Influence of Solute Atoms on Deformation Behaviour of Selected Magnesium Alloys

Magnesium alloys due to their relative high specific strength and low density are used for a wide range of applications – for example in the automobile and transportation industries; they promise significant weight saving. Numerous studies have been performed in order to estimate their mechanical and physical properties. It is well known that many physical and mechanical properties of metals are influenced by alloying. The solute atoms cause an increase in the strengthening of materials. On the other hand, it is difficult to predict the effect of solute atoms on the strength and deformation behaviour of magnesium and its alloys because the experimental data concerning the critical resolved shear stress (CRSS) of single crystals of binary alloys are restricted.


Introduction
Magnesium alloys due to their relative high specific strength and low density are used for a wide range of applications -for example in the automobile and transportation industries; they promise significant weight saving. Numerous studies have been performed in order to estimate their mechanical and physical properties. It is well known that many physical and mechanical properties of metals are influenced by alloying. The solute atoms cause an increase in the strengthening of materials. On the other hand, it is difficult to predict the effect of solute atoms on the strength and deformation behaviour of magnesium and its alloys because the experimental data concerning the critical resolved shear stress (CRSS) of single crystals of binary alloys are restricted.
In this chapter we deal with the effect of solute (foreign) atoms on the mechanical properties of magnesium. The foreign atoms are assumed to substitute for the matrix atoms and/or form precipitates. We restrict ourselves mainly to the yield stress and the true stress-true strain curves measured at a constant strain rate at room and higher temperatures. The deformation behaviour of polycrystals is influenced by the presence of crystal defects. Strength of a material is a result of strengthening mechanisms. One of the strengthening mechanisms is solution hardening defined as the increase of the initial flow stress as foreign atoms are dissolved in it [1,2]. In this chapter original results of authors were used.

Fundamentals of plastic deformation
Plastic deformation of magnesium polycrystals occurs by glide of dislocations and/or twinning. Glide of dislocations with the Burgers vector of 1 / 3 112 0 on (0001) basal plane is the easiest slip mechanism; often called basal slip of <a> type dislocation. The CRSS is required to activate the glide of <a> type dislocations. In order to estimate the CRSS (the stress acting on the slip plane in the slip direction) for a binary magnesium alloy (Mg-X), experimental tests on single crystals are needed. The yield strength of polycrystals is connected with the CRSS of single crystals with help of the relationship σ y =Mτ 0 , where M is the Taylor orientation factor. The deformation behavior of magnesium and magnesium alloy polycrystals may be influenced by twinning and the activity of non-basal slip systems. Glide of <a> dislocations in prismatic planes and glide of<c+a> dislocations in the second-order pyramidal slip systems should be consider. However for explanation, it is important to consider not only the solute influence but also the effect of grain size. These factors may affect not only basal slip but also prismatic slip and twinning responsible for the mechanical properties. Crystallographic textures can also change the value of the yield strength as for instance for the case of rolled sheets deformed in the rolling direction [3,4].
It is widely accepted that the stress necessary for the dislocation motion in the slip plane can be divided into two components: where σ i is the internal (athermal) contribution to the stress, resulting from long-range internal stresses impeding the plastic flow.
where G is the shear modulus, σ 1 is a constant describing interaction between dislocations, b is the Burgers vector of dislocations and ρ t is the total dislocation density. The effective stress σ* acts on dislocations during their thermally activated motion when they overcome short range obstacles. The mean velocity of dislocations υ is connected with the plastic strain rate by the Orowan equation: where ρ m is the mobile dislocation density. The most common equation used in describing the average dislocation velocity as a function of the effective stress is an Arrhenius type. The plastic strain rate ε for a single thermally activated process can be expressed as: where ε 0 is a pre-exponential factor containing the mobile dislocation density, the average area covered by the dislocations in every activation act, the dislocation Burgers vector, the vibration frequency of the dislocation line, and the geometric factor. T is the absolute temperature and k is the Boltzmann constant. ΔG(σ * ) is the change in the Gibbs free energy depending on the effective stress (thermal stress)σ * =σ ap −σ i and the simple form is Here ΔG 0 is the Gibbs free energy necessary for overcoming a short range obstacle without the stress (the barrier activation energy at zero stress) and V=bdL is the activation volume where d is the obstacle wide and L is the mean length of dislocation segments between obstacles. It should be mentioned that L may depend on the stress acting on dislocation segments. In a stress relaxation (SR) test, the specimen is deformed to a certain stress σ 0 and then the machine is stopped and the stress is allowed to relax. The stress decreases with the time t. The specimen can be again reloaded to a higher stress (load) and the SR test may be repeated. The time derivative σ =dσ/dt is the stress relaxation rate and σ=σ(t) is the flow stress at time t during the SR. SR tests are very often analysed under the assumption that the SR rate is proportional to the strain rate ε and then σ(t) can be expressed according to [5] as: where σ (0) ≡σ 0 is the stress at the beginning of the stress relaxation at time t=0, β is a constant and α=kT/V.

Microstructure of Mg-Li alloys
Among Mg alloys, magnesium-lithium alloys, as the lightest metallic materials, are attractive for a large amount of applications. They are of great importance also for medicine purposes. Therefore, it is important to investigate mechanical properties at different temperatures and to estimate the deformation mechanisms responsible for the deformation behaviour of Mg-Li alloys at elevated temperatures. Pure Mg has hexagonal close packed structure. The density of Mg-Li alloy decreases with an increase of lithium content. The addition of Li increases ductility. The Mg-Li phase diagram shows that Li is soluble in hcp α-phase up to 4 wt%, while Mg alloyed with greater than 12 wt% Li has a bcc structure (β-phase) [6]. Ductility of the hcp α-phase are worse in comparison with the bcc alloys that are very good machinable and weldable. Disadvantages of Mg-Li alloys with bcc structure are a high chemical activity and poor corrosion resistivity. Some compromise would be an alloy with 8 wt% of Li (a mixture of phases α+β) that might exhibit both improved mechanical properties as well as a good corrosion resistance. In light micrograph in Fig. 1, light α-phase and darker β-phase may be visible. The alloys were produced by pressure infiltration under an argon pressure (up to 6 MPa) at temperatures of 615-635 K.

Deformation of Mg-Li alloys
Compression tests were performed in an Instron type machine at a constant crosshead speed giving an initial strain rate of 2.4x10 -4 s -1 . The argon atmosphere was used as a protecting atmosphere in the furnace at elevated temperatures. The compression yield stress (CYS), σ 02 , was estimated as the flow stress at 0.2% offset strain. The ultimate compression strength (MCS), σ max , corresponds to the maximum value of the flow stress. Samples were deformed to a predetermined strain of 0.3, and then deformation was interrupted.    Figure 2 shows the true stress-true strain curves estimated at various temperatures. A significant hardening is obvious especially for lower temperatures. Figure 3 shows the temperature variation of the CYS, σ 02 , as well as the MCS (σ max ) of Mg4Li alloy. It is apparent from Fig. 3 that the temperature variation of CYS exhibits a local maximum at a temperature of 70 °C. The MCS of Mg-4Li alloy decreases rapidly with increasing temperature. The differences between MCS and CYS exhibit a rapid decrease with increasing temperature. The true stress-true strain curves of Mg-8Li alloy measured in compression at various temperatures are shown in Fig. 4. A rapid decrease of the flow stresses at temperatures higher than 50 °C is obvious in Fig. 5. The temperature variation of the CYS exhibits a local maximum at 50 °C.
While the stress-strain curves estimated for Mg4Li exhibit a significant strain hardening, the curves observed for Mg12Li are very flat (Fig. 6); the difference between the CYS and MCS is relatively low and decreases with increasing temperature (Fig. 7).
The Mg-4Li alloy has hcp structure. The addition of Li to Mg increases the critical resolved shear stress (CRSS) for basal slip; the solid solution hardening is observed [7]. The CRSS of Mg4Li is almost independent on the temperature above room temperature while the CRSS for non-basal slip decreases with temperature below 200 °C as shown in [8]. The addition of Li causes a decrease of both a and c lattice parameters in Mg-Li solid solution [9].

Magnesium Alloys -Properties in Solid and Liquid States
It is well known that the dominant slip system in Mg and hcp Mg alloys at room temperature is the basal one. To fulfil von Mises criterion, a non-basal slip system should be active. The activity of non-basal slip systems plays an important role in dynamic recovery (softening). The pyramidal slip systems can be considered as non-basal slip systems. During deformation of magnesium alloy polycrystals, the motion not only <a> (basal) dislocations but also <c+a> (pyramidal) dislocations is assumed. Screw components of the <c+a> dislocations can move to the parallel slip planes by double cross slip and then annihilate, which causes a decrease in the strain hardening rate; softening is observed. With the addition of Li the c/a ratio decreases, which may result in a higher activity of non-basal slip [10]. Agnew et al. [11] revealed that the <c+a> dislocations in the pyramidal planes improve ductility of MgLi alloys. Pawelek et al. [12] studying acoustic emission from deformed Mg-Li alloys estimated a high level of acoustic emission in Mg4Li alloy as a result of non-basal slip in the prismatic and pyramidal slip systems.

Microstructure of Mg-xLi-yAl alloys
To improve the mechanical properties, alloying with other elements can be used. The addition of Al atoms to Mg4Li causes the formation of precipitates. A combination of two different hardening mechanisms should be considered: solid solution hardening and precipitation hardening. The microstructure of as-cast Mg8LixAl alloys under consideration consists essentially of hcp magnesium-based α-phase and bcc lithium-based one (β-phase) and AlLi precipitates as well. Accordingly, interpenetrated (α+β) matrix structure with dominating αphase is characteristic for LA83 and LA85 (see Fig. 8) alloys. Light micrograph of the Mg12Li3Al (LA123) alloy shows that the alloy does not contain only one phase (Fig. 9). Both phases (α and β) are present contrary to the alloy without Al because aluminium stabilises the hcpα-phase.

Deformation of Mg-xLi-yAl alloys
The temperature dependence of the CYS and MCS estimated for LA43 (Mg-4Li-3Al) and LA45 (Mg-4Li-5Al) are introduced in Figs. 10 and 11. High differences between CYS and MCS, especially observed at lower temperatures, and moderate decrease of the characteristic stresses with temperature indicate significant hardening during plastic deformation. The presence of AlLi precipitates influences not only the yield stress but also the storage of dislocations during plastic deformation. In the LA43 (Mg4Li3Al) and LA45 (Mg4Li5Al) alloys, there are obstacles of non-dislocation types such as precipitates and the dislocation obstacles (forest dislocations). The observed high difference between the CYS and MCS indicates a significant hardening during the deformation process. A part of the moving dislocations stored at the obstacles contributes to hardening. On the other hand, processes such as cross slip and climb of dislocations contribute to softening-the difference between CYS and MCS decreases with increasing deformation temperature. The dislocation microstructure can change. For simplicity, the total dislocation density is considered as the characteristic parameter of the evolution of microstructure during deformation. According to the model of Lukáč and Balík [13], we take into account storage of dislocations at both impenetrable obstacles and forest dislocations, and annihilation of dislocations due to both cross slip and climb. The true stress-true strain curves of LA85 alloy estimated at various temperatures are shown in Fig. 12. The strain hardening is observed at temperatures up to 100 °C; the stress-strain curves obtained at higher temperatures are flat. The temperature variations of the CYS and MCS for LA83 and LA85 alloys are shown in Figs. 13 and 14. The strengthening effect of Al atoms in the case of LA85 alloy has been found to be really high even at 100 °C. A moderate decrease of both characteristic stresses with temperature classes this alloy as a material for industrial applications.       To conclude it is possible to say that the best mechanical properties of the superlight MgLi alloys were found for Mg8Li alloy with 5 wt% of Al. Combining of the stronger α phase with a more ductile β phase results in a material with the high specific strength.

Microstructure of the Mg-Al-Sr alloys
Special industrial applications require improvement of the high temperature properties. For these elevated temperature applications, alloys containing rare earth elements have been developed. New Mg-Al-Sr alloys are being developed with the aim to find cast alloys with good creep resistance and good strength and replace expensive rare earth alloying elements with some cheaper one. Pekguleryuz [14] reported that Mg-Al-Sr alloys show different microstructures based on the Sr/Al ratio. For Sr/Al ratio below about 0.3, only Al 4 Sr intermetallic phase is present as the second phase in the structure. When the Sr/Al ratio is higher, a second intermetallic phase, a new, ternary Mg-Al-Sr compound, is observed. When the Sr/Al ratio is very low, there is insufficient amount of Sr to bind all Al atoms and the excess Al would form the Mg 17 Al 12 phase. Figure 17 shows light micrograph of the squeeze cast AJ51 alloy. The primary Mg grains are surrounded by the interconnected network of the grain boundary phase. This phase is formed during solidification process and it has lamellar type morphology.  Fig. 19 is given in Fig. 20. Line scan analysis was performed along the light arrow showed in Fig. 19. Small content of Sr is present in the δ solid solution; higher in the position of a needle shaped particle.

Deformation of the AJ alloys
The true stress-true strain curves of AJ51 alloy deformed in compression at various temperatures are shown in Fig. 21. Samples were deformed either to failure or the tests performed at temperatures higher than 100 °C were interrupted at a predetermined strain. Significant hardening at temperatures up to 150 °C is obvious. The curves obtained at temperatures higher are more or less flat -hardening and softening processes are in equilibrium.   Figure 22 shows the temperature variation of the CYS as well as the MCS. Similar characteristics estimated in tension are shown in Fig. 23. While the values of the yield stress are practically the same for tension and compression, the values of the maximum stress are higher in compression tests. It is a consequence of higher ductility of the alloy in compression and significant hardening during plastic deformation at lower temperatures. The yield stress decreases with increasing temperature for samples deformed in compression. A small local maximum in the temperature dependence of the yield strength observed in the vicinity of 50°C was observed in several Mg alloys and composites [15]. It is likely caused by a dynamic age hardening.

Stress components in the AJ alloys
Stress necessary for dislocation motion is possible, according to eq. (1), divided into two components. The components of the applied stress (σ i , σ * ) may be estimated using Li's method [16]. The SR curves are fitted to the power law function in the form: Influence of Solute Atoms on Deformation Behaviour of Selected Magnesium Alloys http://dx.doi.org/10.5772/58949 where a, t 0 and m are fitting parameters. The influence of solute atoms on both stress components of AJ51 and AJ91 is obvious from  it was estimate at three temperatures. At room temperature, an increase in the concentration of solute atoms influences only the internal stress. The observed increase of the internal stress is due to higher density of impenetrable precipitates which are obstacles for the dislocation motion. The effective stress σ* is practically the same for both alloys. From Fig. 27 it is obvious that the internal stress in both alloys is extremely high; it represents more than 90% of the applied stress. The difference between the internal stress of AJ51 and AJ91 alloys at 100 °C ( Fig. 28) is relatively high and it indicates the reinforcing effect of the increased concentration of solute atoms. The effective stress is still for both alloys practically the same but the values of σ * for both alloys are higher in comparison with the values obtained at room temperature. The internal stress estimated for AJ91 alloy at 200 °C ( Fig. 29) is for strains up to approximately ε~ 0.08 higher as the effective stress. While the internal stress for AJ91 alloy decreases with strain, the effective stress continuously increases for both alloys. The decrease of the internal stress with strain estimated for both alloys is a consequence of the intensive activity of softening processes. This mechanism will be discussed in details later.

Microstructure of the AX alloys
When Ca is added to Mg-Al binary alloys, the type of precipitating compound depends on the Ca/Al mass ratio. When this ratio is higher than 0.8 the presence of both Mg 2 Ca and Al 2 Ca were detected. They may contribute to a considerable increase in hardness and the yield stress [17]. For the ratio below 0.8 only Al 2 Ca Laves phase (C15-cubic) was observed to have been formed. Both types of precipitates were observed to form along the grain boundaries [18]. Gjestland et al. [19] showed that the creep resistance of AX alloy at 150 °C is similar to magnesium alloys containing rare earths with the added benefit of good corrosion resistance. Terada et al. [20] studied the creep mechanisms in the Mg-5Al-1.7Ca alloy. They found a change of deformation mechanism at the vicinity of 150 °C. Microstructure and mechanical properties of Mg-Al based alloy with Ca addition (AX series) were investigated by Du et al. [21]. They estimated that the small amount of Ca increased the thermal stability of Mg 17 Al 12 intermetallic phase, so that the creep resistance at elevated temperatures was improved.
Microstructure of the squeeze cast AX41 alloy used in this study exhibits typical dendritic structure with γ Mg grains decorated by particles. SEM showed the details of the particles structure (Fig. 30); Mg 17 Al 12 intermetallic phase surrounded with smaller particles of Al 2 Ca. Microstructure of the squeeze cast AX91 alloy is displayed in Fig. 31. Two types of particles were identified, which is better evident in the back scattered electrons image (see Fig. 32). Dark particles in Fig. 32 are eutectics Mg 17 Al 12 ; lighter skeleton-like particles containing Ca atoms.

Deformation of the AX alloys
The true stress-true strain curves of AX41 alloy deformed in tension are presented in Fig. 33. Low ductility (about 5%) of the alloy was observed at lower temperatures below 100 °C; at higher temperatures ductility increases up to 27%. The temperature variations of the TYS and MTS are presented in Fig. 34.

Magnesium Alloys -Properties in Solid and Liquid States 24
Analogously the values of the CYS and MCS at different temperatures are shown in Fig. 35. It can be seen that the TYS decreases with increasing temperature monotonously whereas the temperature variation of the CYS exhibits a local maximum at about 50 °C. The temperature variations of the TYS and MTS for squeeze cast AX61 alloy are presented in Fig. 36. The values of the TYS are relatively high and decrease only slightly with increasing temperature exhibiting at 200 °C still a value about 100 MPa. The true stress-true strain curves of AX91 alloy measured in tension at various temperatures are shown in Fig. 37. It is obvious from Fig. 37 that ductility of the alloy at temperatures up to 100 °C is limited; it increases up to 25 % at a temperature of 300 °C. The TYS at room temperature was estimated to be approximately equal to that measured for AX61 alloy. The observed rapid decrease of TYS of AX91 with temperature indicates a lower thermal stability of this alloy (Fig. 38). It is a different situation in comparison to the AJ91 alloy, for which the strength was found to be superior.

Stress components in the AX alloys
The applied stress components, σ i , and, σ*, for AX41 and AX91 alloys were estimated at three temperatures in compression (see Figs. [39][40][41]. At lower temperatures, 25 and 100 °C, the solute atom concentration influences only the internal stress. The effective stress is for both alloys the same (at 25°C) or it is a bit higher (at 100 °C) for AJ91 alloy. In both cases the effective stress slightly increases with increasing strain. A different behaviour was found at 200 °C. While the internal stress estimated for AX41 alloy increases with increasing strain up to 12%, the internal stress in AX91 alloy slightly increases with strain up to 8% and then decreases. On the other hand, the effective stress increases in the whole strain range.
According to eq. (2) the internal stress, σ i is proportional to ρ 1/2 where ρ is the density of dislocations. The internal stress, σ i , generally, reflects the resistance of a metallic material against plastic deformation. Considering a constant microstructure, the deformation (flow) stresses are done by the evolution of the dislocation density with strain and temperature. The observed increase of the internal stress for all alloys AJ and AX series indicates an increase in the dislocation density. The moving dislocations can be stored at both non-dislocation and dislocation type obstacles. Non-dislocation obstacles may be grain boundaries, non-coherent precipitates and/or twins; the dislocation type obstacles are formed by reactions between dislocations. As mentioned in paragraph 2, in hcp magnesium alloys dislocations with the The resulting sessile<c> dislocations with the Burgers vector parallel to the c axis are not able to glide in the basal plane; therefore such dislocations are obstacles for moving dislocations.
Twins are another type of obstacles. Twinning plays an important role in plastic deformation of hcp magnesium alloys. Our experiments were performed in compression. It was shown [22][23][24] that {1010} compressive twinning, {1011}-{1012} double twining and {1013}-{1012} double twinning could also accommodate compressive strains along the c-axis at lower temperatures. The nearly constant level or slightly decreasing tendency of the internal stress estimated at a temperature of 200 °C indicates a decrease in the dislocation density as a consequence of recovery process/-es. With rising temperature, the intensity of dynamic recovery is increasing -this can be related to dislocation climb and also to the activity of additional non-basal slip systems. It should be mentioned that <c> dislocations are not able to glide (conservative movement) in the basal plane, however they may climb at elevated temperatures and release the primary glide. Another dislocation reaction may yield a sessile <c+a> dislocation: A combination of two glissile<c+a> dislocations gives rise to a sessile dislocation of <a> type that lays along the intersection of the second order pyramidal planes according to the following reaction: It can be seen that different dislocation reactions may produce both sessile and glissile dislocations. Production of sessile dislocations increases the density of the forest dislocations that are obstacles for moving dislocations. Therefore, an increase in the flow stress with straining (i.e. hardening) follows, which is observed in the experiment.
Dislocations may be stored in front of impenetrable, thermally stable, precipitates and therefore dislocation pile-ups can be formed. These pile-ups are very effective stress concentrators. Local stress produced by the dislocation pile-ups may support cross slip of screw dislocations and so contribute to softening of the alloy. A higher density of precipitates in AJ91 and AX91 alloys compared with AJ51 and AJ41 alloys is the main reason for higher values of the CYS/TYS observed at lower temperatures. On the other hand, the precipitates (significant stress concentrators) may make easier climb of dislocations at elevated temperatures. Higher mobility of dislocations in prismatic and pyramidal slip planes at elevated temperatures increases the probability of dislocation reactions between <c+a> dislocations leading to dynamic recovery in a hcp structure.

Influence of solute atoms on activation volume
While the internal stress is strongly influenced with the content of solute atoms, the effective stress was-up to 100 °C-not affected by solute atoms (in the case of AJxy and AXxy alloys). The observed increase of the effective stress at higher temperatures is not surprising; the thermally activated process at higher temperatures is complex. Solute atoms (or their small clusters) are considered as typical local obstacles for moving dislocations. In high-temperature regime, diffusion-controlled glide should be taken into account.  The values of the activation volume, V, were estimated in the stress relaxation experiments using equation (6). As usual, the values of the activation volume divided by b 3 for samples of AJ51 and AJ91 alloys deformed in tension as well as compression are plotted against the effective stress σ* for all testing temperatures in Figs 42-43 for tension (empty characters) and compression (full characters) deformation. The same analysis was performed for AX41 and AX91 alloys as it can be seen in Figs. [45][46][47]. Plotting values of V against the effective stress for both AJ alloys into one diagram (Fig. 44) and those for both AX alloys in Fig. 47 shows that the activation volumes decrease with the effective stress and all the values lie on one line -"master curve". Kocks et al. [25] suggested an empirical equation between Gibbs free energy ΔG and the effective stress σ* in the following form: where Δ G 0 and σ 0 * are Gibbs energy and the effective stress at 0 K. For the effective stress it follows: where p and q are phenomenological parameters reflecting the shape of a resistance obstacle profile. The possible ranges of values p and q are limited by the conditions 0 < p≤ 1 and 1 ≤ q≤ 2. Ono [26], suggested that Equation (12) with p=1/2, q=3/2 describes a barrier shape profile that fits many predicted barrier shapes. Thermodynamics generally defines the activation volume as Equation (13) can be rewritten as The values of the activation volume should lie at the curve given by the equation (14). Results showing all values of the activation volumes being the same for alloys of AJ as well as AX series indicate that the thermal activation is not affected by various concentrations of solute atoms. It may be concluded that the thermally activated process(-es) is(are) determined with the dislocation motion and the solute atom role is less important. The values of the activation volume may help to identify thermally activated processes considering some of the common short−range barriers to dislocation motion [27]. The dislocation-dislocation interaction mechanism has an activation volume ranging from about 10 2 -10 4 b 3 , with the activation volume and enthalpy varying with strain. Couret and Caillard [28,29] studied prismatic slip in magnesium in a wide temperature range using in situ experiments in TEM. They have reported that screw dislocations with the Burgers vector 1 / 3 112 0 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 those screw dislocation segments. A single controlling mechanism was identified as the Friedel−Escaig cross slip mechanism. This mechanism assumes dissociated dislocations on compact planes, like (0001), that joint together along a critical length L r producing double kinks on non-compact planes. The activation volume is proportional to the critical length between two kinks. Amadieh et al. [30] found for the activation volume of the Friedel−Escaig mechanism a value of 70 b 3 . Prismatic slip was also observed by Koike and Ohyama [31] in deformed AZ61 sheets. The activation of prismatic slip and subsequent annihilation of dislocation segments with opposite sign are probably the main reason for the observed internal stress decrease. The double cross slip may be a thermally activated process controlling the dislocation velocity. Beside this mechanism, the thermally activated glide of <c+a> dislocations should be taken into account. Mathis et al. [32] investigated the evolution of non−basal dislocations as a function of temperature in magnesium by X−ray diffraction. They found a majority of <a> dislocations in the as−cast state. During plastic deformation in tension the <a>−type dislocations remain dominant, however, the dislocation density increased by about a factor of three up to about 100 °C. At higher temperatures the fraction of <c+a>−type dislocations increased at the cost of <a>−type dislocations and the increase of the dislocation density is strongly reduced. The internal stress acting on dislocations is determined by the details of the internal structure at that moment and it is independent of the applied stress. The stress that changes when the applied stress is changed is only the effective stress. The internal stresses during plastic deformation of the alloys investigated here can be considered as the sum of stresses resulting from various dislocation arrangements and obstacles existing in the deformed material [33,34]. At higher temperatures the solute atoms may diffuse to stacking fault and may influence double cross slip from basal to non-basal planes.

Dynamic strain ageing (DSA) in magnesium alloys
Plastic deformation of alloys exhibits many phenomena associated with solute strengthening. When solute atoms can move (they may diffuse) during plastic deformation the microstructure of the deformed alloy is unstable. This microstructure instability is due to solute atoms diffusion towards to moving dislocations-the dynamic strain ageing (DSA) effect. The segregation of solute atoms at dislocations results in many phenomena: • positive or non-monotonous dependence of the flow stress on temperature, • negative strain rate sensitivity in a certain temperature range, • post relaxation effect, • local maximum in the temperature dependence of the activation volume or stress sensitivity parameter, • the Portevin-Le Châtelier effect.
Magnesium alloys exhibit dynamic strain ageing effects at relatively low temperatures. Portevin-Le Châtelier effect (PLC) was observed during plastic deformation of some Mg alloys [35][36][37][38][39]. The unstable microstructure of an alloy can influence the deformation behaviour of the alloy. It should be mentioned that room temperature is high enough to help invoking strain ageing processes in magnesium alloys.

Portevin-Le Châtelier effect
The Portevin-Le Châtelier (PLC) effect is a consequence of a complicated nature of the dislocation dynamics in metals, which depends on many structural parameters as the type of structure, grain size, texture, concentration and distribution of solute atoms. Plastic deformation occurs inhomogeneously on the microscopic scale due to thermally activated dislocation motion through a field of obstacles. Deformation inhomogeneities in time and space, observed experimentally, are caused by collective dislocation motion. These phenomena of unstable plastic deformation are associated with the sharp localised deformation bands. Three types of PLC bands have been found. The continuously propagating type A, intermittently propagating type B with regular stress drops and stochastically nucleating type C. Figure 48 shows a representative microstructure of the undeformed Mg+0.7wt.%Nd sample after T6 temper (homogenisation at 525 °C for 5h, then quenching into water 65 °C warm with subsequent precipitation treating for 8 h at 204 °C). The true stress-true strain curves obtained at various temperatures are presented in Fig. 49 for tension and in Fig. 50 for compression tests. It can be seen a discontinuous character of curves obtained at elevated temperatures. Serrated yielding was observed at temperatures from 200°C to 300 °C in tension and from 200 °C to 250 °C in compression. In compression tests the deformation at 300 °C was already smooth. While the shape of the serrations obtained in tension has character A, serrations found in compression have another shape, which is more of type B. PLC effect was also observed in an AZ91 (Mg-9Al-1Zn) alloy after thermal treatment T4 (homogenisation at 413 °C for 18 h, then quenching into water of ambient temperature). Tensile and compression tests were performed over a wide temperature range from 14 to 100°C at an initial strain rate ranged in the 10 -4 s -1 . The temperature dependence of the yield stress of Mg+0.7Nd exhibits a local maximum -a stress-hump (Fig. 51). of Mg-Nd alloy after T6 temper.
ratures are presented in Fig. 49 for tension and in Fig. 50 for compression obtained at elevated temperatures. Serrated yielding was observed at 00 °C to 250 °C in compression. In compression tests the deformation at ons obtained in tension has character A, serrations found in compression as also observed in an AZ91 (Mg-9Al-1Zn) alloy after thermal treatment into water of ambient temperature). Tensile and compression tests were 00 °C at an initial strain rate ranged in the 10 -4 s -1 . The temperature l maximum -a stress-hump (Fig. 51).  The stress-strain curve of AZ91 alloy obtained in tension at 21 °C is given in Fig. 52 together with the strain dependence of the strain hardening rateθ=dσ/dε. Serrations on stress-strain curves were observed at temperatures from room temperature up to 100 °C, the stress-strain curve obtained at temperature 150 °C exhibited no serrations; it was smooth. Similar experiments were performed in compression at an approximately same strain rate at temperatures from 15 to 100 °C. Character of serrations in compression is different in comparison with the tension tests as it is obvious from Fig.53. The stepwise character of curves indicates sudden elongation of the sample during the compression test.  Lavrentev [40] have reported an important role of the dislocation forest in hcp structures with the main basal slip. Forest dislocations, which density was increased by prior movement of dislocation avalanche, are local obstacles for moving dislocations. Cores of dislocations waiting at forest dislocations during thermally activated motion in the slip plane may be occupied by solutes, which are movable due to pipe diffusion. These smaller dislocation groups of waiting dislocations are probably spread over a set of adjacent slip planes, rather than being strictly coplanar. They produce local stress concentrations, which may be a release pulse for breakaway of dislocation pile ups. Precursor behaviour of the local strain associated with local stress relaxation prior to the strain avalanche may be characterised by the stress drop. This type of unstable flow is characteristic of the PLC flow, in which a drop in the load is possible if the strain rate during the formation of the slip bands exceeds the strain rate imposed by the tensile testing machine. A high level of the internal stress allow pass of these deformation bands through the whole sample. As each PLC band runs through the gauge length, the formation of new forest dislocations ensures that the process repeats itself. As the dislocation movement in the slip bands ceases or becomes too slow for the applied strain rate, for instance after a drop in the load or at the end of a PLC band, the applied stress must increase in order to resume deformation. Activation of new sources can only occurs by cutting through the forest dislocations created by secondary slip around slip bands no longer active. The forest dislocations increase the critical resolved shear stress for dislocation motion, but provide little strain hardening. If the activation of a source occurs under conditions of stable planar glide, dislocations can form a dynamic pile up able to move at increasing speed and decreasing levels of the applied stress because of the development of stress concentration ahead of the moving dislocations. This may spontaneously lead to an avalanche of dislocations that meets the general requirement for unstable tensile flow, since a drop in the load, as observed during the PLC effect, is possible only if the strain rate during the formation of the slip bands exceeds the strain rate imposed by the tensile testing machine. An additional factor is the following: as dislocations pile up in front of obstacles, the average dislocation velocity in the glide plane becomes very low so that moving solute atoms may diffuse towards the dislocations and pin them down.

Other manifestations of the dynamic strain ageing
The temperature dependence of the yield stress, σ 02 , of Mg+0.7Nd alloy deformed in tension and compression (Fig. 51) shows that the course of the temperature dependence is nonmonotonous. A local maximum in the temperature dependence of the yield stress obtained in compression and tension is observed in a temperature range of 150 -250 °C.
Similar local minimum has been observed in the temperature dependence of the yield stress, σ 02 , and the maximum compressive stress, σ max , of ZE41 (Mg-4Zn-1RE) magnesium alloy as it can be seem in Fig. 54. While the local maximum in the temperature dependence is observed in alloys containing rare earths in the temperature interval 150-250 °C, alloys containing Al exhibit this local maximum between room temperature and 100 °C. This is demonstrated in Figs. 55 and 56 for AZ63 (Mg-6Al-3Zn) and AJ51 (Mg-5Al-0.6Sr), respectively. The strain rate dependence of the yield stress of Mg+0.7Nd alloy deformed in tension at 250 °C is presented Similar local minimum has been observed in the temperature dependence o stress, σ max , of ZE41 (Mg-4Zn-1RE) magnesium alloy as it can be seem in dependence is observed in alloys containing rare earths in the temperature int maximum between room temperature and 100 °C. This is demonstrated in F 5Al-0.6Sr), respectively. The strain rate dependence of the yield stress of Mg in Fig.57. Negative strain rate sensitivity was found for three strain rates from the yield stress of ZE41 alloy deformed at three temperatures is given in Fig. an anomalous course. The yield stress usually increases with increasing str lower strain rates. At strain rates higher than 10 -4 s -1 , the yield stress decrease the yield stress is practically independent of the strain rate. Again, the results that the values of the yield stress at 100 ºC are lower than those at 150 ºC at the stress strain curves of AZ91 alloy deformed at room temperature and tw mentioned that the curves are not shifted; accordingly the negative strain rate  in Fig.57. Negative strain rate sensitivity was found for three strain rates from 5.5x10 -5 to 5.5x10 -4 s -1 . The strain rate dependence of the yield stress of ZE41 alloy deformed at three temperatures is given in Fig. 58. It can be seen that the strain rate dependences have an anomalous course. The yield stress usually increases with increasing strain rate. In this case, the yield stress increases only at lower strain rates. At strain rates higher than 10 -4 s -1 , the yield stress decreases with increasing strain rate at 50 and 150 ºC. At 100 ºC the yield stress is practically independent of the strain rate. Again, the results indicate some dynamic strain ageing. It is also obvious that the values of the yield stress at 100 ºC are lower than those at 150 ºC at all imposed strain rates. Examples of short sequences of the stress strain curves of AZ91 alloy deformed at room temperature and two various strain rates are shown in Fig.59. It should be mentioned that the curves are not shifted; accordingly the negative strain rate sensitivity is obvious.
yield and maximum stresses of ZE41 alloy yield stress of AZ63 allo Similar local minimum has been observed in the temperature dependen stress, σ max , of ZE41 (Mg-4Zn-1RE) magnesium alloy as it can be seem dependence is observed in alloys containing rare earths in the temperatur maximum between room temperature and 100 °C. This is demonstrated 5Al-0.6Sr), respectively. The strain rate dependence of the yield stress of in Fig.57. Negative strain rate sensitivity was found for three strain rates the yield stress of ZE41 alloy deformed at three temperatures is given in an anomalous course. The yield stress usually increases with increasing lower strain rates. At strain rates higher than 10 -4 s -1 , the yield stress decr the yield stress is practically independent of the strain rate. Again, the re that the values of the yield stress at 100 ºC are lower than those at 150 ºC the stress strain curves of AZ91 alloy deformed at room temperature an mentioned that the curves are not shifted; accordingly the negative strain  al minimum has been observed in the temperature dependence of the yield stress, σ 02 , and the maximum c x , of ZE41 (Mg-4Zn-1RE) magnesium alloy as it can be seem in Fig. 54. While the local maximum in the e is observed in alloys containing rare earths in the temperature interval 150-250 °C, alloys containing Al exhib between room temperature and 100 °C. This is demonstrated in Figs. 55 and 56 for AZ63 (Mg-6Al-3Zn) and , respectively. The strain rate dependence of the yield stress of Mg+0.7Nd alloy deformed in tension at 250 °C egative strain rate sensitivity was found for three strain rates from 5.5x10 -5 to 5.5x10 -4 s -1 . The strain rate de ress of ZE41 alloy deformed at three temperatures is given in Fig. 58. It can be seen that the strain rate depen ous course. The yield stress usually increases with increasing strain rate. In this case, the yield stress incre n rates. At strain rates higher than 10 -4 s -1 , the yield stress decreases with increasing strain rate at 50 and 150 °C ress is practically independent of the strain rate. Again, the results indicate some dynamic strain ageing. It is a lues of the yield stress at 100 ºC are lower than those at 150 ºC at all imposed strain rates. Examples of short s train curves of AZ91 alloy deformed at room temperature and two various strain rates are shown in Fig.59. that the curves are not shifted; accordingly the negative strain rate sensitivity is obvious.  Very effective tool for studying of strain ageing phenomena are the stress relaxation tests. The SR curves are usually analysed assuming that the mobile dislocation density ρ m and internal stress σ i are constant during the SR test. An unstable structure, changes in the mobile dislocation density and/or in the internal stress, may influence the course of the SR. In some SR tests, we observed a post relaxation effect. The flow stress at the beginning of deformation after stress relaxation σ 1 was higher (or lower) than the stress at the beginning of the stress relaxation σ(0  Solute atoms become mobile with increasing temperature. During a stress relaxatio higher temperatures, the mobility of foreign atoms may be close to that of the dislo dislocations may form. The dislocations are pinned by the solutes and hence, in orde the atmospheres after stress relaxation. Macroscopically, this results in a yield poin   During a stress relaxation test, the dislocation velocity decreases, and at close to that of the dislocations. Thus, atmospheres of foreign atoms on olutes and hence, in order to restart their motion, they must be freed from is results in a yield point due to dynamic strain ageing. The stress at the stress at the beginning of the stress relaxation, which is observed AZ63 AZ91 T6 5 6 Figure 62. Temperature variation of the stress increment after SR at two starting strains of SR (AE42 alloy).
Solute atoms become mobile with increasing temperature. During a stress relaxation test, the dislocation velocity decreases, and at higher temperatures, the mobility of foreign atoms may be close to that of the dislocations. Thus, atmospheres of foreign atoms on dislocations may form. The dislocations are pinned by the solutes and hence, in order to restart their motion, they must be freed from the atmospheres after stress relaxation. Macroscopically, this results in a yield point due to dynamic strain ageing. The stress at the beginning deformation after the SR is higher than the stress at the beginning of the stress relaxation, which is observed experimentally.
Solute atoms become mobile with increasing temperature. During a stress relaxati higher temperatures, the mobility of foreign atoms may be close to that of the dis dislocations may form. The dislocations are pinned by the solutes and hence, in ord the atmospheres after stress relaxation. Macroscopically, this results in a yield poi beginning deformation after the SR is higher than the stress at the beginnin experimentally.  The flow stress, necessary for the dislocation movement, may be expressed as a sum σ = σ d + σ f , whereσ d is the dislocation component due to strong obstacles (e.g. forest dislocat friction stress due to the interaction between the solute atoms and moving disloc dislocation component of the flow stress rather than the friction stress is affected by into account the influence of solute atoms on the both flow stress components in the The local solute concentration increment, ∆c, on the dislocations can be expressed a ∆c = cc 0 = ∆c M [1 -exp(-t a /t 0 ) r ].
Here c is the local solute concentration in the dislocation core, c 0 is the nominal maximum concentration increment. The exponent r is equal 2/3 or 1/3 for bulk or p depends on the binding energy between a dislocation and a solute atom, on solute solute atoms. t 0 is inversely proportional to the diffusion coefficient in the case o Dρ f 3/2 [46], where ρ f is the density of forest dislocations.    ure. During a stress relaxation test, the dislocation velocity decreases, and at y be close to that of the dislocations. Thus, atmospheres of foreign atoms on he solutes and hence, in order to restart their motion, they must be freed from y, this results in a yield point due to dynamic strain ageing. The stress at the the stress at the beginning of the stress relaxation, which is observed train dependence of the stress t after SR at two temperatures loy). t, may be expressed as a sum of two components The first term f 1 corresponds to the dislocation-dislocation interaction influenced by dynamic strain ageing, while the second term f 2 results from the solute atoms-dislocation interaction influenced by dynamic strain ageing. X=(bΩ/ ε t 0 ). Combining the relations (16) - (18), the negative strain rate dependence of the dynamic strain-ageing component follows. This causes the negative strain rate dependence of the yield stress, which is observed at certain temperatures and in a certain strain rate range. The negative slope in the strain rate dependence of the yield stress was also observed in Mg+0.7Nd alloy deformed at room temperature (Fig. 57). The observed decrease in the flow stress (negative values of Δσ) due to changes from a lower strain rate to a higher one is also the result of dynamic strain ageing.
Solute atoms locking dislocations cause the observed stress increase after stress relaxation, which depends on strain and on temperature. An increase in the flow stress is needed to move the dislocations after the stress relaxation. It is reasonable to assume that Δσ is proportional to the number of impurities on the dislocation line. The density of dislocations increases with strain, while the concentration of solute atoms is constant. Thus, the stress increase, Δσ, after relaxation due to dynamic strain ageing should decreases with strain, which is observed. The value of Ω decreases with strain [44,45] and hence, t w also decreases. This leads to the observed decrease in Δσ. It should be mentioned that the post relaxation behaviour and the values of Δσ depend also on the time of relaxation [47].