VARIATION OF PLASTIC STRAIN RATIOS OF t-BRASS SHEET WITH TENSILE STRAIN

A study has been made of the changes in the instantaneous plastic strain ratios along various directions of a-brass sheet as a function of tensile strain. The a-brass sheet was fabricated by 88% cold rolling and subsequent annealing at 450C for 1.5 h, which lead to complete recrystallization. The recrystallization texture of the a-brass sheet could be approximated by 110} (110). The plastic strain ratio along the rolling direction decreased with increasing tensile strain, whereas those along 45 90 to the rolling direction were almost independent of tensile strain. The results were in agreement with those calculated using the recrystallization textures based on the Taylor-Bishop-Hill full constraints model.


INTRODUCTION
Variation of the plastic strain ratio or the Lankford parameter with tensile strain has been reported by many investigators (Hu, 1975a,b;Truzkowski, 1976;Arthey and Hutchinson, 1981;Liu, 1983). In order to understand the phenomenon, it is convenient to classify the plastic strain ratio into the conventional and instantaneous plastic strain ratios.
The conventional plastic strain ratio, Re, suggested by Lankford is defined by Re Ew/Et----Ew/(E1--Ew) (1) where ew, et and el are the true plastic strains in the width, thickness and tensile directions, respectively. It is noted that no volume change in plastic deformation is assumed in Eq. (1). The Re value is usually calculated from the measured ew and el values, and is widely used to evaluate deep drawability of sheet metals.
If the Re value is independent of tensile strain, the e-ew curve will show a linear relation as shown in Fig. 1, Where the slope of line is given by -Re/(Re + 1). If there is no error, the line must start from zero point. However, the measured e-ew results often show relations as in Fig. 2.
The first case shows a linear relation of el-ew except in the initial stage, whereas the second case shows no linear relation at all. The first case may again be classified into two cases as shown in Fig. 3 If the plastic strain ratio is defined by the instantaneous slope of the Cl-ew curve, the results in Fig. 3(a) and (b) will give rise to the curves Ri in  (Welch et al., 1983;Lake et al., 1988). Ri is called the instantaneous plastic strain ratio and is expressed as The instantaneous plastic strain ratio corresponds to the quantity that is usually calculated from the texture. The objective of this article is to measure the instantaneous plastic strain ratio of c-brass sheet as a function of tensile strain and to discuss the results based on its textures.

EXPERIMENTAL METHOD
The 0.8 mm thick c-brass sheet (Cu-28% Zn) was made by 88% cold rolling at room temperature, followed by annealing at 450C for 1.5 h. The tensile specimens of ASTM E8 subsize were prepared by milling the a-brass sheets.
The width and longitudinal displacements during tensile testing were instantaneously measured using two extensometers. The longitudinal displacement was measured up to 10 mm at intervals of4.8 tm, while the width displacement was measured up to 1.5 mm at intervals of 0.69 tm, which is equivalent to about 1000 data at a tensile strain of 0.2. The measured displacements were used to calculate strains, from which the plastic strains were obtained by subtracting the elastic strains. The elastic strains were calculated using the following equation: where superscript e represents elastic property, and u is Poisson's ratio. Equation (3)  In order to reduce the noise of the measured data, an instantaneous plastic strain ratio was calculated from the slope ofa quadratic equation best fitting 50 data obtained from a tensile strain range of 4-0.5%.
The textures of the annealed specimens were measured up to the reflection angle of 80 using a Schultz pole figure device. Incomplete pole figures of (111), (200) and (220) for the a-brass specimen were used to calculate ODFs using the series expansion method with Lmax--22 (Bunge, 1982).  The Ri values of the annealed and tensile deformed specimens were calculated as a function of angle to the rolling direction using Bunge's method (Bunge, 1982) based on the measured textures (Fig. 9). The calculated Ri values of the annealed specimen along 0 , 45 and 90 to the rolling direction are 1.60, 0.86 and 0.46, respectively, which are in good agreement with the measured Ri values at the small tensile strain (Fig. 5(b)). The  Angle to rolling direction These results are in qualitative agreement with the measured Ri values. Therefore, the variations of Ri with tensile strain can be attributed to the texture change in a-brass sheets during tensile deformation.

CONCLUSION
The instantaneous plastic strain ratios and textures of a-brass sheets were measured as functions of tensile strain and angle to the rolling 0 0.0 0.3 0.6 0.9 .2 .5 Tensile Strain direction. The recrystallization texture of c-brass sheet rolled by 88% and annealed at 450C for 1.5 h was approximated by { 110}(110), which changed to the texture approximated by { 110} (111) after a tensile strain of 33%. The Ri values of specimens along 45 and 90 to the rolling direction were almost independent of tensile strain, whereas that of the 0 specimen decreased with increasing tensile strain. The Ri results are attributed to the texture variation during tensile deformation.