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Effect of the fiber orientation on the transient damping in metal matrix composites
Materials Science and Engineering A 387–389 (2004) 862–866
Effect of the fiber orientation on the transient damping in metal matrix composites O. Couteau∗ , R. Schaller Ecole Polytechnique Fédérale de Lausanne, Institut de Physique de la Matière Complexe, CH-1015 Lausanne, Switzerland Received 25 August 2003; received in revised form 12 December 2003
Abstract Mechanical spectroscopy has been used in order to investigate thermal stress relaxation in metal matrix composites. Mg- and Al-based composites reinforced with SiC long fibers have been processed by a gas-pressure infiltration technique. Fiber orientations either parallel or perpendicular to the composite axis have been obtained. Specimens have undergone thermal cycling between 150 and 450 K with different temperature rate T˙ and excitation frequency ω. A model where thermal stresses are relaxed by dislocation motion controlled by a solid friction mechanism has been used to interpret the experimental results. The model is in good agreement with experimental data and two fitting parameters can be calculated. The first parameter is sensitive to the mobile dislocation density during thermal cycling. The second one is sensitive to the interface strength. © 2004 Elsevier B.V. All rights reserved. Keywords: MMC; Thermal stress; Transient damping; Fiber orientation
1. Introduction Because of the thermal expansion mismatch between matrix and reinforcements, thermal stresses arise at the interface of composite materials. As a consequence, the mechanical properties and behavior of such materials depend strongly on the thermo-mechanical solicitation they undergo [1]. Mechanical spectroscopy, which evaluates the capability of materials to absorb mechanical energy (namely damping or mechanical loss [2]), has been intensively used to study thermal stresses and more particularly thermal stress relaxation in metal matrix composites (MMCs) [3–6]. The damping of such materials is composed of an intrinsic part depending on the individual constituents of the composite and a transient part depending on the temperature rate T˙ and the excitation frequency ω when composites are submitted to thermal cycling. During the last decade, models have been developed to interpret thermal stress relaxation in MMCs. Parrini and Schaller observed a sharp peak in the internal friction spectrum of aluminium-based composites, which
was interpreted as due to interface de-cohesion [4]. Formation of micro-plastic zones around reinforcements in aluminium-based MMCs [5] and motion of dislocations due to thermal stresses [6] has also been considered to evaluate the transient damping. All these models concluded that the transient damping varies linearly with the parameter T˙ /ω. Recently, Mayencourt and Schaller [7] developed a model of thermal stress relaxation based on the motion of dislocations controlled by a solid friction mechanism. Measurements were carried out on a wide range of T˙ /ω and Mayencourt evidenced the non-linearity of the transient damping, except for high values of T˙ /ω where the model predicts a linear dependence of the transient damping with T˙ /ω. New measurements of mechanical loss in composites with different matrices and different orientations of fibers have been performed. The aim of the present study is to analyze the influence of reinforcement orientation or matrix nature on the thermal stress relaxation by using the above-mentioned model.
2. Materials and techniques ∗
Corresponding author. Tel.: +41-21-693-3389; fax: +41-21-693-4470. E-mail address: [email protected] (O. Couteau). 0921-5093/$ – see front matter © 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.msea.2004.05.076
Composites used in this study are Mg- and Al- (both commercially pure) based composites reinforced by SiC long
O. Couteau, R. Schaller / Materials Science and Engineering A 387–389 (2004) 862–866
fibers with orientations either parallel or perpendicular to the composite axis. Specimens cut off from processed composite materials are straight bars with rectangular cross-section and with dimensions of 50 mm × 4 mm × 1 mm. Thereafter, orientation of composites will be referred as parallel, perpendicular1 or perpendicular2 depending if the fibers are parallel to the length, the width or the thickness of specimen respectively. The processing route was a gas-pressure infiltration of preforms by molten metal, which was described elsewhere [8]. Fibers have been thermally treated under air to grow an oxide layer (silica) around the SiC fibers in order to increase their wettability by the molten metal. This is a crucial point when fibers are perpendicular to the metal flow during the infiltration process. This oxide layer can also act as a diffusion barrier in the case of Al-based composites, avoiding the formation of Al carbides, which deteriorates the mechanical properties of the resulting composite [9]. Mechanical spectroscopy has been carried out by means of an inverted forced torsion pendulum where the mechanical loss angle tan φ and the dynamic modulus can be measured as a function of temperature, temperature rate T˙ or excitation frequency ω. Specimens were submitted to a torsional cyclic stress in the form τ = τ0 sin(ωt) and they have undergone thermal cycles in the 150–450 K range with T˙ and ω varying between 0 and 4 K/min and 0.01 and 1 Hz, respectively. For all specimens, the strain amplitude was 10−5 .
3. Experimental results Fig. 1a shows the mechanical loss tan φ as measured in a Mg matrix composites during heating and cooling at 2 K/min. During heating, 40 min annealings have been applied every 50 K (vertical parts of the spectrum in Fig. 1a). When temperature is kept constant, damping decreases until it reaches an equilibrium value corresponding to the intrinsic damping (which is independent on transient effect). Fig. 1b
863
illustrates the decrease of transient damping as a function of time during annealing. This method of applying isothermal annealing during thermal cycling is a good way to evidence transient damping. Thereafter, the transient damping is studied as a function of T˙ and ω in the range 0–4 K/min and 0.01–1 Hz, respectively. Values for damping at 0 K/min correspond to its value after the 40 min annealing. Fig. 2 shows the transient damping in a Mg-based composite with the fibers parallel to the axis composite, as a function of temperature for different T˙ (Fig. 2a) and for different ω (Fig. 2b). The transient damping increases when the temperature rate T˙ increases or when the frequency ω decreases. Another way to represent the transient damping is to plot its dependency on T˙ and for a given temperature. This step has been computer-assisted thanks to virtual instruments from graphical programming software LABVIEW. Experimental data have been interpolated in order to obtain values for the wanted temperatures. Results are shown in Fig. 3. It can be noticed that for a reduced interval of T˙ /ω, the transient damping seems to be a linear function of T˙ /ω, but the non-linearity over the whole range of T˙ /ω inspected is obvious.
4. Discussions As already mentioned, the results will be analyzed by using the model of Mayencourt and Schaller [7]. This model considers that thermal stresses generated at the interface of MMCs are relaxed by dislocation motion controlled by a solid friction mechanism. It means that the dislocation will move only when the stress acting on it will exceed a local extremum. For example, such behavior appears when pinning–depinning of the dislocation line occurs due to impurities in the matrix. It results in a hysteretic dislocation motion as it has already been observed by in situ TEM ob-
Fig. 1. (a) Mechanical loss angle tan φ as a function of temperature for a Mg-based composite with fibers parallel to composite axis (T˙ = 2 K/min; ω = 0.5 Hz). Vertical parts of the spectrum correspond to 40 min annealing and arrows indicate heating and cooling. (b) Mechanical loss angle tan φ as a function of time during one of annealings of (a).
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Fig. 2. (a) Mechanical loss angle tan φ as a function of temperature for different temperature rate T˙ for a Mg-based composite with fibers parallel to composite axis (ω = 0.5 Hz). (b) Mechanical loss angle tan φ as a function of temperature for different excitation frequencies ω for a Mg-based composite with fibers parallel to composite axis (T˙ = 3 K/min). Both figures represent the heating part of the thermal cycles.
servations [10]. This model considers these contributions in the local stress near the fiber–matrix interface. The applied and thermal stresses in the composite, respectively denoted τ a and τ th , can be expressed as: τa = τ0 sin(ωt) (1) τth = CEαT˙ t where τ 0 is the maximal applied cyclic stress and ω the circular frequency. τ th is a simplified expression for thermal stress as calculated by Taya and Arsenault [1]. α is the expansion mismatch between reinforcements and matrix, T˙ is the temperature rate during thermal cycling, E is an apparent modulus of the composite and C is a coefficient related to the interface strength and geometry. C is equal to 1 if the interface is perfect (load transfer is total at the interface) and 0 if there is total de-cohesion of the interface (no load
transfer at the interface). Then, considering that the applied and thermal stresses are relaxed by dislocation motion: τR = τa + τth (2) bτR = κu where b is the Burgers vector of dislocations, τ R the relaxed stress, a relaxation coefficient and u the mean dislocation displacement. In the case of cyclic solicitation, the damping is proportional to the ratio of dissipated energy with the total elastic energy over one cycle and can be written as [2]: π/ω 1 1 tan φ = (3) τ dε = τa dεan a an πJel τ02 πJel τ02 0 where Jel is the elastic compliance and εan is the irreversible deformation due to dislocation motion. Since this motion is controlled by a solid friction mechanism, dislocations will move only when τ a and τ th are both positive. This is the reason why the dissipated energy is calculated between 0 and τ/ω in Eq. (3). Thanks to Eqs. (1) and (2) and using Orowan’s law: ε = Λbu
(4)
where Λ is the mobile dislocation density, the transient damping can be calculated: tan φtr = 2C1 C2
Fig. 3. Mechanical loss angle tan φ as a function of T˙ /ω for different temperatures for a Mg-based composite with fibers parallel to composite axis. Solid lines correspond to fitting curves from Eq. (5).
where b2 C1 = Jel κ CEα C2 = τ0
T˙ 1 − π/2C2 (T˙ /ω) ω 1 + π/2C2 (T˙ /ω)
(5)
(6)
The fitting curves from Eq. (5) for the transient damping are shown in Fig. 3. The agreement between experimental
O. Couteau, R. Schaller / Materials Science and Engineering A 387–389 (2004) 862–866
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Fig. 4. (a) and (b) Fitting parameter C1 or heating and cooling as a function of temperature for Mg-based composites. (c) and (d) Fitting parameter C2 for heating and cooling as a function of temperature for Mg-based composites.
data and the model is good. Fitting parameters can be evaluated either for Mg- or Al-based composites and for the three different orientations. Results are presented in Fig. 4 for Mg-based composites and Fig. 5 for Al-based composites. These parameters were not calculated between 150 and 200 K and between 400 and 450 K since these ranges correspond to transitory stages in the heating or cooling processes (T˙ is not constant). First, the general trends of the fitting parameters C1 and C2 will be discussed. In the case of C1 , this parameter is sensitive to the mobile dislocation density. Thus, it should increase when increasing temperature from low temperatures or decreasing temperature from high temperatures since thermal stresses increases and activates dislocations. This is what it is observed in Fig. 4a-b and Fig. 5a-b. It has to be noticed that C1 for Al-based composites slightly decreases below 300 K upon cooling (Fig. 5b). In the case of C2 , this parameter is sensitive to the interface strength via the coefficient C. When temperature increases, the interface strength should decrease since the matrix softens and expands more than reinforcements, resulting in the decrease of load transfer. Consequently, the parameter should decreases when temperature increases, which is observed in Fig. 4c-d and Fig. 5c-d.
The effect of the reinforcement orientation in the matrix will be then considered. In the case of C1 , on one hand, thermal stresses are preferentially parallel to fiber direction. Accordingly, thermal stresses are respectively parallel to the length, the width and the thickness of composites with the parallel, perpendicular1 and perpendicular2 orientations. On the other hand, torsional solicitation is the same in all composites. It is very difficult to know exactly how the applied stress acts in the composite materials because of their multi-phase nature but it can be assumed that it is mainly in the plane perpendicular to composite axis (pure shear). As a consequence, the coupling between thermal and applied stresses is the most effective in composites with fibers perpendicular to the composite axis. This leads to a greater dislocation activity in this type of composites and consequently a bigger parameter C1 as shown in Fig. 4a and Fig. 5a-b. Differences between orientations are not so clear in Fig. 4b. In the case of C2 , differences should come from the interface strength. Specimens with fibers perpendicular to composite axis are cut off from the same processed composite. Thus, they have the same interface strength and the parameter C2 follows the same trend as seen in Fig. 4c-d and Fig. 5c-d.
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O. Couteau, R. Schaller / Materials Science and Engineering A 387–389 (2004) 862–866
Fig. 5. (a) and (b) Fitting parameter C1 for heating and cooling as a function of temperature for Al-based composites. (c) and (d) Fitting parameter C2 for heating and cooling as a function of temperature for Al-based composites.
5. Conclusion
References
It has been shown that thermal stress relaxation in MMCs can be interpreted by dislocation motion controlled by a solid friction mechanism. A model for the transient damping can be deduced and it is in good agreement with experimental data. Two fitting parameters are subsequently calculated. The first parameter C1 is related to the mobile dislocation density during thermal cycling. It is shown that it increases when increasing thermal stresses. The second parameter C2 is related to the interface strength. As temperature increases, the parameter C2 decreases resulting from the decrease of the interface strength. We are convinced that the use of such model for thermal stress relaxation might give precious information about properties of the interface in composite materials and a mean to compare interface strength between different composites. Nevertheless, meanings of parameters C1 and C2 and the subsequent interpretation have to be clarified by working further the model in a microscopic approach.
[1] M. Taya, R.J. Arsenault, Metal Matrix Composites: Thermomechanical Behavior, Pergamon Press, London, UK, 1989. [2] A.S. Nowick, B.S. Berry, Anelastic Relaxation in Crystalline Solids, Academic Press, London, UK, 1972. [3] E. Carreno-Morelli, in: R. Schaller, G. Fantozzi, G. Gremaud (Eds.), Mechanical Spectroscopy Q−1 , Trans Tech Publications, Zürich, Switzerland, 2001. [4] L. Parrini, R. Schaller, Metall. Mater. Trans. A 26 (1995) 1457. [5] E. Carreño-Morelli, S.E. Urreta, R. Schaller, Acta Mater. 48 (2000) 4725. [6] A. Vincent, C. Girard, G. Lormand, X. Zhou, R. Fougères, Mater. Sci. Eng. A 164 (1993) 327. [7] C. Mayencourt, R. Schaller, Acta Mater. 46 (1998) 6103. [8] E. Carreño-Morelli, T. Cutard, R. Schaller, C. Bonjour, Mater. Sci. Eng. A 251 (1998) 48. [9] Z. Shi, J.M. Yang, J.C. Lee, D. Zhamg, H.I. Lee, R. Wu, Mater. Sci. Eng. A 303 (2001) 46. [10] C. Mayencourt, PhD Thesis No. 2060, EPFL, Lausanne, Switzerland, 1999.
Effect of the fiber orientation on the transient damping in metal matrix composites O. Couteau∗ , R. Schaller Ecole Polytechnique Fédérale de Lausanne, Institut de Physique de la Matière Complexe, CH-1015 Lausanne, Switzerland Received 25 August 2003; received in revised form 12 December 2003
Abstract Mechanical spectroscopy has been used in order to investigate thermal stress relaxation in metal matrix composites. Mg- and Al-based composites reinforced with SiC long fibers have been processed by a gas-pressure infiltration technique. Fiber orientations either parallel or perpendicular to the composite axis have been obtained. Specimens have undergone thermal cycling between 150 and 450 K with different temperature rate T˙ and excitation frequency ω. A model where thermal stresses are relaxed by dislocation motion controlled by a solid friction mechanism has been used to interpret the experimental results. The model is in good agreement with experimental data and two fitting parameters can be calculated. The first parameter is sensitive to the mobile dislocation density during thermal cycling. The second one is sensitive to the interface strength. © 2004 Elsevier B.V. All rights reserved. Keywords: MMC; Thermal stress; Transient damping; Fiber orientation
1. Introduction Because of the thermal expansion mismatch between matrix and reinforcements, thermal stresses arise at the interface of composite materials. As a consequence, the mechanical properties and behavior of such materials depend strongly on the thermo-mechanical solicitation they undergo [1]. Mechanical spectroscopy, which evaluates the capability of materials to absorb mechanical energy (namely damping or mechanical loss [2]), has been intensively used to study thermal stresses and more particularly thermal stress relaxation in metal matrix composites (MMCs) [3–6]. The damping of such materials is composed of an intrinsic part depending on the individual constituents of the composite and a transient part depending on the temperature rate T˙ and the excitation frequency ω when composites are submitted to thermal cycling. During the last decade, models have been developed to interpret thermal stress relaxation in MMCs. Parrini and Schaller observed a sharp peak in the internal friction spectrum of aluminium-based composites, which
was interpreted as due to interface de-cohesion [4]. Formation of micro-plastic zones around reinforcements in aluminium-based MMCs [5] and motion of dislocations due to thermal stresses [6] has also been considered to evaluate the transient damping. All these models concluded that the transient damping varies linearly with the parameter T˙ /ω. Recently, Mayencourt and Schaller [7] developed a model of thermal stress relaxation based on the motion of dislocations controlled by a solid friction mechanism. Measurements were carried out on a wide range of T˙ /ω and Mayencourt evidenced the non-linearity of the transient damping, except for high values of T˙ /ω where the model predicts a linear dependence of the transient damping with T˙ /ω. New measurements of mechanical loss in composites with different matrices and different orientations of fibers have been performed. The aim of the present study is to analyze the influence of reinforcement orientation or matrix nature on the thermal stress relaxation by using the above-mentioned model.
2. Materials and techniques ∗
Corresponding author. Tel.: +41-21-693-3389; fax: +41-21-693-4470. E-mail address: [email protected] (O. Couteau). 0921-5093/$ – see front matter © 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.msea.2004.05.076
Composites used in this study are Mg- and Al- (both commercially pure) based composites reinforced by SiC long
O. Couteau, R. Schaller / Materials Science and Engineering A 387–389 (2004) 862–866
fibers with orientations either parallel or perpendicular to the composite axis. Specimens cut off from processed composite materials are straight bars with rectangular cross-section and with dimensions of 50 mm × 4 mm × 1 mm. Thereafter, orientation of composites will be referred as parallel, perpendicular1 or perpendicular2 depending if the fibers are parallel to the length, the width or the thickness of specimen respectively. The processing route was a gas-pressure infiltration of preforms by molten metal, which was described elsewhere [8]. Fibers have been thermally treated under air to grow an oxide layer (silica) around the SiC fibers in order to increase their wettability by the molten metal. This is a crucial point when fibers are perpendicular to the metal flow during the infiltration process. This oxide layer can also act as a diffusion barrier in the case of Al-based composites, avoiding the formation of Al carbides, which deteriorates the mechanical properties of the resulting composite [9]. Mechanical spectroscopy has been carried out by means of an inverted forced torsion pendulum where the mechanical loss angle tan φ and the dynamic modulus can be measured as a function of temperature, temperature rate T˙ or excitation frequency ω. Specimens were submitted to a torsional cyclic stress in the form τ = τ0 sin(ωt) and they have undergone thermal cycles in the 150–450 K range with T˙ and ω varying between 0 and 4 K/min and 0.01 and 1 Hz, respectively. For all specimens, the strain amplitude was 10−5 .
3. Experimental results Fig. 1a shows the mechanical loss tan φ as measured in a Mg matrix composites during heating and cooling at 2 K/min. During heating, 40 min annealings have been applied every 50 K (vertical parts of the spectrum in Fig. 1a). When temperature is kept constant, damping decreases until it reaches an equilibrium value corresponding to the intrinsic damping (which is independent on transient effect). Fig. 1b
863
illustrates the decrease of transient damping as a function of time during annealing. This method of applying isothermal annealing during thermal cycling is a good way to evidence transient damping. Thereafter, the transient damping is studied as a function of T˙ and ω in the range 0–4 K/min and 0.01–1 Hz, respectively. Values for damping at 0 K/min correspond to its value after the 40 min annealing. Fig. 2 shows the transient damping in a Mg-based composite with the fibers parallel to the axis composite, as a function of temperature for different T˙ (Fig. 2a) and for different ω (Fig. 2b). The transient damping increases when the temperature rate T˙ increases or when the frequency ω decreases. Another way to represent the transient damping is to plot its dependency on T˙ and for a given temperature. This step has been computer-assisted thanks to virtual instruments from graphical programming software LABVIEW. Experimental data have been interpolated in order to obtain values for the wanted temperatures. Results are shown in Fig. 3. It can be noticed that for a reduced interval of T˙ /ω, the transient damping seems to be a linear function of T˙ /ω, but the non-linearity over the whole range of T˙ /ω inspected is obvious.
4. Discussions As already mentioned, the results will be analyzed by using the model of Mayencourt and Schaller [7]. This model considers that thermal stresses generated at the interface of MMCs are relaxed by dislocation motion controlled by a solid friction mechanism. It means that the dislocation will move only when the stress acting on it will exceed a local extremum. For example, such behavior appears when pinning–depinning of the dislocation line occurs due to impurities in the matrix. It results in a hysteretic dislocation motion as it has already been observed by in situ TEM ob-
Fig. 1. (a) Mechanical loss angle tan φ as a function of temperature for a Mg-based composite with fibers parallel to composite axis (T˙ = 2 K/min; ω = 0.5 Hz). Vertical parts of the spectrum correspond to 40 min annealing and arrows indicate heating and cooling. (b) Mechanical loss angle tan φ as a function of time during one of annealings of (a).
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O. Couteau, R. Schaller / Materials Science and Engineering A 387–389 (2004) 862–866
Fig. 2. (a) Mechanical loss angle tan φ as a function of temperature for different temperature rate T˙ for a Mg-based composite with fibers parallel to composite axis (ω = 0.5 Hz). (b) Mechanical loss angle tan φ as a function of temperature for different excitation frequencies ω for a Mg-based composite with fibers parallel to composite axis (T˙ = 3 K/min). Both figures represent the heating part of the thermal cycles.
servations [10]. This model considers these contributions in the local stress near the fiber–matrix interface. The applied and thermal stresses in the composite, respectively denoted τ a and τ th , can be expressed as: τa = τ0 sin(ωt) (1) τth = CEαT˙ t where τ 0 is the maximal applied cyclic stress and ω the circular frequency. τ th is a simplified expression for thermal stress as calculated by Taya and Arsenault [1]. α is the expansion mismatch between reinforcements and matrix, T˙ is the temperature rate during thermal cycling, E is an apparent modulus of the composite and C is a coefficient related to the interface strength and geometry. C is equal to 1 if the interface is perfect (load transfer is total at the interface) and 0 if there is total de-cohesion of the interface (no load
transfer at the interface). Then, considering that the applied and thermal stresses are relaxed by dislocation motion: τR = τa + τth (2) bτR = κu where b is the Burgers vector of dislocations, τ R the relaxed stress, a relaxation coefficient and u the mean dislocation displacement. In the case of cyclic solicitation, the damping is proportional to the ratio of dissipated energy with the total elastic energy over one cycle and can be written as [2]: π/ω 1 1 tan φ = (3) τ dε = τa dεan a an πJel τ02 πJel τ02 0 where Jel is the elastic compliance and εan is the irreversible deformation due to dislocation motion. Since this motion is controlled by a solid friction mechanism, dislocations will move only when τ a and τ th are both positive. This is the reason why the dissipated energy is calculated between 0 and τ/ω in Eq. (3). Thanks to Eqs. (1) and (2) and using Orowan’s law: ε = Λbu
(4)
where Λ is the mobile dislocation density, the transient damping can be calculated: tan φtr = 2C1 C2
Fig. 3. Mechanical loss angle tan φ as a function of T˙ /ω for different temperatures for a Mg-based composite with fibers parallel to composite axis. Solid lines correspond to fitting curves from Eq. (5).
where b2 C1 = Jel κ CEα C2 = τ0
T˙ 1 − π/2C2 (T˙ /ω) ω 1 + π/2C2 (T˙ /ω)
(5)
(6)
The fitting curves from Eq. (5) for the transient damping are shown in Fig. 3. The agreement between experimental
O. Couteau, R. Schaller / Materials Science and Engineering A 387–389 (2004) 862–866
865
Fig. 4. (a) and (b) Fitting parameter C1 or heating and cooling as a function of temperature for Mg-based composites. (c) and (d) Fitting parameter C2 for heating and cooling as a function of temperature for Mg-based composites.
data and the model is good. Fitting parameters can be evaluated either for Mg- or Al-based composites and for the three different orientations. Results are presented in Fig. 4 for Mg-based composites and Fig. 5 for Al-based composites. These parameters were not calculated between 150 and 200 K and between 400 and 450 K since these ranges correspond to transitory stages in the heating or cooling processes (T˙ is not constant). First, the general trends of the fitting parameters C1 and C2 will be discussed. In the case of C1 , this parameter is sensitive to the mobile dislocation density. Thus, it should increase when increasing temperature from low temperatures or decreasing temperature from high temperatures since thermal stresses increases and activates dislocations. This is what it is observed in Fig. 4a-b and Fig. 5a-b. It has to be noticed that C1 for Al-based composites slightly decreases below 300 K upon cooling (Fig. 5b). In the case of C2 , this parameter is sensitive to the interface strength via the coefficient C. When temperature increases, the interface strength should decrease since the matrix softens and expands more than reinforcements, resulting in the decrease of load transfer. Consequently, the parameter should decreases when temperature increases, which is observed in Fig. 4c-d and Fig. 5c-d.
The effect of the reinforcement orientation in the matrix will be then considered. In the case of C1 , on one hand, thermal stresses are preferentially parallel to fiber direction. Accordingly, thermal stresses are respectively parallel to the length, the width and the thickness of composites with the parallel, perpendicular1 and perpendicular2 orientations. On the other hand, torsional solicitation is the same in all composites. It is very difficult to know exactly how the applied stress acts in the composite materials because of their multi-phase nature but it can be assumed that it is mainly in the plane perpendicular to composite axis (pure shear). As a consequence, the coupling between thermal and applied stresses is the most effective in composites with fibers perpendicular to the composite axis. This leads to a greater dislocation activity in this type of composites and consequently a bigger parameter C1 as shown in Fig. 4a and Fig. 5a-b. Differences between orientations are not so clear in Fig. 4b. In the case of C2 , differences should come from the interface strength. Specimens with fibers perpendicular to composite axis are cut off from the same processed composite. Thus, they have the same interface strength and the parameter C2 follows the same trend as seen in Fig. 4c-d and Fig. 5c-d.
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O. Couteau, R. Schaller / Materials Science and Engineering A 387–389 (2004) 862–866
Fig. 5. (a) and (b) Fitting parameter C1 for heating and cooling as a function of temperature for Al-based composites. (c) and (d) Fitting parameter C2 for heating and cooling as a function of temperature for Al-based composites.
5. Conclusion
References
It has been shown that thermal stress relaxation in MMCs can be interpreted by dislocation motion controlled by a solid friction mechanism. A model for the transient damping can be deduced and it is in good agreement with experimental data. Two fitting parameters are subsequently calculated. The first parameter C1 is related to the mobile dislocation density during thermal cycling. It is shown that it increases when increasing thermal stresses. The second parameter C2 is related to the interface strength. As temperature increases, the parameter C2 decreases resulting from the decrease of the interface strength. We are convinced that the use of such model for thermal stress relaxation might give precious information about properties of the interface in composite materials and a mean to compare interface strength between different composites. Nevertheless, meanings of parameters C1 and C2 and the subsequent interpretation have to be clarified by working further the model in a microscopic approach.
[1] M. Taya, R.J. Arsenault, Metal Matrix Composites: Thermomechanical Behavior, Pergamon Press, London, UK, 1989. [2] A.S. Nowick, B.S. Berry, Anelastic Relaxation in Crystalline Solids, Academic Press, London, UK, 1972. [3] E. Carreno-Morelli, in: R. Schaller, G. Fantozzi, G. Gremaud (Eds.), Mechanical Spectroscopy Q−1 , Trans Tech Publications, Zürich, Switzerland, 2001. [4] L. Parrini, R. Schaller, Metall. Mater. Trans. A 26 (1995) 1457. [5] E. Carreño-Morelli, S.E. Urreta, R. Schaller, Acta Mater. 48 (2000) 4725. [6] A. Vincent, C. Girard, G. Lormand, X. Zhou, R. Fougères, Mater. Sci. Eng. A 164 (1993) 327. [7] C. Mayencourt, R. Schaller, Acta Mater. 46 (1998) 6103. [8] E. Carreño-Morelli, T. Cutard, R. Schaller, C. Bonjour, Mater. Sci. Eng. A 251 (1998) 48. [9] Z. Shi, J.M. Yang, J.C. Lee, D. Zhamg, H.I. Lee, R. Wu, Mater. Sci. Eng. A 303 (2001) 46. [10] C. Mayencourt, PhD Thesis No. 2060, EPFL, Lausanne, Switzerland, 1999.