Temperature effect and alloying regulation method of magnesium in dislocation dynamics
By constructing a temperature effect synergistic model and an ellipsoidal model, combined with a solid solution strengthening algorithm, the problem of conical surfaces in the plastic deformation of magnesium alloys was solved.<c+a> The three-stage temperature dependence of dislocations was solved, enabling accurate prediction of plastic deformation and strengthening effect in magnesium alloys, breaking through the limitations of traditional models.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- SICHUAN UNIV
- Filing Date
- 2026-01-26
- Publication Date
- 2026-06-02
AI Technical Summary
Existing technologies have failed to effectively explain the conical surface in the plastic deformation of magnesium alloys.
A temperature effect synergistic model and an ellipsoidal model are constructed, and combined with a solid solution strengthening algorithm, cross-slip and basal transformation are described in probabilistic form to accurately simulate the morphology and strengthening effect of precipitated phases in magnesium alloys, and to quantify the influence of solid solution atoms on dislocation motion.
The three-stage temperature anomaly phenomenon of magnesium alloy was successfully reproduced, improving the accuracy of plastic deformation prediction. The yield strength was also improved by alloying control, and the experimental data were in good agreement.
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Figure CN122135819A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of alloy processing technology, specifically to a method for controlling the temperature effect of magnesium in dislocation dynamics and alloying. Background Technology
[0002] As the lightest structural metal, magnesium (Mg) and its alloys have important applications in automobiles, aircraft, and electronic devices. However, their engineering applications are limited by their poor ductility, stemming from the deformation mode characteristics of their hexagonal close-packed (HCP) crystal structure. In magnesium crystals, basal planes exist. Dislocations, Prismatic surfaces Dislocations and cones<c+a> Of the three dislocation slip systems, only the first two can be activated at room temperature, providing only four independent slip modes. However, according to the von Mises criterion, good ductility requires five independent slip modes. Therefore, non-basal slip modes along the c-axis (especially conical slip modes) are more likely to be active.<c+a> Dislocations are crucial for improving ductility. However, conical surfaces...<c+a> Dislocations are difficult to activate due to their high Peierls stress and high dislocation energy, so studying their behavior is of great significance for regulating the plasticity of magnesium alloys.
[0003] To further explore the conical surface<c+a> The properties of dislocations have been observed by researchers through c-axis compression experiments on magnesium single-crystal micropillars or single crystals (a condition that avoids interference from other deformation modes). As early as 1972, Stohr et al. observed that the strength of magnesium single crystals decreased from 77K to 270K, then increased before 375K, and finally decreased again. Ando et al. further discovered that the yield stress of pure magnesium and magnesium-lithium (Mg-Li) and magnesium-zinc (Mg-Zn) alloys exhibited a similar three-stage temperature dependence, and this characteristic existed under both c-axis compression and a-axis tension conditions, and was even prevalent in other HCP metals such as zinc (Zn), cadmium (Cd), and cobalt (Co) (e.g., titanium (Ti), zirconium (Zr), and their alloys). In 1973, Obara's experiments clearly observed conical surfaces.<c+a> Dislocations were found to potentially exist on first-order cone surfaces (Py-I) and second-order cone surfaces (Py-II), and plastic deformation was mainly mediated by screw dislocations or near-screw dislocations, leaving straight dislocations parallel to the basal plane.<c+a> Dislocations also exist in the form of basal plane dislocation loops, and even micro-pillars have been observed to be sheared along the basal plane by basal plane slip (although basal plane slip is not favorable under this condition). These all indicate that the conical surface<c+a> Dislocations have difficulty adapting to c-axis deformation.
[0004] The underlying mechanisms of the high strain hardening rate and three-stage temperature dependence observed in the above experiments are the focus of research. Regarding strain hardening, Tonda et al. pointed out that...<c+a> Dislocations under c-axis compression decompose into components with a Schmitt factor of zero. <c> and< / c> Dislocations lose their slip ability; however, discrete dislocation dynamics (DDD) simulations of beryllium (Aubry et al.) show that dislocation decomposition has a negligible effect on strain hardening. Subsequently, molecular dynamics (MD) simulations by Wu et al. found that the decomposed dislocations... <c> and< / c> Dislocations can recombine to form a basal surface.<c+a> Dislocations (basal plane transition mechanism), and the fact that the basal plane Schmitt factor is zero prevents dislocations from continuing to glide, is considered to be the reason for the high hardening rate. However, this mechanism has previously only applied to individual dislocations, and the impact of collective dislocation behavior still needs to be studied.
[0005] Regarding the three-stage temperature dependence, the first stage is generally considered to be dominated by Pi-Nar stress (decreasing with increasing temperature), but the mechanism of the second stage is controversial: in zinc, Blish et al. believe that dislocation cross-slip leads to a decrease in dislocation velocity, while Tonda proposes that edge dislocations are thermally activated and pinned; in cadmium, Tonda attributes it to double cross-slip, but Stahl et al. did not observe cross-slip; in magnesium, Ando et al. believe that it is due to the decomposition of pyramidal dislocations into... <c> and< / c> Dislocations are pinned, while Wu et al.'s basal transformation mechanism (forming immovable basal planes)<c+a> Dislocations were also used to explain the second stage. Furthermore, while cross-slip exists in almost all face-centered cubic (FCC) and body-centered cubic (BCC) metals (except alloys), it does not exhibit this anomalous temperature dependence, further highlighting the complexity of the mechanism. Meanwhile, the stress in the third stage decreases again with increasing temperature, a phenomenon that existing thermal activation mechanisms struggle to explain.
[0006] Magnesium alloys exhibit diverse morphologies of precipitates: massive (Mg-Zn-Al), basal-plane (AZ91), rod-shaped (Mg-Zn), and columnar-plane (Mg-In-Ca). The strengthening effects of different morphologies / or orientations vary significantly: basal-plane phases offer weak resistance to basal slip (only 5 MPa), but are effective against columnar slip / twins (~25 MPa); rod-shaped phases can resist basal / columnar slip but are ineffective against twins; columnar-plane phases are theoretically predicted to strongly resist dislocations / twins, but in experiments, they are easily sheared by basal dislocations (e.g., MN11 alloy), resulting in a weak practical effect. The debate surrounding the interaction mechanism between precipitates and twins centers on two points: whether twins can shear precipitates (some experiments support shearing, others deny it), and whether the engulfed phase undergoes rigid rotation (the rotation angle is related to thickness). The traditional Orowan model underestimates the twinning strengthening effect by 75%, and the back stress model still has biases because it does not consider local plastic relaxation. The recent energy conservation model (Equation 8) combines interfacial energy and strain energy and predicts that the columnar and plate-like phases have the best potential, but the shear phase problem has not yet been solved.
[0007] Solid solution atoms cause local lattice distortion in the metal matrix, increasing dislocation slip resistance and thus improving strength. This strengthening effect is usually described using a dislocation barrier model: Δτ∝cn (where c is the solute concentration and n is 1 / 2 or 2 / 3). For basal slip in magnesium alloys, aluminum, zinc, and rare earth elements all follow this pattern, but cylindrical slip exhibits anomalies: zinc, aluminum, and lithium show solid solution softening (Δτ_CRSS<0), possibly related to promoting cross-slip. (Pyramidal surface...)<c+a> Studies on dislocation strengthening are limited, with significant effects observed only in magnesium-yttrium alloys. However, due to the ease of dislocation decomposition and frequent cross-slip, traditional models are difficult to apply. The strengthening effect of twinning deformation is even more controversial: zinc and yttrium have increased twinning stress (up to 95 MPa) in some studies, but other studies show that zinc is ineffective, and aluminum / yttrium even softens; in magnesium-yttrium alloys, yttrium significantly strengthens {10-12} twins, but weakly strengthens {11-21} twins. In summary, traditional solid solution strengthening models are only applicable to basal slip, and new mechanisms need to be explored for cylindrical / conical slip and twinning deformation.
[0008] Dislocation slip is a fundamental deformation mode in metallic materials, and discrete dislocation dynamics (DDD) is an effective tool for studying dislocation-mediated plasticity, capable of simulating mechanisms such as cross-slip, dislocation annihilation, and multiplication. Over the past two decades, DDD has been used in HCP metal research: Aubry et al.'s simulations of HCP beryllium support the weak influence of dislocation decomposition on strain hardening; Bertin et al. introduced magnesium dislocation interactions into their simulations, but the strain hardening results were weak; Srivastava et al. introduced anisotropic cone dislocation mobility rules, but the hardening rate problem remains unresolved. It is noteworthy that previous DDD simulations did not consider the basal transformation mechanism, and integrating this mechanism with dislocation collective behavior is crucial for revealing the intrinsic relationship between strain hardening and temperature dependence.
[0009] Current discrete dislocation dynamics (DDD) simulations suffer from systematic deficiencies in predicting the plasticity of magnesium alloys. First, temperature effect modeling is fragmented: the three mechanisms of Pinna force decay, cross-slip, and basal transformation lack a synergistic framework. Taking the mainstream open-source software ParaDiS as an example, its cross-slip triggering relies solely on static stress criteria, completely ignoring the probabilistic nature of the thermal activation process. This results in the inability to reproduce the characteristic three-stage temperature anomaly in magnesium crystals—namely, the non-monotonic change in yield stress under c-axis compression with temperature, exhibiting a "decreasing-increasing-decreasing" pattern.
[0010] Secondly, the alloying effect of magnesium cannot be realized in dislocation dynamics, including the geometric anisotropy of rod-shaped β′ phases and basal panel-shaped β phases in magnesium alloys, as well as the Orowan ring formation mechanism. More importantly, the traditional DDD framework neglects the solid solution strengthening effect and fails to quantify the pinning effect of lattice distortion caused by solute atoms (e.g., the size mismatch δ=12% in Zn in Mg) on dislocation motion, resulting in significant deviations in alloying strengthening predictions. Summary of the Invention
[0011] To address the above problems, this invention proposes a method for controlling the temperature effect and alloying of magnesium in dislocation dynamics.
[0012] The technical solution of this invention is: a method for controlling the temperature effect and alloying of magnesium in dislocation dynamics, comprising the following steps:
[0013] S1. Construct a temperature effect synergistic model;
[0014] S2. Solid solution strengthening of magnesium alloys is performed using an ellipsoidal model;
[0015] S3. Using the temperature effect synergistic model and solid solution strengthening results, the temperature effect on solid solution strengthening is controlled.
[0016] Furthermore, in S1, the temperature effect cooperative model The expression is:
[0017] ;
[0018] In the formula, Indicates the dependent variable. Indicates strain rate. Indicates the frequency of attempts. Indicates the reference length. Represents dislocation density. Indicates a barrier, Represents the Boltzmann constant. Indicates temperature. This represents an exponential function.
[0019] Furthermore, S2 includes the following sub-steps:
[0020] S21. Construct an ellipsoidal model and use the ellipsoidal model to determine the phase morphology of the magnesium alloy;
[0021] S22. Based on the phase morphology of magnesium alloy determined by the ellipsoidal model, determine the phases that can be cut and those that cannot be cut.
[0022] S23. Solid solution strengthening is carried out based on the tangible and intangible phases.
[0023] Furthermore, in S21, the ellipsoidal model The expression is:
[0024] ;
[0025] In the formula, Represents the x-coordinate of the dislocation node position. Represents the x-coordinate of the precipitation phase center. Represents the ordinate of the dislocation node position. Represents the ordinate of the precipitation phase center. Represents the vertical coordinate of the dislocation node position. Represents the vertical coordinate of the precipitation phase center. Indicates the length of the first half-axis. Indicates the length of the second half-axis. This indicates the length of the third half-axis.
[0026] Furthermore, S23 includes the following sub-steps:
[0027] S231. Based on the tangible and intangible phases, randomly generate the coordinates of several precipitate center points;
[0028] S232. Based on the coordinates of several precipitate phase centers, the simulation domain is divided into several sub-cubes;
[0029] S233. Solid solution strengthening is performed based on several sub-cubes.
[0030] Furthermore, in S232, the octree spatial indexing method is used to divide the simulation domain into several sub-cubes.
[0031] Furthermore, in S233, the expression for solid solution strengthening is:
[0032] ;
[0033] In the formula, This represents the increase in shear stress that solid solution strengthening contributes to the material's strength. Represents a constant. This indicates the concentration of atoms in the solid solution.
[0034] The beneficial effects of this invention are as follows: This invention achieves multi-physics field coupling prediction of plastic deformation of magnesium alloys. The temperature-coordinated model successfully reproduces the three-stage anomaly phenomenon, namely, at low temperatures (≤100K), the yield stress decreases with increasing temperature due to the dominance of low-resistance Py-I dislocations; at medium temperatures (100-300K), the yield stress abnormally increases due to the dominance of high-resistance Py-II dislocations caused by the cross-slip of Py-I screw dislocations to the Py-II plane and the transformation of near-edge dislocations to the basal plane; at high temperatures (300-700K), the yield stress decreases again due to the cross-slip of Py-II screw dislocations back to the Py-I plane and the re-dominance of Py-I dislocations. The alloying strengthening algorithm breaks through the limitations of traditional methods. The precipitate module of this invention accurately quantifies the 22% increase in yield strength caused by rod-shaped phases (2% volume fraction), which is consistent with experimental data. Attached Figure Description
[0035] Figure 1 A flowchart of the temperature effect of magnesium and alloying control methods in dislocation dynamics;
[0036] Figure 2 This is a schematic diagram of cross-slip behavior;
[0037] Figure 3 The base surface of the second cone<c+a> A schematic diagram illustrating the mechanism by which dislocations annihilate to form dislocation loops;
[0038] Figure 4 A schematic diagram illustrating the influence of relative dislocation evolution in a single release;
[0039] Figure 5 This is a schematic diagram of a large-scale simulation of multiple precipitates. Detailed Implementation
[0040] The embodiments of the present invention will be further described below with reference to the accompanying drawings.
[0041] like Figure 1 As shown, this invention provides a method for controlling the temperature effect and alloying of magnesium in dislocation dynamics, comprising the following steps:
[0042] S1. Construct a temperature effect synergistic model;
[0043] S2. Solid solution strengthening of magnesium alloys is performed using an ellipsoidal model;
[0044] S3. Using the temperature effect synergistic model and solid solution strengthening results, the temperature effect on solid solution strengthening is controlled.
[0045] In this embodiment of the invention, in S1, the temperature effect cooperative model... The expression is:
[0046] ;
[0047] In the formula, Indicates the dependent variable. Indicates strain rate. Indicates the frequency of attempts. Indicates the reference length. Represents dislocation density. Indicates a barrier, Represents the Boltzmann constant. Indicates temperature. This represents an exponential function.
[0048] The core innovation of this invention lies in constructing a linkage response mechanism for dislocation behavior driven by temperature. The temperature dependence of the Paner force is characterized by an exponential decay model. Pinna force of mixed dislocations Calculated via angle interpolation: ,in, The angle between Burgers vector and dislocation line. The Pinna force for a 0K cone dislocation. The decay constant is 300K. At 0K, Panerly force For pure screw dislocations, Pynae force. Nali is a pure blade dislocation. For the index, For temperature.
[0049] This invention innovatively develops a novel cross-slip thermal activation algorithm, which, based on energy barrier relationships, performs bidirectional cross-slip between conical surfaces in a probabilistic manner. For example... Figure 2 As shown, dislocations undergo bidirectional cross-slip, which has a more physical significance. For screw dislocations with an angle ≤5° between the Burgers vector and the dislocation line, energy barriers for three types of cross-slip paths are defined (Py-I1→Py-I2: ΔE=1.0eV, Py-I→Py-II: ΔE=0.24eV, Py-II→Py-I: ΔE=0.8eV), where Py-I1 represents the current slip first cone, Py-I2 represents other slip first cones, ΔE represents the cross-slip energy barrier, and Py-I / Py-II represent the first / second cones.
[0050] like Figure 3 As shown, basal edge dislocations undergo basal transformation to generate immovable dislocations, and due to the pinning effect of immovable dislocations, dislocation dipoles are formed and annihilated. Cross-slip and basal transformation share the same triggering probability formula, and basal transformation / cross-slip is a thermally activated process. Based on the Arrhenius formula and the Poisson formula, this invention innovatively uses the ratio of strain to strain rate as the integration time and the mean free length of the dislocation as the probability length to obtain the temperature effect model.
[0051] In this embodiment of the invention, S2 includes the following sub-steps:
[0052] S21. Construct an ellipsoidal model and use the ellipsoidal model to determine the phase morphology of the magnesium alloy;
[0053] S22. Based on the phase morphology of magnesium alloy determined by the ellipsoidal model, determine the phases that can be cut and those that cannot be cut.
[0054] S23. Solid solution strengthening is carried out based on the tangible and intangible phases.
[0055] In this embodiment of the invention, in S21, the ellipsoid model The expression is:
[0056] ;
[0057] In the formula, Represents the x-coordinate of the dislocation node position. Represents the x-coordinate of the precipitation phase center. Represents the ordinate of the dislocation node position. Represents the ordinate of the precipitation phase center. Represents the vertical coordinate of the dislocation node position. Represents the vertical coordinate of the precipitation phase center. Indicates the length of the first half-axis. Indicates the length of the second half-axis. This indicates the length of the third half-axis.
[0058] Typical precipitated phase parameters include: rod-like phase (Mg-6Zn: a=b=20nm, c=150nm, volume fraction 2%), lamellar phase (AZ91: a=500nm, b=c=10nm, volume fraction 11.4%), and blocky phase (a=b=c=50nm). When the dislocation node satisfies M<1, the shearable phase (such as the Mg-Zn rod-like phase) can increase the local Peierls stress to 50-100MPa; the inshearable phase (such as the AZ91 base plate-like phase) is assumed to have infinite resistance.
[0059] In this embodiment of the invention, S23 includes the following sub-steps:
[0060] S231. Based on the tangible and intangible phases, randomly generate the coordinates of several precipitate center points;
[0061] S232. Based on the coordinates of several precipitate phase centers, the simulation domain is divided into several sub-cubes;
[0062] S233. Solid solution strengthening is performed based on several sub-cubes.
[0063] In this embodiment of the invention, in S232, the octree spatial indexing method is used to divide the simulation domain into several sub-cubes.
[0064] In this embodiment of the invention, the expression for solid solution strengthening in S233 is:
[0065] ;
[0066] In the formula, This represents the increase in shear stress that solid solution strengthening contributes to the material's strength. Represents a constant. This indicates the concentration of atoms in the solid solution.
[0067] In this embodiment of the invention, unlike the fixed spherical precipitates, the present invention introduces a novel ellipsoidal precipitate algorithm, such as... Figure 4 As shown, this invention demonstrates that a single precipitated phase hinders dislocation movement during dislocation evolution, and that a large number of Orowan rings were successfully observed around the precipitated phase. (For support >10) 4 For large-scale simulation of precipitates, this invention first randomly generates the center coordinates of multiple precipitates and employs an octree spatial indexing technique: the simulation domain is recursively divided into sub-cubes, and dislocation nodes only need to perform collision detection with the precipitates in the bottom-level cube, reducing the computational complexity from O(N²) to O(NlogN). Figure 5 As shown, this invention demonstrates the impact of large-scale multiple precipitates on the evolution of relative dislocations.
[0068] The solid solution strengthening effect algorithm, based on Fleischer's theory, can be quantified into a concentration-dependent equation. Therefore, this invention first obtains the concentration field equation through molecular dynamics: by dividing the BOX into multiple regions in the Lammps software and statistically determining the ratio of solute atoms to solvent atoms, the concentration field equation is determined. The strengthening effect caused by atomic mismatch can be described by the following equation, where 'a' is a constant. The value of 'a' is determined by the ratio of concentration to strengthening value in molecular dynamics and shear experiments, and then applied to dislocation dynamics. Solid solution strengthening increases the lattice friction in dislocation dynamics.
[0069] Those skilled in the art will recognize that the embodiments described herein are intended to help the reader understand the principles of the invention, and should be understood that the scope of protection of the invention is not limited to such specific statements and embodiments. Those skilled in the art can make various other specific modifications and combinations based on the technical teachings disclosed in this invention without departing from the spirit of the invention, and these modifications and combinations are still within the scope of protection of this invention.
Claims
1. A method for controlling the temperature effect and alloying of magnesium in dislocation dynamics, characterized in that, Includes the following steps: S1. Construct a temperature effect synergistic model; S2. Solid solution strengthening of magnesium alloys is performed using an ellipsoidal model; S3. Using the temperature effect synergistic model and solid solution strengthening results, the temperature effect on solid solution strengthening is controlled.
2. The method for controlling the temperature effect and alloying of magnesium in dislocation dynamics according to claim 1, characterized in that, In S1, the temperature effect cooperative model The expression is: ； In the formula, Indicates the dependent variable. Indicates strain rate. Indicates the frequency of attempts. Indicates the reference length. Represents dislocation density. Indicates a barrier, Represents the Boltzmann constant. Indicates temperature. This represents an exponential function.
3. The method for controlling the temperature effect and alloying of magnesium in dislocation dynamics according to claim 1, characterized in that, S2 includes the following sub-steps: S21. Construct an ellipsoidal model and use the ellipsoidal model to determine the phase morphology of the magnesium alloy; S22. Based on the phase morphology of magnesium alloy determined by the ellipsoidal model, determine the phases that can be cut and those that cannot be cut. S23. Solid solution strengthening is carried out based on the tangible and intangible phases.
4. The method for controlling the temperature effect and alloying of magnesium in dislocation dynamics according to claim 3, characterized in that, In S21, the ellipsoid model The expression is: ； In the formula, Represents the x-coordinate of the dislocation node position. Represents the x-coordinate of the precipitation phase center. Represents the ordinate of the dislocation node position. Represents the ordinate of the precipitation phase center. Represents the vertical coordinate of the dislocation node position. Represents the vertical coordinate of the precipitation phase center. Indicates the length of the first half-axis. Indicates the length of the second half-axis. This indicates the length of the third half-axis.
5. The method for controlling the temperature effect and alloying of magnesium in dislocation dynamics according to claim 3, characterized in that, S23 includes the following sub-steps: S231. Based on the tangible and intangible phases, randomly generate the coordinates of several precipitate center points; S232. Based on the coordinates of several precipitate phase centers, the simulation domain is divided into several sub-cubes; S233. Solid solution strengthening is performed based on several sub-cubes.
6. The method for controlling the temperature effect and alloying of magnesium in dislocation dynamics according to claim 5, characterized in that, In step S232, the octree spatial indexing method is used to divide the simulation domain into several sub-cubes.
7. The method for controlling the temperature effect and alloying of magnesium in dislocation dynamics according to claim 5, characterized in that, In S233, the expression for solid solution strengthening is: ； In the formula, This represents the increase in shear stress that solid solution strengthening contributes to the material's strength. Represents a constant. This indicates the concentration of atoms in the solid solution.