Influence of dislocation density and distribution on the aging behavior of 6061 AlSiCw composites

Acta metall, mat¢r. Vol. 38, No. l 1, pp. 2041-2049, 1990 Printt~d in Gi'eat Britain. All rights reserved

0956-7151/90 $3.00 + 0.00 Copyright © 1990 Pergamon Press plc

INFLUENCE OF DISLOCATION DENSITY A N D DISTRIBUTION ON THE AGING BEHAVIOR OF 6061 AI-SiCw COMPOSITES I. D U T T A 1 and D . L. B O U R E L L 2

~Department of Mechanical Engineering, Naval Postgraduate School, Monterey, CA 93943 and 2Center for Materials Science and Engineering, University of Texas at Austin, Austin, TX 78712, U.S.A. (Received 17 April 1989; in revised form 4 May 1990) Abstract--Precipitation hardening metal-matrix composites (MMCs) are known to age more rapidly than the unreinforced matrix alloys. It has been proposed that the accelerated aging is due to some dislocation defect mechanism which enhances nucleation, growth or both. Theoretical Avrami-type precipitation curves were generated assuming dislocation density dependent nucleation only and dislocation density dependent nucleation and growth. Curves were generated for both uniform dislocation density (to model cold work) and a dislocation density gradient (to model MMCs). These theoretical results were compared to precipitation curves generated by differential scanning calorimetry of unstrained and plastically strained unreinforced 6061 AI and 10 vol.% SiC whisker reinforced 6061 A1 MMC. It was found on aging that /3' precipitation in the MMC initiates earlier and is completed later than in the unreinforced alloy with the same amount of plastic work as the composite. The reaction rate order for fl' precipitation was also determined from the calorimetric studies. These experimental results were interpreted in terms of the theoretical calculations. It is concluded that the matrix dislocation density distributions of metal-matrix composites can strongly influence macroscopically observed nucleation and growth rates. R~sum~---On sait que les composites fi matrice m&allique durcie par pr6cipitation (CMM) vieillissent plus rapidement que les alliages ft. matrice non renforc6e. I1 a 6t6 sugg6r6 que ce vieillissement acc616r6 est dfi ~. un m6canisme de dislocations qui favorise la germination, la croissance ou ces deux. Les courbes th6oriques de pr6cipitation de type Avrami ont 6t6 trac6es en supposant que la densit6 de dislocations d6pend uniquement de la germination ou bien qu'elle d6pend de la germination et de la croissance. Ces courbes ont ~t+ trac~es ~i la fois pour une densit6 de dislocations uniforme (pour mod61iser l'6crouissage) et pour un gradient de densit6 de dislocations (pour mod61iser les CMM). On compare ces r6sultats th6oriques aux courbes de pr6cipitation obtenues par calorim6trie en balayaga diff~rentiel de deux mat6riaux--5, l'&at non d6form6, ou d&orm~ plastiquement--: un aluminium 6061, et un composite matrice m6tallique d'aluminium 6061 renforc6e par 10% en volume de whiskers de SiC. Lors du vieillissment, la pr6cipitation de/3' dans le CMM commence plus t6t et s'achi6ve plus tard que dans l'alliage non renforc~ soumis au m~me taux de d6formation plastique que le composite. Ces r~sultats exp6rimentaux sont interpr6tds fi partir des calculs th6oriques. It en ressort que les distributions de densit6s de dislocations de matrica, dans les composites 5. matrice m6tallique, peuvent avoir une grande influence sur les vitesses exp6rimentales de germination et de croissance 5. l'6chelle microscopique. Zusammenfassung--Ausscheidungsgeh~irtete Metallmatrix-Werkstoffe altern rascher--wie bekannt ist-als unverst/irkte Matrixlegierungen. Es wurde vorgeschlagen, dab die beschleunigte Alterung auf einigen Versetzungmechnismen beruht, die die Keimbildung, das Wachstum oder beides beschleunigen. Wir erhalten theoretische Ausscheidungskurven vom Avramityp unter der Annahme einer v o n d e r Versetzungsdichte abhiingigen ausschlieBlichen Keimbildung und von dr Versetzungsdichte abhiingigen Keimbildung und Wachstum. Kurven wurden erhalten sowohl f/Jr gleichmfiBige Versetzungsdichte (Modellierung der Verfestigung) und for einen Gradienten der Versetzungsdichte (Modellierung des ausscheidungsgeh~rteten Werkstoffs). Diese theoretischen Ergebnisse werden mit Ausscheidungskurven verglichen, die aus der differentiellen Kalormetrie unverformtem und plastisch verformtem unverstiirkten 6061 A1 und an mit 10 Vol.-% SiC Whiskern verstS.rktem 6061 A1 erhalten wurden. Es ergab sich, dab bei der Alterung die /3'-Ausscheidung in dem verstfirkten Material frfiher einsetzt und sp~iter beendet ist als in der unverstfirkten Legierung, die dieselbe plastische Dehnung gesehen hat wie der verstiirkte Werkstoff. Die Ordnung der Reaktionsrate der /3'-Ausscheidung wurde ebenfalls aus den kalorimetrischen Daten bestimmt. Diese Ergebnisse werden anhand der theoretischen Ergebnisse gedeutet. Es wird gefolgert, dab die Verteilungen der Versetzungsdichte in der Matrix von Metallmatrix-Verbundwerkstoffen die mikroskopisch beobachten Keimbildungs- uud Wachstumsraten betr/ichtlich beeinflussen krnnen.

1. I N T R O D U C T I O N M e t a l - m a t r i x composites ( M M C ) h a v i n g precipit a t i o n h a r d e n a b l e matrices are k n o w n to age considerably faster t h a n the associated unreinforced m a t r i x alloy [1-7]. A m e c h a n i s m c o m m o n l y p r o p o s e d

to explain this accelerated aging in metal matrix composites is e n h a n c e d nucleation a n d / o r growth in the heavily dislocated matrix regions adjacent t o the reinforcement [4-6]. The increase in dislocation density o f the M M C arises during post-fabrication cooling due to differential thermal c o n t r a c t i o n of the

2041

2042

DUTTA and BOURELL:

AGING BEHAVIOR OF 6061 A1-SiCw COMPOSITES

matrix and the reinforcing phase [1-16]. Large matrix residual stresses are generated in short-fiber reinforced MMCs during cooling [17], part of which is relieved by the generation of prismatic dislocation loops at the fiber ends [16]. Transmission electron microscopy studies have revealed that matrix dislocations in aluminum-SiC composites facilitate nucleation of precipitates, thereby reducing the incubation time for nucleation [6]. Dislocations are known to be sites for heterogeneous nucleation [18-22] and paths for increased atomic transport during growth [23-26], both of which may account for the observed accelerated aging behavior. Prior work by the authors [5] has established the prevalence of a dislocation mechanism of accelerated aging over a residual stress mechanism. Differential scanning calorimetric (DSC) studies have established that the addition of SiC to aluminum alloys does not alter the precipitation sequence of the matrix alloy, although both precipitation and dissolution kinetics are altered and some normally quench insensitive materials such as 6061 aluminum become quench sensitive [7]. Acceleration in precipitation observed in MMCs is in part due to the powder metallurgy process employed in fabrication [7]. However, cast aluminum-SiC composites have also been observed to exhibit accelerated aging [27]. Age-hardenable composites are usually given a solutionize-quench-age heat treatment. During the post-solutionization quench to room temperature, differential thermal contraction of the matrix and reinforcement phases results in the formation of plastically deformed zones in the matrix next to the reinforcements. The size of these plastically deformed zones and the nature of the strain'distribution within them depend on such factors as matrix yield strength, matrix/reinforcement thermal expansion coefficients, solutionizing temperature, quench rate and reinforcement size, morphology, spacing and distribution. Based on the mechanism of plastic zone formation, it is expected that the plastic strain and hence the dislocation density should decrease with distance from the reinforcement-matrix interface.t Since both nucleation rate and diffusivity (and hence growth rate) in alloys are strongly dependent on the dislocation density [18, 28-32], it is expected that not only the dislocation density itself, but also its distribution will affect the overall rate of accelerated aging. This paper is aimed at evaluating the effect of matrix dislocation density and distribution on the precipitation kinetics in a SiC whisker reinforced 6061 aluminum composite from a primarily theoretical standpoint. Existing relationships describing clas-

tSeveral TEM studies of AI-SiC MMCs [4-6, 9, 10, 27] reveal high dislocation densities (~ 10Um 2) around reinforcements, but no observable gradients. One possible explanation is local masking of the gradients due to overlapping plastic zones from clustered reinforcements.

sical dislocation dependent nucleation and growth kinetics were modified to incorporate the combined effects of dislocation density gradients and increased average densities encountered in M M C matrices. Experimental precipitation curves were also generated using differential scanning calorimetry to verify these analytical results. 2. THEORETICAL MODELING 2.1. Reaction rate order for transition phase ([3') precipitation

It has been reported [33] that the sequence of precipitation in aluminum alloy 6061 is: supersaturated solid solution ~ vacancy-silicon clusters ~ vacancy rich coherent AI-Mg-Si GP zones ~ disordered, partially coherent (100)A1 needle shaped phase ordered, partially coherent (100)A1 needles ~ semicoherent, hexagonal (a = 0.705 nm, c = 0.405 nm) rods ~ semicoherent, hexagonal (a = 0.705 nm, c = 1.215 nm) rods --* equilibrium/~-MgzSi platelets. In general, the precipitation process starts with the formation of silicon clusters, followed by the formation of needle-like GP zones which simultaneously lengthen and thicken into rods of the transition ]~' phase. The ]~' rods initially undergo increases in both their length and diameter and eventually transform into platelets of the equilibrium /~-Mg2Si phase by lateral growth [34-36]. Hence, the formation of the transition/~' phase can be modeled as a continuous precipitation process of the type ~ ~ ~ + fl', leading to three-dimensional self-similar growth of cylindrical precipitates. As a cylindrical precipitate grows self-similarly, its radius r (t) and its length h (t) increase with time t. For continuous precipitation, the radius and the length at any instant are given by [37] and h ( t ) = K : ~ t - r )

r(t)=K~v/~-O

(1)

where z is the apparent time of nucleation of the particle, D is the diffusion coefficient of the solute in the matrix and Ki are constants of the order of 1. At any time, the volume V(t) of the cylindrical /3' particle is given by V(t) = nr (t)2h (t).

(2)

The volume of a/~' particle originating at time t = z can therefore be written as V (t ) = nK1KzD3/2(t -- r) 3/2.

(3)

At time t, the volume of all fl' regions V~' is given by g ~" =

fo

(N" V)AD3/Z(t - z) 3/2dr

where A = nK~Kz = constant, V = the volume of supersaturated ~ and N = the overall nucleation rate per unit volume. In AI-Mg-Si alloys with a high dislocation density, nucleation takes place almost exclusively on dislocations [35]. The volume nucleation rate N can therefore be written as pN±, where

DUTTA and BOURELL: AGING BEHAVIOR OF 6061 A1-SiCw COMPOSITES N± is the nucleation rate per unit dislocation line and p is the dislocation density. As suggested by Kovacs et al. [39] and evidenced by the presence of a high precipitate density at the grain boundaries in 6061 A1 with adjacent precipitate free zones (Fig. 1), /3' growth is diffusion controlled rather than interface controlled. This creates a transformed volume V°q~+ P' of fl' and surrounding equilibrium c~, given by veqct +fl'

=

7

t"

(N"

V)AD3/2(t

--

27)3/2 dz

(4)

0

where 7 ~ {C~, + C~s~- 2Coq~}/{C~ss- C0q.~} (Appendix), C B, being the solute concentration in/3', Ceq.~the solute concentration in equilibrium ct, and C~ss the solute concentration in supersaturated e. Using Avrami's extended volume concept [38,40] to separate the geometrical problem of impingement from the kinetic problem of growth, the volume fraction X(t) transformed at any time can be obtained following Christian [37, 41] as

X ( t ) = 1 - exp - 7

f~ NAD3/2(t - z)3/2 dz + NoAD312t3/2]}.

Assuming the nucleation rate N to be a function of time, it may be expressed as N = C't q, where C ' and q are constants and q < 0 [37, 41]. The volume fraction transformed may then be written as

X ( t ) = 1 - exp{ --JD3/2[Not3/2 -t- Ct5/2+q]}

(5)

where J = 7AK2= constant and C = 2C'/5. If the nucleation sites are completely saturated initially, N = 0, and hence

X ( t ) = 1 -- e x p [ - JD3/2Not3/2 ].

i.e. q = 0

X(t) = 1 - e x p [ - jD3/2CtSI2].

(7)

For intermediate cases, where the nucleation rate is decreasing with time, X ( t ) can be expressed in the general form of the Avrami equation [38, 40]

X ( t ) = I -- exp[--(t/r) n]

(8)

where F is a time constant. The exponential n is seen to lie between 1.5 and 2.5, depending on the degree of site saturation and the time dependence of the nucleation rate. Equation (5) may be written in a form similar to that of equation (8)

[ - - 2 J 3'2 ] X(t)=l-exPL~DiNt" j

(9)

where 1.5 ~< n ~< 2.5 if no nuclei are present initially and the nucleation rate decreases with time. This form of the precipitation equation will be used for all successive calculations.

2.2. Dislocation density dependence of fl" precipitation

NAD312(t - z) 3/2dz .

If N Onuclei are already present at time t = 0, then the volume fraction transformed at time t is given by

X(t)= l exp{-[T

2043

(6)

On the other hand, if no nuclei are present at time t = 0, N O= 0 and the nucleation rate is constant,

Fig. 1. Precipitate free zones (PFZ) next to a grain boundary formed after solutionizing, quenching and aging the control 6061 A1 alloy by heating linearly to 390°C at 60°C/min.

In a whisker reinforced discontinuous MMC, the reinforcements are usually oriented randomly, and the matrix around each reinforcement is plastically deformed in a cylindrically symmetric fashion, with the plastic zone extending considerably beyond the fiber ends. The size of the plastically deformed zone has been shown to be a function of the thermal expansion coefficient mismatch between the reinforcement and the matrix and the temperature range of cooling after fabrication/solutionization [3]. The effective plastic strain within the plastically deformed zone, and therefore the matrix dislocation density, were shown to have a non-linear dependence on the distance from the whisker [3]. In this section, expressions have been developed to describe the precipitation kinetics of the transition/7' phase in various matrix dislocation fields adjacent to fibers. Several assumptions were made for modeling expediency. First, the problem of a cylindrically symmetric, non-linear dislocation density distribution around a fiber was simplified into a one dimensional problem by modeling the matrix as a slab with a plate reinforcement at one end, as shown in Fig. 2. The dislocation density was assumed to be a function of distance along only one direction (x direction in Fig. 2), representative of either the radial or axial direction of the fiber in the actual composite. It was assumed that the plastic zone extends a distance L from the fiber-matrix interface, and that the dislocation density outside the plastic zone is negligible compared to that inside. For ease of calculations, the dislocation density within the plastic zone was assumed to be either uniform or to have a linear variation with distance from the interface. Finally, the fibers were assumed to be parallel to each other and well spaced, so that the plastic zones from adjacent fibers do not interact with each other. Two dislocation distributions were considered. These

2044

DUTTA and BOURELL: AGING BEHAVIOR OF 6061 A1-SiCw COMPOSITES energetically identical for the diffusing atom, g ~ 10-18p, if p has units of m -2. Since the dislocation density observed in the composites is about 1013m 2, 1 - g ~ 1, g i v i n g D ~ D p . g + D 1. At temperatures below half the melting point, where most aging is done, Dp .g is much greater than D1 [26], thereby yielding D ~ Dp.g, or

FIBER

MATRIX

D ~ 10-18"Dp.p. ~"

Gradient,MeanDensity= 1.5p UniformDensity=1.5 I~

y

I Prrax- 3/;

L Length of Model Matrix [x 1

Fig. 2. Schematic representation of the matrix of length L next to a fiber in a simplified MMC. Four schematic matrix dislocation density distributions are shown. In the two uniform distributions, the dislocation density is constant (~ or 1.5~) throughout the length L of the matrix. In case of the nonuniform distributions, the dislocation density is maximum at the fiber-matrix interface (L) and decreases linearly to zero at a distance L away from the interface. The mean densities for the nonuniform distributions were chosen to be identical to the uniform densities (~ or 1.5~) to facilitate comparison.

included a uniform dislocation distribution of density M~, M being a constant, and a linear dislocation density distribution of the form p = Pmax x / L along the length L where x is any position along the length. The maximum density Pmax adjacent to the fiber was taken to be 2M~ to yield an average density of M~. Figure 2 illustrates these schematic dislocation density distributions for M = 1 and 1.5. Avrami type precipitation curves were generated for these distributions, assuming (1) dislocation-density-dependent nucleation only, or (2) dislocation-density-dependent nucleation and growth. From Section 2.1, the nucleation rate per unit volume N was given by

N = pN±.

(1 O)

Thus the nucleation rate is seen to be proportional to p, the dislocation density. The growth rate G can be expressed as G-

dr(t) K ~- -~-.~/-D(t-r),/2

(11)

where the diffusion coefficient D may be written as:

D = Dp.g + D,(1 - g )

(12)

where D 0 is the pipe diffusion coefficient, D, is the lattice diffusion coefficient and g is the fraction of time a diffusing atom is associated with a dislocation core [21]. Assuming that all the atom sites are

(13)

Both nucleation rate (N) and the apparent diffusivity (D) in equation (9) are then proportional to the dislocation density, while the growth rate is proportional to the square root of the dislocation density. The precipitation curves in the following sections were generated based on these results and the additional assumption that there is no incubation time required for nucleation to commence. 2.2.1. Dislocation dependent nucleation only. Substituting equation (10) in equation (9), the fraction precipitated at time t in a sample with a uniform dislocation density of M~ is obtained as

X.(t) = 1 - exp[-- M(t/F.)"]

(14)

where F, = i ~

N±~ ) - l/n = time constant

when only the nucleation rate depends on the dislocation density. Here, D is assumed to be dislocation density independent. For the linear dislocation density gradient with the average density M~

X ( x , t) = 1 - e x p [ - - 2 M ( x / L ) ( t / F , ) " ]

(15)

at any position x along the length of the specimen. Integrating equation (15) between x = 0 and x = L, and substituting for X,(t) from equation (14)

X (t) = 1 -- (1/2M)(F./t)"[1 -- {1

-

-

Xu(t)} 2] (16)

for precipitation with a linear dislocation density distribution varying over L from 0 to 2M~. Precipitation curves calculated from equations (14) to (16) for dislocation density dependent nucleation have been plotted in Fig. 3 for M = 1 and 1.5. A time dependent, decreasing nucleation rate was assumed for the calculations, and the reaction rate order n was taken to be 2. It is seen that a higher average dislocation density results a higher precipitation rate. Also, for the same average dislocation density, the presence of a gradient lowers the precipitation rate, the slowdown being greater at later stages of precipitation. 2.2.2. Dislocation dependent nucleation and growth. Substituting equations (10) and (13) in equation (9), the fraction precipitated at time t in a sample with uniform dislocation density of Mp is given by X.(t) = 1 - e x p [ - M S / 2 ( t / r . + g ) " ]

(17)

where F.+g = (2J/5 10 -27 D 3/2 N±~5/2) -I/" = time constant for dislocation density dependent nucleation and growth.

DUTTA and BOURELL:

AGING BEHAVIOR OF 6061 A1 SiCw COMPOSITES

1.00 n=2

0.75

~

....

Gradient,MeanDensity= 1 . 5 ~ ~ UniformDensity= l . 5 ~ , , ~ j ~

0.50

//

orm Density= 0.25 0.00

~ ~

0.00

n ~

0.25

t

,

,I

,

0.50

MeanDnesilly= I

0.75

,

I

,

1.00

I

,

1.25

1.50

t/ F n

Fig. 3. Normalized aging curves for/?' precipitation calculated using the assumption that only the nucleation rate is dislocation density dependent. While a higher dislocation density increases the rate of precipitation, a gradient slows the precipitation rate, the effect being greater at later stages of aging. For a linear dislocation density gradient with the average density M~ X ( x , t) = 1 - e x p [ - ( 2 M ) 5 / 2 ( x / L ) 5 / z ( t / F n + g ) " ]

(18)

at any position x. After replacing the exponential function with its McLaurin series expansion, equation (18) can be integrated between x = 0 and x = L to yield

x(t) = 2 ~ ( - 1)qt/r.+yi-1)(2M)CJ-1)5/2 5j= 2

~:-- ~

_-- ~.T

(19)

for precipitation in a specimen with a linear dislocation density gradient (p = 2 M ~ . x / L ) . Figure 4 shows plots of equations (17) and (19) for dislocation density dependent nucleation and growth. Here, a behavior is apparent which is markedly different from that in Fig. 3, where only the nucleation rate was dependent on dislocation density. It is found that when both nucleation and growth are dislocation density dependent, a gradient not only retards precipitation at the later stages, but also accelerates it at the initial stages. Thus, if two samples with the same average dislocation density, but one with a gradient and the other without, are compared to each other, precipitation will initiate earlier in the sample with the gradient, but end later.

present investigation, the choice of a cast and wrought control alloy was considered acceptable. Three different samples were analyzed: (i) solutionized and quenched 6061 AI-10 vol.% SiC composite (ii) solutionized and quenched unreinforced 6061 A1 (iii) unreinforced 6061 A1 strained 0.36% plastically in uniaxial tension after solutionizing and quenching. The 0.36% plastic strain was imparted to one of the monolithic samples to match the plastic work calculated to be expended in the composite due to plastic deformation during quenching [3]. Since the composite sample and the 0.36% plastically strained sample had identical plastic work and presumably comparable average dislocation densities, the difference in precipitation behavior of the two samples is attributed to the presence of dislocation density gradients and/or residual stress gradients in the composite matrix. It has been shown in Ref. [5] that the effect of residual stress gradients on precipitation in heavily dislocated aluminum based composite matrices is negligible compared to dislocation effects. Hence it is assumed that any difference in the precipitation behavior of the composite and the strained monolithic sample arises from the presence of dislocation density gradients in the composite as opposed to a uniform dislocation density in the monolith. All the samples were wrapped in aluminum foil, solutionized at 560°C for 1 h and water quenched. After solutionizing, quenching, and where required, straining, the bulk samples of the composite and the unreinforced 6061 A1 were cut into 1.6mm thick, 5.5 mm diameter disks using electric discharge machining. The samples were then analyzed immediately using a Perkin Elmer Series 7 differential scanning calorimeter. The DSC runs were started at 50°C and ended at 560°C. A constant heating rate of 10, 20 or 40°C/min was used. A high purity aluminum disk of equal mass was used as the reference. After the completion of the run, data from the first exothermic peak (identified as the fl' peak [5]) were converted into fraction precipitated versus temperature curves 1.00

1

n=2

0.75

3. EXPERIMENTAL

Powder metallurgy processed 6061 A1 MMC reinforced with 10 vol. % discontinuous/?-SIC whiskers of variable aspect ratio ( ~ 3-25) was obtained from Arco Chemical Co. as 0.0064 m x 0.038 m x 0.45 m as-extruded billets. The precipitation behavior of the composite samples was compared to that of a control commercial grade ingot metallurgy 6061 aluminum alloy. Trial DSC runs indicated that the difference between the peak temperatures for/~' precipitation in the control alloy and in the M M C is about an order of magnitude larger than the difference in peak temperatures reported in Ref. [7] due to different processing histories. Hence, for the purpose of the

2045

~

Gradient,MeanDensity= UniformDensity--1.5~'-----~j ~ ~ J

0.25

0.00

"

.....~ " " "

0.25

0.50

t/F

0.75

1.00

II+g

Fig. 4. Normalized aging curves for fl' precipitation calculated using the assumption that both nucleation and growth rates are dependent on dislocation density. A higher dislocation density increases the rate of precipitation. A gradient increases the precipitation rate initially, and then retards it subsequently. Also, a steeper gradient (average density = 1.5~) increases the initial precipitation rate.

2046

DUTTA and BOURELL: AGING BEHAVIOR OF 6061 A1 SiCw COMPOSITES

by partial area integration over the peak. A fraction precipitated versus time plot was then obtained by dividing the temperature scale by the DSC heating rate.

3.0

~

2.5

~N~

6061 AI, Unstrained

2.0 Z

4. EXPERIMENTAL OBSERVATIONS

Calorimetry of both the composite and the unreinforced alloys showed similar precipitation behavior. The peaks in the DSC scans were identified by electron microscopy and the results are described in detail elsewhere [5, 42]. For analysis, the first exothermic reaction, which was identified as fl' (transition Mg2Si) rod formation, was chosen. Precipitation curves generated from the DSC data are shown in Fig. 5. The plots indicate that fl' precipitation is considerably accelerated in the M M C relative to the unstrained unreinforced sample at all heating rates. Based on T E M observations of heterogeneous precipitation in AI-SiC composites, increased dislocation density in the composite leads to a reduction in incubation time for precipitation [6], as seen in Fig. 5 for the present investigation. The 10 vol.% SiC reinforced 6061 A1 M M C sample exhibits almost the same precipitation rate as the strained unreinforced sample. However, it is seen from Fig. 5 that in the composite sample, fl' precipitation starts earlier and ends later, leading to a crossover of the precipitation curves of the composite and the 0.36% plastically lc0~ 10 °C/min

i

S0

i

40

y / ~ . -

_20

ns~ained 20 22 24 TIME (minutes)

100 20OC/min

~O

1"O60

i 270

i 280

i 290

I 300

26

--

-

i 310

320

T E M P E R A T U R E (°C)

Fig. 6. The reaction rate order n for fl' precipitation as a function of temperature obtained from the analysis of DSC scans of the unstrained and 0.36% plastically strained control alloys and the 6061 AI-10 SiC MMC at different heating rates. The value of n is high at the initial stages of precipitation (low temperatures) and decreases as precipitation progresses (high temperatures). The value of n was observed to be between 1 and ~2.5 for all three materials. strained alloy. The same behavior was observed at all three DSC heating rates. From the DSC precipitation plots, the reaction rate order n for fl' precipitation was determined by the Ozawa method [43, 44]. The fraction of fl' precipitated (2") at any instant t is given by the Avrami equation [equation (8)]. For a non-isothermal transformation, e.g., one obtained from a DSC scan, t in equation (8) can be expressed as [T - To]/Q, where T is the absolute temperature at any instant, TOis the starting temperature of the scan and Q is the constant heating rate in °C/min. The reaction rate order n is therefore given by n = d {log~0[ln(1 - X)]}/d lOgl0 Q

6061 AI-10 SiC MMC

18

1.5

~

6061AI, 0.36% Cold Work

16

~

28

•

(20)

where 2" is obtained at the same temperature from a n u m b e r of precipitation exotherms taken at different heating rates. Figure 6 is a plot of reaction rate orders for fl' precipitation as functions of temperature for the composite and the strained/unstrained unreinforced alloy. It is seen that n lies between 1.5 and 2.75 for the strained and unstrained monolithic samples, while for the composite, n falls between 1 and 2.

6061 A 1 , ~Cold ~ Work ~ 0 . 3 6 % 6061 AI- 10 SiC MMC

IO

5. DISCUSSION

12

TIME (minutes)

o°c,oi° ["6O gh

14

/---y--

6051AI 036% Cold Work ' " 6061AI- 10 SiC MMC

20 0 4.5

16

6061 AII, Unstained Unstrained -

5,5

6.~ TIME (minutes)

7.5

8.5

Fig. 5. Fraction of fl' precipitated as a function of aging time, plotted from data obtained from DSC scans at several heating rates. Shown are the unstrained control 6061 AI, 6061 A1 cold worked to a plastic strain of 0.36% after the solutionizing quench and the 6061 AI-10 SiC MMC. All were solutionized and quenched before each DSC run.

Based on the results of modeling (Section 2), the precipitation behavior obtained from the DSC studies is explained as follows. On imparting plastic strain to the unreinforced sample, the dislocation density in the sample rises such that the resultant density is uniform over the long range. This leads to an increased precipitation rate, irrespective of whether only nucleation, or both nucleation and growth are dislocation density dependent. The more rapid initial precipitation and the later retardation in the composite sample with respect to the 0.36% plastically strained sample is explained from two different viewpoints depending on the influence of dislocation density on fl' growth. First, if both growth and nucleation are dislocation density dependent, the presence of dislocation density gradients in the

DUTTA and BOURELL:

AGING BEHAVIOR OF 6061 A1-SiCwCOMPOSITES

composite would give rise to a faster initial precipitation rate, which decreases at a greater rate compared to that in a uniformly dislocated unreinforced alloy of the same average density. This would lead to a crossover of the precipitation curves of the strained monolith and the composite, as observed in Fig. 5. Secondly, if only nucleation is dependent on the dislocation density, the experimental observations can be rationalized if the dislocation density in the 0.36% plastically strained unreinforced sample is somewhat less than the average density in the composite. This would also make precipitation initiate earlier in the composite and retard it at the later stages, resulting in the observed crossover. The presence of a higher average dislocation density in the composite sample as compared to that in the 0.36% plastically strained sample is in fact quite probable, since the finite element analysis used to calculate the expended plastic work, and hence the equivalent tensile strain in the composite [3] incorporated regular whisker arrays and non-interacting matrix plastic zones for modeling ease. Neither of these conditions were satisfied in the actual composite sample used in this work, and therefore it is reasonable that the F E M analysis may slightly underestimate the strain in the composite. In any case, either of the mechanisms, namely dislocation dependent nucleation or dislocation dependent nucleation plus growth, predict crossover of the composite and the strained unreinforced alloy curves, even if the 0.36% plastic strain imparted to the unreinforced sample yielded a dislocation density up to about half the average density in the composite sample. However, the temperature ranges where the two mechanisms are valid are widely different. As discussed earlier, the apparent diffusion coefficient and therefore growth, have high dislocation density dependencies at low temperatures only, where pipe diffusion is the dominating mechanism. On the other hand, at higher temperatures, where the pipe diffusion mechanism is almost negligible compared to lattice diffusion, D ~ D~, and only the nucleation rate will be dependent on the dislocation density. At intermediate temperatures, where both pipe and lattice diffusion are important, the apparent diffusion coefficient can no longer be simplified as either Dp.g or D1, and computations become somewhat more complicated. The reaction rate order n measured from DSC runs was seen to decrease with increasing temperature for all three samples (Fig. 6). From the theoretical calculations, n is expected to be equal to 2.5 if the nucleation rate is constant, greater than 2.5 if the nucleation rate increases with time, and less than 2 if the nucleation rate decreases with time [equations (5)-(8)]. From Fig. 6, it is observed that for the monolithic alloy in the unstrained condition, n ~ 2.7 at the start of the transformation, but drops to about 1.5 soon after. This indicates that the nucleation rate increases with time (q > 0) during the initial stages of AM38/II--B

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precipitation, levels out quickly at some point, and then decreases with time (q > 0) through the rest of the transformation. In a DSC experiment, both time and test temperature vary simultaneously. The observed initial increase in nucleation rate probably arises due to the increase in test temperature. The decrease late in the test can be attributed to progressive site saturation. In the strained monolithic alloy, the same trend as in the unstrained alloy is observed, except that the nucleation rate seems to be constant (n ~ 2.5) at the beginning of the transformation. This suggests that the effect of increased initial nucleation rate due to increasing test temperature is balanced by the decrease in the overall nucleation rate due to the presence of embryos at many of the available nucleation sites (dislocations and vacancy loops). In the composite, the nucleation rate is found to decrease from the very start, indicating that most of the available nucleation sites are already saturated by the time fl' precipitation begins. It is also observed that the final value of the reaction rate order n in the composite is about 1 instead of the predicted 1.5 for complete site saturation, suggesting that towards the end of the precipitation process the fl' rods probably grow principally by thickening (2-dimensional growth) with little or no lengthening. Some of the limitations of this study deserve mention. First, the composite was modeled as a matrix slab adjacent to a plate fiber instead of being cylindrically symmetric. This could potentially cause some difference between the calculated precipitation curve and that of an actual composite. However, the overall effect of the' dislocation density gradient in enhancing the initial precipitation rate and retarding it at later stages should remain unchanged, as evidenced by the experimental precipitation curves. Both analytical and experimental evidence available in the literature suggest that the principal sites of dislocation generation in metal-matrix composites are fiber ends rather than the fiber sides [6, 9, 16]. The necessity of modeling a cylindrically symmetric dislocation distribution around fibers is therefore obviated as the model in its present form approximates the dislocation gradients at fiber ends. Secondly, the control material chosen for the experimental part of this work was produced via an ingot metallurgy (IM) route, whereas the composite was a powder metallurgy (PM) product. It has been demonstrated that PM processing may cause some acceleration in aging relative to IM processed materials [7]. Hence, it is possible that some of the experimentally observed acceleration may be due to differences in processing histories. However, the M M C showed not only an overall acceleration of the precipitation process, as would be expected due to a different processing history and/or a higher uniform matrix dislocation density than the monolith, but also exhibited a progressive slowdown in kinetics with continued precipitation. This is evident from a comparison of the slopes of the precipitation curves of the monolith

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and the composite in Fig. 5. F r o m this it is reasonable that while the PM process used to fabricate the composite may have been responsible for part o f the observed overall acceleration of precipitation relative to the monolith, it did not obfuscate the effect of dislocation density distributions on the kinetics of precipitation. 6. SUMMARY AND CONCLUSIONS Theoretical models were developed which predict the aging response of metal matrix composites, incorporating the effects of dislocation density and distribution on nucleation and growth. At low aging temperatures, when both nucleation and growth is enhanced by presence of dislocations, dislocation density gradients raise the initial precipitation rate relative to samples with the same average dislocation density. At relatively high aging temperatures, when lattice diffusion dominates and growth is not so dependent on dislocation distribution, accelerated aging becomes less pronounced in composites. At all temperatures, the late stages of precipitation are retarded in samples with dislocation density gradients relative to samples having uniform dislocation density distributions with the same average density. Such dislocation density distribution effects on precipitation are expected to be prominent in M M C s with low volume fraction reinforcement, since high reinforcement volume fractions tend to generate fairly uniform dislocation densities throughout the matrix. Finally, the dimensionality of growth during the final stages of precipitation seems to be altered in the composite, although the reasons for this phenomenon are not clear yet. Acknowledgements--This research was supported in part by DARPA/ARO under contract No. N00014-84-K-0687. The authors gratefully acknowledge the assistance of Drs A. Manthiram and J. B. Goodenough with the calorimetric analyses.

REFERENCES 1. T. G. Nieh and R. F. Karlak, Scripta metall. 18, 25 (1984). 2. R. J. Arsenault and R. M. Fisher, Seripta metall. 17, 67 (1983). 3. I. Dutta, D. L. Bourell and D. Latimer, J. comp. Mater. 22, 829 (1988). 4. T. Christman, A. Needleman, S. Nutt and S. Suresh, Mater. Sci. Engng. 107A, 49 (1989). 5. I. Dutta and D. L. Bourell, Mater. Sci. Engng All2, 67 (1989). 6, T. Christman and S. Suresh, Acta metall. 36, 1691 (1988). 7. J. M. Papazian, Metall. Trans. A 19A, 2945 (1988). 8. K. K. Chawla and M. Metzger, J. Mater. Sci. 7, 34 (1972). 9. M. Vogelsang, R. J. Arsenault and R. M. Fisher, Metall. Trans. A 17A, 379 (1986). 10. R. F. Arsenault and N. Shi, Mater. Sci. Engng 81, 175 (1986). 11. Progress in Science and Engineering of Composites, Proc. 4th Int. Conf. on Composite Materials, Tokyo (edited by T. Hayashi et al.), Japan Soc. Comp. Mater. (1982).

12. B. Derby and J. R. Walker, Scripta metall. 22, 529 (1988). 13. L. J. Broutman and R. H. Krock (editors) Composite Materials, Vol. 1-4. Academic Press, New York (1974). 14. G. J. Dvorak, M. S. M. Rao and J. Q. Tam, J. comp. Mater. 7, 194 (1973). 15. C. A. Hoffman, J. Engng Mater. Tech. 95, 55 (1973). 16. M. Taya and T. Mori, Acta metall. 35, 155 (1987). 17. R. J. Arsenault and M. Taya, Acta metall. 35, 651 (1987). 18. J. W. Cahn, Acta metall. 5, 169 (1957). 19. F. S. Ham, J. appl. Phys. 30, 915 (1959). 20. S. Harper, Phys. Rev. 83, 709 (1951). 21. A. H. Cotterell and B. A. Bilby, Proc. Phys. Soc. Lond. A62, 49 (1949). 22. A. Pawloski, Scripta metall. 13, 791 (1979). 23. A. Pawloski, Scripta metall. 13, 785 (1979). 24. J. C. Fisher and J. H. Holloman, Acta metall. 3, 608 (1955). 25. D. Turnbull, Diffusion Short Circuits and Their Role in Precipitation, Defects in Crystalline Solids. The Physical Society, London (1955). 26. P. G. Shewmon, Diffusion in Solids, p. 175. McGrawHill, New York (1963). 27. S. Suresh, T. Christman and Y. Sugimura, Scripta metall. 23, 1599 (1989). 28. E. P. Butler and P. Swann, Acta metall. 24, 343 (1976). 29. I. S. Servi and D. Turnbull, Acta metall. 14, 161 (1964). 30. I. M. Lifshitz and V. V. Slyozov, J. Phys. Chem. Solids 19, 35 (1961). 31. C. Wagner, Z. Electrochem. 65, 581 (1961). 32. D. Turnbull and H. N. Treaftis, Acta metall. 3, 43 (1955). 33. H. J. Rack and R. W. Krenzer, Metall. Trans. A gA, 335 (1977). 34. G. Thomas, J. Inst. Metals 90, 57 (1961~52). 35. P. A. Beaven, A. P. Davidson and E. P. Butler, Proc. Int. Conf. on Solid-Solid Phase Transformation (Aaronson et al.), p. 661. TMS-AIME, New York (1982). 36. W. F. Smith, Structure and Properties o f Engineering Alloys, pp. 191-192. McGraw-Hill, New York (1981). 37. Physical Metallurgy (edited by R. W. Cahn), p. 477. North Holland, Amsterdam (1965). 38. M. Avrami, J. Chem. Phys. 7, 1103 (1939). 39. I. Kovacs, J. Lendvai and E. Nagy, Acta metall. 20, 975 (1972). 40. M. Avrami, J. Chem. Phys. 8, 212 (1940). 41. J. W. Christian, The Theory o f Transformations in Metals and Alloys, 2nd edn. Pergamon Press, Oxford (1975). 42. I. Dutta, Ph.D. dissertation, Univ. of Texas at Austin (1988). 43. T. Ozawa, Polymer 12, 150 (1971). 44. H. Yinnon and D. R. Uhlmann, J. Non-Cryst. Solids 54, 253 (1983).

APPENDIX Cylindrical fl' particles are assumed to precipitate from a supersaturated ~tmatrix. The ct phase is assumed to be richer in component A, while fl' is richer in component B. It is also assumed that the fl' phase precipitates in the form of rods which undergo self-similar growth with time. This is shown in Fig. A1. As the /3' rod grows, the adjacent at region is depleted of B. It is assumed that corresponding to a growth of the fl' rods by dr in the radial direction and dh in the axial direction, the region of depletion widens by dR and lengthens by dH as shown in Fig. A1. The amount of component B entering fl' when the rod diameter increases by dr and the rod length increases by dh equals (Cp,- Ceq.~), dV ~', where dV ~' is the corresponding increase in the volume of a fl' rod. Likewise, the amount of

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Therefore d V eq'~ _ C/~,- Ceq.~ (A1) dV~' C ~ s - Ceq. ~ The increase in the total transformed volume (d V ~q~+ P') can be written as d V °q~+#' = d V eq'~ q- d V C Equilibriuma,

H

Assuming that aspect ratios of the fl' rod and the equilibrium a regions are constant with time (i.e. both grow self similarly), the ratio of the total transformed volume to that of fl' can be expressed as dVeq'~+/~' dVeq'~ KR2dR d V ~'

.....

~ ....

.3 Supersaturateda

Fig. AI. Schematic showing the self-similar growth of a 13' rod in an ~t matrix. Adjacent to the/3' rod (dark) is a region o f equilibrium ~ (shaded) where the solute concentration is less than that in the supersaturated ~ surrounding it (no shading). The thickening of the/3' rod from a radius of r to r + dr leads to a widening of the entire transformed region (shaded) consisting of equilibrium ct and 13' from a radius of R to R + dR. Likewise, the lengthening of the 13' rod from h to h + dh leads to lengthening of the transformed region from H to H + dill c o m p o n e n t B leaving supersaturated ~ can be written as ( C ~ , s s - C e q . ~ ) d V eq'~, where d ~ eq'~ is the increase in the volume of equilibrium ~. Conservation of mass requires that the a m o u n t of B leaving the supersaturated ~t equal the a m o u n t of B entering 13'.

d V eq~'

+ 1-

k r 2 dr

(A2)

where R and K are the radius and the aspect ratio of the transformed region consisting of equilibrium ~ and 13' and r and k are the radius and the aspect ratio of the 13' cylinder at any instant. Substituting equation (A1) in (A2) and writing ~ = 1 + ( C a. - Coq.~)/(C~ - Ceq.~) and r = K / k R 2 dR = ~- r 2 dr. K

(A3)

Integrating the left side of equation (A3) from 0 to R and the right side from 0 to r and simplifying R3 ~c~T = ~" (A4) Assuming that the aspect ratios of the total transformed volume (~ + 13') and 13' are constant with time veq'~ +/~' R3 K Vp' r3 and therefore equation (A4) becomes V eq'~+~' V~" = ~ where 7 is a constant.

Clr .4- C~ss - 2Ceq. ~

C ~ - Coq.~

(A5)