15.5. BCJ Model

BEGIN PARAMETERS FOR MODEL BCJ
  #
  # Elastic constants
  #
  YOUNGS MODULUS = <real>
  POISSONS RATIO = <real>
  SHEAR MODULUS  = <real>
  BULK MODULUS   = <real>
  LAMBDA         = <real>
  TWO MU         = <real>
  #
  #
  #
  C1 = <real>c1
  C2 = <real>c2
  C3 = <real>c3
  C4 = <real>c4
  C5 = <real>c5
  C6 = <real>c6
  C7 = <real>c7
  C8 = <real>c8
  C9 = <real>c9
  C10 = <real>c10
  C11 = <real>c11
  C12 = <real>c12
  C13 = <real>c13
  C14 = <real>c14
  C15 = <real>c15
  C16 = <real>c16
  C17 = <real>c17
  C18 = <real>c18
  C19 = <real>c19
  C20 = <real>c20
  DAMAGE EXPONENT = <real>damage_exponent
  INITIAL ALPHA_XX = <real>alpha_xx
  INITIAL ALPHA_YY = <real>alpha_yy
  INITIAL ALPHA_ZZ = <real>alpha_zz
  INITIAL ALPHA_XY = <real>alpha_xy
  INITIAL ALPHA_YZ = <real>alpha_yz
  INITIAL ALPHA_XZ = <real>alpha_xz
  INITIAL KAPPA = <real>initial_kappa
  INITIAL DAMAGE = <real>initial_damage
  YOUNGS MODULUS FUNCTION = <string>ym_function_name
  POISSONS RATIO FUNCTION = <string>pr_function_name
  SPECIFIC HEAT = <real>specific_heat
  THETA OPT = <integer>theta_opt
  FACTOR = <real>factor
  RHO    = <real>rho
  TEMP0  = <real>temp0
END [PARAMETERS FOR MODEL BCJ]

The BCJ plasticity model is a state-variable model for describing the finite deformation behavior of metals. It uses a multiplicative decomposition of the deformation gradient into elastic, volumetric plastic, and deviatoric parts. The model considers the natural configuration defined by this decomposition and its associated thermodynamics. The model incorporates strain rate and temperature sensitivity, and damage, through a yield-surface approach in which state variables follow a hardening-minus-recovery format.

Because the BCJ model has such an extensive list of parameters, we will not present the usual synopsis of parameter names with command lines. As with most other material models, the thermal strain option is used to define thermal strains. See the Sierra/SM User Manual for further information on defining and activating thermal strains. In addition, only two of the five elastic constants are required. The user should consult [[1], [2], [3]] for a description of the various parameters. The parameters for the SPECIFIC HEAT, THETA OPT, FACTOR, RHO, and TEMP0 command lines are used to accommodate changes to the model for heat generation due to plastic dissipation. For coupled solid/thermal calculations, the plastic dissipation rate is stored as a state variable and passed to a thermal code as a heat source term. For uncoupled calculations, temperature is stored as a state variable, and temperature increases due to plastic dissipation are calculated within the material model.

If temperature is provided from an external source, theta_opt is set to 1. If the temperature is calculated by the BCJ model, theta_opt is set to 1.

Output variables available for this model are listed in Table 15.3.

Table 15.3 State Variables for BCJ Model

Name	Description
BACK_STRESS_XX	back stress tensor - xx component
BACK_STRESS_YY	back stress tensor - yy component
BACK_STRESS_ZZ	back stress tensor - zz component
BACK_STRESS_XY	back stress tensor - xy component
BACK_STRESS_YZ	back stress tensor - yz component
BACK_STRESS_ZX	back stress tensor - zx component
KAPPA	hardening scalar
DAMAGE	damage term
DAMAGE_RATE	rate of change of damage term
EQPS	equivalent plastic strain
THETA	temperature for adiabatic heating
HEAT	rate of heating due to plastic dissipation
YM	Young’s modulus
PR	Poisson’s ratio

Warning

Strongly rate-dependent models may fare poorly in implicit quasistatic solution. In implicit analyses the rate term used to evaluate the current load step is the rate seen by the model in the previous load step. This may cause the solution to oscillate between high- and low-rate equilibrium states from step to step.

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[1]

D.J. Bammann, M.L. Chiesa, and G.C. Johnson. Modelling large deformation and failure in manufacturing processes. In T. Tatsumi, E. Watanabe, and T. Kambe, editors, Proceedings of the 19th International Congress of Theoretical and Applied Mechanics, 359–376. Amsterdam, 1997. Elsevier Science Publishers.

[2]

D.J. Bammann, M.L. Chiesa, M.F. Horstemeyer, and L.E. Weingarten. Failure in ductile materials using finite element methods. In N. Jones and T. Wierzbicki, editors, Structural Crashworthiness and Failure, 1–53. London, 1993. Elsevier Applied Science.

[3]

D.J. Bammann. Modeling temperature and strain dependent large deformations in metals. Applied Mechanics Reviews, 43(5):312–319, 1990. doi:10.1115/1.3120834.