A rationalization of stress-strain behavior of two-ductile phase alloys
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I.
INTRODUCTION
T w o - d u c t i l e phase alloys are technologically important. This class of materials includes alpha-beta brasses, twophase steels, and alpha-beta titanium alloys. However, there is a lack of understanding as to the stress-strain behavior of two-phase alloys in terms of the stress-strain behavior of the component phases. The lack of understanding stems from the complex deformation behavior of two-phase materials. Neither the strains ~-j8 nor the stresses 12a3A6 18 are uniform wherever a two-phase material consisting of component phases with different stress-strain behavior is subjected to strain. In addition, "interaction stresses"* develop as a result of interac*Authors in Reference 16 used this term to separate the stresses resulting from the interaction between phases from the applied stresses.
tions between phases to maintain compatibility. Interaction stresses develop in elastic ~6 as well as plastic deformation. 13'~7't8 As shown by the authors, ~6'~7,~8the nature and magnitude of inhomogeneous deformation and the interaction stresses depend on morphology and volume fraction of phases and crystallographic relationships between phases. Therefore, it is reasonable to suggest that the following factors must be considered to rationalize the stressstrain behavior of two-ductile phase materials: 1. stress-strain behavior of component phases, 2. grain and particle sizes and morphologies of phases, 3. texture and crystallographic relationships between phases, 4. inhomogeneous stress and strain distributions, and 5. interaction stresses. Because of the number of factors involved, rationalization of stress-strain behavior of two-phase materials is S. ANKEM is Assistant Professor, Engineering Materials Program, Department of Chemical and Nuclear Engineering, University of Maryland, College Park, MD 20742. H. MARGOLIN is Professor, Department of Metallurgy and Materials Science, Polytechnic University, Brooklyn, NY 11201. Manuscript submitted September 23, 1985. METALLURGICAL TRANSACTIONS A
not an easy task. Sometimes the "law of mixtures rule" appears .to predict the tensile properties of two-phase materials, but, in many instances, this rule cannot be applied. For example, Davis 2j'2z'23 showed that the law of mixtures rule applies to 0.2 pct yield strength of ferrite-martensite steels. In some other cases, 24 27 the law of mixture can be applied to some of the tensile properties, but others do not follow this law. In addition, a large number of other investigations showed that the law of mixture cannot be applied for tensile properties of various two-phase alloy systems including titanium alloys,~3'~7'~8-3J ZIRCALLOY*-4-0xygen alloys, 32 *ZIRCALLOY is a trademark of General Electric Company.
and two-phase s t e e l s . 33-36 In general, the law of mixtures rule is not expected to be applicable for tensile properties of two-phase materials, for the simple reason that it assumes either constant stress or constant strain. As presented earlier, 1-~8neither stress nor strain is constant in each pha
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