Peak temperatures observed for various frequencies.
In practice, some problems connected with undesirable mechanical vibrations or interruption of acoustic bridges may be solved using high damping materials. Especially, transport industry needs high damping light materials with proper mechanical properties. Magnesium alloys and magnesium alloys‐based metal matrix composites may be considered as materials exhibiting such behaviour. Damping of mechanical vibrations and their conversion to the heat (internal friction) is conditioned by the movement and redistribution of various defects in the crystal lattice. Generally, internal friction depends on the material microstructure and conversely changes in the material microstructure may be studied using the internal friction measurements. The strain amplitude‐dependent internal friction was investigated at room temperature in commercially available Mg alloys and Mg alloys‐based composites with the aim to identify changes in the microstructure invoked by thermal and mechanical loading. The temperature‐dependent internal friction indicated the following effects: (a) mechanisms connected with dislocations and grain boundaries in the microcrystalline pure Mg, (b) precipitation and phase transformations in alloys and (c) generation as well as relaxations of thermal stresses in composites. The internal friction was measured in the bending mode in two frequency regions: I.: units and tens of Hz and II.: units of kHz.
- magnesium alloys
- magnesium alloys‐based composites
- amplitude‐dependent internal friction
- temperature‐dependent internal friction
- solute atoms
- thermal stresses
Internal friction is an anelastic relaxation connected with dissipation of the mechanical energy carried by the sonic or ultrasonic wave in a material and their conversion mostly into heat. In a solid material, it is manifested by deviations from Hooke's law and stress‐strain hysteresis in the case of cyclic loading. Defects in the microstructure as point defects, grain boundaries, phase transformations, electrons, phonons or redistribution of the heat are responsible for internal friction. The general quantities describing the internal friction is the
It should be mentioned that such proportionality is valid for small values of damping Ψ<<1, which is valid for most metallic materials. Very effective sources of internal friction are dislocations. If a material containing dislocations is submitted to a harmonic applied stress
The maximum stored energy can be well approximated by the maximum elastic stored energy
The logarithmic decrement,
In experiments, three types of dependences can be estimated:
Amplitude (strain/stress) dependence of damping capacity;
Temperature dependence of the damping capacity;
Frequency dependence of the damping capacity.
Because the damping capacity is in many cases connected with the atomic jumps, Arrhenius equation may be used
The dynamic strain dependence of the damping capacity can be divided into a strain‐independent and a strain‐dependent component. If the logarithmic decrement is measured, the experimental finding can be expressed as
While amplitude‐dependent component of internal friction is only due to the presence of dislocation in the material, amplitude‐independent part is influenced by several contributions as dislocations, grain boundaries, precipitates, interfaces, or heat transfer. The damping capacity of materials is a function of the microstructure, stress, temperature, or frequency. The anelastic strain can result from the motion of structural defects, such as point defects, dislocation, grain boundaries, and phase transformations, and conversely the internal friction can be used to study such motions. Two basic dependencies were measured: amplitude‐dependent internal friction (ADIF) and temperature relaxation spectrum of internal friction (TDIF).
It is often stated in the literature that magnesium and magnesium alloys have good damping properties. Damping depends on many factors: purity, grain size, alloy composition, thermomechanical treatment of magnesium materials; their microstructure and substructure, temperature, frequency and the stress amplitude. Therefore the universal statement that magnesium and magnesium alloys have high damping capacity is not true. Experiments are necessary to establish to what extent damping occurs for each particular case. The first internal friction effect observed in magnesium was established by Kê . One relaxation peak found at 490 K was attributed to the grain boundary sliding. Similar results of polycrystalline magnesium and magnesium alloys were found by several authors [5–11]. Internal friction peaks measured at low temperatures in magnesium by Fantozzi et al.  and Seyed Reihani et al.  were attributed to the so‐called Bordoni relaxation, that is, the intrinsic mobility of dislocations through the Peierls barriers. Relaxation peaks found in the vicinity of 0.4
2. Amplitude‐dependent internal friction
2.1. Cast alloys
Gravity cast magnesium alloys AM20, AX41 and AZ31 were annealed step by step for 20 min at increasing temperature of the thermal cycle. The temperature step was 20°C. Immediately after thermal cycling, amplitude dependence of internal friction was measured. Amplitude dependences of decrement estimated for AM20 alloy are introduced inFigure 1a–c for various upper temperatures of the thermal cycle. The amplitude dependences of decrement are practically identical for thermal cycling with the upper temperatures up to 200 °C. Thermal cycling with higher temperatures between 200 and 260 °C causes a decrease in the amplitude dependent component while the amplitude independent component remains unchanged. Thermal cycling with the upper temperatures between 260 and 400 °C causes an increase in the amplitude dependent component. The amplitude dependence of decrement obtained at 400°C achieved similar values as in the case of the as‐cast sample.
According to Eq. (8), the
The temperature dependence of the
When the stress (strain) amplitude reaches its critical value, the dislocation motion has features typical for avalanche motion. Long free dislocation segments may operate in the slip plane and damping rapidly increases. Such collective pinning is obvious from Figure 3a for AX41 alloy. The critical strain (stress) for break‐away of dislocations depends only slightly on the thermal treatment, that is, the microstructure is very stable due to the formation of Mg2Ca precipitates which are more thermally stable in comparison with Mg17Al12. The constant length of shorter dislocation segments is manifested by a nearly constant
Different results were found in the case of an AZ31 alloy in the as‐cast state (see Figure 4a, b). The alloy was thermally treated in the similar way as the AM20 alloy. ADIF measured in the as‐cast sample and after the thermal cycling up to 240°C showed no changes in the microstructure (Figure 4a). Thermal treatment at higher temperatures influenced both the amplitude‐independent as well as amplitude‐dependent components of the decrement (Figure 4b). Both increased with increasing upper temperature of the thermal cycle. A rapid increase of the
From the ADIF investigations in AM, AX and AZ magnesium alloys, it can be concluded that changes in the microstructure of alloys may be detected using the internal friction measurement. Thermodynamic processes occurring in the alloys change the effective length of the dislocation segments. These processes take place mainly at temperatures higher than 200°C. Free solute atoms occupy the dislocation line and the stress necessary for the break‐away of dislocations is very high. Avalanche release of dislocation lines (and also their length) leads to a rapid increase in the internal friction.
2.2. Magnesium alloys‐based composites reinforced with short fibres
Metal matrix composites (MMCs) are materials combining two or more components with different physical and chemical properties. The commercial Mg alloys AZ91, ZC63 were reinforced by
Figure 7a shows the plots of the logarithmic decrement against the strain amplitude for the ZC63 magnesium alloy reinforced with 24.9 vol.% Saffil fibres before and after thermal cycling between room temperature and an increasing upper temperature of the thermal cycle. Figure 7b shows results obtained for higher temperatures. From Figure 7a,b, it can be seen that the strain dependencies of the logarithmic decrement exhibit two regions in good accord with Eq. (7). The values of
In the lower‐strain amplitude region, the decrement is only weakly dependent on the strain amplitude. In the second region, for higher strains (or stresses, according to Hooke‘s law they are proportional), the decrement increases strongly with increasing strain amplitude. A number of possible damping mechanisms can be identified in MMCs. Interfaces present in composites are very effective source of damping (interfacial frictional sliding, local dissipative interfacial processes and interfacial diffusion). Grain boundary sliding can occur in the same way as in the unreinforced materials. A finer grain size, which is typical for most MMCs, means that there this process may occur with the higher intensity. On the other hand, ceramic reinforcements exhibit low dislocation density, then dislocation motion and grain boundary sliding are limited; the damping effect from these mechanisms will be reduced in proportion to the remaining volume fraction of the matrix. All these effects (dislocation damping, interface and grain boundary damping) may influence the amplitude‐independent
The experimental data were analysed using relationship (14). Values of the
Metallic matrices and ceramic reinforcement are in the equilibrium at the manufacture temperature. Cooling to the room temperature induces thermal stresses . The coefficient of thermal expansion (CTE) of ceramic reinforcement is lower than that of most metallic matrices. This means that when the composite is subjected to a temperature change, thermal stresses will be generated. Generally, these thermal stresses may be formulated in the following form:
The observed results 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. This process may be influenced by the thermodynamic processes occurring in the matrix during the thermal cycling. Chmelík and co‐workers  measuring the acoustic emission from the thermally treated composite (without any applied stress) have shown that new dislocations are formed in the cooling part of the thermal cycle. Higher dislocation density decreased the effective length of dislocation segments considering that the number of pinning points is constant. Number of free foreign atoms or their small clusters can be modified by thermodynamic processes in the matrix. A redistribution of solute atoms may be studied by electrical resistivity measurements. Residual resistivity ratio RRR (RRR‐1 = ρe(77 K)/ρe(293 K)) measured for step‐by‐step annealed sample at increasing temperature is introduced in Figure 10a for ZC63/Al2O3 MMC. A sharp drop in RRR‐1 detected in the temperature range from 160 to 240°C may be explained by the solute redistribution. This decrease of the resistivity reflects very complex processes; precipitates of various types can be formed in the matrix. The absence of the expected ageing effect might be due to the massive CuMgZn consuming a high amount of alloying elements. Electrical resistivity measurements have shown that the precipitation processes occur in some Mg‐based MMCs approximately between 200 and 300°C [32–34]. Similarly, the matrix alloy is purified from the free solute atoms also in the AZ91 alloy as it will be shown in Section 3.3.
From Figure 9a, b, it is obvious that the
The radius of this plastic zone is given by the following approximate relationship :
If the volume fraction of the plastified matrix increases above a certain value, the plastic zones may overlap. In the overlapped zones, the dislocation loops formed near the interfaces have the opposite sign on both sides of the fibre. At higher temperatures, the yield stress in the matrix is lower than internal stress and at temperatures higher than 260–340°C, the tensile stresses change to compression ones. At this moment, dislocations move in the plastic zones and annihilation of dislocations can occur and hence the dislocation density decreases.
Chmelík and co‐workers  have measured acoustic emission of samples thermally cycled between room temperature and an increasing upper temperature of the thermal cycle. At elevated temperatures from 200°C (in the case of AZ91 MMC) to 280°C, permanent elongation of the sample was detected, followed by rapid shortening of the sample after cycling at temperatures higher. These characteristic temperatures were different for various magnesium alloys used as the matrix alloys, but in each case, the critical temperature at which the sample became to be shorter accords with the critical temperature obtained in the internal friction experiments (AZ91/Al2O3 280°C, ZC63/Al2O3 260°C (temperature 280°C was not measured), ZE41/Al2O3 300°C, QE22/Al2O3 360°C). A decrease of the amplitude‐dependent component of the decrement is observed in the region where the sample is plastically deformed by thermal stresses. Acoustic emission signal was detected only in the cooling parts of the thermal cycle while high‐temperature strain of the sample was completely noiseless.
The temperature dependence of the critical strain
Thermal stresses are generated after the thermal cycling of magnesium alloys reinforced by short Saffil fibres. These stresses may be relaxed by anelastic as well as plastic strain. Internal friction measurements can detect newly created dislocations in the vicinity of fibres ends.
Internal friction measurements showed that changes in the microstructure start at temperatures above about 200°C. Precipitation processes and solute atoms migration are responsible for these changes. Thermal internal stresses generated at temperatures higher than 220–280°C are high enough to invoke motion of newly created dislocations. Thermal cycling at temperatures higher than ~300°C causes movement and annihilation of new dislocations (which are only slightly pinned and well movable) in the matrix, under appearing compressive thermal stresses, which leads to a decrease of internal friction.
2.3. Influence of mechanical cycling on ADIF
The same composite as in Section 2.2, that is, AZ91 alloy with 14.6% of Saffil fibres, was mechanically cycled in the same apparatus in which the ADIF was measured. The sample vibrated certain number of cycles at the resonant frequency, and then the amplitude dependence of decrement was measured.
The end of the fatigue life of the sample was manifested by the rapid increase of the resonant frequency. The sample was cycled up to the sample failure. It was reached at
The amplitude‐dependent internal friction curves determined in the as‐received state and after definite numbers of cycles are introduced in Figure 11a. A rapid increase of the decrement was observed between the first measured curve for
Changes in the composite response upon cyclic loading are primarily caused by plastic deformation in the matrix . The cycling response in the material containing particles impenetrable for dislocations leads to a rapid increase in the dislocation density during cyclic loading until a saturated state is reached. Composites typically exhibit a higher dislocation density compared with their monolithic counterparts. The dislocations have to circumvent the impenetrable ceramic fibres and in the case of the AZ91 alloy also precipitates Mg17Al12. New dislocations are generated at the matrix/obstacles interfaces. According to Eq. (9), the amplitude‐independent component of the logarithmic decrement depends on the dislocation density and the length of the shorter dislocation segments ℓ. The observed increase of the decrement at the onset of the cycling process is a result of the increase in the dislocation density. Because the number of the pinning points is constant and the effective length of the shorter dislocation segments ℓ is higher, the decrement increases. During further cycling, the dislocations are trapped by the interface, and induce disordered three dimensional dislocation structures with a few dislocations extending in the matrix. The density of movable dislocations is reduced. Shuttling of these dislocations accommodates the imposed strain but the damping decreases as it is obvious from Figure 11a, b. A rapid increase of the logarithmic decrement for the number of cycles higher than 4.7 × 107 (Figures 11b and 12a) indicates nucleation and growth of fatigue cracks. We observed also influences of the number of cycles on the sample resonant frequency. A rapid increase of the damage parameter of the specimen after
A smooth local maximum in the amplitude dependence of the logarithmic decrement was observed after very high numbers of cycles (see Figures 11a and 12b). This maximum is caused by the formation of cracks in the fatigued matrix. A simple rheological model taking into account the crack origin of damping was developed by Göken and Riehemann . According to the model, one elementary crack is assumed to be represented by a frictional grip that is attached in series to a spring
Fatigue can successfully be studied by the measurement of strain amplitude‐dependent damping after increasing numbers of mechanical cycles. For mechanical cycling of AZ91/Saffil composite mainly dislocation effects could also be found for cycle numbers up to 4.7 × 107. For further cycling, a strong increase of damping can be attributed to nucleation and growth of cracks leading to fracture of the sample. Smooth relative maxima appearing on the damping versus strain curve can be explained and evaluated by a rheological model of the effect of cracks on damping.
2.4. Magnesium zirconia nanocomposite
Magnesium with 3 vol% of zirconia nanoparticles was prepared by powder metallurgical route. Powder from Mg was mixed with ZrO2 nanoparticles (the mean size of 14 nm) and milled together for 1 h in a planetary ball mill. The mixture was subsequently pre‐compressed followed by hot extrusion at a temperature of 350°C under a pressure of 150 MPa. After extrusion, the originally more or less equiaxial grains changed into elliptical grains with the long axis parallel to the extrusion direction. The grain size in the cross section was about 3 μm and in the extrusion direction 10 μm. ADIF was measured after mechanical cycling at room temperature. Experiments were performed in similar way as in the case of AZ91/Saffil composite. Decrement estimated for two strain amplitudes depending on the number of cycles is shown in Figure 13a.
Mechanical cycling in the region from 3 × 103 to 2.4 × 106 leads to the decrement increase. Observed increase of decrement is very probably a consequence of the dislocation density increase and also an increase of the effective length between weak pinning points. Further cycling up to 2.9 × 107 cycles decreased the decrement. This drop is caused by a decrease of the dislocation density, which is a consequence of interactions between dislocations. The higher dislocation density limited the slip length of vibrating dislocation segments. Rapid increase of the decrement is caused by the cracks creation. Rapid decrease of the damage parameter shown in Figure 13b observed for the number of cycles of
Magnesium zirconia nanocomposite was cycled at room temperature and after certain number of cycles the logarithmic decrement was measured. Plastic deformation during cycling increased the dislocation density and also the measured decrement. The loss of stiffness at the end of the fatigue process is a consequence of the cracks formation and propagation.
2.5. Ultra‐fine‐grained magnesium
Ultra‐fine‐grained magnesium (UFG‐Mg) samples were prepared by ball milling of powder in an inert atmosphere and subsequent consolidation and hot extrusion. The linear grain size of specimens estimated by X‐ray line profile analysis was about 100–150 nm. Samples were cyclically loaded until failure with bending vibrations in the apparatus also used for damping measurements. The resonant frequency of the system ranged from 59 to 62 Hz. The end of the fatigue life of a sample was manifested by a rapid decrease of the resonant frequency. The sample was cycled up to failure, which was reached at
The amplitude‐independent component,
The accumulation of plastic deformation mainly due to an increase of the dislocation density is the significant feature of the fatigue process. Cycling higher than 108 cycles led to nucleation and growth of cracks. Newly created and propagated cracks increased the logarithmic decrement and damage parameter.
3. Temperature relaxation spectrum of internal friction
3.1. Microcrystalline Mg
Microcrystalline magnesium was prepared using the powder metallurgical route. The temperature dependence of the loss angle tan
From the slope and intercept of the straight line, the mean activation enthalpy Δ
|Mg99.999%||76.8||1–2||Seyed Reihani |
|Mg99.9999%||67||1||Nó et al. |
|Mg99.9999%||157||1||Nó et al. |
|High purity Mg||146.8||Fantozzi et al. |
|UFG‐Mg||102||1||0.95||Trojanová et al. |
|UFG‐Mg||358||1||1.77||Trojanová et al. |
|UFG‐Mg+3nGr||78||1||1.08||Trojanová et al. |
In the case of a relaxation processes linked to dislocation motion, the activation area
using Eq. (23) and the condition
where the energy barrier has a width
The main deformation mode in magnesium is basal slip of <a> dislocations. The secondary conservative slip may be realised by <a> dislocations on prismatic and pyramidal planes of the first kind. Couret and Caillard studied by TEM prismatic glide in magnesium in a wide temperature range [46, 47]. They showed that the screw dislocations with the Burgers vector of are able to glide on prismatic planes and their mobility is much lower than the mobility of edge dislocations. The deformation is controlled by thermally activated glide of these screw dislocation segments. A single controlling mechanism has been identified as the Friedel‐Escaig mechanism. This mechanism assumes a dissociated dislocation on a compact plane (0001) that joins together along a critical length
The theoretical prediction leads to a value of 2
The high‐temperature peak has been observed at temperature ~325°C (0.5Hz). The cold prestraining of the sample did not affect the strength of the high‐temperature peak. Position and height of the peak are very stable during heating as well as cooling. The activation energy was obtained from the frequency dependence of the peak temperature (Arrhenius plot) to be 1.40 ± 0.05 eV (see Figure 15b). Existence of the high‐temperature peak in magnesium has been reported by Kê  and other authors [5, 6, 10, 11]. They described this peak as being related to the grain boundary relaxation. Grain boundary sliding is realized by the slip and climb (providing a maintenance of vacancy sources and sinks) of grain boundary dislocations. Since both modes of dislocation motion must occur simultaneously, the slower one will control the grain boundary sliding. The climb mode involves jog formation and grain boundary diffusion and both modes may be affected by the interaction with impurities segregated in grain boundaries. According to ref. , grain boundary dislocation segments vibrate under applied cyclic stress, restoring force
Microcrystalline magnesium was prepared by milling and hot extrusion. Internal friction was measured as a function of temperature with three frequencies 0.5, 5 and 50 Hz. Two relaxation peaks were observed: a peak at 85 (0.5 Hz) with activation energy of 1.02 eV, and a peak at 325°C (0.5 Hz) with activation energy of 1.40 eV. The estimated small values of the activation volume and the peak sensitivity to the stress amplitude lead us to conclude that the low‐temperature peak is due to the screw dislocation motion on the prismatic plane controlled by the Friedel‐Escaig mechanism. Grain boundary sliding is probably the reason for appearing at the high‐temperature peak.
3.2. Mg‐Gr nanocomposite
The Mg with 3 vol% of Gr nanoparticles was prepared by the similar procedure as the microcrystalline Mg (see Chapter 3.1). The Mg micropowder with a median particle diameter of about 40 μm was mixed for 8 h with 3 vol.% of graphite powder and milled for 8 h in the planetary ball mill in a sealed argon atmosphere. The composite was encapsulated in an evacuated Mg container, degassed at 350°C, and extruded by the preheated (350°C) 400 t horizontal extrusion press. The material was studied in a transmission electron microscope; the mean grain size of the material was found to be about 200 nm. Temperature relaxation spectra of internal friction were measured in a DMA 2980 (TA Instruments) apparatus while heating and cooling. In a temperature range from room temperature up to 480°C, the measurements were performed in the multi‐frequency mode at three frequencies 0.5, 1 and 2 Hz. Throughout the measurements, the strain amplitude was 1.2 × 10‐4. The heating as well as cooling rate was 1 K/min. No grain growth during heating up to 480°C was observed.
Figure 17a shows the temperature dependence of the mechanical loss angle tanφ measured at three frequencies during first heating sub‐cycle. Two types of peak have been found: the weak low‐temperature peak and the more pronounced two high‐temperature peaks. While the low‐temperature peak position in the temperature scale depends on the measuring frequency, position of both high‐temperature peaks does not depend on the frequency. Figure 17b shows the temperature dependence of mechanical loss angle measured during cooling. It is seen that the two high‐temperature peaks developed into one peak. Position of this peak is not depending on frequency and it remained constant in the next heating‐cooling cycles. The low‐temperature peaks extracted from the internal friction spectrum subtracting the background damping are introduced in Figure 18a, b which shows the Arrhenius plot for the low‐temperature peak. An estimated activation enthalpy of 1.08 ± 0.05 eV is close to activation enthalpies found for μMg and UFG‐Mg as it is given in Table 2. This fact and together with found peak temperature from a range of 67–102°C indicates that the low‐temperature peak is due to the reversible screw dislocation motion on the prismatic plane controlled by the Friedel‐Escaig mechanism as it was described in paragraph 3.1.
Observed independence of the high‐temperature peak on the frequency indicates that this peak has no Debye nature. Its existence is due to newly created dislocations and their motion. An increase in the dislocation density near reinforcement with the different CTE compared with the matrix has been calculated according to Arsenault & Shi 
In the absence of thermal stresses, the vibrating dislocation segments do the dislocation damping IFd. If the composite material is heated, compressive thermal stresses
Mg with 3 vol.% of Gr nanoparticles prepared by milling and hot extrusion has been characterised by mechanical spectroscopy during continuous heating as well as cooling. Internal friction was measured as a function of temperature with three frequencies ranging from 0.5 to 2 Hz. Two internal friction peaks were observed in the temperature relaxation spectrum. The peak observed in the vicinity of ≈ 80°C, having the activation energy of 1.08 eV, has been described to the reversible screw dislocation motion in the Mg grains on the prismatic plane controlled by the Friedel‐Escaig mechanism. Thermal stresses generated due to thermal mismatch during heating as well as cooling are very probably the reason for the peak observed at ≈ 300°C. Position of this peak is insensitive to the measuring frequency. Increased dislocation density induced by thermal stresses and movement of dislocations under the thermal stress as well as the applied stress is the reason for the existence of this peak.
3.3. AZ magnesium alloys
TDIF was measured in cast magnesium alloys AZ31, AZ63 and AZ91 after homogenisation treatment (22 h at 390°C). The resonant frequency and damping analyser (RFDA) was used to determine the damping and resonant frequency. The measurements were performed in a wide temperature range from room temperature up to 400°C. The prism‐shaped samples 75 × 20 × 10 mm3 were excited to vibrations in the resonant frequency using a small striker. Damping of the sample‐free vibrations was registered with a microphone and processed using special software. The resonant frequency exhibiting ~8 kHz was estimated by means of Fourier transform. The linear heating rate was chosen in the range from 1 to 4 K/min. The AZ alloys are formed by the solid solution of Al and Zn atoms in Mg (
The temperature dependences of the logarithmic decrement measured at the heating rate of 2 K/min for AZ31, AZ63 and AZ91 alloys are introduced in Figure 19a. The temperature dependence of the logarithmic decrement was measured in the AZ91 sample after the homogenisation treatment while heating is introduced in Figure 19b. The heating rate was 60 K/h, the cooling rate was not controlled. The temperature record showed the linear decrease of temperature up to 120–140°C. When room temperature was reached, a new measurement was started. The measurements were repeated three times. It is obvious from Figure 19b that the decrement is more or less constant up to approximately 220°C, and then it increases with increasing temperature. At temperature ~320°C, a local maximum of the logarithmic decrement is observed. The height of this maximum decreases in the second and third run of the measurement. The position of maximum in the temperature axis is the same for all runs.
The temperature dependence of the logarithmic decrement was measured for three heating rates as it is shown in Figure 20a. Note that before each measurement, a new homogenisation treatment was performed. Only the first runs of the measurements are given in Figure 20a. The higher heating rate, the higher temperature of the local maximum is observed. The height of the maximum simultaneously decreases with the increasing heating rate. To reveal the physical nature of the observed local maximum in the temperature dependence of the logarithmic decrement, a sample with the smaller thickness was tested. Maximum position in the temperature scale was not shifted for the measurement with the resonant frequency of ~7 kHz (see Figure 20b). This fact indicates that the observed maximum is not of the Debye type. Some transitory effects must be considered.
In the temperature dependence of the logarithmic decrement, four characteristic points were selected: 220, 320, 360 and 390°C. Samples were subjected to the homogenisation treatment and then put into a furnace with the predetermined heating rate of 1 K/min. Reaching the chosen temperature, samples were step by step removed from the furnace and quenched into water of 60°C. Scanning electron microscopy (SEM) observations were performed at room temperature. After heating of the sample with the heating rate of 1 K/min up to 220°C supersaturated solid solution decomposed; DP appeared in the vicinity of grain boundaries as it is obvious from Figure 21a, small precipitates visible as light points are CP, their size slowly increased. Tiny CPs are situated primarily in the annealing twins, the matrix in the vicinity of twins is purified, density of CPs is in these places lower (Figure 21b).
When temperature increased up to 320°C, decomposition of DPs started, and then the growing of CPs (Figure 22a) followed. Original lamellae were reshaped into small discs as it is visible in Figure 22b. CPs depicts the twin; small discs of CPs are ordered in twin/grain boundaries. Note that a temperature of 320°C corresponds to the peak temperature in the temperature dependence of decrement.
Microstructure of the sample annealed up to 360°C (local minimum in the temperature dependence of decrement) is characterised by the growth of CP (Figure 23a). Light points are small Mn particles; small content of Mn (0.24 wt.%) was used for grain refining. In the vicinity of grain boundaries, purified places were established (Figure 23b). Meander‐like grain boundaries are decorated with larger precipitates (Figure 23a, b).
At 390°C, the transformation of DP into CP is finished. The CPs decorate the grain boundaries (Figure 24a), DP vanished as it is obvious from Figure 24b and the size of CP increased. It is possible to conclude from the microstructure observations that, in the temperature range from 220 to 360°C, a transformation of DP originally formed up to 220°C stepwise passed off. Disc‐shaped CP changed into small spheres and at the highest temperatures into larger particles with a complex shape. Increasing the heating rate, time for the transformation of DP into CP is shorter. It is very probably the reason why the maximum height decreases with increasing heating rate and at the same time, the maximum is shifted to higher temperatures. DPs are formed when the grain boundary diffusion is dominant, whereas the CPs are formed at higher temperatures from solid solution when volume diffusion becomes faster. As it was shown in previous paragraphs, internal friction is very sensitive to the material microstructure, volume fraction and distribution of structural defects. Any modification in the microstructure induces changes in the internal friction course. Thus, the internal friction measurements may provide information about processes occurring at the atomic scale. Internal friction maxima were found in the AZ magnesium alloys by several authors. Lambri and co‐workers  found the internal friction peak at about 152°C using the measuring frequency of 1 Hz. Authors ascribed this peak to the grain boundary sliding. The peak height may be controlled by a decrease in solute atoms due to precipitation process. The activation energy estimated from the Arrhenius plot was evaluated as 1.13 eV. Similarly, Liu and co‐workers  found the internal friction peak situated at 165°C and a frequency of 1 Hz. They determined the corresponding activation energy of 1.26 eV. The peak was ascribed to the grain boundary relaxation. Two internal friction peaks were observed in .
Internal friction measurements of the AZ31, AZ63 and AZ91 alloys showed an exponential increase of the logarithmic decrement with temperature. In AZ63 and AZ91 alloys, this increase is modulated by a local maximum at about of 320°C. The maximum height decreased in the second and third run while the maximum temperature remained the same. The position of the local maximum was sensitive to the heating rate and insensitive to the frequency. Increasing heating rate shifted the peak temperature to higher temperatures. The occurrence of the internal friction maximum is connected with the transformation of discontinuous precipitates to continuous ones. Strain (stress)‐supported flux of solute atoms and movement of the
Z.T. and P.L. gratefully acknowledge the financial support from the Czech Science Foundation under Grant 107‐15/11879S. P.P. and M.C. are grateful to the Ministry of Education and Academy of Science of the Slovak Republic for the support by the project VEGA No. 1/0683/15. Parts of this chapter are reproduced from authors’ recent publications [34, 41] and conference contributions [15, 36]. We thank our co‐authors for permission to reuse parts of the papers. This chapter is dedicated in the memory of Professor Werner Riehemann from the Clausthal University of Technology, who passed away in January 2016.