- Email: [email protected]
Effects of hot extrusion parameters on the tensile properties and microstructures of SiCw-2124Al composites
IL,,~IfllIAI~
ELSEVIER
Materials Science and Engineering A206 (1996) 225 232
A
Effects of hot extrusion parameters on the tensile properties and microstructures of SiCw-2124A1 composites Soon H. Hong a, Kyung H. Chung a, Chi H. Lee b "Department ~)/'Materials Science and Engineering, Korea Advanced Institute ~)[ Science and Technology, 373-1 Kusung-dong, Yusung-gu, Taejon, South Korea bDepartment of Metallurgical Engineering, Inha University, 253 Yonghyun-dong, Nam-gu, lnehon, South Korea Received 3 October 1994; in revised form 12 July 1995
Abstract
The effects of extrusion ratio and extrusion temperature on tensile strengths and microstructures of 20 volY,, SiCw-2124AI composites were investigated. The alignment of SiC whiskers along the extrusion direction in SiCw-2124AI composites was improved and the aspect ratio of SiC whiskers was decreased with increasing extrusion ratio from 10:1 to 25:1. The SiCw-2124AI composite exhibited the highest tensile strength at the extrusion ratio of 15:1. The aspect ratio of whiskers and the relative density of composite increased with increasing extrusion temperature from 470 °C to 530 °C. The tensile strength of SiCw-2124A1 composite increased with increasing extrusion temperature up to 530 °C. Based on the concept of the load transfer efficiency of misoriented SiC whiskers in the 2124A1 matrix, the two microstructural parameters of the alignment and aspect ratio of whiskers, which influenced on the tensile strength in an opposite way, were combined into a single parameter proposed as an effective aspect ratio. The highest tensile strength of SiCw-2124A1 composite at the extrusion ratio of 15:1 is explained by the largest effective aspect ratio due to the balance of the alignment and aspect ratio of SiC whiskers. A modified phenomenological equation describing the tensile strength of SiCw-2124A1 composites as a function of microstructural parameters was proposed by introducing the effective aspect ratio as a substitute for the average aspect ratio of SiC whiskers.
Keywords: Hot extrusion; Tensile properties; Microstructures; SiC-A1 composites
1. Introduction Metal matrix composites (MMCs) are attractive structural materials since their properties can be enhanced or tailored through the addition of selected reinforcements. In particular, S i C - A I composites have been focused on with special interest owing to their high specific strength and specific modulus at room or elevated temperatures [1-4]. The commercial fabrication processes of SiC whisker reinforced A1 matrix composites are generally classified into two major types, powder metallurgy process and casting process [5]. The powder metallurgy process is generally known to give better mechanical properties even though the fabrication cost is higher than the casting process [5,6]. The powder metallurgy process of M M C s consists of several fabrication steps and the process variables at each step are required to be optimized for good properties. The effects of vacuum hot 0921-5093/96/$15.00 © 1 9 9 6 - Elsevier Science S.A. All rights reserved SSDI 0921-5093(95)09996-4
pressing parameters on the tensile strength and microstructures of SiCw-2124A1 composites have already been discussed in our previous work [7]. In order to achieve the maximum composite strengthening effect by the addition of SiC whiskers, the whiskers need to be aligned parallel to one direction. Thus the consolidated billets are usually processed by primary deformation processing, such as extrusion, forging or rolling, at elevated temperature to align the SiC whiskers [8]. The hot extrusion process is the deformation process commonly used to align the whiskers in MMCs. In addition to the alignment of whiskers, the whiskers break as a result of the damage during hot extrusion. The damage of SiC whiskers reduces the aspect ratio of the whiskers and decreases the load transfer efficiency in composites [9-11]. These two microstructural variations during hot extrusion influence the mechanical properties of composites in opposite ways. The improved alignment of whiskers
226
S.H. Hong et al. / Materials Science and Engineering A206 (1996) 225 232
enhances the strength, while the reduced aspect ratio of whiskers decreases the strength. Therefore, it is very important to optimize the hot extrusion conditions which maximize the reinforcing effect of whiskers by balancing the two microstructural factors, i.e. alignment of whiskers and aspect ratio of whiskers. In this study, the effects of extrusion temperature and extrusion ratio on tensile strength and microstructure were investigated in 20 vol.% SiCw-2124A1 composites. The relationships between the microstructural parameters, i.e. aspect ratio of whiskers, alignment of whiskers and density of composites, and tensile strength of composites are discussed. A modified phenomenological equation is proposed to estimate the tensile strength from the measured microstructural parameters including the degree of whisker alignment after hot extrusion.
2. Experimental procedures The atomized 2124A1 powders with average diameter of 20 pm were used as a matrix, and r - s i c whiskers with average diameter of 1.5 pm and length of 4050 pm were added as the reinforcement. 80 vol.% of 2124A1 powders and 20 vol.% of r - s i c whiskers were wet mixed in ethyl alcohol of pH 9 with continuous stirring. The mixtures of 2124A1 powders and SiC whiskers were dried for 12 h at 70 °C and then consolidated into billets by vacuum hot pressing. The mixtures of powders with whiskers were placed in a die and consolidated in a hot pressing chamber. The hot pressing chamber was evacuated to 1 × 10 5 Torr during heating of the die to 570 °C and the mixtures of powders with whiskers were hot pressed at 90 MPa for 10 min to make cylindrical billets. In order to investigate the effects of hot extrusion parameters on the tensile strength and microstructure of SiCw-2124A1 composites, the cylindrical billets were hot extruded into bars with different extrusion ratios of 10:1, 15:1 and 25:1 at various temperatures of 470, 500 and 530 °C. The extruded bars were T6 heat treated by solution treatment at 493 °C for 3 h and followed by aging at 190 °C for 8 h. The tensile tests of SiCw-2124A1 composites were performed using an Instron 4206 system with an initial strain rate of 1.66 x 1 0 - 3 S-1. The densities of extruded composites were measured by an ASTM standard test procedure [12]. The aspect ratios of SiC whiskers in extruded composites were measured in the optical and scanning electron microscopy (SEM) micrographs from the overetched surface parallel to the extrusion axis. The degree of SiC whisker alignment along the extrusion axis was analysed by X-ray pole figures constructed from the (l 1l) diffraction peak of SiC whiskers.
3. Results and discussion Microstructures showing the distribution of SiC whiskers in SiCw-2124AI composites extruded with various extrusion ratio are presented in Fig. 1. The aspect ratio of SiC whiskers decreased with increasing extrusion ratio, since the average length of SiC whiskers decreased owing to the damage of whiskers at higher extrusion ratio. At the same time, the alignment of whiskers became more parallel to the extrusion axis with increasing extrusion ratio. The variation in tensile strength and relative density of SiCw-2124A1 composites with varying extrusion ratio is shown in Fig. 2. The maximum tensile strength of 505 MPa was obtained at an extrusion ratio of 15:1. The relative density of composites increased to 99.5% after hot extrusion compared with about 96% in the as-hot-pressed billet. The variation in relative density of composites with varying extrusion ratio was less than 0.2%. On the contrary, the average aspect ratio of whiskers decreased with increasing extrusion ratio from 10:1 to 25:1 as shown in Fig. 3. Fig. 2 shows that the tensile strength of composites extruded at 15:1 was about 40 MPa higher than that of
Extrusion Direction
Fig. 1. SEM micrographs of SiCw-2124AI composites showing the variation in the alignmentand aspect ratio of SiC whiskersin 2124A1 matrix: (a) extrusion ratio of 10:1; (b) extrusion ratio of 15:1; (c) extrusion ratio of 25:1.
S.H. Hong et al./ Materials Science and Engineering A206 (1996) 225 232
550 A
t~ a.
520.
227
100 O,..,,.,,,.,O
O
'99
Jr-
490. c
'9B
"~
'97
o~
e,-
Q 460.
0D
w e-
•~ •~
430.
400
, 10
strength density
>
96
, 20
95 30
0
Extrusion Ratio Fig. 2. The variation in tensile strength and relative density of SiC,~- 2124A1 composites with extrusion ratio.
(b)
composites extruded at 10:1. The higher relative density of composites extruded at 15:1 is considered as one reason for the higher tensile strength compared with the composite extruded at 10:1. However, the difference in relative density of 0.2% results in a difference in tensile strength of only 15 MPa from the following equation, which was proposed as a phenomenological equation relating the tensile strength to the porosity in SiCw2124A1 composites from our previous work [7]: o"
- exp(- 15.5P)
(1)
av where o- is the tensile strength of a porous powder metallurgy material, a v is the tensile strength of a powder metallurgy material with full density, and P is the porosity in a porous powder metallurgy material.
.=
.=¢ _= 5 o
e-
o
,m
4
!
1
10
20
30
Extrusion Ratio Fig. 3. The variation in average aspect ratio of whiskers in composites with extrusion ratio.
'
~
( ~ Exl~usino
Fig. 4. X-ray pole figures constructed from (111) peak intensity in SiC whiskers of SiC~ 2124A1 composites: (a) extrusion ratio of 10:1; (b) extrusion ratio of 15:1; (c) extrusion ratio of 25:1,
Furthermore, the average aspect ratio of whiskers decreased with increasing extrusion ratio as shown in Fig. 3. From the modified shear lag model [13], the average aspect ratio of reinforcements is known to be an important factor influencing the tensile strength of composite. The tensile strength of composites decreases with decreasing aspect ratio of whiskers. Therefore, the higher tensile strength in the composite extruded at 15:1 cannot be simply explained by the differences in relative density of composites and aspect ratio of whiskers. As the alignment of whiskers along the extrusion axis improved with increasing extrusion ratio, the alignment of SiC whiskers needs to be considered as another factor influencing the tensile strength of composites. The traces of (111) X-ray diffraction peak intensity from fl-SiC whiskers represent the variation in whisker alignment with varying extrusion ratio as shown in Fig. 4.
228
S.H. Hong et al. / Materials Science and Engineering A206 (1996) 225-232
Extrusion Axis
In order to analyse the degree of whisker alignment, the variation in (111) peak intensity from fl-SiC was examined using an X-ray pole figure technique and was plotted against the misorientation angle 0, as shown in Fig. 5. The (111) peak intensity from SiC whiskers in X-ray pole figure is proportional to the amount of whiskers aligned with the misorientation angle 0 from the extrusion axis. As the (111) peak intensity exponentially decreased with increasing misorientation angle, it is proposed that the density function F(O) of whiskers which represents the density of whiskers aligned with misorientation angle 0 to the extrusion axis, is given by the following equation: F(O) = A e x p ( - K 0 )
(2)
where 0 is the misorientation angle from extrusion axis and A and K are constants. The amounts dD of whiskers aligned between misorientation angles of 0 and 0 + dO can be expressed as a product of the area of shaded strip in Fig. 6, 2re sin 0 dO, and the density function F(O) of whiskers as follows: d D = F(O) x 2re sin 0 dO
(3)
As the total fraction of SiC whiskers in composites, which is calculated by integrating dD from 0 = 0 to 0 = to/2, was fixed as 20 vol.%, a boundary condition for Eq. (3) can be expressed as DlO:I = D15:1 = D25:1
(4)
where Dlo:l , DIS:l and D25:1 are the integrated values of the amount of whiskers in SiCw-2124A1 composites extruded with 10:1, 15:1 and 25:1 respectively. The constants A and K in the density function F(O) were obtained by curve fitting of the normalized (111) peak intensity with varying misorientation angle considering the boundary condition of Eq. (4). 1.0.
e-
dO
0.8.
Fig. 6. A schematic diagram of the three-dimensionalgeometry of SiC whisker alignment showing the division of the integration area. It is generally accepted that the load is transferred from the matrix to whiskers at the whisker-matrix interfaces parallel to the loading axis. When a composite is loaded, the whisker and matrix have different axial displacements owing to different moduli of the components. The difference in axial displacements induces shear strain parallel to the whisker axis at the whisker-matrix interface. The magnitude of the shear strain in a whisker having misorientation angle 0 is proportional to cos 0. Thus the load transferred to a whisker with aspect ratio S along the whisker axis will be proportional to S cos 0. At the same time, the load-sharing effect of the whisker along the stress axis needs to be multiplied again by cos 0. Therefore, the load transfer efficiency of whiskers with average aspect ratio S and aligned with misorientation angle 0 from the loading axis is assumed to be dependent on S cos 2 0, which is defined as an effective aspect ratio of whiskers. Then the differential effective aspect ratio, dSefr contributed by the whiskers aligned within the misorientation angle range from 0 to 0 + dO, as indicated by the shaded strip in Fig. 6, can be expressed as
_=
3 ~L
dSeff = (S cos 20)F(O)(2zr sin 0) dO
0.6-
By integrating dS~fr for the half-sphere from 0 = 0 to 0 = re/2 in Fig. 6, the effective aspect ratio Sefr contributed by all whiskers in composites is calculated as follows:
98"
0.4 q,.,
o o n-
(5)
0.2
Serf ~ ~or~/2 (S cos 20)F(O)(2rc sin 0) dO
25:1
0.0
0
i
|
i
!
10
20
30
40
50
M i s o r i e n t a t i o n A n g l e (Degree)
Fig. 5. The variationin the (l l 1) peak intensityof SiC whiskersfrom the X-ray pole figures with misorientation angle.
=
fo ~z/2 (S cos 20)A exp(--K0)(2re sin 0) dO
=A2r[ 1 - K exp(--Krc/2) 2 + K_exp(--Krc/2)] S 2(1 + K 2) + 2(9 + K 2) A
=CoS
(6)
229
S.H. Hong et al. / Materials Science and Engineering A206 (1996) 225-232 550-
where AtJ-.1 - K exp(-KTr/2)
<,
2(1 + K 2)
3 + _,Kexp(-Krr/2)-I __ -%
2(9 %" K 2)
J
99
is the alignment compensation factor related to the degree of whisker alignment and S is the average aspect ratio of whiskers. The alignment compensation factors, which represent the load transfer efficiency of whiskers related with the degree of alignment and average aspect ratio, were calculated from Eq. (6). The alignment compensation factor increased with increasing extrusion ratio from 10:1 to 15:1, but the increase in alignment compensation factor was negligible when the extrusion ratio increased from 15:1 to 25:1 as shown in Fig. 7. The effective aspect ratio of whiskers, which is the product of average aspect ratio and alignment compensation factor, was the largest in composites extruded at 15:1, while the average aspect ratio of whiskers was the largest in composites extruded at 10:1. The variation in tensile strength agrees well with the variation in effective aspect ratio with varying extrusion ratio. This result strongly indicates that the tensile strength of a composite is directly dependent on the effective aspect ratio of whiskers rather than average aspect ratio of whiskers. The relationships between tensile strength and microstructural factors in SIC,,, 2124A1 composites are explained as follows. The whisker alignment along the extrusion axis was improved and the aspect ratio of whiskers decreased owing to the damage of whiskers during the hot extrusion process. These changes in two microstructural factors, alignment of whiskers and aspect ratio of whiskers, influenced the tensile strength of
0.8 O k.
o
I.,I.
O
0.7
, m
m
ee
c O
u
&
m e-
0.6
w
<
E
O ¢.) o5
iii
E
c ot
'~'
0.4 0
100
•~ ' D - -
Alignment Compensation Factor
•" - " O - -
Effective Aspect Ratio ,
,
10
20
2
30
Extrusion Ratio Fig, 7. The variation in alignment compensation actor Co and effective aspect ratio of whiskers in SiCw 2124AI composites with extrusion ratio.
a.
500 J~
98
"~ C
c
2
_e
97 450'
G)
._
q)
¢:
ClE density
400
460
,
48o
ioo
5'20
96
95
540
Extrusion Temperature (°C) Fig. 8. The variation in tensile strength and relative density of SiC~ 2124Al composites with extrusion temperature.
composites in opposite ways. The improved alignment of whiskers represented by the alignment compensation factor enhances the tensile strength, while the reduced aspect ratio of whiskers decreases the tensile strength. These effects of two microstructural parameters are combined into one parameter, the effective aspect ratio. Consequently, with increasing extrusion ratio to 15:1, the tensile strength of composites increased as a result of the increase in both the effective aspect ratio of the whiskers and the relative density of the composite. However, the damage to the whiskers increased at an extrusion ratio of 25:1 and this resulted in a decrease in the effect aspect ratio of whiskers. Therefore, the tensile strength of composites decreased at an extrusion ratio of 25:1 owing to the rapid decrease in the effective aspect ratio of whiskers, although the relative density of composites increased slightly with increasing extrusion ratio. The tensile strength of composites extruded with an extrusion ratio of 15:1 rapidly increased from 430 MPa to 520 MPa with increasing extrusion temperature from 470 to 530 °C as shown in Fig. 8. The relative density of the composite significantly increased from 98.5% at an extrusion temperature of 470 °C to 99.6% at an extrusion temperature of 530 °C owing to the enhanced densification caused by the softening of 2124A1 matrix at higher extrusion temperatures. To analyse the degree of whisker alignment with varying extrusion temperature, the average aspect ratio and effective aspect ratio were measured and are plotted in Fig. 9. Both the average aspect ratio and the effective aspect ratio increased with increasing extrusion temperature, indicating that the damage to whiskers decreased at higher extrusion temperatures.
S.H. Hong et al. / Materials Science and Engineering A206 (1996) 225-232
230
J¢
4,
~.
2
0 460
~ ~
, 480
MeasuredAspectRatio EffectiveAspectRatio
l 500
Extrusion Temperature
, 520
540
ment was sensitively dependent on the extrusion ratio but was not strongly influenced by the extrusion temperature. On the contrary, the aspect ratio of whiskers was sensitively dependent on both the extrusion ratio and the extrusion temperature. The average aspect ratio of whiskers increased with increasing extrusion temperature and with decreasing extrusion ratio. The relative density was strongly influenced by the extrusion temperature but was not sensitively dependent on the extrusion ratio. In our prevous work [7], a phenomenological equation describing the quantitative relationship between tensile strength and microstructural parameters, i.e. aspect ratio of whiskers and relative density of SiCw2124A1 composite, was proposed as follows: SVf+2 = ~ro SoVf+ 2 e x p ( - k P )
(°C)
Fig. 9. The variation in average aspect ratio and effective aspect ratio of whiskers in SiCw 2124A1 composites with extrusion temperature.
The increase in tensile strength of SiCw-2124A1 composite with increasing extrusion temperature is considered to result from the increase in both the relative density of the composite and the aspect ratio of the whiskers. However, if the extrusion temperature was increased to 530 °C, the surface temperature became so high as to lead to a surface cracking, known as fir-tree cracking (Fig. 10), on the extruded composite [8]. Although the relative density of the composite and aspect ratio of the whiskers increased with increasing extrusion temperature, the upper limit of the extrusion temperature was restricted to below 530 °C owing to the surface cracking of composite. The SiC whiskers were damaged and aligned more parallel to the extrusion axis during hot extrusion, and thus the degree of alignment and the aspect ratio were influenced by the extrusion ratio. The degree of align-
(7)
where o is the tensile strength of a composite with arbitrary aspect ratio and arbitrary relative density, o-c is the tensile strength of composites with critical aspect ratio and full density, S and Sc are the arbitrary average aspect ratio and critical aspect ratio respectively of whiskers, Vf is the volume fraction of whiskers, P(%) is the porosity of the composite and k is a constant. The modified shear lag theory, for MMCs with a small aspect ratio of the reinforcements, was introduced in deriving Eq. (7). The critical aspect ratio is calculated from O'fu/2"t'i, where aru is tensile strength of the reinforcement and zi is the shear yield strength; o-r~for SiC is 7 GPa and ~i for 2124A1 is 275 MPa. Therefore the critical aspect ratio for the SiCw-2124A1 composite system is calculated to be about 12.7 and the experimentally observed aspect ratio of whiskers was less than 6, much lower than critical aspect ratio, so the modified shear lag model was introduced for this study and the critical aspect ratio was considered as the reference state. Since the alignment of whiskers is strongly influenced by the extrusion conditions, Eq. (7) needs to be modified to include the effect of whisker alignment along the extrusion axis. Considering the effect of whisker alignment, the load transfer efficiency is changed and the tensile strength of the composite is expressed by substituting the effective aspect ratio Sefr for the average aspect ratio S of whiskers in Eq. (7). A new modified equation for the tensile strength of SiCw2124A1 composites can be written as follows: Sefr V f + 2 tr=ac ScVf+2 exp(-kP)
iiiili!ii~iii~¸¸¸¸~!!I !ii i~ii~ii:::~~' '~'~:~~'~'~:::'~¸¸:¸¸¸''¸~'~¸~¸¸~¸' ¸ ~~~'~¸¸~"~~~~"~¸~¸~~'~:~¸'~:'~~~'¸~¸'¸.... ¸¸¸ ' ~~ ii~;iiiii~!;iiiii ~
....
:~!~:~i~i~i:~illi;!¸
Fig. 10. An extruded SiCw-2124Al composite showing the fir-tree cracking on the surface at the extrusion temperature of 530 °C.
CoSVr+ 2 = ao Sc Vr + 2 e x p ( - kP)
(8)
where o'c is the tensile strength of composites with full density and containing perfectly aligned whiskers of critical aspect ratio and full density and Co is the
231
S.H. Hong et al./ Materials Science and Engineering A206 (1996) 225 232 700.
600-
0.9 v
500.
5 c
400. 0.8.
/
_.e
•
J
/ s /
t,, ,s
J
s
300.
0.7
0.00
200
i
0.01
0.02
0
i
i
i
i
1
2
3
4
Porosity Fig. 11. The variation in the ratio of measured tensile strength cr to calculated tensile strength a v, compensated by the effective aspect ratio of whiskers, with porosity in SiC~-2124A1 composite: Z'. results from different extrusion conditions; Q, results from different vacuum hot pressing conditions from our previous results [7].
Effective Aspect Ratio Fig. 12. The variation in tensile strength of 20 vol.% SiC~ 2124AI composites with effective aspect ratio S~..
4. Conclusions
alignment compensation factor. The larger Co value, which means that the whiskers have a larger aspect ratio and are aligned more parallel to extrusion axis, results in a higher tensile strength in Eq. (8). To determine the value of k in Eq. (8), the ratio of measured tensile strength to calculated tensile strength was plotted with varying porosity as shown in Fig. 11. Assuming the exponential relationship between tensile strength and porosity as proposed by Squire [14], a k value of 13 was obtained in SiCw-2124A1 composites from the curve fitting of data points in Fig. 11. The measured k value is smaller than 15.5 found in our previous work [7]; however the measured value is still larger than the 7.7 9 for powder metallurgy iron [15,16] or 7 for sintered aluminal [17] and zirconia [18]. The larger k values in composites, which indicate that the tensile strength is more sensitive to the porosity, than those in other powder metallurgy materials are due to the higher stress concentration with reduced load transfer efficiency at the pores since they are mainly located at whisker-matrix interfaces as observed in our previous work [7]. The tensile strength of composites increases linearly with increasing effective aspect ratio, while it decreases exponentially with increasing amount of porosity as shown in Eq. (8). The measured tensile strengths of composites with varying extrusion ratio were plotted in Fig. 12 using the data in Fig. 2 as a function of the effective aspect ratio. Fig. 12 shows that there is a linear relationship between effective aspect ratio and tensile strength of composites and this result strongly supports the theoretical linear dependence predicted by Eq. (8).
The alignment of whiskers in SiCw-2124Al composites along the extrusion direction increased and the aspect ratio of whiskers decreased with increasing extrusion ratio from 10:1 to 25:1. The two microstructural factors, the alignment and aspect ratio of whiskers, influenced the tensile strength in opposite ways. The tensile strength of SiC w 2124A1 composites was highest at an extrusion ratio of 15:1. The aspect ratio of whiskers and relative density of composites increased with increasing extrusion temperature from 470 °C to 530 *C. A new microstructural parameter called the effective aspect ratio was proposed; this combined two important microstructural parameters, the alignment of whiskers and the aspect ratio of whiskers, based on the concept of load transfer in fibre-reinforced composites. A modified phenomenological equation describing the tensile strength of composites was proposed by introducing the effective aspect ratio.
References [1] B.F. Quigley, G.J. Abbaschian, R. Wunderlin and R. Mehrabian, Metall. Trans. A, 13 (1982) 93. [2] S. Abkowitz and P. Weihrauch, Adv. Mater. Proc., (7) (1989) 31. [3] J.C. Bittence, Adv. Mater. Proc., (7) (1987) 45. [4] K.U. Kainer, H.W. Bergman and B.L. Mordike, Powder Metall, 27 (1984) 30. [5] D,L. Erich, Int. J. Powder Metall., 23 (1987) 45. [6] F. Kloucek, Int. J. Powder Metall., 23 (1987) 701. [7] S.H. Hong and K.H. Chung, Mater. Sci. Eng., A194 (1995) t65. [8] S. Kalpakjian, Manufacturing Process L/Or Engineering Materials, Addison-Wesley, Reading, MA, 1984, p. 365.
232
S.H. Hong et al. / Materials Science and Engineering A206 (1996) 225-232
[9] J.H. ter Haar and J. Duszczyk, Mater. Sei. Eng. A, 135(1991) 65. [10] S. Suganuma, T. Okamoto and N. Suzuki, J. Mater. Sci. Lett., 6 (1987) 1347. [11] C.A. Standford-Beale and T.W. Clyne, Compos. Sci. Technol., 35 (1987) 121. [12] Standard test method for density and interconnected porosity of sintered metal powder structural parts, A S T M B328, ASTM, Philadelphia, PA, 1983.
[13] V.C. Nardone and K.M. Prewo, Ser. Metall., 20 (1986) 43. [14] A. Squire, Trans. A1ME, 171 (1942) 485. [15] A. Salak, V. Miskovic, E. Dudrovaad and E. Rundayova, Powder Metall. Int., 6 (1974) 128. [16] F.J. Esper, H.E. Exner and H. Metzler, Powder Metall., 18 (1975) 107. [17] E. Ryshkewitch, J. Am. Ceram. Soc., 36 (1953) 65. [18] W. Duckworth, J. Am. Ceram. Soc., 36(1953) 68.
ELSEVIER
Materials Science and Engineering A206 (1996) 225 232
A
Effects of hot extrusion parameters on the tensile properties and microstructures of SiCw-2124A1 composites Soon H. Hong a, Kyung H. Chung a, Chi H. Lee b "Department ~)/'Materials Science and Engineering, Korea Advanced Institute ~)[ Science and Technology, 373-1 Kusung-dong, Yusung-gu, Taejon, South Korea bDepartment of Metallurgical Engineering, Inha University, 253 Yonghyun-dong, Nam-gu, lnehon, South Korea Received 3 October 1994; in revised form 12 July 1995
Abstract
The effects of extrusion ratio and extrusion temperature on tensile strengths and microstructures of 20 volY,, SiCw-2124AI composites were investigated. The alignment of SiC whiskers along the extrusion direction in SiCw-2124AI composites was improved and the aspect ratio of SiC whiskers was decreased with increasing extrusion ratio from 10:1 to 25:1. The SiCw-2124AI composite exhibited the highest tensile strength at the extrusion ratio of 15:1. The aspect ratio of whiskers and the relative density of composite increased with increasing extrusion temperature from 470 °C to 530 °C. The tensile strength of SiCw-2124A1 composite increased with increasing extrusion temperature up to 530 °C. Based on the concept of the load transfer efficiency of misoriented SiC whiskers in the 2124A1 matrix, the two microstructural parameters of the alignment and aspect ratio of whiskers, which influenced on the tensile strength in an opposite way, were combined into a single parameter proposed as an effective aspect ratio. The highest tensile strength of SiCw-2124A1 composite at the extrusion ratio of 15:1 is explained by the largest effective aspect ratio due to the balance of the alignment and aspect ratio of SiC whiskers. A modified phenomenological equation describing the tensile strength of SiCw-2124A1 composites as a function of microstructural parameters was proposed by introducing the effective aspect ratio as a substitute for the average aspect ratio of SiC whiskers.
Keywords: Hot extrusion; Tensile properties; Microstructures; SiC-A1 composites
1. Introduction Metal matrix composites (MMCs) are attractive structural materials since their properties can be enhanced or tailored through the addition of selected reinforcements. In particular, S i C - A I composites have been focused on with special interest owing to their high specific strength and specific modulus at room or elevated temperatures [1-4]. The commercial fabrication processes of SiC whisker reinforced A1 matrix composites are generally classified into two major types, powder metallurgy process and casting process [5]. The powder metallurgy process is generally known to give better mechanical properties even though the fabrication cost is higher than the casting process [5,6]. The powder metallurgy process of M M C s consists of several fabrication steps and the process variables at each step are required to be optimized for good properties. The effects of vacuum hot 0921-5093/96/$15.00 © 1 9 9 6 - Elsevier Science S.A. All rights reserved SSDI 0921-5093(95)09996-4
pressing parameters on the tensile strength and microstructures of SiCw-2124A1 composites have already been discussed in our previous work [7]. In order to achieve the maximum composite strengthening effect by the addition of SiC whiskers, the whiskers need to be aligned parallel to one direction. Thus the consolidated billets are usually processed by primary deformation processing, such as extrusion, forging or rolling, at elevated temperature to align the SiC whiskers [8]. The hot extrusion process is the deformation process commonly used to align the whiskers in MMCs. In addition to the alignment of whiskers, the whiskers break as a result of the damage during hot extrusion. The damage of SiC whiskers reduces the aspect ratio of the whiskers and decreases the load transfer efficiency in composites [9-11]. These two microstructural variations during hot extrusion influence the mechanical properties of composites in opposite ways. The improved alignment of whiskers
226
S.H. Hong et al. / Materials Science and Engineering A206 (1996) 225 232
enhances the strength, while the reduced aspect ratio of whiskers decreases the strength. Therefore, it is very important to optimize the hot extrusion conditions which maximize the reinforcing effect of whiskers by balancing the two microstructural factors, i.e. alignment of whiskers and aspect ratio of whiskers. In this study, the effects of extrusion temperature and extrusion ratio on tensile strength and microstructure were investigated in 20 vol.% SiCw-2124A1 composites. The relationships between the microstructural parameters, i.e. aspect ratio of whiskers, alignment of whiskers and density of composites, and tensile strength of composites are discussed. A modified phenomenological equation is proposed to estimate the tensile strength from the measured microstructural parameters including the degree of whisker alignment after hot extrusion.
2. Experimental procedures The atomized 2124A1 powders with average diameter of 20 pm were used as a matrix, and r - s i c whiskers with average diameter of 1.5 pm and length of 4050 pm were added as the reinforcement. 80 vol.% of 2124A1 powders and 20 vol.% of r - s i c whiskers were wet mixed in ethyl alcohol of pH 9 with continuous stirring. The mixtures of 2124A1 powders and SiC whiskers were dried for 12 h at 70 °C and then consolidated into billets by vacuum hot pressing. The mixtures of powders with whiskers were placed in a die and consolidated in a hot pressing chamber. The hot pressing chamber was evacuated to 1 × 10 5 Torr during heating of the die to 570 °C and the mixtures of powders with whiskers were hot pressed at 90 MPa for 10 min to make cylindrical billets. In order to investigate the effects of hot extrusion parameters on the tensile strength and microstructure of SiCw-2124A1 composites, the cylindrical billets were hot extruded into bars with different extrusion ratios of 10:1, 15:1 and 25:1 at various temperatures of 470, 500 and 530 °C. The extruded bars were T6 heat treated by solution treatment at 493 °C for 3 h and followed by aging at 190 °C for 8 h. The tensile tests of SiCw-2124A1 composites were performed using an Instron 4206 system with an initial strain rate of 1.66 x 1 0 - 3 S-1. The densities of extruded composites were measured by an ASTM standard test procedure [12]. The aspect ratios of SiC whiskers in extruded composites were measured in the optical and scanning electron microscopy (SEM) micrographs from the overetched surface parallel to the extrusion axis. The degree of SiC whisker alignment along the extrusion axis was analysed by X-ray pole figures constructed from the (l 1l) diffraction peak of SiC whiskers.
3. Results and discussion Microstructures showing the distribution of SiC whiskers in SiCw-2124AI composites extruded with various extrusion ratio are presented in Fig. 1. The aspect ratio of SiC whiskers decreased with increasing extrusion ratio, since the average length of SiC whiskers decreased owing to the damage of whiskers at higher extrusion ratio. At the same time, the alignment of whiskers became more parallel to the extrusion axis with increasing extrusion ratio. The variation in tensile strength and relative density of SiCw-2124A1 composites with varying extrusion ratio is shown in Fig. 2. The maximum tensile strength of 505 MPa was obtained at an extrusion ratio of 15:1. The relative density of composites increased to 99.5% after hot extrusion compared with about 96% in the as-hot-pressed billet. The variation in relative density of composites with varying extrusion ratio was less than 0.2%. On the contrary, the average aspect ratio of whiskers decreased with increasing extrusion ratio from 10:1 to 25:1 as shown in Fig. 3. Fig. 2 shows that the tensile strength of composites extruded at 15:1 was about 40 MPa higher than that of
Extrusion Direction
Fig. 1. SEM micrographs of SiCw-2124AI composites showing the variation in the alignmentand aspect ratio of SiC whiskersin 2124A1 matrix: (a) extrusion ratio of 10:1; (b) extrusion ratio of 15:1; (c) extrusion ratio of 25:1.
S.H. Hong et al./ Materials Science and Engineering A206 (1996) 225 232
550 A
t~ a.
520.
227
100 O,..,,.,,,.,O
O
'99
Jr-
490. c
'9B
"~
'97
o~
e,-
Q 460.
0D
w e-
•~ •~
430.
400
, 10
strength density
>
96
, 20
95 30
0
Extrusion Ratio Fig. 2. The variation in tensile strength and relative density of SiC,~- 2124A1 composites with extrusion ratio.
(b)
composites extruded at 10:1. The higher relative density of composites extruded at 15:1 is considered as one reason for the higher tensile strength compared with the composite extruded at 10:1. However, the difference in relative density of 0.2% results in a difference in tensile strength of only 15 MPa from the following equation, which was proposed as a phenomenological equation relating the tensile strength to the porosity in SiCw2124A1 composites from our previous work [7]: o"
- exp(- 15.5P)
(1)
av where o- is the tensile strength of a porous powder metallurgy material, a v is the tensile strength of a powder metallurgy material with full density, and P is the porosity in a porous powder metallurgy material.
.=
.=¢ _= 5 o
e-
o
,m
4
!
1
10
20
30
Extrusion Ratio Fig. 3. The variation in average aspect ratio of whiskers in composites with extrusion ratio.
'
~
( ~ Exl~usino
Fig. 4. X-ray pole figures constructed from (111) peak intensity in SiC whiskers of SiC~ 2124A1 composites: (a) extrusion ratio of 10:1; (b) extrusion ratio of 15:1; (c) extrusion ratio of 25:1,
Furthermore, the average aspect ratio of whiskers decreased with increasing extrusion ratio as shown in Fig. 3. From the modified shear lag model [13], the average aspect ratio of reinforcements is known to be an important factor influencing the tensile strength of composite. The tensile strength of composites decreases with decreasing aspect ratio of whiskers. Therefore, the higher tensile strength in the composite extruded at 15:1 cannot be simply explained by the differences in relative density of composites and aspect ratio of whiskers. As the alignment of whiskers along the extrusion axis improved with increasing extrusion ratio, the alignment of SiC whiskers needs to be considered as another factor influencing the tensile strength of composites. The traces of (111) X-ray diffraction peak intensity from fl-SiC whiskers represent the variation in whisker alignment with varying extrusion ratio as shown in Fig. 4.
228
S.H. Hong et al. / Materials Science and Engineering A206 (1996) 225-232
Extrusion Axis
In order to analyse the degree of whisker alignment, the variation in (111) peak intensity from fl-SiC was examined using an X-ray pole figure technique and was plotted against the misorientation angle 0, as shown in Fig. 5. The (111) peak intensity from SiC whiskers in X-ray pole figure is proportional to the amount of whiskers aligned with the misorientation angle 0 from the extrusion axis. As the (111) peak intensity exponentially decreased with increasing misorientation angle, it is proposed that the density function F(O) of whiskers which represents the density of whiskers aligned with misorientation angle 0 to the extrusion axis, is given by the following equation: F(O) = A e x p ( - K 0 )
(2)
where 0 is the misorientation angle from extrusion axis and A and K are constants. The amounts dD of whiskers aligned between misorientation angles of 0 and 0 + dO can be expressed as a product of the area of shaded strip in Fig. 6, 2re sin 0 dO, and the density function F(O) of whiskers as follows: d D = F(O) x 2re sin 0 dO
(3)
As the total fraction of SiC whiskers in composites, which is calculated by integrating dD from 0 = 0 to 0 = to/2, was fixed as 20 vol.%, a boundary condition for Eq. (3) can be expressed as DlO:I = D15:1 = D25:1
(4)
where Dlo:l , DIS:l and D25:1 are the integrated values of the amount of whiskers in SiCw-2124A1 composites extruded with 10:1, 15:1 and 25:1 respectively. The constants A and K in the density function F(O) were obtained by curve fitting of the normalized (111) peak intensity with varying misorientation angle considering the boundary condition of Eq. (4). 1.0.
e-
dO
0.8.
Fig. 6. A schematic diagram of the three-dimensionalgeometry of SiC whisker alignment showing the division of the integration area. It is generally accepted that the load is transferred from the matrix to whiskers at the whisker-matrix interfaces parallel to the loading axis. When a composite is loaded, the whisker and matrix have different axial displacements owing to different moduli of the components. The difference in axial displacements induces shear strain parallel to the whisker axis at the whisker-matrix interface. The magnitude of the shear strain in a whisker having misorientation angle 0 is proportional to cos 0. Thus the load transferred to a whisker with aspect ratio S along the whisker axis will be proportional to S cos 0. At the same time, the load-sharing effect of the whisker along the stress axis needs to be multiplied again by cos 0. Therefore, the load transfer efficiency of whiskers with average aspect ratio S and aligned with misorientation angle 0 from the loading axis is assumed to be dependent on S cos 2 0, which is defined as an effective aspect ratio of whiskers. Then the differential effective aspect ratio, dSefr contributed by the whiskers aligned within the misorientation angle range from 0 to 0 + dO, as indicated by the shaded strip in Fig. 6, can be expressed as
_=
3 ~L
dSeff = (S cos 20)F(O)(2zr sin 0) dO
0.6-
By integrating dS~fr for the half-sphere from 0 = 0 to 0 = re/2 in Fig. 6, the effective aspect ratio Sefr contributed by all whiskers in composites is calculated as follows:
98"
0.4 q,.,
o o n-
(5)
0.2
Serf ~ ~or~/2 (S cos 20)F(O)(2rc sin 0) dO
25:1
0.0
0
i
|
i
!
10
20
30
40
50
M i s o r i e n t a t i o n A n g l e (Degree)
Fig. 5. The variationin the (l l 1) peak intensityof SiC whiskersfrom the X-ray pole figures with misorientation angle.
=
fo ~z/2 (S cos 20)A exp(--K0)(2re sin 0) dO
=A2r[ 1 - K exp(--Krc/2) 2 + K_exp(--Krc/2)] S 2(1 + K 2) + 2(9 + K 2) A
=CoS
(6)
229
S.H. Hong et al. / Materials Science and Engineering A206 (1996) 225-232 550-
where AtJ-.1 - K exp(-KTr/2)
<,
2(1 + K 2)
3 + _,Kexp(-Krr/2)-I __ -%
2(9 %" K 2)
J
99
is the alignment compensation factor related to the degree of whisker alignment and S is the average aspect ratio of whiskers. The alignment compensation factors, which represent the load transfer efficiency of whiskers related with the degree of alignment and average aspect ratio, were calculated from Eq. (6). The alignment compensation factor increased with increasing extrusion ratio from 10:1 to 15:1, but the increase in alignment compensation factor was negligible when the extrusion ratio increased from 15:1 to 25:1 as shown in Fig. 7. The effective aspect ratio of whiskers, which is the product of average aspect ratio and alignment compensation factor, was the largest in composites extruded at 15:1, while the average aspect ratio of whiskers was the largest in composites extruded at 10:1. The variation in tensile strength agrees well with the variation in effective aspect ratio with varying extrusion ratio. This result strongly indicates that the tensile strength of a composite is directly dependent on the effective aspect ratio of whiskers rather than average aspect ratio of whiskers. The relationships between tensile strength and microstructural factors in SIC,,, 2124A1 composites are explained as follows. The whisker alignment along the extrusion axis was improved and the aspect ratio of whiskers decreased owing to the damage of whiskers during the hot extrusion process. These changes in two microstructural factors, alignment of whiskers and aspect ratio of whiskers, influenced the tensile strength of
0.8 O k.
o
I.,I.
O
0.7
, m
m
ee
c O
u
&
m e-
0.6
w
<
E
O ¢.) o5
iii
E
c ot
'~'
0.4 0
100
•~ ' D - -
Alignment Compensation Factor
•" - " O - -
Effective Aspect Ratio ,
,
10
20
2
30
Extrusion Ratio Fig, 7. The variation in alignment compensation actor Co and effective aspect ratio of whiskers in SiCw 2124AI composites with extrusion ratio.
a.
500 J~
98
"~ C
c
2
_e
97 450'
G)
._
q)
¢:
ClE density
400
460
,
48o
ioo
5'20
96
95
540
Extrusion Temperature (°C) Fig. 8. The variation in tensile strength and relative density of SiC~ 2124Al composites with extrusion temperature.
composites in opposite ways. The improved alignment of whiskers represented by the alignment compensation factor enhances the tensile strength, while the reduced aspect ratio of whiskers decreases the tensile strength. These effects of two microstructural parameters are combined into one parameter, the effective aspect ratio. Consequently, with increasing extrusion ratio to 15:1, the tensile strength of composites increased as a result of the increase in both the effective aspect ratio of the whiskers and the relative density of the composite. However, the damage to the whiskers increased at an extrusion ratio of 25:1 and this resulted in a decrease in the effect aspect ratio of whiskers. Therefore, the tensile strength of composites decreased at an extrusion ratio of 25:1 owing to the rapid decrease in the effective aspect ratio of whiskers, although the relative density of composites increased slightly with increasing extrusion ratio. The tensile strength of composites extruded with an extrusion ratio of 15:1 rapidly increased from 430 MPa to 520 MPa with increasing extrusion temperature from 470 to 530 °C as shown in Fig. 8. The relative density of the composite significantly increased from 98.5% at an extrusion temperature of 470 °C to 99.6% at an extrusion temperature of 530 °C owing to the enhanced densification caused by the softening of 2124A1 matrix at higher extrusion temperatures. To analyse the degree of whisker alignment with varying extrusion temperature, the average aspect ratio and effective aspect ratio were measured and are plotted in Fig. 9. Both the average aspect ratio and the effective aspect ratio increased with increasing extrusion temperature, indicating that the damage to whiskers decreased at higher extrusion temperatures.
S.H. Hong et al. / Materials Science and Engineering A206 (1996) 225-232
230
J¢
4,
~.
2
0 460
~ ~
, 480
MeasuredAspectRatio EffectiveAspectRatio
l 500
Extrusion Temperature
, 520
540
ment was sensitively dependent on the extrusion ratio but was not strongly influenced by the extrusion temperature. On the contrary, the aspect ratio of whiskers was sensitively dependent on both the extrusion ratio and the extrusion temperature. The average aspect ratio of whiskers increased with increasing extrusion temperature and with decreasing extrusion ratio. The relative density was strongly influenced by the extrusion temperature but was not sensitively dependent on the extrusion ratio. In our prevous work [7], a phenomenological equation describing the quantitative relationship between tensile strength and microstructural parameters, i.e. aspect ratio of whiskers and relative density of SiCw2124A1 composite, was proposed as follows: SVf+2 = ~ro SoVf+ 2 e x p ( - k P )
(°C)
Fig. 9. The variation in average aspect ratio and effective aspect ratio of whiskers in SiCw 2124A1 composites with extrusion temperature.
The increase in tensile strength of SiCw-2124A1 composite with increasing extrusion temperature is considered to result from the increase in both the relative density of the composite and the aspect ratio of the whiskers. However, if the extrusion temperature was increased to 530 °C, the surface temperature became so high as to lead to a surface cracking, known as fir-tree cracking (Fig. 10), on the extruded composite [8]. Although the relative density of the composite and aspect ratio of the whiskers increased with increasing extrusion temperature, the upper limit of the extrusion temperature was restricted to below 530 °C owing to the surface cracking of composite. The SiC whiskers were damaged and aligned more parallel to the extrusion axis during hot extrusion, and thus the degree of alignment and the aspect ratio were influenced by the extrusion ratio. The degree of align-
(7)
where o is the tensile strength of a composite with arbitrary aspect ratio and arbitrary relative density, o-c is the tensile strength of composites with critical aspect ratio and full density, S and Sc are the arbitrary average aspect ratio and critical aspect ratio respectively of whiskers, Vf is the volume fraction of whiskers, P(%) is the porosity of the composite and k is a constant. The modified shear lag theory, for MMCs with a small aspect ratio of the reinforcements, was introduced in deriving Eq. (7). The critical aspect ratio is calculated from O'fu/2"t'i, where aru is tensile strength of the reinforcement and zi is the shear yield strength; o-r~for SiC is 7 GPa and ~i for 2124A1 is 275 MPa. Therefore the critical aspect ratio for the SiCw-2124A1 composite system is calculated to be about 12.7 and the experimentally observed aspect ratio of whiskers was less than 6, much lower than critical aspect ratio, so the modified shear lag model was introduced for this study and the critical aspect ratio was considered as the reference state. Since the alignment of whiskers is strongly influenced by the extrusion conditions, Eq. (7) needs to be modified to include the effect of whisker alignment along the extrusion axis. Considering the effect of whisker alignment, the load transfer efficiency is changed and the tensile strength of the composite is expressed by substituting the effective aspect ratio Sefr for the average aspect ratio S of whiskers in Eq. (7). A new modified equation for the tensile strength of SiCw2124A1 composites can be written as follows: Sefr V f + 2 tr=ac ScVf+2 exp(-kP)
iiiili!ii~iii~¸¸¸¸~!!I !ii i~ii~ii:::~~' '~'~:~~'~'~:::'~¸¸:¸¸¸''¸~'~¸~¸¸~¸' ¸ ~~~'~¸¸~"~~~~"~¸~¸~~'~:~¸'~:'~~~'¸~¸'¸.... ¸¸¸ ' ~~ ii~;iiiii~!;iiiii ~
....
:~!~:~i~i~i:~illi;!¸
Fig. 10. An extruded SiCw-2124Al composite showing the fir-tree cracking on the surface at the extrusion temperature of 530 °C.
CoSVr+ 2 = ao Sc Vr + 2 e x p ( - kP)
(8)
where o'c is the tensile strength of composites with full density and containing perfectly aligned whiskers of critical aspect ratio and full density and Co is the
231
S.H. Hong et al./ Materials Science and Engineering A206 (1996) 225 232 700.
600-
0.9 v
500.
5 c
400. 0.8.
/
_.e
•
J
/ s /
t,, ,s
J
s
300.
0.7
0.00
200
i
0.01
0.02
0
i
i
i
i
1
2
3
4
Porosity Fig. 11. The variation in the ratio of measured tensile strength cr to calculated tensile strength a v, compensated by the effective aspect ratio of whiskers, with porosity in SiC~-2124A1 composite: Z'. results from different extrusion conditions; Q, results from different vacuum hot pressing conditions from our previous results [7].
Effective Aspect Ratio Fig. 12. The variation in tensile strength of 20 vol.% SiC~ 2124AI composites with effective aspect ratio S~..
4. Conclusions
alignment compensation factor. The larger Co value, which means that the whiskers have a larger aspect ratio and are aligned more parallel to extrusion axis, results in a higher tensile strength in Eq. (8). To determine the value of k in Eq. (8), the ratio of measured tensile strength to calculated tensile strength was plotted with varying porosity as shown in Fig. 11. Assuming the exponential relationship between tensile strength and porosity as proposed by Squire [14], a k value of 13 was obtained in SiCw-2124A1 composites from the curve fitting of data points in Fig. 11. The measured k value is smaller than 15.5 found in our previous work [7]; however the measured value is still larger than the 7.7 9 for powder metallurgy iron [15,16] or 7 for sintered aluminal [17] and zirconia [18]. The larger k values in composites, which indicate that the tensile strength is more sensitive to the porosity, than those in other powder metallurgy materials are due to the higher stress concentration with reduced load transfer efficiency at the pores since they are mainly located at whisker-matrix interfaces as observed in our previous work [7]. The tensile strength of composites increases linearly with increasing effective aspect ratio, while it decreases exponentially with increasing amount of porosity as shown in Eq. (8). The measured tensile strengths of composites with varying extrusion ratio were plotted in Fig. 12 using the data in Fig. 2 as a function of the effective aspect ratio. Fig. 12 shows that there is a linear relationship between effective aspect ratio and tensile strength of composites and this result strongly supports the theoretical linear dependence predicted by Eq. (8).
The alignment of whiskers in SiCw-2124Al composites along the extrusion direction increased and the aspect ratio of whiskers decreased with increasing extrusion ratio from 10:1 to 25:1. The two microstructural factors, the alignment and aspect ratio of whiskers, influenced the tensile strength in opposite ways. The tensile strength of SiC w 2124A1 composites was highest at an extrusion ratio of 15:1. The aspect ratio of whiskers and relative density of composites increased with increasing extrusion temperature from 470 °C to 530 *C. A new microstructural parameter called the effective aspect ratio was proposed; this combined two important microstructural parameters, the alignment of whiskers and the aspect ratio of whiskers, based on the concept of load transfer in fibre-reinforced composites. A modified phenomenological equation describing the tensile strength of composites was proposed by introducing the effective aspect ratio.
References [1] B.F. Quigley, G.J. Abbaschian, R. Wunderlin and R. Mehrabian, Metall. Trans. A, 13 (1982) 93. [2] S. Abkowitz and P. Weihrauch, Adv. Mater. Proc., (7) (1989) 31. [3] J.C. Bittence, Adv. Mater. Proc., (7) (1987) 45. [4] K.U. Kainer, H.W. Bergman and B.L. Mordike, Powder Metall, 27 (1984) 30. [5] D,L. Erich, Int. J. Powder Metall., 23 (1987) 45. [6] F. Kloucek, Int. J. Powder Metall., 23 (1987) 701. [7] S.H. Hong and K.H. Chung, Mater. Sci. Eng., A194 (1995) t65. [8] S. Kalpakjian, Manufacturing Process L/Or Engineering Materials, Addison-Wesley, Reading, MA, 1984, p. 365.
232
S.H. Hong et al. / Materials Science and Engineering A206 (1996) 225-232
[9] J.H. ter Haar and J. Duszczyk, Mater. Sei. Eng. A, 135(1991) 65. [10] S. Suganuma, T. Okamoto and N. Suzuki, J. Mater. Sci. Lett., 6 (1987) 1347. [11] C.A. Standford-Beale and T.W. Clyne, Compos. Sci. Technol., 35 (1987) 121. [12] Standard test method for density and interconnected porosity of sintered metal powder structural parts, A S T M B328, ASTM, Philadelphia, PA, 1983.
[13] V.C. Nardone and K.M. Prewo, Ser. Metall., 20 (1986) 43. [14] A. Squire, Trans. A1ME, 171 (1942) 485. [15] A. Salak, V. Miskovic, E. Dudrovaad and E. Rundayova, Powder Metall. Int., 6 (1974) 128. [16] F.J. Esper, H.E. Exner and H. Metzler, Powder Metall., 18 (1975) 107. [17] E. Ryshkewitch, J. Am. Ceram. Soc., 36 (1953) 65. [18] W. Duckworth, J. Am. Ceram. Soc., 36(1953) 68.