rizt. 160_2..Acis2)14).5 -- -142_2. DEFORMATION MAPS FOR TITANIUM AND ZIRCONIUM P.M. SARGENT and M.F. ASHBY Cambridge University, Engineering Department, Trumpington Street, Cambridge CB2 1PZ, England INTRODUCTION Zirconium, Titanium and Hafnium are a group of metals with similar properties. Titanium and its alloys are increasingly used in both aerospace and chemical engineering. Zirconium, and alloys based on it, has important structural applications in certain nuclear reactors. These uses of Ti and Zr require that the designer has a good understanding of both their low temperature plasticity and their high temperature strength. The maps given below summarise recent data and current understanding. They are constructed using the method and equations given by Frost and Ashby (1]; the rate equations, and data-reduction procedure can be found there. Symbols are defined in Table 1. The maps are complicated by a phase change and by ano- malies in both the moduli and the diffusion coefficients. THE MAPS Figs. 1 to 4 show maps for Ti and Zr. They are based on data plotted on Figs. 1 to 7, and on the parameters listed in Table 1. The stress/temperature maps (Figs. 1 and 3) resemble each other closely. They are divided at the phase boundary (near 0.6 Tm) into two parts. The low temperature a-phase shows a field of low and high-temperature creep and a field of diffusional flow (similarly subdivided). Above the phase boundary, the 0 phase exhibits power-law creep and diffusional flow. There is a discontin- uity in strain-rate at the phase boundary. The strain-rate/stress maps are similarly divided, but in this case there is an inaccessible region and an overlapping region (broken field boundaries) separating the two phases. ORIGINS OF THE DATA Moduli The shear moduli of a-Ti and a-Zr are means of the bounds calculated by Simmons and Wang [2) from the single crystal data of Fisher and Renken [3], shown in Figs. 5 and 6. The maps are normalised by the melting point of the B-phase (1933 K for Ti and 2130 K for Zr). Doing so leads to the large temperature dependence (about - 1.3) given in Table 1. Using Ardell's 14] estimates of TM for the ci-phase (1957 K for a--Ti, 1880 K for a-Zr) does not change this signifi- cantly. Data for the moduli of the B phases are much more limited. Fisher and Dever [5], give single crystal constants for Ti at 1273 K, from which we have calculated the mean shear modulus V " (i cyi, (cli - c12))i giving 15.3 GN/m2 at 1273 K. Assuming a "typical" temperature de- pendence of -0.5 leads to the value for pc , given in Table 1. Ashkenazi et al. (6 ] give single crystal data for B-Zr-30 at Z Nb for a wide range in temperature. Again using p = (i cyi, (c11 c12))i gives p o = 25300 MPa at 300 °K, with a temperature dependence of -0.62 (using the alloy melting point of 2020 °K). The modulus of pure 6-Zr may be a little lowr than this, but the data do not justify changing it. The large temperature dependence of the a--)hase shear moduli, and the low values of a and 3-phase moduli near 0.6 TM reflect the law stiffness of the lattice with respect to the shear which produces the phase transformation.