S. Deville et al. Acta Materialia 52(2004 )5709-5721 the remaining volume seems fairly good, supporting the ses are so high that reaching a fourfold configuration proposed interpretation. The underlying physical origin with partial transformation(like the one of Fig. l(a)) of this behavior may be related to the presence of a gra- was not favorable at all. The energy disequilibrium is dient of residual stresses at the surface [20]. The layer too high to allow partial transformation close to the free surface will be more affected by the pres- ence of residual compressive stresses opposed to the 3.3. Grain boundary effects transformation. The stresses can oppose the propaga tion of the habit plane in the near surface layer, in a sim- Several transformation induced relief can be ac- ilar manner to the action of oxide layers in the case of counted for by the presence and path of grain bounda- martensitic transformation in metals. However when ries and will be described now the transformation propagates (internal growth), the The first feature is related to the presence of external surface effects take more and more importance. Though variants, as described in [17], where secondary external ill speculative, this effect could explain the observed variants are observed on the sides of simple variants trend of growth rate. A program is under way in the lab- arrangement. An example of this is given in Fig. 7, with oratory to assess more precisely the role of the surface the corresponding interpretation of the variants residual stresses on the transformation propagation. arrangement below the free surface. The interesting The last trend (stage III) is only observed in the case point to note is the straightforward relationship between of needle growth, and corresponds to an"explosive" the apparent width of variants at the surface and the rowth. It has been shown for this mode that transfor- variants penetration depth below the free surface Vari mation strain is not accommodated and stresses conse- ations of variants width and height at surface will there- quently building up with the needle growth. These fore be directly related to a modification of the stresses will act to slow down the transformation prop- penetration depth, as shown in Fig. 7. Since the trans- agation, their magnitude being so high that the transfor- formation is, at least in the first stages, stopped by the mation is momentarily stopped presence of grain boundaries, it can be assumed the pen The energy necessary to complete the transformation etration depth variations reflects the path of grain was probably brought by an event exterior to the grain. boundaries in the volume of the grain, below the free If a neighboring grain is transforming(as it is the case surface. Triggering the transformation on the other side here), long range stresses can be induced in the sur- of the grain boundary requires additional stresses, which rounding grains. These stresses can overcome the energy are not provided in the first stage of the transformation barrier and trigger the transformation of the comple- The transformation induced relief appears thus as mentary variants all at once, so as to reach a final directly related to the grains boundaries path and shape arrangement where the transformation strains are below the free surface accommodated on the long range. It is worth noticing The second effect related to grain boundaries pres that only a minimum value of the growth rate in this ence has some very important consequences as far as stage can be provided here. Transformation completion the transformation propagation is concerned, and is re- could have occurred at any time during the treatment lated to the formation of microcracks. Fig 8 provides a step. Considering the fact that very large stresses are case where two parts of the surface(a and b) present a accumulated, it seems safe assuming the transformation fourfold symmetry, though with a slight disorientation, completion occurred all at once(explosive or burst while the third part(c)presents a very different orienta- growth), at a speed approaching the sound speed Stres- tion. The approximate grain orientation, deduced from Fig. 7. Observation and interpretation of more complex relief features with secondary external variants. The decrease of the width and height at surface is related to a decrease of the penetration depth of the variantsthe remaining volume seems fairly good, supporting the proposed interpretation. The underlying physical origin of this behavior may be related to the presence of a gra￾dient of residual stresses at the surface [20]. The layer close to the free surface will be more affected by the pres￾ence of residual compressive stresses opposed to the transformation. The stresses can oppose the propaga￾tion of the habit plane in the near surface layer, in a sim￾ilar manner to the action of oxide layers in the case of martensitic transformation in metals. However, when the transformation propagates (internal growth), the surface effects take more and more importance. Though still speculative, this effect could explain the observed trend of growth rate. A program is under way in the lab￾oratory to assess more precisely the role of the surface residual stresses on the transformation propagation. The last trend (stage III) is only observed in the case of needle growth, and corresponds to an ‘‘explosive’’ growth. It has been shown for this mode that transfor￾mation strain is not accommodated and stresses conse￾quently building up with the needle growth. These stresses will act to slow down the transformation prop￾agation, their magnitude being so high that the transfor￾mation is momentarily stopped. The energy necessary to complete the transformation was probably brought by an event exterior to the grain. If a neighboring grain is transforming (as it is the case here), long range stresses can be induced in the sur￾rounding grains. These stresses can overcome the energy barrier and trigger the transformation of the comple￾mentary variants all at once, so as to reach a final arrangement where the transformation strains are accommodated on the long range. It is worth noticing that only a minimum value of the growth rate in this stage can be provided here. Transformation completion could have occurred at any time during the treatment step. Considering the fact that very large stresses are accumulated, it seems safe assuming the transformation completion occurred all at once (explosive or burst growth), at a speed approaching the sound speed. Stres￾ses are so high that reaching a fourfold configuration with partial transformation (like the one of Fig. 1(a)) was not favorable at all. The energy disequilibrium is too high to allow partial transformation. 3.3. Grain boundary effects Several transformation induced relief can be ac￾counted for by the presence and path of grain bounda￾ries, and will be described now. The first feature is related to the presence of external variants, as described in [17], where secondary external variants are observed on the sides of simple variants arrangement. An example of this is given in Fig. 7, with the corresponding interpretation of the variants arrangement below the free surface. The interesting point to note is the straightforward relationship between the apparent width of variants at the surface and the variants penetration depth below the free surface. Vari￾ations of variants width and height at surface will there￾fore be directly related to a modification of the penetration depth, as shown in Fig. 7. Since the trans￾formation is, at least in the first stages, stopped by the presence of grain boundaries, it can be assumed the pen￾etration depth variations reflects the path of grain boundaries in the volume of the grain, below the free surface. Triggering the transformation on the other side of the grain boundary requires additional stresses, which are not provided in the first stage of the transformation. The transformation induced relief appears thus as directly related to the grains boundaries path and shape below the free surface. The second effect related to grain boundaries pres￾ence has some very important consequences as far as the transformation propagation is concerned, and is re￾lated to the formation of microcracks. Fig. 8 provides a case where two parts of the surface (a and b) present a fourfold symmetry, though with a slight disorientation, while the third part (c) presents a very different orienta￾tion. The approximate grain orientation, deduced from Fig. 7. Observation and interpretation of more complex relief features with secondary external variants. The decrease of the width and height at surface is related to a decrease of the penetration depth of the variants. S. Deville et al. / Acta Materialia 52 (2004) 5709–5721 5715