Multiscale modeling of plasticity: application to forming processes

 Engineering alloys are heterogeneous materials formed by aggregation of grains with different orientation of one or more metallic phases. Plastic deformation occurs by dislocation and/or twinning in each microscopic grain and depends on the grain orientation, size and shape, the stresses acting on the grain, and the constraint imposed by the deformation of the neighbor grains. From a macroscopic viewpoint, the plastic flow of engineering alloys is usually modeled by means of phenomenological models (such as J2 or Drücker-Prager), which parameters can be obtained from simple tension tests. These models cannot establish, however, the relationship between the microstructure and the macroscopic behavior (because of their phenomenological foundation) and its accuracy is doubtful during processes in which the grain size, shape and orientation changes dramatically during deformation, as in the case of many forming processes (rolling, forging, ECAP, etc.).

To overcome these limitations, researchers from IMDEA Materials Institute and UPM – in collaboration with Los Alamos National Laboratory – has developed a novel multiscale modeling tool to simulate the plastic deformation of polycrystalline materials at the microscopic and macroscopic scales [1]. The simulation tool is based in a continuum crystal plasticity approximation of the grain deformation at the microscopic scale. At the macroscale, each point of the solid corresponds to a polycrystal formed by a few hundred grains and its plastic response is obtained using a homogenization technique (the visco-plastic self-consistent scheme [2]). This information is used within the framework of the finite element model to determine the macroscopic mechanical response. The macroscopic fields provided by the finite element analysis are used as input to compute the deformation of each polycrystal in which the evolution of the microstructure is updated during the simulation (Fig. 1).

The new tool is able to carry out accurate simulations of complex forming processes such as cold rolling, forging or ECAP. For instance, the simulation of cold rolling of a 6061 Al alloy sheet is depicted in Fig. 2. The finite element model is able to incorporate the macroscopic details (cylinders size, rolling speed, friction, etc.), while the microstructure at each point is represented by a polycrystal containing 500 grains whose shape and orientation evolves during the simulation. Thanks to the multiscale approach, both macroscopic fields and microscopic information are solved simultaneously and, for instance, the grain orientation distribution (texture) in each point of the sheet is obtained, Fig 2(c). 


Figura 1

Figure 1: Multiscale modeling framework to simulate the plastic deformation of polycrystalline engineering alloys [1]. (a) Macroscale, where the global geometry and boundary conditions of the solid are defined and (b) Microscale representing the polycrystalline microstructure at each point of the solid.

Figura 2

Fig 2: (a) Actual rolling of an Al alloy plate. (b) Schematic of the rolling process (c) Multiscale simulation of cold rolling of an Al alloy with 50% of reduction. The pole figures corresponding to the <111> direction are shown for two points (near the center and near the surface) of the plate.


[1] J. Segurado, R. A. Lebensohn, J. Llorca, C. N. Tomé. Multiscale modeling of plasticity based on embedding the viscoplastic self-consistent formulation in implicit finite elements. Int. J. Plasticity 28, 124-140, 2012

[2] R. A. Lebensohn, C. N. Tomé. A self-consistent anisotropic approach for the simulation of plastic deformation and texture development of polycrystals: Application to zirconium alloys .Acta Metall. Mater, 41, 2611–2624, 1993