Variation of the Thermal Stress in the Al18B4O33W/Al Composite during Low Temperature Cycling

Variation of the Thermal Stress in the Al

B

O

/Al Composite

during Low Temperature Cycling

Chuanhai Jiang

_{and Bo Hong}

School of Materials Science and Engineering, Shanghai Jiao Tong University, Shanghai 200030, P. R. China

With the method for measurement of triaxial stress in material by the X-ray diffraction, the variation of the thermal stress of matrix in a 25 vol%Al18B4O33W/6061Al composite during low temperature cycling was investigated. It was found that the matrix of composite undergoes a

process of tensile mismatch plastic strain when cooling, while it undergoes a process of unloading for mismatch stress when warming. After low temperature cycling, the thermal residual stress of composite was decreased obviously. If the secondary low temperature cycling was carried out, the thermal residual stress can be decreased again when the temperature of secondary cycling is lower than that of the first cycling.

(Received November 29, 2004; Accepted March 4, 2005; Published May 15, 2005)

Keywords: composite, triaxial thermal stress, X-ray diffraction, low temperature cycling

1. Introduction

The composites of aluminum borate whiskers and alumi-num (Al18B4O33W/Al) can be widely applied in many

industrial fields because they have high specific strength, high specific modulus, low thermal coefficient of expansion and so on. However, when the composite is cooled down from high temperature in fabrication, the thermal residual stress is unavoidable because of the significant difference in coefficients of thermal expansion between the reinforcement and matrix-alloy.1,2)It was verified that, the thermal residual stress of matrix can affects on the properties of composite, such as mechanical behavior, dimensional stability and so on. The thermal residual stresses of composite induced by thermal mismatch between reinforcement and matrix, espe-cially in those reinforced with discontinuous reinforcements, are in nature of three dimensional (triaxial) on the surface of the composite within a penetrated thickness of X-ray diffrac-tion.3,4) _{By using the conventional method of X-ray stress}

measurement, the plane stress on the surface of material can be easily measured, but it does not adapt to measure the triaxial thermal residual stress on the surface of compo-site. The methods of measuring triaxial stress with X-ray dif-fraction had been reported in references,3–5)but those meth-ods required a tedious measuring process. So it is necessary to simplify the method of measuring triaxial thermal residual stress of composite. In addition, the thermal residual stress in the matrix of composite can be modified by the treatment of low temperature cycling,6,7) _{but there have been only a}

limited number of investigations on the principle of modifi-cation for the thermal residual stress of the composite.

For these reasons, the simplified method for measuring of triaxial thermal stress in composite by X-ray diffraction was introduced in this paper. The variation of thermal mismatch stress of matrix in a 25 vol%Al18B4O33W/6061Al composite

during low temperature cycling was also dynamically investigated. These investigations are believed to be helpful to understand the principle of modification for the thermal residual stress of the composite by the low temperature cycling.

2. Experimental

The material used in the experiment was an Al18B4O33

-whisker reinforced 6061Al-alloy composite, which was produced by the squeeze-cast procedure. The volume fraction (vol%) of whisker is 25%, and the whisker size are 0.2–1mm

in diameter and 10–20mmin length. The crystal structure of Al18B4O33-whisker is the orthorhombic lattice, and the

interface between whisker and Al-matrix of composite is in the good condition.

The specimens in disc shape were machined, of which the dimensions and geometry relation for X-ray stress measure-ments are shown as Fig. 1. In this figure, theZ-axis is along the direction of squeeze cast. For the squeeze-cast composite, the distribution of whisker orientation is in the random state on the XOY plane, so the X-direction is full same as

Y-direction in distribution of whisker orientation. All of the specimens were chemically polished in a 20%NaOH solution for 10 min at 70_{C. Typically, more than about 100mmwas}

removed from the surface of specimen. With the cooling and heating equipment, the low temperature cycling of25_C!

78_{C!25C and 25C! 196C!25C for the}

composite specimens were carried out.

By using the X-ray stress analyzer and the computational software for data processing in stress measurement, the thermal stresses of matrix in the composites were measured during low temperature cycling. The parameters of stress

Z (σ33)

2 O

Φ

Ψ L (εΦΨ)

Y(σ22)

10 X (σ11)

Fig. 1 Dimensions (mm) of the 25 vol%Al18B4O33W/6061Al composite

specimen and the geometry relation in the X-ray stress measurement.

*_{Corresponding author, E-mail: chjiang@sjtu.edu.cn}

analyzer are: tube voltage 28 kV, tube current 8 mA, Cr-K

radiation, diffraction plane Al(222), radiated area 3mm

3mm, time constant 2 s, step speed 3_{/min, angle 0–45,}

angle 0 _{and 90, using the method of half-value-breadth}

center to determine the peak location,8,9)_{which was carried}

out by the software of the stress analyzer.

In Fig. 1, the elastic strain" in the direction ofOLcan

be written as,3–5)

"¼ ðS2=2Þð11cos2þ12sin 2

þ22sin233Þsin2þ ðS2=2Þð13cos

þ23sin Þsin 2þ ðS2=2Þ33

þS1ð11þ22þ33Þ

ð1Þ

S1¼ =E; S2=2¼ ð1þÞ=E ð2Þ

where,is the Poission ratio of matrix,Ethe elastic modulus of matrix,ij (i;j¼1, 2, 3) are various vectors of stress in

matrix of composite for the coordinate system provided in Fig. 1.

On the other hand, according to Bragg equation

2dsin¼, the elastic strain " in the direction of OL

can be also obtained as,

"¼

dd0

d0

¼ 1

2

180cot0 ð220Þ ð3Þ

where20is the diffraction angle of matrix-alloy in the state

of stress-free, it can be measured from the 6061Al-powder at 25C,78C and196C respectively.

Parameterb1 can be defined as,4,10)

b1¼ 1

2ð2þþ2Þ ð4Þ

where, 2þ and 2 are the two diffraction angles of

measured at the sameplane but in two opposite direction of equivalenttilts.

According to eqs. (1), (2), (3) and (4), consequently,

@b1

@sin2¼ 1

Kð11cos

2_þ

12sin 2

þ22sin233Þ ð5Þ

K¼ E

2ð1þÞ

180cot0 ð6Þ

whereKis the X-ray stress constant of matrix in composite. With the measured value ofb1at¼0, utilizing eq. (5),

follow equation can be obtained,

1133¼K

@b1ð¼0_Þ

@sin2 ð7Þ

Similarly, with theb1at¼90, utilizing eq. (5), follow

equation be also obtained,

2233¼K

@b1ð¼0_Þ

@sin2 ð8Þ

Besides, the expression of elastic strain in the direction of

¼0_{, according to eq. (1), can be simplified as,}

"33 ¼

S2

2 33þS1ð11þ22þ33Þ ð9Þ

Because the "ð¼0_Þ of eq. (3) equate to the of eq. (9),

combining eqs. (2), (3), (6) and (9), follow equation can be obtained,

33þ

S1

S2=2

ð11þ22þ33Þ ¼K

2ð¼0_Þ2₀

ð10Þ

where 2ð¼0_Þ is the diffraction angle of the specimen

measured at¼0_.

If the diffraction angle of2 equates to2, eq. (4)

can be simplified as,

b1¼2 ð11Þ

By using eqs. (2), (7), (8), (10) and (11), the three normal components of stress in matrix of composite can be obtained,

11¼K

S0 2ð¼0_Þ2₀

ðS001Þ@2ð¼0Þ

@sin2 S

00@2ð¼90_Þ

@sin2

ð12Þ

22¼K

S0 2ð¼0_Þ2₀

S00@2ð¼0Þ @sin2 ðS

00_1Þ@2ð¼90_Þ

@sin2

ð13Þ

33¼K

S0 2ð¼0_Þ2₀

S00@2ð¼0Þ @sin2 S

00@2ð¼90_Þ

@sin2

ð14Þ

s0¼ ð1þÞ=ð12Þ; s00¼ =ð12Þ ð15Þ

For the specimen of this paper, the direction ofX-axis is equivalent to Y-axis, that is 2ð¼0_Þ¼2_ð¼90Þ. The

eqs. (12), (13) and (14) can be simplified as,

11 ¼22

¼K S0 2ð¼0_Þ2₀

ð2S001Þ @2

@sin2

ð16Þ

33 ¼K S0 2ð¼0_Þ2₀

2S00 @2 @sin2

ð17Þ

If the angles were only selected as 0 _{and 45, the}

eqs. (16) and (17) be also simplified as,

11¼22¼K

S0 2ð¼0_Þ2₀

ð4S002Þ 2ð¼0_Þ2_ð¼45Þ ð18Þ

33¼K

S0 2ð¼0_Þ2₀

4S00 2ð¼0_Þ2_ð¼45Þ

ð19Þ

Therefore, by using this method to measure the triaxial-stress of material is more simple and convenient.

3. Results and Discussion

Figure 2 shows the typical X-ray diffraction profile of Al-matrix in the 25 vol%Al18B4O33W/6061Al composite.

Be-cause the K1 profile overlapped with the K2 profile, the

K1 profile can be obtained in Fig. 2(b), which is useful to

determine the precise peak position of diffraction angle by the method of half-value-breadth center. In measuring the triaxial thermal stress of matrix in the composite, the diffraction angle 20 of 6061Al-powder should be

deter-mined which is related to the testing temperature of powder. With the measured values of2and20, the triaxial thermal

stress of matrix in the composite can be obtained by the eqs. (18) and (19).

Figure 3 shows the variation of thermal stresses of matrix in the 25 vol%Al18B4O33W/6061Al composite during the

low temperature cycling of 25_{C! 78C!25C and}

25_{C! 196C!25C, also shows the actual error range}

of the measured stress. The result showed that, the triaxial thermal stress really existed on the surface of composite within the penetrated thickness of X-ray diffraction. Among three of the thermal stress components, 33 is the lowest

stress tensor, which is mainly due to the preferable orientation of whisker in theXOYplane. During manufactur-ing of the composite by the squeeze-cast method, because the compressive stress along theZ-direction was applied, many of whiskers were rotated toward to the XOY plane, so the orientation of those whiskers must preferred to the XOY

plane in the composite as squeeze-cast. Under the consid-eration of the distribution of whisker orientation above, the relation among three stress tensors will be11¼22> 33.

With the varying of the temperature during low temper-ature cycling, the triaxial stresses changed at same time. It can also be found from this figure that the increased extent of thermal stress in the matrix is not evident during the cooling process (25_{C! 78C and 25C! 196C) of low}

temperature cycling, although the thermal stress keep a slight increasing tendency. During the warming process (78_{C!25Cand196C!25C) of the low}

temper-ature cycling, the decreased extent of thermal stress is very evident. Namely, the curve of stress with temperature during warming process deviate from that during cooling process. After the low temperature cycling of 25_{C! 78C!}

25_{C and 25C! 196C!25C, the thermal residual}

stress of matrix in the composite decreased obviously. In manufacturing process of the 25 vol%Al18B4O33W/

6061Al composite, the cast temperature of the 6061Al-liquid is 800_{C, and the solidification temperature of 6061Al-liquid}

is about 600_{C. Due to the larger thermal expansion}

coefficient of matrix, the shrinkage of matrix far exceed that of whisker during the cooling process from the manufactur-ing temperature of composites to room temperature, which leads to a fast increase of the tensile thermal mismatch in matrix of composite. The theoretical analysis results showed that11,12)the thermal mismatch stress of matrix had already reached the yield strength of matrix in the area near the interface between two phases after the composite cooled

154o ₁₅₅o ₁₅₆o ₁₅₇o ₁₅₈o ₁₅₉o ₁₆₀o

0 400 800 1200 1600 2000

2θ

Intensity

(a)

0 300 600 900 1200 1500

2θ

Intensity 0.5 Imax Imax

Regression Gauss-curve

154o ₁₅₅o ₁₅₆o ₁₅₇o ₁₅₈o ₁₅₉o ₁₆₀o

(b)

Fig. 2 Typical X-ray diffraction profile of matrix in the 25 vol% Al18B4O33W/6061Al composite: (a) primary profile, (b) cut off

back-ground and stripped off theK2profile.

-200 -150 -100 -50 0 50

22 11 σ

σ =

33

σ

0 30 60 90 120 150

Stress ,

σ/MPa

Temperature , T/°C

(a)

-200 -150 -100 -50 0 50

0 30 60 90 120 150

22 11 σ

σ =

33

σ

Stress ,

σ/MPa

Temperature , T/°C

(b)

Fig. 3 Variation of thermal stresses in matrix of the 25 vol%Al18B4O33W/

down from manufacture temperature to room temperature, and the matrix in local areas had already encountered the tensile mismatch plastic strain and work-hardening.

When the composite cooled down from the room temper-ature to low tempertemper-ature (25_{C! 78C and 25C!}

196_{C), the mismatch degree between matrix and whisker}

went on increasing, the local area in matrix near the interface went on encountering the tensile mismatch plastic strain and work-hardening. Because of the mismatch plastic strain of matrix, the increasing extent of thermal stress in matrix of composite is not evident during the cooling process. More-over, when the composite warming up from the low temper-ature to room temperature (78_{C!25C and}

196C!25C), both of matrix and whisker in composite encountered the expansion process at same time. The expansion extent of matrix is larger than that of whisker during warming up, so the thermal mismatch stress of matrix encountered an unloading process, and lead to a obvious decrease of the thermal residual stress in matrix. By the analysis above, it can be summarized that the cooling process of low temperature cycling can lead to the pre-tensile mismatch plastic strain of matrix, while the whisker is always in the elastic state. When the composites go back from the low temperature to room temperature, the mismatch degree between matrix and whisker will be relaxed, and lead to a decrease of the thermal residual stress of matrix. The lower the temperature during cooling process, the larger the pre-tensile mismatch plastic strain occurred in matrix near the interface between two phases, and the lower the thermal residual stress of matrix in the composite at room temper-ature is.

Figure 4 shows the variation of thermal stresses in matrix of the 25 vol%Al18B4O33W/6061Al composite during the

secondary low temperature cycling, also shows the actual error range of the measured stress. It can be seen from Fig. 5(a) that when the composite undergoes the secondary low temperature cycling 25_{C! 78C!25Cafter the first}

cycling 25_{C! 196C!25C, the curve of stress with}

temperature in warming process coincide with that in cooling process during secondary cycling, and the thermal stress cannot be evidently changed by the secondary cycling. After the first low temperature cycling, the tensile thermal mismatch stress between whisker and matrix in the compo-site had been decreased. Therefore, if the low temperature of secondary cycling is not lower than that of first cycling, the tensile mismatch strain of matrix will be not occurred during the cooling process of secondary cycling. In such a case, the thermal residual stress of matrix cannot be evidently changed after the secondary cycling.

It can be also found from Fig. 5(b) that when the composite undergoes the secondary temperature cycling 25_C!

196_{C!25C after the first cycling25C! 78C!}

25_{C, the curve of stress with temperature in warming}

process deviate from that in cooling process during secon-dary cycling, and the thermal stress can be decreased again by the secondary cycling. If the low temperature of secondary cycling is lower than that of the first, the tensile mismatch strain of matrix will occur again during cooling process of secondary cycling. In such a case, the thermal residual stress of matrix would be decreased again after the secondary

cycling. Based on the experimental results above, it can be concluded that the key-factor of affecting on the thermal residual stress of composite is the low temperature other than the times of cycling. Only when the low temperature of secondary cycling is lower than that of first cycling, the thermal residual stress of composite can be reduced again.

The thermal residual stress of matrix can evidently affect on the tensile behavior of the composite. For the tensile residual stress of matrix, it would enlarge the tensile strain of matrix and decrease the tensile strength during tensile test of composite specimen. Based on the result of investigation above, the lower temperature of cycling, the lower thermal residual stress of matrix at room temperature, and the higher tensile strength of the composite naturally. In our future study, the influence of low temperature cycling on the properties of the composite will be investigated.

4. Conclusions

The triaxial-stresses were directly expressed as algebraic equations in this paper, which is more simple and convenient for measuring the triaxial thermal stress of the 25 vol% Al18B4O33W/6061Al composite. It was verified that the

thermal residual stress could be modified by the treatment of low temperature cycling. During the low temperature

-200 -150 -100 -50 0 50

0 30 60 90 120 150

22 11 σ

σ =

33

σ

Stress ,

σ

/MPa

Temperature , T/°C

(a)

-200 -150 -100 -50 0 50

0 30 60 90 120 150

22 11 σ

σ =

33

σ

Stress ,

σ

/MPa

Temperature , T/°C

(b)

Fig. 4 Variation of thermal stresses in matrix of the 25 vol%Al18B4O33W/

cycling, the matrix of composite undergoes a process of tensile mismatch plastic strain when cooling, while it undergoes a process of unloading for mismatch stress when warming. Therefore the curve of stress with temperature in warming process deviates from that in cooling process. The lower temperature of cycling, the lower thermal residual stress of composite at room temperature is. If the secondary low temperature cycling was carried out for the composite, the thermal residual stress can be decreased again when the low temperature of secondary cycling is lower than that of the fist cycling. So the key factor of affecting on the thermal residual stress of composite is the low temperature other than the times of cycling.

Acknowledgments

Supported by the Major Fundamental Research Project of Shanghai Science and Technology Committee under Grant No. 04DZ14002.

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