y}}}^{}$ valid at ambient value __a for the specified $\kappa$ 's. Values syb1 to sybn are valid at ambient value __b etc.
TEMYLD: specifies temperature influence, values tea to tez are temperatures T .
CONYLD: specifies concentration influence, values coa to coz are concentrations C .
MATYLD: specifies maturity influence, values mva to mvz are maturity variables M .

(file.dat)

'MATERI'
  1   YIELD    VMISES
      KAPPA             0.00   0.01   1.00
      TEMYLD   -100.0  500.0  700.0  700.0
                100.0  500.0  700.0  700.0
                500.0  400.0  450.0  450.0
                700.0  300.0  300.0  300.0

5.1.1.2 User-supplied

DIANA offers the user-supplied subroutine mechanism for cases where the hardening or the ambient influence on the yield stress for the Tresca or Von Mises criterion cannot be input as described. In this case the criterion name as indicated in the previous sections must be specified together with the data records in this section. It is not necessary to specify the constant values. The yield stress can be a function of equivalent plastic strain, temperature, concentration, maturity and time.

Hardening (syntax)

$\begin{figure}\centering \begin{tabbing} \texttt{'MATERI'} \\ [-1.0ex] \rule{14... ...{USRPAR}\>\texttt{\textit{usrpar}}$_{r\ldots}\,${]} \end{tabbing} \end{figure}$

SQVCRV: USRCRV specifies that the yield stress is determined via the user-supplied subroutine USRCRV [§11.3.1].
USRPAR: usrpar are the parameters of the hardening curve.

DIANA passes the following information to subroutine USRCRV: the character string 'SQVCRV' via argument parnam and parameters usrpar via argument usrpar.

(file.dat)

'MATERI'
  1   YIELD    VMISES
      SQVCRV   USRCRV
      USRPAR   1.5 0.02

Next: 5.1.2 Mohr-Coulomb or Drucker-Prager Up: 5.1 Isotropic Plasticity Previous: 5.1 Isotropic Plasticity Contents Index

DIANA-9.3 User's Manual - Material Library
First ed.

Copyright (c) 2008 by TNO DIANA BV.