With the rapid development of the shipping, nuclear and seawater desalted industry in recent years, the increasing requirement for cupronickels has been proposed . Cupronickel alloys are commonly used as heat exchanger tube materials in the auxiliary coolant system/moderator system owing to their high strength, good thermal conductivity and excellent corrosion resistance [2, 3, 4, 5]. BFe10-1-2 cupronickel alloy is a typical Cu-Ni alloy employed as pipelines, structural materials and ship hulls in marine environments. At present, the main processing methods of BFe10-1-2 cupronickel alloy pipes are semi-solid casting ingots and subsequent hot extrusion, which lead to considerable problems, such as long process time, high energy consumption, low product yield and high cost. Therefore, hot deformation is an important processing step during the manufacture of BFe10-1-2 cupronickel alloy products, affecting the microstructure and consequently the mechanical properties of the deformed material. However, the hot deformation of metallic materials is a complex process . Various physical mechanisms, such as work-hardening, dynamic recovery and dynamic recrystallization, are affected by various influential factors such as the chemical composition of metals and alloys, deformation temperature, strain and strain rate . Understanding the flow behaviors of metals and alloys at hot deformation conditions has a great importance for designers of metal forming processes owing to its effective role on metal flow pattern and the kinetics of metallurgical transformation . Meanwhile, various defects such as fracture, overload and die failure can be often found during high temperature extrusion process for cupronickel alloy pipes. Therefore, a thorough study on high temperature deformation behavior of BFe10-1-2 cupronickel alloy is essential to properly design the thermo-mechanical process parameters. However, few efforts have been done to understand, evaluate and predict the high temperature deformation behavior of this alloy.
The aim of present paper is to investigate the high temperature deformation behavior BFe10-1-2 cupronickel alloy. To achieve this aim, isothermal hot compression tests were conducted at the temperatures of 1,023, 1,073, 1,123, 1,173, 1,223 and 1,273 K, and strain rates of 0.001, 0.01, 0.1, 1, and 10 s–1. On the basis of orthogonal experiment and variance analysis, the effect of deformation parameters on the flow behavior of BFe10-1-2 cupronickel alloy was analyzed. And a constitutive model amongst strain, strain rate and deformation temperature was developed to predict high temperature flow behavior. Finally, the validity of developed constitutive equation was examined in terms of standard statistical parameters.
The chemical composition (wt. %) of BFe10-1-2 cupronickel alloy used in the present investigation is as follows: Ni, 10.80; Mn, 2; Fe, 1.38; and Cu, bal. Furthermore, the original microstructure of as received BFe10-1-2 cupronickel alloy is given in Figure 1 with a typical cast microstructure.
Isothermal compression experiments were carried out by a Gleeble-3800 thermal simulator. The cylindrical specimens with 10 mm in diameter and 15 mm in height were machined from a bar. Thereafter, the specimens were heated to the test temperatures at a heating rate of 10℃/s, and then held for 5 min at the compression temperature to secure heat balance prior to deformation. The samples were compressed at temperatures of 1,023, 1,073, 1,123, 1,173, 1,223 and 1,273 K, with strain rates of 0.001, 0.01, 0.1, 1, and 10 s–1 to the true strain of 0.8. After deformation, the specimens were cooled to room temperature in air, and the strain–stress curves were recorded automatically in isothermal compression. The typical macropicture of the isothermal compression samples before and after tests is shown in Figure 2 .
Results and discussion
The flow stress curves at the deformation temperature of 1,073 K and strain rate of 10 s–1 are given in Figure 3. It can be seen from figure that the flow stress is sensitively dependent on the deformation temperature and strain rate. The flow stress increases with the increase of the strain rate at a curtain temperature, and decreases with the increase of the temperature at a curtain strain rate. At the beginning of deformation stage, the flow stress increases rapidly with the increase of strain, leading to the evident work hardening process. Then, owing to the occurrence of dynamic softening, the rate of work hardening decreases with the increase of strain till a peak stress is reached. Subsequently, the flow stress keeps at a steady level, exhibiting the typical characteristics of dynamic recovery (DRV).
Furthermore, strongly single peak can be observed in flow stress at the strain of 0.05 for low strain rates (0.01 and 0.001 s–1), as shown in Figure 3(a). The reason for this phenomenon is not very clear. Similar flow stress was reported by Lin [9, 10] in BFe10-1-1 cupronickel alloy at the strain rates of 10 and 20 s–1, and BFe30-1-1 cupronickel alloy at the strain rate of 20 s–1. Lin argued that dynamic recrystallization (DRX) lead to the drop of flow stress for BFe10-1-1 cupronickel alloy. As is well known, DRX results in an equiaxed structure . Figure 4 illustrates the microstructures of BFe10-1-2 alloy under the deformation conditions of 1,123 K, 0.01 s–1. It can be seen from Figure 4 that only deformed flat grains can be observed, but no equiaxed DRX grains can be detected. Meanwhile, similar drops can also be found in 42CrMo steel  at the strain rates of 10 s–1 and 50 s–1. Further research needs to be done to draw a firm conclusion. Furthermore, the phenomenon of periodic fluctuation can be observed at high strain rate, as can be seen in Figure 3(b). Similar fluctuation was found in Ti-6Al-4V alloy at the strain rate of 10 s–1 , 42CrMo steel in 50 s–1 , and Ti600 titanium alloy in 10 s–1 . This may attribute to the noise during the compression process.
In order to analyze the significance of the effect of deformation parameters, i. e. strain, deformation temperature and strain rate, some stress values corresponding to the deformation parameters for BFe10-1-2 cupronickel alloy are introduced to support the orthogonal experiment. The impact factors of test alloy are given in Table 1, and a L25(56) orthogonal table is introduced for experiment arrangement, as shown in Table 2. The values of flow stress corresponding to the relevant deformation conditions are used as objective functions to evaluate the significance of the impact of those factors.
The range Ki of each factor in Table 2 is employed for variance analysis. The sum of squares of deviations for total experiment SST can be expressed as: (1)where n is the number of experiment, is the flow stress (MPa). And the sum of squares of deviations for each factor SSj is: (2)where r is the repetition of each level, and sum of squares of deviations for error is: (3)The degree of freedom , mean value of squares of deviations , and f-distribution in Mathematic Statistic . The calculation results of BFe10-1-2 cupronickel alloy via employing variance analysis are depicted in Table 3. From Table 3, it is noted that the values of F for deformation temperature and strain rate are both much higher than F0.01(4,12), which indicate that the flow stress of BFe10-1-2 cupronickel alloy is extremely sensitive to deformation temperature and strain rate. However, the value of F for strain is a little higher than F0.05(4,12) but lower than F0.01(4,12), which indicates that strain has a relatively small effect on the flow stress.
Influence of deformation parameters on the flow stress
On the basis of orthogonal analysis mentioned above, the influence of strain, strain rate and temperature on the flow stress can be analyzed quantitatively by the mean values of flow stress ki in Table 2: (4)
Figure 5 demonstrates the relationship between flow stress and strain. It can be seen the flow stress increases monotonically with the increase of strain, and the rate of flow stress rising decreases with the increase of strain. In theory, the deformation at high temperature is presented as the competing process of work hardening and dynamic softening. At the initial stage, the dislocation density generation is significant with the increase of deformation, resulting in the evident work hardening. Then, the energy of deformation accumulating with the increase of strain is able to stimulate the occurrence of dynamic softening, which can diminish the dislocation density and offset the influence of work hardening . When the work hardening and dynamic softening reach a balance, the dislocation density remains relatively constant, and a saturation flow stress appears.
According to the DRX mechanism during high temperature deformation, the flow stress will show a peak stress due to the occurrence of recrystallization, and then the flow stress will decrease until it reaches a steady stress . However, it is clear that there is no peak stress in Figure 5, indicating only the occurrence of DRV during deformation. Microstructures of BFe10-1-2 alloy under the deformation conditions of 1,123 K, 10 s–1 and 1,223 K, 0.1 s–1 are given in Figure 6. As can be seen from the figure, the grains after deformation tend to be elongated perpendicular to the compression direction, but no DRX grains can be observed. Therefore, the main flow softening mechanism for BFe10-1-2 cupronickel alloy is DRV not DRX.
The evolution of dislocation density can be regarded as a result of the multiplication and annihilation of dislocations due to work-hardening and DRV respectively, and can be expressed as follows : (5)where is the increasing rate of dislocation density ρ with strain ε; U represents the dislocation storage during the deformation; represents DRV due to dislocation annihilation and rearrangement, and is the coefficient of DRV. When plastic strain ε=0, dislocation density , where is the initial dislocation density, and the corresponding flow stress is the initial yield stress . Then the variations in the dislocation density during the hot deformation can be obtained by integrating eq. (5) as : (6)Then taking the natural logarithms of both sides of eq. (6), the following expression can be derived: (7)
Therefore, dislocation density increases with the increase of strain. Meanwhile, the flow stress σ can be introduced in a relationship with dislocation density by Taylor equation : (8)where is the Taylor constant, G is the shear modulus of material, M denotes Taylor factor, and b is the Burgers vector. Therefore, flow stress will increase with the increase of strain. Subsequently, a quadratic equation is use to represent the influence of strain on the mean flow stress (as shown in Figure 5): (9)where k is the mean flow stress corresponding to the impact factor strain (Column A in Table 2).
The relationship between deformation temperature, strain rate and dislocation density is expressed as : (10)where is the mobile dislocation density, f is about 0.1 representing the proportion of the mobile dislocation density in the total dislocation density ρ. A is a materials constant, and c is the Boltzmann constant. Taking the natural logarithms of both sides of eq. (10), eq. (11) can be derived: (11)It can be found from eq. (11) that the dislocation density increases with the increase of strain rate, and decreases with the increase of deformation temperature. Therefore, from eq. (8), the flow stress increases with the increase of strain rate, and decreases with the increase of deformation temperature, as shown in Figure 7. A linear and a quadratic equation are employed to represent the influence of strain rate and deformation temperature on the mean flow stress respectively (as shown in Figure 7): (12) (13)
During hot deformation, constitutive equation of metals can be expressed as: The effect of strain, strain rate and temperature on the flow stress can be expressed in another form as : (14)where is the initial stress of BFe10-1-2 cupronickel alloy under current experimental conditions; , and are the influence coefficient of the strain, strain rate and temperature, respectively. And eq. (14) is rewritten as: (15)Equations (9), (12) and (13) are used to regress the equations of , and . Table 4 shows the regression of values of . The values of k at different strains are calculated from eq. (9). Based on eq. (15), the values of at various strain can be obtained from k/k0, and k0 is the value of k at the minimum level of each factor (i. e. stain 0.1, strain rate 0.001 s–1, and temperature 1,023 K in this study), as shown in Table 4.
The relationship between and is shown in Figure 8(a), and a quadratic equation is used to characterize the influence coefficient of the strain : (16)
Figure 8(b) and (c) illustrate the relationship between - and -T respectively, and equations of and can be obtained as: (18) (19)Flow stress corresponding to the minimum level of all factors in Table 2 should be chosen as the initial stress (49.33 MPa). Therefore, the developed constitutive model of BFe10-1-2 cupronickel alloy during hot working can be summarized as: (20)
Verification of constitutive equation
The validity of the developed constitutive equation of BFe10-1-2 cupronickel alloy is estimated by comparing the experimental and predicted data, as demonstrated in Figure 9. It can be seen that the predicted flow stress data from the constitutive equation can track the experimental data of BFe10-1-2 cupronickel alloy throughout the entire temperature and strain rate range. Only under some processing conditions (i. e. at 1,023 K, 1,073 K, 1,173 K in 10 s–1 and 1,123 K, in 1 s–1), an obvious variation between experimental and computed flow stress data can be observed.
The main reason of this variation may be due to the fact that the response of flow behavior of metal materials during high temperature deformation is a highly nonlinear process. Many influencing factors for the flow stress are nonlinear, which reduce the accuracy of the developed constitutive equation . Moreover, temperature rise due to deformation heating at high strain rates may lead to flow softening because the deformation time is too short to allow for heat transfer . The influence of the temperature rise on the flow stress is more significant at lower temperatures, while the influence is relatively weaker at higher temperatures. It should be noted that the flow stress data obtained from hot compression test above 10 s–1 are not suitable for constitutive analysis unless adiabatic temperature changes are accounted . Mandal  reported that a hyperbolic sine constitutive equation could predict the flow stress of Ti-modified austenitic stainless steel throughout the entire temperatures and strain rates range except at low temperature (1,123 K) and high strain rates (10 and 100 s–1). Yuan  et al. proposed a double multiple nonlinear regression constitutive equation for Ti-6Al-4V alloy, significant deviation in prediction were observed at and higher strain rate. Sun et al.  established Arrhenius-type and modified Johnson-Cook constitutive equation of Al-0.62Mg-0.73Si Aluminum Alloy, and both of the developed models provide unreliable prediction of flow stress at low temperature and high strain rate. Meanwhile, similar results were also found in modified 9Cr-1Mo steel , 7050 aluminum alloy , and Fe-23Mn-2Al-0.2C twinning induced plasticity steel .
Standard statistical parameters such as correlation coefficient R and average absolute relative error AARE are introduced to quantify the predictability of the developed constitutive equation. These are expressed as : (21) (22)where E is the experimental flow stress and P is the predicted flow stress calculated from the developed constitutive equation considering strain compensation. and are the mean values of E and P respectively. N is the total number of data used in this study. R is a commonly employed statistical parameter and provides information on the strength of the linear relationship between the experimental and predicted data. AARE is calculated through a term by term comparison of the relative error and therefore is an unbiased statistical parameter for determining the predictability of the equation . As can be seen from Figure 10, the values of R and AARE are found to be 0.9831 and 8.441 % respectively, which indicate that the developed constitutive model can predict the high temperature flow behavior of BFe10-1-2 cupronickel alloy accurately.
The high temperature deformation behavior of BFe10-1-2 cupronickel alloy have been investigated in terms of compressed tests in a wide range of temperatures (1,023~1,273 K) and strain rates (0.001~10 s–1). Based on this study, the following conclusions are obtained:
On the basis of the results of orthogonal analysis, it can be found that deformation temperature and strain rate have significant influence on the flow stress of BFe10-1-2 cupronickel alloy, while strain has a relatively small effect on the flow stress.
A constitutive equation based on orthogonal analysis is proposed. The proposed constitutive equation can predict the flow stress accurately under most deformation conditions. The validity of presented constitutive equation is quantified in terms of correlation coefficient (R) and average absolute relative error (AARE). The results of R and AARE are calculated to be 0.983 and 8.441 % respectively, which reflect the good prediction capabilities of the developed constitutive equation.
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About the article
Published Online: 2016-09-10
Published in Print: 2017-07-26
The authors gratefully acknowledge the financial support received from Planned Scientific Research Project of Education Department of Shaanxi Provincial Government (15JS056); Pre-research Foundation of Jinchuan Company-Xi’an University of Architecture and Technology (YY1501).