An analysis for the effect of a grain size gradient on torsional and tensile properties
- PDF / 1,015,182 Bytes
- 7 Pages / 613 x 788.28 pts Page_size
- 24 Downloads / 230 Views
I.
INTRODUCTION
A novel concept recently arising in alloy design is that processing methods, which select and assemble the constituents into composites or aggregates, must have greater design potential than the more conventional cast and wrought approaches. Such conventional approaches usually have the express aim of achieving homogeneity and a preoccupation with macroscopic and microscopic defects. In contrast, materials with "tailored" variations in composition from one location to another can offer great potential for applications where resistance to stress or to environmental attack is desired to be nonuniform. Such materials with "tailored" variations are termed as gradient materials. For example, case hardening by carburizing or nitriding may be loosely classified as a gradient material approach. The objective of this work is to present a continuum mechanics analysis of flow properties which vary with position as a result of a gradient microstructure. In the past, there have been numerous investigations on various gradient materials such as dual-property discs and surface coatings. For example, Lahoti et al. 1 studied the gradient properties of a compressor disc, whose bore region requires high tensile and high low-cycle fatigue properties while its rim demands good creep and stress rupture properties. However, detailed analyses of the flow properties of these materials are not yet available. For further understanding of the usefulness of gradient structures, this work theoretically examines the flow behavior of cylindrical bars with a radial gradient in grain size subjected to both torsion and tension tests. For experimental comparison, a mild carbon steel of AISI 1018 is thermomechanically prepared to produce a grain size gradient and tested for the torque vs twist angle relationship in torsion and the engineering stress-strain in tension. II.
section. The behavior of such a gradient material under a torsion test is first analyzed, which is followed by an analysis of a tensile test. A.
T o r q u e d u r i n g a Torsion Test
To understand the torque vs twist angle relationship during a torsion test, we first consider a homogeneous case in which the average grain size is uniform everywhere. 1. H o m o g e n e o u s case
Torsion analysis for a uniform material has been made by many investigators 2'3'4 in the past, but is reformulated here to facilitate the analysis of a gradient structure and its comparison with a homogeneous case in the next section. For mathematical simplicity, we assume the material to follow linear strain-hardening behavior, but it will be shown that nonlinear cases can be numerically treated. For a linear strain-hardening case, the flow shear stress vs shear strain relationship is in the form of if T -< "Yy
"r = TG r = ry + m(T -
'Yy)
[1]
if T ~ "Yy
where G = shear modulus, m = linear strain-hardening parameter, % = shear yield stress, and "yy = shear yield strain which is equal to "ry/G. To a linear approximation, 2 the shear strain 3' is given by [21
Y = r4)/L
where L = gag
Data Loading...
