- Email: [email protected]
SiCp
Journal of Materials Processing Technology 143–144 (2003) 1–4
Strain hardening behaviour and temperature effect on Al-2124/SiCp E. Mart´ın∗ , A. Forn, R. Nogué Department of Materials Science, Polytechnic University of Catalonian, Vilanova i la Geltrú 08800, Spain
Abstract An understanding of the strain hardening behaviour of discontinued reinforced aluminium alloys is essential in optimising the parameters for deformation processes of these materials. The 2124 aluminium alloy reinforced with SiC particles has been studied in T4 condition in order to determine the stress–strain response at different temperatures. The strain hardening exponent, n, decreases with the temperature. A non-linear value of the exponent n with the strain has been observed, and two regions are clearly characterised for each temperature. © 2003 Elsevier Science B.V. All rights reserved. Keywords: Aluminium; Metal matrix composites; Strain hardening; Deformation processes; Mechanical properties
1. Introduction One of the major driving forces for research and development in the area of metal matrix composites (MMCs) is the need for structural materials with high specific strength and stiffness. In order to tailor a composite material for strength base applications, it is important to optimise the processing parameters. The process control is now mainly based on computer simulation in combination with empirical rules and experimental measurements. An understanding of the flow behaviour of the material over the entire rang of stresses and strains, prior to the instability of necking, is essential to optimise the deformation processing of these materials. Mechanical properties such as elastic modulus, yield stress, ultimate tensile strength and elongation are used by the most popular software; other characteristics of the stress–strain curves, such as work-hardening behaviour, have not been incorporated enough in the analysis. Until now, considerable effort has been directed toward developing empirical laws that describe the work-hardening of alloys and composites. The parameters involved in these relationships, particularly the work-hardening exponent, n, have been correlated to the changes in the microstructure and deformation processes [1–4]. An increase in n with reinforcing particles is reported as a general rule, and softening mechanism in the last stage of deformation is justified by the presence of broken reinforced particles. The goal of the present work is to present an experimental study on the temperature behaviour of Al–SiCp MMCs, ∗ Corresponding author. Tel.: +349-3-98967733. E-mail address: [email protected] (E. Mart´ın).
manufactured using PM techniques compared to the unreinforced alloy.
2. Experimental procedures 2.1. Materials A 2124 Al alloy and a 2124 Al alloy reinforced with SiC particles were processed by powder metallurgy (AMC, United Kingdom). The composite contained 17 vol.% SiC particles, of an average size of 1.4 m. The produced billets were forged at 505 ◦ C (Forges de Bologne, France), then water quenched and naturally aged (T4 condition). The microstructure was studied and detailed [5], and showed a fine matrix grain size, with an average diameter of about 1 m, in both materials. 2.2. Tensile testing Round cross-section specimens were machined, from the forged ingot along the forged direction, in order to determine the mechanical behaviour. The end-specimens were threaded to the applied load. The specimens were 4 mm in diameter. An extensometer with a gauge length of 20 mm was used in all tests. Tensile tests were carried out at a strain rate of 3 × 10−3 s−1 , according to the EN 10002/1 and EN 10002/5 European Standards. The range of testing temperatures was room temperature (298 K), 100 ◦ C (373 K), 150 ◦ C (423 K) and 200 ◦ C (473 K). These testing temperatures are equivalent to 0.31Tm , 0.4Tm , 0.45Tm and 0.51Tm , respectively, where Tm is the melting point of the aluminium alloy matrix.
0924-0136/$ – see front matter © 2003 Elsevier Science B.V. All rights reserved. doi:10.1016/S0924-0136(03)00292-9
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E. Mart´ın et al. / Journal of Materials Processing Technology 143–144 (2003) 1–4
Fig. 1. Tensile stress–strain curves of: (a) composite and (b) unreinforced alloy, at testing temperatures.
3. Results and discussion 3.1. Tensile properties Fig. 1 shows engineering stress–engineering strain curves for the matrix material and MMC. The tensile properties of these materials are summarised in Table 1, where the elastic modulus (E), yield strength (σ ys ), tensile strength (σ u ) and strain at failure (εu ) are given. The 2124 T4 material has good strength and ductility, with total elongation exceeding 21% at room temperature and 27% at 200 ◦ C. The addition of SiC particles increases the strengthening properties as elastic modulus, but decreases the failure strain. The change on the properties is better accused starting from 200 ◦ C. The increase in monotonic strength of composites compared to the unreinforced alloys has been attributed to several mechanisms. Load transfer from the matrix to the reinforcement is a significant contributor to composite strengthening. Reinforcement particles impede dislocation motion and lead to dislocation pileups at particle–matrix interfaces; this effect is most pronounced in composites with extremely fine reinforcement particles, with sizes below 1 m [6]. In T4 condition, coherent precipitate combinations in the Al matrix are present, and are sheared by dislocations. While the precipitates are deformable, the SiC particles are non-deformable, acting as obstacles to dislocation mo-
tion and refining the slip length in the matrix. A combination of non-deformable particles in a matrix of shearable precipitates can result in a beneficial change in the deformation mechanisms. This condition occurs when the microstructure consists of non-deformable particles with a particle spacing of around 1 m [6]. The interparticle spacing (λ) for SiC particles in the present study, considered to be the average center-to-center spacing between two particles minor than the particle diameter, is given by [7] 1 1/8 λ≈d −1 , (1) 2f where d is the particle diameter, and f the volume fraction of particles. The calculated value for interparticles spacing is 0.5 m. At a higher temperature (T > 0.5Tm or hot working condition), that is, at 200 ◦ C, plasticity increases due to dislocation annihilation or activation of dislocation motion by a mechanism other than glide, for example climb [8], and by stress relaxation at matrix–particle interfaces and the enhancement of recovery processes at these interfaces [3]. 3.2. Strain hardening The Hollomon analysis is the most commonly used empirical stress–strain analysis method. This analysis assumes that the stress–strain curves can be described as σ = Kεn ,
Table 1 Tensile properties of test materials Material
Temperature (◦ C)
E (GPa) σ ys (MPa) σ u (MPa) εu (%)
2124 T4
RT 100 150 200
75 66 69 61
358 343 335 261
497 451 429 318
21.7 19.6 20.4 27.8
2124–SiC T4 RT 100 150 200
99 87 78 83
404 414 400 339
602 573 526 444
7.1 7.5 6.8 12.1
(2)
where σ is the true flow stress, ε the true plastic strain, n the strain hardening exponent and K the strength coefficient. The parameter n relates to the strain hardening rate, or flow stress, dσ/dε, through [9] n=
ε dσ . σ dε
(3)
The strain hardening exponent also measures the maximum uniform strain of the specimen before instability in tension or localised necking, and represents the maximum practical elongation in engineering application [10], so an increase in the strain hardening increases the strain to failure.
E. Mart´ın et al. / Journal of Materials Processing Technology 143–144 (2003) 1–4
3
Table 2 Summary of hardening parameters of 2124 T4 material Temperature (◦ C)
n
K (MPa)
n1
K1 (MPa)
n2
K2 (MPa)
True strain change
20 100 150 200
0.36 0.29 0.29 0.25
937 801 765 569
0.26 0.21 0.20 0.17
756 533 613 464
0.42 0.34 0.34 0.31
978 844 803 602
0.193 0.105 0.151 0.148
Table 3 Summary of hardening parameters of 2124–SiC T4 material Fig. 2. Strain hardening exponent for the 2124 T4 and 2124–SiC T4 at different temperatures.
Fig. 3. Strain hardening regions vs. strain, for 2124–SiC, at room temperature.
The curves in Fig. 1 have been replotted as true stress–true plastic strain and fitted by functions in the form of Eq. (2). The usual definitions were used for calculating true stresses and the corresponding true strains. Fig. 2 shows the values for the strain hardening exponent for both materials at different temperatures. The 2124–17% SiCp shows lower values than the unreinforced alloy, which agrees with the strains at failure. By plotting log–log curves of true stress–true strain (Fig. 3), two regions were detected
Temperature (◦ C)
n
20 100 150 200
0.28 1111 0.25 1008 0.25 928 0.22 760
K (MPa)
n1
K1 (MPa)
0.25 1004 0.22 898 0.20 822 0.17 647
n2
K2 (MPa)
0.30 1140 0.27 1030 0.27 955 0.27 805
True strain change 0.087 0.077 0.086 0.106
for each material, with a strain hardening exponent for lower strains and another for higher strains. The results are summarised in Tables 2 and 3, and also the true strain values for the change are indicated. The strain range dominated by strain hardening decreased as the deformation temperature increased. The change in strain hardening exponent is higher on 2124 alloy than on composite material from room temperature to 200 ◦ C. In the first stage both materials show low hardening (n1 values), and high hardening in the second stage (n2 values); that behaviour is in agreement with other works on naturally aged aluminium alloys [11]. The strain hardening rate dσ/dε has been plotted as a function of true plastic strain ε in Fig. 4 for both materials and testing temperatures. According to some bibliographic results [12,13], the plastic deformation mechanism in the naturally aged composites differed from those in the unreinforced alloy. In the latter, the deformation is heterogeneous, while it is homogeneous in
Fig. 4. Strain hardening rate vs. true plastic strain for: (a) composite and (b) unreinforced alloy.
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E. Mart´ın et al. / Journal of Materials Processing Technology 143–144 (2003) 1–4
Table 4 Hardening parameters related to true and engineering strain for 2124–SiC material Temperature (◦ C)
True strain change
Engineering strain change (%)
Engineering strain max. vs. n (%)
20 100 150 200
0.087 0.077 0.086 0.106
1.85 1.65 1.82 2.29
6.6 5.84 5.68 5.15
the reinforced alloy. The homogeneous deformation would increase the dislocation interaction chances; consequently, the strain hardening exponent would increase. However, our results have shown a different behaviour. The lower values for the strain hardening exponent on composite materials related to unreinforced alloys are explained by the apparent plastic localisation start. In order to analyse hardening properties, the elastoplastic transition has been considered at conventional yield strength. However, the plastic strain starts at true limit of proportionality. The limits of proportionality of the composites, measured at the point with linearity are lost in the stress–strain curves, and show a decrease from the value of the unreinforced alloys [13]. For the studied materials, at room temperature, the measured limit of proportionality has been 340 MPa for 2124 material and 314 MPa for reinforced 2124–SiC material. So, the 2124–SiC material starts hardening at lower stress values than the 2124 material does. At yield strength the reinforced material has achieved a higher hardening than the unreinforced alloy due to the previous range of plastic deformation. Fig. 4 shows a weak reduction in the strain hardening rate for both materials, with the strain increment. A sudden decrease in those values has been observed by other authors in composite materials [14], associated with the failure of the composites due to reinforcement particle fracture. In this study, this phenomenon has not been observed, and the fractographic analysis has only revealed some broken particles [5]. The temperature has a lower effect on hardening mechanism between room temperature and 200 ◦ C. Strain hardening exponent decreases weakly with the temperature, and the plastic strain range has a higher effect. Table 4 summarises the relation between temperature, true strain at n change, engineering strain at n change and maximum engineering strain at necking (engineering strain max. versus n on table).
4. Conclusions The following conclusions can be drawn: • The addition of SiC particles to 2124 alloy increases the strengthening properties as elastic modulus but decreases the failure strain.
• At higher temperature, that is 200 ◦ C, plasticity increases for both materials. • Two regions were detected for each material, with a strain hardening exponent for lower strains and another one for higher strains. • The lower values for the strain hardening exponent on composite materials related to unreinforced alloys are explained by the true plastic localisation starting. • The plastic strain range has a higher effect on strain hardening than the temperature does.
Acknowledgements The authors would like to take this opportunity to thank the EC which has founded this work through the BRITE Euram Project “Development of models for the prediction of the in-service performance of MMC components (MISPOM)”, contract no. BRPR-CT97-0396, and also to the Spanish Ministerio de Ciencia y Tecnologia for their support through a CICYT MAT97-1603CE.
References [1] M. Umemoto, Z.G. Liu, S. Sugimoto, K. Tsuchiya, Metall. Mater. Trans. A 31 (2000) 1785–1794. [2] I. Poschmann, H.J. McQueen, Mater. Sci. Technol. 14 (1998) 1101– 1108. [3] A.A. Mazen, J. Mater. Eng. Perf. 8 (4) (1999) 487–495. [4] P. Poza, J. Llorca, Metall. Mater. Trans. A 30 (1999) 869–878. [5] A. Forn, E. Mart´ın, R. Nogué, Proceedings of the Eighth National Congress on Heat Treatment Surface, Barcelona, Spain, 2000, pp. 159–166. [6] N. Chawla, U. Habel, Y.L. Shen, C. Andres, J.W. Jones, J.E. Allison, Metall. Mater. Trans. A 31 (2000) 531–640. [7] N. Chawla, C. Andres, J.W. Jones, J.E. Allison, Metall. Mater. Trans. A 29 (1998) 2843–2854. [8] R.W. Hertzberg, Deformation and Fracture Mechanics of Engineering Materials, Wiley, New York, 1996, p. 66. [9] G.E. Dieter, Mechanical Metallurgy, McGraw-Hill, New York, 1986, p. 287. [10] C.H. Cáceres, T. Din, A.K.M.B. Rashid, J. Campbell, Mater. Sci. Technol. 15 (1999) 711–716. [11] N. Mart´ın, J.M. Badia, A. Garc´ıa, J.M. Antoraz, P. Tar´ın, Proceedings of the Eighth National Congress on Heat Treatment Surface, Barcelona, Spain, 2000, pp. 149–157. [12] P. Poza, J. Llorca, Metall. Mater. Trans. A 30 (1999) 845–855. [13] S.S. Kim, K.S. Shin, N.J. Kim, Metall. Mater. Trans. A 30 (1999) 2254–2258. [14] A. Roatta, P.A. Turner, M.A. Bertinetti, R.E. Bolmaro, Metall. Mater. Trans. A 30 (1999) 2875–2884.
Strain hardening behaviour and temperature effect on Al-2124/SiCp E. Mart´ın∗ , A. Forn, R. Nogué Department of Materials Science, Polytechnic University of Catalonian, Vilanova i la Geltrú 08800, Spain
Abstract An understanding of the strain hardening behaviour of discontinued reinforced aluminium alloys is essential in optimising the parameters for deformation processes of these materials. The 2124 aluminium alloy reinforced with SiC particles has been studied in T4 condition in order to determine the stress–strain response at different temperatures. The strain hardening exponent, n, decreases with the temperature. A non-linear value of the exponent n with the strain has been observed, and two regions are clearly characterised for each temperature. © 2003 Elsevier Science B.V. All rights reserved. Keywords: Aluminium; Metal matrix composites; Strain hardening; Deformation processes; Mechanical properties
1. Introduction One of the major driving forces for research and development in the area of metal matrix composites (MMCs) is the need for structural materials with high specific strength and stiffness. In order to tailor a composite material for strength base applications, it is important to optimise the processing parameters. The process control is now mainly based on computer simulation in combination with empirical rules and experimental measurements. An understanding of the flow behaviour of the material over the entire rang of stresses and strains, prior to the instability of necking, is essential to optimise the deformation processing of these materials. Mechanical properties such as elastic modulus, yield stress, ultimate tensile strength and elongation are used by the most popular software; other characteristics of the stress–strain curves, such as work-hardening behaviour, have not been incorporated enough in the analysis. Until now, considerable effort has been directed toward developing empirical laws that describe the work-hardening of alloys and composites. The parameters involved in these relationships, particularly the work-hardening exponent, n, have been correlated to the changes in the microstructure and deformation processes [1–4]. An increase in n with reinforcing particles is reported as a general rule, and softening mechanism in the last stage of deformation is justified by the presence of broken reinforced particles. The goal of the present work is to present an experimental study on the temperature behaviour of Al–SiCp MMCs, ∗ Corresponding author. Tel.: +349-3-98967733. E-mail address: [email protected] (E. Mart´ın).
manufactured using PM techniques compared to the unreinforced alloy.
2. Experimental procedures 2.1. Materials A 2124 Al alloy and a 2124 Al alloy reinforced with SiC particles were processed by powder metallurgy (AMC, United Kingdom). The composite contained 17 vol.% SiC particles, of an average size of 1.4 m. The produced billets were forged at 505 ◦ C (Forges de Bologne, France), then water quenched and naturally aged (T4 condition). The microstructure was studied and detailed [5], and showed a fine matrix grain size, with an average diameter of about 1 m, in both materials. 2.2. Tensile testing Round cross-section specimens were machined, from the forged ingot along the forged direction, in order to determine the mechanical behaviour. The end-specimens were threaded to the applied load. The specimens were 4 mm in diameter. An extensometer with a gauge length of 20 mm was used in all tests. Tensile tests were carried out at a strain rate of 3 × 10−3 s−1 , according to the EN 10002/1 and EN 10002/5 European Standards. The range of testing temperatures was room temperature (298 K), 100 ◦ C (373 K), 150 ◦ C (423 K) and 200 ◦ C (473 K). These testing temperatures are equivalent to 0.31Tm , 0.4Tm , 0.45Tm and 0.51Tm , respectively, where Tm is the melting point of the aluminium alloy matrix.
0924-0136/$ – see front matter © 2003 Elsevier Science B.V. All rights reserved. doi:10.1016/S0924-0136(03)00292-9
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E. Mart´ın et al. / Journal of Materials Processing Technology 143–144 (2003) 1–4
Fig. 1. Tensile stress–strain curves of: (a) composite and (b) unreinforced alloy, at testing temperatures.
3. Results and discussion 3.1. Tensile properties Fig. 1 shows engineering stress–engineering strain curves for the matrix material and MMC. The tensile properties of these materials are summarised in Table 1, where the elastic modulus (E), yield strength (σ ys ), tensile strength (σ u ) and strain at failure (εu ) are given. The 2124 T4 material has good strength and ductility, with total elongation exceeding 21% at room temperature and 27% at 200 ◦ C. The addition of SiC particles increases the strengthening properties as elastic modulus, but decreases the failure strain. The change on the properties is better accused starting from 200 ◦ C. The increase in monotonic strength of composites compared to the unreinforced alloys has been attributed to several mechanisms. Load transfer from the matrix to the reinforcement is a significant contributor to composite strengthening. Reinforcement particles impede dislocation motion and lead to dislocation pileups at particle–matrix interfaces; this effect is most pronounced in composites with extremely fine reinforcement particles, with sizes below 1 m [6]. In T4 condition, coherent precipitate combinations in the Al matrix are present, and are sheared by dislocations. While the precipitates are deformable, the SiC particles are non-deformable, acting as obstacles to dislocation mo-
tion and refining the slip length in the matrix. A combination of non-deformable particles in a matrix of shearable precipitates can result in a beneficial change in the deformation mechanisms. This condition occurs when the microstructure consists of non-deformable particles with a particle spacing of around 1 m [6]. The interparticle spacing (λ) for SiC particles in the present study, considered to be the average center-to-center spacing between two particles minor than the particle diameter, is given by [7] 1 1/8 λ≈d −1 , (1) 2f where d is the particle diameter, and f the volume fraction of particles. The calculated value for interparticles spacing is 0.5 m. At a higher temperature (T > 0.5Tm or hot working condition), that is, at 200 ◦ C, plasticity increases due to dislocation annihilation or activation of dislocation motion by a mechanism other than glide, for example climb [8], and by stress relaxation at matrix–particle interfaces and the enhancement of recovery processes at these interfaces [3]. 3.2. Strain hardening The Hollomon analysis is the most commonly used empirical stress–strain analysis method. This analysis assumes that the stress–strain curves can be described as σ = Kεn ,
Table 1 Tensile properties of test materials Material
Temperature (◦ C)
E (GPa) σ ys (MPa) σ u (MPa) εu (%)
2124 T4
RT 100 150 200
75 66 69 61
358 343 335 261
497 451 429 318
21.7 19.6 20.4 27.8
2124–SiC T4 RT 100 150 200
99 87 78 83
404 414 400 339
602 573 526 444
7.1 7.5 6.8 12.1
(2)
where σ is the true flow stress, ε the true plastic strain, n the strain hardening exponent and K the strength coefficient. The parameter n relates to the strain hardening rate, or flow stress, dσ/dε, through [9] n=
ε dσ . σ dε
(3)
The strain hardening exponent also measures the maximum uniform strain of the specimen before instability in tension or localised necking, and represents the maximum practical elongation in engineering application [10], so an increase in the strain hardening increases the strain to failure.
E. Mart´ın et al. / Journal of Materials Processing Technology 143–144 (2003) 1–4
3
Table 2 Summary of hardening parameters of 2124 T4 material Temperature (◦ C)
n
K (MPa)
n1
K1 (MPa)
n2
K2 (MPa)
True strain change
20 100 150 200
0.36 0.29 0.29 0.25
937 801 765 569
0.26 0.21 0.20 0.17
756 533 613 464
0.42 0.34 0.34 0.31
978 844 803 602
0.193 0.105 0.151 0.148
Table 3 Summary of hardening parameters of 2124–SiC T4 material Fig. 2. Strain hardening exponent for the 2124 T4 and 2124–SiC T4 at different temperatures.
Fig. 3. Strain hardening regions vs. strain, for 2124–SiC, at room temperature.
The curves in Fig. 1 have been replotted as true stress–true plastic strain and fitted by functions in the form of Eq. (2). The usual definitions were used for calculating true stresses and the corresponding true strains. Fig. 2 shows the values for the strain hardening exponent for both materials at different temperatures. The 2124–17% SiCp shows lower values than the unreinforced alloy, which agrees with the strains at failure. By plotting log–log curves of true stress–true strain (Fig. 3), two regions were detected
Temperature (◦ C)
n
20 100 150 200
0.28 1111 0.25 1008 0.25 928 0.22 760
K (MPa)
n1
K1 (MPa)
0.25 1004 0.22 898 0.20 822 0.17 647
n2
K2 (MPa)
0.30 1140 0.27 1030 0.27 955 0.27 805
True strain change 0.087 0.077 0.086 0.106
for each material, with a strain hardening exponent for lower strains and another for higher strains. The results are summarised in Tables 2 and 3, and also the true strain values for the change are indicated. The strain range dominated by strain hardening decreased as the deformation temperature increased. The change in strain hardening exponent is higher on 2124 alloy than on composite material from room temperature to 200 ◦ C. In the first stage both materials show low hardening (n1 values), and high hardening in the second stage (n2 values); that behaviour is in agreement with other works on naturally aged aluminium alloys [11]. The strain hardening rate dσ/dε has been plotted as a function of true plastic strain ε in Fig. 4 for both materials and testing temperatures. According to some bibliographic results [12,13], the plastic deformation mechanism in the naturally aged composites differed from those in the unreinforced alloy. In the latter, the deformation is heterogeneous, while it is homogeneous in
Fig. 4. Strain hardening rate vs. true plastic strain for: (a) composite and (b) unreinforced alloy.
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E. Mart´ın et al. / Journal of Materials Processing Technology 143–144 (2003) 1–4
Table 4 Hardening parameters related to true and engineering strain for 2124–SiC material Temperature (◦ C)
True strain change
Engineering strain change (%)
Engineering strain max. vs. n (%)
20 100 150 200
0.087 0.077 0.086 0.106
1.85 1.65 1.82 2.29
6.6 5.84 5.68 5.15
the reinforced alloy. The homogeneous deformation would increase the dislocation interaction chances; consequently, the strain hardening exponent would increase. However, our results have shown a different behaviour. The lower values for the strain hardening exponent on composite materials related to unreinforced alloys are explained by the apparent plastic localisation start. In order to analyse hardening properties, the elastoplastic transition has been considered at conventional yield strength. However, the plastic strain starts at true limit of proportionality. The limits of proportionality of the composites, measured at the point with linearity are lost in the stress–strain curves, and show a decrease from the value of the unreinforced alloys [13]. For the studied materials, at room temperature, the measured limit of proportionality has been 340 MPa for 2124 material and 314 MPa for reinforced 2124–SiC material. So, the 2124–SiC material starts hardening at lower stress values than the 2124 material does. At yield strength the reinforced material has achieved a higher hardening than the unreinforced alloy due to the previous range of plastic deformation. Fig. 4 shows a weak reduction in the strain hardening rate for both materials, with the strain increment. A sudden decrease in those values has been observed by other authors in composite materials [14], associated with the failure of the composites due to reinforcement particle fracture. In this study, this phenomenon has not been observed, and the fractographic analysis has only revealed some broken particles [5]. The temperature has a lower effect on hardening mechanism between room temperature and 200 ◦ C. Strain hardening exponent decreases weakly with the temperature, and the plastic strain range has a higher effect. Table 4 summarises the relation between temperature, true strain at n change, engineering strain at n change and maximum engineering strain at necking (engineering strain max. versus n on table).
4. Conclusions The following conclusions can be drawn: • The addition of SiC particles to 2124 alloy increases the strengthening properties as elastic modulus but decreases the failure strain.
• At higher temperature, that is 200 ◦ C, plasticity increases for both materials. • Two regions were detected for each material, with a strain hardening exponent for lower strains and another one for higher strains. • The lower values for the strain hardening exponent on composite materials related to unreinforced alloys are explained by the true plastic localisation starting. • The plastic strain range has a higher effect on strain hardening than the temperature does.
Acknowledgements The authors would like to take this opportunity to thank the EC which has founded this work through the BRITE Euram Project “Development of models for the prediction of the in-service performance of MMC components (MISPOM)”, contract no. BRPR-CT97-0396, and also to the Spanish Ministerio de Ciencia y Tecnologia for their support through a CICYT MAT97-1603CE.
References [1] M. Umemoto, Z.G. Liu, S. Sugimoto, K. Tsuchiya, Metall. Mater. Trans. A 31 (2000) 1785–1794. [2] I. Poschmann, H.J. McQueen, Mater. Sci. Technol. 14 (1998) 1101– 1108. [3] A.A. Mazen, J. Mater. Eng. Perf. 8 (4) (1999) 487–495. [4] P. Poza, J. Llorca, Metall. Mater. Trans. A 30 (1999) 869–878. [5] A. Forn, E. Mart´ın, R. Nogué, Proceedings of the Eighth National Congress on Heat Treatment Surface, Barcelona, Spain, 2000, pp. 159–166. [6] N. Chawla, U. Habel, Y.L. Shen, C. Andres, J.W. Jones, J.E. Allison, Metall. Mater. Trans. A 31 (2000) 531–640. [7] N. Chawla, C. Andres, J.W. Jones, J.E. Allison, Metall. Mater. Trans. A 29 (1998) 2843–2854. [8] R.W. Hertzberg, Deformation and Fracture Mechanics of Engineering Materials, Wiley, New York, 1996, p. 66. [9] G.E. Dieter, Mechanical Metallurgy, McGraw-Hill, New York, 1986, p. 287. [10] C.H. Cáceres, T. Din, A.K.M.B. Rashid, J. Campbell, Mater. Sci. Technol. 15 (1999) 711–716. [11] N. Mart´ın, J.M. Badia, A. Garc´ıa, J.M. Antoraz, P. Tar´ın, Proceedings of the Eighth National Congress on Heat Treatment Surface, Barcelona, Spain, 2000, pp. 149–157. [12] P. Poza, J. Llorca, Metall. Mater. Trans. A 30 (1999) 845–855. [13] S.S. Kim, K.S. Shin, N.J. Kim, Metall. Mater. Trans. A 30 (1999) 2254–2258. [14] A. Roatta, P.A. Turner, M.A. Bertinetti, R.E. Bolmaro, Metall. Mater. Trans. A 30 (1999) 2875–2884.