Rang a Nath 1996

Acta mater. Vol. 44, No. 3, 921-935, pp. 1996 Elsevier Science Ltd

0956-7151(95)00242-l Copyright 0 1996 Acta Metallurgica Inc. Printed in Great Britain. All rights reserved

1359-6454/96 $15.00 + 0.00

Pergamon

STEADY STATE CREEP BEHAVIOUR OF PARTICULATE-REINFORCED TITANIUM MATRIX

COMPOSITES

S. RANGANATH and R. S. MISHRAt Defence. Metallurgical Research Laboratory, P.O. Kanchanbagh, Hyderabad 500258, India

(Received 28 November 1994; in revised form 2 June 1995)

Abstract-The steady state creep behaviour of unreinforced Ti, Ti-T&C and Ti-TiETi,C composites has been examined in the temperature range 823-923 K. It is shown that the creep deformation of unreinforced Ti is governed by climb-controlled creep mechanism for which the stress exponent is between 4.1 and 4.3 and the activation energy is 236 kJ mol-. For composites, the stress exponents are between 6 and 7 at 823 K but are similar to unreinforced Ti at 923 K. The measured steady state creep rate of composites is found to be 2-3 orders of magnitude lower than unreinforced Ti in the investigated temperature range. It is then established that the origin of creep strengthening at 823-923 K is due to the combined effects of increased modulus of composites and the refined microstructure. It is further shown that the change of stress exponent of composites at 823 K is because of the change in creep mechanism from lattice- diffusion controlled dislocation climb to pipe-diffusion controlled dislocation climb. By analyzing the creep data, a modification in the dimensionless constant, A = 3.2 x 10 exp( - 24.2V,) for lattice-diffusion regime and A = 9.4 x lo5 exp( -28.1 V,) for pipe-diffusion regime, where V, is the volume fraction of reinforcements, is suggested to account for the influence of reinforcements on creep kinetics.

1. INTRODUCTION

The use of particulate-reinforced titanium matrix composites for high temperature applications would require a fundamental knowledge of the mechanisms affecting their creep hehaviour. The creep studies of these composites have not heen reported in any detail, perhaps due to the non-availability of cost effective processes for production, unwanted formation of reaction products at the processing temperatures and lack of stability of some reinforcements during creep deformation at high temperatures. The results of Zhu er al. [l] on Ti_6Al_4V-15 ~01% TIC composite indicate creep strengthening over the unreinforced matrix. Further, it shows a change in the stress exponent from n = 3 for Ti-6Al-N alloy to n = 4 for the Tic particulate reinforced composite. Also, a few other creep studies have been reported on TiAl matrix composites [2-6]. The results appear to he inconsistent in the terms of creep strengthening. While Riisler et al. [4] observed a loss in the creep strength at high temperatures, the results of Kampe et al. [5] indicate creep strengthening after heat treatment. Further, the values of stress exponent and activation energies are similar for unreinforced TiAl and TiAl matrix composites. This is quite different from the trends observed in aluminium matrix com-

tPresent address: University of California, Department of Materials Science, Davis, CA 95616, U.S.A.

posites. For example, the stress exponent values for Al-SIC composites are usually in the range of N 15-25 and the activation energy values are often higher than 200 kJ mol-I [7-131. It is thought that the presence of a threshold stress, as included in the following power-law creep equation, results in such observations:

where i is the creep rate, Q the applied stress, e0 the threshold stress, E the Youngs modulus, n, the true stress exponent, Q the activation energy, R the gas constant, k the Boltzmann constant, T the test temperature, D, the frequency factor for diffusion, b the Burgers vector and A a dimensionless constant. Fur- ther, the creep strength of aluminium matrix composites is always higher than the unreinforced matrix. As mentioned earlier, this is not the case for titanium matrix composites, where troth strengthening and weakening have been reported. This indicates that the matrix microstructure plays a more important role in titanium matrix composites. Therefore, the role of microstructure on the creep hehaviour of a titanium matrix composite needs critical examination.

The lack of creep strengthening in some titanium matrix composites raises some fundamental ques- tions. It is well established that non-deformable cer- amic reinforcements enhance the strength because of the constraint they impose on the plastic flow [14].

927

928 RANGANATH and MISHRA: STEADY STATE CREEP

The constraint originates from the difference in the deformation of two phases and depends on the particle shape, distribution and volume fraction. Hence, the room temperature and creep strength should equally benefit from the second phase reinforcements. It is possible that the unexpected creep weakening is associated with the microstructural changes which take place with the addition of second phase reinforcements. Bryant et al. [15] have shown that the addition of TiBz particles leads to significant reduction in the colony size. In a detailed study of the influence of microstructure on steady state creep behaviour of a T&Al-Nb alloy, Mishra and Banerjee [16, 171 observed a strong microstructural dependence (which is quite common for both disordered and ordered titanium alloys). They suggested that the Weertman model [18] for climb controlled creep can explain the microstructure dependence through the slip band length. In addition, the suggestions involv- ing creep deformation by the formation of the two- phase TiAl/Ti, Al lamellar structure [3] and diffusional matter transport along the matrix/particle interface [4] are noteworthy. A detailed analysis is required to evaluate these possibilities.

The purpose of the present study was three-fold: (a) to generate systematic data on unreinforced Ti and Ti-TizC and Ti-TiB-T&C composites; (b) to establish the strengthening/weakening trend with the volume fraction of the second phase and consider the micromechanism of steady state creep; and (c) to evaluate the applicability of threshold stress concept. The steady state creep results are then combined with the microstructural examination to determine the origin of strengthening and the rate controlling deformation mechanisms operating during creep.

2. EXPERIMENTAL

The composites used in this study were prepared through the Combustion-Assisted Synthesis (CAS) route [19]. The control samples and the composites were tested in the rolled and annealed condition. Annealing was done at 1073 K for 4 h followed by air cooling. A constant-load creep machine with compression grip was used to study the steady state creep behaviour of the materials. Cylindrical compression specimens of 5 mm gauge diameter and 10 mm gauge length were machined from the flat rolled plates with the specimen axis parallel to the rolling direction. The creep strain of the sample was measured using two parallel linear variable displacement transducers (LVDTs) mounted on the ridges provided on the compression grips. The temperature of the sample was monitored using three separate thermocouples tied, one at the specimen and the other two at the grips. The specimen temperature was controlled within + 1 K.

Ti-25 ~01% T&C, Ti-10 and 15 ~01% TiB + T&C and Ticontrol samples were tested at 823, 873 and 923 K. A few samples of Ti-20 ~01% TiB + T&C were also tested at 923 K. Using a Philips EM430 transmission electron microscope (TEM), dislocation configurations of a few samples (deformed to 2% strain) were studied. Thin foil preparation was carried out using the ion beam thinning (IBT) technique.

3. RESULTS

3.1. Microstructure

The microstructure of a typical composite used in the present study is shown in Fig. 1. The sample was deep etched to show the high aspect ratio of TiB

Fig. 1. A representative SEM micrograph of rolled and annealed (1073 K) 15 ~01% TiB + T&C composite.

RANGANATH and MISHRA: STEADY STATE CREEP 929

Fig. 2. Bright field TEM image showing a clean particle/matrix interface in an as-crept 15 vol% composite

specimen.

particles. On the other hand, T&C particles were observed to be finer and equiaxed (not identifiable in Fig. 1). The shape was confirmed by electron probe micro-analysis X-ray images [20]. Figure 2 shows a TEM micrograph of a 15 ~01% TiB + T&C composite after creep deformation at 873 K. The matrix/particle interface is clean even after the creep deformation. Also, there is no damage to the reinforcements, indicating that these phases are in thermodynamic equilibrium with the matrix even at high temperatures.

Figure 3 shows a TEM micrograph of an as-crept sample. The presence of second phase particles stabil- izes the grain size. The grain size after creep is around 2 pm, the same as the grain size before the creep test. This means that the microstructure was stable during the creep test and the scale of microstructure is much finer than the grain size in unreinforced material, N 170 pm. The dislocation structure after creep is shown in Fig. 4 for composites with 10 and 15 ~01% of TiB + T&C particles. The dislocation distribution appears to be random. Also, the movement of dislocations appears to be across the grain and not much dislocation-dislocation interaction is noticed.

3.2. Creep behaviour

A typical creep curve of a Ti,C reinforced composite tested at 923 K and an applied stress of 39 MPa is shown in Fig. 5(a). A normal primary stage is followed by the steady state stage. A similar behaviour was observed in all the composites as well as the unreinforced control specimen of pure titanium.

The response to a stress change is shown in Fig. 5(b). Again, a normal primary stage is observed at both of the stress levels. The primary stage after stress jump is quite short.

The variation of steady state creep with stress for the control sample of titanium, Ti-T&C and Ti-TiBTi,C composites are plotted in Fig. 6, both on the logarithmic scales. The data can be fitted by straight lines with slopes equal to the value of the stress exponent n. The observed linearity on these plots indicates that the data follow a power law equation:

i =F (%yexp( -&), (2) where the various symbols have the same meaning as in equation (1). The n-values of the composites are indicated in Fig. 6. For unreinforced Ti and 10 ~01% TiB + T&C composite, IZ appears to be independent of the test temperature, whereas for 15 ~01% TiB + T&C and 25 ~01% T&C composites, n-values increased at 823 K. Moreover, the value of n is higher for all composites than unreinforced titanium at 823 K, whereas the difference in values is not much at 873 and 923 K.

Figure 7 shows the Arrhenius plots as the variation of creep rate with l/T for the control sample and various composites. The observed activation energy of 236 + 5 kJ mol- for control Ti specimens [Fig. 7(a)] agrees well with the value of 241 kJ mol- reported by Malakondaiah and Rao [21] for dislocation creep of alpha titanium. The apparent activation

Fig. 3. Bright field TEM image of an as-crept 15 ~01% composite showing the matrix grains.


energy values for composites range from 284 to these possibilities are considered here. The values of 353 kJ mol-. These values are significantly higher q, for composites were obtained from the plots of u than the activation energy for the control Ti. The against i14. (Fig. 8). From the extrapolation of the activation energy values for all the composites are linear regression line to zero creep rate, the value of summarized in Table 1. It can be noted that the CJ~ was determined. The same is tabulated in Table 2. apparent activation energy increases with the increas- It is noticed that the threshold stress decreases with ing volume fraction of the second phase increasing temperature. After compensating for CT,, , reinforcement. and Q-values obtained for various composites are

Further analysis of these results depends on the given in Table 1. The Q-values now range from 197 origin of the high stress exponent at 823 K and the to 248 kJ mol-. higher activation energy for composites. Two possi- The other possibility is that a transition occurs at bilities exist: (a) the presence of a threshold stress; and 823 K. The transition from lattice-diffusion control (b) a change in the creep mechanism at 823 K. Both (n = 5) to pipe diffusion control (n = 7) is expected at

Fig. 4. (a) Bright field. (b) Dark field images from one grain of 10 ~01% TiB + T&C composite specimen observed after creep at 873 K and 46.6 MPa. (c) Bright field. (d) Dark field images from one grain of 15 ~01% TiB + Ti,C composite specimen observed after creep at 873 K and 52.4 MPa. Note the random

orientation of dislocations.


8

0.0 I 1 8 10 20 30 40 50 Time (h)

923K W

LJ 120

Time (h)

Fig. 5. (a) A creep curve for Ti-25 ~01% T&C composite showing a distinct primary followed by the steady state stage. (b) The effect of a stress increase on the creep curve

of Ti-25 ~01% Ti,C composite.

lower temperatures [22]. The observed stress exponent of -6-7 at 823 K could be related to this. This aspect is further discussed at the end of this section.

lo"

Temp., K Vol % 0 923 IO 0 873

The dependence of steady state creep rate on the effective stress at a constant temperature of 873 K for composites and unreinforced Ti is compared in Fig. 9. The creep rates of composites are 2-3 orders of magnitude lower than the unreinforced material and decrease with increasing volume fraction of the second phase (V,). The implication of this observation is far reaching. Usually, the influence of second phase particles is considered to be limited to the introduction of a threshold stress, as can be inferred from a comparison of equations (1) and (2). We note from Fig. 9 that increasing the volume fraction of reinforcements increases the creep strength of titanium composite even after considering the threshold stress. This indicates kinetics strengthening. To evaluate this aspect, further analysis can be carried out to determine the constitutive creep equation for lattice-diffusion controlled creep regime. Figure 10 shows the variation of the dimensionless creep constant A,_ with a volume fraction of second phase reinforcements. Linear regression of the data gives a relationship between A, and V, such as

d I 100

Stress (MPa)

1 100

Stress (MPa)

A, = 3.2 x 10 exp( -24.2V,).

Fig. 6. The variation of steady state creep rate as a function of applied stress for: (a) control sample and 25~01% T&C composite; (b) 10 ~01% TiB + T&C composite; and (c) 15 ~01% TiB + T&C composite. The apparent stress

(3) exponent values are indicated.

This means that the constitutive equation for creep behaviour of composites should include a volume fraction term as well. Then, the true dimensionless constant is 3.2 x 105. By incorporating this volume fraction dependence and threshold stress in equation (2), the constitutive equation for Ti-matrix composites can be written as:

4. , (4)

where D, is the lattice self-diffusion coefficient. This equation can account for the creep strengthening because of the second phase particles in the lattice- diffusion controlled regime.

For 15 ~01% TiB + T&C and 25 ~01% T&C composites, the observed n-value at 823 K is between 6 and 7. As pointed out earlier, this could be because of a transition to the pipe-diffusion controlled regime. Because of the limited data it is difficult to ascertain

IV5

Temp..K vol. % (a

o 523

1 10 100

Stress (MPa)

-I

(b) :

RANGANATH and MISHRA STEADY STATE CREEP

10-s I , 0 a=10 MPa (0 vol.%) (a)

0 a=40 MPa (10 vol.%) 0 a=40 MPa (15 vol.%)

IiT (K-)

Fig. 7. Arrhenius plots of steady state creep rate vs inverse of test temperature for: (a) the control sample; and (b)

composites.

the nature of the relationship between A and the volume fraction of reinforcements. However, in view of the observed relationship for a lattice-diffusion controlled regime, a similar relationship can be as- sumed for this regime as well. From Fig. 10, where the variation of the dimensionless constant A, for pipe diffusion is also plotted against the volume fraction of reinforcements, it appears that the above assumption is valid. A similar trend for both the lattice diffusion and the pipe diffusion data is noteworthy in this figure. Therefore, the variation of a dimensionless constant with volume fraction for the pipe-diffusion controlled regime can be written as:

A,=9.4 x lOexp(-28.11/,). (5)

From the limited data, the constitutive equation for the pipe-diffusion controlled creep regime can, therefore, be represented by:

Table 1. Activation energy for steady state creep

Activation energy (kT mol-)

Vol% reinforcement

0 10 IS

TlUe Apparent (compensated for ao)

- 236 k 5 284 + 21 225 + 101 336 + 28 248

,; 353 + 34 197= Only the data for 873 and 923 K were considered because of the

transition at 823 K.

where D, is the pipe diffusion coefficient. A stress exponent value of 6.1 has been taken for equation (6) because the stress exponent for pipe diffusion controlled dislocation climb creep is always II + 2 [22] and the value of n in equation (4) is 4.1.

4. DISCUSSION

4.1. Unreinforced titanium

As noted from Fig. 5, the n-values are between 4.1 and 4.3 for unreinforced titanium. These values of n agree well with the reported values for creep of pure titanium [23]. This stress exponent value is expected for lattice diffusion controlled dislocation climb creep [18,24,25]. Doner and Conrad [23] found that their experimental results of cc-Ti were in better accord with Weertmans glide and climb mechanism [ 181 and concluded that the high temperature deformation of unalloyed cc-Ti is controlled by dislocation climb. Since the value of n obtained in the present study is close to the ones obtained by them, one can conclude that the deformation of unreinforced Ti (control sample) is governed by climb controlled creep mechanism. The activation energy in this regime for unreinforced Ti was found to be 236 + 5 kJ mol-, which is close to the value of 242 kJ mol- reported by Conrad [26] and 241 kJmol_ reported by Malakondaiah and Rao [21].

Using equation (2), value of the creep constant A calculated at 923 K for unreinforced Ti is reported in

0.05 .., ., . . . . . . . . . . * ..,....,....I

o 823 K ?? 873 K

0.04

t

A 923 K

r:

- I P 3 0.03

t / / I

Stress (MPa)

Fig. 8. A plot of (creep rate)14. vs applied stress for a representative Ti-25 ~01% T&C composite (extrapolation of linear regression line to zero creep rate gives the threshold

stress).


Table 2. Values of threshold stress for composites detemined by the extrapolation technique

Vol% reinforcement

10 (TiB + T&C)

15 (TiB + T&C)

20 (TiB + T&C) 25 (Ti? C)

Temperature (K)

823 873 923 823 873 923 873 823 873 923

Threshold stress (MPa)

n =4.1 n =6.1

11.1 +9.1 7.0 2 4.6 3.1 * 1.9

25.4 + 2.0 8.8 + 1.1 3.4 * 3.1

0.0 - 5.3 k 1.8

27.2 + 3.6 1.1 i9.1 8.3 f 3.5 2.7 k 1.4

Table 3. From the present data, a generalized creep equation for titanium can be written as:

i = 4.7 x 105 $J exp( .z.?!$)(~~. (7)

4.2. Ti-TiB-Ti,C and Ti-Ti2C composites

The presence of second phase particles in titanium matrix composites has influenced the steady state creep behaviour in several ways:

(i) higher creep strength over the entire temperature range used in the present study,

(ii) higher stress exponent at 823 K, (iii) higher apparent activation energy, (iv) a correlation between the dimensionless con-

stant and the volume fraction of the second phase, and

(v) a temperature dependent threshold stress.

10-s

104

; 3 B 2

1 o-7

%

s

1 o-8

10-s

I-- I I

Vol. % 873 K 0 0 0 10

d I I

10 100

(0-Q WW

7

Fig. 9. The variation of steady state creep rate as a function of effective stress for composites at 873 K. Note that even after compensating for the threshold stress the data does not

merge, indicating a kinetics strengthening.

In this investigation the creep strength of the composites was found to be significantly higher than the unreinforced matrix (Fig. 9) and increased with the increasing volume fraction of the reinforcements. This is unlike the loss in strengthening in TiAl-Ti,AlC reported by Riisler et al. [4]. Rosier and Evans [27] have attributed it to diffusional matter transport along the matrix/reinforcement interface which contributes to the deformation process at the location of the reinforcement. Based on this assumption and considering interface diffusion to be rate controlling, they derived an expression for the critical particle size at which the transition from constrained flow to diffusional assisted flow occurs:

(~)~n~=[(~)u-n1660bg(~,il v)]. (8) (AbD,)

where R is the atomic volume, G the shear modulus, 6 the interface thickness, D, the interface diffusivity, D, the volume diffusivity, g(l/t, V) a function of l/t, V [28]. Choosing the various parameters for y-TiAl reinforced with Ti,CAlC platelets, they found that particles of sizes t _ 1 /*m and l/t - 20 are ineffective during creep testing, as it is easier to deform the volume associated with a carbide platelet by diffusional creep than the surrounding matrix material.

OS8

a

Volume Fraction

Fig. 10. Variation of creep constant, A (for lattice- and pipe-diffusion) with the volume fraction of reinforcement.


Table 3. A comparison of creep constants in climb controlled creep of Ti composites

Vol% reinforcement Creep constant, A

0 4.7 x 10 10 (TiB + T&C) 1.3 x 104 1.5 (TiB + T&C) 1.0 x 104 25 (Ti,C) 9.2 x 102

In the present study, although the TiB needles are in a similar size range as the reinforcements used in the above study, significant creep strengthening over the matrix material was observed. This can be attributed to the increase in diffusion distances for material transport in high aspect ratio particles. This is in contrast to the above-mentioned findings and, therefore, Riislers model cannot explain the present results.

As seen from a representative TEM micrograph of a 15 ~01% TiB + T&C composite (Fig. 2), the interface between the particle and the matrix is clean even after creep deformation at 873 K. Also, there is no damage to the reinforcements. This means that effective load transfer from the matrix to the particles could occur at higher temperatures. For composites the value of A determined at 923 K is found to be l-2 orders of magnitude lower than that for the control sample of titanium (Table 3). It is important to note that the stress exponent is similar for the matrix and all the composites at 923 K, but the composites have higher creep strength. This strengthening can orig- inate from: (a) load transfer to the stiffer phase; and/or (b) microstructure strengthening. Load transfer to the stiffer phase results in an overall increase in composite modulus. From equation (2) it is clear that an increase in the modulus would lower the creep rate of the material. This can explain the creep strengthening without a change in the stress exponent value. The

I . I . I

Vol. %

lattice-diffusion controlled climb regime

I ,... I . . I . . . .

800 850 900 950 1

Temperature (K)

0

Fig. 11. Variation of modulus compensated stress with temperature for 0~01% and 15~01% TiB + T&C composites. The map depicts a transition in a creep mechanism at lower temperature for the experimental 15~01% com-

posite.

other possibility is microstructural strengthening which can arise from the finer graimsubgrain size (hereafter the fine grains/subgrains will be referred to as grains, as no information regarding the misorienta- tion of the boundaries is available). In unreinforced titanium with large grains, the dislocation creep is governed by generation and mutual annihilation of dislocations within the grain. But in titanium composites, the presence of particles refines the structure to such a level where no intragranular dislocation sources could be present. In such cases, the creep rate can depend upon microstructure. Mishra and Baner- jee [ 161 have observed that the Weertman model [18] for climb controlled creep can explain the microstructural dependence through slip band length. It is easy to visualize that if the structure is so fine that dislocation generation and annihilation can take place only at the boundaries, a microstructural dependence would arise. The kinetics strengthening indicated by correlation in equations (3) and (5) could be a result of the influence of the volume fraction of reinforcement on the grain size. Further TEM work is required to quantify the dependence of grain size on the volume fraction of second phase particles in these composites.

The change in n-value with temperature for 15 ~01% TiB + T&C and 25 ~01% T&C composites could be due to a threshold stress or a change in operative creep mechanism at lower temperatures. But the combination of activation energies and n -values for these composites determined using the threshold stress concept cannot be explained with the available creep models. Therefore, this approach appears unlikely. It is possible that the lower temperature range of 823 K falls in a transition regime where, with a change in temperature, there is a change in the steady state creep mechanism from lattice-diffusion control (n = 5) to pipe-diffusion control for which n = 7 is expected [22]. To establish this properly, the change in activation energy with temperature should be determined over a wider range of temperatures.

Equations (4) and (6) can be used to draw a transition map for dislocation creep in Ti-matrix composites. Figure 11 shows the transition line for unreinforced Ti and a 15 ~01% TiB + T&C composite. It can be seen that the transition is both stress and volume fraction dependent. In this figure, the experimental stress-temperature range of the present study is also shown. It can be noted that at a higher temperature the transition stress is much above the experimental combination of stress and temperature to effect any transition. Nevertheless, at the lower temperature of 823 K the transition stress is reached for the TiB + T&C composite but not for unreinforced Ti. This is attributed to the higher strength of the composite compared with the unreinforced material. So the role of a higher volume fraction of reinforcements is to increase the strength level of composites which effectively shifts the transition temperature for


creep mechanism (from pipe-diffusion controlled climb to lattice-diffusion controlled climb) to relatively higher temperatures.

5. CONCLUSIONS

The creep rate of composites is found to be 2-3 orders of magnitude lower than unreinforced Ti. Both control sample and the composites show power-law creep behaviour with stress exponents between 4 and 5 at 873-923 K. The value of apparent activation energy (Q = 236 kJ mol-) for Ti is found to be consistent with the reported value of 241 kJ mol- for lattice self- diffusion of Ti. However, the apparent activation energy of composites is significantly higher than that for unreinforced Ti. The presence of second phase leads to lower values of creep kinetics constant even after compensating for a threshold stress. Therefore, the constitutive equation for composites should include a volume fraction term to explain the creep strengthening. From the constitutive equations, a transition map is drawn to depict the lattice-diffusion controlled climb and the pipe-diffusion controlled climb regimes. This explains the observed transition in the stress exponent for composites with a higher volume fraction of reinforcements at 823 K.

Acknowledgements-The authors wish to acknowledge Dr T. Roy and Shri K. S. Prasad for the TEM work. They are grateful to Shri S. L. N. Acharyulu, Director, DMRL for his constant encouragement and permission to publish this paper.

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Rang a Nath 1996