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Review of Processing Maps and Development of Qualitative Processing Maps
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ScienceDirect Materials Today: Proceedings 4 (2017) 946–956
www.materialstoday.com/proceedings
5th International Conference of Materials Processing and Characterization (ICMPC 2016)
Review of Processing Maps and Development of Qualitative Processing Maps
A. Anitha Lakshmi a*, Ch.SrinivasaRaob, J.Gangadharc, Ch.Srinivasud, Swadesh Kumar Singh e, acde
b
Department of Mechanical Engineering, GRIET, Hyderabad, AP – India – 500090. Department of Mechanical Engineering, Andhra University, Visakhapatnam, AP, India-530003
Abstract Significant investigations in the area of theory of processing maps for hot working of different materials are reviewed. Special attention is focused on Dynamic Material Model, Power Dissipation Maps, Instability Maps, Hot Deformation Mechanisms, which are generally believed to be the dominant factors for determining processing maps at different temperatures and strain rates. The basic constitutive equation describing the process in which power is converted at any instant into different forms is presented along with a general survey of the numerous papers, investigating specific linear and nonlinear effects on these models. Estimates of the associated temperature ranges and strain rates are discussed, and a summary of relevant experimental results is given. Studies of the Hot Deformation Mechanisms like Dynamic Recrystallization (DRX), Super plastic Deformation, Dynamic recovery (DRY) are also surveyed. Methodology for development of qualitative processing maps for warm forming of different materials is discussed. © 2017 Published by Elsevier Ltd. Selection and peer-review under responsibility of Conference Committee Members of 5th International Conference of Materials Processing and Characterization (ICMPC 2016). Keywords:Dynamic Material Model, Power Dissipation Maps, Instability Maps, Dynamic Recrystallization (DRX), super plastic Deformation, Dynamic recovery (DRY)
1.
Introduction:
Mechanical processing is an essential step in shaping materials into engineering components which require not only dimensional accuracy but also specified microstructures and mechanical properties. The techniques of mechanical processing involve bulk metal working using rolling, forging, extrusion generally conducted at elevated temperatures in order that large strains may be imposed in asingle step of the operation without the onset of the fracture. The secondary metal working process generally use cold working which ensures good surface finish, high dimensional tolerance and better strength.
*Corresponding author. E-mail address: [email protected] 2214-7853 © 2017 Published by Elsevier Ltd. Selection and peer-review under responsibility of Conference Committee Members of 5th International Conference of Materials Processing and Characterization (ICMPC 2016).
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However processes like sheet metal working, cold forging, impact extrusion, coining, wire tube drawing involve smaller strains and require large number of steps with intermediate annealing to restore the ductility. In recent years, with the advent of rapid solidification processes and atomization techniques for producing powders of desired shape and size, powder metallurgy has assumed a significant role in shape making. Using this technique it is now possible to make complicated shapes with exotic alloys for critical applications like gas turbine components.Among all the mechanical processing methods, the bulk metal working stage is considered to be of primary importance. Firstly, in this stage major micro structural changes occur and have profound influence on the subsequent processing steps in view of the large tonnage of materials being processed by bulk metal working processes. The ultimate objective is to manufacture components with controlled micro structure and properties without macro or microstructural defects, on a repeatable basis in a manufacturing environment. Manufacturers are forever striving to reduce the cost of production and raw materials. Price slashing is becoming so dominant that quality is often sacrificed for other considerations. In order to deal with quality issues, industries need to use more effective design practices and adopt upstream design processes that enable them to deliver customized services and products at relatively lower cost. Historically, the design of metal-forming processes is based on expensive trial and error techniques. The geometry of the piece and the capability of the machine are the main considerations, while behavior of the materials is often ignored. This trial and error method is unsuitable for the production of small batches and newer materials, which has restricted work involving forming. It is to be emphasized that our Indian industries often handle small batches and newer materials. Hence, any scientific methodology explored and employed to optimize processing parameters to produce quality products at low cost is a significant research contribution to the area of manufacturing engineering. In recent years, however, the trial and error techniques are replaced by modelling techniques which are developed on the basis of science based principles. These techniques address the following design and manufacturing issues involved. The design requirements are: 1.Arriving at optimum processing conditions 2. Controlling the microstructure of the component 3.Designing optimum die shapes or performing geometry without restoring to shop floor trails 4.Obtaining the process limits for the design of control systems An optimization procedure has been proposed by Venugopal[1] for the selection of safe temperature zone for processing based on various technical parameters as given in figure 1(a). This procedure involves establishing the relationships between various process variables and properties of billet and tool materials.
The process variables are optimized based on correlation, empirical criteria and fracture models are proposed for the optimization of workability, in particularly cold workability. In this approach, compression tests are performed for establishing experimental fracture criteria for bulk forming processes. Compression test specimens are provided with small grid markings at the mid-height of the cylindrical surface. Measurements of the grid displacements at various stages of the test permit calculation of principal strains and stress histories. The test is performed by compressing a series of
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identical specimens in sequence to progressively larger reductions until fracture occurs. The locus of principal surface strains at fracture gives the limit for safe working. An example is given in figure 1(b) for cold deformation of 1045 steel. The straight-line relationship between principal compressive and tensile surface strains at fracture is a characteristic result of the ductile fracture process, and the line can be treated as a fracture criterion representing the workability of the material. Though these methods are better than the trial and error technique but they are tedious and expensive. Optimization of workability requires an understanding of the constitutive behavior of the material under processing conditions. Earlier, attempts have been made by Frost , Ashby and Raj to understand the effects of strain, strain rate, temperature and microstructure on the flow behavior of metals during deformation processing. They have developed maps that describe the deformation and fracture modes which occur during processing.In the Ashby maps [3] normalized shear stress is plotted against absolute temperature. Figure 2 gives a typical example of an Ashby Map.
The maps are divided into regimes, within each of which a particular mechanism is dominant. The regime boundaries are the loci of the points at which two mechanisms contribute equally to the overall strain rate. The contours of constant strain rate are superimposed on the fields and they show the net strain rate produced at given combination of stress and temperature. There are other kinds of maps with different axes like: (i) Shear strain rate and normalized shear stress with contours of temperature, (ii) axes of strain rate and temperature (or reciprocal temperature) with contours of constant stress. These maps can theoretically be constructed for any polycrystalline material, showing the area of dominance of each flow mechanism. Ashby and co-workers developed similar maps, which give domains of various fracture processes. Raj maps [4] are developed considering the failure mechanisms that can operate in a material over ranges of strain rate and temperature. These maps are useful for processing in the sense that they define the regions in which it is “safe” to process the work piece material and avoid defect nucleation. Raj Map for austenitic stainless steel is shown in figure 3. Both Ashby and Raj maps are deterministic since they use shear strain rate equations, which are valid for steady states. The equations depend on a number of basic atomic processes such as dislocation motion, diffusion, grain boundary sliding, twinning and phase transformations. Both the maps are limited to simple systems and cannot be applied to complex commercial alloys since in these materials it is not always possible to identify the atomistic mechanisms unequivocally.
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2. Description of processing Map: A Processing map is an explicit representation of the response of a material, in terms of microstructural mechanisms, to the imposed process parameters consisting of superimposition of power dissipationand an instability map. These are developed on the basis of the Dynamic materials model, essentially a continuum model built using the concepts of system engineering, extremum principles of irreversible thermodynamics. Dynamic material model processing maps [5] have shown potential for direct industrial application in arriving at optimum processing parameters. In this model, the work piece is considered to be a dissipator of power. The constitutive equation describes the manner in which the power is converted at any instant into two forms: thermal and micro structural, which are not recoverable by the system. The dissipator element is considered to be nonlinear, dynamic and irreversible. 2.1. Power dissipation maps: On the basis of the description of the work piece characteristics, the instantaneous response (σ) of the work piece material to the applied strain rate (έ) to impose a given plastic strain at constant temperature(T) and for a given M history is given by the dynamic constitutive equation: σ = K·έm/T,M (5) Here σ is the effective stress, έ is the effective strain rate and K & m are constants. The instantaneous total power dissipated will be given by a rectangle of area (σ.έ). The constitutive equation describes the path choosen by the system to reach the applied strain rate (limiting condition). A different strain rate will have different k and m values. The total power (p) consists of two complementary functions G content and J content P = G+J =σ.έ (6) Fig. 5 showsthe schematic representation of the constitutive equation in a non-linear power dissipator andan Ideal linear dissipator. For finding the instantaneous (dynamic) values of G and J for deformation at a temperature and strain rate, m is a constant as chosen by the system, while for different and widely varying strain rates, m may be dependent on sttrain rate. The physical interpretations of G and J are from the thermodynamic principles discussed by malvern[8]. The total power dissipated is related to the rate of entropy production [9]as: P = σ.έ=
di S dt
T≥ 0
(7) di S
Where T is temperature, is rate of entropy production and the inequality sign applies for dt irreversible deformation.A processing map is obtained by superimposition of the variationof efficiency of forming parameter with temperature and strain rate and the variation of instability parameter as a function of the same variables. The approach follows the “Dynamic Material Model” which considers the tool as a source of power and the material as a power dissipator; the total provided power is obtained by έ
σ
P = σ. έ = ∫0 σdέ + ∫0 έdσ (8) Where σ is the instantaneous stress and describes the response of the material to the applied strain rate (έ) for a given strain (ε). The first integral represents the temperature increase during deformation, while the second is the amount of power dissipated through metallurgical transformations such as recovery, phase transformations and material damage. The strain rate sensitivity values are used to calculate the efficiency of forging parameter. The parameter is mapped in order to recognize the best hot working regions in terms of temperature and strain rate defined as regions of high power dissipation. However the higher values sometimes correspond, to high levels of damage in the material. For this reason the instability maps have been introduced and they are based on the principles of irreversible thermodynamics for large plastic flows and consider the variation of entropy produced by the change of strain. The instability criteria, based on this assumption, permit to identify the regions of flow instability. The power partitioning between G and J is controlled by the constitutive flow behavior of the material and is decided by the strain rate
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sensitivity (m) of flow stress [4] dJ έdσ έσd ln σ ∆ log σ = = ≈ =m dG
σdέ
σέd ln έ
∆ log έ
(9)
And thus m is a power partioning factor. For the evaluation of an instantaneous value of J cocontent at each strain rate and temperature, m has a constant value corresponding to the limiting strain rate hence J is evaluted from the integral : σ σ J = ∫0 έdσ = ∫0 kσ(1/m)dσ (10) Where k is constants. By combining equation 10 with equation 5 we get mσέ J= m+1 (11) The matallurgical dissipation process may be characterized by the variation of J co-content with temperature and strain rate but normalization with the input power (σ.έ) sharpens the variation. Thus comparsion with a linear dissipatior (m=1)in which maximum possible dissipation through j co-content [Jmax = (σέ)/2], leads to the definition of a dimensionless parametre called efficiency of power dissipation, ɳ is given by: J 2m ɳ= = Jmax
m+1
(12) This parameter may be ploted as a function of temperature and strain rate to obtain the power dissipation map. The efficiency represents the relative rate of production of internal entropy during hot deformation and characterizes the dissipative microstructure under different temperatures and strain rate conditions. As the maps of Ashby’s and Raj’s are based on the atomistic theory, it is difficult to integrate them with continuum approaches. Also, process optimization is difficult to achieve, using these atomistic approaches. Though these developments have lead to the understanding of the mechanisms of hot deformation, it is difficult to use them directly for the design of deformation processes. A continuum approach has been therefore developed by Prasad and is briefly described below.
5. Instability Maps: The stability condition described in the Dynamic Materials Models is considered by Ziegler[9]. Stable flow will occur if the differential quotient satisfies the inequality. dD D > (13) dR R Where R = √έ.έ and D is the dissipative function which represents the constitutive behavior of the material. Since J determines the dissipation through metallurgical processes, the dissipation function related to metallurgical stability is given by J and by putting D = J in the above equation. One gets the condition for microstructural stability at a constant temperature in terms of a dimensionless parameter ξ (έ), given by ξ(έ) = (∂ ln (m/(m + 1))/(∂ ln έ ) + m > 0
(14)
Theξ(έ) parameter may be evaluated as a function of temperature and strain rate to obtain an instability map, where metallurgical instability during plastic flow occur in regimes where ξ (έ) is negative. The well-known flow instabilities are dynamic strain aging, adiabatic shear bands, flow localization, mechanical twinning and flow rotations. The presence of these instabilities in the microstructure of the component will have to be avoided by keeping away from the processing conditions of the unstable regimes.
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7. Processing maps for various Ferrous and Non –Ferrous materials: 304L stainless steel: 304L stainless steel is widely used in industry, not only for its superior corrosion resistance but also for its excellent formability and mechanical behaviour. Because the behaviour of this material is affected strongly by many processing parameters and different loading conditions.Many investigators have studied the changes in 304L stainless steel material behaviour and microstructure under different conditions. Under low strain rate conditions, standard mechanical properties have been obtained by tensile, compressive, plane-strain testing or using such similar tests [10 – 14]. For example, Semiatin and Holbrook [12] studied the isothermal plastic flow behaviour of annealed 304L stainless steel in uniaxial compression and torsional modes of deformation at strain rates ranging from 10-4to 10-1 s-1 under a wide temperature range. Venugopal et al. [13]and Sundaraman et al. [14] discussed the workability andmicrostructure of 304L stainless steel at low strainrates.
The overlap of power dissipation map and instability map at strain of 0.3 is presented in figure 4. The Dynamic recrystallization (DRX) in the temperatures range of 1000- 1200ºC and strain rates in the range of 0.02-2 s-1, with a peak efficiency of 29% occurring at 1125º C and 0.1 s-1, The Dynamic recovery (DRY) at a temperature of 850 °C and strain rate 0.001 s-1with an efficiency of about 31%, The Grain growth occurs at temperatures higher than 1000 °C and strain rates lower than 0.01 s-1 . Flow instabilities occur at temperatures and strain rates diagonally above the DRX and DRY domains. In different regions, these are manifested as dynamicstrain ageing, adiabatic shear-band formation,flow localization and ferrite formation is shown in figure 5. Nickel base super alloy Nickel based super alloys are an unusual class of metallic materials with an exceptional combination of high temperature strength, toughness, and resistance to degradation in corrosive or oxidizing environments. These materials are widely used in aircraft and power-generation turbines, rocket engines, and other challenging environments, including nuclear power and chemical processing plants. Intensive alloy and process development activities during the past few decades have resulted in alloys that can tolerate average temperatures of 10500C with occasional excursions (or local hot spots near airfoil tips) to temperatures as high as 12000C[15], which is approximately 90% of the melting point of the material.
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On the basis of hot deformation microstructural studies as in Fig. 6, it can be concluded that DRX occurs at the temperatures in the range of 1100–1150 ºC and strain rates in the range 0.01–0.001 s-1, with a peak efficiency of 56% occurring at about 1125 ºC and 0.001 s-1. Thus, the full recrystallization region can be identified in Figure.7. Wrought 2205 duplex stainless steel: Duplex stainless steels with an excellent combination of mechanical properties and corrosion resistance are attractive alternatives to the single-phase austenite and ferritic grades [16–21]. As a member in the family of the duplex stainless steels, 2205 steel is the most popular material for thick walled pipes large in diameter for oil extraction, papermanufacturing and chemical industries [2223]. In the pipe production process, in order to obtain high production rate, the casting billets usually are hot processed to forging blanks by rough forge at the beginning and subsequently processed by hot-forge at finishing [24]. Even the processing of the wrought steels still requires special care due to poor hot workabilityresulting in presence of cracks when hot working parameters are not in the optimum conditions [25–27]. According to reference [28], a different mechanical behaviour of a 23Cr–4.8Ni–1.3Mn–0.1N duplex stainless steel has been found between as-cast and wrought condition during hot working. Processing maps exhibits peak efficiency of about 44% occurring at 1273 K and strain rate 0.01s1 and 50% occurring at 1423 K and 0.01 s-1. Generally, the domain with peak efficiency, in principle, may be interpreted to correspond DRX [29-31].The processing map of wrought 2205 duplex stainless steel at strains of 1.0, may be considered. It is possible to represent steady-state flow and provide much more information on the deformation behaviour under this strain. The numbers against each contour represent the efficiency of power dissipation in percent and shaded regions correspond to unstable hot deformation domains as shown in figure 8. The processing maps for different strains exhibit similar characteristics. Qualitative processing Maps: Formability of sheet metals is described by constructing forming limit diagrams (FLD). Factors affecting the forming limit curve are strain hardening, rate sensitivity, ductile fracture, inhomogeneity and anisotropy. The forming limit curve intercepts the major strain axis at approximately the value of the strain-hardening index n. As n decreases, the height of the curve will also decrease as shown in figure 9. Processes in which biaxial stretching is required to make the part usually demand fully annealed, high n sheet; unfortunately, materials with a high n usually have a low initial strength [32]. Many strengthening processes, particularly coldworking, will drastically reduce n and this will make forming more difficult. It is found that as n → 0, the plane strain forming limit along the vertical axis will tend to zero, however, along the equal biaxial direction (the right-hand diagonal) for which ε1 = ε2, the forming limit is not zero and
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fully cold-worked sheet can be stretched in biaxial tension, but not in any other processes. Except in drawing processes with high negative minor strain, i.e. ε2 ≈ −ε1, strain-hardening is usually the most important factor affecting formability.Rate sensitivity will not affect the strain at which the tension reaches a maximum, but it will influence the rate of growth of a neck.In biaxial stretching, it has been shown that necking is a gradual process beyond the maximum tension condition and is controlled by the shape of the yield locus. The forming limit curve for a material with high rate sensitivity could intercept the major strain axis at a strain greater than n.
Inhomogeneity has not been well characterized in typical sheet. It may beexpected that the greater the imperfection, the lower will be the limit strain so that with large imperfections, the plane strain limit strain may be less than the trainhardeningindex n.In the tensile test, stress strain data can only be obtained up to the onset of diffuse necking,i.e. up to an effective strain ε ≤ n. The envelope of this strain is shown in Figure.10 and it may be seen that local necking occurs at strains rather greater than this. In manyanalyses, the tensile data is extrapolated, assuming that the strain-hardening index remainsthe same at high strains. This may not be the case and caution should be exercised.There may also be an interaction between material properties in the way that theyinfluence the forming limit curve. In Figure 11, we can see with increasingstrain-hardening index may not increase the forming limits in all forming paths, if thechange in, n, is an accompanied by a reduction in the fracture strain. As seen here, fracturewill reduce the forming limit in equal biaxial tension, even though the forming limit isincreased in other regions by an increase in the strain-hardening index. In the lubricated Olsen and Erichsen tests in which sheet is stretched over a well-lubricated hemisphericalpunch, failure occurs nearly in biaxial tension; in comparing some materials, differencesmay be due to different fracture properties rather than differences in strain-hardening.
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By taking all these factors into account a forming window has to identified in which plane stress sheet forming is possible as shown in figure 12.
Forming limit diagrams are constructed for isothermal problems at variable temperatures and neglects phase transformation and martensitic transformation at higher pressures. The wrinkling phenomenon cannot be predicted from FLD which is an important factor affecting surface quality. The qualitative processing maps are three dimensional maps constructed with major strain as first axis, minor strain as second axis and temperature as the third axis to give the perfect forming window. Conclusions: Processing maps are applied to industrial metal working processes for newer materials by designing the process to suit the constitutive requirements of the material from view point of optimum workability and microstructural control. Processing maps are used for optimizing the existing processes and establishing proper process control to improve product quality and yield. The application of processing maps is to design and optimize bulk metal working processes to various metals and alloys. Validation of processing maps for 304L stainless steel using hot forging, rolling and extrusion are done by correlating with the microstructural studies conducted on products formed at different temperatures and strain rates using industrial processing operations. Hot deformation behaviour of a Ni-base alloy is characterized by developing processing maps based on variations of efficiency of power dissipation with temperature and strain rate. Processing map on a wrought 2205 duplex stainless steel under hot compression conditions has been developed based on the dynamic material model theories in the range 1223–1473 K and 0.01–10 s-1.The hot deformation characteristics of wrought 2205 duplex stainless steel have been studied using processing map in combination of microstructural observations. The shear processing map was developed in order to determine the optimum processing condition, which was found to be 300 oC and 1.2 – 10-3 s-1. Domains of the processing map are also interpreted on the basis of the associated microstructural observations. It was found that the post-deformation microstructure is sensitive to the Zener–Holloman parameter, so that DRX was encouraged with decreasing Z-value.The hot deformation behaviour and microstructure evolution of twin-roll-cast of Mg–2.9Al–0.9Zn–0.4Mn (AZ31) alloy has been studied using the processing map. Processing map for twin-roll-cast AZ31 alloy has been obtained at the hot working temperature range of 150–400 0C and the strain rate range from0.0004 to4s-1. The different efficiency domains and flow instability region corresponding to various microstructural characteristics have been identified.
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Acknowledgement: The financial support received for this research work from Science and Engineering Research Board(SERB),Department of Science and Technology(DST), Government of India, SR/S3/MERC/0129/2012, is gratefully acknowledged. REFERENCES: [1] Venugopal. Optimization of workability and control of microstructures in deformation
processing of Austenitic
stainless steels: Development and application of processing maps for stainless steels type AISI 304 and 316 L. PhD thesis, Indian Institute of Technology Madras, Chennai. 1981. [2] Khun, P.W. Lee, T. Erturk. A fracture criterion for cold forming. Eng. Mater. Technol. 1973; [3]Frost, M.F. Ashby. Deformation mechanism maps.1982. [4] R. Raj. Development of processing maps of use in warm forming and hot forming processes. Metall. Trans. 1981; A12; 1089. [5] Y.V.R.K. Prasad, T. Seshacharyulu. Modeling of hot deformation for microstructural control. Int. Mater. Rev. 1998; 43; 243–258. [6] H.L. Gegel, J.C. Malas, S.M. Doraivelu, Innovations in materials processing. Plenum Press, New York. 1985; 137. [7] W. Roberts. Deformation Processing and Structure.ASM, Metals Park, OH.1984; 109. [8] L.E. Malvern. Introduction to the mechanics of continuous medium.Prentice-Hall. Eaglewood Cliffs. N J. 1969; 197. [9] H.J. McQueen, E. Evangelista, N.D. Ryan, Proc. Recrystallization, TMS-AIME, warrendale.Pa.1990. [10] S.Venugopal Validation of processing maps for 304L stainless steel using hot forging, rolling and extrusion. [11] CaiDayong characterization of hot deformation behavior of a Ni-base super alloy using processing map [12] R. Schafrik, C. Sprague. “Saga of Gas Turbine Materials: Part III”. Advance Materials and Processes. May 2004; 162; 27–30. [13] Lei Chen. Processing map for hot working characteristics of a wrought 2205 duplex stainless steel [14] J.O. Nilson. Super duplex stainless steels. Mater Sci Technol. 1992; 8; 685–700. [15] R.M, Davison, J.D Redmond. A guide to using duplex stainless steels. Mater Des.1991; 12; 187–92. [16] V.S. Moura, L.D. Lima, J.M. Pardal, A.Y. Kina, R.R.A. Corte, S.SM. Tavares. Influence of microstructure on the corrosion resistance of the duplex stainless steel UNSS31803.Mater Characterisation.2008; 5; 127–32. [17] G. Berglund, P. Wilhelm son. Fabrication and practical experience of duplex stainless steels. Mater Des.1989; 10; 23– 28. [18] E. Evangelista, H.J. McQueen, M Niewczas, M. Cabibbo. Hot workability of 2304 and 2205 duplex stainless steels. Can Metall Quarterly. 2004; 43; 339–54. [19] J.M. Cabrera, A. Mateo, L. Lanes, J.M. Prado, M. Anglada. Hot deformation of duplex stainless steels. J Mater Proc Technol. 2003; [20] G.S. Reis Jr, AMJ, O.Balancin. Influence on the microstructure of duplex stainless steels on their failure characteristics during hot deformation. Mater Res. 2000; 3(2); [21] A. Dehghan-Manshadi, M.R. Barnett, P.D. Hodgson. Microstructural evolution during hot deformation of duplex stainless steel. Mater Sci Technol. 2007; 23; 1478–84. [22] A. Iza-Mendia, A. Piñol-Juez, J.J. Urcola, I. Gutiérrez. Microstructural and mechanical behavior of a duplex stainless steel under hot working conditions. Metall Mater Trans. 1998; 29; 2975–85. [23] M karami, Hot deformation constitutive analysis and processing map of extruded Mg-12Li-1Zn bcc alloy [24] S.A. Torbati-Sarraf, R. Mahmudi. Microstructure and mechanical properties of extruded and ECAPed AZ31 Mg alloy, grain refined with Al–Ti–C master alloy. Mater Sci Eng. 2010; A527; 3515–20.
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[25] M. Karami, R. Mahmudi. Shear punch super plasticity in equal-channel angularly pressed Mg–12Li–1Zn alloy. Mater Sci Eng. 2013; A576; 156–9. [26] N. Srinivasan, Y.V.R.K. Prasad, K.P. Rao. Hot deformation behavior of Mg–3Al alloy– a study using processing map. Mater Sci Eng. 2008; A476; 146–56. [27] W.P.Peng, Hot deformation behavior and microstructure evolution of twin-roll-cast Mg–2.9Al–0.9Zn alloy. [28] S.E. Ion, F.J. Humphreys, S.H. White. Acta Mater. 1982; 30; 1909–1919. [29] Galiyev, R.O. Kaybishev, G. Gottstein, Acta Mater. 2001; 49; 1199-1207. [30] Y.V.R.K. Prasad, Processing maps for hot deformation of rolled AZ31 magnesium alloy plate: Anistropy of hot workability. [31] Juan Liu, Analysis of metal workability by integration of FEM and 3-D processing maps of magnesium alloy AZ31B [32] Z. Marciniak , J.L. Duncan., S.J. HU Mechanics of sheet Metal Formin.
ScienceDirect Materials Today: Proceedings 4 (2017) 946–956
www.materialstoday.com/proceedings
5th International Conference of Materials Processing and Characterization (ICMPC 2016)
Review of Processing Maps and Development of Qualitative Processing Maps
A. Anitha Lakshmi a*, Ch.SrinivasaRaob, J.Gangadharc, Ch.Srinivasud, Swadesh Kumar Singh e, acde
b
Department of Mechanical Engineering, GRIET, Hyderabad, AP – India – 500090. Department of Mechanical Engineering, Andhra University, Visakhapatnam, AP, India-530003
Abstract Significant investigations in the area of theory of processing maps for hot working of different materials are reviewed. Special attention is focused on Dynamic Material Model, Power Dissipation Maps, Instability Maps, Hot Deformation Mechanisms, which are generally believed to be the dominant factors for determining processing maps at different temperatures and strain rates. The basic constitutive equation describing the process in which power is converted at any instant into different forms is presented along with a general survey of the numerous papers, investigating specific linear and nonlinear effects on these models. Estimates of the associated temperature ranges and strain rates are discussed, and a summary of relevant experimental results is given. Studies of the Hot Deformation Mechanisms like Dynamic Recrystallization (DRX), Super plastic Deformation, Dynamic recovery (DRY) are also surveyed. Methodology for development of qualitative processing maps for warm forming of different materials is discussed. © 2017 Published by Elsevier Ltd. Selection and peer-review under responsibility of Conference Committee Members of 5th International Conference of Materials Processing and Characterization (ICMPC 2016). Keywords:Dynamic Material Model, Power Dissipation Maps, Instability Maps, Dynamic Recrystallization (DRX), super plastic Deformation, Dynamic recovery (DRY)
1.
Introduction:
Mechanical processing is an essential step in shaping materials into engineering components which require not only dimensional accuracy but also specified microstructures and mechanical properties. The techniques of mechanical processing involve bulk metal working using rolling, forging, extrusion generally conducted at elevated temperatures in order that large strains may be imposed in asingle step of the operation without the onset of the fracture. The secondary metal working process generally use cold working which ensures good surface finish, high dimensional tolerance and better strength.
*Corresponding author. E-mail address: [email protected] 2214-7853 © 2017 Published by Elsevier Ltd. Selection and peer-review under responsibility of Conference Committee Members of 5th International Conference of Materials Processing and Characterization (ICMPC 2016).
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However processes like sheet metal working, cold forging, impact extrusion, coining, wire tube drawing involve smaller strains and require large number of steps with intermediate annealing to restore the ductility. In recent years, with the advent of rapid solidification processes and atomization techniques for producing powders of desired shape and size, powder metallurgy has assumed a significant role in shape making. Using this technique it is now possible to make complicated shapes with exotic alloys for critical applications like gas turbine components.Among all the mechanical processing methods, the bulk metal working stage is considered to be of primary importance. Firstly, in this stage major micro structural changes occur and have profound influence on the subsequent processing steps in view of the large tonnage of materials being processed by bulk metal working processes. The ultimate objective is to manufacture components with controlled micro structure and properties without macro or microstructural defects, on a repeatable basis in a manufacturing environment. Manufacturers are forever striving to reduce the cost of production and raw materials. Price slashing is becoming so dominant that quality is often sacrificed for other considerations. In order to deal with quality issues, industries need to use more effective design practices and adopt upstream design processes that enable them to deliver customized services and products at relatively lower cost. Historically, the design of metal-forming processes is based on expensive trial and error techniques. The geometry of the piece and the capability of the machine are the main considerations, while behavior of the materials is often ignored. This trial and error method is unsuitable for the production of small batches and newer materials, which has restricted work involving forming. It is to be emphasized that our Indian industries often handle small batches and newer materials. Hence, any scientific methodology explored and employed to optimize processing parameters to produce quality products at low cost is a significant research contribution to the area of manufacturing engineering. In recent years, however, the trial and error techniques are replaced by modelling techniques which are developed on the basis of science based principles. These techniques address the following design and manufacturing issues involved. The design requirements are: 1.Arriving at optimum processing conditions 2. Controlling the microstructure of the component 3.Designing optimum die shapes or performing geometry without restoring to shop floor trails 4.Obtaining the process limits for the design of control systems An optimization procedure has been proposed by Venugopal[1] for the selection of safe temperature zone for processing based on various technical parameters as given in figure 1(a). This procedure involves establishing the relationships between various process variables and properties of billet and tool materials.
The process variables are optimized based on correlation, empirical criteria and fracture models are proposed for the optimization of workability, in particularly cold workability. In this approach, compression tests are performed for establishing experimental fracture criteria for bulk forming processes. Compression test specimens are provided with small grid markings at the mid-height of the cylindrical surface. Measurements of the grid displacements at various stages of the test permit calculation of principal strains and stress histories. The test is performed by compressing a series of
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identical specimens in sequence to progressively larger reductions until fracture occurs. The locus of principal surface strains at fracture gives the limit for safe working. An example is given in figure 1(b) for cold deformation of 1045 steel. The straight-line relationship between principal compressive and tensile surface strains at fracture is a characteristic result of the ductile fracture process, and the line can be treated as a fracture criterion representing the workability of the material. Though these methods are better than the trial and error technique but they are tedious and expensive. Optimization of workability requires an understanding of the constitutive behavior of the material under processing conditions. Earlier, attempts have been made by Frost , Ashby and Raj to understand the effects of strain, strain rate, temperature and microstructure on the flow behavior of metals during deformation processing. They have developed maps that describe the deformation and fracture modes which occur during processing.In the Ashby maps [3] normalized shear stress is plotted against absolute temperature. Figure 2 gives a typical example of an Ashby Map.
The maps are divided into regimes, within each of which a particular mechanism is dominant. The regime boundaries are the loci of the points at which two mechanisms contribute equally to the overall strain rate. The contours of constant strain rate are superimposed on the fields and they show the net strain rate produced at given combination of stress and temperature. There are other kinds of maps with different axes like: (i) Shear strain rate and normalized shear stress with contours of temperature, (ii) axes of strain rate and temperature (or reciprocal temperature) with contours of constant stress. These maps can theoretically be constructed for any polycrystalline material, showing the area of dominance of each flow mechanism. Ashby and co-workers developed similar maps, which give domains of various fracture processes. Raj maps [4] are developed considering the failure mechanisms that can operate in a material over ranges of strain rate and temperature. These maps are useful for processing in the sense that they define the regions in which it is “safe” to process the work piece material and avoid defect nucleation. Raj Map for austenitic stainless steel is shown in figure 3. Both Ashby and Raj maps are deterministic since they use shear strain rate equations, which are valid for steady states. The equations depend on a number of basic atomic processes such as dislocation motion, diffusion, grain boundary sliding, twinning and phase transformations. Both the maps are limited to simple systems and cannot be applied to complex commercial alloys since in these materials it is not always possible to identify the atomistic mechanisms unequivocally.
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2. Description of processing Map: A Processing map is an explicit representation of the response of a material, in terms of microstructural mechanisms, to the imposed process parameters consisting of superimposition of power dissipationand an instability map. These are developed on the basis of the Dynamic materials model, essentially a continuum model built using the concepts of system engineering, extremum principles of irreversible thermodynamics. Dynamic material model processing maps [5] have shown potential for direct industrial application in arriving at optimum processing parameters. In this model, the work piece is considered to be a dissipator of power. The constitutive equation describes the manner in which the power is converted at any instant into two forms: thermal and micro structural, which are not recoverable by the system. The dissipator element is considered to be nonlinear, dynamic and irreversible. 2.1. Power dissipation maps: On the basis of the description of the work piece characteristics, the instantaneous response (σ) of the work piece material to the applied strain rate (έ) to impose a given plastic strain at constant temperature(T) and for a given M history is given by the dynamic constitutive equation: σ = K·έm/T,M (5) Here σ is the effective stress, έ is the effective strain rate and K & m are constants. The instantaneous total power dissipated will be given by a rectangle of area (σ.έ). The constitutive equation describes the path choosen by the system to reach the applied strain rate (limiting condition). A different strain rate will have different k and m values. The total power (p) consists of two complementary functions G content and J content P = G+J =σ.έ (6) Fig. 5 showsthe schematic representation of the constitutive equation in a non-linear power dissipator andan Ideal linear dissipator. For finding the instantaneous (dynamic) values of G and J for deformation at a temperature and strain rate, m is a constant as chosen by the system, while for different and widely varying strain rates, m may be dependent on sttrain rate. The physical interpretations of G and J are from the thermodynamic principles discussed by malvern[8]. The total power dissipated is related to the rate of entropy production [9]as: P = σ.έ=
di S dt
T≥ 0
(7) di S
Where T is temperature, is rate of entropy production and the inequality sign applies for dt irreversible deformation.A processing map is obtained by superimposition of the variationof efficiency of forming parameter with temperature and strain rate and the variation of instability parameter as a function of the same variables. The approach follows the “Dynamic Material Model” which considers the tool as a source of power and the material as a power dissipator; the total provided power is obtained by έ
σ
P = σ. έ = ∫0 σdέ + ∫0 έdσ (8) Where σ is the instantaneous stress and describes the response of the material to the applied strain rate (έ) for a given strain (ε). The first integral represents the temperature increase during deformation, while the second is the amount of power dissipated through metallurgical transformations such as recovery, phase transformations and material damage. The strain rate sensitivity values are used to calculate the efficiency of forging parameter. The parameter is mapped in order to recognize the best hot working regions in terms of temperature and strain rate defined as regions of high power dissipation. However the higher values sometimes correspond, to high levels of damage in the material. For this reason the instability maps have been introduced and they are based on the principles of irreversible thermodynamics for large plastic flows and consider the variation of entropy produced by the change of strain. The instability criteria, based on this assumption, permit to identify the regions of flow instability. The power partitioning between G and J is controlled by the constitutive flow behavior of the material and is decided by the strain rate
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sensitivity (m) of flow stress [4] dJ έdσ έσd ln σ ∆ log σ = = ≈ =m dG
σdέ
σέd ln έ
∆ log έ
(9)
And thus m is a power partioning factor. For the evaluation of an instantaneous value of J cocontent at each strain rate and temperature, m has a constant value corresponding to the limiting strain rate hence J is evaluted from the integral : σ σ J = ∫0 έdσ = ∫0 kσ(1/m)dσ (10) Where k is constants. By combining equation 10 with equation 5 we get mσέ J= m+1 (11) The matallurgical dissipation process may be characterized by the variation of J co-content with temperature and strain rate but normalization with the input power (σ.έ) sharpens the variation. Thus comparsion with a linear dissipatior (m=1)in which maximum possible dissipation through j co-content [Jmax = (σέ)/2], leads to the definition of a dimensionless parametre called efficiency of power dissipation, ɳ is given by: J 2m ɳ= = Jmax
m+1
(12) This parameter may be ploted as a function of temperature and strain rate to obtain the power dissipation map. The efficiency represents the relative rate of production of internal entropy during hot deformation and characterizes the dissipative microstructure under different temperatures and strain rate conditions. As the maps of Ashby’s and Raj’s are based on the atomistic theory, it is difficult to integrate them with continuum approaches. Also, process optimization is difficult to achieve, using these atomistic approaches. Though these developments have lead to the understanding of the mechanisms of hot deformation, it is difficult to use them directly for the design of deformation processes. A continuum approach has been therefore developed by Prasad and is briefly described below.
5. Instability Maps: The stability condition described in the Dynamic Materials Models is considered by Ziegler[9]. Stable flow will occur if the differential quotient satisfies the inequality. dD D > (13) dR R Where R = √έ.έ and D is the dissipative function which represents the constitutive behavior of the material. Since J determines the dissipation through metallurgical processes, the dissipation function related to metallurgical stability is given by J and by putting D = J in the above equation. One gets the condition for microstructural stability at a constant temperature in terms of a dimensionless parameter ξ (έ), given by ξ(έ) = (∂ ln (m/(m + 1))/(∂ ln έ ) + m > 0
(14)
Theξ(έ) parameter may be evaluated as a function of temperature and strain rate to obtain an instability map, where metallurgical instability during plastic flow occur in regimes where ξ (έ) is negative. The well-known flow instabilities are dynamic strain aging, adiabatic shear bands, flow localization, mechanical twinning and flow rotations. The presence of these instabilities in the microstructure of the component will have to be avoided by keeping away from the processing conditions of the unstable regimes.
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7. Processing maps for various Ferrous and Non –Ferrous materials: 304L stainless steel: 304L stainless steel is widely used in industry, not only for its superior corrosion resistance but also for its excellent formability and mechanical behaviour. Because the behaviour of this material is affected strongly by many processing parameters and different loading conditions.Many investigators have studied the changes in 304L stainless steel material behaviour and microstructure under different conditions. Under low strain rate conditions, standard mechanical properties have been obtained by tensile, compressive, plane-strain testing or using such similar tests [10 – 14]. For example, Semiatin and Holbrook [12] studied the isothermal plastic flow behaviour of annealed 304L stainless steel in uniaxial compression and torsional modes of deformation at strain rates ranging from 10-4to 10-1 s-1 under a wide temperature range. Venugopal et al. [13]and Sundaraman et al. [14] discussed the workability andmicrostructure of 304L stainless steel at low strainrates.
The overlap of power dissipation map and instability map at strain of 0.3 is presented in figure 4. The Dynamic recrystallization (DRX) in the temperatures range of 1000- 1200ºC and strain rates in the range of 0.02-2 s-1, with a peak efficiency of 29% occurring at 1125º C and 0.1 s-1, The Dynamic recovery (DRY) at a temperature of 850 °C and strain rate 0.001 s-1with an efficiency of about 31%, The Grain growth occurs at temperatures higher than 1000 °C and strain rates lower than 0.01 s-1 . Flow instabilities occur at temperatures and strain rates diagonally above the DRX and DRY domains. In different regions, these are manifested as dynamicstrain ageing, adiabatic shear-band formation,flow localization and ferrite formation is shown in figure 5. Nickel base super alloy Nickel based super alloys are an unusual class of metallic materials with an exceptional combination of high temperature strength, toughness, and resistance to degradation in corrosive or oxidizing environments. These materials are widely used in aircraft and power-generation turbines, rocket engines, and other challenging environments, including nuclear power and chemical processing plants. Intensive alloy and process development activities during the past few decades have resulted in alloys that can tolerate average temperatures of 10500C with occasional excursions (or local hot spots near airfoil tips) to temperatures as high as 12000C[15], which is approximately 90% of the melting point of the material.
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On the basis of hot deformation microstructural studies as in Fig. 6, it can be concluded that DRX occurs at the temperatures in the range of 1100–1150 ºC and strain rates in the range 0.01–0.001 s-1, with a peak efficiency of 56% occurring at about 1125 ºC and 0.001 s-1. Thus, the full recrystallization region can be identified in Figure.7. Wrought 2205 duplex stainless steel: Duplex stainless steels with an excellent combination of mechanical properties and corrosion resistance are attractive alternatives to the single-phase austenite and ferritic grades [16–21]. As a member in the family of the duplex stainless steels, 2205 steel is the most popular material for thick walled pipes large in diameter for oil extraction, papermanufacturing and chemical industries [2223]. In the pipe production process, in order to obtain high production rate, the casting billets usually are hot processed to forging blanks by rough forge at the beginning and subsequently processed by hot-forge at finishing [24]. Even the processing of the wrought steels still requires special care due to poor hot workabilityresulting in presence of cracks when hot working parameters are not in the optimum conditions [25–27]. According to reference [28], a different mechanical behaviour of a 23Cr–4.8Ni–1.3Mn–0.1N duplex stainless steel has been found between as-cast and wrought condition during hot working. Processing maps exhibits peak efficiency of about 44% occurring at 1273 K and strain rate 0.01s1 and 50% occurring at 1423 K and 0.01 s-1. Generally, the domain with peak efficiency, in principle, may be interpreted to correspond DRX [29-31].The processing map of wrought 2205 duplex stainless steel at strains of 1.0, may be considered. It is possible to represent steady-state flow and provide much more information on the deformation behaviour under this strain. The numbers against each contour represent the efficiency of power dissipation in percent and shaded regions correspond to unstable hot deformation domains as shown in figure 8. The processing maps for different strains exhibit similar characteristics. Qualitative processing Maps: Formability of sheet metals is described by constructing forming limit diagrams (FLD). Factors affecting the forming limit curve are strain hardening, rate sensitivity, ductile fracture, inhomogeneity and anisotropy. The forming limit curve intercepts the major strain axis at approximately the value of the strain-hardening index n. As n decreases, the height of the curve will also decrease as shown in figure 9. Processes in which biaxial stretching is required to make the part usually demand fully annealed, high n sheet; unfortunately, materials with a high n usually have a low initial strength [32]. Many strengthening processes, particularly coldworking, will drastically reduce n and this will make forming more difficult. It is found that as n → 0, the plane strain forming limit along the vertical axis will tend to zero, however, along the equal biaxial direction (the right-hand diagonal) for which ε1 = ε2, the forming limit is not zero and
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fully cold-worked sheet can be stretched in biaxial tension, but not in any other processes. Except in drawing processes with high negative minor strain, i.e. ε2 ≈ −ε1, strain-hardening is usually the most important factor affecting formability.Rate sensitivity will not affect the strain at which the tension reaches a maximum, but it will influence the rate of growth of a neck.In biaxial stretching, it has been shown that necking is a gradual process beyond the maximum tension condition and is controlled by the shape of the yield locus. The forming limit curve for a material with high rate sensitivity could intercept the major strain axis at a strain greater than n.
Inhomogeneity has not been well characterized in typical sheet. It may beexpected that the greater the imperfection, the lower will be the limit strain so that with large imperfections, the plane strain limit strain may be less than the trainhardeningindex n.In the tensile test, stress strain data can only be obtained up to the onset of diffuse necking,i.e. up to an effective strain ε ≤ n. The envelope of this strain is shown in Figure.10 and it may be seen that local necking occurs at strains rather greater than this. In manyanalyses, the tensile data is extrapolated, assuming that the strain-hardening index remainsthe same at high strains. This may not be the case and caution should be exercised.There may also be an interaction between material properties in the way that theyinfluence the forming limit curve. In Figure 11, we can see with increasingstrain-hardening index may not increase the forming limits in all forming paths, if thechange in, n, is an accompanied by a reduction in the fracture strain. As seen here, fracturewill reduce the forming limit in equal biaxial tension, even though the forming limit isincreased in other regions by an increase in the strain-hardening index. In the lubricated Olsen and Erichsen tests in which sheet is stretched over a well-lubricated hemisphericalpunch, failure occurs nearly in biaxial tension; in comparing some materials, differencesmay be due to different fracture properties rather than differences in strain-hardening.
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By taking all these factors into account a forming window has to identified in which plane stress sheet forming is possible as shown in figure 12.
Forming limit diagrams are constructed for isothermal problems at variable temperatures and neglects phase transformation and martensitic transformation at higher pressures. The wrinkling phenomenon cannot be predicted from FLD which is an important factor affecting surface quality. The qualitative processing maps are three dimensional maps constructed with major strain as first axis, minor strain as second axis and temperature as the third axis to give the perfect forming window. Conclusions: Processing maps are applied to industrial metal working processes for newer materials by designing the process to suit the constitutive requirements of the material from view point of optimum workability and microstructural control. Processing maps are used for optimizing the existing processes and establishing proper process control to improve product quality and yield. The application of processing maps is to design and optimize bulk metal working processes to various metals and alloys. Validation of processing maps for 304L stainless steel using hot forging, rolling and extrusion are done by correlating with the microstructural studies conducted on products formed at different temperatures and strain rates using industrial processing operations. Hot deformation behaviour of a Ni-base alloy is characterized by developing processing maps based on variations of efficiency of power dissipation with temperature and strain rate. Processing map on a wrought 2205 duplex stainless steel under hot compression conditions has been developed based on the dynamic material model theories in the range 1223–1473 K and 0.01–10 s-1.The hot deformation characteristics of wrought 2205 duplex stainless steel have been studied using processing map in combination of microstructural observations. The shear processing map was developed in order to determine the optimum processing condition, which was found to be 300 oC and 1.2 – 10-3 s-1. Domains of the processing map are also interpreted on the basis of the associated microstructural observations. It was found that the post-deformation microstructure is sensitive to the Zener–Holloman parameter, so that DRX was encouraged with decreasing Z-value.The hot deformation behaviour and microstructure evolution of twin-roll-cast of Mg–2.9Al–0.9Zn–0.4Mn (AZ31) alloy has been studied using the processing map. Processing map for twin-roll-cast AZ31 alloy has been obtained at the hot working temperature range of 150–400 0C and the strain rate range from0.0004 to4s-1. The different efficiency domains and flow instability region corresponding to various microstructural characteristics have been identified.
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Acknowledgement: The financial support received for this research work from Science and Engineering Research Board(SERB),Department of Science and Technology(DST), Government of India, SR/S3/MERC/0129/2012, is gratefully acknowledged. REFERENCES: [1] Venugopal. Optimization of workability and control of microstructures in deformation
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