An investigation of the precipitation-hardening process in aluminum alloy 2219 by means of sound wave velocity and ultrasonic attenuation

Materials Science and Engineering, 53 (1982) 163 - 177

163

An Investigation of the Precipitation-hardening Process in Aluminum Alloy 2219 by Means of Sound Wave Velocity and Ultrasonic Attenuation M. ROSEN and E. HOROWITZ

Center for Materials Research, The Johns Hopkins University, Baltimore, MD 21218 (U.S.A.) S. FICK, R. C. RENO* and R. MEHRABIAN

Metallurgy Division, National Bureau of Standards, Washington, DC 20234 (U.S.A.) (Received June 19, 1981)

SUMMARY

The precipitation-hardening process in aluminum alloy 2219 has been investigated by means o f dynamic measurements of sound wave velocity, ultrasonic attenuation and hardness. Measurements o f these properties as a function of aging time at constant temperatures (150, 175 and 220 °C) were found to exhibit prominent changes and anomalies that were related to the formation o f 0" and O' precipitates in aluminum alloy 2219. From the temperature dependence o f the sound velocity and ultrasonic attenuation, the activation energies for formation o f 0" and O' were found to be 4.7 hcal mo1-1 and 9.9 kcal mol -J respectively. A thermally activated process, with an activation energy of 26.6 kcal mo1-1, was apparently responsible for the loss o f coherency o f O' precipitates and the resulting decrease in hardness. The occurrence o f contemporaneous peaks in both hardness and ultrasonic attenuation provides the experimental evidence for this assumption. The growth law for O' particles was determined from the precipitation kinetics. The O' precipitates, in their semicoherent form, follow a two-dimensional growth law. The coarsening o f O' and the subsequent loss o f coherency are approximately governed by a three-dimensional growth law. Sound wave velocity measurements indicate that the ultimate value o f the elasticity of aluminum alloy 2219 depends on the agehardening temperature. The elastic moduli *On leave from the Department of Physics, University of Maryland, Baltimore County, Catonsville, MD 21228, U.S.A. 0025-5416/82/0000-0000/$02.75

increase with increasing aging temperature. This behavior is attributed to the relatively larger volume fraction o f precipitates, o f intrinsically higher elastic moduli than the matrix, that results from aging at increased temperatures. The plastic behavior, however, as manifested by peak values o f the hardness, was found to decrease with increasing aging temperature. The frequency dependence o f the ultrasonic attenuation indicates that a relaxational mechanism is operative. The fact that the occurrence o f attenuation peaks depends also on the average distribution o f the precipitate size is evidenced by the effect o f plastic deformation prior to aging on the location o f the attenuation peaks. The present investigation has demonstrated the operational feasibility o f an ultrasonic non-destructive evaluation method for monitoring the precipitation process, over a wide temperature interval, in aluminum alloys during its progress.

1. INTRODUCTION

The extensive use of aluminum-base alloys in the aerospace industries is due primarily to the high specific strength-to-weight ratio of these alloys, their weldability and their substantial toughness over a wide temperature range. Alloying and cold working can improve the yield strength and the hardness of aluminum-base alloys. In certain systems an additional increase in hardness can be achieved by an appropriately controlled thermomechanical treatment. A condition for the hardening process to occur is the precipitation of particles from an aluminum-base supersatu© Elsevier Sequoia/Printed in The Netherlands

164

rated solid solution. The basic requirement for precipitation hardening of an alloy system is that the solid solubility limit should decrease with decreasing temperature. In aluminum-base alloys the rapid cooling suppresses the separation of the ~ phase so that the alloy exists at the lower temperatures in an unstable supersaturated state. If the alloy is allowed to age at temperatures within an interval, specific to each alloy system, the second phase precipitates out. The formation of precipitates contributes to the strengthening of the alloy. The increase in yield strength and hardness depends, largely, on the structure, spacing, size, shape and distribution of the precipitated particles, as well as on the degree of structural and crystallographic coherency with the matrix. The age-hardening process also involves atomic rearrangements accompanying the breakdown of the supersaturated solid solution. This occurs by a diffusional nucleation and growth process. The rate of growth of the nuclei is controlled by the rate of atomic migration in the alloy; thus the temperature of aging has a pronounced effect. Guinier [1, 2] and Preston [3, 4] determined, independently, the nature of the precipitates through the application of diffuse X-ray diffraction techniques. Anomalous Xray diffraction affects detected at the early stages of the aging process were attributed to the segregation of clusters of copper atoms on the {100} planes of the aluminum lattice. These Guinier-Preston (GP(1)) zones have a thickness of a few atomic planes and are structurally coherent with the aluminum solid solution matrix; they are formed rapidly and homogeneously by an enhanced diffusion process driven by the excess of vacancies in quenched alloys. The rapid migration of copper in the aluminum matrix, preceding zone formation, is due to vacancy-solute coupling [5 - 7]. The 0" particles in AI-Cu alloys are coherent intermediate precipitates, rather than zones, as they have a definite crystallographic structure [8 - 10]. The thickness of the 0" particles is about 100 A and their diameter is approximately 1500 A. The aluminum planes, parallel to the 0" platelet, are distorted by elastic coherency strains [ 11]. The 0' precipitate is of tetragonal structure with the c axis parallel to the AI[100] direction [9]. Structural dislocations are

found near 0' precipitates, thus producing a quasi-coherent interface [12]. The formation of these dislocation rings causes the relaxation of strains near the precipitates and consequently contributes to a reduction in hardness and strength of the alloy. It has been observed [9] that under suitable circumstances GP(1), 0" and 0' can be the precipitates detected first, suggesting that 0" and 0' can be nucleated independently. The equilibrium CuA12 incoherent ~ precipitate is also of tetragonal structure. The heterogeneous nucleation of 0, occurring at planar grain boundaries in the aluminum matrix or at metastable 0' precipitates, can be observed in the overaged condition. The contribution of 0" and 0' particles to hardness strongly depends on the size and the distribution of the precipitates in the matrix. The coherency strains near the precipitates affect the matrix nearest to them. As the precipitates grow, their adjacent strain fields become larger and at peak hardness they extend from one precipitate to the next [13]. The precipitation-hardening process in aluminum alloys has been extensively studied by X-ray diffraction [1, 4, 9], electron microscopy [11, 14], electrical resistivity [7, 15, 16] and hardness [15 - 17]. However, relatively few studies have been devoted to the investigation of the relationship between the absorption of ultrasonic waves and changes in the precipitate structures occurring during the aging process. Low frequency internal friction studies revealed relaxation phenomena that were attributed to different mechanisms, involving the effects of mechanical vibration on solute atoms [18, 19], vacancies [20] and stress concentrations. The degree of coherency will then determine the magnitude of the sound wave absorption [ 21]. An investigation of the attenuation of ultrasonic waves during the precipitation process in A1-Cu-Mg alloy [22] at low aging temperatures revealed two maxima, at the aging times when the interaction between acoustic waves and certain configurations of stress around the precipitates was maximal. No studies of the behavior of the sound velocities, i.e. the elastic properties, during the progress of the aging process in aluminum alloys have been reported. The purpose of the present investigation was twofold: first, to investigate the mecha-

165

nism and kinetics of the precipitationhardening process in aluminum alloy 2219 by means of dynamic measurements of sound velocity, ultrasonic attenuation and hardness while the alloy is undergoing age hardening and, second, to develop a non-destructive evaluation method appropriate for examination and control of age hardening of the alloy during thermomechanical heat treatments.

2. EXPERIMENTAL DETAILS

2.1. Specimen preparation The specimens used in this investigation were prepared from aluminum alloy 2219 supplied in the F condition by ReynoldsMcCook (Chicago). The results of the chemical constituent analysis are given in Table 1. Prior to thermomechanical treatment the specimens were machined into rectangular bars 170 mm X 25.4 mm × 12.5 mm. Parallelism between the two largest faces was maintained to within 3 × 10-a mm. Solution treatment carried out at 535 °C for 75 min was followed by ice-water quenching. The specimens were then stored in a freezer at subzero temperatures. Hardness measurements before and after storage verified that no natural aging had occurred. Selected specimens of the samples were stretched to 5% elongation on a Satec tensile machine of 50 tonf capacity. A number of small samples were sectioned from each stretched specimen to allow ultrasonic attenuation and velocity measurements to be correlated with the results of hardness testing and a posteriori optical and transmission electron microscopy. The specimens were aged in a Braun thermostatic bath containing heated peanut oil kept in continuous circulation by a mechanical circulator. The bath could be maintained at any temperature between 100 and 250 °C,

to within 0.05 °C. The sound velocities and ultrasonic attenuation were continuously monitored and recorded. Specimens for hardness measurements and microscopic examination were periodically removed from the bath. Hardness measurements were made, using a Wilson hardness tester, at intervals throughout the aging treatment; the accuracy of the hardness values (HRB) on the Rockwell B scale was 0.5 units. Foils suitable for transmission electron microscopy were prepared by jet electropolishing disks of selected samples in a solution of 30% nitric acid and 70% methanol at a temperature of --15 °C. The foils were examined at 100 kV in a Philips EM200 electron microscope. 0" and 0' precipitates were identified by their characteristic diffraction patterns and their plate-like structure.

2.2. Specimen mounting Ultrasonic evaluation was performed by means of a quartz disk ultrasonic transducer held in direct contact with the specimen. The transducer element was co-axially plated and equipped with a ground ring lead to allow transducer grounding to be electrically independent of the specimen. The transducer was held in intimate contact with the specimen surface by a strap bolted directly to the specimen. A slight deformation was imparted to the hold-down strap on assembly to stabilize changes in contact pressure that might otherwise have resulted from the compliance of the perforated glass-epoxy circuit board insulators. When quartz disks not equipped with bonded leads were used, contact with the transducer electrodes was made by wire grids woven through the insulator perforations. The peanut oil used as the thermal medium in the bath served also as the acoustical couplant; a small amount of oil was applied to the specimen and transducer surfaces before assembly.

TABLE 1 The chemical composition of aluminum alloy 2219 Element

Cu

Mn

Fe

Si

Zn

Ti

V

Zr

Ni

Mg

A m o u n t (wt.%)

5.9

0.35

0.21

0.064

0.03

0.04

0.08

0.12

0.03

0.01

166

2.3. Ultrasonic pulse-echo method The velocity and attenuation of ultrasound in the specimens were determined through the use of a pulse-echo overlap technique [23]. Electrical signals applied to and extracted from the transducer were generated and received by a Matec 6600 pulser-receiver with a Matec model 755 plug-in unit, operating at either 6 or 10 MHz. Tuning was done by watching the video display of the received echoes and adjusting to optimize the radiated ultrasonic field pattern of the transducer, as evidenced by uniformity in the decay rate between adjacent echo pairs. Pulser tuning was verified by checking for such effects as interference at tuning positions adjacent to the optimal position. The pulse repetition rate was approximately 2500 Hz; the exact value was determined with the apparatus used for sound velocity measurements.

Fig. 1. Pulse superposition waveforms.

The sound velocity was determined from calculations based on the specimen thickness and the ultrasonic transit time. The thickness was measured before and after each agehardening run and was corrected for thermal expansion in order to calculate the velocity at elevated specimen temperatures. The transit time was determined by overlapping two successive members of the echo train on an oscilloscope display. This method, by stroboscopic identification of the two echoes, allows the time interval between pulses successively transmitted into the specimen to be adjusted to a known integer representing a multiple of the transit time to be measured. Considerable precision is inherent in the procedure for overlapping the echoes, provided that they are displayed as r.f. rather than video waveforms. As can be seen in Fig. 1, the echo waveforms have a fine structure that

167 varies from cycle to cycle so that a particular feature suitable for matching with its counterpart within a successive echo can readily be found. Because the features being matched represent small parts of events which themselves have a short duration (e.g. 100 ns for a test frequency of 10 MHz), errors due to operator uncertainty are small. Successive attempts at matching typically result in transit time discrepancies of 1 part in 105. The accuracy of the pulse-echo overlap technique is limited by this factor, as the electronic measurement of the pulse repetition interval can easily be made much more accurately. The implementation of this m e t h o d is shown in Fig. 2. A frequency counter is used in conjunction with a stable oscillator (Matec model 110). Its operation at a high frequency allows high accuracy in the frequency measurement from which the pulse repetition interval is calculated. The frequency divider and strobe generator were embodied in a Matec model 122B. Velocity measurements were made as often as practicable during each experimental run, usually about every 2 or 3 min. Some of the velocity measurements were made using an HP 1743A oscilloscope in lieu of the justmentioned Matec equipment. In both cases the accuracy of the measurements was identical. Because of uncertainty in the measurements of thickness, the overall accuracy of the calculated velocity was approximately 2 × 10 -5 The arrangement for monitoring attenuation is shown in Fig. 3. A Matec model 2470 automatic attenuation recorder provided analog processing of the video o u t p u t of the pulser-receiver by generating a d.c. voltage proportional to the logarithm of the ratio of the peak amplitudes of two echoes selected from the train of reverberations within the specimen. The inner workings of this device are partly shown in the diagram: two electronic switches (delayed gates) close at appropriate time intervals and select the echoes whose amplitude is to be peak detected. Not shown is a path by which signals controlling these switches are also used to intensify portions of the oscilloscope display corresponding to the particular echoes selected for the attenuation measurement. To overcome the effects of slight electronic drift, an automatic gain control (AGC) circuit stabilizes the amplitude of one of the two echoes by appropriately changing the gain of the receiver. A

R F ECHOES .,

.

~ TRANSOUCER I PULSER/

[

/ RECEIVER / 1, |

STROBE

I . T,G '

/

'

TR'Gh

- -

/

~

I k ~ Z ~GENERATOR~-~SYNC"

" ]

/

SPECIMEN

/ PROGRAMMABLEI I I FREQUENCY DIVIDER /

STABLE OSCILLATOR FREQUENCY COUNTER

]

Fig. 2. The velocity-measuring system (CRO, cathode ray oscilloscope).

"

l

I ~ A K ~ - L O G ] . ! [ ] GATE]--[OET]

~ I v'°E°

F - ~ SYNC

ATT. OUT [ x -J

--IRATIOFJ

I

]

X-T

I

RECORDER l

Fig. 3. The ultrasonic-attenuation-monitoring system. strip chart recorder was used to obtain a continuous record of ultrasonic attenuation. The accuracy (+1%) of the electronics was a small factor in the overall uncertainty of these measurements. Unlike velocity measurements, attenuation measurements are highly sensitive to specimen-to-specimen variations in such characteristics as surface flatness, finish and parallelism and in other characteristics that result in differences in transducer coupling and radiation pattern and in efficiency of u n w a n t e d mode conversion. Thus, successive attenuation measurements on the same specimen can be interpreted with greater confidence than can measurements on different specimens. In neither case can the measurements be considered absolute. Additional complications caused by the thermally hostile environment needed for this study were overcome by appropriate features in the design of the transducer-specimen assembly and by careful placement of the specimen in the isothermal oil bath. The overall uncertainty in absolute measurements in this study was 1 dB cm -1, while the uncertainty in relative measurements (i.e. on the same specimen) was 0.1 dB cm z. A typical video representation for an echo train for the determination of the ultrasonic attenuation is shown in Fig. 4.

168

volume fraction of incoherent 0' and 0 particles which contribute to the increased elastic moduli of the age-hardened alloy. The velocity of sound in a material is directly proportional to the elastic moduli of the material. Therefore, the present data suggest that age hardening at higher temperatures results in increased elasticity of the aluminum alloy 2219. The 150 and 175 °C isotherms show prominent dips in the variation of the sound velocity with aging time. These minima are due to the sequential, although possibly independent, formation of 0" and 0' precipitates. The minima of velocity appear to occur at the time of maximal rate of formation of these precipitates rather than at the initial stages of the process. The curve for 220 °C contains only one, rather minute, dip in the sound velocity. This dip can be attributed to the enhanced formation of 0' precipitates at 220 °C. In this context, it should be noted that the state of coherency of the 0' precipitates with the aluminum matrix may differ according to the aging temperature. In principle, the sound velocity, or the elastic moduli, should not be sensitive to the degree of coherency but rather to the volume fraction of 0'. The degree of coherency of the precipitates will, however, affect the behavior of the ultrasonic attenuation and the macroscopic hardness of the alloy. Figure 5 shows that corresponding dips {denoted by 2) on the sound velocity curves are shifted toward higher aging times as the aging temperature decreases. This is consistent with a thermally activated diffusional process

t

Fig. 4. A video representation of an echo train.

3. RESULTS AND DISCUSSION

3.1. Sound wave velocity and microstructures The longitudinal time dependence of the changes in sound wave velocity of aluminum alloy 2219 stretched by 5% during isothermal aging at 150, 175 and 220 °C is shown in Fig. 5. The absolute value of the sound velocity of the aluminum alloy 2219 before aging at 25 °C was found to be 6343 + 2 m s-1. The value 26 × 10 -~ °C-1 was taken as the coefficient of thermal expansion in order to determine sound velocity values at different temperatures. The salient features of the variation in the sound velocity with aging (Fig. 5) include an increase in slope, and in ultimate values of velocity, as the aging temperature increases. This behavior is attributable to the increased

50.0 E

n/220°C ~n/I:~

G 40.0

~j 30.0

zo 20.0

z

I0.0

z '~ u

0.0

0.5

I

2 AGING

5 TiME

I0 (hrs)

20

40

6090

Fig. 5. The change in sound velocity in 5% stretched aluminum alloy 2219 as a function of time during isothermal aging at 150, 175 and 220 °C.

169

governing the precipitation kinetics in aluminum alloys. The quantitative treatment, and the implications related to the mechanism of the process, will be described later. Electron micrographs of samples aged at 150 °C are shown in Fig. 6. Selected area diffraction patterns taken on samples aged for 1 and 2 h indicate the presence of significant amounts of 0" precipitates and some small (about 300 A in diameter) 0' disks. Aging for 42 h at 150 °C causes an increase in both the 0' fraction and the 0' size (about 1000 A in diameter). Figure 7 shows micrographs of samples aged at 175 °C. Aging for less than 2 h produces dense 0" precipitates and some small 0'. As the aging time increases b e y o n d 2 h, a significant increase in the number and size of 0' precipitates is observed. A micrograph of a sample aged for 22 h at 175 °C is shown in

Fig. 8. The large 0' precipitates (about 1000 h in diameter) distributed uniformly, patches of m u c h smaller 0" precipitates, and globular 0 precipitates along the grain boundary should be noted. Micrographs of samples aged at 220 °C are shown in Fig. 9. Samples aged for 0.5 - 6 h all contain primarily 0' precipitates. As the aging time increases, the 0' structure coarsens. 3.2. Hardness The increase in hardness of an aged alloy depends on the variation in the stress fields in the vicinity of the precipitate. The contribution to hardness will depend on the coherency of the precipitate with the matrix, size and distribution of the precipitates and the proximity of, or mean free path between, the particles. Homogeneously distributed precipitates that are coherent with the matrix and constitute a substantial volume fraction will contrib-

(a) (a)

--

(b) Fig. 6. Transmission electron mierographs of alumin u m alloy 2219 samples aged at 150 °C: (a) 1 h aging time; (b) 42 h aging time.

I =~

(b) Fig. 7. Aluminum alloy 2219 samples aged at 175 °C: (a) 2 h aging time; (b) 30 h aging time.

170

® 80

~)

~ -

T0 a 5oc

"=6o

5O

Fig. 8. An aluminum alloy 2219 sample aged at 175 °C for 22 h.

(a)

(b) Fig. 9. Aluminum alloy 2219 samples aged at 200 °C: (a) 0.5 h aging time; (b) 6 h aging time.

ute significantly. Large semicoherent or incoherent particles regardless of their hardness or elasticity cause softening of the matrix. The alloy begins to overage, or to soften, when the

~/

I

0.5

I

I

I

I

I

2 5 I0 AGING TIME ( h r s )

I

20

I

I

4 0 60

Fig. i0. The variationin hardness in a 5% stretched aluminum alloy 2219 as a function of time during isothermal aging at 150, 175 and 220 °C.

degree of coherency between the precipitates and the matrix decreases. Figure 10 exhibits the variation in hardness of aluminum alloy 2219 as a function of aging time. As the aging temperature increases, the peak hardness (denoted by 3) decreases. Thus, in contrast with the elastic behavior of alumin u m alloy 2219, the plastic properties, e.g. hardness and tensile strength, decrease with increasing precipitation temperature. As can be seen in Fig. 10, the maximal peak hardness is attained for the 150 °C isotherm. The initialslopes of the hardness curves are steeper for higher aging temperatures. Noteworthy is the extremely high slope of the curve for the 220 °C isotherm. This behavior at increased temperature can be explained by considering the enhanced mobility, as the temperature increases, of the species which diffuse during the formation of semicoherent O" and 0'. These precipitates are the major contributors to the substantial increase in hardness resulting from the aging process. However, the ultimate hardness value is higher for lesser aging temperatures although its attainment requires longer aging times. Precipitation hardening at 150 °C is a twostage process. A similar behavior has been observed [22] during the low temperature aging of the AI-Cu-Mg alloy 2024. The variation in the 150 °C hardness curve (Fig. 10) suggests that prior to the development of the plateau separating the two stages the main determinant of hardness is the growth of 0" precipitates. A n additional component of hardness, up to the peak value, is provided by

171

the formation of 0', in the semicoherent form. The 175 and 220 °C hardness curves do not exhibit well-defined two-stage processes. It can be conjectured that, during aging at 220 °C, the volume fraction of 0" is relatively insignificant. The main contribution to hardness should then arise from 0' particles in the semicoherent state. In the aluminum alloy 2219 the peak hardness followed by a softening process may be indicative of a loss of coherency of 0' precipitates. At peak hardness, the initially semicoherent 0' particles would have grown to dimensions necessitating some form of relaxation of elastic strains. This notion is supported by the fact that dislocation rings have been observed to form around 0' particles in A1-Cu alloys [12]. The strain field is then localized around the particle rather than across the matrix. Therefore, as the elastic strains between the precipitate and the matrix are relaxed, the strength and hardness of the alloy will decrease. According to this model, the hardness peaks in aluminum alloy 2219 signify the loss of coherency of the grown 0' precipitates. The actual formation of the dislocation interface is thermally activated and is limited by an activation barrier analogous to that of the process of diffusion of copper atoms in an aluminum matrix. The shifts with respect to aging time of the hardness maxima (Fig. 10) are compatible with such a thermally activated process. The elastic properties of the 0' precipitates, as determined by sound wave velocity measurements, are independent of the state of coherency between the precipitate and the matrix. Moreover, an increase in the fractional volume of 0' particles will increase the elastic properties of the bulk material. It is not surprising, therefore, that the occurrence of peak hardness is not manifested in the sound velocity data. However, the aging times to attain peak hardness and loss of coherency of 0' precipitates are marked by changes in the ultrasonic attenuation.

series of concentration fluctuations. A steady state nucleation rate can be expressed as I = K e x p { - ( Q + A ) / R T } where K = K(N,f), N is the n u m b e r of atoms per unit volume, f is the characteristic frequency (of the order of the Debye frequency) and A is the energy increase due to the formation of a nucleus of a critical size. A is temperature dependent. Q is the activation energy for atomic migration across an interface region. In terms of the reciprocal rate theory, when Q >> A, a(ln t)

Q

a(1/T)

R

Thus, if t is the aging time for a fixed a m o u n t of precipitation, then by plotting In t against l I T a value proportional to the activation energy of the precipitation process can be obtained. Figure 11 shows the activation energies using this m e t h o d of analysis applied to the sound velocity and hardness data for the various aging temperatures studied. From the slopes of the straight lines, the following values of activation energies were obtained: sound velocity (dips 1 on the 150 and 175 °C isotherms), Q1 = 4.7 kcal mol-1;

T (°C}

I0 0 0 0

I

175

150

I

I

1000 c E

+ w

j//

.10/

i--

I01 20

3. 3. Temperature dependence o f the precipitation kinetics In the classical theory of nucleation [24] it is assumed that the formation of critically sized stable nuclei which have the capability of further growth is characterized by a

fJ

220

I 2.1

I 2.2 I0001

I 23 T (K)

Fig. 11. Determination of the activation energies during precipitation processes in a l u m i n u m alloy 2219: [], sound velocity dips 1, Q1 = 4.7 kcal t o o l - l ; o, sound velocity dips 2, Q2 = 9.9 kcal t o o l - l ; +, from hardness peaks, Q3 = 26.6 kcal tool -1.

172 sound velocity (dips 2 on the 150, 175 and 220 °C isotherms), Q2 = 9.9 kcal mol-1; hardness (peak values 3 at 150, 175 and 220 °C), Q3 = 26.6 kcal mo1-1. The dips 1 in the sound velocity curves can be associated with the maximal rates of formation of 0" precipitates. The activation energy Q2 corresponds to the formation of 0' precipitates. The hardness peaks occur at aging times where loss of coherency of the 0' precipitates is achieved by a thermally activated process. The relatively low values (4.7 kcal mo1-1 and 9.9 kcal mo1-1 respectively) of the activation energies for the formation of O" and semicoherent 0' indicate that these precipitates are formed by means of a fast diffusional process. The low activation energy for the formation of 0" is suggestive of easy, generally homogeneous, nucleation of a uniform precipitate distribution and of low interfacial energy. The presence of quenched-in vacancies plays an important part in enhancing the diffusion responsible for the formation of 0". Because the activation energy for the formation of 0' was found to be quite low (Q2 = 9.9 kcal mol-1), it is conceivable that the relatively easy heterogeneous nucleation of 0' is facilitated by the presence of dislocations (introduced by the stretching process prior to aging) and by the presence of 0" particles serving as nucleation sites for O'. It was remarked earlier that the occurrence of the hardness peaks is indicative of a thermally activated process, resulting in the loss of coherency of the grown O' precipitates and growth of incoherent 0 particles at the grain boundaries. These are relatively slow processes controlled by the diffusion of copper atoms through the aluminum matrix. Because of the large diffusional distances involved, the activation energy as determined from the shift of the hardness peaks (denoted by 3) is high: Q = 26.6 kcal tool -1. The substantial difference between the values of Q1 and Q2 (4.7 kcal mo1-1 and 9.9 kcal mo1-1) and that of Q3 (26.6 kcal mo1-1) provides quantitative evidence that the dips in the sound velocity (Fig. 5) and the peaks in hardness (Fig. 10) represent different processes occurring during aging of aluminum alloy 2219. This point will further be discussed in Section 3.5.

3.4. Time dependence of the precipitation kinetics The rate of precipitation, determined from the kinetic theory of diffusional reactions, is dx -

KI(1

--

dt

x)t"-I

where x is the extent of precipitation, K1 is a temperature-dependent constant (K1 = K0 × exp(--Q/RT)) and n is a constant related to the mode of growth and geometry of the precipitates. Integration of dx/dt gives the wellknown Johnson and Mehl [25] or Avrami [26] equation x = 1 -- exp(--Klt") or x = 1 - - e x p ( - - t/r)" where T is a time constant. In the logarithmic form lnlln(1--~)f

= n In t - - n lnT

where n is the slope of this linear equation. Figure 12 exhibits the variation in the extent of 0' precipitation as a function of aging time at 175 °C. The fraction of precipitated O' was determined from the change in the sound wave velocity with aging. The slope of the straight line, representing the equation In[In(I/(1 --x)}] versus In t, yields a value of 2/3. A similar analysis for the 220 °C isotherm yields a value for n of 0.8. The surface energy term in the classical nucleation theory favors the precipitation of spherical particles. However, Nabarro [27] has shown that the elastic energy due to the difference between the specific volumes of + 1.5

/ +

+1.0

/

+0.5

0.0 -0.5 - 1.0 + -I.25 4.0

~ .5.0

]

6.0 7.0 In t

I

8.0

I

9.0

Fig. 12. Extent of precipitation as a f u n c t i o n o f aging 175 °C o f a l u m i n u m Mloy 2219 (n = 2/3).

t i m e at

173

the precipitates and the matrix can be reduced by a change in shape from spheres to plates. In this manner the free-energy change will be reduced. The surface energy terms decrease for crystallographic planes on which perfect matching exists. Coherency strains will arise only when a mismatch between the lattice structures of the precipitates and the matrix occurs. In aluminum alloy 2219 the 0' precipitates are shaped like elongated thin plates. For such a geometry of cylindrical particles, of plates thickening radially and of segregation on dislocations [28] the value of n is between 2/3 and 1. The calculated n values for the 175 and 220 °C isotherms are in agreement with electron microscopy results which show increased coarsening of the precipitates in specimens subjected to higher aging temperatures or longer aging times. Coarsening of the precipitates is due to the tendency of the small particles to dissolve in the matrix, thus allowing the larger particles to grow. The redistribution of the solute in the matrix will be carried out by a relatively slow diffusional process. As was shown in Section 3.2, the activation energy for this process is 26.6 kcal mo1-1. The driving force for this reaction is the decrease in interfacial free energy caused by coarsening of the large rather than the small precipitates. Coarsening arises because of the G i b b s - T h o m s o n effect which requires that the concentration of the solute in the matrix adjacent to small precipitates be higher than that in the region of larger precipitates. Thus, a solute concentration gradient is established, triggering a diffusional flow of solute towards the large particles. The rate-limiting factors for this process are the diffusion of the solute through the matrix and the rate of change of the precipitate dimensions. A detailed theory of precipitate coarsening is given by Lifshitz and Slyuzov [29]. They show that the growth law under these conditions is d = k t ~ = k t 1/3, where k = k ( D , 7 , T , C ) , d is the linear dimension of growth, D is the coefficient for the diffusion of the solute in the matrix, 7 is the interfacial energy, T is the temperature of the diffusional process and C is related to the concentration variations of the solute in the matrix in the proximity of the precipitates. Application of this theory of coarsening to the kinetics of the precipitation of 0' particles in aluminum alloy 2219 gives values for n of

2/3 and 0.8 respectively for the process at temperatures of 175 °C and 220 °C. These values suggest two- and three-dimensional growth laws. Results of electron microscopy indicate that 0' precipitate coarsening at 220 °C closely follows a three-dimensional growth law. 3.5. Ultrasonic attenuation

Investigations of the relationships between the absorption of ultrasonic waves and changes induced by aging in the precipitate structures have previously received only limited attention. Low frequency internal friction studies [ 1 8 - 21] revealed relaxation maxima due to interactions between the applied mechanical vibrations and solute atoms, vacancies and internal stresses. One investigation dealt specifically with ultrasonic attenuation behavior during the precipitationhardening process in aluminum alloy 2024 [22]. The interaction between dislocations and high frequency alternating stress waves has been studied extensively [30 - 33]. Read [30] was the first to suggest a model predicting the observed attenuation effects. Subsequent theoretical models assume that, when a stress wave is externally applied to a material containing dislocations, t w o coexisting strains will result: an elastic strain and a dislocation strain. The dislocation strain is caused by dislocation displacements resulting from the applied ultrasonic stress wave. The dislocation stress-strain law is found to be frequency dependent and non-linear. Figure 13 shows the variation in the ultrasonic attenuation as a function of aging time

2,ol

® 75°C

z 1.0

z

0.o

I AGING

T IM E

(h ts )

Fig. 13. T h e variation in the ultrasonic attenuation of aluminum alloy 2 2 1 9 as a f u n c t i o n of aging time at 150, 1 7 5 a n d 2 2 0 °C.

174

at 150, 175 and 220 °C. The attenuation peaks labelled 2 and 3 correspond to appropriate dips on the sound velocity curves (Fig. 5) and hardness peaks {Fig. 10). The ultrasonic attenuation curves for all three temperatures exhibit the decrease in attenuation that occurred immediately after immersion of the specimen in the isothermal bath. It is believed that the drop in attenuation, analogously to the decrease in hardness observed {Section 3.2) during the first few minutes at elevated temperatures, is caused by the annealing of stresses introduced by stretching prior to aging. At 150 and 175 °C the initial drop in attenuation is followed by a relatively sharp increase (particularly at 175 °C) and then a plateau {region 1) preceding the peak denoted by 2. These features are absent on the 220 °C curve. The plateaux 1 are associated with the formation of 8" precipitates, whereas the attenuation peaks 2 are related to the appearance of semicoherent 8' particles. The plateaux 1 and the attenuation peaks 2 on Fig. 13 appear earlier in the aging process than the corresponding dips in the variation of the sound velocity (Fig. 5). As will be discussed in connection with Fig. 15, this behavior can be understood by considering the frequency dependence of ultrasonic attenuation and the relaxational nature of the process. Figure 13 exhibits prominent peaks (peaks 3) in the data for 175 and 220 °C. These peaks in ultrasonic attenuation correspond to the hardness peaks of Fig. 10 and represent the loss of coherency of 8' particles with the aluminum matrix. The 220 °C curve (Fig. 13) contains only this one attenuation peak as this temperature is sufficiently high for rapid diffusional growth of heterogeneously nucleated 8' precipitates. Although the 8' precipitates form semicoherently at 220 °C and cause the alloy to harden relatively quickly {Fig. 10), at 220 °C the structure overages rapidly by loss of coherency. Related to loss of coherency, the peaks 3 in ultrasonic attenuation arise from an interaction between the acoustic vibrations of the ultrasonic waves propagating through the material and the interphase dislocations surrounding the grown O' precipitates. Internal friction studies [21] have shown that such peaks are generated by semicoherent or incoherent particles but not by coherent ones.

As was observed in the present study (Fig. 13), coherent particles (0") may increase the background attenuation but do not produce distinct peaks that are relaxational in character. A loss of coherency by the formation of shear dislocation loops that relieve the structural mismatch between the particle and the matrix has been discussed by Ashby and Johnson [34]. The strength of interaction between elastic waves and the dislocations surrounding the precipitates will depend on the total volume of the particles and their size, shape and distribution. It is possible that the breadth and height of the peak in attenuation on the 220 °C curve (Fig. 13), compared with those of the peak 3 of the 175 °C curve, are related to the more extensive loss of coherency (and decrease in hardness) accompanying aging at the higher temperature. The peak value of attenuation can therefore qualitatively be correlated with the total volume of coherent precipitates or that of semicoherent precipitates that lost coherency with the matrix because of their increased size. The temperature dependence indicated by the shift in the attenuation peaks 3 of Fig. 13 permits the determination of the activation energy responsible for the loss of coherency (the procedure for calculation was presented in Section 3.3). Figure 14 shows that the T (°C) 220

175

I

I

150

I000

~g w

o z

I00

/.-

20

Q2=59 KCel tool -I

2ii

2i2 IO00/T

213

(K)

Fig. 14. Activation energies derived from the temperature dependence of attenuation peaks.

175

value of Qa is 21.4 kcal mo1-1, in fair agreem e n t with the value of 26.6 kcal mo1-1 obtained from the temperature dependence of the hardness peaks of Fig. 10. Figure 14 shows also that the activation energy Q2 obtained from the shift in the attenuation peaks 2 is 5.9 kcai tool -1. Although this value is smaller than the 9.9 kcal mo1-1 obtained from the corresponding dips in the sound velocity (Fig. 5), the notion that the shifts in peak values result from the formation of 0' precipitates is supported by the order-ofmagnitude agreement between the two activation energy values. The absorption of acoustic energy can be assumed to result from a single relaxational mechanism in the form of an interaction between a specific size distribution of particles and the propagating ultrasonic waves. A continuous variation in the size distribution with the progress of the precipitation process and with particle growth should therefore cause the absorption to exhibit a frequency dependence. However, the sound velocity exhibits no such dependence at vibration frequencies in the megahertz range. The ultrasonic attenuation for a single relaxational mechanism can be described by 6

ACOT

7T

1 + ¢O2T2

where A is the relaxation strength, 8 is the logarithmic decrement of the acoustic energy at the m a x i m u m value, co is the angular frequency of the ultrasonic waves and r is the relaxation time. A m a x i m u m in attenuation appears when w r = 2 • f r = 1 where f is the ultrasonic vibration frequency. The variations in the frequency dependence observed in attenuation measurements made at various temperatures may therefore be taken into account by considering r to be a function of aging time and temperature. The relaxational character of the attenuation behavior during the precipitation process in aluminum alloy 2219 is manifested in Fig. 15. The attenuation peaks 2 and 3, measured at two frequencies during aging at 175 °C, shift with aging time as expected [ 3 5 ] ; later attenuation peaks are indicated by the measurement at the lower frequency. Consequently, the relaxation time r must vary progressively during the aging process and follow the continuous variation in the size distribution of the parti-

30 _O OMHz w

_Z

I

I

t llllJi

I 0.5

u AGING

J I TIME

I 2

J 5

i I0

I 20

t 1 l 40 60 I00

(hrs)

Fig. 15. The frequency dependence of the time of occurrence o f attenuation peaks in aluminum alloy 2219 aged at 175 °C.

cles. Maxima in ultrasonic attenuation occur at aging times when the interaction of the acoustic waves with certain sizes or certain configurations of stress around the precipitates is maximal. The relaxation time r = TO e x p ( Q / R T ) will also be temperature dependent and governed in some fashion by the activation energy of the process, with the pre-exponential relaxation time factor r0 dependent on the character of the interaction between the sound waves and the constituents of the matrix. At resonance, where the attenuation peak occurs, r = 1/¢o = 1 / 2 7 r f . Thus, r will be 1.6 X 10 - s s and 2.41 X 10 -8 s for 10 MHz and 6.6 MHz respectively. Figure 15 shows that the aging time of the peak 2 shifts from 95 to 340 min when the applied ultrasonic frequency is varied from 10 to 6.6 MHz. In a similar fashion peak 3 shifts from 440 to 1650 min. If a linear relationship of the form r = A t r" (where r is the relaxation time, t is the aging time and A is a constant) is assumed, then m will be related to the kinetics of the process responsible for relaxation. Then

•

( 0t

rl0

\t-~0/

where the subscripts 6 and 10 denote the values of the relaxation times r and aging times t for the ultrasonic frequencies 6 and 10 MHz. It is found that for peak 2 and peak 3 the values of m are 0.32 and 0.31 respectively. The similar values of the relaxational exponents m indicate that similar relaxation processes operate in both cases. It does n o t follow, however, that the origins of attenuation peaks 2 and 3 are identical. The fact that the

176 nature of these peaks is different is evidenced by the difference between the corresponding activation energies. An elucidation of the physical meaning of the relaxation exponent rn awaits a systematic investigation of the mechanisms governing attenuation during precipitation hardening as a function of frequency, over a wide frequency range.

3. 6. Effect of cold work prior to aging Plastic deformation, induced by stretching aluminum alloy 2219 prior to age hardening, is meant to have a beneficial effect on the ultimate mechanical properties of the material. The industrial thermomechanical processing of aluminum alloy 2219 involves stretching the metal by 2.25%. The stretching deformation induces a high dislocation density, homogeneously distributed. Consequently, nucleation of the 0' precipitates can be controlled and made to be predominantly homogeneous. Dislocation-free regions will mainly yield 0" particles that may eventually become nucleation sites for 0' particles. The effect of plastic deformation on the kinetics and mechanisms of aging is ambiguous. Plastic deformation contributes to the creation of a relatively homogeneous distribution of nucleation sites for 0'. However, since dislocations are also very effective vacancy sinks, they may trap frozen-in vacancies and render them immobile with respect to the process of clustering atoms. Thus, dislocations may inhibit the subsequent formation of zones and coherent precipitates. In Cu-Be alloys, plastic deformation has been found to be detrimental to the precipitation-hardening process. Nevertheless, prior deformation can foster uniformity of properties, by generating additional defects which prevent formation of precipitation-free zones near grain boundaries. The background attenuation was found to be lower in the unstretched samples than in samples which had been stretched to 5% elongation. In addition, the attenuation peak (Fig. 13, peak 3) occurred at a later time, 1000 min instead of 440 min, for the stretched sample aged isothermally at 175 °C. In view of the relaxational character of the ultrasonic attenuation this behavior may indicate that prior plastic deformation accelerates the nucleation of 0' precipitates but retards their growth. Consequently, the critical size of precipitates for maximal interaction with

the acoustic waves and the occurrence of an attenuation peak are observed after a longer aging time.

4. SUMMARIZING REMARKS AND

CONCLUSIONS The precipitation-hardening process in aluminum alloy 2219 has been investigated by means of dynamic measurements of the sound velocity, ultrasonic attenuation, hardness and electron microscopy. (1) The variation in the sound velocity as a function of aging time at constant temperatures (150, 175 and 220 °C) was found to exhibit prominent dips associated with the formation of 0" and 0' precipitates in aluminum alloy 2219. The activation energies of formation of 0" and 0' were found to be 4.7 kcal mo1-1 and 9.9 kcal mo1-1 respectively. These values from sound velocity data are in satisfactory agreement with those determined from the variation in ultrasonic attenuation. (2) A thermally activated process, with an activation energy of 26.6 kcal mo1-1, is apparently responsible for loss of coherency of O' precipitates and the resulting subsequent decrease in hardness. The occurrence of peaks in the ultrasonic attenuation concurrent with the hardness peaks provides corroborative experimental evidence for this inference. The activation energy calculated from the temperature dependence of the peaks in the ultrasonic attenuation was found to be 21.4 kcal mo1-1, in satisfactory agreement with that derived from hardness data. (3) The growth law for the 0' particles was determined from the precipitation kinetics. The O' precipitates, in their semicoherent form, follow a two-dimensional growth law. Coarsening of 0' and the subsequent loss of coherency are approximately governed by a three-dimensional growth law. (4) Sound wave velocity measurements indicate that the ultimate value of the elasticity of aluminum alloy 2219 depends on the age-hardening temperature. The elastic moduli increase with increasing aging temperature. This behavior was attributed to the relatively larger volume fraction of precipitates formed at the higher temperatures. The elastic behavior of aluminum alloy 2219 was found to be contrary to its plastic behavior as peak hard-

177

ness decreased with increased aging temperatures. {5) The initial rate of increase of hardness was higher for higher aging temperatures. This can be caused by the enhanced rate of formation of semicoherent 0" and 0' at increased temperatures. (6) The frequency dependence of the ultrasonic attenuation indicates that a relaxational mechanism is operative. Attenuation maxima occur at aging times when the interaction of acoustic waves with certain precipitate sizes and stress concentrations is maximal. (7) In plastically deformed specimens, the occurrence in the aging process of attenuation peaks at later times than those for undeformed specimens shows that the appearance of the critical size of precipitates for interaction with acoustic waves is delayed. This behavior is not unexpected as plastic deformation prior to aging contributes to the creation of a predominantly homogeneous distribution of nucleation sites for 0' precipitation.

ACKNOWLEDGMENTS

This research was carried out on behalf of the Center for Materials Research, The Johns Hopkins University, in the Acoustic Characterization Laboratory, Metallurgy Division, National Bureau of Standards, Washington, DC. Thanks are due to Drs. Stephen Ridder and Francis Biancaniello for the preparation o f specimens. The authors benefited from discussions with Professor R o b e r t Green, Jr., The Johns Hopkins University, and with colleagues in the Metallurgy Division, National Bureau of Standards.

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