- Email: [email protected]
Interface debonding from bottom face and frictional transition during pushout testing of a tungsten fiber-epoxy matrix composite
COMPOSITES SCIENCE AND TECHNOLOGY Composites Science and Technology 65 (2005) 1808–1814 www.elsevier.com/locate/compscitech
Interface debonding from bottom face and frictional transition during pushout testing of a tungsten fiber-epoxy matrix composite Shuqi Guo a
a,*
, Kouichi Honda a, Yutaka Kagawa
a,b,*
Institute of Industrial Science, The University of Tokyo, 4-6-1 Komaba, Meguro-ku, Tokyo 153-8505, Japan b Department of Materials Engineering, Graduate School of Engineering, The University of Tokyo, Japan Received 5 March 2004; received in revised form 7 January 2005; accepted 14 March 2005 Available online 21 April 2005
Abstract The progress of interface debonding behavior in a tungsten fiber-reinforced epoxy matrix composite, which has an initially debonded interface due to thermal mismatch stress, has been studied by using the thin-specimen pushout test. Load drop behavior just after the maximum load in the load–displacement curve is discussed with respect to the interface debonding and frictional load transfer mechanism. The interface debonding propagates from the initially existing debond crack tip at the bottom face while no interface debonding crack propagation is observed from that located at the top face. This characteristic interface debonding behavior is explained by the interaction of interface shear stresses which originated from the thermal misfit and the applied load. Near the top face, the two shear stresses are opposite while those at the bottom face are added. This creates a condition of interface debonding from the bottom face when the thermal expansion coefficient of fiber is smaller than that of matrix. The load drop observed just after the maximum load in the load–displacement curve is not related with the interface debonding but with the transition of interface frictional sliding resistance from static to dynamic. The maximum pushout load is predicted by the static coefficient of friction and the load after the drop is predicted by dynamic coefficient of friction. 2005 Elsevier Ltd. All rights reserved. Keywords: Polymer–matrix composite; Tungsten fiber; Pushout; Interface debonding
1. Introduction A thin-sliced specimen pushout test has been widely applied for the evaluation of interface mechanical properties in various kinds of fiber-reinforced composites because of the broad specimen preparation and relatively simple experimental procedure [1–5]. To obtain interfacial mechanical properties from a pushout test, it is important to know the corresponding correlation between experimentally obtainable load–displacement relation and interface debonding sliding behaviors [6– * Corresponding authors. Tel.: +81 298592223; fax: +81 298592401 (S. Guo), Tel.: +81 354525086; fax: +81 354525087 (Y. Kagawa). E-mail addresses: [email protected] (S. Guo), kagawa@iis. u-tokyo.ac.jp (Y. Kagawa).
0266-3538/$ - see front matter 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.compscitech.2005.03.011
11]. Because analytical forms usually used to obtain the interfacial shear properties from the experiment are varied only under the assumed boundary conditions, the matching between the boundary condition and actual interface debonding sliding process should be compared before application of these forms. Although various analytical forms are available and applied for the evaluation of interfacial mechanical properties [6–10], few experimental papers have attempted to examine the corresponding relationship by using the theoretical analyses. Reports on the progress of interface debonding, in particular, are very scarce [2,11]. Additionally, the interface debonding sliding behavior sometimes differs from the ideally assumed conditions, as a result of the presence of various factors that are usually not included in the analysis. Generally, the interface
S. Guo et al. / Composites Science and Technology 65 (2005) 1808–1814
debonding is assumed to initiate from the pushing surface and some reports clearly demonstrated this behavior [2,11]. On the other hand, other papers have discussed the possibility of onset of interface debonding behavior from the bottom face [4,12] because of the effect of combination of thermal residual stresses and applied load at that location. No detailed evidence is available on the debonding from the bottom face, however. This paper demonstrates the possibility of the interface debonding phenomenon from the bottom face for the composite with Ef > Em and af < am (E and a are YoungÕs modulus and thermal expansion coefficients respectively, the subscripts f and m refer to fiber and matrix respectively). The effect of thermal mismatch stress on the interface debonding behavior from the bottom face as well as the effect of debonding behavior on the load–displacement curve are also discussed.
2. Experimental procedure The composite material used in this study was a tungsten (W: Tokyo Tungsten Co. Ltd., Tokyo, Japan) fiberreinforced epoxy matrix composite. The diameter of the fiber (2Rf) was 150 lm. An epoxy resin mixture (Epikote 828, of Yuka-shell Epoxy Corp., Tokyo, Japan) was cast into a Teflon tray in which a single W fiber was located. Then, the tray was put under a vacuum of 102 Pa for 20 min, to expel dissolved air introduced during the mixing process. The composite was then cured at 373 K for 2 h, post-cured for 5 h at 383 K and cooled to room temperature (298 K). More details of the fabrication process of the epoxy matrix can be obtained from the earlier report [13]. Table 1 lists properties of the W fiber and the epoxy matrix. Thin pushout specimens were prepared by a conventional mechanical cutting procedure and polishing procedure. Both the top and bottom faces of the specimens were carefully polished up to 1 lm using a diamond paste. The specimen was 4 · 4 mm square and the thickness, L, was 1.5 mm which corresponded to a fiber aspect ratio of L/2Rf 10. It contained a single fiber in the central position and an initial debond length of L0d 100 lm at the interface near both the top and bottom faces. The nominal fiber volume fraction was 0.001. Fig. 1 shows the shape and dimensions of the pushout specimen subjected to the pushout test.
Table 1 Properties of the tungsten fiber and the epoxy matrix
Tungsten fiber Epoxy matrix
1809
Fig. 1. Shape and dimensions of pushout test specimen.
The specimen was dried before the test to avoid any effect of water at the debond interface on the results [14]. A schematic illustration of the pushout equipment was reported elsewhere [1,2]. The composite specimen was mounted on a support block, which had a 500 lm diameter hole at the center, this diameter being a factor of 3 larger than that of the fiber diameter. The center of the fiber was placed at the center of the hole to allow the fiber to be pushed out freely from the specimen. The adjustment was made by means of an optical microscope, which was provided with the pushout test equipment. A hard steel spherical indenter (YoungÕs modulus 550 GPa) with a tip diameter 100 lm was used. Positioning the indenter to the fiber center was done by a video-microscope. The pushout test was conducted in air at room temperature (298 K) and a load was applied by moving the specimen support block upward at a constant displacement rate of 5 · 107 m/s. The applied load was measured by a load cell (maximum capacity of 500 N, Tokyo Sokki, CLS-50KA, Tokyo, Japan) which was attached to the holder. The displacement of the fiber end surface was continuously monitored by a reflective type laser displacement meter (minimum resolution of 0.2 lm, Keyence, LC-2440, Tokyo, Japan). 10 specimens were used for this test. In situ observations of the interface debonding and sliding behavior during the pushout testing were carried out using a video-microscope (Keyence, VH-5910) with a typical magnification of 200· at the CRT monitor. The change of reflective light at the interface was stored in a videotape recorder. The selected images were processed using the ‘‘NIH’’ Image public domain software. The detailed observation process has been reported elsewhere [1,2].
YoungÕs modulus, E (Gpa)
PoissionÕs ratio, m
Coefficient of thermal expansion, a, (·106 K1)
3. Results and discussion
370 3
0.17 0.37
5.0 60
Fig. 2 shows an example of typical pushout results presented in terms of load–fiber end displacement
1810
S. Guo et al. / Composites Science and Technology 65 (2005) 1808–1814
25 (d)
Load,P(u) (N)
20 15 (c)
10 (b)
5 (a)
0
0
20
40
60
80
100
120
140
Fiber Displacement, u (mm) Fig. 2. A typical example of the load–displacement curves obtained during the pushout testing of the composite specimens.
response. The curve shows an initial linear part which begins to deviate the linear regime when the load reaches 40% of a maximum load (21 N). Just after reaching maximum load, the load suddenly decreases to about 40% without noticeable increase of the displacement, u. Thereafter, the load initially gradually decreases and then tends to remain essentially constant with the increase of the fiber-end displacement, accompanied with
fiber protrusion from the bottom face. The maximum load corresponds to the onset of the fiber protruding from the bottom face [3,10]. The letters (a)–(d) in Fig. 2 represent before loading (a), onset of debonding propagation from the existing debonding crack tip (b), progress of debonding interface (c), and whole interface debonding (d), respectively. A typical example of the direct observation result of the progress of interface debonding during the pushout testing is shown in Fig. 3; the letters (a)–(d) correspond to those in Fig. 2. The partially reflected light area observed on the fiber surface corresponds to the debond interface area (tip of the identified debond interface is indicated by an arrow). Before loading, the interface from both the polished top and bottom faces initially debonded about 100 lm (L0d =L 0:07Þ; this initial debonding in the specimen preparation process is caused by a thermal misfit shear stress during the fabrication and it is difficult to avoid in a W fiber-reinforced epoxy matrix system [13]. The important finding in the observations during the present pushout testing is that the interfacial debonding proceeded spontaneously from the existing debonded crack front only at the bottom face and not at the top face. This interfacial debond progress behavior was observed for each instance. Based on the above in situ observations, the interface debonding
Fig. 3. In situ observation of the fiber–matrix interface by video microscope with debonding length obtained by image analysis.
S. Guo et al. / Composites Science and Technology 65 (2005) 1808–1814
1811
Load
Initial debonding Fiber S2 S1 Initial debonding
Matrix
Support Support block block Fig. 4. Schematic drawing of interface debond progress observed during the pushout testing, (S1-Spontaneous debonding 1, and S2-Spontaneous debonding 2).
behavior in the composite specimen studied was schematically drawn, which illustration was shown in Fig. 4. The relation between the normalized interface debond length from the bottom face, Ld/L, and normalized applied load, P/Pmax, obtained from the direct observation is shown in Fig. 5. Here, Pmax is the maximum load (21 N) in the load–displacement curve and Ld is the overall debond length-including the initially existing debond length. When the applied load reaches 8 N (P/Pmax 0.4), the interface debonding from the bottom face propagates and the debonding proceeds spontaneously with a typical debond increment in a single unit of debonding length 200 lm (dLd/L 0.13).
Complete debonding
Normalized Applied Load, P/Pmax
1.0
(d)
0.8 Onset of debond propagation
0.6
δLd (c)
(b)
0.4
(a)
0.2
Initial debonding
0 0
0.2 0.4 0.6 0.8 Normalized Debond Length from Back Surface, Ld/L
1.0
Fig. 5. Relation between the normalized interface debond length from the bottom face, Ld/L, and normalized applied load, P/Pmax, obtained from in situ observation.
Note that the incremental lines between (b) and (d) (C part in Fig. 5) represent the spontaneous interfacial debonding behavior during the pushout process. The unit of debonding length, dLd, tends to increase gradually with the increase of applied load as interface debonding progresses. Finally, when the debonding length from the bottom face reaches 1.4 mm, i.e., Ld/L = 0.93, the debonding crack propagated from this face becomes unstable, the crack tip propagates immediately and the crack joins together the initially existing debond crack front at the top face once the pushout load begins to continuously increase; this results in complete debonding of the entire interface. However, the pushouting load continuously increases after the entire interface complete debonding. This rapid interface debond progress occurs when the load reaches about 80% of maximum, indicating that the load increase after the complete debonding is achieved by a purely frictional force. At the maximum load in the load–displacement curve, the interface is completely debonded and the load is totally supported by a frictional force at the debonded interface. It was reported that interfacial shear stress state at the interface plays an important role in the interface debonding behavior [2,15]. In the case of af < am with DT > 0, before the pushout test thermally induced shear stress at the interface initially caused the interface debonding at both the top and bottom faces (DT = Tg T0 is the temperature change when thermal stress is introduced, Tg and T0 are the glass transition temperature of the epoxy matrix and room temperature (Tg > T0), respectively). As the pushout load is applied, the resulting shear stress along the fiber/matrix interface becomes a superposition of thermal residual stress and stress induced by the applied load. In particular at the tip of interface debonding located at the pushing surface the larger stress is expected under the loading, as a result of stress concentration at the debonding crack tip. The
1812
S. Guo et al. / Composites Science and Technology 65 (2005) 1808–1814
total interface shear stress along the bonded interface, s(z), is given by [2] sðzÞ ¼ sT ðzÞ þ sa ðzÞ;
ð1Þ
T
where s (z) is the interface shear stress by thermal misfit stress and sa(z) is the interface shear stress by the applied load. Thus, the absolute value of s(z) is affected not only by the absolute value of sT(z) and sa(z) but by the sign of the shear stresses. The sign of these interface shear stresses was previously defined by Honda and Kagawa [2] in a SiC(SCS-6) fiber-reinforced borosilicate glass matrix, which results are schematically shown in Fig. 6. At the top face (pushing surface), sT ðL0d Þ < 0 and sa ðL0d Þ > 0, the sign of these shear stresses is opposite while at the bottom face it is the same, i.e., sT ðL L0d Þ < 0 and sa ðL L0d Þ < 0. Thus, the interface shear stresses at the top face cancel each other when the pushout load is applied, and consequently the total interface shear stress decreases, i.e., sðL0d Þ ¼ sa ðL0d Þ sT ðL0d Þ. On the other hand, the interface shear stress near the bottom face increases from the initial state after pushing, i.e., sðL L0d Þ ¼ sa ðL L0d Þ þ sT ðL L0d Þ. When the total interface shear stress at the bottom face is larger than that at top face, i.e., jsa ðL L0d Þ þ sT ðL L0d Þj > jsa ðL0d Þ sT ðL0d Þj, the interface debond progress initiates from the bottom face. Because the interface debonding behavior is also related to the clamping stress state at the interface, the explanation on the interface debonding behavior observed in this experiment is qualitative and rough. However, it is undoubted that this difference of thermally induced shear stress along the interface is a strong source for promoting the interface debonding behavior from the bottom face (Fig. 6). That is, the decrease of shear stress near the top face enhances crack stability and the increase of shear stress near the bottom face weakens it. Even though the interface stress concentration at the debond crack tip near the top face also increases with the increase of applied load, the initial Shear stress by applied load,, τ (z )
Shear stress by thermal misfit,, τ (z )
a
T
z =0 L0d
(α f < α m)
Fiber Fiber
Matrix
L −L
0 d
Z=L
Initial interface debonding Fig. 6. Schematic illustration of signs in the interfacial shear stresses at the top face and the bottom face.
debond crack at the top face remains stabile and does not propagate due to high radial clamping stress at that location, resulting from the PoissonÕs expansion of the loaded fiber as well as from the bending of specimen associated with the test specimen thickness[12]. This high radial clamping stress prohibits a shear failure at the top face. The present composite system is af < am and thus the interface debond progress likely occurs from the bottom face. On the contrary, if the af > am relationship is satisfied, the interface debonding is likely to occur from the top face. In the latter case, the evidence was experimentally proved by the authors using SiC(SCS-6) fiber-reinforced borosilicate glass matrix composite [2]. Moreover, previous investigations [4,12] have reported the interfacial debonding behavior occurring at the bottom face during pushout testing of SiC(SCS-6) fiber-reinforced Ti alloy matrix composites. Ghosn et al. [12] have studied the interfacial stress state and the relation of the stress state to the interface debonding behavior by using finite element method (FEM). Their analysis showed that the residual shear stress at the top face is tend to oppose the externally applied load during pushout testing while at bottom face the shear stress increase adds to the existing large residual stress. Additionally, their observations showed that the interfacial debonding always occurs from the bottom face. They concluded that the applied load must be able to overcome the residual thermal shear stress near the top face as well as the compressive radial stress before debonding can occur, and interfacial debonding also can occur preferentially near the bottom face where the local shear stress are the greatest. This agrees with our experimental observations in W fiber-epoxy matrix composite, showing the interfacial failure initiation in the case of af < am tends to occur at the bottom face. During the progressive spontaneous interface debonding, the applied load is supported by (i) interface shear frictional stress at the debond interface and (ii) elastic stress transfer at the bond interface. The increase of applied load during spontaneous debonding is due to both these factors [5,6,10]. It is usually assumed that unstable interface debonding occurs at the maximum load and the load drop after the maximum load is related to an interface debond strain energy release rate [5,6]. In the present experiment, the interface debonding propagation occurred at about 40% of the maximum load and the increase of the load during the interface debonding progress was could be predicted by both the shear frictional stress at the debond interface and resistance to the interface debond progress. The radial clamping stress acts at the debond interface because of af < am. Just before the maximum load, almost all of the interface is debonded and thus the applied load is supported by purely interface frictional resistance, i.e., the load drop during the pushout testing up to the
S. Guo et al. / Composites Science and Technology 65 (2005) 1808–1814
maximum load is achieved by the interfacial frictional resistance at the debond interface. After the entire interface debonding, a static-dynamic frictional transition front will propagate up to the point where the entire fiber is set in motion because of ls P ld, accompanied further increase in the pushout load. Thus, at the maximum load, the entire load is supported by the interfacial shear frictional force. It is well known that a static frictional coefficient is larger than that of a dynamic one (ls > ld). Before the maximum load, static friction is acting on most of the debond interface and the interface retains a stick state. The transition from stick to slip occurs at the maximum load and the change of interfacial frictional coefficient leads to a sudden load drop. The load drop, DP, and the maximum load, Pmax, relate to DP ¼ 2pRf Lðls ld Þrr ;
ð2Þ
P max ¼ 2pRf Lls rr ;
ð3Þ
where rr is the average radial clamping stress along the sliding interface. Assuming that the interfacial radial stress caused by Poisson expansion of the fiber during the loading is neglected, the rr is simply given by Z DT Em Ef rr ¼ ðaf am ÞdT ; ð4Þ Ef ð1 þ mm Þ þ Em ð1 mf Þ 0 where mf and mm are the PoissonÕs ratio of the fiber and matrix, respectively. Note that the calculated value of the frictional coefficient in the absence case of Poisson ratio effect is rough and large. Zhou and Mai [16] showed that the interfacial radial stress caused by Poisson expansion of fiber sometimes should significantly affect the total radial clamping stress at the interface when the fiber is under compression. In the present experiment, in order to avoid complex calculation, the above assumption was applied to calculate the radial clamping stress by using Eq. (4). This assumption seems to be useful because the fiber volume fraction is 0.001 for the composite specimen used in this investigation as well as because our aim is to comparing role of static and dynamic frictional coefficients during the interface debonding. Based on the above assumption, the estimated radial clamping stress and the frictional coefficients are 11 MPa, ls 4.2 and ld 2.1, respectively. The value of the static frictional coefficient is a factor of 2 larger than the dynamic frictional coefficient. The result indicates that the maximum load in the load–displacement relation does not always cause an interface debonding event. The experiment result indicates a different aspect of the interface debonding behavior in the load–displacement relation, especially the meaning of maximum load. However, it should be noted that the interface debond condition at the maximum load is strongly dependent on the shear frictional stress and interface debonding resistance.
1813
4. Conclusion Progress of interface debonding in a W fiber-reinforced epoxy matrix composite during the pushout testing has been observed in situ. The result shows that the interface debonding always proceeds from an initially existing debond front at the bottom face. The debond length increases with the increase of applied load. When the debond length reaches approximately 93% of specimen thickness (Ld/L = 0.93), the debonding proceeds rapidly and joins with the initial debond tip located at the top face. The behavior is simply explained by the interaction of the thermal residual stress and stress induced by applied load at both top and bottom faces in the composite specimen. The entire interface debonding occurs before the maximum load and the load drop just after the maximum load is caused by the change in frictional condition at the debond interface. Therefore, the load drop immediately after the maximum load indicates a change of condition from static to dynamic friction at the interface between the fiber and the matrix.
References [1] Kagawa Y, Okura A. Measurement of interfacial shear strength in SiC(CVD) fiber-reinforced Ti–15Mo–5Zr–3Al composite by push-out technique. J Jap Inst Metall 1992;56(3): 278–84. [2] Honda K, Kagawa Y. Debonding criterion in the pushout process of fiber-reinforced ceramics. Acta Mater 1996;44(8):3267–77. [3] Guo SQ, Kagawa Y. Characterization of interface sliding damage in SiC fiber-reinforced Ti-15-3 matrix composite by cyclic fatigue. Acta Mater 1997;45(6):2257–70. [4] Eldridge IJ, Ebihara BT. Fiber push-out testing apparatus for elevated temperatures. J Mater Res 1994;9(4):1035–42. [5] Dollar A, Steif PS. Cohesive zone approach to interpreting the fiber push-out test. J Am Ceram Soc 1993;76(4):897–903. [6] Kerans RJ, Parthasarathy TA. Theoretical analysis of the fiber pullout and pushout tests. J Am Ceram Soc 1991;74(7): 1585–96. [7] Shetty DK. Shear-lag analysis of fiber push-out tests for estimating interfacial friction stress in ceramic-matrix composites. J Am Ceram Soc 1988;71(2):C-107–9. [8] Liang C, Hutchinson JW. Mechanics of the fiber pushout test. Mech Mater 1993;14(3):207–21. [9] Hutchinson JW, Jensen HM. Model of fiber debonding and pullout in brittle composites with friction. Mech Mater 1990;9(2):139–63. [10] Waeren PD, Mackin TJ, Evans AG. Design, analysis and application of an improved push-through test for the measurement of interface properties in composites. Acta Metall Mater 1992;40(6):1243–9. [11] Watson MC, Clyne TW. The use of single fiber pushout testing to explore interfacial mechanics in SiC monofilament-reinforced TiII. Application of the test to composite material. Acta Metall Mater 1992;40(1):141–8. [12] Ghosn LJ, Eldridge JI, Kantzos P. Analytical modeling of the interfacial stress state during pushout testing of SCS-6/ Ti-based composites. Acta Metall Mater 1994;42(11): 3895–908.
1814
S. Guo et al. / Composites Science and Technology 65 (2005) 1808–1814
[13] Kagawa Y, Hsueh CH. Model experiment on a protrusion method for measurement of interface shear sliding stress in fiberreinforced composite. Mater Sci Eng A 1999;271:70–8. [14] Honda K, Kagawa Y. Effect of H2O in specimen and loading rate on the interfacial shear sliding stress in SiC/LAS composite. J Jpn Inst Metal 1992;56(4):481–6.
[15] Honda K, Kagawa Y. Analysis of shear stress distribution in pushout process of fiber-reinforced ceramics. Acta Metall Mater 1995;43(4):1477–87. [16] Zhou LM, Mai YW. On the single fiber pullout and pushout problem: Effect of fiber anisotropy. Z Angew Math Phys 1993;44:769–75.
Interface debonding from bottom face and frictional transition during pushout testing of a tungsten fiber-epoxy matrix composite Shuqi Guo a
a,*
, Kouichi Honda a, Yutaka Kagawa
a,b,*
Institute of Industrial Science, The University of Tokyo, 4-6-1 Komaba, Meguro-ku, Tokyo 153-8505, Japan b Department of Materials Engineering, Graduate School of Engineering, The University of Tokyo, Japan Received 5 March 2004; received in revised form 7 January 2005; accepted 14 March 2005 Available online 21 April 2005
Abstract The progress of interface debonding behavior in a tungsten fiber-reinforced epoxy matrix composite, which has an initially debonded interface due to thermal mismatch stress, has been studied by using the thin-specimen pushout test. Load drop behavior just after the maximum load in the load–displacement curve is discussed with respect to the interface debonding and frictional load transfer mechanism. The interface debonding propagates from the initially existing debond crack tip at the bottom face while no interface debonding crack propagation is observed from that located at the top face. This characteristic interface debonding behavior is explained by the interaction of interface shear stresses which originated from the thermal misfit and the applied load. Near the top face, the two shear stresses are opposite while those at the bottom face are added. This creates a condition of interface debonding from the bottom face when the thermal expansion coefficient of fiber is smaller than that of matrix. The load drop observed just after the maximum load in the load–displacement curve is not related with the interface debonding but with the transition of interface frictional sliding resistance from static to dynamic. The maximum pushout load is predicted by the static coefficient of friction and the load after the drop is predicted by dynamic coefficient of friction. 2005 Elsevier Ltd. All rights reserved. Keywords: Polymer–matrix composite; Tungsten fiber; Pushout; Interface debonding
1. Introduction A thin-sliced specimen pushout test has been widely applied for the evaluation of interface mechanical properties in various kinds of fiber-reinforced composites because of the broad specimen preparation and relatively simple experimental procedure [1–5]. To obtain interfacial mechanical properties from a pushout test, it is important to know the corresponding correlation between experimentally obtainable load–displacement relation and interface debonding sliding behaviors [6– * Corresponding authors. Tel.: +81 298592223; fax: +81 298592401 (S. Guo), Tel.: +81 354525086; fax: +81 354525087 (Y. Kagawa). E-mail addresses: [email protected] (S. Guo), kagawa@iis. u-tokyo.ac.jp (Y. Kagawa).
0266-3538/$ - see front matter 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.compscitech.2005.03.011
11]. Because analytical forms usually used to obtain the interfacial shear properties from the experiment are varied only under the assumed boundary conditions, the matching between the boundary condition and actual interface debonding sliding process should be compared before application of these forms. Although various analytical forms are available and applied for the evaluation of interfacial mechanical properties [6–10], few experimental papers have attempted to examine the corresponding relationship by using the theoretical analyses. Reports on the progress of interface debonding, in particular, are very scarce [2,11]. Additionally, the interface debonding sliding behavior sometimes differs from the ideally assumed conditions, as a result of the presence of various factors that are usually not included in the analysis. Generally, the interface
S. Guo et al. / Composites Science and Technology 65 (2005) 1808–1814
debonding is assumed to initiate from the pushing surface and some reports clearly demonstrated this behavior [2,11]. On the other hand, other papers have discussed the possibility of onset of interface debonding behavior from the bottom face [4,12] because of the effect of combination of thermal residual stresses and applied load at that location. No detailed evidence is available on the debonding from the bottom face, however. This paper demonstrates the possibility of the interface debonding phenomenon from the bottom face for the composite with Ef > Em and af < am (E and a are YoungÕs modulus and thermal expansion coefficients respectively, the subscripts f and m refer to fiber and matrix respectively). The effect of thermal mismatch stress on the interface debonding behavior from the bottom face as well as the effect of debonding behavior on the load–displacement curve are also discussed.
2. Experimental procedure The composite material used in this study was a tungsten (W: Tokyo Tungsten Co. Ltd., Tokyo, Japan) fiberreinforced epoxy matrix composite. The diameter of the fiber (2Rf) was 150 lm. An epoxy resin mixture (Epikote 828, of Yuka-shell Epoxy Corp., Tokyo, Japan) was cast into a Teflon tray in which a single W fiber was located. Then, the tray was put under a vacuum of 102 Pa for 20 min, to expel dissolved air introduced during the mixing process. The composite was then cured at 373 K for 2 h, post-cured for 5 h at 383 K and cooled to room temperature (298 K). More details of the fabrication process of the epoxy matrix can be obtained from the earlier report [13]. Table 1 lists properties of the W fiber and the epoxy matrix. Thin pushout specimens were prepared by a conventional mechanical cutting procedure and polishing procedure. Both the top and bottom faces of the specimens were carefully polished up to 1 lm using a diamond paste. The specimen was 4 · 4 mm square and the thickness, L, was 1.5 mm which corresponded to a fiber aspect ratio of L/2Rf 10. It contained a single fiber in the central position and an initial debond length of L0d 100 lm at the interface near both the top and bottom faces. The nominal fiber volume fraction was 0.001. Fig. 1 shows the shape and dimensions of the pushout specimen subjected to the pushout test.
Table 1 Properties of the tungsten fiber and the epoxy matrix
Tungsten fiber Epoxy matrix
1809
Fig. 1. Shape and dimensions of pushout test specimen.
The specimen was dried before the test to avoid any effect of water at the debond interface on the results [14]. A schematic illustration of the pushout equipment was reported elsewhere [1,2]. The composite specimen was mounted on a support block, which had a 500 lm diameter hole at the center, this diameter being a factor of 3 larger than that of the fiber diameter. The center of the fiber was placed at the center of the hole to allow the fiber to be pushed out freely from the specimen. The adjustment was made by means of an optical microscope, which was provided with the pushout test equipment. A hard steel spherical indenter (YoungÕs modulus 550 GPa) with a tip diameter 100 lm was used. Positioning the indenter to the fiber center was done by a video-microscope. The pushout test was conducted in air at room temperature (298 K) and a load was applied by moving the specimen support block upward at a constant displacement rate of 5 · 107 m/s. The applied load was measured by a load cell (maximum capacity of 500 N, Tokyo Sokki, CLS-50KA, Tokyo, Japan) which was attached to the holder. The displacement of the fiber end surface was continuously monitored by a reflective type laser displacement meter (minimum resolution of 0.2 lm, Keyence, LC-2440, Tokyo, Japan). 10 specimens were used for this test. In situ observations of the interface debonding and sliding behavior during the pushout testing were carried out using a video-microscope (Keyence, VH-5910) with a typical magnification of 200· at the CRT monitor. The change of reflective light at the interface was stored in a videotape recorder. The selected images were processed using the ‘‘NIH’’ Image public domain software. The detailed observation process has been reported elsewhere [1,2].
YoungÕs modulus, E (Gpa)
PoissionÕs ratio, m
Coefficient of thermal expansion, a, (·106 K1)
3. Results and discussion
370 3
0.17 0.37
5.0 60
Fig. 2 shows an example of typical pushout results presented in terms of load–fiber end displacement
1810
S. Guo et al. / Composites Science and Technology 65 (2005) 1808–1814
25 (d)
Load,P(u) (N)
20 15 (c)
10 (b)
5 (a)
0
0
20
40
60
80
100
120
140
Fiber Displacement, u (mm) Fig. 2. A typical example of the load–displacement curves obtained during the pushout testing of the composite specimens.
response. The curve shows an initial linear part which begins to deviate the linear regime when the load reaches 40% of a maximum load (21 N). Just after reaching maximum load, the load suddenly decreases to about 40% without noticeable increase of the displacement, u. Thereafter, the load initially gradually decreases and then tends to remain essentially constant with the increase of the fiber-end displacement, accompanied with
fiber protrusion from the bottom face. The maximum load corresponds to the onset of the fiber protruding from the bottom face [3,10]. The letters (a)–(d) in Fig. 2 represent before loading (a), onset of debonding propagation from the existing debonding crack tip (b), progress of debonding interface (c), and whole interface debonding (d), respectively. A typical example of the direct observation result of the progress of interface debonding during the pushout testing is shown in Fig. 3; the letters (a)–(d) correspond to those in Fig. 2. The partially reflected light area observed on the fiber surface corresponds to the debond interface area (tip of the identified debond interface is indicated by an arrow). Before loading, the interface from both the polished top and bottom faces initially debonded about 100 lm (L0d =L 0:07Þ; this initial debonding in the specimen preparation process is caused by a thermal misfit shear stress during the fabrication and it is difficult to avoid in a W fiber-reinforced epoxy matrix system [13]. The important finding in the observations during the present pushout testing is that the interfacial debonding proceeded spontaneously from the existing debonded crack front only at the bottom face and not at the top face. This interfacial debond progress behavior was observed for each instance. Based on the above in situ observations, the interface debonding
Fig. 3. In situ observation of the fiber–matrix interface by video microscope with debonding length obtained by image analysis.
S. Guo et al. / Composites Science and Technology 65 (2005) 1808–1814
1811
Load
Initial debonding Fiber S2 S1 Initial debonding
Matrix
Support Support block block Fig. 4. Schematic drawing of interface debond progress observed during the pushout testing, (S1-Spontaneous debonding 1, and S2-Spontaneous debonding 2).
behavior in the composite specimen studied was schematically drawn, which illustration was shown in Fig. 4. The relation between the normalized interface debond length from the bottom face, Ld/L, and normalized applied load, P/Pmax, obtained from the direct observation is shown in Fig. 5. Here, Pmax is the maximum load (21 N) in the load–displacement curve and Ld is the overall debond length-including the initially existing debond length. When the applied load reaches 8 N (P/Pmax 0.4), the interface debonding from the bottom face propagates and the debonding proceeds spontaneously with a typical debond increment in a single unit of debonding length 200 lm (dLd/L 0.13).
Complete debonding
Normalized Applied Load, P/Pmax
1.0
(d)
0.8 Onset of debond propagation
0.6
δLd (c)
(b)
0.4
(a)
0.2
Initial debonding
0 0
0.2 0.4 0.6 0.8 Normalized Debond Length from Back Surface, Ld/L
1.0
Fig. 5. Relation between the normalized interface debond length from the bottom face, Ld/L, and normalized applied load, P/Pmax, obtained from in situ observation.
Note that the incremental lines between (b) and (d) (C part in Fig. 5) represent the spontaneous interfacial debonding behavior during the pushout process. The unit of debonding length, dLd, tends to increase gradually with the increase of applied load as interface debonding progresses. Finally, when the debonding length from the bottom face reaches 1.4 mm, i.e., Ld/L = 0.93, the debonding crack propagated from this face becomes unstable, the crack tip propagates immediately and the crack joins together the initially existing debond crack front at the top face once the pushout load begins to continuously increase; this results in complete debonding of the entire interface. However, the pushouting load continuously increases after the entire interface complete debonding. This rapid interface debond progress occurs when the load reaches about 80% of maximum, indicating that the load increase after the complete debonding is achieved by a purely frictional force. At the maximum load in the load–displacement curve, the interface is completely debonded and the load is totally supported by a frictional force at the debonded interface. It was reported that interfacial shear stress state at the interface plays an important role in the interface debonding behavior [2,15]. In the case of af < am with DT > 0, before the pushout test thermally induced shear stress at the interface initially caused the interface debonding at both the top and bottom faces (DT = Tg T0 is the temperature change when thermal stress is introduced, Tg and T0 are the glass transition temperature of the epoxy matrix and room temperature (Tg > T0), respectively). As the pushout load is applied, the resulting shear stress along the fiber/matrix interface becomes a superposition of thermal residual stress and stress induced by the applied load. In particular at the tip of interface debonding located at the pushing surface the larger stress is expected under the loading, as a result of stress concentration at the debonding crack tip. The
1812
S. Guo et al. / Composites Science and Technology 65 (2005) 1808–1814
total interface shear stress along the bonded interface, s(z), is given by [2] sðzÞ ¼ sT ðzÞ þ sa ðzÞ;
ð1Þ
T
where s (z) is the interface shear stress by thermal misfit stress and sa(z) is the interface shear stress by the applied load. Thus, the absolute value of s(z) is affected not only by the absolute value of sT(z) and sa(z) but by the sign of the shear stresses. The sign of these interface shear stresses was previously defined by Honda and Kagawa [2] in a SiC(SCS-6) fiber-reinforced borosilicate glass matrix, which results are schematically shown in Fig. 6. At the top face (pushing surface), sT ðL0d Þ < 0 and sa ðL0d Þ > 0, the sign of these shear stresses is opposite while at the bottom face it is the same, i.e., sT ðL L0d Þ < 0 and sa ðL L0d Þ < 0. Thus, the interface shear stresses at the top face cancel each other when the pushout load is applied, and consequently the total interface shear stress decreases, i.e., sðL0d Þ ¼ sa ðL0d Þ sT ðL0d Þ. On the other hand, the interface shear stress near the bottom face increases from the initial state after pushing, i.e., sðL L0d Þ ¼ sa ðL L0d Þ þ sT ðL L0d Þ. When the total interface shear stress at the bottom face is larger than that at top face, i.e., jsa ðL L0d Þ þ sT ðL L0d Þj > jsa ðL0d Þ sT ðL0d Þj, the interface debond progress initiates from the bottom face. Because the interface debonding behavior is also related to the clamping stress state at the interface, the explanation on the interface debonding behavior observed in this experiment is qualitative and rough. However, it is undoubted that this difference of thermally induced shear stress along the interface is a strong source for promoting the interface debonding behavior from the bottom face (Fig. 6). That is, the decrease of shear stress near the top face enhances crack stability and the increase of shear stress near the bottom face weakens it. Even though the interface stress concentration at the debond crack tip near the top face also increases with the increase of applied load, the initial Shear stress by applied load,, τ (z )
Shear stress by thermal misfit,, τ (z )
a
T
z =0 L0d
(α f < α m)
Fiber Fiber
Matrix
L −L
0 d
Z=L
Initial interface debonding Fig. 6. Schematic illustration of signs in the interfacial shear stresses at the top face and the bottom face.
debond crack at the top face remains stabile and does not propagate due to high radial clamping stress at that location, resulting from the PoissonÕs expansion of the loaded fiber as well as from the bending of specimen associated with the test specimen thickness[12]. This high radial clamping stress prohibits a shear failure at the top face. The present composite system is af < am and thus the interface debond progress likely occurs from the bottom face. On the contrary, if the af > am relationship is satisfied, the interface debonding is likely to occur from the top face. In the latter case, the evidence was experimentally proved by the authors using SiC(SCS-6) fiber-reinforced borosilicate glass matrix composite [2]. Moreover, previous investigations [4,12] have reported the interfacial debonding behavior occurring at the bottom face during pushout testing of SiC(SCS-6) fiber-reinforced Ti alloy matrix composites. Ghosn et al. [12] have studied the interfacial stress state and the relation of the stress state to the interface debonding behavior by using finite element method (FEM). Their analysis showed that the residual shear stress at the top face is tend to oppose the externally applied load during pushout testing while at bottom face the shear stress increase adds to the existing large residual stress. Additionally, their observations showed that the interfacial debonding always occurs from the bottom face. They concluded that the applied load must be able to overcome the residual thermal shear stress near the top face as well as the compressive radial stress before debonding can occur, and interfacial debonding also can occur preferentially near the bottom face where the local shear stress are the greatest. This agrees with our experimental observations in W fiber-epoxy matrix composite, showing the interfacial failure initiation in the case of af < am tends to occur at the bottom face. During the progressive spontaneous interface debonding, the applied load is supported by (i) interface shear frictional stress at the debond interface and (ii) elastic stress transfer at the bond interface. The increase of applied load during spontaneous debonding is due to both these factors [5,6,10]. It is usually assumed that unstable interface debonding occurs at the maximum load and the load drop after the maximum load is related to an interface debond strain energy release rate [5,6]. In the present experiment, the interface debonding propagation occurred at about 40% of the maximum load and the increase of the load during the interface debonding progress was could be predicted by both the shear frictional stress at the debond interface and resistance to the interface debond progress. The radial clamping stress acts at the debond interface because of af < am. Just before the maximum load, almost all of the interface is debonded and thus the applied load is supported by purely interface frictional resistance, i.e., the load drop during the pushout testing up to the
S. Guo et al. / Composites Science and Technology 65 (2005) 1808–1814
maximum load is achieved by the interfacial frictional resistance at the debond interface. After the entire interface debonding, a static-dynamic frictional transition front will propagate up to the point where the entire fiber is set in motion because of ls P ld, accompanied further increase in the pushout load. Thus, at the maximum load, the entire load is supported by the interfacial shear frictional force. It is well known that a static frictional coefficient is larger than that of a dynamic one (ls > ld). Before the maximum load, static friction is acting on most of the debond interface and the interface retains a stick state. The transition from stick to slip occurs at the maximum load and the change of interfacial frictional coefficient leads to a sudden load drop. The load drop, DP, and the maximum load, Pmax, relate to DP ¼ 2pRf Lðls ld Þrr ;
ð2Þ
P max ¼ 2pRf Lls rr ;
ð3Þ
where rr is the average radial clamping stress along the sliding interface. Assuming that the interfacial radial stress caused by Poisson expansion of the fiber during the loading is neglected, the rr is simply given by Z DT Em Ef rr ¼ ðaf am ÞdT ; ð4Þ Ef ð1 þ mm Þ þ Em ð1 mf Þ 0 where mf and mm are the PoissonÕs ratio of the fiber and matrix, respectively. Note that the calculated value of the frictional coefficient in the absence case of Poisson ratio effect is rough and large. Zhou and Mai [16] showed that the interfacial radial stress caused by Poisson expansion of fiber sometimes should significantly affect the total radial clamping stress at the interface when the fiber is under compression. In the present experiment, in order to avoid complex calculation, the above assumption was applied to calculate the radial clamping stress by using Eq. (4). This assumption seems to be useful because the fiber volume fraction is 0.001 for the composite specimen used in this investigation as well as because our aim is to comparing role of static and dynamic frictional coefficients during the interface debonding. Based on the above assumption, the estimated radial clamping stress and the frictional coefficients are 11 MPa, ls 4.2 and ld 2.1, respectively. The value of the static frictional coefficient is a factor of 2 larger than the dynamic frictional coefficient. The result indicates that the maximum load in the load–displacement relation does not always cause an interface debonding event. The experiment result indicates a different aspect of the interface debonding behavior in the load–displacement relation, especially the meaning of maximum load. However, it should be noted that the interface debond condition at the maximum load is strongly dependent on the shear frictional stress and interface debonding resistance.
1813
4. Conclusion Progress of interface debonding in a W fiber-reinforced epoxy matrix composite during the pushout testing has been observed in situ. The result shows that the interface debonding always proceeds from an initially existing debond front at the bottom face. The debond length increases with the increase of applied load. When the debond length reaches approximately 93% of specimen thickness (Ld/L = 0.93), the debonding proceeds rapidly and joins with the initial debond tip located at the top face. The behavior is simply explained by the interaction of the thermal residual stress and stress induced by applied load at both top and bottom faces in the composite specimen. The entire interface debonding occurs before the maximum load and the load drop just after the maximum load is caused by the change in frictional condition at the debond interface. Therefore, the load drop immediately after the maximum load indicates a change of condition from static to dynamic friction at the interface between the fiber and the matrix.
References [1] Kagawa Y, Okura A. Measurement of interfacial shear strength in SiC(CVD) fiber-reinforced Ti–15Mo–5Zr–3Al composite by push-out technique. J Jap Inst Metall 1992;56(3): 278–84. [2] Honda K, Kagawa Y. Debonding criterion in the pushout process of fiber-reinforced ceramics. Acta Mater 1996;44(8):3267–77. [3] Guo SQ, Kagawa Y. Characterization of interface sliding damage in SiC fiber-reinforced Ti-15-3 matrix composite by cyclic fatigue. Acta Mater 1997;45(6):2257–70. [4] Eldridge IJ, Ebihara BT. Fiber push-out testing apparatus for elevated temperatures. J Mater Res 1994;9(4):1035–42. [5] Dollar A, Steif PS. Cohesive zone approach to interpreting the fiber push-out test. J Am Ceram Soc 1993;76(4):897–903. [6] Kerans RJ, Parthasarathy TA. Theoretical analysis of the fiber pullout and pushout tests. J Am Ceram Soc 1991;74(7): 1585–96. [7] Shetty DK. Shear-lag analysis of fiber push-out tests for estimating interfacial friction stress in ceramic-matrix composites. J Am Ceram Soc 1988;71(2):C-107–9. [8] Liang C, Hutchinson JW. Mechanics of the fiber pushout test. Mech Mater 1993;14(3):207–21. [9] Hutchinson JW, Jensen HM. Model of fiber debonding and pullout in brittle composites with friction. Mech Mater 1990;9(2):139–63. [10] Waeren PD, Mackin TJ, Evans AG. Design, analysis and application of an improved push-through test for the measurement of interface properties in composites. Acta Metall Mater 1992;40(6):1243–9. [11] Watson MC, Clyne TW. The use of single fiber pushout testing to explore interfacial mechanics in SiC monofilament-reinforced TiII. Application of the test to composite material. Acta Metall Mater 1992;40(1):141–8. [12] Ghosn LJ, Eldridge JI, Kantzos P. Analytical modeling of the interfacial stress state during pushout testing of SCS-6/ Ti-based composites. Acta Metall Mater 1994;42(11): 3895–908.
1814
S. Guo et al. / Composites Science and Technology 65 (2005) 1808–1814
[13] Kagawa Y, Hsueh CH. Model experiment on a protrusion method for measurement of interface shear sliding stress in fiberreinforced composite. Mater Sci Eng A 1999;271:70–8. [14] Honda K, Kagawa Y. Effect of H2O in specimen and loading rate on the interfacial shear sliding stress in SiC/LAS composite. J Jpn Inst Metal 1992;56(4):481–6.
[15] Honda K, Kagawa Y. Analysis of shear stress distribution in pushout process of fiber-reinforced ceramics. Acta Metall Mater 1995;43(4):1477–87. [16] Zhou LM, Mai YW. On the single fiber pullout and pushout problem: Effect of fiber anisotropy. Z Angew Math Phys 1993;44:769–75.