Towards mechanical performance paradox and behind thermo-kinetic origins of aluminum alloys with additional solutes (X = Mg, Cu and Si) from atomistic simulations
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Abstract
Dislocation glide and/or deformation twinning, which can be uniformly described as the kinetic behaviors of atoms driven by thermodynamics, play important roles in dominating mechanical performance and strength-ductility paradox of metallic alloys. In this work, the physical origins behind the mechanical performance paradox are investigated in light of thermo-kinetic synergy upon materials processing. Combining the classical dislocation theories with common strengthening mechanisms, the quantitative connections among yield strength, plastic strain and dislocation density are bridged by the driving force and energy barrier of dislocation motion. The FCC-Al and Al alloys with Mg, Cu and Si solutes are studied as typical representatives by performing molecular dynamics (MD) simulations to analyze the tensile behaviors. It turns out that the thermo-kinetic synergy is responsible for the strength-ductility exclusive behaviors. The yield strength and flow stress are enhanced with Mg, Cu and Si solutes adding in FCC-Al, due to the increased interactions between dislocations and solute atoms. All the Mg, Cu and Si solutes can benefit the mechanical responses of Al alloys. Increasing Mg content enhances the driving force and yield stress of Al-Mg alloys, but reduces the energy barrier and plastic strain. The solute Si addition can further increase the driving force and yield stress, but decrease the energy barrier and plastic strain of Al-Mg-Si alloys. Our investigation provides an innovative viewpoint for understanding the mechanical performance paradox of metallic alloys, and offers insightful guidance for designing advanced Al alloys with good mechanical performance.
Keywords
INTRODUCTION
As one of the lightweight metallic materials, aluminum (Al) alloys have widespread applications in aerospace, construction, and automotive manufacturing industries due to their outstanding performance including high specific strength, good processing formability and environmental friendliness[1-3]. For the engineering requirements of Al alloys used in the components with large thermo-mechanical loads, high strength is usually needed to ensure stability and safety, whereas, in the components with complex shapes such as architectural decorative parts, good ductility is required to satisfy the processing techniques[4-6]. However, the strength and ductility of Al alloys exhibit exclusive behaviors. This mechanical performance paradox is known as the strength enhancement generally as a sacrifice of ductility, and vice versa[7-12], which is attributed to the microstructural characteristics and deformation mechanisms. In practical applications, such as aircraft envelopes and automobile body frames, both initial yield strength and uniform elongation are important for Al alloys to withstand impact loads and avoid component breakage[5-8]. Therefore, achieving an ideal strength-ductility match becomes both scientifically significant and technologically important for the development of advanced Al alloys with good comprehensive mechanical performance, which depends on clarifying the physical origins behind the above performance paradox and breaking through the primitive trade-off correlation between strength and ductility.
During the past decades, much more efforts from both theoretical and experimental works[13-19] have been devoted to understanding the mechanical performance paradox in terms of the strengthening/toughening mechanisms and microstructure-property correlations, aiming to find the influential factors contributing to an ideal strength and ductility match by methods such as adjusting the additional solutes and/or optimizing the thermomechanical processing parameters of Al alloys[20-26]. Nevertheless, the underlying mechanism behind the above mechanical performance paradox remains an unsolved mystery, which impedes the development of higher-performing Al alloys. In general, the mechanical performance of materials can be reflected by loading the microstructure, where the interactions between dislocations and different kinds of crystalline defects (such as solutes/vacancies, atomic clusters, other different kinds of dislocations, grain/phase boundary and the second phase precipitated in the alloy system) play dominant roles in controlling the strength and ductility of Al alloys[27-32]. Plastic deformation is primarily governed by dislocation glide and deformation twinning[2,33-36], which is actually a kinetic process of atoms or atomic groups driven by thermodynamics[37,38]. Therefore, it is believed to be a pertinent viewpoint to understand the above mechanical performance paradox in light of the thermo-kinetic synergy upon materials processing. With this respect, the thermo-kinetic partition and/or generalized stability[37,39] was proposed from the connectivity and correlation between thermodynamics and kinetics for phase transition and deformation[12,18,40-44]. Its applications have been verified in the reverse austenite transition by interface movement and the plastic deformation by dislocation motion in different metals such as magnesium alloys and alloy steels[45,46]. By integrating this concept with respect to nucleation and growth processes of the microstructure formation and deformation, it is found that alloys with high strength and high ductility correspond to the large driving force and large energy barrier[12,45]. However, these previous studies are mostly qualitative descriptions with unknowing the specific values of generalized stability from relevant thermo-kinetic calculations. Thus, everlasting investigations on the thermodynamics and kinetics of dislocation behaviors are required to understand the above mechanical performance paradox in terms of establishing the quantitative strength and ductility models.
In the present work, the exclusive behaviors of strength and ductility, along with the physical origins, of FCC-Al and Al alloys are investigated from the viewpoint of thermo-kinetic synergy upon materials processing in combination with classical dislocation theories and atomistic simulations. Theoretical models for quantitative correlations between the driving force and flow stress, together with that between the plastic strain and effective energy barrier for dislocation motion, are established. The tensile behaviors and mechanical responses of FCC-Al and Al alloys with additional solutes Mg, Cu and Si are analyzed by performing molecular dynamics (MD) simulations. The generalized stability concerning the thermo-kinetic calculations on driving force and energy barrier in terms of dislocation density are obtained based on the common strengthening-toughening mechanisms of Al alloys. Accordingly, the effects of additional Mg, Cu and Si solutes on the mechanical behaviors of Al alloys are discussed for validation of the established quantitative models. Afterwards, the thermo-kinetic origins behind the strength-ductility exclusive behaviors of Al alloys are analyzed, along with the prospect of the current thermo-kinetic models applied in design higher-performing alloys.
MATERIALS AND METHODS
Thermo-kinetic description for dislocation behaviors
Following the classical dislocation theories, the effective driving force (ΔG or Δσ) for dislocation motion during irreversible deformation is regarded as the difference between the applied stress σf (or flow stress) and the glide resistance σres (usually induced by different crystalline defects including solute atoms, dislocations, grain/phase boundaries, precipitates, etc.) derived from interactions between these defects and dislocations[47-50], as given by:
In general, the dislocation glide resistance[47,51] can be expressed as:
where the exponent n varies between 1 and 2, especially n = 1 when the weak particles are dominant, and
where m is the number of solute i, ki is the temperature-dependent factor of solute i, and Ci is the mole fraction of solute i. Δσgb denotes the glide resistance contributed from grain boundaries[53], which can be estimated from:
where K is the Hall-Petch coefficient, and d is the mean grain size. Δσdis denotes the dislocation glide resistance contributed by interaction among dislocations[33], which can be evaluated from:
where M is the Taylor factor, α is the numerical factor with respect to temperature and strain rate, b is the Burgers vector, μ is the shear modulus, and ρt is the total dislocation density. Δσpre denotes the glide resistance contributed from the second phase precipitated in alloy system[54], which can be predicted from:
where F is the maximum force interacted between dislocations and precipitates, and l is the effective distance between two precipitates. In general, a large glide resistance σres in Equation (1) implies a more difficult deformation to occur, and a more contribution from thermodynamics than kinetics. This is reflected by a smaller activation volume or thermo-kinetic partition[37], which corresponds to a weaker work hardening effect.
In parallel, the effective energy barrier (Q) or activation energy for dislocation motion upon deformation can be obtained in combination with the Orowan equation and dislocation kinetics[50,55-57], as given by:
where ε is the plastic strain, v0 is the attack frequency for thermal fluctuation, ρm is the mobile dislocation density, Leff is the effective separation of dislocation slip,
Following the thermo-kinetic correlation[38], the effective energy barrier at any transient state during dislocation evolution after yielding can be obtained in light of the activation volume and stress increment, which corresponds to the activation energy in terms of the driving force variation Δσ[58,59], as expressed by:
where Q0 is the effective activation energy without applied stress driven (Δσ = 0), V* is the activation volume. Especially, the effect activation energy at the yield point is written as Equation (8a), where Qy and Δσy denotes the corresponding energy barrier and driving force, respectively. Such derivation is analogous to the simplified version for the Olson-Cohen model[49]. Following Equation (8), the activation volume is written as:
which is denoted by the ratio between energy barrier and driving force, and thus named as the thermo-kinetic partition for dislocation motion.
In principle, the dislocation nucleation is mostly initiated at the yield point upon deformation. By taking the yield point as the reference state and normalizing the numerator and denominator via Qy and Δσy in the right hand of Equation (9), there is:
For convenience, a dimensionless parameter was introduced as generalized stability Δgs[38,39] to describe the durability of dislocation motion during irreversible deformation, i.e.,
Apparently, the value of generalized stability is zero at the yield point. An increased ductility for uniform elongation or plastic deformation (with a smaller activation volume or thermo-kinetic partition) should correspond to the dislocation behaviors with continuously decreased generalized stability[37]. As such, the generalized stability and the thermo-kinetic partition, which can be used to quantitatively describe the system energy accumulation or dissipation speed of irreversible deformation, were introduced to describe the persistence of dislocation motion. In general, the dislocation evolution is accompanied by an enhanced driving force and reduced energy barrier[38], and thus consecutively reduced generalized stability, which derives from the continuously increased thermo-kinetic partition reflecting the continuously increased ductility. For any transient state during deformation, by comparing series dislocation motion processes, a higher generalized stability reflects both a lower sustainability and a more stable status that possesses greater potential to continue the uniform deformation, i.e., better ductility. The more contribution from dislocation nucleation and/or multiplication (larger ρt), the higher the driving force and/or the strength, while the more contribution from dislocation slip (larger ρm), the higher the generalized stability and/or the ductility. Thus, the generalized stability and/or thermo-kinetic partition can be used to reflect the ductility.
By considering the glide resistance from solid solution, grain boundary and dislocations in Equations (1) and (2), i.e., the dislocation-solute along with dislocation-grain boundary and dislocation-dislocation interactions, the alloy strength with respect to the driving force for dislocation motion can be obtained from:
Meanwhile, the plastic strain associated with the energy barrier for dislocation motion can be acquired from:
As such, the critical thermo-kinetic parameters including driving force and energy barrier during irreversible deformation can be obtained, with inputs being listed in Table 1. Accordingly, the underlying physical origins behind the exclusive behaviors of strength and ductility can be understood from the synergistic effects of thermodynamics and kinetics upon materials processing.
Relevant inputs for determination of the thermo-kinetic parameters for dislocation motion upon deformation of FCC-Al and Al alloys, including the Taylor factor, the Taylor hardening coefficient, the shear modulus, the Burgers vector, the solid solution constant, the gas constant, and the Hall-Petch coefficient
| Parameters | Value | Ref. |
| Taylor factor, M | 3.06 | [32,47] |
| Taylor hardening coefficient, α | 0.3 | [32,33] |
| Shear modulus of FCC-Al, µ | 27 GPa | [26] |
| Burgers vector of FCC-Al, b | 0.286 nm | [32,47] |
| Solid-solution constant of Mg, kMg | 29.0 MPa/wt.%2/3 | [52] |
| Solid-solution constant of Si, kSi | 66.3 MPa/wt.%2/3 | [52] |
| Gas constant, R | 8.314 J/(mol·K) | [98] |
| Hall-Petch coefficient, K | 0.12 MPa/m1/2 | [78] |
Computational methods
All the MD simulations herein were performed by the Large-scale Atomic/Molecular Parallel Simulator (LAMMPS) package[60]. The modified embedded atom method (MEAM) potential developed by Jelinek
The Open Visualization Tool (OVITO)[70] offers post-processing abilities to obtain snapshots at transient loading moments and to visualize the stretching configurations of the simulated alloy samples. Thus, the results obtained from MD simulations were visualized by the OVITO package to capture and trace the variations in dislocation distributions and atomic configurations by the dislocation extraction algorithm (DXA) techniques[71]. The supercell size for the MD simulations is set as 32.4 × 32.4 × 32.4 nm3, i.e., 80a ×
Figure 1. Schematic illustration for the tensile tests of (A) FCC-Al and Al-Mg alloy samples with average grain size of 22 nm, where the atoms in the structural model are described in terms of (B) the atomic type of constitutional elements, (C) the common-neighbor analysis, (D) the defects presentation, and (E) the dislocation distribution. Note that the red spheres and blue spheres in (B) represent the matrix Al atoms and solute Mg atoms, respectively. The regions with green, red, blue and light grey colors in (C) represent the FCC structure, the HCP structure, the BCC structure and the other structure (including atoms at the grain boundaries and/or interstices), respectively. The blue, pink, green, yellow, cyan, and red lines in (D) and (E) represent the <110>/2, <110>1/6, <112>1/6, <100>/3, <111>/3, and other type of dislocation, respectively.
RESULTS AND DISCUSSION
Tensile behaviors of FCC-Al and Al-based alloys
The tensile stress-strain curves of FCC-Al and its alloys were obtained to investigate the Mg, Cu and Si alloying effects on their mechanical behaviors. The results are shown in Figure 2, where insert maps present the according variations of mobile dislocation density. Specifically, the tensile curves of FCC-Al along with binary Al-0.78at.%Mg and Al-0.78at.%Cu alloys are presented in Figure 2A. It is found that the stress increases linearly with the strain at the first stage (e.g., strain < 0.04 for FCC-Al), which corresponds to the elastic deformation before the yield point. Subsequently, the tensile curves become steady at the second stage (e.g., strain within 0.04-0.10 scope for FCC-Al) corresponding to the uniform plastic deformation. The flow stress reaches a near-constant value in this stage, where the dislocation multiplication and annihilation are balanced with each other, as the evolution of dislocation distribution is reflected in Figure 3. Such variations in the tensile stress-strain curves are in agreement with that reported in previous work[72], where analogous tensile behaviors of Al alloys were observed. The addition of both Mg and Cu solutes enhances the yield strength and flow stress of Al alloys due to the increased glide resistance from the interactions between dislocations and these solute atoms in the systems. As reflected by the tensile curves in Figure 2A, the yield strength and flow stress (at strain ε = 0.1) increase to 6.25% and 11.5% for the Al-0.78at.%Cu alloy, respectively, while to 6.77% and 11.5% for the Al-0.78at.%Mg alloy in comparison with pure Al. Thus, the influences on mechanical responses of the 0.78at.%Mg solute (red curve) are more apparent than that of the 0.78at.%Cu solute (blue curve) added in FCC-Al (black curve).
Figure 2. The stress-strain curves of FCC-Al and Al alloys. (A) Tensile curves of binary Al-0.78at.%X alloy with additional Mg and Cu solutes; (B) Tensile curves of binary Al-Mg alloys with different Mg solute contents; (C) Tensile curves of ternary Al-Mg-Si alloys with different solutes Mg and Si contents. Insert map shows the corresponding variations of mobile dislocation density upon tensile deformation. The averaged values of three tests were taken for plotting the tensile curves.
Figure 3. Thermo-kinetic variations of FCC-Al and Al alloys at the yield point. The calculated values of thermodynamic driving force and kinetic energy barrier at the yield point of (A) binary Al-Mg alloys and (B) ternary Al-Mg-Si alloys with different solutes Mg and Si contents, respectively.
Figure 2B shows the tensile curves of binary Al-Mg alloys with different solute Mg contents. It is observed that the yield strength and flow stress increase gradually with the Mg solutes in FCC-Al. The tensile curves of ternary Al-Mg-Si alloys with different Mg and Si solute contents are shown in Figure 2C. Consistent with FCC-Al, Al-Mg and Al-Cu alloys, the tensile curves of the Al-Mg-Si alloys exhibit analogous variation trends, which are accompanied by the gradually increased mobile dislocation density from the yield point to the second stage. Notably, the Cu, Mg and Si solutes added in FCC-Al cause high flow stress and large mobile dislocation density. With increasing contents of Mg and Si solutes, the lattice resistance increases at the early strain stage where the dislocations are relatively scarce, accompanied by increased strength. These predicted results are in agreement with the experimental findings[73-75] that alloying Mg, Cu and Si solutes with FCC-Al can strengthen the Al alloys. The resistance of dislocation motion is enhanced via the increased interactions between dislocations and these solute Mg, Cu and Si atoms added in FCC-Al.
Note that an apparent problem on the tensile behaviors determined from the MD simulations is the over-prediction for flow stress by a larger factor than that from experimental results[76]. Such distinctions are attributed primarily to the following reasons. (i) The strain rate: the mechanical behaviors as reflected by yield strength and/or flow stress of metallic alloy is sensitive to strain rate, and in general, a higher strain rate condition corresponds to a larger flow stress[77]. The tensile tests in practical cases are usually performed at quasi-static conditions with an initial strain rate of 10-4-10-3 s-1[45], which is several orders of magnitude smaller than that (e.g., 108-109 s-1) used in the MD simulations. The high strain rate of 1 × 108 s-1 used in the present MD simulations results in the predicted flow stress of Al alloys higher than experimental values. (ii) The grain size: the MD simulations mostly focus on the nanocrystals, while the grain size of Al alloys is usually at the micrometer scale in practical situations[76,78]. For instance, the mean grain size for the present MD simulations is set as ~22 nm, which is considerably smaller than the measured grain size of Al alloys at micrometer scale in experiments, e.g., 1.07-150 μm reported in the literature[45,79]. Following the Hall-Petch correlation, such distinctions in grain size lead to the predicted stress higher than the experimental value. With this respect, it was reported that the strength from grain boundary is generally negligible, and for medium-to-high strength alloys, the grain boundary strengthening is swamped by other strengthening modes[80], unless ultra-high cooling rates result in the nano-size grains[81]. (iii) The initial dislocations: there are initial dislocations mostly in practical alloy systems. The yielding is governed by multiplication of the existing dislocations in practical cases, which needs a smaller stress than that of the ideal crystals without initial dislocations in the present MD simulations.
Thermo-kinetic variations upon tensile deformation
Based on Equations (12) and (13) introduced in terms of thermo-kinetic synergy, the driving force and energy barrier for dislocation motion upon deformation of FCC-Al and Al alloys were obtained. Figure 3 shows the variation of driving force and energy barrier for dislocation motion of FCC-Al and Al alloys at the yielding point. Specifically, the thermo-kinetic variation in binary Al-Mg alloys with respect to different Mg contents is presented in Figure 3A, while that in ternary Al-Mg-Si alloys with respect to different contents of Mg and Si solutes in Figure 3B. It is observed that the increase of thermodynamic driving force is accompanied by the decrease of the kinetic energy barrier for dislocation motion. Such intrinsic thermo-kinetic trade-off correlations are exhibited in both binary Al-Mg alloys and ternary Al-Mg-Si alloys. At the yield point, the driving force is enhanced but the energy barrier is reduced with increasing contents of Mg and Si solutes in FCC-Al. For example, the driving force (energy barrier) for dislocation motion at the yield point enhances (reduces) from 0.15 GPa (6.39 kJ/mol) for FCC-Al to 0.52 GPa (6.25 kJ/mol) for Al-0.78at.%Mg alloy and to 0.83 GPa (4.93 kJ/mol) for Al-1.56at.%Mg alloys. Further addition of 0.78at.%Si in Al-Mg alloys enhances (reduces) the driving force to 0.85 GPa (6.21 kJ/mol) for Al-0.78Mg-0.78Si alloy and to 0.98 GPa (6.17 kJ/mol) for Al-1.56Mg-0.78Si alloys.
The irreversible deformation governed by dislocation behaviors corresponds to a process featured by the enhanced driving force and reduced energy barrier from the yielding to the necking point[38]. From the MD simulations, the dislocation nucleation and slip at the yield point induces abrupt reorientation of the crystal lattice caused by strain, along with the enhanced flow stress and driving force for dislocation motion in FCC-Al and Al alloys. After yielding, the mobile dislocation density increases with dislocation propagation in the alloy systems, resulting in an increased energy barrier. Such a phenomenon was also observed in previous MD simulations on the deformation of tantalum crystals[76]. In addition, the yield point is postponed with the Mg, Cu and Si solutes added in FCC-Al. For instance, the strain at the yield point was delayed from 0.054 for FCC-Al to 0.06 for Al-0.78Mg alloys and to 0.09 for Al-0.78Cu alloys. The addition of 0.78at.%Si in the Al-Mg alloys can further postpone the yield point to 0.068 for Al-0.78Mg-0.78Si alloy and to 0.064 for Al-1.56Mg-0.78Si alloy. With increasing contents of Mg and Si solutes, the driving force at the yield point enhances, while the energy barrier reduces. This confirms the trade-off correlation between the driving force and energy barrier for dislocation motion in these Al alloys. The underlying reason is attributed to the Mg and Si solutes restricting the mobile dislocations in the α-Al matrix, which induces enhancement of external stress to overcome the increased glide resistance with respect to the reduced mobile dislocations in the alloy systems.
Such thermo-kinetic variations are in accordance with the experimental findings[74,75], where the additional solutes resulting in the hardening effects correspond to an enhanced driving force for dislocation motion, while the exhaustion and/or trapping of mobile dislocations induces the decreased mobile dislocations in terms of the reduced energy barrier. This signifies the trade-off correlation between thermodynamic driving force and kinetic energy barrier for dislocation motion of Al-based alloys. In general, a larger dislocation motion velocity and total dislocation density are related to a small mobile dislocation density due to an enough high rate for dislocation exhaustion. The simultaneous increase of total dislocation density and decrease of mobile dislocation density corresponds to an enhanced driving force and reduced energy barrier for dislocation motion. Thus, the work hardening stage requires continuously enhanced applied stress, which favors dislocation nucleation rather than dislocation glide, as reflected by the high strength but low ductility.
Thermo-kinetic origins behind the mechanical performances paradox
According to the above thermo-kinetic analysis, the generalized stability of FCC-Al and Al alloys is obtained to estimate the dynamic stability during plastic deformation. Figure 4 shows stress at the yield point and generalized stability at the strain point of 0.1 for FCC-Al and Al alloys with different solutes X = Mg, Cu and Si. The predicted stress of 1.92 GPa at the yield point for FCC-Al agrees with that of
Figure 4. Yield stress and generalized stability upon tensile deformation of the FCC-Al and Al alloys. The stress at yield point and the generalized stability at strain of ε = 0.1 derived from the driving force and energy barrier for dislocation motion during tensile deformation of (A) binary Al-Mg alloys with different Mg solute contents and (B) ternary Al-Mg-Si alloys with different solutes Mg and Si contents, respectively. Note that the results calculated in this work are denoted by the solid point and the value referred from the literature[82] by the hollow point.
With increasing contents of Mg solute in FCC-Al, the increased yield stress of Al-Mg alloys is accompanied by decreased generalized stability. For example, with Mg solute rising from 0.78at.% to 1.56at.%, the yield stress of the Al-Mg alloys grows from 2.05 to 2.13 GPa, while the generalized stability (at ε = 0.1) decreases from 0.71 to 0.54. Further addition of 0.78at.%Si solute enhances (reduces) the yield stress (generalized stability) to 2.14 GPa (0.43) for Al-0.78Mg-0.78Si alloys. The addition of 0.78at.%Mg in Al-0.78Mg-0.78Si alloys further enhances the yield stress to 2.17 GPa but decreases the generalized stability to 0.39 for Al-1.56Mg-0.78Si alloys. Specifically, the generalized stability increases from 0 at the yield point to 0.99 at the strain point of ε = 0.1 for FCC-Al. At the same strain point, the Al alloy (X = Mg, Cu and Si) systems show more stable states and easier to sustain more continuous dislocation evolution than the FCC-Al. Within the same strain scope (e.g., 0.05-0.1), the FCC-Al possesses lower flow stress and higher generalized stability in comparison with the Al alloys with Mg, Cu and Si solutes studied in the present work.
Apparently, an increased strain during irreversible deformation corresponds to a more sustainable process of dislocation evolution, which favors lower dynamic stability. Although different trends of generalized stability vary between experiments and MD simulations, the tensile behaviors are uniform as the low flow stress is accompanied by small generalized stability. In this context, the present work explains the experimental results[73-75,85,86] that alloying Cu, Mg and Si solutes with FCC-Al improves the strength and ductility of the according Al alloys. With this respect, Lee et al. experimentally found that adding small amounts of Mg solutes in FCC-Al results in Al-Mg alloys with both high strength and large ductility compared with pure Al[85]. The underlying mechanism can further be understood from variations in the SFE[87,88]. The first-principle calculations on composition-dependent three-dimensional misfit potentials[36] indicated the addition of Mg, Cu and Si solutes can decrease the intrinsic SFE values of Al alloys. In principle, the magnitude of SFE values determines the ease with the cross-slip of screw dislocations that occurs in Al alloys[89]. The reduced SFE can promote grain refinement and restrict dynamic recovery, favoring the formation of high-density stacking faults[85,90], which are beneficial to both strength and ductility. Due to the large SFE of FCC Al (~119.6 mJ/m2), the partial dislocations that move under shear stress can easily recombine to form the full dislocations, facilitating the cross-slip of dislocations[36]. The SFE is reduced by increasing the Mg solute in FCC-Al[36], suggesting that the solute Mg in FCC Al makes the cross-slip more difficult to occur. The tangled dislocation structure leads to work hardening of the deformed region and the dispersion of deformation to the neighboring regions, thus reducing the strain localization degree and promoting spread-out deformation[85]. Thus, the Mg solute in FCC-Al can accommodate plastic strain via the dispersion of deformation in the alloy. Due to the lower SFE of Al-Mg alloys than that of FCC-Al, the partial dislocations can be widely spaced in Al-Mg alloys with increasing Mg contents. Consequently, the recombination of partial dislocations becomes more difficult, restricting the occurrence of dislocation cross-slip. These dislocations tend to move along the slip planes and form tangled dislocations along with dislocation band structure, which enhances the dislocation storage capacity and improves the strain-hardening effects[85]. The according manifestation is a high work hardening degree during plastic flow and reduced tendency for strain localization, which results in the high-strength Al-Mg alloys also exhibiting good ductility.
The distribution and evolution of mobile dislocations in the Al alloys with different solutes Mg and Si contents is shown in Figure 5, where the different lines represent multiple types of dislocations, including the <110>/2, <112>/6, and other dislocations marked by blue, green and red lines, respectively. The results indicate that the dislocations in alloy systems are initially activated at the yield point. With deformation proceedings, the dislocation behaviors become complex, which are accompanied by dislocation entanglement and dislocation reactions such as dislocation decomposition or synthesis. The interactions between these solutes and dislocations raise the complexity of irreversible deformation due to increased Mg and Si solutes in the alloy systems, which exert influences on the competition between dislocation storage and dislocation annihilation. As reflected in Figure 5B(i)-D(i), the full dislocation (denoted by the blue lines) with Burgers vector of <110>/2 is decomposed into two partial dislocations (denoted by the green lines) with Burgers vector of <112>/6, or the reverse dislocation reaction occurs during the irreversible deformation. The result is consistent with that predicted from the classical Peierls-Nabarro model for the FCC-Al and Al-based alloys[36,91].
Figure 5. Dislocation arrangement and evolution of Al alloys with additional Mg and Si solutes. Snapshots of the mobile dislocation distribution of [A(i)-D(i)] the Al-1.17Mg alloy, [A(ii)-D(ii)] the Al-1.56Mg alloy, and [A(iii)-D(iii)] the Al-0.78Mg-0.78Si alloy at different magnitudes of strain during tensile deformation, respectively.
Such dislocation reactions and defects interactions can generate sources for mobile dislocations, while the dislocation exhaustion occurs after the mobile dislocations move over a mean-free path. Due to distinctions in dislocation structure, formation energetics and immobility, the different types of dislocations and their interactions contribute differently to the strain-hardening effects[92]. The varied degree of Shockley partial dislocations (the green line shown in Figure 5) in these Al alloys with respect to their SFE exert different influences on the mechanical behaviors. Besides, more dislocation nucleation is associated with higher driving force for dislocation motion and faster rate for dislocation evolution. In this context, initiating new dislocation is more difficult than the primitive one, resulting in the small generalized stability and/or thermo-kinetic partition. The primary dislocations in Al-Mg and Al-Mg-Si alloys upon irreversible deformation are the Shockley partial dislocations represented by the green lines in Figure 5. This indicates that the deformation is dominated by partial dislocations of these Al alloys, which agrees well with the previous results[91,93].
Prospect of current thermo-kinetic models in designing higher-performing alloys
It is worth noting that the present work focuses on dilute alloys, where the solute contents are lower than the maximum solid solubility[36,94]. Once the amount of additional solutes in the α-Al matrix is over the maximum solubility, precipitation will occur and different kinds of precipitates will form in Al alloys. For instance, when the solutes Mg and Si contents are over their maximum solubility, the precipitates including the solute clusters, β’ and β’’ phases will form in the Al-Mg-Si alloys[45,95]. These precipitates exert interactions with dislocations in the alloy system, thus influencing the mechanical properties of the Al alloys. Within the present framework, the mechanical properties of these precipitation-strengthened Al alloys can be predicted via the theoretical models developed on the basis of the thermo-kinetic synergistic effects in Section “Materials and Methods”. The precipitates and the interactions between dislocations and precipitates affect the dislocation evolution (i.e., the total dislocation density ρt and the mobile dislocation density ρm) upon deformation. These exert direct influences on the glide resistance and the effective separation of dislocation slip, which is finally reflected in the variations of thermo-kinetic partition and generalized stability.
Upon deformation, the system energy accumulated by dislocation nucleation is mostly dissipated by dislocation motion. In principle, a more sustainable work hardening (or work softening) stage can be obtained by adjusting a slower speed for system energy accumulation (or dissipation)[96,97]. As such, the variation in activation volume or thermo-kinetic partition for microstructure deformation derives from that for microstructure formation in terms of phase transition. Hence, acquiring an ideal deformation mode by designing the activation volume or thermo-kinetic partition in terms of alloy composition and processing parameters becomes the central point to obtain an ideal match between strength and ductility of Al alloys. With a sufficiently sustainable process of dislocation motion, the primitive thermo-kinetic partition can be changed to obtain a more persistent work hardening process, which requires high applied stress as the driving force for dislocation evolution. Thus, the mechanical performance paradox with respect to a primitive work hardening mode[79-81] can be modified in terms of an enhanced activation volume or thermo-kinetic partition, which corresponds to an ideal thermo-kinetic synergy, as schematically illustrated in Figure 6. Therefore, the critical point for designing an ideal strength-ductility match lies in obtaining a high strain hardening capability by making the dislocation initiation more difficult to occur and the propagation of dislocation more persistent. As such, following the thermo-kinetic synergy upon materials processing, the prediction for mechanical performances directly from composition/processing and the inverse design for composition/processing of advanced Al-based alloys with good comprehensive mechanical performance can be achieved. Our continuous investigations in this direction are still underway, the results of which will be reported in the near future.
Figure 6. Schematic illustration of prediction for the mechanical performances from composition/processing, or the inverse design of the composition/processing for Al alloys with desired mechanical performances, based on the thermo-kinetic synergistic effects of phase transition and deformation bridged by the microstructure in terms of the defects interactions with respect to the classical strengthening/toughening modes (including the solid solution hardening, the dislocation hardening, the phase/grain boundary hardening, and the precipitation hardening modes), the quantitative correlations between strength (σ) and ductility (ε) along with thermodynamic driving force (ΔG) and kinetic energy barrier (Q), as denoted in the reaction coordinate diagram with respect to the initial state (IS), the transition state (TS) and the final state (FS) of alloy system during phase transition and/or deformation, respectively.
CONCLUSIONS
In summary, the physical origins behind the strength-ductility paradox of aluminum alloys were investigated from the thermo-kinetic synergy in combination with the MD simulations. Following the classical dislocation theories and strengthening/toughening mechanisms, the theoretical models for quantitative connections among yield strength, plastic strain and dislocation density are established in terms of the driving force and energy barrier. It turns out that the thermo-kinetic synergy upon materials processing is responsible for mechanical performance paradox. The yield strength (plastic strain) and driving force (energy barrier) for dislocation motion behave in positive correlations. These quantitative models are validated in FCC-Al and Al alloys with Mg, Cu and Si solutes. The tensile performances and dislocation behaviors of these Al alloys are analyzed to determine the generalized stability with respect to the driving force and energy barrier in terms of dislocation density. Compared with FCC-Al, a typical thermo-kinetic partition of large driving force and small generalized stability presents for the Al alloys with Mg, Cu and Si solutes, which explains the very reason behind different combinations of strength and ductility of these alloys. The present work provides an insightful thermo-kinetic guideline to understand the exclusive behaviors of strength and ductility of metallic alloys. By making the dislocation initiation more difficult and the propagation of dislocation more persistent to achieve a high strain hardening capability, advanced Al alloys with an ideal strength-ductility match can be designed by adjusting the thermo-kinetic partition or activation volume in terms of the composition/processing dependent driving force and energy barrier.
DECLARATIONS
Authors’ contributions
Conceptualization, supervision: Du, J.; Liu, F.
Investigation, writing original draft: Du, J.; Liu, Y.; Zhao, C.
Writing review and editing: Du, J.; Song, K.; Liu, F.
Investigation, methodology, data curation, discussion: Du, J.; Liu, Y.; Zhao, C.; Xue, H.; Gao, K.; Fang, X.
Funding acquisition: Du, J.; Liu, F.
Availability of data and materials
The data that support the findings of this study are available from the corresponding author upon reasonable request.
Financial support and sponsorship
This work is financially supported by the National Natural Science Foundation of China (Grant Nos. 52171013 and 52130110), the Natural Science Foundation of Chongqing (Grant No. CSTB2022NSCQ-MSX0369), the Research Fund of the State Key Laboratory of Solidification Processing (NPU) China (Grant No. 2023-QZ-03), and the “2020-2022 Youth Talent Promotion Project” of China Association for Science and Technology (Grant No. 2020QNRC001). The authors acknowledge the Analytical & Testing Center and the High-Performance Computing Center of NPU for access to supercomputing facilities.
Conflicts of interest
All authors declared that there are no conflicts of interest.
Ethical approval and consent to participate
Not applicable.
Consent for publication
Not applicable.
Copyright
© The Author(s) 2025.
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Du, J.; Liu, Y.; Zhao, C.; Xue, H.; Gao, K.; Fang, X.; Song, K.; Liu, F. Towards mechanical performance paradox and behind thermo-kinetic origins of aluminum alloys with additional solutes (X = Mg, Cu and Si) from atomistic simulations. J. Mater. Inf. 2025, 5, 10. http://dx.doi.org/10.20517/jmi.2024.68
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