Finite Element Method (FEM) Calculations of Stress-Strain Behavior of Alpha-Beta Ti-Mn Alloys: Part I. Stress-Strain Rel
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SREERAMAMURTHY ANKEM and HAROLD MARGOLIN By use of a NASTRAN TM Computer Program, the Finite Element Method (FEM) has been employed to calculate the effect of particle size, matrix, and volume fraction on the stress-strain relations of a-/3 titanium alloys. It was found that for a given volume fraction, the calculated stress-strain curve was higher for a finer particle size than for a coarse particle size within the range of the strains considered, and this behavior was seen for all the different volume fraction alloys considered. For a 50: 50 vol pct t~-/3 alloy, the stress-strain curve with/3, the stronger phase, as the matrix was higher than that with c~, the softer phase, as the matrix. The calculated stress-strain curves for four different vol pct c~ alloys were compared with their corresponding experimental curves, and in general, good agreement was found. Whenever there were discrepancies, they were discussed by comparing the morphology of the mesh used in the calculations with the morphology of the actual materials.
I.
INTRODUCTION
Two ductile phase structures occur in many technologically important alloys. Increasing interest is developing in calculating the stress-strain behavior of the two-phase structures from the stress-strain curves of the component phases. In the present calculations FEM has been employed to calculate the effect of particle size, matrix, and volume fraction of phases on the stress-strain behavior of a-/3 Ti alloys. In Part I, stress-strain relations will be shown and compared with the experimental curves for four different volume fractions. In Part II, stress-strain distributions will be shown, and strain distributions will be compared with experimentally determined strain distributions. Two simple hypotheses have been suggested by Dorn and Starr I to calculate the stress-strain curve of a two ductile phase mixture from the stress-strain curve of each phase and volume fractions: one is based on constant strain in each phase, and the other is based on constant stress in each phase. Usually, the experimental curves of the two phase mixtures will lie somewhere between the two curves which are calculated according to the above two hypotheses, a fact that Dorn and Starr anticipated. Davies 2'3'4 studied the deformation behavior of dual phase, ferrite-martensite steels and has found that the 0.2 pct YS linearly varied with the volume fraction of the martensite and followed a law of mixture rule. Interestingly, he 2'3'4 also found that the tensile strength and ductility of the dual phase steels are in agreement with the theory of Mileiko, 5 Garmong and Thompson. 6 Since this theory 5"6 has been developed for mechanical properties of fiber composites of two ductile phases tested in tension parallel to the fiber axis, it will have only a limited applicability because it 5'6 does not consider the morphology of the phases, which can affect the stress-strain behavior, as will be shown later. Tomota et al 7 have calculated the flow-stresses of alloys consisting of two ductile phases, a - y , F
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