Influence of Al addition on CYS and MCS of Mg4Li, Mg8Li and Mg12Li 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.
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.
2. 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 on (0001) basal plane is the easiest slip mechanism; often called basal slip of <
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, σ1 is a constant describing interaction between dislocations, b is the Burgers vector of dislocations and ρt 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 for a single thermally activated process can be expressed as:
where 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−σi and the simple form is
Here ΔG0 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 σ0 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 =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 and then σ(t) can be expressed according to  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=k
3. Mg-Li-Al (LAxy) alloys
3.1. 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
3.2. 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), σ02, was estimated as the flow stress at 0.2% offset strain. The ultimate compression strength (MCS), σmax, 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, σ02, as well as the MCS (σmax) 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
It is well known that the dominant slip system in Mg and
3.3. 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
3.4. 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 , 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.
The temperature variations of both CYS and MCS are shown for LA123 and LA125 alloys in Figs. 15 and 16, respectively. The CYS is significantly higher for the alloy containing 5% of Al, while MCS exhibits higher values for the LA123 alloy. Thermal stability is higher in the case of LA125 alloy. The influence of Al on the mechanical characteristics of Mg-Li alloys at two temperatures is summarised in Table 1.
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
4. Mg-Al-Sr (AJxy) alloys
4.1. 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  reported that Mg-Al-Sr alloys show different microstructures based on the Sr/Al ratio. For Sr/Al ratio below about 0.3, only Al4Sr 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 Mg17Al12 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. The
4.2. 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 . It is likely caused by a dynamic age hardening.
The true stress-true strain curves estimated for AJ91 alloy in compression are presented in Fig. 24. The values of the CYS and TYS (Figs. 25 and 26) are higher than the yield stress of the mostly used cast alloy AZ91. The temperature variations of MCS and MTS are shown in Figs. 25 and 26. Ductility of AJ91 alloy deformed in tension is low, at ambient temperature only several percent. Thermal stability is in comparison with AZ91 alloy also better; the CYS as well as TYS do not decrease with increasing test temperature up to 200 °C below 100 MPa. It is done by the thermal stability of Al4Sr precipitates. Solid solution hardening plays in this case only minor role.
4.3. 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 (σi, σ*) may be estimated using Li’s method . The SR curves are fitted to the power law function in the form:
where a, t0 and m are fitting parameters. The influence of solute atoms on both stress components of AJ51 and AJ91 is obvious from Figs 27-29; 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.
5. Mg-Al-Ca (AXxy) alloys
5.1. 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 Mg2Ca and Al2Ca were detected. They may contribute to a considerable increase in hardness and the yield stress . For the ratio below 0.8 only Al2Ca Laves phase (C15-cubic) was observed to have been formed. Both types of precipitates were observed to form along the grain boundaries . Gjestland et al.  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.  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. . They estimated that the small amount of Ca increased the thermal stability of Mg17Al12 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
5.2. 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.
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.
5.3. Stress components in the AX alloys
The applied stress components, σi, and, σ*, for AX41 and AX91 alloys were estimated at three temperatures in compression (see Figs. 39-41). 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, σi is proportional to ρ1/2 where ρ is the density of dislocations. The internal stress, σi, 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
The resulting sessile
Twins are another type of obstacles. Twinning plays an important role in plastic deformation of
A combination of two glissile<
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 <
6. 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 b3 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. 45-47. 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.  suggested an empirical equation between Gibbs free energy ΔG and the effective stress σ* in the following form:
where Δ G0 and 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 , 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 . The dislocation–dislocation interaction mechanism has an activation volume ranging from about 102–104 b3, 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 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
7. 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 [35-39]. 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.
7.1. 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).
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  have reported an important role of the dislocation forest in
7.2. Other manifestations of the dynamic strain ageing
The temperature dependence of the yield stress, σ02, of Mg+0.7Nd alloy deformed in tension and compression (Fig. 51) shows that the course of the temperature dependence is non-monotonous. 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, σ02, and the maximum compressive stress, σmax, 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 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.
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 ρm and internal stress σi 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
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.
The flow stress, necessary for the dislocation movement, may be expressed as a sum of two components
The mean ageing time
If we consider that both the dislocation stress component and the friction stress are influenced by solutes, then the flow stress may be decomposed into a non-aged part
The first term
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 Δ
|σ, ε true stress, true strain;||LA40 Mg-4wt%Li|
|σi, internal (athermal) stress;||LA43 Mg-4wt%Li-3wt%Al|
|σ* effective (thermal) stress;||LA45 Mg-4wt%Li-5wt%Al|
|σf friction stress;||LA80 Mg-8wt%Li|
|σd dislocation stress;||LA83 Mg8wt%-Li-3wt%-Al|
|ΔG Gibbs free enthalpy;||LA85 Mg-8wt%Li-5wt%Al|
|V activation volume;||LA120 Mg-12wt%Li|
|plastic strain rate||LA123 Mg-12wt%Li-3wt%Al|
|b Burgers vector of dislocations||LA125 Mg-12wt%Li-5wt%Al|
|ρm mobile dislocation density||AJ51 Mg-5wt%Al-0.6wt%Sr|
|ρt total dislocation density||AJ91 Mg-9wt%Al-1wt%Sr|
|k Boltzmann constant||AJ62 Mg-6wt%Al-2wt%Sr|
|c atomic concentration of solute atoms||AX41 Mg-4wt%Al-1wt%Ca|
|CRSS critical resolved shear stress (τ0)||AX62 Mg-6wt%Al-2wt%Ca|
|CYS compression yield stress (σ02)||AX91 Mg-9wt%Al-1wt%Ca|
|MCS maximum compression strength (σmax)||AZ63 Mg-6wt%Al-3wt%Zn|
|TYS tensile yield stress (σ02)||AZ91 Mg-9wt%Al-1wt.%Zn|
|MTS maximum tensile strength (σmax)||AE42 Mg-4wt%Al-2wt%RE|
|SR stress relaxation||ZE41 Mg-4wt%Zn-1wt%RE|
|SEM scanning electron micrograph||QE22 Mg-2wt%Ag-2wt%RE|
Z.T. and P.L. are grateful for the financial support of the Czech Science Foundation (project P204/12/1360). P.P. is grateful for the financial support to the Slovak Grant Agency for Science (project VEGA No. 1/0797/12).