Jtam-A4.dvi JOURNAL OF THEORETICAL AND APPLIED MECHANICS 56, 2, pp. 457-469, Warsaw 2018 DOI: 10.15632/jtam-pl.56.2.457 EXPERIMENTAL INVESTIGATION AND MODELLING OF HOT FORMING B4C/AA6061 LOW VOLUME FRACTION REINFORCEMENT COMPOSITES Kailun Zheng, JIANGUO LIN Imperial College London, Department of Mechanical Engineering, United Kingdom e-mail: k.zheng13@imperial.ac.uk; jianguo.lin@imperial.ac.uk Gaohui Wu Harbin Institute of Technology, School of Material Science and Engineering, Harbin, China e-mail: wugh@hit.edu.cn Roger W. Hall Marbeau Design Consultancy, Paris, France e-mail: marbeau.dc@sfr.fr Trevor A. Dean University of Birmingham, Department of Mechanical Engineering, Birmingham, United Kingdom e-mail: t.a.dean@bham.ac.uk This paper presents an experimental investigation of the hot deformation behaviour of 15% B4C particle reinforced AA6061 matrix composites and the establishment of a novel cor- responding unified and physically-based visco-plastic material model. The feasibility of hot forming of a metal matrix composite (MMC) with a low volume fraction reinforcement has been assessed by performing hot compression tests at different temperatures and strain ra- tes. Examination of the obtained stress-strain relationships revealed the correlationbetween temperature and strain hardening extent. Forming at elevated temperatures enables obvious strain rate hardening and reasonably high ductility of theMMC.The developed unifiedma- terial model includes evolution of dislocations resulting from plastic deformation, recovery and punching effect due to differential thermal expansion betweenmatrix and reinforcement particles during non-steady state heating and plastic straining. Good agreement has been obtained between experimental and computed results. The proposedmaterial model contri- butes greatly to amore thoroughunderstanding of flow stress behaviour andmicrostructural evolution during the hot forming ofMMCs. Keywords: Metal Matrix Composite (MMC), hot compression, AA6061, B4C, dislocation 1. Introduction Metal matrix composites (MMC) comprise a relatively wide range of materials defined by com- position of matrix and of reinforcement together with its geometry (Kaczmar et al., 2000). Particle-reinforced aluminium alloy/B4CMMC is a popular candidate in automotive, aerospace and nuclear industries, since boron carbide (B4C) exhibits very high hardness, relatively low density and good thermal and chemical stability (Guo and Zhang, 2017). Raw MMCs are ma- nufactured today usingmostly either particle introduction techniques through liquid-stirring or casting, pressure infiltration or powder metallurgy (Ye and Liu, 2004). The final geometry of MMCpartswith a high volume fraction reinforcement is usually obtained bymachining.Where- as, a low volume fractionMMCsmay be processed by extrusion, drawing or rolling in which the plasticity of thematrix material is exploited. The resultant bar or sheet often requires seconda- ry manufacturing operations to produce the final product geometry. It is advisable to perform 458 K. Zheng et al. suchmanufacturing processes onMMCs at elevated temperatures where ductility is higher and forming load is lower (Aour andMitsak, 2016). This combination increasesmanufacturing capa- bility and results in an increased material yield compared with machining to achieve final part geometry. Therefore, it is important to characterize the deformation behaviour of MMCs with the low volume fraction of reinforcement under hot working conditions, including mechanisms of deformation and correspondingmicrostructural evolution. Significant research has been performed on hot forming of MMCs and related deformation mechanisms. The mechanism of matrix strengthening and microstructure evolution during hot deformation becomes more complicated with the addition of reinforcement particles of different materials, shapes and sizes. Wang et al. (2017) found that a dynamic recrystallization (DRX) phenomenon, which depends on temperature and strain rate, was the main softening mecha- nism when hot compressing AA6061/B4C composite. Ganesan et al. (2004) observed dynamic recrystallization and wedge cracking characterising the hot working of AA6061/15% SiCp. Ho- wever, although relative microstructural evolutions were identified, steady flow stress was still modelled phenomenologically using the Zener-Hollomon parameter and the Arrhenius constitu- ent model. The evolution of dislocations associated with hardening was not taken into account. Physically-based models of hot formedMMCs are lacking this phenomenon. High strength ceramic particles, such as SiCp, B4CandZrB2, are commonly used to increase MMC strength and thermal stability (Ibrahim et al., 1991). When these MMCs are heated to elevated temperatures, the differential thermal expansion between the particles andmatrix alloy can induce dislocation punching (Chawla and Chawla, 2004) during thermal quenching, which is also believed to affect the hardening during deformation. Furthermore, plastic deformation produces temperature increase which can further aggravate dislocation punching.The dominant mechanisms influencing material flow stress behaviour of low volume fraction reinforcement MMCs are punching dislocation and dislocation evolution during deformation of the matrix material, exemplified by plastic strain induced dislocation accumulation and recovery (Lin et al., 2005). Bothmechanisms should be included in constitutive models for this type of material. The objectives of this study are to investigate hot deformation behaviour of MMCs and to further develop a unified physically-based visco-plastic constitutive model for hot forming of discontinuously reinforcedMMCswith a low volume fraction of high strength particles. Streng- theningmechanismsofdiscontinuousparticle reinforcedMMCsarebrieflyreviewed in thispaper, then the development of a visco-plastic material model based on a dislocation evolution mecha- nism is presented. The feasibility of hot forming ofMMCswas proved through hot compression tests. In addition, the constitutive equations of thematerial model were calibrated using experi- mentally generated stress-strain relationships. The established model is believed to be the first one ever presented, which is based on the physical mechanisms of particle strengthening and dislocation evolution during hot deformation. 2. Strengthening mechanisms in hot working particle reinforced MMCs 2.1. Modulus Various methods have been proposed to predict the elastic modulus of composites. Each of the existing models has limits and is unable to cover factors of reinforcement volume fraction, shape, contiguity and distribution. Hashin and Shtrikman (1963) proposed upper and lower bounds for an isotropic aggregate, based on variational principles of linear elasticity. For high volume fraction cases, normally greater than 0.5, Kröner (1958) and Budiansky (1965) propo- sed a self-consistent methodology to model effective Young’s modulus of MMCs with spherical reinforcements. The relationships between Young’s modulus E, shear modulus G and bulk mo- dulus K is given in Eq. (2.1)1. On the assumption of an unchanged Poisson’s ratio, Young’s Experimental investigation and modelling of hot forming B4C/AA6061 low... 459 modulus can be obtained from shear and bulkmodulus.Mura (1987) provided an estimation of the effectivemoduli for relatively small volume fractions of reinforcingparticles, as shown inEqs. (2.1)2 and (2.1)3. The moduli of a composite are determined by the reinforcement and matrix material for a certain volume percentage of reinforcements. In this theory, the reinforcement geometry is assumed to be spherical. Then, the effective Young’s modulus of composite can be obtained from Eq. (2.1)1. It should be noted that the theory was focused on finite concentra- tions of reinforcements, and the approach is only valid for a relatively small volume fraction of reinforcements, normally less than 0.25 E =2G(1+ν)= 3K(1−2ν) Gc = Gm [ 1+Vp(Gm−Gp) /{ Gm+2(Gp−Gm) 4−5νm 15(1−νm) }] −1 Kc = Km [ 1+Vp(Km−Kp) /{ Km+ 1 3 (Kp−Km) 1+νm 1−νm }] −1 (2.1) where ν is thePoisson’s ratio, G is the shearmodulus and K is the bulkmodulus of thematerial. Gc, Gm and Gp are the shearmodulus of the composite, matrix and reinforcement, respectively. Kc, Km and Kp are the bulkmodulus of the composite, matrix and reinforcement, respectively. νc, νm and νp are the Poisson’s ratio of the composite, matrix and reinforcement, respectively. Vp represents the volume fraction of reinforcements. 2.2. Strengthening 2.2.1. Direct strengthening Direct strengthening is common in continuous fiber-reinforced (Khosoussi et al., 2014) and discontinuously fiber or particle reinforced composites. Themainmechanismof direct strengthe- ning is load transfer from the point of application through the low strength matrix to the high strength reinforcement across the matrix/reinforcement interface. Therefore, apparent streng- thening results from the additional load carried by the reinforcements. Tomodel such a streng- thening phenomenon, Nardone and Prewo (1986) proposed amodified shear-lag model for load transfer in particulate materials. The model incorporates load transfer from the particle ends (which is not applicable to continuous-fiber reinforced composites due to the large aspect ra- tio). The yield strength of the particulate composite σcy is increased over the matrix yield strength σmy σcy =σmy [ Vp (S +4 4 ) +Vm ] (2.2) where S is the aspect ratio of the particle, Vp is the volume fraction of particles, and Vm is the volume fraction of the matrix. The relation shown in Eq. (2.2) does not include effects of particle size and matrix microstructure on the load transfer. Wu et al. (2016) investigated the effects of particle size and spatial distribution on the mechanical properties of B4C reinforced composites. It is demonstrated that for a given volume fraction, reducing the particle size of the B4C leads to a greater increase in the strength. The contribution of reducing the particle size can be estimated using as ∆σd ∝ √ 1 d (2.3) where∆σd represents the increment of the yield strengthdue toparticle size, andd is the average size of particles in the spherical assumption. 460 K. Zheng et al. 2.2.2. Indirect strengthening Indirect strengthening is believed to be caused by changes of matrix microstructure and properties with the addition of the reinforcement. Thermal expansion mismatch between the reinforcementandmatrix alloy can result in abuild-upof internal stresseswhere there is a change in temperature, such as occurs during thermal quenching (Suh et al., 2009). Suchamismatch is a general and important feature ofMMCs, especially with the combination of a high coefficient of thermal expansion (CTE)metallic matrix and a low CTEhigh strength ceramic reinforcement. If the internal stress generatedbydifferential thermal expansion is greater than theyield stress of the matrix, then dislocations form at reinforcement/matrix interfaces and accumulate within a domain surroundingthe reinforcement, as shown inFig. 1.Hence, “thermally induceddislocation Fig. 1. Schematic of dislocation punching micromechanics (Suh et al., 2009) punching” results in an indirect strengthening of thematrix. Besides the thermal effects of CTE mismatch during thermal quenching, the internal stress related to differential thermal expansion may also occur if the composite experiences a positive temperature variation under hot forming conditions, such as externally applied heating or temperature rise due to plastic deformation. The matrix domain expands but is constrained by the reinforcements. The matrix material strength is much lower at elevated temperatures, so it is easier for the induced internal stress to exceed the matrix yield strength resulting in dislocations being punched into the matrix. It should be noted that the phenomenon of punched dislocations should be considered only if the heating rate is high and if the soaking time is short. Otherwise, static recoverywill eliminate the punched dislocations during the non-steady positive temperature variation. Arsenault and Shi (1986) developed amodel to quantify the degree of dislocation punching due to CTEmismatch between a particle and thematrix, schematically shown in Fig. 1. The dislocation density of the punched zone due to differential thermal expansion is given by ρCTE = DεTMVp b(1−Vp)d (2.4) where D is a geometric constant, b is the Burgers vector, d is the diameter of the reinforcement particle, and εTM is the thermal misfit strain, εTM = ∆α∆T . ∆α is the difference in the coef- ficient of thermal expansion between thematrix and reinforcement, and ∆T is the temperature variation. The incremental increase in strength due to dislocation punching can be given as ∆σind = ψGmb √ ρCTE (2.5) where ψ is a constant. Substituting Eq. (2.4) into Eq. (2.5), the strength increment due to this indirect strengtheningmechanism is given by Eq. (2.6) with further consideration of the aspect ratio of the reinforcement particles S Experimental investigation and modelling of hot forming B4C/AA6061 low... 461 ∆σind = ψGmb √ DεTMVpS b(1−Vp)d (2.6) 3. Development of the visco-plastic constitutive model 3.1. Modelling of modulus The addition of reinforcement particles significantly increases the stiffness of composites compared with that of the matrix alone. For simplicity, Eq. (2.1)3 may be used to represent approximately the relationship between Young’s modulus and shear modulus by assuming the Poisson’s ratio to be constant. Young’s modulus of composites can be also approximated by a formulation shown as Ec = Em 1+Vp(Em−Ep) Em+ δ1(Ep−Em)δ2 (3.1) where δ1 and δ2 are constants. Ec, Em and Ep are Young’s moduli of composite, matrix and reinforcement, respectively. In order to simplify Eq. (3.1), giving E1 = δ1δ2, substitute E1 into Eq. (3.1). Equation (3.1) can be rewritten as follows Ec = Em [(1−E1+Vp)Em+(E1−Vp)Ep (1−E1)Em+E1Ep ] −1 (3.2) In terms of hot forming low volume fraction composite materials, in this study, Young’s modulus of the matrix metal is considered dependent on bulk temperature, while that of rein- forcement particles is considered as constant. 3.2. Modelling punched dislocation density Thedislocation punching feature is determinedby temperature variation duringhot forming, which can be divided into two parts. Contribution of the first part comes from heating the composite fromthe roomtemperature to its forming temperature.The initial dislocation density due to differential thermal expansion is considered to be zero. During heating and according to Eq. (2.4), the rate of punched dislocation density can be expressed as a function of temperature history. Considering the instantaneous heating rate, this becomes as defined in ρ̇CTE = D∆α∆ṪVp b(1−Vp)d (3.3) where ∆Ṫ represents the rate of temperature change. Contribution of the second part results from adiabatic heating during hot working (Bai et al. 2013). Adiabatic heating is believed to result from plastic work during hot working (Khan et al., 2004). The temperature increment can be calculated from experimental stress-strain curves using ∆T = η cmρm εp ∫ 0 σ(εp) dεp (3.4) where η represents the fraction of heat dissipation caused by plastic deformation (Khan et al., 2004), cm and ρm are specific heat andmass density of thematrixmaterial, respectively, σ is the instant flow stress and εp is the plastic strain. In this study, the variable related to temperature 462 K. Zheng et al. increase arising from plastic deformation is expressed in terms of a derivative in order to unify the constitutive equations Ṫε = η σ cmρm |ε̇p| (3.5) whereTε is temperature rise due to plastic straining. In ideal isothermal deformation conditions, the instantaneous temperature T is equal to the initial temperature T0. However, when heat ge- nerated due to large plastic deformation cannot be neglected, the instantaneous temperature T equals (T0+∆T), where ∆T is the temperature rise regarded as a function of the deforma- tion and deformation rate. According to Eq. (3.5), deformation induced temperature increase can be determined through numerical integration based on the stress-strain relationships for a fixed strain rate and stress state. Therefore, substituting Eq. (3.5) into Eq. (3.3), the rate of accumulated dislocation due to thermal expansion mismatch can be rewritten as ρ̇CTE = D Vp 1−Vp η σ cmρm |ε̇p| (3.6) 3.3. Formulation of constitutive equations Physically-based visco-plastic constitutive equations have been proposed for the modelling of plastic deformation of many metals, especially in hot forming conditions. The significant contribution of these models is to enable a variety of phenomena to be modelled, including dislocation accumulation and annealing, dynamic recovery and recrystallization, based on the specific deformation mechanisms. Each aspect of microstructural evolution can be treated as a variable in the constitutive equations. These constitutive equations are also suitable for hot working discontinuous particle reinforced MMCs. However, high strength reinforcement adds newmechanisms and effects on the modulus andmicrostructural evolutions which also need to be considered andmodelled. As interactions between differentmicrostructural phenomena exist, it is impossible to express all the physical phenomena active duringhot formingbyusing a single equation. To thoroughly understand their evolution, this study uses a constitutive model based on an advanced dislocation dominated mechanism (Lin and Dean 2005). A set of unified visco-plastic constitutive equations is established to model the contribution of particles on the modulus and strength, evolution of dislocation, temperature increase due to adiabatic deformation, and rationalise their effects on the steady plastic flow. This developed material model derives from the dislocation evolution during isothermal hot deformation. The relationships between dislocation density and strain hardening and recovery are characterised in this model. Compared to conventional metals, the dislocation density in this model is divided intoplastic deformation inducedand thermal expansion induced types.For simplification, several assumptions are used in thismodel, they are (1) dynamic recrystallization of thematerial during the initial deformation process is not considered for low-volume fraction reinforcement and relatively high strain rates; (2) thermal strain is not taken into account compared with the great total strain; (3) effects of precipitation on dislocation density are not considered. The set of unified viscoplastic constitutive equations for modelling hot deformation of MMCs with low-volume fraction reinforcements is summarised as follows ε̇p = (σ−R−ke K )n1 Ṙ = 1 2 B ρ̇√ ρ (3.7) and ρ̇str = A(1−ρstr)|ε̇p|−Cρn2str ρ̇ = ρ̇str+ ρ̇CTE σ = Ec(ε−εp) (3.8) Experimental investigation and modelling of hot forming B4C/AA6061 low... 463 The fundamental equations used are Eq. (3.7)1 to Eq. (3.8)3, given above. Tomake it clear, general description of each equation representing a particular microstructure mechanism is in- troduced. Details of the form of each equation are given in the literature (Lin and Dean 2005). Equation (3.7)1 represents the traditional power-law of visco-plastic flow formulation (Mohamed et al. 2012), ke represents the initial yield stress of composites and R represents hardening stress due to dislocation evolution. Equation (3.7)2 represents the evolution of material hardening, which is a function of the normalised dislocation density ρ defined by ρ =(ρ−ρi)/ρmax, where ρi is the initial dislocation density and ρmax is the maximum (saturated) dislocation density. Therefore, the range of ρ is between 0 and 1 during the whole process. Unlike hot forming of metals, the dislocation density in this study is divided into two parts; dislocation density evolu- tion of hot straining of the matrix material ρstr and punched dislocation density evolution due to differential thermal expansion ρCTE as given in Eq. (3.6). Equation (3.8)1 represents the rate of accumulation of dislocations induced by the plastic deformation, which takes into account de- formation and recovery. Equation (3.8)2 represents the sum of dislocation density arising from plastic deformation and punched dislocations, Eq. (3.6), due to the difference of thermal expan- sion of thematrix and reinforcement. It should benoted that the difference in thermal expansion arises from the temperature increase resulting from plastic deformation, which is different from the applied heating at the initial stage. Equation (3.8)3 is Hook’s law for a simple uniaxial state. In this equation set, ke, K, n1, B, A, C and Ec are temperature dependent variables defined in Eqs. (3.9) and (3.10), while n2 is temperature independent material constant ke = k1exp ( Qk RgT ) (VpS +Vm) √ 1 d +k2 √ Vp∆T (1−Vp)d (3.9) and K = K0exp (−QK RgT ) n1= n11 ε̇ n12 p exp (Qn1 RgT ) B = B0exp ( QB RgT ) A = A0exp ( QA RgT ) C = C0exp (−QC RgT ) Em = E0exp ( QE RgT ) (3.10) Equation (3.9) represents the initial yield strength of theMMC considering direct and indi- rect strengthening of the reinforcement particles, Vp and Vm represent volume fractions of the reinforcement and matrix respectively. ∆T is the temperature increment during rapid heating. Equations (3.9) to (3.10) represent theArrhenius equations of temperature dependent variables, where Q describes the activation energy for each variable, and Rg is the universal gas constant. All the material constants in Eqs. (3.9) to (3.10) are temperature independent. It should be noted thatYoung’smodulus ofMMC is a function of thematrixmodulus and particlemodulus, which is modelled in the previous Section. Considering the thermal stability of high strength reinforcements, only Young’s modulus of the matrix is temperature dependent, defined in Eq. (3.10), while Young’s modulus of reinforcements is considered to be a constant. 4. Hot compression tests 4.1. Materials ExperimentshavebeenundertakenusingAA6061/B4CprovidedbyHarbin Institute ofTech- nology. The composite samples were produced with a 15% volume fraction reinforcement using a pressure infiltrationmethod. Single crystal B4Cparticles were used having an average particle 464 K. Zheng et al. size of 17.5µm (Zhou et al. 2014). The bulk composite material was then extruded into circular bars and then machined into standard cylindrical samples with length of 12mm and diameter of 8mm. The selection of sample dimensions was chosen so as to avoid inelastic buckling prior to plastic deformation. The matrix material was AA6061. The main chemical compositions of B4C and AA6061 are given in Tables 1 and 2, respectively. Table 1.Main chemical composition of B4C [%] Element B C Fe Si Ca F wt [%] 80.0 18.1 1.0 0.5 0.3 0.025 Table 2.Main chemical composition of AA6061 [%] Element Fe Si Mn Cr Mg Zn Al wt [%] 0.70 0.80 0.15 0.35 1.2 0.25 Remain 4.2. Experimental set-up and test programme High temperature uniaxial compression tests were performed using the thermo-mechanical simulator Gleeble 3800. Specimens were heated at a pre-determined heating rate by resistance heating, and temperature was precisely controlled by feedback from a thermocouple welded to themiddle of the specimen. Graphite foil and high-temperature graphite paste were used at the interfaces between the specimen and Gleeble anvils to reduce interfacial friction and obtain a more uniform deformation. Strain was measured using a C-gauge which detected a change in the specimen diameter. The experimental set-up is shown in Fig. 2. Fig. 2. Experimental set-up for hot compression test (all dimensions are in mm) Figure 3 shows the temperatureprofile of a specimen in thehot compression test.A two-stage heating strategy was utilised to obtain a uniform temperature and to avoid overshoot. Initially, the specimen was heated up at a rate of 5◦C/s to 50◦C below the specified target deformation temperature. Then, it was further heated to the target temperature at a rate of 2.5◦C/s. After soaking for 1 min, the specimen was uniaxially hot compressed at different strain rates. In this study, the temperatures selectedwere 350◦C, 400◦C, 450◦C.The strain rates usedwere 0.01s−1, 0.1s−1 and 1s−1. Experimental investigation and modelling of hot forming B4C/AA6061 low... 465 Fig. 3. Temperature profile of the hot compression test 5. Results and discussion 5.1. Determination of constitutive equations The experimental results from hot compression tests were used to determine material con- stants in the developed constitutive relationships. Firstly, according to Eqs. (3.2), (3.9) and (3.10), Young’s modulus and the initial yield strength of the composite vary with the tempera- ture from the applied heat, and are also significantly greater than those of thematrix. Figure 4 shows the similarity between the equation fitted and experimentally determined values. Good agreement exists between the fitted curves and experimental results. Differences that exist are believed to be due to the difficulty in determining accurate values from hot compression results, considering the slopes of themodulus are very sharp.Table 3 gives thematerial properties of the matrix alloy and reinforcement particles at room temperature. Tables 4 lists values of material constants used for calculating the strength variables. Fig. 4. Comparisons of numerical fitting (solid lines) and experimental results (solid symbols) of strength variables, where (a) Young’s modulus and (b) initial yield strength Table 3.Material properties of the matrix alloy and reinforcement Vp Vm d Ep η cm ρm [µm] [MPa] [J/(kgK)] [kg/m3] 0.15 0.85 17.5 362000 0.9 890 2700 Othermaterial constants in the dominant equation set were determined using a combination of Evolutionary Programming (EP) optimisation techniques (Li et al., 2002) as well as trial and 466 K. Zheng et al. Table 4.Determined constants for Young’s modulus and initial yield strength E0 QE E1 k1 Qk k2 590 20140 0.67 0.0017 40950 0.075 error methodology. The explanation of the optimisation method and description of numerical procedures for determining the material constants of constitutive equations are described by Cao and Lin (2008). Table 5 shows the determinedmaterial constants of Eqs. (3.10)1-5. Table 5.Determined constants for material constants K0 B0 C0 A0 n11 n12 326.5 0.2774 114.9 0.144 0.04691 −0.4111 QK QB QC QA Qn1 n2 9634 21780 51760 18420 29760 1 5.2. Comparison of experimental results and the constitutive model Figures 5 and 6 show comparisons between the Gleeble experimental results (symbols) and the modelling results (solid lines). Three typical hot forming temperatures 350◦C, 400◦C and 450◦C and three different strain rates from 0.01s−1 to 1s−1 were chosen. As can be seen in both figures, good fitting accuracy was obtained. Dynamic recrystallization at the beginning of deformationwhich results in the strain softening is neglected in the currentmodel for simplicity of numerical fitting. Figure 5 shows that MMC stress level reduces with the increasing forming temperature, and is lower than that at the room temperature (Chen et al., 2015). When the Fig. 5. Comparison of stress-strain relationships from hot compression tests at different temperatures and a strain rate of 0.1s−1. Symbols represent experimental results and solid lines are computed predictions from the model compositewas compressed at higher temperatures, such as 450◦Cand lower strain rates, such as 0.01s−1, the stress level exhibited a plateau. The absence of strain hardening is believed to be beneficial for bulk forming, such as extrusion and forging, as the strain hardeningwould increase the forming load significantly andmay cause cracks of the forming dies. In addition, the extent of strain hardening increasedwith the decreasing temperature at a fixed strain rate, considering dislocation recovery was not significant and visco-plastic feature was not obvious. The diffusion process was not sufficient at lower temperatures.Moreover, compared with forming at the room Experimental investigation and modelling of hot forming B4C/AA6061 low... 467 temperature, an increased strain limit without crack was observed representing a reasonable ductility improvement, which enhanced the feasibility of hot forming MMCs. For temperature 400◦C, a clear strain rate effectwas also observed in the hardening curves.With increasing strain rate, the stress level increased, as shown in Fig. 6. In summary, higher temperatures and lower strain rates are recommended for hot bulk forming the low volumeMMC materials. Fig. 6. Comparison of stress-strain relationships from hot compression tests at different strain rates and temperature of 400◦C. Symbols represent experimental results and solid lines are computed predictions from the model 6. Conclusions It is concluded that hot forming processes can be used to shape MMCs with a low volume fraction of reinforcements. Stress-strain relationships obtained from hot compression tests of AA6061/15% B4CMMC show that strain hardening is only obvious at relatively low tempera- tures, and the flow stress and the flow stress remains relatively constant at higher temperatures, which is believed to bebeneficial for bulk forming.The strain rate hardening is also significant at high temperatures dominated by the visco-plastic mechanism. In addition, the first ever unified physically-based visco-plastic material model has been developed for hot forming of low volume fraction reinforcement MMCs. The evolution of dislocations has been modelled taking into ac- count the effects of temperature history and plastic deformation. 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