Phase-field Modeling Of α Precipitation In The Presence Of Crystalline Defects In α/β Titanium Alloys

The mechanical properties of two-phase α/β titanium alloys,e.g.,strength,fracture toughness and fatigue life,depend strongly on the texture of the a phase.To optimize the comprehensive performance of Ti-alloys through manipulating the micro structure during thermo-mechanical processing has been a reseach focus for years.Crystalline defects introduced during thermo-mechanical processing will influence the spatial orientation,distribution and morphology of a phase,leading to drastically different microstructures and,consequently,considerable variations in mechanical properties.Such influences could be quite complex as the orientation variants of a precipitates within every single β grain are up to 12 types,among which only a subset would be preferred by crystalline defects.So far,extensive experimental characterizations have provided certain correlation between processing and microstructure.Nevertheless,a direct dynamic relationship between fundamental crystalline defects and a precipitation is still beyond the capacity of current experimental techniques.To this end,computation and simulation become an effective means to reveal such precipitation behavior near different types of crystalline defects.Through three-dimentional(3-D)phase field simulation,together with dislocation theory and anisotropic elasticity,the present work systematically investigate the effects of crystalline defects with different dimensions,i.e.,dislocations(1-D),grain boundaries(2-D)and pre-existing a lath(3-D)on the dynamic precipitation behavior of a phase and micro structure development during diffusional β→α transformation.The precipitation behavior of a phase is found to alter with the types of defects.The main content and major findings include:The effects of dislocations on the a precipitation process are studied by incorporating three types of dislocations within the β matrix,i.e.,straight edge/screw dislocations and a dislocation loop of mixed type.In the presence of dislocations,the elastic interaction between a precipitates and dislocations dominates the types and distribution of a variants at the nucleation stage,while the habit plane orientation of a precipitates relative to the dislocation lines plays a more important role at the growth stage.Detailed calculation shows that the elastic interaction energy between a precipitates and dislocations ranges from 350～1500J/mol,depending on the type of dislocations.In general,only some of the 12 crystallographically equivalent a variants are preferred by dislocations,i.e.,variant selection(VS)process takes place during precipitation.The edge dislocation exhibits a much more prominent effect on VS process than the screw dislocation,leading to a larger degree of variant selection(DVS).The effect of undercooling on variant selection is also investigated in the context of competition between the chemical driving force for a precipitation and the elastic interaction between dislocation and a precipitates.A new measure is proposed to quantify the degree of variant selection or micro texture of a phase by incorporating orientation data from either simulations or experimental observations.The effects of low-angle grain boundaries(GB s)of both tilt and twist type on the precipitation behavior and variant selection of grain boundary allotriomorphs(GB a)and Widmanstatten side-plates(WS)are studied.The structures of different types of GBs are modeled as discrete dislocation networks using Frank-Bilby theory.It is shown that the morphology,distribution and relative volume fractions of GBa and WS depend largely on the type of GBs,misorientation angles and evolution time.While for the tilt GBs,GB a are mainly comprised of individual equiaxed particles at smaller misorientation angles between neighboring dislocations and disappear gradually as the misorientation angle increases,for the twist GBs,however,GBa consists mainly of a layer of two groups,one group consisting of a variants extend along dislocation lines in 1-D mode at lower θm and the other one consisting of a variants spread over the GBs in both 1-D and 2-D modes at higher θm.On the other hand,the WS are found to form directly from GB dislocations and grow into the interior of β grain.The volume fraction and variants of WS show distinct trends with GB characters.Quantitative analysis indicates that precipitate morphology and VS are determined by the interplay of multiple factors,which include:i)the magnitude and distribution of elastic interaction between a nucleating a precipitate and the GB dislocation networks,ii)growth anisotropy determined by the relative inclination of the habit plane with respect to the GB dislocations and GB plane,and iv)the misorientation angle.Different factors will dominate the VS process at different stages(nucleation or growth)in different mechanisms that could be competing against or complementary to each other.Finally,the elastic interaction between different a variants and its relationship with the formation of a clusters of special orientations are investigated quantitatively.Calculation based on micro-elasticity theory shows that the stress field of a primary a lath exhibits strong anisotropy.From phase field simulations,the secondary a precipitated stimulated by the primary a lath during subsequent phase transformation are limited to certain variants,which keep special misorientation with primary a lath.Such misorientation between primary and selected secondary a variants is consistent with the three most frequently observed α/α misorientation types in experiments between variants within a clusters.The formation of these special a/a misorientation originates from elastic interaction between primary/secondary a precipitates and the competition between secondary/secondary a precipitates.The interaction between variants drives the so-called auto-catalytic " effect during the precipitation process in the presence of a primary a lath,which is also one of the controlling factors leading to the phenomenon of VS during the β→α phase transformation.Current work carefully investigates the precipitation behavior of a phase during diffusional phase transformation in the presence of different crystalline defects,which provides theoretic evidence and prediction for the formation of typical micro structure in Ti-6A1-4V alloys,and proposes a useful framework and new thoughts for the study of relevant issues within other alloy systems.