Microstructural changes in ZE41 composite estimated by acoustic measurements

Journal of Alloys and Compounds 355 (2003) 113–119

L

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Microstructural changes in ZE41 composite estimated by acoustic measurements ´ ˇ a , F. Chmelık ´ a , W. Riehemann b Z. Trojanova´ a , *, P. Lukac a

b

Department of Metal Physics, Charles University, Ke Karlovu 5, Prague 2 CZ-121 16, Czech Republic Institute of Materials Engineering and Technology, Technical University Clausthal, Agricolastrasse 6, Clausthal-Zellerfeld D-38678, Germany

Abstract The strain dependencies of the logarithmic decrement and stress relaxation have been measured for magnesium alloy ZE41 (4%Zn–1%RE–balance Mg) reinforced by short Saffil fibres. Prior to the measurements, the samples were subjected to thermal cycling with increasing upper temperatures. The response of the composite on thermal loading has been characterised by measurements of acoustic emission (AE) and dilatation during thermal cycling. The AE activity during sample cooling was found to intensify with increasing upper temperature of the cycle, which indicates that the internal thermal stresses exceed the matrix yield stress in certain temperature intervals. The thermal stresses may relax by collective dislocation generation and motion. Thus, the threshold values of the upper cycle temperature for matrix yielding and thereby pronounced AE activity have been found. The combination of in situ dilatation and in situ AE measurements helped to clarify the contribution of various deformation mechanisms to the dimensional changes during thermal cycling of ZE41 composite.  2003 Elsevier Science B.V. All rights reserved. Keywords: Metals; Casting; Dislocations; Acoustic properties; Ultrasonics

1. Introduction When the coefficients of thermal expansion (CTE) of two components of a composite are different, thermal stresses are generated upon temperature changes in both matrix and reinforcement. After cooling the composite, the dislocation density in the matrix increases as observed using etch pits [1] or transmission electron microscopy [2,3]. An increase in the dislocation density near reinforcement has been calculated as [2,4] B f Da DT 1 r 5 ]]] ] b (1 2 f ) t

(1)

where f is the volume fraction of the reinforcing phase, t its minimum size, b the magnitude of the Burgers vector of dislocations, B a geometrical constant, Da the absolute value of the CTE difference between the matrix and the reinforcement, DT the temperature difference. The dislocations produced by thermal cycling or cooling from manufacture temperature influence many mechanical and physical properties of materials. In this paper we present

indirect experimental evidence of dislocation emission in composite material subjected to thermal loading. Following nondestructive methods were used:

1.1. Mechanical damping If a material containing dislocations is submitted to a harmonic applied stress s 5 s0 sin v t with an angular frequency v 5 2p f, one can define the mechanical loss factor h as 1 DWdiss h 5 ] ? ]] 2p Wmax

(2)

where DWdiss is the mechanical energy dissipated in one cycle of the applied stress, and Wmax is the maximum mechanical energy stored on it. In the case of an anelastic dislocation strain DWdiss 5 r´d ds

(3)

The maximum stored energy can be well approximated by the maximum elastic stored energy s0

* Corresponding author. Tel.: 1420-22191-1357; fax: 1420-221911490. ´ E-mail address: [email protected] (Z. Trojanova).

Wmax 5

0925-8388 / 03 / $ – see front matter  2003 Elsevier Science B.V. All rights reserved. doi:10.1016 / S0925-8388(03)00242-1

Es d´ 0

el

1 5 ] Jel s 20 2

(4)

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where Jel is the elastic compliance related to the shear modulus G 21 5 Jel . The mechanical loss factor is 1 h 5 ]]2 ? r´d ds p Jel s 0

(5)

1.2. Stress relaxation In stress relaxation (SR) tests strain is constant and then the stress s (t) as a function of time t is recorded. Assuming a relaxation process that depends on a single relaxation time, the stress is given by [5]

s (t) 5 ´0 [ER 1 DE exp 2 (t /t )]

(6)

where ER is the unrelaxed modulus. At relatively high homologous temperatures, damping of most materials increases continuously to high values. This phenomenon known as high temperature background is highly structural sensitive. Schoeck et al. [6] considered that the high temperature background is produced by a broad spectrum of diffusion controlled relaxation (involving dislocations moving in a viscous manner). They derived the relationship between the quality factor Q 21 ¯ h and temperature as A Q 21 5 ]]]]]]n f v exp sDH0 /kTdg

(7)

where n and DH0 are constants, A is related to dislocation structure, DH0 is the true activation enthalpy of the controlling mechanism. In the experiments, the apparent activation enthalpy, nDH0 , is measured from the temperature dependence of the internal friction. The value of the apparent activation enthalpy is meaningless unless n is determined by the frequency dependence of the internal friction. DH0 was found to be close to the activation enthalpy for self-diffusion DHv [7].

1.3. Acoustic emission Acoustic emission (AE) stems from transient elastic waves generated within a material due to sudden and irreversible structural changes. AE is a suitable procedure for monitoring microstructural changes during thermal cycling of some Mg-based composites [8]. Dislocation motion and microstructural damage are generally recognized to produce significant AE [9]. The additional use of dilatometry provides an opportunity to measure directly the inherent thermal expansion occurring within a composite during temperature cycling as manifest in the form of shape changes during testing. To date, there are only limited results demonstrating the use of AE in monitoring the structural response and matrix deformation of Mgbased composites during thermal loading [8,10].

2. Experimental The matrix used in this investigation was a ZE41 alloy (4 wt.% Zn, 1 wt.% rare earths, balance Mg). The alloy was reinforced with 20 vol.% of Saffil  (d-Al 2 O 3 ) short fibres using squeeze casting procedure. Saffil short fibre preforms had planar isotropic fibre distributions. Test specimens for the damping measurements were machined as bending beams (88 mm long, thickness of 3 mm) with the reinforcement planes parallel to the longest specimen axes. The damping measurements were performed in vacuum (about 30 Pa) at room temperature. Damping was measured as the logarithmic decrement d of the free decay of the vibrating beam. The signal amplitude is proportional to the strain amplitude ´.

s0 2 s (t) Fstd 2 Fst 1d DE(t) DF(t) ]]] 5 ]] 5 ]] 5 ]]]] s0 E F Gst 1d

(8)

The reversible stress relaxation was performed with an electronic balance that allows one to apply a certain strain to the bending beam by lifting or lowering the scale of the balance. The time dependent change of the stress in the beam is proportional to the change of the weight that is read out. Strain is constant and Eq. (8) is valid: where E is the Young’s modulus and F is the weight. The stress relaxation Ds /s0 was determined over the time period t53–3600 s to t 1 5 3 s. The test temperature was kept constant at 3160.02 8C. A more detailed description of the procedure is given elsewhere [11,12]. Specimens for acoustic emission measurements were machined as rods (50 mm long, diameter of 5 mm) with the reinforcement planes parallel to the longitudinal axes. Thermal cycling of specimens was conducted in situ by placing the specimens within a dilatometer equipped with a radiant furnace. The residual strain was measured after each cycle and the AE signal was transmitted through a quartz rod in contact with the specimen. The AE counts were monitored directly using a computer-controlled Dakel-LMS-16 AE facility. The procedure is described elsewhere [13].

3. Results and discussion

3.1. Damping measurements Damping was studied on specimens which were thermally treated at increasing upper temperature of the cycle. Fig. 1a shows the plots of the logarithmic decrement d 5 p Q 21 against the logarithm of the maximum strain amplitude ´ for the ZE41 composite before and after thermal cycling between room temperature and increasing upper temperature. Fig. 1b shows the results obtained at higher temperatures. It can be seen that the strain depen-

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115

by the largest double loop in a segment and it depends on the distribution of the pinning points. With increasing temperatures, the stress decreases because the breakaway process is thermally activated [14]. At higher temperatures the breakaway can occur at lower stresses than at T50, but higher activation energies are required because the breakaway is simultaneous from several neighboring pinning points. At high temperatures and low frequencies, the stress dependence of dH can be expressed as [14]

S D S D

r LN n 3p kT dH 5 ]] ? ] ? ]] 6 v 2U0 3 exp

Fig. 1. (a) Amplitude dependence of decrement obtained for lower temperatures of thermal treatment. (b) Amplitude dependence of decrement for higher temperatures of thermal treatment.

dencies of the logarithmic decrement exhibit two regions; i.e. d can be expressed as a sum of two components

d 5 d0 1 dH (´)

F

1/2

3

2

, s ]]0 U0 G

1/2

S D G

4 U0 U0 G 2 ] ] ]] 3 kT , 3

1/2

1 ] s0

(10)

where G is the shear modulus, s0 is the amplitude of the applied stress and v its frequency, y the dislocation frequency, U0 is the activation energy and k is the Boltzmann constant. This relationship has a similar form ¨ as the original formula given by Granato and Lucke [15,16]. The dH component depends exponentially on the stress amplitude. The experimental data were analysed using Eq. (10) in the form d 5 d0 1 C1 ´ exp (2C2 /´). Values of the C2 parameter are introduced in Fig. 2 depending on temperature of thermal treatment. The C2 parameter is proportional C2 ~ , 22 / 3 , then, with increasing temperature the length of dislocation segments increases, too. Above 200–220 8C, the C2 slightly increases; then it is practically constant. A rapid increase of C2 is observed at temperatures T .320 8C. The observed behaviour may be explained if we consider that during cooling, and also during thermal cycling, new dislocations are created due to the difference in the CTE [see Eq. (1)] and / or that new pinning points on existing dislocations are formed (by reactions between matrix and reinforcement). Number of free foreign atoms or their small clusters in the matrix can be modified by thermodynamic processes.

(9)

where d0 is the amplitude strain independent component, for low strain amplitudes and dH is the strain amplitude dependent component of d. While the amplitude independent component depends weakly on the upper temperature of the cycle, the values of dH increase very strongly with increasing temperature up to 320 8C and then, above 320 8C, the values of dH decrease with increasing upper temperature. Considering the dislocation structure to consist of segments of LN along which weak pinning points are randomly distributed. The mean distance between two weak pinning points is , with , < LN . The mean total density of dislocations is r. At T50 and at sufficiently high stress, dislocations are able to break away from the weak pinning points. Only ends of the longer segments LN are assumed to be unbreakable pinning points. The stress required for the breakaway of dislocations is determined

Fig. 2. Dependence of the C2 parameter on upper temperature of thermal cycle.

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116

3.2. Stress relaxation The anelastic relaxation processes were studied on specimens thermally treated for damping measurements. Immediately after damping measurement, specimens were put into the balance and the stress relaxation was measured. Stress drops s (t) against time are presented in Fig. 3 for various states of the cycled specimens. After annealing treatment at increasing temperature, the amount of the stress relaxation after 3600 s increases with increasing temperature up to 100 8C, then it rapidly decreases. SR performed at the specimens treated at temperatures above 180 8C are practically the same. Considering that the high temperature damping is produced by an activation energy spectrum [6], the principle of superposition should be considered and hence

s (t) 5 ´0

FE 1ODE exp 2 (t /t ) G R

i

i

(11)

i

3.3. Acoustic emission

if relaxation processes are independent of each other. Lower energies are responsible for the faster relaxation (i.e. shorter relaxation times) process, while for the slower (i.e. longer times) processes, higher activation energies are involved. These combined processes give rise to a continuous monotonous relaxation that does not reach its saturation state. The relation between SR and the specific damping factor Q 21 is given by the equation Q 21 (v ) 5

≠ln s S]] D ≠ln t

t 51 / v

Fig. 4. Frequency dependence of the internal friction.

(12)

The SR was converted to the Q 21 vs. time as shown in Fig. 4a. It can be deduced that isothermal internal friction rises monotonously with the time. Frequency dependence given in Fig. 4b allows to extend internal friction measurements to higher temperatures.

Fig. 3. Stress relaxation obtained for increasing upper temperature of thermal cycle.

Fig. 5 shows the variation with time of the AE count rate, N~ C1 , the specimen deformation, Dl, and the temperature, T, during a single temperature cycle having an upper temperature, T top , of 400 8C. It is apparent that there is significant AE but only during the cooling at temperatures between |160 8C and room temperature. After this cycle, a residual contraction was measured in the specimen. The behaviour of the composite during thermal cycling was characterised in detail by using a stepped incremental temperature technique. The results are documented in Fig. 6 where the residual strain, Dl /l 0 , and the AE counts per cycle, NC1 and NC2 for the two different detection levels, are plotted against T top . l 0 is the original length of the specimen and one cycle was performed for each upper temperature corresponding to each separate experimental point recorded for the residual strain. This plot demonstrates that there is no residual strain up to an upper temperature of 200 8C, followed by a slight tendency to a

Fig. 5. Value of the AE count rate, N~ C1 , temperature, T, and sample deformation, Dl, as measured during a temperature cycle to an upper temperature of 400 8C: the deformation changes from 221.5 mm at the beginning to 228.6 mm at the end of the cycle, thereby showing the occurrence of a residual contraction.

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117

and stress continuity across the interface requires that:

´f 5 ´m

(14)

where sf and sm represents stress in fibres and matrix, respectively, and V is volume fraction. The total strain ´ of each component is given by:

´ 5 ´thermal 1 ´elastic 1 ´creep

(15)

where thermal strain is T2

´ Fig. 6. Residual strain, Dl /l 0 , and AE counts for two different detection levels, NC1 and NC2 , versus the upper cycling temperature, T top : the residual strain was estimated with reference to a temperature of 30 8C and the AE counts were evaluated for the entire cooling period of each cycle.

compressive contraction. Then, from 240 to 280 8C a small residual elongation prevails, and for higher upper temperatures, there is a residual contraction that increases in magnitude with increasing T top . The AE response increases significantly at a critical value of T top and intense AE bursts appear with further increases in T top . It has been shown that more than 1000 thermal cycles are needed to produce any measurable damage in specimens [17]. Thus, the AE counts recorded in these experiments must be attributed to the occurrence of structural changes in the matrix and to any associated plastic deformation. The composite fabricated by squeeze casting contains thermal residual stresses at room temperature [18]. The magnitude of these stresses is of the order of the minimum stress required for creep in the matrix. In practice, the matrix in the composite experiences tensile stresses whereas the fibres experience compressive stresses. Therefore, when the composite is heated, the internal tensile stresses acting on the matrix reduce to zero and, on further heating, compressive stresses are built up. On cooling, the internal stresses behave in the opposite way. Thermal stresses concentrated near the matrix–fibre interfaces and at the ends of the fibres may exceed the matrix yield stress within a temperature range. The generation of new dislocations and plastic deformation within the matrix may occur. The model of longitudinal strain response of the unidirectional reinforced composite during thermal cycling was developed by Garmong [19]. He assumed that the fibre remains elastic throughout the whole temperature range whereas the matrix can deform by creep. He also assumed that there is no sliding at the matrix–fibres interfaces during heating and the effect of transverse stress due to Poisson ratio differences. CTE mismatch along the transverse direction between the matrix and the fibres was ignored. Then, in the absence of any applied stress, stress equilibrium requires that:

sfVf 1 smVm 5 0

(13)

i thermal

5

Ea dT

(16)

i

T1

and elastic strain is si i ´ elastic 5] Ei

(17)

where i represents either fibre or matrix, a represents CTE, T is temperature and E is the elastic modulus. The plastic strain in the matrix can be expressed as sm 2 sys ´ mplastic 5 ]]] (18) q where sys is the instantaneous matrix yield strength and q 5 ≠sm / ≠´m the instantaneous work hardening rate. For creep strain the following may be used [20]: T2 m ´ creep 5

s Gb DH dt D D exp S 2 ] D ?S] DdT E A S] D S] G kT kT dT m

1

s

0

T1

(19) where A 1 and s are constants, G is the matrix shear modulus, b is the Burgers vector, D0 is the diffusion constant and DH is the activation energy for diffusion. Plastic deformation mechanisms may be dislocation glide and / or twinning and at higher temperatures grain boundary sliding. In general, it is reasonable to anticipate that the compressive deformation that appears on heating will give some form of diffusion-controlled high temperature creep, whereas the tensile deformation appearing on cooling will lead to dislocation glide and twinning. Thus, and in support of the experimental observations, a larger AE is expected during cooling at lower temperatures. Small compressive strain observed at 180–260 8C is very probably caused by precipitation processes in the matrix. The stress for dislocation glide in matrix increased and then the creep strain at higher temperatures in the heating part of the cycle has a higher value than dislocation deformation in the cooling part of the cycle. This asymmetry is not significant and it is compensated by tensile strain at higher upper temperatures of the cycle. With respect to the dependence of the residual strain on the upper cycle temperature as plotted in Fig. 6, a quantitative analysis of internal thermal stresses has been developed for a short fibre reinforced aluminium compo-

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site [21]. More recently, this approach has been further developed and applied to experimental data [22,23]. The thermal stresses, sTS , produced by a temperature change at the interfaces of DT are given by Ef EM sTS 5 ]]]]] ? fDaDT sEf f 1 EMs1 2 fdd

(20)

where Ef and EM are the values of Young’s modulus for the reinforcement and the matrix, respectively. For the ZE41-Saffil composite used in these experiments, Ef 5 300 GPa and EM 5 45 GPa at room temperature, f 5 0.2, Da 5 20 3 10 26 K 21 and the decrease in EM with increasing temperature is |50 MPa K 21 . Thus, Eq. (20) predicts that the temperature change by 1 8C produces an increment in the thermal stress of |0.6 MPa and at temperatures above |250 8C this increment decreases to |0.4 MPa K 21 . It is shown in Fig. 6 that measurable compressive deformation occurs during heating at upper temperatures above 200 8C and tensile deformation appears during cooling from upper temperatures above 240 8C. It follows from Eq. (20) that a temperature change of 170 8C produces a thermal stress of 90 MPa, which may be compared with the reported compressive yield stress for the sand cast unreinforced ZE41 matrix alloy at 200 8C [24]. This implies the absence of any significant initial internal tensile stress. A similar calculation may be performed for cooling of the specimen since, on heating, a temperature change of 210 8C produces a thermal stress of 100 MPa, so that the matrix would experience a compressive stress of 100 MPa at 240 8C. In practice, this stress would be relaxed to |40–50 MPa by compressive deformation. Cooling of the composite to room temperature produces an estimated thermal stress of 140 MPa. Consequently, a tensile stress approaching 100 MPa should appear at temperatures near to room temperature, which is more than the acoustic yield point. This effect leads to a small tensile deformation, as observed experimentally. Fig. 6 shows also that AE first appears after cooling from an upper temperature of 220 8C. On heating, a temperature change of 190 8C produces, through Eq. (20), a thermal stress of 90 MPa, which would be relaxed to |40–50 MPa by compressive deformation. Cooling the composite to room temperature, where significant AE first appears, produces a thermal stress of |125 MPa. Consequently, a tensile stress approaching |80 MPa should appear at room temperature and this would be of the same order as the acoustic yield stress of the matrix alloy [24]. This calculation suggests there should be an intense AE on cooling, starting at temperature which increases with an increment in T top , as is clearly evident in Fig. 6. It follows from these calculations that there is a very good correlation between the experimental data and the predictions of a model developed earlier to explain the characteristics of internal damping in an aluminium composite containing short fibres [21].

4. Summary The thermal cycling response of ZE41 magnesium alloy reinforced by short Saffil fibres is characterised by thermal stresses which can relax by anelastic as well as elastic strain. New dislocations created in the vicinity of fibre ends can be detected by internal friction measurements and by acoustic emission. From the internal friction measurements and stress relaxation measurements it can be concluded that changes in the microstructure occur at temperatures above about 180 8C. These changes are very probably connected with migration of solute atoms and precipitation processes. Thermal internal stresses generated at temperatures higher than 220–240 8C are high enough to invoke motion of new dislocations, as documented by residual strain measurements. Thermal cycling at temperature higher than |300 8C causes movement and annihilation of new dislocations in the matrix, under appearing compressive internal stresses, which leads to shortening of the specimen and to a decrease of the decrement.

Acknowledgements This work was supported by the Grant Agency of the Czech Republic (grant no. 103 / 01 / 1058) and the Grant Agency of Academy of Sciences (grant no. A2041203). The authors are grateful for the support offered by the Czech and German authorities under the Exchange Programme CZE 01 / 029.

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