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High Temperature Creep and Fatigue of Cu-Cr Alloys
High Temperature Creep and Fatigue of Cu-Cr Alloys N. Y. Tang*, D. M. R. Taplin* and G. L. Dunlop* * 'Department
of Mechanical Engineering, University of Ontario N2L 3GI, Canada
* 'Department
of Physics, Chalmers University of S-412 96 Göteborg, Sweden
Waterloo, Technology,
ABSTRACT The high temperature creep and fatigue properties of high conductivity Cu-Cr alloys with and without Mg and Zr additions are related to their detailed microstructure. It is shown that improved properties are obtained with the Mg and Zr additions. This is largely due to the influence of Zr on the inter granular microstructure. KEYWORDS High conductivity Cu-Cr alloys, high temperature, creep, fatigue. INTRODUCTION Alloys of the Cu-Cr type are important as high conductivity materials with good strength at elevated temperatures. Because of these properties they are being used as electrical conductors and connectors and also in applications where rapid heat transport at high temperatures is necessary. Recently, new alloy variations have been introduced which seem to provide improved high temperature mechanical properties without any impairment of the high conductivity of basic Cu-Cr alloys. One alloy of this type contains small additions of Mg and Zr to a basic Cu -0.6 wt% Cr composition (Taubenblat, Opie and Hsu, 1972). In the present work we have attempted to isolate the effect of Mg and Zr additions by comparing three commercial alloys based around simple Cu-Cr (See Table 1). One of these alloys contained a small addition of Mg while the other had additions of both Mg and Zr. Previous work has indicated that these additions can have a substantial influence on the high temperature low cycle fatigue properties (Collins, 1978). The present investigation has aimed at investigating this effect in more detail and also studying the high temperature uniaxial creep behaviour. TABLE 1
Experimental alloys (wt%) 1. 2. 3.
Cu - 0.80 Cr Cu - 0.88 Cr - 0.08 Mg Cu - 0.58 Cr - 0.05 Mg - 0.07 Zr (AMAX MZC) 665
EXPERIMENTAL The experimental alloys were supplied in the cold worked (40% for alloys 1 and 2, 50% for alloy 3) (See Table 1) and aged (4h 450°C for alloys 1 and 2 2h 450°C for alloys 3) condition. All fatigue testing and some creep testing was carried out on these as-received conditions while further creep testing on all three alloys was conducted after solution treatment (2h 960 C ) , quenching and ageing at 450°C for 8h. These heat treatments were conducted with the specimens in evacuated silica capsules under a partial pressure of helium. The equiaxed linear intercept grain sizes after heat treatment were 50 ym for alloys 1 and 2 and 42 ym for alloys 3 (MZC). The push-pull low cycle fatigue tests were performed under stroke control in a vacuum of approximately 10"^ torr at 400°C. Creep testing was conducted in air under constant load conditions at the same temperature. Transmission electron microscopy was conducted on thin foils prepared by electropolishing in 33% HNO3 i n methanol at ^-30°C. RESULTS The as-received (cold worked and aged) microstructures All three alloys had a high density of dislocations with a fine dispersion of Cr-rich precipitates in the matrix. The Cu-Cr alloy was found to contain a large number of small voids (^ 0.1 ym diameter) and these were predominantly concentrated at the grain boundaries (Fig. 1). It is thought that these were due to gas bubble (1^0) precipitation during processing. Voids were not present in the other two alloys.
Fig. 1.
Intergranular voids (arrowed) in Cu-Cr alloy in the asreceived condition.
Fig. 2.
Precipitation of Cr-rich precipitates in Cu-Cr-Mg-Zr, 450°C 8h. Dark field micrograph.
Heat treated (solution and aged 450 C 8h) microstructures The ageing treatment resulted in the formation of a fine dispersion of Crrich precipitates (^ 20 Â diameter) in the matrix of all three alloys (Fig.2). Grain boundary precipitate free zones were present (Fig. 3a) and the half width of these zones was ^ 1000 Â for Cu-Cr and ^ 400 Â for the other two alloys. The voids in the Cu-Cr alloy became fewer in number but somewhat increased in size during the heat treatment. Cr-rich precipitates were present on the grain boundaries in all three alloys (Fig. 3a). The major difference here was that the Cu-Cr-Mg-Zr alloy also contained another type of intergranular precipitate. This precipitate was present on some boundaries as dis666
crete particles (Fig. 3b) while other boundaries contained a thin continuous film which was about 50 A thick (Fig. 4a). STEM/EDX analysis has shown that this type of precipitate contains significant amounts of Zr (Fig. 4b) and electron diffraction of a number of precipitates suggests that they are of the orthorhombic compound Cu,Zr.
Fig.
3.
.
(a)
(b)
Intergranular precipitation after ageing 450 C, 8h. (a) Cr-rich precipitates in the Cu-Cr alloy. Note the precipitate free zone, (b) Zr-rich precipitates in the Cu-Cr-Mg-Zr-alloy. Cu 4 Zr
Cu L
Ί
«Hfr»fr* %#!»<¥
1 1 1 1 1 1 1 1 ΓΠ 6
8
10
1 1 1 Γ 12
16
ENERGY (keV)
Fig. 4
(a) (b) Intergranular film of Cu4Zr in Cu-Cr-Mg-Zr. (a) Dark field micrograph. (b) STEM/EDX spectrum.
Creep testing at 400 C Secondary creep rates for the heat treated alloys are plotted as a function of applied stress in the log-log plot of Fig. 5. At low stresses (σ<70 MPa) the stress sensitivity exponent, n, in the Dorn equation έ = Aanexp-Q/kT was found to be approximately unity. This suggests that diffusion creep dominates at these lower stresses. At stresses above ^ 70 MPa, n ^ 4-18. Activation energy measurements of the steady state creep rate were made for Cu-Cr-Mg-Zr by changing the temperature in^10 C intervals. At σ = 60 MPa the activation energy was found to be 118 kj/mole which is approximately the same as that for grain boundary diffusion in Cu(104 k.J/mole) (Ashby, 1972). At σ = 140 MPa the activation energy was 205 kJ/mole which is close to that for self diffusion in Cu (207 kj/mole) (Peterson, 1968). Thus, the creep results indicate that Coble grain boundary diffusion creep dominated 667
at low stresses and power law dislocation creep dominated at the higher stresses. 10"e
■ Cu-Cr A Cu-Cr-Mg X Cu-Cr-Zr-Mg
J k ^l
V *I
10-7
ft*
/[
10-8
" _ 10-»
1 0- i o
fI
.■
/} '/
i I
/
I
x
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r xx
i i 1
i
1 L_L
Fig. 6.
STRESS Mpa
Fig. 5.
Secondary creep rates for all three alloys, heat treated.
Intergranular creep cavities in Cu-Cr-Mg-Zr, heat treated condition. σ=160 MPa, ε=0.4%.
It can be noted from Fig. 5 that the diffusion creep rates for the Cu-Cr-MgZr alloy were considerably lower than for the other two alloys. Power law creep rates were also somewhat lower. Creep tests on as-received Cu-Cr and Cu-Cr-Mg gave similar results to that shown in Fig. 5 with the possible exception that the maximum stress for diffusion creep dominated flow was reduced. No comparative study of creep cavitation was made between the three alloys. However, scanning electron microscopy of polished sections of crept Cu-CrMg-Zr showed that intergranular cavities formed during the early stages of creep deformation (Fig. 6 ) . Low cycle fatigue at 400 C (as-received condition) Low cycle fatigue results at three frequencies are shown for the Cu-Cr alloy in Fig. 7. It can be seen from this diagram that the fatigue life of this alloy was strongly frequency dependent. The Cu-Cr-Mg alloy showed a weaker frequency dependence and Cu-Cr-Mg-Zr was frequency independent. Results for all three alloys at 10~3 Hz are shown in Fig. 8. Here it can be seen that at this low frequency Cu-Cr-Mg-Zr gave considerably improved fatigue lives over the two other alloys. The fatigue fracture behaviour was such that Cu-Cr always failed intergranularly, apparently from the interlinkage of intergranular cavities (Fig. 9a). The Cu-Cr-Mg alloy tended to fail intergranularly at low frequencies (10~^Hz) but transgranular fracture was more common at higher frequencies (lO'-'-Hz) . The Cu-Cr-Mg-Zr alloy in the as-received condition failed by ductile fatigue striations at all frequencies. It can be mentioned here that Cu-Cr-Mg-Zr fatigue tested in the heat treated condition contained some intergranular fracture facets. This was apparently associated with the formation of intergranular cavities at the Zr-rich grain boundary precipitates (see Fig. 9b).
668
Q.
ω
<
ΚΓ1
< ce
lu"2 ce
\CO
o
— Cu-Cr - A 1 0 - 1 Hz "B 10" 2 Hz _#10_3Hz
10-3 10 υ
7. Fig. 7.
I
I I II
^ ^ ^ ^ \ Α * · ^ ^
I _._ I
I I I
I
I
I
I I
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10 10* 10* NUMBER OF CYCLES TO FAILURE, N
10* 0.5 The effect of frequency on low cycle fatigue properties of Cu-Cr.
CO
o
FREQUENCY 1 0 " 3 H z
CO
<
10" 10 u
i i i l i I i i i i il 101 102 10 J NUMBER OF CYCLES TO FAILURE, N Q
10* 6
Fig. 8.
Low cycle fatigue properties of all three alloys at 10 Hz.
Fig. !9.
Intergranular cavitation in fatigue tested material. Transmission electron micrographs, (a) Cu-Cr as-received condition, 5 cycles, 10 - 2 Ηζ,Δερ=0.4%. (b) Cu-Cr-Mg-Zr, heat treated condition, 500 cycles, 10" 1 Hz, Δερ=1.2%.
669
DISCUSSION Transmission electron microscopy has shown the very fine nature of the precipitate dispersion in alloys of this type. These Cr-rich precipitates are predominantly responsible for the good high temperature strength. It is also apparent that Mg and Zr additions have a strong effect on the high temperature creep and fatigue properties. From the point of view of microstructure this effect is clearer in the case of Zr. The intergranular precipitation of Cu-Zr compounds such as Cu4Zr, which can often be in the form of thin grain boundary films (Fig. 4 ) , may be expected to have a strong effect on such high temperature grain boundary properties as sliding and diffusion creep. The equations for diffusion creep quoted by Ashby (1972) and the diffusion data of Peterson (1968) and Ashby (1972) for Cu were used to calculate the expected diffusion creep rates at σ=40 MPa and a linear intercept grain size of 42 ym. The estimated contribution from Coble creep (Coble, 1963) is 2.4χΚΓ 1 0 s"1 and 4.6xl0"12 s _ 1 from Nabarro-Herring creep (Nabarro, 1948; Herring, 1950). Thus, as indicated by the activation energy measurements Coble creep can be expected to dominate at these low stresses. The measured creep rate at this stress for the Cu-Cr-Mg-Zr alloy was lxlO"10 s~l which is only a factor of 2.4 slower than the predicted creep rate. The agreement is very good when the vagaries of diffusion data are considered. However, the diffusion creep rates for the two alloys not containing Zr were about one order of magnitude faster than Cu-Cr-Mg-Zr while their slightly larger grain size (50 ym) would predict slower creep rates. Thus, it seems likely that intergranular precipitates and grain boundary films in the Zr containing alloy (see Fig. 3 and 4) may play an important role in inhibiting diffusion creep by limiting the ability of boundaries to act as perfect sources and sinks of vacancies (Burton, 1977). An alternative view of this is that grain boundary dislocation creep, which is considered to be necessary for grain boundary sliding and diffusion creep (Dunlop and Howell, 1981; Howell and Dunlop, 1981), is impeded by precipitates of this type. The high temperature fatigue life of Cu-Cr was found to be strongly frequency dependent and fracture occurred intergranularly. It would seem that this was largely due to the intergranular voids which were present in the as-received material. By way of contrast the fatigue life of Cu-Cr-Mg-Zr in the as-received condition was frequency independent and fracture was transgranular. No voids were present in this material prior to testing. However, even in this alloy fatigue cavitation can occur under certain conditions (Fig. 9) and this can adversely affect the high temperature fatigue behaviour. This points to the need for careful microstructural control for optimum high temperature properties. REFERENCES Ashby, M.F. (1972). Acta Met. 2i0, 896. Burton, B. (1977). Diffusional Creep of Polycrystalline Materials, Trans.Tech. Coble, R.L. (1963). J. Appl. Phys., Γ7, 909. Collins, A.T. (1978). Ph.D. Thesis, University of Waterloo, Ontario, Canada. Dunlop, G.L. and P.R. Howell (1981). Deformation of Polycrystals: Mechanisms and Microstructures, Ris^. Herring, C. (1950). J. Appl. Phys., 7\_y 437. Howell, P.R. and G.L. Dunlop (1981). Creep and Fracture of Engineering Materials and Structures, Pineridge Press, Swansea, 127. Nabarro, F.R.N. (1948). Conf. on Strength of Solids, Phys. S o c , London. Peterson, N.L. (1968). Solid State Physics, 22, 409-512. Taubenblat, P.W., W.R. Opie, and Y.T. Hsu (1972) . Met. Engg. Quart. , 12, 41-45. 670
of Mechanical Engineering, University of Ontario N2L 3GI, Canada
* 'Department
of Physics, Chalmers University of S-412 96 Göteborg, Sweden
Waterloo, Technology,
ABSTRACT The high temperature creep and fatigue properties of high conductivity Cu-Cr alloys with and without Mg and Zr additions are related to their detailed microstructure. It is shown that improved properties are obtained with the Mg and Zr additions. This is largely due to the influence of Zr on the inter granular microstructure. KEYWORDS High conductivity Cu-Cr alloys, high temperature, creep, fatigue. INTRODUCTION Alloys of the Cu-Cr type are important as high conductivity materials with good strength at elevated temperatures. Because of these properties they are being used as electrical conductors and connectors and also in applications where rapid heat transport at high temperatures is necessary. Recently, new alloy variations have been introduced which seem to provide improved high temperature mechanical properties without any impairment of the high conductivity of basic Cu-Cr alloys. One alloy of this type contains small additions of Mg and Zr to a basic Cu -0.6 wt% Cr composition (Taubenblat, Opie and Hsu, 1972). In the present work we have attempted to isolate the effect of Mg and Zr additions by comparing three commercial alloys based around simple Cu-Cr (See Table 1). One of these alloys contained a small addition of Mg while the other had additions of both Mg and Zr. Previous work has indicated that these additions can have a substantial influence on the high temperature low cycle fatigue properties (Collins, 1978). The present investigation has aimed at investigating this effect in more detail and also studying the high temperature uniaxial creep behaviour. TABLE 1
Experimental alloys (wt%) 1. 2. 3.
Cu - 0.80 Cr Cu - 0.88 Cr - 0.08 Mg Cu - 0.58 Cr - 0.05 Mg - 0.07 Zr (AMAX MZC) 665
EXPERIMENTAL The experimental alloys were supplied in the cold worked (40% for alloys 1 and 2, 50% for alloy 3) (See Table 1) and aged (4h 450°C for alloys 1 and 2 2h 450°C for alloys 3) condition. All fatigue testing and some creep testing was carried out on these as-received conditions while further creep testing on all three alloys was conducted after solution treatment (2h 960 C ) , quenching and ageing at 450°C for 8h. These heat treatments were conducted with the specimens in evacuated silica capsules under a partial pressure of helium. The equiaxed linear intercept grain sizes after heat treatment were 50 ym for alloys 1 and 2 and 42 ym for alloys 3 (MZC). The push-pull low cycle fatigue tests were performed under stroke control in a vacuum of approximately 10"^ torr at 400°C. Creep testing was conducted in air under constant load conditions at the same temperature. Transmission electron microscopy was conducted on thin foils prepared by electropolishing in 33% HNO3 i n methanol at ^-30°C. RESULTS The as-received (cold worked and aged) microstructures All three alloys had a high density of dislocations with a fine dispersion of Cr-rich precipitates in the matrix. The Cu-Cr alloy was found to contain a large number of small voids (^ 0.1 ym diameter) and these were predominantly concentrated at the grain boundaries (Fig. 1). It is thought that these were due to gas bubble (1^0) precipitation during processing. Voids were not present in the other two alloys.
Fig. 1.
Intergranular voids (arrowed) in Cu-Cr alloy in the asreceived condition.
Fig. 2.
Precipitation of Cr-rich precipitates in Cu-Cr-Mg-Zr, 450°C 8h. Dark field micrograph.
Heat treated (solution and aged 450 C 8h) microstructures The ageing treatment resulted in the formation of a fine dispersion of Crrich precipitates (^ 20 Â diameter) in the matrix of all three alloys (Fig.2). Grain boundary precipitate free zones were present (Fig. 3a) and the half width of these zones was ^ 1000 Â for Cu-Cr and ^ 400 Â for the other two alloys. The voids in the Cu-Cr alloy became fewer in number but somewhat increased in size during the heat treatment. Cr-rich precipitates were present on the grain boundaries in all three alloys (Fig. 3a). The major difference here was that the Cu-Cr-Mg-Zr alloy also contained another type of intergranular precipitate. This precipitate was present on some boundaries as dis666
crete particles (Fig. 3b) while other boundaries contained a thin continuous film which was about 50 A thick (Fig. 4a). STEM/EDX analysis has shown that this type of precipitate contains significant amounts of Zr (Fig. 4b) and electron diffraction of a number of precipitates suggests that they are of the orthorhombic compound Cu,Zr.
Fig.
3.
.
(a)
(b)
Intergranular precipitation after ageing 450 C, 8h. (a) Cr-rich precipitates in the Cu-Cr alloy. Note the precipitate free zone, (b) Zr-rich precipitates in the Cu-Cr-Mg-Zr-alloy. Cu 4 Zr
Cu L
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1 1 1 1 1 1 1 1 ΓΠ 6
8
10
1 1 1 Γ 12
16
ENERGY (keV)
Fig. 4
(a) (b) Intergranular film of Cu4Zr in Cu-Cr-Mg-Zr. (a) Dark field micrograph. (b) STEM/EDX spectrum.
Creep testing at 400 C Secondary creep rates for the heat treated alloys are plotted as a function of applied stress in the log-log plot of Fig. 5. At low stresses (σ<70 MPa) the stress sensitivity exponent, n, in the Dorn equation έ = Aanexp-Q/kT was found to be approximately unity. This suggests that diffusion creep dominates at these lower stresses. At stresses above ^ 70 MPa, n ^ 4-18. Activation energy measurements of the steady state creep rate were made for Cu-Cr-Mg-Zr by changing the temperature in^10 C intervals. At σ = 60 MPa the activation energy was found to be 118 kj/mole which is approximately the same as that for grain boundary diffusion in Cu(104 k.J/mole) (Ashby, 1972). At σ = 140 MPa the activation energy was 205 kJ/mole which is close to that for self diffusion in Cu (207 kj/mole) (Peterson, 1968). Thus, the creep results indicate that Coble grain boundary diffusion creep dominated 667
at low stresses and power law dislocation creep dominated at the higher stresses. 10"e
■ Cu-Cr A Cu-Cr-Mg X Cu-Cr-Zr-Mg
J k ^l
V *I
10-7
ft*
/[
10-8
" _ 10-»
1 0- i o
fI
.■
/} '/
i I
/
I
x
Ï
•
r xx
i i 1
i
1 L_L
Fig. 6.
STRESS Mpa
Fig. 5.
Secondary creep rates for all three alloys, heat treated.
Intergranular creep cavities in Cu-Cr-Mg-Zr, heat treated condition. σ=160 MPa, ε=0.4%.
It can be noted from Fig. 5 that the diffusion creep rates for the Cu-Cr-MgZr alloy were considerably lower than for the other two alloys. Power law creep rates were also somewhat lower. Creep tests on as-received Cu-Cr and Cu-Cr-Mg gave similar results to that shown in Fig. 5 with the possible exception that the maximum stress for diffusion creep dominated flow was reduced. No comparative study of creep cavitation was made between the three alloys. However, scanning electron microscopy of polished sections of crept Cu-CrMg-Zr showed that intergranular cavities formed during the early stages of creep deformation (Fig. 6 ) . Low cycle fatigue at 400 C (as-received condition) Low cycle fatigue results at three frequencies are shown for the Cu-Cr alloy in Fig. 7. It can be seen from this diagram that the fatigue life of this alloy was strongly frequency dependent. The Cu-Cr-Mg alloy showed a weaker frequency dependence and Cu-Cr-Mg-Zr was frequency independent. Results for all three alloys at 10~3 Hz are shown in Fig. 8. Here it can be seen that at this low frequency Cu-Cr-Mg-Zr gave considerably improved fatigue lives over the two other alloys. The fatigue fracture behaviour was such that Cu-Cr always failed intergranularly, apparently from the interlinkage of intergranular cavities (Fig. 9a). The Cu-Cr-Mg alloy tended to fail intergranularly at low frequencies (10~^Hz) but transgranular fracture was more common at higher frequencies (lO'-'-Hz) . The Cu-Cr-Mg-Zr alloy in the as-received condition failed by ductile fatigue striations at all frequencies. It can be mentioned here that Cu-Cr-Mg-Zr fatigue tested in the heat treated condition contained some intergranular fracture facets. This was apparently associated with the formation of intergranular cavities at the Zr-rich grain boundary precipitates (see Fig. 9b).
668
Q.
ω
<
ΚΓ1
< ce
lu"2 ce
\CO
o
— Cu-Cr - A 1 0 - 1 Hz "B 10" 2 Hz _#10_3Hz
10-3 10 υ
7. Fig. 7.
I
I I II
^ ^ ^ ^ \ Α * · ^ ^
I _._ I
I I I
I
I
I
I I
I
I I I
10 10* 10* NUMBER OF CYCLES TO FAILURE, N
10* 0.5 The effect of frequency on low cycle fatigue properties of Cu-Cr.
CO
o
FREQUENCY 1 0 " 3 H z
CO
<
10" 10 u
i i i l i I i i i i il 101 102 10 J NUMBER OF CYCLES TO FAILURE, N Q
10* 6
Fig. 8.
Low cycle fatigue properties of all three alloys at 10 Hz.
Fig. !9.
Intergranular cavitation in fatigue tested material. Transmission electron micrographs, (a) Cu-Cr as-received condition, 5 cycles, 10 - 2 Ηζ,Δερ=0.4%. (b) Cu-Cr-Mg-Zr, heat treated condition, 500 cycles, 10" 1 Hz, Δερ=1.2%.
669
DISCUSSION Transmission electron microscopy has shown the very fine nature of the precipitate dispersion in alloys of this type. These Cr-rich precipitates are predominantly responsible for the good high temperature strength. It is also apparent that Mg and Zr additions have a strong effect on the high temperature creep and fatigue properties. From the point of view of microstructure this effect is clearer in the case of Zr. The intergranular precipitation of Cu-Zr compounds such as Cu4Zr, which can often be in the form of thin grain boundary films (Fig. 4 ) , may be expected to have a strong effect on such high temperature grain boundary properties as sliding and diffusion creep. The equations for diffusion creep quoted by Ashby (1972) and the diffusion data of Peterson (1968) and Ashby (1972) for Cu were used to calculate the expected diffusion creep rates at σ=40 MPa and a linear intercept grain size of 42 ym. The estimated contribution from Coble creep (Coble, 1963) is 2.4χΚΓ 1 0 s"1 and 4.6xl0"12 s _ 1 from Nabarro-Herring creep (Nabarro, 1948; Herring, 1950). Thus, as indicated by the activation energy measurements Coble creep can be expected to dominate at these low stresses. The measured creep rate at this stress for the Cu-Cr-Mg-Zr alloy was lxlO"10 s~l which is only a factor of 2.4 slower than the predicted creep rate. The agreement is very good when the vagaries of diffusion data are considered. However, the diffusion creep rates for the two alloys not containing Zr were about one order of magnitude faster than Cu-Cr-Mg-Zr while their slightly larger grain size (50 ym) would predict slower creep rates. Thus, it seems likely that intergranular precipitates and grain boundary films in the Zr containing alloy (see Fig. 3 and 4) may play an important role in inhibiting diffusion creep by limiting the ability of boundaries to act as perfect sources and sinks of vacancies (Burton, 1977). An alternative view of this is that grain boundary dislocation creep, which is considered to be necessary for grain boundary sliding and diffusion creep (Dunlop and Howell, 1981; Howell and Dunlop, 1981), is impeded by precipitates of this type. The high temperature fatigue life of Cu-Cr was found to be strongly frequency dependent and fracture occurred intergranularly. It would seem that this was largely due to the intergranular voids which were present in the as-received material. By way of contrast the fatigue life of Cu-Cr-Mg-Zr in the as-received condition was frequency independent and fracture was transgranular. No voids were present in this material prior to testing. However, even in this alloy fatigue cavitation can occur under certain conditions (Fig. 9) and this can adversely affect the high temperature fatigue behaviour. This points to the need for careful microstructural control for optimum high temperature properties. REFERENCES Ashby, M.F. (1972). Acta Met. 2i0, 896. Burton, B. (1977). Diffusional Creep of Polycrystalline Materials, Trans.Tech. Coble, R.L. (1963). J. Appl. Phys., Γ7, 909. Collins, A.T. (1978). Ph.D. Thesis, University of Waterloo, Ontario, Canada. Dunlop, G.L. and P.R. Howell (1981). Deformation of Polycrystals: Mechanisms and Microstructures, Ris^. Herring, C. (1950). J. Appl. Phys., 7\_y 437. Howell, P.R. and G.L. Dunlop (1981). Creep and Fracture of Engineering Materials and Structures, Pineridge Press, Swansea, 127. Nabarro, F.R.N. (1948). Conf. on Strength of Solids, Phys. S o c , London. Peterson, N.L. (1968). Solid State Physics, 22, 409-512. Taubenblat, P.W., W.R. Opie, and Y.T. Hsu (1972) . Met. Engg. Quart. , 12, 41-45. 670