On the evaluation of efficiency parameters in processing maps
- PDF / 207,273 Bytes
- 2 Pages / 612 x 792 pts (letter) Page_size
- 78 Downloads / 185 Views
THE mechanical behavior of materials under processing is generally characterized by the constitutive equations, which relate the flow stress (s) to the strain (ε), strain rate (εz ), and temperature (T ). The constitutive equations are experimentally evaluated using mechanical testing techniques and represented either in the form of empirical rate equations, which aid in identification of the specific atomic rate-controlling mechanisms, or in the form of simple algebraic equations, which can be used in process modeling. Recognizing the practical difficulty in making use of deformation, fracture, and processing maps based on atomic mechanisms, Prasad et al.[1] suggested the dynamic materials modeling (DMM) approach for describing the material behavior under processing conditions. This approach is reviewed by Gegel et al.[2] and Alexander.[3] In brief, the model considers the workpiece as a dissipator of power, and the constitutive equation describes the manner in which the power is converted at any instant in two forms: thermal and microstructural, which are not recoverable by the system. The dissipative element can be considered to be nonlinear, dynamic, and irreversible. At any instant, the total power dissipated consists of two complementary parts: G content, representing the temperature rise, and J co-content, representing the dissipation through metallurgical processes. The factor that partitions power between G and J is the strain-rate sensitivity (m) of the flow stress (s). For an ideal linear dissipator, J 5 Jmax 5 1/2 s εz . The variation of the efficiency parameter, h ([J/Jmax) with ε, εz , and T, represents the power dissipation characteristics of the workpiece material occurring through microstructural changes. In order to create the processing map, Ravichandran and Prasad[4] recommend the following procedure for the evaluation of h from the effective stress and the effective strain rate values, which were extracted through hot compression testing at various strain levels and temperatures: log (s)log (εz ) data at a constant ε and T are fitted using a cubic spline, and the strain-rate sensitivity (m), i.e., the slope of the log (s)-log (εz ) curve, is calculated as a function of εz . This is repeated at different ε and T. The efficiency parameter, h ([2m/(m 1 1)) is then calculated from a set of m values as a function of εz and T and plotted as a threedimensional (3-D) map. The 3-D variation is better viewed as an isoefficiency contour map in the εz -T plane. The objective of this study is to suggest a modification in the preS.V.S. NARAYANA MURTY, Scientist/Engineer, Materials and Metallurgy Group, M.S. SARMA, Scientist/Engineer, Applied Mathematics Division, and B. NAGESWARA RAO, Scientist/Engineer, Structural Engineering Group, are with the Vikram Sarabhai Space Centre, Trivandrum 695 022, India. Manuscript submitted February 3, 1997. METALLURGICAL AND MATERIALS TRANSACTIONS A
ceding procedure by introducing a reliable numerical scheme for the evaluation of h. According to the DMM, the power P (rate o
Data Loading...
