An analysis of the flow stress of a two-phase alloy system, Ti-6Al-4V
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I.
INTRODUCTION
A power law was used in several recent articles, based on the Yokobori[1] activation enthalpy
~!
s*0 H 5 H ln s* o
stress, by definition[3] does not vary during an isothermal change in strain rate. In terms of the power law, Eq. [4] may be written S5
[1]
RT z s* Ho
In practice, S is determined experimentally using
where H is a constant related to the work done by the applied stress during an activated event,[2] s* the effective stress, and s*0 its 0 K value. In these articles, it was shown that it is possible to model the tensile deformation behavior of body-centered cubic (bcc) commercial-purity niobium[3] and hexagonal close-packed (hcp) commercial-purity titanium.[4] It will now be demonstrated that this power-law model is also capable of rationalizing the two-phase (hcpbcc) Ti-6Al-4V stress-strain data of De Meester et al.[5] Basically, the model assumes the effective stress s* is a function of the strain rate o
s* 5 s*0
~ ! εz εz 0
RT Ho
[2]
where εz is the strain rate, εz 0 a material constant equal to the strain rate that makes s* equal to s*0 at any temperature, R the universal gas constant, and T the Kelvin temperature. At a constant εz , Eq. [1] may be expressed as ln s* 5 ln s*0 1 b T [3] whose slope is b 5 (R/Ho) ln (εz /εz 0). Note that b has dimensions T21 and is a function of both εz 0 and Ho. This latter is important because, to properly identify the slope for a given material, one needs to determine both εz 0 and Ho. An important parameter in empirical stress-strain analysis is the strain-rate sensitivity S5
d s* ds 5 d ln εz d ln εz
[4]
where it is assumed that ds 5 ds* since sµ, the internal R.E. REED-HILL, Professor Emeritus, C.V. ISWARAN, Research Scientist, and M.J. KAUFMAN, Professor, are with the Department of Materials Science and Engineering, University of Florida, Gainesville, FL 32611. Manuscript submitted February 27, 1996. METALLURGICAL AND MATERIALS TRANSACTIONS A
[5]
Sm 5
Ds D ln εz
[6]
where Sm is the measured strain-rate sensitivity and Ds the incremental change in flow stress for a finite change in strain rate. Equation [4] assumes infinitesimal changes in ln εz and s*, whereas experimentally, finite increments are used. It is possible to correct for this difference[6] with the following equation: S5
[k(RT /H o) 2 1] z s* ln k
[7]
where k is the strain-rate change factor (k 5 5 for the de Meester et al.[5] data). Equation [7] reduces to Eq. [3] in the limit as k → 1. Finally, the exponent in Eq. [2] is also considered a strain-rate sensitivity factor, normally written as n, so that n5
RT Ho
[8]
Experimentally, n is determined by n5
d ln s * d ln (εz )
[9]
With the aid of the procedures in References 3, 4, and 6, the internal stress sµ for the de Meester et al. data was determined to be
sm 5 sµ0 2 0.309T, MPa
[10]
where sµ 0 5 595 MPa. In Eq. [10], sµ has the temperature dependence of the Ti-6Al-4V shear modulus as given by de Meester et al.[5] In addition to sµ, it was determined that the material parameters in Eqs. [2] and [3] cou
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