A study of typical yields of metals
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I.
INTRODUCTION
W H E N a metal deforms from elastic to plastic state, a very complex yield process often occurs within it. The yield stress is regarded as an important strength parameter of materials, because it is related closely to many problems, such as the relationship between the brittle fracture and the delayed yield timett] and the relationship between the fracture strength and the yield stress.t2] Figure 1 shows several typical yield modes: (a) the mode of continuous transition, in which there is no macrostress drop in the stress-strain curve; (b) the mode of nonhomogeneous yield, in which some small fluctuations appear on the yield platform; (c) the mode of homogeneous yield, whose stress-strain curve is much smoother than that of the nonhomogeneous yield; and (d) the mode with yield platform but without stress drop, which often occurs in the deformation of mediumcarbon steels. Previous research puts emphasis on modes (b) and (c). Some nonhomogeneous yield theories have been developed, such as the Hall-Petch t h e o r y , [3,4} the Cottrell theory,t51 the work-hardening theory of Conrad, t6,71 the stress concentration theory of Russel e t al., rS~ and the Meyerstg] and Armstrong e t al. t~~ theories. LitHJ developed a theory regarding the grain boundaries as dislocation sources. The theories of Hall and Petch[3.4] and Cottrell[51 were criticized by some researcherst~21and then modified by the authors.t~31 Petch thought that the upper yield stress corresponded to the stress of a minority of grain boundaries being passed through and that the lower yield stress corresponded to the stress at which a certain number of grain boundaries in the specimen were passed through and the L~iders bands were just formed. All of the preceding theories can result in Hall-Petch formula: o-:
! Oo + kLd ~
[1]
in which cr denotes the applied stress, O'o denotes the frictional stress of lattices, kL is the Petch gradient related to the material, and d is the grain diameter. This relation between the stress and grain size has been verified by many experiments. But the present author thinks that there are still some drawbacks in these theories. (1) The theories based on dislocation pileups (without grain boundary being passed through) are not supported by experiments. (2) When the grain diameter tends toward zero, an unlimited
ZONGYAN HE is Postdoctor, Department of Mechanical Engineering and Mechanics, Drexel University, Philadelphia, PA 19104. Manuscript submitted January 10, 1995. METALLURGICAL AND MATERIALS TRANSACTIONS A
stress is obtained according to Eq. [1]. (3) All of the preceding theories give only the o--d relation; the kinetic yield equation, the upper and lower yield stresses, and the stressstrain curves cannot be obtained from them. (4) Except for the g-d relation, many nonhomogeneous yield phenomena cannot be explained quantitatively. Some homogeneous yield theories were also developed by researchers such as Johnston[14] and Hahn.t151 They derived the relation between macrostress and strain (or displacement)
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