Improved model to predict properties of
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I.
INTRODUCTION
ALL precipitation-hardenable-aluminum alloy products progressively lose their ability to develop the maximum strength attainable with a particular aging treatment as rate of cooling from the solution temperature decreases. This quench sensitivity is attributed to loss of solute by precipitation during the quench as coarse, heterogeneously nucleated particles of the equilibrium phase and to loss of vacancies to sinks. Cahn has shown that kinetics of continuous transformation can be predicted using isothermal transformation kinetics, m His approach was modified to predict the ability of precipitation-hardenable-aluminum alloy products to develop strength after continuous cooling. 12~ The model has been improved and implemented over the years. 131 The inputs are a time-temperature-property (TTP) C-curve analogous to a time-temperature-transformation (TTT) C-curve and a measured or postulated time-temperature cooling curve (quench curve). In the usual implementation of the model, the C-curve is described mathe matically using constants determined by regression analysis of data obtained from isothermal quenching experiments. The C-curve equation, Eq. [1], is given in terms of empirically determined constants, K~ to Ks, but uses a form based on the accepted theory of nucleation) 4J -
\RT(k4 - T) ~ exp
[I]
where C,(T) = critical time at temperature T for attainable strength ~r; k2 --- constant which includes the reciprocal of number of potential nucleating sites; J.T. STALEY, Corporate Consultant, and A.P. J A W O R S K I , Staff Scientist, are with Alcoa Technical Center, Alcoa Center, PA. R.D. DOHERTY, Professor, is with Drexel University, Philadelphia, PA. Manuscript submitted October 2, 1992. METALLURGICAL TRANSACTIONS A
constant which includes the change in free energy associated with formation of a nucleus; k 4 -= constant related to solvus temperature; k5 = mobility term; and R = gas constant.
k 3 -~
To describe a particular level of o-, another term, k j, is added:
C,(T)~ = klk2 exp
exp \ R Y ( k 4 -- T ) 2
[21 "~
where C,(T), = critical time to decrease attainable strength ~r to a level where ~r equals ~rx; kl = - l o g e (o~, - O ' m i n / / O ' m a x - - O V m i n ) ; o~, = usually chosen to equal 0.995 Crm,x; O'max = maximum level of ~; and O'mi n = minimum level of ~. To simplify the mathematics in the original version of the model, an approximation was made that strength after infinitely long hold times at temperatures below the solvus, ~rmin, would equal zero. This model was able to predict loss in strength accurately for those quench paths which result in a loss of up to about 0.10"m,x- In a subsequent version of the model, a better approximation was made which assumed that O'mi. is a constant that is independent of temperature, m Predictions with this model were useful to losses of about 0.15 of ~rm,x.
II.
NEW MODEL
This article describes a new model which recognizes that ~r,,i, is a function of temperature. The model is developed on a sounder mathematical basis and increase
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