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Indentation creep in a short fibre-reinforced metal matrix composite
Materials Science and Engineering A272 (1999) 145 – 151 www.elsevier.com/locate/msea
Indentation creep in a short fibre-reinforced metal matrix composite G. Cseh a, J. Ba¨r b, H.-J. Gudladt b, J. Lendvai a,*, A. Juha´sz a a
Institute for General Physics, Eo¨t6o¨s Uni6ersity Budapest, Pa´zma´ny Pe´ter s. 1, H-1117 Budapest, Hungary b Institut fu¨r Werkstoffkunde, Uni6ersita¨t der Bundeswehr Mu¨nchen, D-85577 Neubiberg, Germany
Abstract Creep properties of an unreinforced M124 (AlSi12CuMgNi) base alloy and an Al203 (Saffil) fibre reinforced M124 +s metal matrix composite (MMC) were investigated by indentation tests performed between 250 and 350°C. It has been found that the creep curve of the base alloy consists of two stages (transient and steady state), whereas the curve of the composite material contains a decelerating third stage as well. This creep behavior is correlated with the changes of the microstructure below the indenter during the deformation process. In the region of steady state creep the stress exponent and the activation energy was determined for both materials. © 1999 Elsevier Science S.A. All rights reserved. Keywords: Composite; Creep; Indentation
1. Introduction
2. Materials and methods
During the indentation creep (IC) test a cylindrical indenter is pressed into the surface of the sample at a constant load and temperature. Simultaneously, the indentation depth (h) is recorded as the function of the elapsed time (t). This method is both theoretically and experimentally well established for the investigation of secondary creep properties of metals, glasses and glass ceramics at high homologous temperatures [1 – 7]. Comparing the IC to the tensile creep tests, equivalent stress (s) and strain rate (o; ) data can be evaluated from the indentation rate (dh/dt), the pressure under the punch (P = 4F/pd 2) at a given load (F) and punch diameter (D) as:
The composition of the unreinforced M124 alloy is shown in Table 1. The M124+ s metal matrix composite (MMC) containing 13.9 vol% Saffil fibre was produced by a squeeze casting process and provided by Mahle GmbH, Stuttgart. The microstructure of the MMC alloy was investigated and described in a previous paper [8]. It has been found that in the composite, the fibres are fixed by intermetallic phase particles and Si precipitates which form preferentially at the nodes of the fibres. Therefore, the MMC is composed of a ductile Al matrix and a rigid three-dimensional network, consisting of fibres and precipitates. The samples were homogenized for 10 h at 480°C and quenched into room temperature (RT) oil. Following a RT storage for at least 100 h an annealing treatment was performed for 24 h at 350°C for both materials to obtain a stable matrix microstructure for the creep tests. The IC tests were performed in the temperature range of 250–350°C. The accuracy of the displacement measurement and the thermal control were 0.1 mm and 9 1°C, respectively. The samples were plates 2–4 mm high and 8–12 mm wide. Cylindrical indenters with diameters between 0.5 and 1.25 mm were applied.
s =c1p
and
o; = c2
dh/dt D
(1)
where c1 : 1/3 and c2 :1 are constants for a wide range of materials [1–7].
This paper is dedicated to Professor Herbert Herman on the occasion of his 65th birthday. * Corresponding author. Tel.: + 36-1-3722809; fax: + 36-13722811. E-mail address: [email protected] (J. Lendvai)
0921-5093/99/$ - see front matter © 1999 Elsevier Science S.A. All rights reserved. PII: S 0 9 2 1 - 5 0 9 3 ( 9 9 ) 0 0 4 6 6 - 9
G. Cseh et al. / Materials Science and Engineering A272 (1999) 145–151
146
Table 1 The composition of the M124 matrix alloy (wt%) M124
Si
Fe
Cu
Mn
Mg
Ni
Zn
Ti
Al
11–13
50.7
0.8–1.3
50.3
0.8–1.3
51.3
50.2
50.2
Balance
Typical indentation depth – time curves obtained on the unreinforced M124 alloy are shown in Fig. 1(a). It can be seen that, similarly to the curves obtained on several Al alloys [4,5] exist, the curves consist of two stages, corresponding to transient (I) and steady state (II) creep. From the slope of the second part of the curve a nearly constant steady state indentation creep rate can be determined, and the equivalent stress and strain rate data can be evaluated. In this part the strain rate is slightly decreasing, as can be seen directly from Fig. 1(b), in which the strain rate data are plotted
against the indentation depth. This effect can be attributed to the friction between the material and the surface of the indenter. In Fig. 2(a) steady state creep rates (o; ) versus equivalent stress (s) determined from creep tests at different temperatures are plotted. The stress exponent (n) determined from the slope of the log o; − 1og s curves between 250 and 350°C decreases from 7.6 to 6.5. Plotting the o; data at constant stresses in a semi-logarithmic presentation against the reciprocal temperature (Fig. 2(b)), the activation energy of the creep deformation process was found to be between 140 and 160 kJ mol − 1, depending on the stress level. These values are close to the energy of self-diffusion in pure aluminium ( 142 kJ mol − 1), and this suggests that the rate of
Fig. 1. Indentation curves of the M124 alloy at different stresses and temperatures (a) and strain rate–indentation depth at different stresses and temperatures (b).
Fig. 2. Strain rate vs., equivalent stress at different temperatures for the M124 base alloy (a) and strain rate vs., the reciprocal temperature (b).
3. Results and discussion
3.1. Indentation creep of the unreinforced M124 alloy
G. Cseh et al. / Materials Science and Engineering A272 (1999) 145–151
147
steady state IC is controlled by climb of edge dislocations [9,10].
3.2. Indentation creep of the M124+ s composite The indentation curves of the M124+s composite differ significantly from those of the unreinforced alloy. Typical IC curves, obtained at different temperatures and loads, can be seen in Fig. 3(a). Three stages can be distinguished on each of the curves, apart from the instaneous initial deflection of the samples occurring during uploading. The first stage: (I) is characterized by a gradually increasing indentation rate (o; ); the second stage (II) by a constant o; ; whereas in the third stage (III) the creep rate is gradually decreasing. This trend can be seen directly from Fig. 3(b) where the strain rate measured at 350°C is plotted against the indentation depth at different values of the stress. The changes in the composite microstructure during the course of the indentation were investigated by metallographic methods. The mi-
Fig. 4. Microstructure of an M124 + s sample under a D= 0.8 mm punch in the first stage of indentation (a) and the section near to the edge of the indenter at higher magnification (b).
Fig. 3. Indentation curves of M124 + s at different stresses and temperatures (a) and strain rate vs., indentation depth at different equivalent stresses (b).
crostructure of the material under a 0.8 mm diameter indenter in stage (I) is shown in Fig. 4(a). At higher magnification (Fig. 4(b)) it can be seen that the failure of the fibres appears first in the vicinity of the rim of the indenter, where, according to theoretical considerations, the shear stress concentration is the highest [11]. This has also been established by our calculations with the help of the ANSYS [12,13] finite element analysis program. The plastic shear strain values obtained from the equilibrium solution of the elastic plastic model, are plotted in the plane of the indentation axis adjacent to the edge of the indenter in Fig. 5. It can be seen that the plastic deformation zone extends gradually from the edge to underneath the indenter in the model, which is in agreement with the observed microstructure (Fig. 4(b)). The presence of the accelerating stage at the low values of the penetration depth can be explained as follows: initially the matrix deforms slowly, the movement of dislocations is hindered by the rigid fiber network and dislocation pile-ups are forming. When the fracture of the fibers takes place, effected by the local stress increase at the leading dislocation of the pile-up, the dislocations start moving, inducing failure of further fibers, thereby accelerating the deformation. This is confirmed by Fig. 6 showing the first part of the indentation curve in higher resolution, in which
148
G. Cseh et al. / Materials Science and Engineering A272 (1999) 145–151
Fig. 5. Plastic shear strain near to the edge of the indenter at s=69 MPa computed with the ANSYS finite element analysis program.
steps of several microns height can be observed corresponding to a fracture event in the fiber network. Similar serration on the deformation curve has been observed previously around the minimum creep rate during tensile creep tests in fibre reinforced MMCs, and was also attributed to fiber fracture [14]. The microstructure of the sample corresponding already to stage (II) indentation is shown in Fig. 7. Around the penetrating indenter an approximately spherical deformation zone can be observed, in which the fracture of the fibers takes place. The deformation zone moves in front of the indenter and a constant strain rate is attained, as is characteristic of a region in the steady state secondary creep. Similar observations about the propagation of the deformation zone have been reported previously for unreinforced age-hardeneable Al alloys [5]. The microstructure of the sample in the third stage is shown in Fig. 8(a). At this stage crater formation is observed on the surface of the specimen, indicating a material transport from the bottom of the crater to the specimen surface at the rim of the indenter. Broken fibres change their orientation and tend to align in the direction of flow within the bulk material, as represented by a kind of flow pattern in Fig. 8(a). This effect can be ascribed to the extensive shear deformation taking place below the indenter as shown also by the result of the FEM analysis (Fig. 5).
In addition, it can be seen that fragments of multiply broken fibres accumulate immediately in front of the indenter. These fibre fragments can be seen in higher magnification close to the edge of the indenter (Fig. 8(b)). The accumulation of fibre fragments hinder the undisturbed flow of the material and, therefore, the progress of the deformation zone in front of the indenter. This leads to the gradual deceleration of the indentation in the third stage of the creep process, in contrast to the tensile creep tests where the multiple fracture of fibers leads to an accelerating tertiary creep and finally to the rupture of the sample [14]. The friction between
Fig. 6. The first part of the indentation curve at s= 106 MPa and T =350°C.
G. Cseh et al. / Materials Science and Engineering A272 (1999) 145–151
149
Fig. 7. Cross section of an M124 + s sample in the second stage.
the sample and the indenter surface may lead to an additional decrease of the strain rate in case of the reinforced as well as of the unreinforced alloy. It should be mentioned that the mechanisms in stage III are characteristic for indentation tests, and quite different from conventional tensile creep tests. In the case of the M124+s composite sample the Arrhenius plot of strain rate data evaluated from the slope of the steady state part of the indentation curves at s = 166 MPa (Fig. 9) yielding the activation energy of 177 kJ mol − 1, which is somewhat higher than the values obtained for the unreinforced alloy. Fig. 10 shows the steady state creep rate of the two samples as a function of the applied stress. Besides the data obtained from the present IC measurements results of tensile creep tests on the same materials [15] are also included in the figure. The stress exponent of the MMC determined from the IC tests with n = 9.8 is significantly higher then the n =7.4 value of the unreinforced alloy. There is a significant difference also in the creep resistance of the two materials, at the same stress values the steady state indentation creep rate of the MMC is two or three orders of magnitude lower. In the overlapping range of the IC and tensile creep test, the
agreement between the measured o; versus s values are satisfactory. The differences between the stress exponents determined from IC tests and tensile creep tests of Bindlingmaier et al. [15], respectively, should be attributed to the numerous small pores, which are already present in the as cast composite material, and which lead to a higher creep rate in tensile mode [16]. The values of the stress exponent obtained from the present investigation are close to those obtained from other creep measurements performed on similar conventional alloys and MMC materials [14]. It is also worth noting that the scatter in the data of the MMC is considerably higher than in the unreinforced sample, which is probably as a result of the local changes in the volume fraction as well as in the orientation distribution of the fibres under the punch in different samples. Considering the linearity of the log s− log o; and the log o; − 1/T relationships the creep behavior of the investigated materials can be described by the classical power law creep:
o; stat = As nexp
−Q kT
(2)
150
G. Cseh et al. / Materials Science and Engineering A272 (1999) 145–151
where A and k are constants, and n is the stress exponent. In contrast to tensile creep the o; stat quantity represents a maximum indentation creep rate in case of
the short fibre reinforced alloy. Nevertheless, the mechanisms controlling the creep in stage (II) of the IC curves may be the same as in tensile creep.
Fig. 8. Cross section of an M124+ s sample in the third stage (a) and the section close to the edge of the indenter at higher magnification (b).
G. Cseh et al. / Materials Science and Engineering A272 (1999) 145–151
Fig. 9. Strain rate data plotted against the reciprocal temperature for M124 + s.
151
an accelerated transient in contrast to the unreinforced alloy where the creep rate is decreasing in stage (I). With progressing penetration a material flow is setting in along the cylinder surface of the indenter from regions under the punch towards the surface of the specimen. The crater formation is a result of this process. In the case of the MMC in the course of this process fibre fragments produced by the multiply fractures of the fibers, become arrested by the unbroken elements of the fibre network, and the piling-up of these fragments leads to the decelerating stage (III). Therefore, steady state creep rates are expected to be several orders of magnitude lower in the MMC than in the unreinforced alloy. In this region the stress exponent n obtained for both the base alloy and the MMC are about 7 and 10, while the activation energy values are approximately 150 and 180 kJ mol − 1, respectively. Acknowledgements Financial support of the Hungarian Scientific Research Fund (OTKA) contract No. T-022976 is acknowledged. This work was carried out within the German-Hungarian Intergovernmental S&T Cooperation Program (D-6/97; Ung 232.21). References [1] [2] [3] [4] [5] [6]
Fig. 10. Comparison of strain rate vs., equivalent stress data obtained from indentation and tensile creep tests, respectively.
4. Summary and conclusion
[7] [8] [9]
The IC tests revealed significant differences in the creep behavior of the unreinforced and the composite material. While in the unreinforced material the short initial transient is followed only by a steady stage with nearly constant creep rate, in the MMC a third stage occurs in which the creep rate decreases with increasing penetration depth. A crater-shaped protrusion is forming on the surface of both the unreinforced and the MMC samples around the indenter, consequently this cannot be the reason for the occurrence of the decelerating stage in the case of the MMC. Metallographic investigations revealed fibre fracture in the MMC in a zone below the punch. In stage (I) the occurrence of fibre fractures promotes the movement of the dislocations initially, giving rise to .
[10]
[11] [12] [13]
[14] [15]
[16]
E.C. Yu, J.C.M. Li, Phil. Mag. 36 (1977) 911. E.C. Yu, J.C.M. Li, J. Mater. Sci. 12 (1977) 2200. S.N.G. Chu, J.C.M. Li, J. Appl. Phys. 51 (1980) 3338. P. Tasnadi, A. Juhasz, N.Q. Chinh, I. Kovacs, Res. Mech. 24 (1988) 355. P. Tasnadi, A. Juhasz, N.Q. Chinh, P. Szaszvari, I. Kovacs, Mater. Sci. Forum 13/14 (1987) 421. T.H. Hyde, K. Yehia, A.A. Becker, Int. J. Mech. Sci. 35 (1993) 451. G. Cseh, N.Q. Chinh, P. Tasnadi, A. Juhasz, J. Mat. Sci. 32 (1997) 1733. J. Ba¨r, H.-G. Klussmann, H.-J. Gudladt, Scripta Met. Mater. 29 (1993) 787. H.J. Frost, M.F. Ashby, Deformation-Mechanism Maps, The Plasticity and Creep of Metals and Ceramics, Pergamon Press, Oxford, 1982. W. Blum, Plastic deformation and fracture of materials, in: H. Mughrabi (Ed.), Materials Science and Technology, 6 edn, V.C.H. Verlag, Weinheim, 1993, p. 359. I.N. Sneddon, Int. J. Eng. Sci. 3 (1965) 245. K.-J. Bathe, Finite-Elemente-Methoden, Springer, Berlin, 1990. G. Mu¨ller, C. Groth, FEM fu¨r Praktiker: die Methode der finiten Elemente mit dem Fe Programm ANSYS, 3. Auflage, Expert-Verlag (Edition expertsoft; 23), Rennningen– Malmsheim, Germany, 1997. A. Dlouhy, G. Eggeler, Mechanical Behaviour of Materials at High Temperature, Kluwer, Dordrecht, 1996, p. 495. T. Bidlingmaier, D. Vogt, A. Wanner, in: G. Zieglwr (Ed.), Werkstoffe und Werkstoffverbunde, DGM Informationsgesellschaft, Frankfurt, 1996, p. 245. J. Ba¨r, H.-J. Gudladt, G. Cseh, A. Juhasz, J. Lendvai, in: W.J. Muster, J. Ziebs, R. Link (Eds.), Proc. Werkstoffwoche 1998, vol. 10, Wiley-V.C.H. Verlag, Weinheim, 1999, pp. 115–120.
Indentation creep in a short fibre-reinforced metal matrix composite G. Cseh a, J. Ba¨r b, H.-J. Gudladt b, J. Lendvai a,*, A. Juha´sz a a
Institute for General Physics, Eo¨t6o¨s Uni6ersity Budapest, Pa´zma´ny Pe´ter s. 1, H-1117 Budapest, Hungary b Institut fu¨r Werkstoffkunde, Uni6ersita¨t der Bundeswehr Mu¨nchen, D-85577 Neubiberg, Germany
Abstract Creep properties of an unreinforced M124 (AlSi12CuMgNi) base alloy and an Al203 (Saffil) fibre reinforced M124 +s metal matrix composite (MMC) were investigated by indentation tests performed between 250 and 350°C. It has been found that the creep curve of the base alloy consists of two stages (transient and steady state), whereas the curve of the composite material contains a decelerating third stage as well. This creep behavior is correlated with the changes of the microstructure below the indenter during the deformation process. In the region of steady state creep the stress exponent and the activation energy was determined for both materials. © 1999 Elsevier Science S.A. All rights reserved. Keywords: Composite; Creep; Indentation
1. Introduction
2. Materials and methods
During the indentation creep (IC) test a cylindrical indenter is pressed into the surface of the sample at a constant load and temperature. Simultaneously, the indentation depth (h) is recorded as the function of the elapsed time (t). This method is both theoretically and experimentally well established for the investigation of secondary creep properties of metals, glasses and glass ceramics at high homologous temperatures [1 – 7]. Comparing the IC to the tensile creep tests, equivalent stress (s) and strain rate (o; ) data can be evaluated from the indentation rate (dh/dt), the pressure under the punch (P = 4F/pd 2) at a given load (F) and punch diameter (D) as:
The composition of the unreinforced M124 alloy is shown in Table 1. The M124+ s metal matrix composite (MMC) containing 13.9 vol% Saffil fibre was produced by a squeeze casting process and provided by Mahle GmbH, Stuttgart. The microstructure of the MMC alloy was investigated and described in a previous paper [8]. It has been found that in the composite, the fibres are fixed by intermetallic phase particles and Si precipitates which form preferentially at the nodes of the fibres. Therefore, the MMC is composed of a ductile Al matrix and a rigid three-dimensional network, consisting of fibres and precipitates. The samples were homogenized for 10 h at 480°C and quenched into room temperature (RT) oil. Following a RT storage for at least 100 h an annealing treatment was performed for 24 h at 350°C for both materials to obtain a stable matrix microstructure for the creep tests. The IC tests were performed in the temperature range of 250–350°C. The accuracy of the displacement measurement and the thermal control were 0.1 mm and 9 1°C, respectively. The samples were plates 2–4 mm high and 8–12 mm wide. Cylindrical indenters with diameters between 0.5 and 1.25 mm were applied.
s =c1p
and
o; = c2
dh/dt D
(1)
where c1 : 1/3 and c2 :1 are constants for a wide range of materials [1–7].
This paper is dedicated to Professor Herbert Herman on the occasion of his 65th birthday. * Corresponding author. Tel.: + 36-1-3722809; fax: + 36-13722811. E-mail address: [email protected] (J. Lendvai)
0921-5093/99/$ - see front matter © 1999 Elsevier Science S.A. All rights reserved. PII: S 0 9 2 1 - 5 0 9 3 ( 9 9 ) 0 0 4 6 6 - 9
G. Cseh et al. / Materials Science and Engineering A272 (1999) 145–151
146
Table 1 The composition of the M124 matrix alloy (wt%) M124
Si
Fe
Cu
Mn
Mg
Ni
Zn
Ti
Al
11–13
50.7
0.8–1.3
50.3
0.8–1.3
51.3
50.2
50.2
Balance
Typical indentation depth – time curves obtained on the unreinforced M124 alloy are shown in Fig. 1(a). It can be seen that, similarly to the curves obtained on several Al alloys [4,5] exist, the curves consist of two stages, corresponding to transient (I) and steady state (II) creep. From the slope of the second part of the curve a nearly constant steady state indentation creep rate can be determined, and the equivalent stress and strain rate data can be evaluated. In this part the strain rate is slightly decreasing, as can be seen directly from Fig. 1(b), in which the strain rate data are plotted
against the indentation depth. This effect can be attributed to the friction between the material and the surface of the indenter. In Fig. 2(a) steady state creep rates (o; ) versus equivalent stress (s) determined from creep tests at different temperatures are plotted. The stress exponent (n) determined from the slope of the log o; − 1og s curves between 250 and 350°C decreases from 7.6 to 6.5. Plotting the o; data at constant stresses in a semi-logarithmic presentation against the reciprocal temperature (Fig. 2(b)), the activation energy of the creep deformation process was found to be between 140 and 160 kJ mol − 1, depending on the stress level. These values are close to the energy of self-diffusion in pure aluminium ( 142 kJ mol − 1), and this suggests that the rate of
Fig. 1. Indentation curves of the M124 alloy at different stresses and temperatures (a) and strain rate–indentation depth at different stresses and temperatures (b).
Fig. 2. Strain rate vs., equivalent stress at different temperatures for the M124 base alloy (a) and strain rate vs., the reciprocal temperature (b).
3. Results and discussion
3.1. Indentation creep of the unreinforced M124 alloy
G. Cseh et al. / Materials Science and Engineering A272 (1999) 145–151
147
steady state IC is controlled by climb of edge dislocations [9,10].
3.2. Indentation creep of the M124+ s composite The indentation curves of the M124+s composite differ significantly from those of the unreinforced alloy. Typical IC curves, obtained at different temperatures and loads, can be seen in Fig. 3(a). Three stages can be distinguished on each of the curves, apart from the instaneous initial deflection of the samples occurring during uploading. The first stage: (I) is characterized by a gradually increasing indentation rate (o; ); the second stage (II) by a constant o; ; whereas in the third stage (III) the creep rate is gradually decreasing. This trend can be seen directly from Fig. 3(b) where the strain rate measured at 350°C is plotted against the indentation depth at different values of the stress. The changes in the composite microstructure during the course of the indentation were investigated by metallographic methods. The mi-
Fig. 4. Microstructure of an M124 + s sample under a D= 0.8 mm punch in the first stage of indentation (a) and the section near to the edge of the indenter at higher magnification (b).
Fig. 3. Indentation curves of M124 + s at different stresses and temperatures (a) and strain rate vs., indentation depth at different equivalent stresses (b).
crostructure of the material under a 0.8 mm diameter indenter in stage (I) is shown in Fig. 4(a). At higher magnification (Fig. 4(b)) it can be seen that the failure of the fibres appears first in the vicinity of the rim of the indenter, where, according to theoretical considerations, the shear stress concentration is the highest [11]. This has also been established by our calculations with the help of the ANSYS [12,13] finite element analysis program. The plastic shear strain values obtained from the equilibrium solution of the elastic plastic model, are plotted in the plane of the indentation axis adjacent to the edge of the indenter in Fig. 5. It can be seen that the plastic deformation zone extends gradually from the edge to underneath the indenter in the model, which is in agreement with the observed microstructure (Fig. 4(b)). The presence of the accelerating stage at the low values of the penetration depth can be explained as follows: initially the matrix deforms slowly, the movement of dislocations is hindered by the rigid fiber network and dislocation pile-ups are forming. When the fracture of the fibers takes place, effected by the local stress increase at the leading dislocation of the pile-up, the dislocations start moving, inducing failure of further fibers, thereby accelerating the deformation. This is confirmed by Fig. 6 showing the first part of the indentation curve in higher resolution, in which
148
G. Cseh et al. / Materials Science and Engineering A272 (1999) 145–151
Fig. 5. Plastic shear strain near to the edge of the indenter at s=69 MPa computed with the ANSYS finite element analysis program.
steps of several microns height can be observed corresponding to a fracture event in the fiber network. Similar serration on the deformation curve has been observed previously around the minimum creep rate during tensile creep tests in fibre reinforced MMCs, and was also attributed to fiber fracture [14]. The microstructure of the sample corresponding already to stage (II) indentation is shown in Fig. 7. Around the penetrating indenter an approximately spherical deformation zone can be observed, in which the fracture of the fibers takes place. The deformation zone moves in front of the indenter and a constant strain rate is attained, as is characteristic of a region in the steady state secondary creep. Similar observations about the propagation of the deformation zone have been reported previously for unreinforced age-hardeneable Al alloys [5]. The microstructure of the sample in the third stage is shown in Fig. 8(a). At this stage crater formation is observed on the surface of the specimen, indicating a material transport from the bottom of the crater to the specimen surface at the rim of the indenter. Broken fibres change their orientation and tend to align in the direction of flow within the bulk material, as represented by a kind of flow pattern in Fig. 8(a). This effect can be ascribed to the extensive shear deformation taking place below the indenter as shown also by the result of the FEM analysis (Fig. 5).
In addition, it can be seen that fragments of multiply broken fibres accumulate immediately in front of the indenter. These fibre fragments can be seen in higher magnification close to the edge of the indenter (Fig. 8(b)). The accumulation of fibre fragments hinder the undisturbed flow of the material and, therefore, the progress of the deformation zone in front of the indenter. This leads to the gradual deceleration of the indentation in the third stage of the creep process, in contrast to the tensile creep tests where the multiple fracture of fibers leads to an accelerating tertiary creep and finally to the rupture of the sample [14]. The friction between
Fig. 6. The first part of the indentation curve at s= 106 MPa and T =350°C.
G. Cseh et al. / Materials Science and Engineering A272 (1999) 145–151
149
Fig. 7. Cross section of an M124 + s sample in the second stage.
the sample and the indenter surface may lead to an additional decrease of the strain rate in case of the reinforced as well as of the unreinforced alloy. It should be mentioned that the mechanisms in stage III are characteristic for indentation tests, and quite different from conventional tensile creep tests. In the case of the M124+s composite sample the Arrhenius plot of strain rate data evaluated from the slope of the steady state part of the indentation curves at s = 166 MPa (Fig. 9) yielding the activation energy of 177 kJ mol − 1, which is somewhat higher than the values obtained for the unreinforced alloy. Fig. 10 shows the steady state creep rate of the two samples as a function of the applied stress. Besides the data obtained from the present IC measurements results of tensile creep tests on the same materials [15] are also included in the figure. The stress exponent of the MMC determined from the IC tests with n = 9.8 is significantly higher then the n =7.4 value of the unreinforced alloy. There is a significant difference also in the creep resistance of the two materials, at the same stress values the steady state indentation creep rate of the MMC is two or three orders of magnitude lower. In the overlapping range of the IC and tensile creep test, the
agreement between the measured o; versus s values are satisfactory. The differences between the stress exponents determined from IC tests and tensile creep tests of Bindlingmaier et al. [15], respectively, should be attributed to the numerous small pores, which are already present in the as cast composite material, and which lead to a higher creep rate in tensile mode [16]. The values of the stress exponent obtained from the present investigation are close to those obtained from other creep measurements performed on similar conventional alloys and MMC materials [14]. It is also worth noting that the scatter in the data of the MMC is considerably higher than in the unreinforced sample, which is probably as a result of the local changes in the volume fraction as well as in the orientation distribution of the fibres under the punch in different samples. Considering the linearity of the log s− log o; and the log o; − 1/T relationships the creep behavior of the investigated materials can be described by the classical power law creep:
o; stat = As nexp
−Q kT
(2)
150
G. Cseh et al. / Materials Science and Engineering A272 (1999) 145–151
where A and k are constants, and n is the stress exponent. In contrast to tensile creep the o; stat quantity represents a maximum indentation creep rate in case of
the short fibre reinforced alloy. Nevertheless, the mechanisms controlling the creep in stage (II) of the IC curves may be the same as in tensile creep.
Fig. 8. Cross section of an M124+ s sample in the third stage (a) and the section close to the edge of the indenter at higher magnification (b).
G. Cseh et al. / Materials Science and Engineering A272 (1999) 145–151
Fig. 9. Strain rate data plotted against the reciprocal temperature for M124 + s.
151
an accelerated transient in contrast to the unreinforced alloy where the creep rate is decreasing in stage (I). With progressing penetration a material flow is setting in along the cylinder surface of the indenter from regions under the punch towards the surface of the specimen. The crater formation is a result of this process. In the case of the MMC in the course of this process fibre fragments produced by the multiply fractures of the fibers, become arrested by the unbroken elements of the fibre network, and the piling-up of these fragments leads to the decelerating stage (III). Therefore, steady state creep rates are expected to be several orders of magnitude lower in the MMC than in the unreinforced alloy. In this region the stress exponent n obtained for both the base alloy and the MMC are about 7 and 10, while the activation energy values are approximately 150 and 180 kJ mol − 1, respectively. Acknowledgements Financial support of the Hungarian Scientific Research Fund (OTKA) contract No. T-022976 is acknowledged. This work was carried out within the German-Hungarian Intergovernmental S&T Cooperation Program (D-6/97; Ung 232.21). References [1] [2] [3] [4] [5] [6]
Fig. 10. Comparison of strain rate vs., equivalent stress data obtained from indentation and tensile creep tests, respectively.
4. Summary and conclusion
[7] [8] [9]
The IC tests revealed significant differences in the creep behavior of the unreinforced and the composite material. While in the unreinforced material the short initial transient is followed only by a steady stage with nearly constant creep rate, in the MMC a third stage occurs in which the creep rate decreases with increasing penetration depth. A crater-shaped protrusion is forming on the surface of both the unreinforced and the MMC samples around the indenter, consequently this cannot be the reason for the occurrence of the decelerating stage in the case of the MMC. Metallographic investigations revealed fibre fracture in the MMC in a zone below the punch. In stage (I) the occurrence of fibre fractures promotes the movement of the dislocations initially, giving rise to .
[10]
[11] [12] [13]
[14] [15]
[16]
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