S. Deville et al Acta Materialia 52(2004)5709-5721 that of external growth(Fig. 5). The width increase of the variants is proportional to the treatment time: the growth rate is thus constant. As far as the internal growth is concerned(Fig. 4), transformation occurs in two stages. In the first one, the variants width increases rapidly, and then approaches a lower and nearly con- stant growth rate, until transformation completion. A more complex behavior is observed needle growth mode untransformed volume (Fig. 6); transformation occurs in three stages. The first 0 two stages are similar to that of internal growth, with a age(hrs)at 140C progressive decrease of the growth kinetics. A third stage is finally observed with a very fast growth speed Fig. 4. Normalized variant width as a function of its age, internal to complete the transformation. growth mode The distinction between these three stages is based on of growth ven in Table 1 and can be discussed on the basis of strain accommodation arguments. For the three modes, the initial growth rate very similar(Il nm/h at 413 K), and must be therefore elated to a similar mechanism. It is therefore proposed to correspond to the unconstrained growth. At the very beginning of transformation, the magnitude of transfor mation induced stress due to non-accommodation(for needle growth)is so low that the variants are free to grow at a similar speed than in the case of a nearly tses fect accommodation demonstrated for the two ot modes(internal and external growth). However, as these back stresses are building up very rapidly in the regions of misfit as the variant thickens, the growth rate falls age(hrs)at 140C down very rapidly. This corresponds to the steady rate Fig. 5. Normalized variant width as a function of its age, external of growth(stage ID), where the growth rate is smaller than 3 nm/h and continuously decreasing with aging time. The growth rate of stage II of the internal growth is similarly low, but must be related to a different phe nomenon. In this case. it has been shown the transfor mation strains were continuously accommodated during the transformation. No induced stresses will act to slow down the transformation. Considering the pro posed analysis (Fig. I(b)), the progressive diminution age Il stage Ill of the size of the inner untransformed part is likely to 04 decrease the driving force for transformation, so that the overall growth rate decreases. By using the model 02 proposed for the volumic arrangement of the variants [17. it was possible calculating the remaining volume of untransformed tetragonal phase by using the 304050 remen its of the apparent traces of habit planes at sur- face. The estimation of the remaining untransformed Fig. 6. Normalized variant width as a function of its age, isolated volume(also normalized) is plotted on the same graph needle growth The correlation between the variants growth speed and Growth rate of martensite variants for the different growth modes Growth rate(nm/hatl40°)±1 Initial rate(stage D) Steady rate(stage n) Burst rate(stage In External growththat of external growth (Fig. 5). The width increase of the variants is proportional to the treatment time; the growth rate is thus constant. As far as the internal growth is concerned (Fig. 4), transformation occurs in two stages. In the first one, the variants width increases rapidly, and then approaches a lower and nearly con￾stant growth rate, until transformation completion. A more complex behavior is observed needle growth mode (Fig. 6); transformation occurs in three stages. The first two stages are similar to that of internal growth, with a progressive decrease of the growth kinetics. A third stage is finally observed with a very fast growth speed to complete the transformation. The distinction between these three stages is based on the measurements of growth rate, given in Table 1, and can be discussed on the basis of strain accommodation arguments. For the three modes, the initial growth rate is very similar (11 nm/h at 413 K), and must be therefore related to a similar mechanism. It is therefore proposed to correspond to the unconstrained growth. At the very beginning of transformation, the magnitude of transfor￾mation induced stress due to non-accommodation (for needle growth) is so low that the variants are free to grow at a similar speed than in the case of a nearly per￾fect accommodation demonstrated for the two other modes (internal and external growth). However, as these back stresses are building up very rapidly in the regions of misfit as the variant thickens, the growth rate falls down very rapidly. This corresponds to the steady rate of growth (stage II), where the growth rate is smaller than 3 nm/h and continuously decreasing with aging time. The growth rate of stage II of the internal growth is similarly low, but must be related to a different phe￾nomenon. In this case, it has been shown the transfor￾mation strains were continuously accommodated during the transformation. No induced stresses will act to slow down the transformation. Considering the pro￾posed analysis (Fig. 1(b)), the progressive diminution of the size of the inner untransformed part is likely to decrease the driving force for transformation, so that the overall growth rate decreases. By using the model proposed for the volumic arrangement of the variants [17], it was possible calculating the remaining volume of untransformed tetragonal phase by using the meas￾urements of the apparent traces of habit planes at sur￾face. The estimation of the remaining untransformed volume (also normalized) is plotted on the same graph. The correlation between the variants growth speed and 0 0.2 0.4 0.6 0.8 1 0 10 20 30 40 50 60 age (hrs) at 140˚C variant width and untransformed volume (normalised) Stage I Stage II variant width untransformed volume Fig. 4. Normalized variant width as a function of its age, internal growth mode. Stage I 0 0.2 0.4 0.6 0.8 1 0 10 20 30 40 50 60 age (hrs) at 140˚C variant width (normalised) Fig. 5. Normalized variant width as a function of its age, external growth mode. 0 0.2 0.4 0.6 0.8 1 0 10 20 30 40 50 60 70 80 age (hrs) at 140˚C variant width (normalised) stage I stage III stage II Fig. 6. Normalized variant width as a function of its age, isolated needle growth mode. Table 1 Growth rate of martensite variants for the different growth modes Growth rate (nm/h at 140 C) ± 1 Initial rate (stage I) Steady rate (stage II) Burst rate (stage III) Needle growth 11 <3 >50 Internal growth 11 <1 – External growth 13 – – 5714 S. Deville et al. / Acta Materialia 52 (2004) 5709–5721