Model Anisotropic Behaviour and Texture Evolution with DEFORM

When performing large deformation simulations, it is typically assumed that the workpiece is isotropic. This means that the thermomechanical properties of the material do not have any directional dependence. However, this assumption may not always be appropriate since many polycrystalline materials develop anisotropic (directionally-dependent) properties with increasing deformation. Anisotropy can be caused by changes in the microstructure due to deformation. This article describes how DEFORM offers several options to modal anisotropic behaviour and texture evolution.

Texture and Anisotropy

A polycrystalline material contains many grains, each of which has an independent orientation. Depending on the previous thermomechanical processing, a polycrystalline material may initially appear to be isotropic due to a random orientation distribution of grains. When a bulk polycrystalline material is plastically deformed, the grains will rotate to accommodate the deformation and to align their active slip systems with the direction of deformation. As deformation continues, the orientation distribution of the grains will become less random. When the concentration of the grains with similar orientations is significant, the material is said to have texture. A material will begin to demonstrate anisotropic behaviour as texture develops, and the degree of anisotropy is proportional to the amount of ‘texturing’ in the material.

Anisotropic Yield Criteria

The simplest way to model anisotropic behaviour, without modelling the evolution of texture, is an anisotropic yield criterion. A yield criterion describes the elastic limit of a material for any and all loading conditions. In plasticity, the Quadratic Hill yield criterion is the most frequently used anisotropic model. Hill’s yield surface is defined by the applied stress state and six anisotropic material coefficients (three normal and three shear). To account for anisotropy in a bulk of forming simulation, DEFORM uses generalised Hill yield definition together with location dependent material axes. To account for planer anisotropy, typical for sheet forming applications, the six coefficients can be reduced to three Lankford coefficients. During the simulation, the orientation of the material axes at each element update with deformation. The deformation of each element is based on the orientation of the local material axes and the global anisotropic coefficients. For this type of anisotropic simulation, the overall simulation procedure and computational requirements are similar to a typical isotropic simulation. When using one of these models, the anisotropic coefficients usually do not evolve with deformation. The first example used Hill’s model to predict anisotropic distortion during an upset. Two cylindrical billets were cute form material that was strengthened only in the longitudinal direction (LD). When upset, the final shape and forming load were affected by the orientation of the compression axis with respect to LD. It demonstrates a higher forming load and uniform radial deformation. The transverse billet (TS) was upset normal to LD, resulting in a distorted shape and lower forming load.

Crystal Plasticity

Crystal Plasticity (CP) models are useful when directly modelling the evolution of texture with deformation. In general, CP models use a set of weighted orientations to represent a polycrystalline as a discrete number of grains. In the ideal case, texture and texture-dependent anisotropic are computed and updated for each integration point at every step of simulation. However, CP models often have extremely long runtimes which diminish the practicality of using ‘runtime’ CP model in an industrial setting. In DEFORM, a viscoelastic self-consistent (VPSC) and a Taylor CP model are available as a postprocessor material point simulator. Results are obtained in a reasonable amount of time by only evaluating the evolution of texture at specific points of interest. However, since this model is implemented as a post processing tool, a nominal run is required prior to use. The texture evolution calculations are then made from the deformation and temperature history carried over from the nominal run. The provided inverse pole figures were obtained using the VPSC CP model to predict evolution of texture at the centre of copper wire cold drawn to a 54% reduction. The figures show the concentration of material directions parallel to the drawing direction. From left to right, the figures represent the initial texture, texture after the first pass, and the final texture. A texture develops that is typical for drawn FCC materials (strong 111 and weak 100). This example took advantage of a tool available in Material Suite that fits CP model parameters to experimental flow stress data.

Texture Based Yield Surface

The texture based yield surface uses the generalised Hill model and local material axes to simultaneously account for evolving texture and anisotropic material properties during deformation. To minimise the computing time, a crystal plasticity model is converted to pre-computed Hill coefficients for each orientation. The initial texture is represented at each element, and can be defined as EBSD or a user specified orientation distribution of the grains. The overall anisotropic material flow stress coefficients for each element ate computed based on local texture, material axes, and associated pre-computed single crystal responses. Like many other state variables, the texture for each element is updated at the end of each solution step. Computational efficiency is achieved by eliminating the need to calculate the texture-dependant flow stress at every integration point for each step. This allows the user to run a coupled texture and anisotropic metal flow simulation in a reasonable amount of time. A tool I available in Material Suite that will convert a working CP model into this pre-computed tabular data form.

Conclusions

DEFORM offers a variety of options to model texture evolution and anisotropic behaviour. Outlined in the table below, each method has capabilities and limitations that make it suitable for certain applications. For more information, please contact us.

DEFORM V11.0.2 Release

DEFORM V11.0.2 was released in December 2014. Important GUI improvements include:

• Target value calculations were restored in Forming Express (3D).
• Report generator was improved.
• Support was added for scheduled rotation across passes in ALE shape rolling with quarter symmetry.
• Picture-in picture was revamped in the postprocessor.
• Updating of reference points across multiple operations was enhanced.
• Improvements were made to coupled die stress analysis and EP objects.
• The sub-stepping procedures were improved for hyper-elastic models.
• Frictional heat computations were enhanced for models with multiple deforming objects containing regular and mixture materials.

New Features in V11.1

DEFORM V11.1 is being targeted for early 2016 release. Some of the new features include:

• New pre-processor
• Improved license manager
• Enhanced batch queue server
• Revamped simulation server
• Multiple DOE simulation servers
• CAD (SolidWorks) integration
• Improved postprocessor
• Improved material suite
• New DEFORM viewer
• 2.5D FEM functionality in new shape rolling template
• New 2D and 3D cutting templates
• New Forming Express
• Database comparison in postprocessor
• Improved contact search options
• 64 Bit 2D FEM engine
• Discrete DOE variables
• Domain decomposition FEM solver
• Duel mesh FEM solver
• Solidification and melting modelling
• Multiple 64 bit modules
• Various bug fixes

For further information on DEFORM software, training and consultancy services please contact us.

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