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Journal of Powder Technology

Volume 2013 (2013), Article ID 183713, 14 pages

http://dx.doi.org/10.1155/2013/183713

## Investigations into Deformation Characteristics during Open-Die Forging of SiC_{p} Reinforced Aluminium Metal Matrix Composites

^{1}School of Mechanical Engineering, KIIT University, Bhubaneswar 751024, Odisha, India^{2}Research Scholar, IIT Kharagpur, Paschim Midnapur, West Bengal 721302, India

Received 27 March 2013; Accepted 23 August 2013

Academic Editor: Thierry Barriere

Copyright © 2013 Deep Verma et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

The deformation characteristics during open-die forging of silicon carbide particulate reinforced aluminium metal matrix composites (SiC_{p} AMC) at cold conditions are investigated. The material was fabricated by liquid stir casting method in which preheated SiC particles were mixed with molten LM6 aluminium casting alloy and casted in the silicon mould. Finally, preforms obtained were machined in required dimensions. Two separate cases of deformation, that is, open-die forging of solid disc and solid rectangular preforms, were considered. Both upper bound theoretical analysis and experimental investigations were performed followed by finite element simulation using DEFORM, considering composite interfacial friction law, barreling of preform vertical sides, and inertia effects, that is, effect of die velocity on various deformation characteristics like effective stress, strain, strain rate, forging load, energy dissipations, and height reduction. Results have been presented graphically and critically investigated to evaluate the concurrence among theoretical, experimental, and finite element based computational findings.

#### 1. Introduction

Metal matrix composite (MMC) as hybrid materials has attracted attention of many researchers in recent years. MMCs provide significantly enhanced properties over conventional monolithic materials, for example, higher strength, stiffness, hardness, elastic modulus, and wear resistance and thus may be subjected to various forming operations like rolling, extrusion, forging, and so forth to manufacture numerous engineering components Sulaiman et al. and Murashkevich et al. [1, 2]. Automobile pistons, valves, cylinder liners, piston rings, connecting rods, crankshaft, gear parts, suspension arms, turbocharger impellers, guide vanes in gas turbines, ventral fins and fuel-access cover doors in military aircrafts, rotor blade sleeves in helicopters, flight-control hydraulic manifolds, brake discs of transport vehicles, bicycle frames, and so forth are the most common engineering applications seen as cited by Kainer et al. and Matejka et al. [3, 4]. Various composite products tailored-made to the demands of different industrial applications by suitable combinations of matrix materials, reinforcements, and processing routes were also reported by Surappa [5]. The present paper is an attempt to investigate the various deformation characteristics during open-die forging of SiC_{p} reinforced aluminium metal matrix composites (AMC). The objective was to synthesize a metal matrix composite material and further process it mechanically to manufacture engineering components with superior mechanical properties as compared to individual elements.

Investigations during mechanical processing of conventional monolithic materials have been reported from various aspects, but very little work has been reported on the forging of metal matrix composites. The production of metal matrix composites from aluminium and copper alloy chips through hot extrusion process is demonstrated by Gronostajski et al. and Kaczmar et al. [6, 7]. A numerical mathematical model formulated for the prediction of the stress during forging of AMC and possible damage zones were predicted based on the simple relationship for generation and relaxation of internal stresses by Roberts et al. [8]. The effect of forging by temperature and heat treatment on the mechanical properties of Al-Cu metal matrix composites were investigated and it was found that conditions of heat treatment have an essential influence on their mechanical properties as reported by szczepanik et al. [9]. Extensive studies have been carried out on the mechanical properties like tensile strength, yield strength, hardness, and ductility of SiC particle reinforced aluminium metal matrix composites Chung and Lau [10]. The closed-die hot forging of aluminium-silicon alloy (Al-5% Si-0.2% Mg) with different volume fractions of SiC particulate and microstructure, as well as the mechanical properties of the matrix alloy, as-cast state and after the forging operation, was critically investigated by Ozdemir et al. [11]. The forging behavior of aluminium composites having 26 vol.% of reinforcements both at room temperature and elevated temperature, been studied, and further tensile testing, microphotographic study was performed to investigate the mechanism controlling the fracture of specimens by Badini [12]. Young’s modulus, tensile strength, strain-to-fracture, fatigue strength of sinter-forged SiC particle reinforced matrix composites, and the fatigue fractography were conducted, and it was found that Fe-rich inclusions were extremely detrimental to the fatigue life of the composites which were investigated by Chawla et al. [13]. The isothermal forging of 2618 aluminium alloy reinforced with 20 vol.% of Al_{2}O_{3} particles and reported on the recrystallization behavior of composites by means of deformation efficiency was carried out by Cavaliere and Evangelista [14]. The effect of forging temperature on the microstructure and mechanical properties of in situ Ti/TiC matrix composites by performing hot forging experiments was reported by Ma et al. [15]. Investigations on the cold-forging aspects of iron and aluminium metal alloy composites fabricated by powder metallurgy route were carried out and their behaviour against the relative density and barrel radius has been systematically analyzed by Narayanasamy et al. [16]. The forging of AA618/Al_{2}O_{3} particulate composites having 20 vol.% of reinforcements and studying the effects of formability characteristics on the microstructure and tensile properties of composites were performed by Ceschini et al. [17]. The combination of forging and extrusion process on SiC_{p}/AZ91 magnesium matrix composites fabricated by stir casting technology and investigated the effect of deformation characteristics on the yield stress and ultimate tensile strength of material by Wu et al. [18]. Formability analysis of aluminium metal matrix composite specimen manufactured through PM route was analyzed by finite element method. Material factors like volume fraction of reinforcements, shape and size of reinforced particles, compaction pressure, and sintering temperature along with process parameters like die-wall friction, friction between particles, matrix powder, and forming limits were investigated by Ramesh and Senthilvelan [19]. Preliminary experimental investigations into the formability and machinability analysis of SiC_{p} reinforced aluminium metal matrix composites were carried out by Sutradhar et al. [20]. Though Singh et al., Jha et al., and Chandrasekhar et al. [21–23] reported the analysis of dynamic effects during open-die forging of sintered materials, no work has been reported to analyze these effects, that is, effect of die velocity on various deformation characteristics during mechanical processing of metal matrix composites.

In the present work, various deformation characteristics like effective stress, effective strain, effective strain rate, flow of material, strain rates, energy dissipations, and die loads during open-die forging of SiC_{p} AMCs at cold conditions have been analyzed. Experimental investigations and upper bound theoretical analysis along with finite element simulation (FEM) of forging of SiC_{p} AMC have been performed. The SiC_{p} AMC has been prepared by stir casting method, and preforms of required dimensions were machined from the cast specimen. The present investigations considered heterogeneous deformation due to barreling of vertical sides, composite die-workpiece interfacial friction conditions, and inertia effects. It is expected that the present work will be useful for assessment of various deformation characteristics during mechanical processing of AMCs.

#### 2. Experimental Investigations

In general, metal matrix composite material consists of metal matrix and reinforcements, where metal matrix main function is to transfer and distribute load to reinforcements, which are commonly boron, silicon carbide, or graphite particles. In the present research work, aluminium metal matrix composite has been produced by liquid metal stir casting process from LM6 aluminium casting alloy (having high silicon content of 10–13 wt%) with SiC particles as reinforcements with an idea to synthesize a composite material with superior mechanical properties. Liquid metal stir casting process was preferred due to simplicity in operation and lower processing cost, which was also established by Mithun and Devaraj [24] in their research work. They fabricated aluminum based composite material with aluminum as base alloy (AA443.0) and silicon carbide and magnesium oxide as reinforcement materials through stir casting method. It was found out that although aluminum metal in its pure form has excellent mechanical properties, its strength is too low to be used as functional component, and hence, its properties need to be modified to increase its capabilities.

In the present case also, SiC particles have been added primarily to increase the strength and stiffness of the aluminium matrix. During liquid stir casting process, LM6 aluminium casting alloy was melted in a clay-graphite crucible using an electric resistance furnace, and 5 wt% of magnesium was added to the molten metal to have strong bonding between matrix metal and reinforcement particles. Addition of magnesium decreases the surface energy and wetting angle as well as increases the flowability of the molten metal. The SiC powder particles having mesh size +400 *μ* were preheated in the temperature range of 850 to 900°C and were added to the molten metal. The mixture was stirred briskly using a mechanical impeller installed on the electric resistance furnace (refer to Figure 1) at a speed of about 500 rpm, and an optimum mixing temperature of about 720°C was maintained. Two groups of AMC samples having 5 wt% and 13 wt% SiC_{p} were prepared by this manufacturing route. The molten mixture was immediately poured into the silica mould and subsequently cooled to the room temperature. The mould was prepared prior to casting using core sand, bentonite, charcoal powder, and parting sand. Parting gate structure was preferred for simplicity and alignment, as well as sealing of the mould was done with utmost care to decrease the chance of mould erosion, air entrapment, run out, and dross formation. The cast was obtained by breaking the core and gently tapping it after cooling, which was later machined to obtain preforms with desired dimensions (refer to Table 1) for further experiments.

The cold-forging experiments on SiC_{p} AMC preforms were conducted at room temperature employing hydraulic press having maximum load capacity of 200 tons with stationary upper die platen till the onset of fracture. The SiC_{p} AMC preforms placed on the lower die platen were compressed, and data for deformation and corresponding forging load were recorded from the digital display of data acquisition system of the press. In all the experiment run, deformations were carried out under dry interfacial friction conditions (without any lubricant) till the onset of fracture, that is, maximum forgeability at room temperature. The engineering stress and strain data were calculated from the corresponding recorded data of forging load and deformation and were later also uploaded in the material library of DEFORM software as shown in Figure 2 for further FEM analysis. Figures 3 and 4 show the solid disc and solid rectangular preforms before and after open-die forging, respectively, for both 5 wt% and 13 wt% SiC_{p} reinforcements. It can be seen that for the same deformation conditions, AMC preforms having higher wt% of SiC_{p} were observed to have less forgeability, and those preform surfaces showed severe cracking at equatorial bulged regions. The photomicrographs for SiC_{p} AMC preforms were obtained at 500X to illustrate the distribution of SiC_{p} reinforcements within the aluminium metal matrix. As evident from Figure 5, 13 wt% SiC_{p} AMC is having higher density of silicon carbides particulate distribution as compared to 5 wt% SiC_{p} AMC.

#### 3. Theoretical Analysis

The present theoretical analysis based on upper bound approach for open-die forging of SiC_{p} AMC solid disc and solid rectangular preforms has been performed using axisymmetric and plane strain conditions of deformation, respectively. The following assumptions were considered during the present analysis.

(i) Die platens are incompressible, rigid, and parallel.

(ii) Deformation is homogeneous and insensitive to hydrostatic stress component, and hence, von-Mises yield criterion was considered, which is given as

(iii) Die-preform interfacial friction conditions are composite in nature including both sliding and sticking frictions, where sticking friction is a function of adhesion factor. According to Downey et al. [25] such composite interfacial friction laws can be given mathematically as

*solid disc preform:*

*solid rectangle preform:*
Sticking zone distances “” and “” can be approximated by modified Rooks [26] equations as

(iv) Compatibility equations have been derived from volume constancy principle based on the work done by Jha et al. [27] as

*solid disc preform:*

*solid rectangle preform:*

(v) Bulging of workpiece vertical sides has been considered by including a barreling parameter “” in the kinematically admissible exponential velocity fields.

(vi) Redundant energy dissipation due to velocity discontinuities has been neglected.

(vii) Quarter portion of the preform has been considered during the analysis due to symmetry along the horizontal and vertical axes.

(viii) Circumferential flow of preform vertical sides has been neglected in case of solid disc preforms, and deformation conditions are essentially axisymmetric in nature.

(ix) Lateral flow of preform vertical sides in the longitudinal direction has been neglected in case of solid rectangular preforms, and deformation is essentially plane-strain in nature.

Kinematically admissible velocity field and corresponding strain rates were formulated for both cases separately satisfying compatibility conditions and flow rule (refer to Appendix). According to Avitzur [28], total energy dissipations during plastic deformation based on upper bound approach are given as

##### 3.1. Solid Disc Preform

Internal energy dissipation “” after substituting strain rates in (8), integrating, and simplifying is given as Frictional shear energy dissipation at die-preform interface “” after substituting frictional stress equation and velocity field in (8), integrating, and simplifying is given as Energy dissipation due to inertia forces “” after substituting velocity field and corresponding strain rates in (1), integrating, and simplifying is given as

##### 3.2. Solid Rectangular Preform

Internal energy dissipation “” after substituting strain rates in (8), integrating, and simplifying is given as
Frictional shear energy dissipation at die-preform interface “” after substituting frictional stress equation and velocity field in (8), integrating, and simplifying is given as
Energy dissipation due to inertia forces “” after substituting velocity field and corresponding strain rates in (8), integrating, and simplifying is given as
The average forging load for both cases was computed separately by substituting the above energy dissipation equations in (15):
Dynamic effects, that is, effect of die velocity on relative magnitudes of various energy dissipations involved during open-die forging of SiC_{p} AMC preforms are illustrated using inertia factor “”, which is defined as the ratio of inertia energy dissipated to total energy supplied by die platen during deformation and given as

#### 4. Finite Element Analysis

Finite element simulation of open-die forging of SiC_{p} AMC preforms has been performed using DEFORM-3D, which is based on the implicit Lagrangian finite element code. In the present solution, preform mesh deforms under the die load, and elasticity of the material has been neglected, as plastic strains outweigh elastic strains and material behaves like an elastic-viscoplastic material as stated by Kobayashi et al. [29].

The stress-strain curve of type MPa for SiC_{p} AMC material was uploaded in the material library of software as described in the previous section. The material properties of SiC_{p} AMC used in the present analysis are given in Table 2. The geometry of die platens was generated in DEFORM, and the die platens were modeled as rigid, parallel, and flat bodies with plastic preform placed in between them. The geometry of preforms was generated using CATIA using part design module/workbench, and data was imported to DEFORM in form of STL files. Figures 6(a) and 6(b) show the 2D and 3D models of the solid disc and solid rectangular preforms, respectively. The composite frictional law was considered to model the interfacial frictional conditions represented by suitable composite interfacial frictional shear stress (refer to (3) and (4)). Tetrahedral elements were used to mesh the preforms, and small meshes were generated close to the edges of preforms in order to better scope the forging process. The complete forging simulation was performed in 120 steps having time for movement of die platens in each step equal to 0.064 seconds. The deformation criterion considered was maximum forgeability of SiC_{p} AMC preforms at room temperature, which was experimentally found to be about 49% and 47%, respectively, for 5 wt% and 13 wt% SiC_{p} reinforced AMC preforms.

#### 5. Results and Discussions

Figure 7 shows that the maximum deformation of preforms is about 47–49% at room temperature under dry interfacial friction conditions, and preforms start cracking at maximum stress of about 1.4–1.5 GPa. The stress required to produce the same amount of strain is higher in case of 13 wt% SiC_{p} preforms as well as higher in case of solid rectangular preforms. This indicates that the increases in the perecentage of SiC_{p} increases the stress required to deform the preforms. Also, solid rectangular preforms exhibit higher constraint deformation due to existence of sharp corners as compared to solid disc preforms.

Figure 8 shows that the percentage of height reduction of preform increases gradually during the initial phase of deformation, and only after forging load attains a magnitude of about 5–7 tons, it increases exponentially. This continues till cracks start appearing on the outer surfaces of preforms, that is, maximum forgeability of preforms. In both axisymmetric and plane strain deformations, the height reduction for preforms having 5 wt% SiC_{p} is found to be more as compared to 13 wt% SiC_{p} preforms, which indicates that the percentage of increase in SiC_{p} decreases the forgeability of preforms. Also, the load requirements are higher for the same amount of deformation in case of solid disc preforms indicating better flow of material. The experimental data are found to be in close agreement with the theoretical ones, which validates the present upper bound approach used to solve the forging problems considered in the present paper.

Figure 9 shows the variation of strain rate (mm/mm sec) with forging load (tons) for SiC_{p} AMC preforms. As evident from the figure, maximum strain rate of magnitude 0.024 sec^{−1} is being observed at forging load of about 20 tons for both 5 wt% and 13 wt% SiC_{p}. Initially, strain rates are higher for solid rectangular preforms, but after the load attains a magnitude of about 10 tons, strain rates for 13 wt% SiC_{p} preforms are higher irrespective of the shape of preforms. Also, at the end of forging operations, strain rates are found to decrease slightly after attaining the highest value. These two behaviors are attributed due to the consolidation of SiC_{p} particles within the AMC preforms during the end of forging operation. It can be concluded that the effect of SiC_{p} particles on stress, strain, and strain rate is predominant up to 40% of height reduction at forging load of about 20 tons, and thereafter, these particles consolidate within the matrix, and hence, they least influence the forging characteristics.

It can be seen from Figure 10 that the energy dissipation increases with the increase in the forging load and deformation. The total energy requirement for deformation of AMC preforms having higher SiC_{p} is found to be higher due to higher strength of material and is also higher if the process is carried at higher die acceleration, leading to higher inertia energy dissipation (refer to (11) and (14)). Also, energy requirements are higher for solid rectangular preforms as compared to solid disc preforms due to more constraint deformation in the former case.

The variation of inertia factor with die velocity for SiC_{p} AMC preforms is shown in Figure 11. It is clearly evident that inertia factor increases exponentially with increase in the die velocity and is higher for higher die acceleration in solid rectangular preforms. Also, it can be noticed that proportion of inertia energy can be as high as 30% of the total energy dissipation and hence cannot be neglected during the present investigation.

Figure 12 shows that both axial and radial strains increase exponentially with increases in the forging load. Also, the corresponding values of axial strains are higher than radial strains for same forging load and higher percentage of SiC_{p}. It also depicts the measure of Poisson’s ratio, that is, ratio of radial strain to axial strain for present SiC_{p} AMC material.

Figure 13 shows the effective stress (MPa) distribution on SiC_{p} AMC preforms. It is clearly evident that magnitudes of effective stresses are higher in 13 wt% SiC_{p} preforms as compared to 5 wt% SiC_{p} preforms in the corresponding regions. The edges are subjected to higher stresses, whereas the centremost regions are having lower stresses of magnitude about 150 MPa and 300 MPa for solid disc and solid rectangular preforms, respectively. This indicates that as the percentage of SiC_{p} increases, stress also increases due to increase in the strength of preforms.

Figure 14 shows the effective strain (mm/mm) distribution on SiC_{p} AMC preforms. It can be seen that the major portion of preform is subjected to strain in the order 0.3–0.6 magnitude, except at the edges. The strains are higher in 5 wt% SiC_{p} preforms as compared to 13 wt% SiC_{p} preforms, which indicate that ductility of 5 wt% SiC_{p} is higher. In case of 5 wt% SiC_{p} preforms, the edges are subjected to severe strain of magnitude about 0.7–0.9, which leads to the fracture of vertical surfaces and is also confirmed from Figure 3. In this case, no appreciable variation in the strain distribution has been observed for preforms having 13 wt% and 5 wt% SiC_{p}. Also, the strains at the central region of preform are low and eventually almost zero at the centermost regions near to the upper and bottom flat surfaces. The dissected section also reveals that the variation of strain in the central region is in the form of an inverted cone. This confirms the presence of sticking friction zone at those regions, which confirms and validates the variable interfacial composite friction law considered during the present theoretical analysis.

The distribution of effective strain rate (mm/mm-sec) on SiC_{p} AMC preforms is shown in Figure 15. It can be clearly seen that the major portion of solid disc preforms is subjected to strain rate of about 2 mm/mm-sec and only the edges are subjected to higher strain rates in the order 3.2–3.5 mm/mm-sec. In case of solid rectangular preforms, the edges are subjected to strain rate of 2.5–2.9 mm/mm-sec. The solid disc preforms are having higher strain rates as compared to solid rectangular preforms indicating better metal flow in the former case as well as presence of constraint deformation in case of solid rectangular preforms.

The velocity (mm/sec) distribution on SiC_{p} AMC preforms is shown in Figure 16. It can be observed that solid disc and solid rectangular preforms are subjected to the highest flow velocity of about 10–13 mm/sec and 15–17 mm/sec, respectively. Also, the outer regions of preform are having higher flow velocity as compared to the inner regions, which is in close agreement with the composite interfacial friction law considered in the present paper. The strain rates are higher in case of 5 wt% SiC_{p} preforms as compared to 13 wt% SiC_{p}, which indicates that ductility of preform decreases with the increase in the perecentage of SiC_{p}. The variation of flow velocity in the vertical direction leads to the barreling of preforms, which confirms the inclusion of barreling parameter “” during the present theoretical analysis.

Figure 17 shows the variation of effective stress (MPa) with forging time (sec) for SiC_{p} AMC preforms. It can be observed that stress requirement for preforms having 13 wt% SiC_{p} is higher as compared to preforms having 5 wt% SiC_{p}, which indicates that the percentage of increase in SiC_{p} increases the hardness of preforms. It can be also seen that solid rectangular preforms are subjected to higher effective stresses as compared to solid disc preforms indicating better material flow in case of solid disc preforms as well as constraint deformation in case of solid rectangular preforms.

The variation of effective strain (mm/mm) with forging time (sec) is shown in Figure 18, and it was found that it increased exponentially with respect to forging time. Also, it is clearly evident that effective strains for solid rectangular preforms are higher as compared to solid disc preforms due to constraint deformation.

Figure 19 shows the variation of effective strain rate (mm/mm-sec) with forging time (sec) for SiC_{p} AMC preforms. The strain rate for 5 wt% SiC_{p} preforms is found higher than preforms having 13 wt% SiC_{p}, which indicates that percentage of increase in SiC_{p} decreases the ductility and forgeability of preforms. Also, the strain rates are higher for solid disc preforms as compared to solid rectangular preform due to constraint deformation in the latter case.

Figure 20 shows the variation of forging load (kN) with forging time (sec) for solid disc and solid rectangular preforms which is found to increase rapidly with forging time. It can be clearly seen that the preforms can withstand maximum load of about 270–300 kN without the onset of fracture. It can also be noted that solid rectangular preforms require higher load to deform as compared to solid disc preforms.

#### 6. Conclusions

The major conclusions may be summarized as follows.(i)Maximum formability of AMC material at room temperature and under dry interfacial frictional conditions was found to be about 47-47% of height reduction. The deformations in AMC preforms having 5 wt% SiC_{p} were found to be higher as compared to 13 wt% SiC_{p} indicating that as the percentage of SiC_{p} particulate increases, forgeability of the preforms decreases. The experimental result was found to be in close agreement with theoretical ones and hence validates the present theoretical analysis based on upper bound approach. (ii)Engineering stress required to produce the same amount of strain was found to be higher in case of AMC preforms having higher weight % of SiC_{p} as well as higher for solid rectangular preforms. This was attributed due to the fact that the increase in weight % of SiC_{p} increases the hardness of the preform. Also, solid rectangular preforms exhibit higher constraint deformation due to the presence of sharp corners.(iii)The highest strain rate in the order of 0.24 was experienced during the open-die forging of AMC preforms irrespective of the percentage of SiC_{p}. The effect of SiC_{p} particles over various deformation characteristics like strain, stress, and strain rate is predominant only up to nearly 44% of height reduction, and thereafter, these particles consolidate within the metal matrix and have the least influence on the various forging parameters.(iv)Total energy requirements during open-die forging of AMC preforms having higher SiC_{p} are found to be higher due to higher strength of the material. Also, the energy requirements are higher if the process is carried out at higher die acceleration, due to inertia effects. Also, the effect of die velocity was clearly depicted using inertia factor, which indicated that energy dissipation due to inertia effects may be as high as 30% of the total energy dissipations and thus must be considered during the analysis of forging operations carried out especially at higher die velocities. (v)Lower magnitude of strains was observed at the central region of preforms and was found to be almost zero at the centermost region near to top and bottom flat surfaces indicating the presence of variable interfacial friction zone in the form of inverted cone. This confirmed the composite interfacial friction law considered during the present investigations. This was also confirmed by the results of velocity distribution, where flow velocity was found to be zero at the centermost regions of preforms indicating the existence of nondeforming zone due to the presence of high sticking friction conditions.(vi)Simulation of open-die forging of SiC_{p} AMC material was performed using DEFORM and the distribution of effective stress, effective strain, effective strain rate, and velocity vector profile was generated for both solid disc and solid rectangular preforms. Higher magnitudes of effective stress, strain, and strain rate were found at the corners and edges of preforms indicating that the onset of fracture will take place at those regions only. This was also confirmed by the presence of severe cracks at those regions during the present experimental investigations.(vii)Validation of simulation was done by comparing its results with the theoretical and experimental results and was found to reasonably agree with each other, which indicated that present finite element simulation represents fairly well the present open-die forging of SiC_{p} AMC.

It is expected that the present work will be useful for the assessment of various deformation characteristics during mechanical processing of AMCs.

#### Appendix

Consider open-die forging of a SiC_{p} AMC between two perfectly flat, parallel, and rigid die platens at room temperature with lower die platen moving upwards with velocity “” and upper die platen stationary as shown in Figure 21.

The boundary conditions, velocity field, and corresponding strain rate equations for solid disc preforms are given as

The boundary conditions, velocity field, and corresponding strain rate equations for solid rectangular preforms are given as

#### Nomenclature

: | Acceleration field |

: | Strain rate field |

: | Interfacial relative velocity |

: | Die pressure |

: | Average forging load |

: | Surface area |

: | Radius of solid disc preform |

: | Width of solid rectangular preform |

: | Length of solid rectangular preform |

: | Internal energy dissipation |

: | Inertia energy dissipation |

: | Flow stress of SiC_{p} AMC material |

: | Frictional shear stress |

: | Effective coefficient of friction |

: | Barreling factor |

: | Velocity field |

: | Die velocity |

: | Die acceleration |

: | Average pressure |

: | Average cross sectional area |

: | Volume |

: | Sticking zone radius |

: | Sticking zone width |

: | Height of preform |

: | Friction energy dissipation |

: | External energy supplied |

: | Density of SiC_{p} AMC preform |

: | Second invariant of stress |

: | Specific cohesion factor |

: | Inertia factor. |

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