The Split Of Aging Precipitates In Ni-base Alloys Simulated With Phase-field Method

The elastic misfit strain energy is induced by the mismatch of lattices be-tween??and?phases,and which effect evidently on the morphology and ar-rangement of the precipitating particles in Ni-base alloys during aging.Because of the mismatch?increasing along with the coarsening,the elastic misfit strain energy dominates the growth of the nucleus.The phenomena in the following would accur during the coarsening of precipitate.The first,the morphology of the precipitating particle transforms from sphere to cube.The second,the isolated particle would split into octet or doublet.The third,the precipitating particles would string into a chain or arranges periodically.This kind of coarsening be-havior is quite different from the LSW theory in which the misfit strain elastic energy are not considered.The L1₂-??precipitates separating from FFC-?matrix during aging in Ni-base alloys may be regarded approximately as the isostructrual phase trans-formation.The MSC effect in the isostructural phase transformations may be characterized by the MSC function which is related to the MSC temperature in evidence.The MSC temperature is the intersection point of the two temperature dependent crystal lattices a_???T?and a_??T?,and the intersection point is named MSC point.If the cooling curve passes by the MSC point,the MSC point is called the real MSC point.On the contrary,if the cooling curve doesn't pass by the MSC point,the MSC point is called the imaginary MSC point.For transformation from?to??in Ni-base alloys,the formation and splitting of dendritic??particles are all correlated to the MSC effect between the precipi-tates and the matrix.The MSC effect is the responce of the misfit strain between the precipitate and the matrix to the variation of the temperature during heat treatment.The MSC effect may be simplified to the MSC function h?t?.The MSC function is a hyperbolic tangent function which may be expressed by three parameters,the MSC delay t₀,the MSC rate?and the intial value of the MSC function??The MSC delay t₀denotes the duration time at the first order aging temperature,the MSC rate?is determined by the cooling rate during heat treat-ment,the initial value of the MSC function?is related to the difference between the first order aging temperature T_sand the MSC temperature,i.e.?_s^c=T_c-T_s.The growth of the isolated precipitating particle is not consonant with the LSW law which implies that the radius of the partilce r?t?is proportional to t^1/3.In effect,the radius of the precipitating particles would grow to the supreme value,and the greatest value of the radius is determined by the conservation of the solute atoms.The existence of the maximum radius indicates that,if the anti-phase boundary?APB?is not taken into account,the volume of the stable morphology of the isolated precipitating particle generated in the isostructural phase transformations would occupy as far as posible the whole single crystal do-main until the solute atoms are depleted.In fact,the APB prevents the merging of different domains,and each particle would grow possiblly to the maximum radius.Therefore,the size of the isolated domain determins directly the radius of the precipitating particle.If the interfacial anisotropy is ignored,the split of the precipitating??particle in Ni-base alloys is the competition between the interfacial energy and the misfit strain energy.If the alloys is aged at MSC point,the precipitate grows only under the control of interfacial energy but no misfit strain energy,the particle would grow to sphere.When it starts to cool during aging at t₀,the different changing rate of the lattice constant of??and?with respect to temperature t results in the misfit strain energy between the precipitate and the matrix.The interfacial energy attempt to cause the precipitate to grow into sphere,but the misfit strain energy forces the particle to grow into cube.During the isostructural phase transformation,the morphology evolution routines is determined by two conditions,The first condition is whether the first order aging is carried out at MSC temperature.If the first order aging temperature is not in the MSC,the??precipitates is dominated by misfit strain energy dring the whole precipitation,which leads to the precipitating particle growing into plate.If the first order aging temperature is at MSC temperature,due to the absence of misfit strain elastic energy,the particles can only grow under the control of interfacial energy,which results in the potential of dendrite formation.In the case of the first aging temperature at MSC point,whether or not the precipitated particles grow into dendrites depends on the MSC delay time t₀.if t₀is small,precipitating particles may split but not have time to form a dendrite.If t₀is large,the precipitating particles would split after growing into dendrite.