The relationship between plastic anisotropy of steel sheet and temper rolling strain
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The Relationship between Plastic Anisotropy of Steel Sheet and Temper Rolling Strain J.S.H. LAKE and H.G. FLEMING The measurement of the plastic strain ratio, or r-value, of steel sheet is normally performed by determining the width and length strains of a tensile test piece at a nominal elongation and calculating the ratio of width-tothickness strains. Liu tq proposed that the instantaneous r-value over the range of strain of the tensile test is apJ.S.H. LAKE, formerly with BHP Steel Coated Products Division, is Senior Principal Research Officer, BHP Steel Wire Products Division, Newcastle, New South Wales, Australia. H.G. FLEMING, Principal Technical Officer, is with BHP Steel Coated Products Division, Port Kembla, New South Wales, Australia. Manuscript submitted July 17, 1990. 2156--VOLUME 22A, SEPTEMBER 1991
proximately strain independent and that r-value may be calculated by lineal" regression of width strain, ew, on length strain, ez: ew = A - bez
[1]
where b is the contraction ratio in the Taylor theory and A is the width strain intercept for zero length strain. The relationship between the linear regression r-value, r, and b is b r --- - (1 -
[2] b)
Analysis of the anisotropic behavior of a number of types of sheet steel tel supported the use of the linear regression method using data between the end of the yield elongation and uniform elongation. The regression did not always intersect the origin, especially for steel sheet which had not been temper-rolled or leveled, for which A could be in excess of -+0.01. The relationship between width and length strains was not exactly linear. The most effective indicator of nonlinearity is the width strain deviation, Aew, calculated from the regression data: e" = A - bel Aew = e'w -
ew
[3a] [3b]
Values of Ae,~ can be as large as 0.001. Plots of A e w v s length strain were repeatable for replicate tests on test pieces cut from a single sheet sample, indicating that the deviation pattern is a characteristic of the material behavior. The plots varied considerably from one coil of steel to another, even when there were two or more of nominally the same product with similar r-values in each testing direction. There was also no indication that the amplitude of the plot was related to r-value. During temper rolling of steel sheet, TM Luders bands are formed transverse to the rolling direction. The spacing decreases with temper reduction until it reaches a stable spacing. Further reduction increases the proportion of the plastically deformed to undeformed volume of material until a level of reduction is reached at which the sheet is completely deformed. Most of the samples tested in Reference 2 were examined in both the asannealed state and after temper rolling during industrial processing. Temper rolling did not affect the r-value determined by linear regression; however, it changed the pattern of Aew with tensile strain. The influence of the temper reduction, consequently, appeared to persist at tensile strains considerably higher than those at which plastic defor
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