The behavior of materials can be modeled at three different hierarchical levels with varying spatial scales. A structure or a specimen with a scale greater than 10^{-3} m represents the macroscopic scale where the principle of continuum mechanics is generally used. At this level, only materials macrostrcuture and global properties are considered; At the other extreme, atomic scale spans the lengths of a few nanometers (10^{-9}-10^{-6} m), which is compatiable with the length scale of crystalline defects (e.g. vacancy, impurity, dislocation, grain boundary and interface). Though at this level the microstructure is difficult to directly related to materials macro-level property, it provides very useful information for the high level (mesoscopic) study. Such information is vital for understanding the materials behavior and guiding materials design; In between the two levels lies the mesoscopic scale where the action of individual grains are (10^{-6}-10^{-3} m) modeled. It is at this level, that materials property is directly related to the structure.
Grain boundary sliding (GBS) is believed to be the dominant strain producing mechanism during superplastic deformation. Most of the existing models relate the strain rate of the accommodation processes of GBS to the macroscopically measured superplastic strain rate. Such a relationship implies that the total strain in a superplastic material is governed purely by the accommodation processes. Based on this concept, we have developed a micromechanical polycrystalline model to predict the behavior of superplastic deformation with various grain sizes and temperatures. This model significantly differs from the existing models in that it is developed from the grain level to the level of the aggregate in an explicit manner.
The overall strain rate is considered as the sum of the strain rates contributed by diffusional flow (bulk and boundary diffusion) and dislocation movements. In our micromechanical model, diffusion is the dominant rate controlling mechanism at low stress region. Hence the threshold stress is introduced in the diffusion processes in both the boundary and lattice diffusion in order to describe the experimentally observed macro level threshold stresses. This numerical mode l based on micromechanics is appl ied to both conventional superplastic materials (e.g. 7475 aluminum alloy and Al-Zn-Mg-Cu alloy) and high strain-rate superplastic (HSRS) materials (e.g. IN905XL), to predict the superplastic behavior of materials in all the three regions of the flow stress vs. strain rate plot and to predict the presence or absence of superplasticity in a given material. With the introduction of the threshold stress, the influence of temperature and grain size on the behavior of these materials can be predicted over a wider range of strain rates. In addition the strain-rate sensitivity as a function of strain rate can be fairly accurately predicted. The variation of threshold stress with respect to temperature is also studied.
Self-Consistent Relations Used in Our Model |  |
Prediction of Temperature Effect on Superplasticity |  |
Prediction of Grain Size Effect on Superplasticity |  |
1. N. Chandra and P. Dang, "Numerical Modeling of Superplastic Deformation Mechanism", Materials Science Forum (Proceedings of 1997 International Conferenceon Superplasticity), vol. 243-245, 1997, pp53-58.
2. N. Chandra and P. Dang, "Application of Micromechanical Model to High Strain-Rate Superplastic Materials", Accepted for publication in Scripta Metallurgica, January, 1997 (in print).
3. N. Chandra, J. Rama, and P. Dang, "Application of Micromechanical Polycrystalline Model in the Study of Threshold Stress Effect on Superplasticity", Accepted for publication in Materials Science and Engineering A, January, 1997 (in print).
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