Understanding hot workability of power plant P92 creep resistant steels using dynamic material modelling (DMM) and microstructural evolution

This study reports the hot workability of two P92 creep-resistant steels with different chromium and tungsten contents, all within the ASME specification. These steels are used in manufacturing modern power plant boiler pipes. Uniaxial compression tests were done using a Gleeble® 3500 thermal-mechanical equipment. The test conditions were: deformation temperature of 850–1000 °C and strain rate of 0.1–10 s−1. Experimental flow stress values obtained from isothermal hot compression tests were used to construct processing maps employing the dynamic material model approach. The flow stress-strain curve results of the two steels exhibited dynamic recovery characteristics. The flow stress increased with a decrease in temperature or an increase in strain rate. The correlation between the processing maps and the microstructure of the deformed samples reveals that the optimal processing window for the two steels occurred at a deformation temperature of 850 °C and 1000 °C and a lower strain rate of 0.1 s−1 for the conditions studied. These regions had maximum power efficiency of 26% (P92-A steel) and 19% (P92-B steel). The findings from this study have provided a new approach to process parameter optimisation using a dynamic material model technique of industrial metal forming of P92 steels. Hence, reducing manufacturing time and cost.

(CO 2 ) emissions [5]. Some ferritic steels currently used for boiler piping systems include P91, P92, E911 and P122 [1,4]. Recently, P92 steel has become the potential candidate for advanced ultra-supercritical power plants [7,8]. Most research focuses on the creep performance of this steel [7,9]. However, the performance of this steel depends on the production process. The production process involves casting billets followed by the metal forming processes such as forging or extrusion [10]. In the metal-forming process, component production involves several stages under which a material experiences large forces and complex stresses [10]. During forming, the plastic deformation cause generation of internal heat, which result in grain growth [11]. The forming parameters such as temperature, strain rate and strain affect the final product microstructure, which impacts the overall mechanical properties of the product [12]. Therefore, the optimisation of forming parameters is paramount. Processing maps based on the Dynamic Material Model (DMM) have become handy as the technique for process optimisation of hot working parameters [13][14][15][16].
Researchers have used the DMM technique to study the hot forming of many metals and alloys [17][18][19][20][21][22][23]. DMM technique provides an accurate and reliable approach to optimise the deformation parameters to ensure a cost-effective production process. The dynamic material model describes the metal flow pattern during forming by correlating deformation and microstructure evolution. A brief discussion of the DMM technique is given in this article. Processing maps are built on the log strain rate and temperature frame, thus delineating the 'safe' and 'unsafe' working conditions. The processing map is developed by superimposing the instability map onto the power dissipation map [24]. The workpiece acts as a power dissipator during forming [25]. The total power generated is divided into two sections: the internal heat generated due to plastic deformation G and the energy dissipated during microstructure changes J, such as DRX, DRV and phase transformation [13,22]. This relationship is given by Murty and Rao [26] as: where σ is the flow stress andε is the strain rate. The constitutive response of the material during forming describes the power dissipation of the material. The power law in Eq. 2 shows the relationship between the flow stress distribution and deformation conditions during deformation [27]: where K is the stress coefficient m is the strain rate sensitivity. Solving Eq. 2 gives: Equation 3 is an equation of straight line, therefore, m is obtained using Eq. 4: The m-value varies with different deformation conditions. The relationship between the flow stress and strain rate at constant temperature and strain can be expressed as Eq. 5 [17,20,28].
The m-value in Eq. 4 is a function of strain rate. Taking the derivatives of Eqaution 5 gives: where a, b, c and d are material constants obtained from the log-log plot of the flow stress and strain rate. From Eq. 6, the m values can be obtained at different deformation conditions. The power dissipation efficiency η which represents power dissipation is given as [29]: The parameter η (Eq. 7) defines the deformation mechanisms that occur during deformation. The ï-value represents the power dissipation percentage used during microstructure changes to the total power dissipated during deformation. The power dissipation efficiency varies with the deformation conditions, thus constituting the power dissipation map [30,31].
During deformation, defects such as shear bands, microvoids and cracks may occur [29]. Therefore, these instability regions must be identified [32]. Murty et al. [29] have discussed several instability criteria. However, the Murty instability criterion (Eq. 8) for stable materials has been widely used [33].
Solving Eq. 8 gives: A cubic spline function has been utilised to calculate the instability values ξ (ε) (Eq. 9) under all the deformation conditions investigated. The instability map is a plot of temperature and strain rate at different values of ξ (ε). Negative ξ (ε) value indicates an instability regime characterised by deformation defects such as adiabatic shear bands, microvoids and flow localisation [34]. The strain rate sensitivity value plays a role in developing the processing maps and optimising the process parameters. Montheillet et al. [35] have criticised this method of processing maps based on the DMM technique. The authors argued that the DMM is a heuristic approach with no basis in material laws, and instead, they recommended strain rate sensitivity for optimisation of process parameters. The argument is that DMM is not directly related to workability but power dissipation efficiency. Despite this, most studies have used the DMM technique proposed by Prasad et al. [21] and modified by Murty et al. [29] to study and optimise the metal forming process parameters. This technique develops processing maps, which assist in identifying the optimal working conditions and process defects during deformation [13,36]. Moreover, the use of DMM to optimise the deformation process parameters has been well accepted and validated for most materials, such as Modified 9Cr-1Mo steel [13], Plain eutectoid steel [17]. Super austenitic stainless steel S32654 [18], BSTMUF601 superalloy [19], Aluminium alloys [20], 410 martensitic stainless steel [22], Titanium alloys [37], Low carbon steel [38], P92 steel [23,39]. Therefore, the current study used the DMM technique to optimise the process parameters of two P92 steels with chromium and tungsten content, all within the ASME specification over a wide range of deformation conditions. Previous studies on P92 steel focussed on the creep and welding properties during service [40][41][42][43]. However, a few researchers have investigated and reported on metal flow behaviour using constitutive modelling equations of P92 steel. The information about the optimisation of process parameters and their effect on microstructure evolution mechanisms during forming is conspicuously missing in the literature. Therefore, this study used a dynamic material model to optimise the process parameters during forming and reports on the microstructure evolution mechanism. The findings from this study provide a new approach to process parameter optimisation of industrial metal forming of P92 steels. Hence, reduce production time and cost.

Experimental procedure
Two P92 pipe sections were machined into cylindrical specimens of 8 mm diameter and 12 mm height (aspect ratio 1.5). Hot compression tests were done using a Gleeble 3500® thermomechanical simulator following the Gleeble-APN001 standard procedure [44]. This procedure has been used widely by other researchers such as [17,18,32,37,38,45,46]. The chemical composition of the two steels studied is given in Table 1. The specimens were heated at the rate of 5°C/s to the austenitisation temperature of 1100°C and held for 180 s. At this condition, microstructure homogenisation of the test sample occurs. Then, the test samples were cooled to the deformation temperature (850-1000°C) at a rate of 10°C/s and soaked for 60 s to reduce the thermal gradient before compression (Fig. 1). The samples were deformed to 60% (a true strain of 0.5) at a constant strain rate (0.1, 1 and 10 s −1 ), then rapidly air-cooled to room temperature. K-type thermocouples were welded at the specimen surface to control and monitor the test temperature. Graphite foil and nickel paste placed at the work piece-anvil interface acted as a lubricant. This lubricant minimised friction, hence barrelling effects during deformation. The nickel paste prevents sticking between the specimen and anvil surfaces during testing. The deformed specimens were sectioned parallel to the compression axis at the centre and then prepared for metallography. Samples were prepared following the standard metallography procedures for microstructure analysis. The specimens were ground and polished. The polished specimens were etched using Villella's reagent (1 g picric acid, 100 ml ethanol and 5 ml HCl) for 3 min. Fieldemission scanning electron microscopy was used to study the microstructure of deformed specimens.

Flow stress behaviour of P92 steel
appears, followed by constant flow stress, hence achieving steady-state flow stress occurred, as defined by Laasraoui and Jonas [47]. At strain lower than 0.3, work hardening controls the deformation mechanism at this strain, causing the flow stress to increase rapidly. At a higher deformation degree (> 0.4), the slopes of the stress-strain curves of the two steels decreased steadily until the flow stress attained a steady-state condition. This characteristic flow curve behaviour is due to the balance between work hardening and dynamic recovery (a softening mechanism) until the saturation flow stress (σ sat ) is reached [47]. Therefore, in the two steels, the flow stressstrain curves show the characteristic behaviour of a material experiencing work hardening at strains < 0.3, followed by dynamic recovery as the softening mechanism at ε > 0.3. The stress-strain curves show the flow stress dependency on deformation conditions. The flow stress decreased with an increase in the deformation temperature for a given strain rate. The decrease in flow stress occurs due to the diffusional mobility of atoms and dislocation mobility as the temperature increases [48]. For a given temperature, the flow stress increased as the strain rate increased. Higher deformation temperature and lower strain rate cause the generation of atomic vacancies and dislocation diffusion, thus reducing the flow stress.
Higher deformation temperatures than the dissolution temperatures of carbides will cause carbides to dissolve in the matrix. Hence, reducing precipitation hardening. The absence of carbides in the matrix enhanced dislocation motion to occur, thus causing lower flow stress values [23]. Higher temperatures and lower strain rates are favourable for metalworking. Forming at lower deformation temperature and higher strain rate causes high flow stress values. High flow stress values are due to the higher generation of dislocation density, impeding dislocation motion. The reason is that the deformation rate is quick, and there is sufficient time for dislocation annihilation [48]. Figure 2 shows that at 850°C, the flow stress values for P92-A steel increased bỹ 45% as the strain rate increased from 0.1 to 10 s −1 , while P92-B increased by~33% (Fig. 3). These results show that the flow stress behaviour is sensitive to the deformation conditions.

Strain rate sensitivity maps
The strain rate sensitivity factor m values were calculated using experimental flow stress and strain rate as points. A plot of log-log scale of flow stress and strain rate at a strain of 0.5 is as shown in Fig. 4. Each curve was fitted with a third-order polynomial function (Fig. 4). At constant strain rate and temperature, the first derivative of Eq. 4 was used to calculate the m-values. Figure 5 shows the plot of strain rate sensitivity m values as a function of temperature and strain rate. The contour maps show that the m values were higher than 0.05 for the two steels. Higher m-values show that a higher percentage (> 20%) of energy generated was consumed by microstructure evolution such as DRX and DRV [49]. The two steels had good workability under the tested hot deformation conditions, indicating that they were deformed in a stable region. The obtained m-values were then used to compute the power dissipation efficiency and the instability parameter using Eqs. 7 and 9.

Deformation maps
The processing maps were constructed by superimposing the power dissipation efficiency η and the instability parameter ξ(ε) maps. The values of η and ξ(ε) were determined using Eqs. 7 and 9 at 850-1000°C, 0.1-10 s −1 and a true strain of 0.5. Cubic spline interpolation was used for determining η and ξ(ε). The power efficiency and instability maps for the two steels are given in Figs. 6 and 7. However, the constructed dissipation and instability maps for hot deformation showed no marked differences, the contour maps in this study will be referred to as deformation maps. The power dissipation maps were then used to identify the optimum processing conditions. The power dissipation efficiency maps in Figs. 5 and 6, shows the relationship between the deformation temperature and strain rate at 0.5 strain. At 0.5 strain, the flow stress curves had steady-state flow characteristics. The contour lines in the power dissipation maps represent the percentage of power dissipation efficiency. Figure 6a shows the power dissipation map for P92-A steel at a strain of 0.5. The peak efficiency was 26% at 850°C and 0.1 s −1 (Fig. 6b). There was lower power efficiency (6-8.5%) at the higher strain rate of 10 s −1 and temperatures of 850°C and 1000°C. Under these conditions, lower power efficiency shows that microstructure changes and phase transformation were limited. This lower efficiency indicates that a lower percentage of energy is consumed to cause microstructural changes. Hence, deformation (lower ï-values) under these conditions is undesirable. At a strain rate of 10 s −1 (Fig. 6a,  b), there was an efficiency peak of~13.5% at 900°C and 21% at 950°C. These conditions show that dynamic softening occurred. However, low peak efficiency indicates that material deformed under these conditions will have low ductility. A dynamic recovery DRV is dominant when the peak efficiency is~30% [34]. At 0.1 s −1 /850°C and 10 s −1 / 950°C, the deformation mechanism was mainly by dynamic recovery. For all temperatures at a strain of 0.5 and a strain rate of 1 s −1 , the peak efficiency was 16%.

Deformation maps for P92-A steel
At a strain rate of 10 s −1 , the power efficiency was 15.5-20.8% in the temperature range of 900-950°C (Fig. 6a,  b). Under all test temperatures and at 1 s −1 , the power efficiency was 13-20.8%. The power efficiency varied from 18 to 26% at 850-900°C and 1000°C for a strain rate of 0.1 s -1 . At deformation temperatures of 900-950°C and a strain rate of 10 s -1 , power efficiency was 13.5-21%. These results show that the workability of the materials investigated is better at a lower strain rate. Figure 7 shows the power dissipation efficiency maps for P92-B at 0.5 strain. There were peak efficiencies of 19% at 1000°C, 17.5% at 850°C for 0.1 s −1 and 11.5-19% for all deformation temperatures. At 10 s −1 , the lower power efficiency of 7% was observed at 850°C, while at 900-1000°C the efficiency was 10-14%. At 1 s −1 , the power efficiency varied from 10 to 16% for all deformation temperatures (850-1000°C). The power dissipation efficiency indicates the rate of relative internal entropy of production and microstructure changes during hot deformation at different temperatures and strain rates [17]. The power efficiency value categorises the deformation softening mechanisms occurring during deformation at any given deformation conditions. When the power dissipation efficiency values range from 20 to 30%, dynamic recovery (DRV) is the softening mechanism, while 35-50% shows the dynamic recrystallisation (DRX) [50], and high efficiency (> 60%) corresponds to super-plasticity. For this steel, the power efficiencies were lower than 20%, indicating the difficulty in deforming this steel under the investigated condition. However, the steel had good workability since the instability maps (Fig. 7) did not show any instability.

Deformation maps for P92-B steel
In this study, power dissipation efficiency values were less than 33%. These analyses show that dynamic recovery was the only softening mechanism, which is more pronounced for materials having high stacking fault energy such as P92 steel. These results are similar to the behaviour seen in the flow stress-strain curves given in Figs. 1 and 2. The safe processing regions were at a strain rate of 0.1 s −1 at 850°C and 1000°C for P92-A and P92-B steel. The results show that the optimum processing conditions occurred at the lowest strain rate. Under these conditions, the deformation is slow, and there is enough time for heat conduction and dislocation movement [38]. Hence, providing good workability conditions.
The power efficiency for P92-A and P92-B remained relatively constant as strain increased from 0.2 to 0.5 (not provided). However, power efficiency decreased from 24% at a strain of 0.2 to 19% at 0.5 strain for P92-B. A decrease in the power dissipation efficiency with an increase in strain during hot deformation has been reported [51]. The stability region gets smaller with an increase in the strain [38]. However, Wang et al. [50] indicated that the strain does not influence the processing map. Therefore, the strain contribution to flow behaviour during deformation of this type of steel investigated was unclear. A study on the effect of deformation degree on the flow behaviour is through conducting several III I II Fig. 8 An illustration of strain distribution (Regions: I-Intense Shear Zone, II-Dead Metal Zone, and III-Moderate Deformation Zone) in a deformed sample (FEM) compression tests at a different true strain. After compression tests, processing maps should be constructed and correlated with the deformed microstructure. The results showed that increasing the deformation degree from 0.2 to 0.5 does not affect the power dissipation efficiency of P92-A, but P92-B steel. However, the study did not explore in detail on this aspect. The extent to which strain affects power efficiency, in this case, deformation behaviour, was not fully understood. The only reason might be the contribution of chromium and tungsten content for the two steels.

Flow instability maps
The power dissipation maps cannot conclusively determine the 'safe' working conditions by relying on the higher power efficiency values. Unsafe conditions such as localised flow, adiabatic heating, wedge cracking and shear banding may occur during deformation [52]. Flow instabilities that occur during deformation can be identified by plotting flow instability maps. These show the effect of deformation temperature on the logarithm of strain rate for different instability parameters (ξ). The unsafe regions having ξ < 0 are identified from the flow instability map. These regions are unsuitable for deformation [38]. Figures 5 and 6c, d show the instability maps for the two P92 steels. These figures show that all the instability parameters (ξ) were higher than zero, so the tested deformation conditions for the two steels were within the safe working conditions using instability maps. However, this does not necessarily mean that thermo-mechanical processing within these deformation conditions has good workability.
The power efficiency and instability maps for the two steels tested show almost similar profiles (Figs. 5 and 6). These results confirm that the deformation behaviour of the two steels investigated was relatively the same since no flow instability was observed within the tested conditions. The power dissipation and instability maps provide a quick, simple, efficient and accurate method of identifying safe processing windows [17]. Care should be taken when choosing processing conditions since high power dissipation efficiency may be due to flow instabilities [14]. Optimum working conditions are determined by the correlation of the deformation maps and microstructure.

Microstructural analysis
During the compression test, friction between the diework piece interfaces causes barrelling effect resulting in heterogeneous deformation in the specimen. The metalforming process causes a heterogeneous deformation, causing three distinct regions [39]. Figure 8 illustrates the three zones of the deformed sample during simulation using FEM Deform 3D software. The deformation regions are [53]: • Intense shear zone (Region I) This region is the most severely deformed region at the centre of the specimen.
• Dead metal zone (Region II) The region occurs at the die-work piece interface. The contact surfaces remain stationary during compression and have a low strain. • Moderate zone (Region III) This region is the outer lateral surface of the specimen, which experiences a relatively higher strain than Region II and has maximum tensile stress during deformation.
The microstructure evolution during forming of the two steels was analysed in three deformation zones, as shown by the different deformation regions in the FEM images (Fig. 8). prior austenite grain boundaries outline the deformed, elongated grains as shown in Fig. 9 a) at 850°C and 0.1 s −1 . This region had a high power efficiency η of 26%, indicating that a large amount of energy was consumed for the microstructure evolution [34]. At a higher strain rate of 10 s −1 and 850°C, the microstructure exhibited "pancaked" grains ( Fig. 9b). At higher temperatures and lower strain rates (1000°C and 0.1 s −1 ), the microstructure had elongated grains and grain boundaries (Fig. 9c). An increase in the strain rate to 10 s −1 and a temperature of 1000°C caused the microstructure to have a few elongated grains, as shown in Fig. 8d). At 1000°C, there were fewer elongated grains for a higher strain rate of 10 s −1 than at the low strain rate of 0.1 s −1 (Fig. 9). This characteristic behaviour might have occurred due to the lower amount of dissipation energy available for microstructure change. DRV was the only softening mechanism observed in the flow stress-strain curves. Region II showed well-defined austenite grain boundaries and lath martensite. The orientation of martensite laths differed between austenite grains at 850°C/0.1 s −1 , as shown in Fig. 10a. In the same region, for 850°C/10 s −1 , the microstructure showed pancaked prior austenite grains. At 1000°C, uniform lath martensite was seen at strain rates of 0.1 s −1 and 10 s −1 (Fig. 11). Under all deformation conditions, Region III exhibited uniform martensitic structure, as shown in Figs. 9 and 10. Region III experienced lower deformation than the other two regions. In this region, higher tensile stresses were expected to occur, thus causing cracking. However, the microstructure in this region did not show any form of cracks in this steel (Figs. 10and11).  Figure 12 shows the SEM-BSE micrographs of P92-B steel for Region I after hot deformation at 850°C and 1000°C for strain rates of 0.1 s −1 and 10 s −1 . The micrographs show that the microstructure exhibits lath martensite structures. At a lower strain rate of 0.1 s −1 and temperatures of 850°C and 1000°C, the microstructure had elongated grains due to DRV softening. At 850°C and 1000°C/0.1 s −1 deformation conditions, the power efficiency was between 16 and 19%, as shown in Fig. 7. Hence, the results show a stable deformation region. As the strain rate increased to 10 s −1 at 850°C and 1000°C, the microstructure exhibited elongated lath martensitic structure. These regions (850°C/10 s −1 and 1000°C/10 s −1 ) had the lowest power dissipation efficiency (< 8.5%). Thus, microstructure evolution took lower energy. Regardless of the low power dissipation efficiency, DRV was the only softening mechanism, also flow stress curves, as shown in Fig. 3. Region I (the intense shear zone) had a well-defined austenite grain (Fig. 12) and lath martensite under all deformation conditions. Region II (Dead metal Zone) at deformation conditions of 1000°C/ 0.1 s −1 and 10 s −1 , and also Region III for all the deformation conditions (850°C and 1000°C, strain rates of 0.1 s −1 and 10 s −1 ), there were similar elongated martensite laths (as shown Figs. 13and14). Region III experienced higher tensile stress that caused elongation of grains and lath boundaries perpendicular to the direction of deformation. Region II: For deformation conditions of 850°C/0.1 s −1 , the microstructure showed well-defined lath martensite, as shown in Fig. 13. This behaviour indicates that there was no change in lath orientation after deformation. As the strain rate increased to 10 s −1 , the microstructure showed grain elongation.

Conclusion
Hot uniaxial compression tests of two P92 steels conducted using Gleeble® 3500 thermal-mechanical equipment formed the basis of this study. The compression test conditions were: deformation temperature of 850-1000°C and strain rate of 0.1-10 s −1 . Experimental flow stress values were used to construct processing maps. From this study, these were the observations: 1. The flow stress-strain curves exhibited dynamic recovery behaviour for the two steels: the flow curves had work hardening and dynamic softening deformation mechanism. The flow stress increased with a decrease in deformation temperature or an increase in strain rate. These results show that the metal forming process is sensitive to the deformation conditions. 2. The correlation between the processing maps and the microstructure of the deformed samples revealed that the optimum processing window occurred at a lower strain rate (0.1 s −1 ) and deformation temperatures of 850°C and 1000°C for the two P92 steels. The results clearly show that variation in the chemical composition Region II Region III of the two steels investigated had minimal effect on flow behaviour. Therefore, the study confirmed that processing maps help to describe the complexity of metal flow patterns during forming. Hence, assist in identifying the optimum processing window. 3. Under this optimal condition, the microstructure showed well-defined grain boundaries and elongated (pancaked) grains for the two steels. The SEM-BSE micrographs of the deformed samples showed typical dynamic recov-ery characteristics. Under all the deformation conditions, DRV was the dominant softening mechanism. The flow stress-strain curves for the two P92 steel reflect this softening mechanism. 4. The study has shown the DMM technique can been effectively used for process parameter optimisation of P92 steel during industrial metal forming process in the manufacture of large boiler pipes.