Interpretation of microstructural evolution using dynamic materials modeling
- PDF / 54,987 Bytes
- 2 Pages / 612 x 792 pts (letter) Page_size
- 99 Downloads / 229 Views
]
where s and «˙ are flow stress and strain rate, respectively. The area under the stress-strain rate curve is denoted by G, where «˙
G5
es d«˙
[2]
0
G has been termed as the dissipater content. This component, according to DMM, causes temperature rise in the workpiece. The complementary part, which is denoted by J, is termed as the dissipater power co-content and is described as follows: s
J5
e«˙ ds
[3]
0
When the workpiece material follows the constitutive equation
s 5 K(«˙ )m
[4]
where m is the strain rate sensitivity and K is a constant, the dissipater co-content can be written as J5
s m«˙ m11
J 2m 5 Jmax m 1 1
[6]
SUDIPTO GHOSH, Scientist, is with the Process Modeling Group, Tata Research Development and Design Centre, Pune, India 411 013. Manuscript submitted December 7, 1999.
METALLURGICAL AND MATERIALS TRANSACTIONS A
(1) Pure diffusional flow and dynamic recrsytallization (DRX): As per the DMM, h is 1 (maximum possible value) for pure diffusional flow and much less (0.3 to 0.5) in the case of DRX.[2] However, in the case of DRX, it is well known that some fraction of external energy supplied gets stored in the form of potential energy due to high dislocation density and, subsequently during DRX, is converted into heat. On the other hand, during pure diffusional flow, which as per DMM should dissipate more energy through a microstructural mechanism, no energy is added to the material in the form of microstructural change. (2) Structural superplasticity (SSP): Structurally superplastic materials usually exhibit a sigmoidal relationship between the steady-state flow stress and strain rate, when the data are plotted logarithmically. As per this variation, the strain rate domain is divided into three regimes, commonly referred to as region I, region II, and region III of superplasticity. The intermediate regime of strain rate, i.e., region II, exhibits higher strain rate sensitivity (0.4 , m , 1) as compared to low (region I) and high (region III) strain rate regimes. Consequently, h in region II is higher than in region I and region III. Let us now analyze the variation in h with strain rate in terms of microstructural mechanisms, in the case of structural superplasticity. Two types of power dissipation through microstructural mechanisms are possible during SSP.
[5]
At one extreme, J can be as high as G when m 5 1, and, on the other hand, J 5 0 when m 5 0. The case of m 5 1 has been considered to be an ideal case and an efficiency term has been defined as
h5
According to Prasad et al.,[1] when two major processes having different characteristics occur simultaneously, the value of J will reach its maximum when the energy of dissipation of one process equals that of the other. Although Montheillet et al.[6] have highlighted the importance of G and J in calculations based on variational principles in mechanics of solids, they have pointed out that quality of dissipation and dynamic metallurgical processes should not be identified with G and J, respectively. According to them, the strain rate
Data Loading...
