Dislocation density-based constitutive model for metal forming simulation


Dislocation-density-dependent physical-based constitutive models of metal plasticity are computationally efficient. These models consider material history and accurately account for varying process parameters such as strain rate and temperature; and also for different loading modes such as continuous deformation, creep and relaxation; microscopic metallurgical processes; and varying chemical composition within an alloy family.

Since these models are based on essential microstructural phenomena dominating the deformation, they have a larger range of usability and validity. In addition, they are suitable for simulating manufacturing chain simulations since they efficiently compute the cumulative effect of the various manufacturing processes by following the material state through the entire manufacturing chain including interpass periods. Thus, a realistic prediction of the material behavior and final product properties can be given.

The physical-based constitutive material model for cold metal forming presented in this study can describe the behavior of polycrystalline materials using microstructural/physical state-dependent variables (MSDVs) such as dislocation density and effective grain size.

The evolution of these internal variables are calculated using equations describing physical processes dominating the material behavior during plastic deformation. The model is numerically implemented in general implicit isotropic elasto-viscoplasticity algorithm as a user-defined material subroutine (UMAT) in ABAQUS/Standard and used for finite element simulation of upsetting tests and a complete cold forging cycle of case hardenable MnCr steel family.

As an application, an actual industrial cold forging process of bevel gear has been modelled consisting of four steps: preform forging, interpass, final forging, and air cooling. These four steps are thermo-mechanically simulated using the developed constitutive model implemented as a UMAT in ABAQUS/Standard.

The FE simulations that are performed using this fully coupled thermomechanical-metallurgical material model confirm that it has the following advantages:

  • In contrary to the common thermo-mechanical empirical constitutive models of metal plasticity that regard the (accumulated) equivalent plastic strain as the main internal variable, the main internal variable of the introduced physical-based constitutive model (dislocation density) is a function of temperature and strain rate.
  • The dislocation density is calculated in each step in the manufacturing chain of a product. Therefore, the material model can be effectively applied for through-process simulation.
  • The model predicts the material behavior in static recovery condition for instance during relaxation tests and in interpass time. Whereas, common empirical models that are applied for continuous loading modes are not able to predict static material behavior that occurs in the interpass time.
  • The FE-simulated and experimental results of cold metal forming are in good agreement for various loading parameters while the simulations are computationally efficient. The simulation costs are not considerably higher from those of empirical models.
  • The material model can be used for different alloy grades with various chemical compositions that belong to the same alloy family.
  • The main physical internal variable of the model (dislocation density) can be used for calculation of some other useful physical variables such as volumetric stored elastic energy, damage, and Vickers hardness.
  • The stored dislocation density distribution is in good accordance with the measured geometrically necessary dislocation (GND) density and the evolution of microstructure during subsequent heat treatment process. Regions of the bevel gear with high dislocation density show fine-grained structure whereas areas of low dislocation density show abnormal grain growth.
  Dislocation density [1014 m-2] distribution at the end of cold forging of bevel gear; and EBSD images of geometrically necessary dislocation (GND) density as well as microstructure (local prior austenite grain size) development after heat treatment. Copyright: © IEHK Figure: Dislocation density [1014 m-2] distribution at the end of cold forging of bevel gear; and EBSD images of geometrically necessary dislocation (GND) density as well as microstructure (local prior austenite grain size) development after heat treatme