M oxygen free coppers (OFCs) using processing maps

Materials Science and Engineering A 552 (2012) 276–282

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Materials Science and Engineering A journal homepage: www.elsevier.com/locate/msea

Characterization of hot deformation behaviors of wrought and P/M oxygen free coppers (OFCs) using processing maps Youngmoo Kim ∗ , Sung Ho Lee, Seong Lee, Joon-Woong Noh Defense Materials and Evaluation Technology Directorate, Agency for Defense Development, 462 Jochiwongil, Yuseong-gu, Daejeon 305-600, Republic of Korea

a r t i c l e

i n f o

Article history: Received 18 June 2011 Received in revised form 6 April 2012 Accepted 11 May 2012 Available online 2 June 2012 Keywords: Oxygen free copper (OFC) Hot deformation Processing map

a b s t r a c t Wrought and powder sintered (P/M) oxygen free coppers (OFC) were subjected to hot deformation testing over the range of strain rates (0.01–10.0 s−1 ) and temperatures (200–800 ◦ C). Processing maps of both materials have exhibited different deterministic domains representing dynamic recrystallization (DRX), which occurs in the following temperature and strain rate ranges: for wrought copper, 400–600 ◦ C and 0.01–0.1 s−1 , 600–800 ◦ C and 0.01–10.0 s−1 ; for P/M one, 600–800 ◦ C and 0.01–1.0 s−1 . The domain for wrought copper has higher efficiency of power dissipation with increasing temperature and decreasing strain rate. For P/M OFC, the region at temperature of 600 ◦ C and strain rate of 10−2 s−1 showed peak efficiency. The results on processing maps have well correlated with those obtained from kinetic analysis. The apparent activation energies estimated in the DRX domains are 146.04 and 190.67 kJ/mol for wrought and P/M OFCs, respectively, which suggest that dislocation core diffusion and lattice self-diffusion are the rate controlling mechanism each. In all domains, the average grain diameter varies linearly with Zener–Holloman parameter. © 2012 Elsevier B.V. All rights reserved.

1. Introduction Oxygen free copper (OFC) is extensively used in shaped charge liners due to its high density and excellent ductility which ensure favorable penetration performance [1]. This capability is known to be strongly related with the metallurgical factors of the liner, such as grain size, grain orientation and purity [2]. Several processes for fabricating the liners have been developed; machining from a billet, deep drawing, flow turning, cold, warm and hot forging processes, high-energy rate forming (HERF) and electroplating [3]. Among these, warm and hot forging processes have been considered as the most effective process in respect of feasibility to control the grain structures of liners. Copper has medium to low stacking fault energy (about 40 mJ/m2 ) and exhibits discontinuous dynamic recrystallization (DDRX) during deformation, which is characterized by a peak in the flow stress followed by steady state at large strains. Oscillations in flow stress could appear at a low strain rates. Prasad and Rao [4–6] have studied hot deformation behavior and its mechanism of electrolytic tough pitch (ETP) and OFHC coppers considering the deformation conditions and oxygen contents by processing maps. In this study, the effect of raw materials on the hot deformation behaviors were investigated for wrought and powder sintered

(P/M) OFCs, since these are the major materials of shaped charge liners. The processing maps and rate controlling mechanisms were obtained from a number of hot compression tests at various temperatures and strain rates. The concept of a processing map was firstly introduced by Prasad et al. [7] and it is an explicit representation of the response of a material to the imposed process parameters, such as strain rate, strain and temperature. The map is composed of a superposition of a power dissipation and instability developed on the basis of the Dynamic Materials Model which is based on the continuum mechanics of large plastic flow, physical system modeling, and irreversible thermodynamics [7]. The flow stress, when strain and deformation temperature are constants, is given by  = K ε˙ m

(1)

where K is a material constant and m is strain rate sensitivity. This can be rewritten as follows: m=

∂(ln ) ˙ ∂(ln ε)

(2)

The workpiece undergoing hot deformation can be considered as a dissipater of power. The total power P may be separated into two complementary functions: G content and J co-content:

 ∗ Corresponding author. Tel.: +82 42 821 2909; fax: +82 42 821 2393. E-mail address: [email protected] (Y. Kim). 0921-5093/$ – see front matter © 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.msea.2012.05.040

P =  ε˙ = G + J =



ε˙

dε˙ + 0



˙ εd 0

(3)

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G content represents the power dissipation due to plastic deformation, most of which is transformed into viscoplastic heat and J co-content, due to metallurgical changes. The power partitioning between G and J is controlled by the constitutive flow behavior of the material and is decided by strain rate sensitivity (m). ε¯˙ d¯ dJ = =m dG d ¯ ε˙

(4)

By comparison of J co-content with the maximum possible dissipation Jmax , the efficiency of power dissipation, a dimensionless parameter,  is given by: =

J 2m = Jmax m+1

(5)

The power dissipation map is obtained by plotting iso-efficiency contour of parameter , which represents the power dissipation through microstructure evolution at different temperatures and strain rates. Instability map is developed on the basis of an instability criterion which is derived from the extremum principle of irreversible thermodynamics and is applied to continuum mechanics of large plastic flow. The instability criterion is proposed by Ziegler [8]. Unstable flow will occur if the differential quotient satisfies the following inequality: D dD < dε˙ ε˙

(6)

where D is the dissipative function which represents the constitutive behavior of the material. Since J determines the dissipation through metallurgical processes, the dissipative function D can be substituted by J, J dJ < dε˙ ε˙

(7) Fig. 1. Typical microstructures of (a) wrought and (b) P/M OFC specimens prior to deformation.

Eq. (7) can be rewritten as follows: d ln J <1 d ln ε˙

(8)

According to Eq. (3), the following equation can be obtained



J=



˙ = εd 0

˙  εm m+1

(9)

The natural logarithm of J is as follows: ln J = ln

 m  m+1

+ ln  + ln ε˙

(10)

Both sides of Eq. (10) are divided by ln ε˙ and the following equation can be obtained. d ln(m)/(m + 1) d ln  d ln J = + +1 d ln ε˙ d ln ε˙ d ln ε˙

(11)

Thus, a dimensionless parameter for microstructural instability is given by: ˙ = (ε)

∂ ln(m)/(m + 1) +m<0 ∂ ln ε˙

(12)

The instability map can be obtained by plotting  at different temperatures and strain rates where  is negative. The flow instabilities are mainly in the form of adiabatic shear bands or flow localizations in the microstructure. 2. Experimental The starting materials used in this study were wrought rods and powder sintered parts of OFC purity. The main impurity contents (ppm) in OFC (Cu: 99.95%) were as follows – O: 10, Pb: 1, Fe: 1, Bi: 1, P: 3, Ag: 10. The wrought specimen was extruded and annealed in vacuum resulting in average grain size of 70 ± 8 ␮m as shown

in Fig. 1(a). The copper powder was sintered at 1000 ◦ C for 1 h under vacuum atmosphere. The sintered density was 96% of theoretical one and its average grain size was 20 ± 5 ␮m as illustrated in Fig. 1(b). Cylindrical compression specimens of 8 mm in diameter and 12 mm in height were machined. A computer controlled servo-hydraulic Gleeble 3500 machine was used for compression testing. Hot compression experiments were conducted under isothermal condition at constant strain rates of 0.01, 0.1, 1.0 and 10.0 s−1 and at temperatures of 200, 400, 600 and 800 ◦ C up to strain of 0.1. Temperature control was within ±1 ◦ C. The adiabatic temperature rise in the specimen during testing was measured by a R-type thermocouple wire embedded in a 0.5 mm hole machined up to the center at mid-height of the specimen. Test specimens were heated to test temperature at the rate of 5 ◦ C/s and soaked for 5 min to secure temperature uniformity prior to deformation. The flow stress was corrected for the adiabatic temperature rise assuming linear relationship between logarithm of flow stress and inverse of temperature within the intervals of experimental data points [9]. To avoid welding of the specimen to the dies during hot deformation, tantalum foil of 0.1 mm thick was used between the specimens and dies. The load-stroke data were converted into true stress–strain curves using standard equations with the elastic deflection of the machine and the grips taken into account [10]. After the measurements, the deformed specimens were quenched in water to freeze the microstructure, sectioned parallel to the compression axis and polished at the level of 0.25 ␮m abrasive powder. The etchant was made of 120 mL of distilled water, 30 mL of hydrochloric acid and 10 g of iron chloride. The average grain diameter was measured using linear intercept method. Processing maps were developed

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Fig. 2. True stress–true strain curves of wrought OFC deformed in compression at (a) 200 ◦ C and (b) 600 ◦ C.

Fig. 3. True stress–true strain curves of P/M OFC deformed in compression at (a) 200 ◦ C and (b) 600 ◦ C.

by the procedures mentioned earlier using the flow stress data at strain of 1.0 for various temperatures and strain rates.

DRX in copper [11,12]. In metals with low stacking fault energy like copper, nickel and austenitic iron, climb and cross-slip of dislocations tend to be hindered during deformation. Therefore, thermal activation is required for these metals to plastically flow. When a critical deformation condition is reached, DRX may take place instead of dynamic recovery. The flow stress values of both materials are given in Tables 1 and 2, which were corrected for adiabatic temperature increase.

3. Results and discussion 3.1. Hot deformation behaviors The flow curves obtained at 200 and 600 ◦ C for wrought and P/M OFCs are shown in Figs. 2 and 3, respectively. At 200 ◦ C, for both specimens, the flow stress is saturated with increasing strain at all strain rates. During initial stage of deformation, there is an increase in the stress as dislocations interact and multiply. However, as the dislocation density increases, the rate of recovery increases resulting in sub-grain formation. At the strain of 0.7, the rates of work hardening and recovery reach a dynamic equilibrium, the dislocation density remains constant and steady-state flow is obtained as illustrated in Figs. 2(a) and 3(a). However, as the temperature was increased up to 600 ◦ C, the flow curves exhibited a peak at small strain followed by steady-state flow, except the strain rate of 1.0 and 10.0 s−1 for P/M specimens, as shown in Figs. 2(b) and 3(b). For wrought OFC at strain rates lower than 1.0 s−1 , multiple peaks have appeared before a steady-state is reached. The effects of temperature and strain rate on the strain at peak stress suggest that this phenomenon is thermally activated. The flow softening behavior described above is a typical manifestation of the occurrence of

3.2. Processing maps The processing maps obtained for wrought and P/M OFCs are shown in Fig. 4(a) and (b), respectively, which corresponds to strain of 1.0. The numbers on each contour represent the efficiency of power dissipation in percent. The dotted line delineates the regions of flow instability (marked as “INST” in the map) from stable flow. As shown in Fig. 4(a), the efficiency for wrought copper is increased with increasing temperature and reducing strain rate. DRX domain for this material occurs in the temperature range 400–600 ◦ C and 600–800 ◦ C and strain rate range 0.01–0.1 s−1 and 0.01–10.0 s−1 , respectively, with peak efficiency of 35% occurring at 800 ◦ C and 0.01 s−1 as shown in Table 3. The instability zone is estimated in the temperature range 200–350 ◦ C and strain rate range 0.01–1.0 s−1 . The microstructures of specimens compressed at 400 ◦ C/0.1 s−1 and 600 ◦ C/1.0 s−1 , which represents DRX domains

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Table 1 Flow stress (in MPa) of wrought OFC for various strain rates, temperatures and strains (corrected for adiabatic temperature increase). Strain

0.2

0.4

0.6

0.8

1.0

Strain rate (s−1 )

0.01 0.1 1.0 10.0 0.01 0.1 1.0 10.0 0.01 0.1 1.0 10.0 0.01 0.1 1.0 10.0 0.01 0.1 1.0 10.0

Temperature (◦ C) 200

400

600

800

194.41 210.37 219.81 215.11 223.21 236.93 245.38 249.93 238.34 252.58 261.73 264.62 245.47 261.82 269.19 270.55 253.85 266.74 271.78 271.90

125.37 142.20 147.62 162.32 111.18 163.60 177.91 190.95 117.72 152.13 192.71 201.58 112.69 145.76 194.45 206.45 112.50 143.62 191.35 203.99

48.47 67.35 94.66 106.63 45.11 62.42 82.21 125.40 43.53 59.91 84.89 114.16 42.69 59.86 82.40 106.54 39.37 59.60 81.76 94.30

35.73 51.15 66.16 81.99 32.50 47.45 60.00 88.42 34.11 46.33 65.53 84.50 33.16 44.57 63.92 81.73 31.90 45.00 67.04 73.46

Table 2 Flow stress (in MPa) of P/M OFC for various strain rates, temperatures and strains (corrected for adiabatic temperature increase). Strain

0.2

0.4

0.6

0.8

1.0

Strain rate (s−1 )

0.01 0.1 1.0 10.0 0.01 0.1 1.0 10.0 0.01 0.1 1.0 10.0 0.01 0.1 1.0 10.0 0.01 0.1 1.0 10.0

Temperature (◦ C) 200

400

600

800

179.77 183.90 188.73 195.12 218.98 219.55 226.37 236.12 240.78 242.21 247.10 258.70 251.84 252.64 258.64 266.26 253.33 255.91 262.88 268.81

127.26 135.91 141.46 147.45 151.69 164.02 170.90 177.55 165.11 179.20 188.60 193.80 171.59 187.65 200.58 201.11 170.80 187.51 202.56 198.58

69.88 93.50 100.86 115.80 68.53 107.18 120.68 136.03 66.55 97.48 129.73 147.78 63.37 92.32 135.30 150.28 61.67 91.98 134.54 150.73

17.13 25.62 37.19 61.76 14.25 24.71 37.29 57.54 13.57 23.79 37.41 57.54 13.43 23.05 38.43 55.24 13.03 23.37 40.36 51.64

were shown in Fig. 5(a) and (b). It can be seen that the microstructure is significantly refined compared to the typical microstructure (Fig. 1(a)). The original grain boundaries had disappeared and new small grains formed along with the boundaries by DRX (Fig. 5(a)) and at the further temperature (600 ◦ C), the size of dynamic recrystallized grains increased (Fig. 5(b)). For P/M OFC specimens, the

Fig. 4. Processing maps for (a) wrought and (b) P/M OFCs at strain of 1.0. The numbers on each contour represents efficiency of power dissipation in percent. The dotted line shows the limits for flow instability, with this regions marked as “INST”.

DRX domains represents in the temperature range 600–800 ◦ C and strain rate range 0.01–1.0 s−1 as illustrated in Fig. 4(b). The peak efficiency of 30% shows at 600 ◦ C and 0.01 s−1 . The instability domain represents in 400–550 ◦ C and 0.3–10 s−1 . Compressed at 600 ◦ C/0.1 s−1 , new refined grains were created by DRX and the grain growth occurred at 800 ◦ C/1.0 s−1 as shown in Fig. 6(a) and (b), respectively. The average DRX grain size of P/M parts is smaller than that of wrought ones because the initial particle size of P/M specimens was rather small compared to wrought ones. The microstructures of instability regions in wrought and P/M OFCs were shown in Figs. 7 and 8, which corresponds with the specimen deformed at 200 ◦ C/10.0 s−1 for wrought part and 400 ◦ C/10.0 s−1 for P/M one. The grains were visibly elongated and

Table 3 Stress exponent (n) and apparent activation energy (Q) in the DRX domains of the processing maps for wrought and P/M OFCs. The correlations between grain size (d) and Zener–Hollomon parameter (Z) in the DRX domain are also given. Specimen

Wrought copper P/M copper

Temperature (◦ C) ranges

400–600 600–800 600–800

Strain rate (s−1 ) ranges

0.01–0.1 0.01–10.0 0.01–1.0

Kinetic parameters n

Q (kJ/mol)

5.9

146.04

6.7

190.67

Grain size (d, (m) versus Z (s−1 ) correlation

log d = 2.64 − 0.17 log Z log d = 1.99 − 0.11 log Z

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Fig. 5. Typical microstructures of wrought OFC specimen deformed at (a) 400 ◦ C/0.1 s−1 and (b) 600 ◦ C/1.0 s−1 corresponding to the DRX domain.

Fig. 6. Typical microstructures of P/M OFC specimen deformed at (a) 600 ◦ C/0.1 s−1 and (b) 800 ◦ C/1.0 s−1 corresponding to the DRX domain.

the grain boundaries were irregular and indistinct. However, unstable microstructures such as shear band and flow localization were not found in the instability region for both materials. 3.3. Kinetic analysis According to Jonas et al. [13], the relationship between steadystate flow stress (), strain rate and temperature (T) during hot deformation is generally expressed in the form of a standard power law type kinetic rate equation: ε˙ = A n exp

 −Q  RT

(13)

where A is constant; , flow stress; n, stress exponent (n = 1/m, m is strain rate sensitivity); Q, activation energy; R, gas constant (8.31 J/mol K) and T, absolute temperature. Based on this equation, the relevant rate controlling mechanisms of the wrought and P/M OFCs were evaluated in the DRX domains. The plots of log () versus ˙ are shown in Fig. 9, where flow stress is corresponding log (ε) to a strain rate of 1.0. From this plot, the values of stress exponent (n) have been estimated to be 5.9 and 6.7 in DRX domains of wrought and P/M specimens, respectively as shown in Table 3. The value for wrought copper was slightly less than that of P/M one. Similar to the previous result [14], stress exponent is nearly independent upon strain. The flow stress is normalized with respect to the temperature dependence of shear modulus (, 48 GPa) and Arrhenius plot of log (/) versus (1/T) is shown in Fig. 10 for the stress data at strain of 1.0. The slope of the lines and the

Fig. 7. Typical microstructures of wrought OFC specimen deformed at 200 ◦ C under 10.0 s−1 corresponding to the flow instability region.

corresponding activation energy values were obtained as reported in Table 3. The estimated apparent activation energy of wrought OFC was 146.04 kJ/mol and this matches the value for dislocation core-diffusion (158 kJ/mol) [15]. On the other hand, for P/M OFC, the energy was estimated to be 190.67 kJ/mol and this is similar to the value for lattice self-diffusion (195 kJ/mol) [16]. Though the rate controlling mechanisms of both materials are different, it is found

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Fig. 8. Typical microstructures of P/M OFC specimen deformed at 400 ◦ C under 10.0 s−1 corresponding to the flow instability region.

Fig. 10. Arrhenius plots of flow stress at strain of 1.0 (normalized with shear modulus) for (a) wrought and (b) P/M OFCs.

that thermal activation is needed for both wrought and P/M copper deformed as mentioned above. For wrought copper, more energy is required for deformation than P/M one. Such tendency is in good agreement with flow stress–strain relation in Fig. 3. It is reported that the activation energies for dynamic recrystallization during hot deformation of other P/M materials, such as FGH4096 superalloys [17] and TiAl-based alloys [18], have been determined to be 922 and 313.53 kJ/mol, respectively. The values are much greater than that of P/M coppers (190.67 kJ/mol) and the difference seems to be caused by the formability. It is well established that grain size variation under DRX may be correlated the temperature compensated strain rate parameter (Zener–Hollomon) Z, given by [19]: Z = ε˙ exp

Fig. 9. Variations of log (flow stress) and log (strain rate) at different test temperatures in (a) wrought and (b) P/M OFCs.

Q  RT

(14)

Average grain sizes were plotted against Z on a log–log scale in Fig. 11. The activation energy values estimated above were used to calculate the relation. The plot exhibits a linear relationship in the DRX domains of both OFCs and the relationship is expressed by the equation as illustrated in Table 3. Using this relation, one can control the grain size of copper after deformation.

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2. From the kinetic analysis, the apparent activation energies in DRX domains of wrought and P/M OFCs are 146.04 and 190.67 kJ/mol, respectively. These values suggest that dislocation core diffusion and lattice self-diffusion are the rate controlling mechanisms. 3. In all DRX domains, the average grain diameter exhibits a linear relation with the Zener–Holloman parameter. 4. These results may provide the informative data for fabricating OFC shaped charge liners with desired microstructures through warm or hot forging processes. References

Fig. 11. Variation of log (average grain size) with log (Z) obtained in DRX domains of (a) wrought and (b) P/M OFCs.

4. Conclusions Processing maps and kinetic analysis have been investigated for hot deformation of wrought and P/M OFCs in the temperature range 200–800 ◦ C and strain rate range 0.01–10.0 s−1 . The following conclusions have been drawn from the results of this research. 1. The processing maps of wrought OFC reveal the two DRX domains in the following temperature and strain rate ranges: (1) 400–600 ◦ C and 0.01–0.1 s−1 , (2) 600–800 ◦ C and 0.01–10.0 s−1 . For P/M OFC, the DRX domain is exhibited in the ranges: 600–800 ◦ C and 0.01–1.0 s−1 .

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