A discrete dislocation dynamics modeling method considering twin evolution

Abstract

The present invention relates to a discrete dislocation dynamics modeling method considering twin evolution, the method comprising: constructing a discrete dislocation dynamics geometric model based on the material constants of a target material and the computational information required for simulation; applying preset plastic deformation boundary conditions to the target material to determine the microstructural changes of the target material during the plastic deformation process; when twin nuclei exist in the target material, calculating the growth rate of the twins and determining the twin evolution size based on the growth rate; in the geometric model, defining an elliptical twin boundary according to the twin evolution size, and implementing a slip plane direction reconstruction algorithm within the twin domain to update the crystal orientation and dislocation source position in real time to simulate the growth of twins; after the twin growth is completed, iteratively correcting the dislocation evolution in the target material according to the twin growth state. In this way, the authenticity of the material plastic deformation simulation can be improved.

Description

Technical Field

[0001] The present invention relates to the field of material science and technology, and in particular to a discrete dislocation dynamics modeling method considering twin evolution. Background Art

[0002] In the study of plastic deformation in metals, twin evolution significantly influences the mechanical behavior of materials, such as the strong anisotropy of magnesium / titanium alloys. Its ability to coordinate strain through crystallographic reorientation is directly related to the material's strength, toughness, and anisotropy. Discrete dislocation dynamics (DDD), which can directly track dislocation motion and interactions, is widely used to reveal the deformation mechanisms of twinning.

[0003] However, the prior art usually relies on the preset twin interface properties, and regards the twin boundary as a fixed rigid boundary, and its migration behavior can only be approximately characterized by equivalent or indirect means. A common equivalent method is to utilize the dissociation reaction of dislocations on the twin boundary, and induce plastic strain by presetting the slip of twin dislocations on the interface, thereby indirectly reflecting the migration of the twin boundary. Although it can characterize the competitive relationship between twin growth and size effect to a certain extent, it completely ignores the natural starting process of twins spontaneously nucleating and evolving from nano-embryos driven by external forces, and the growth mechanism of the entire early evolution is simplified or directly skipped. Another approximate solution is to use a discrete twin dislocation array to simulate the twin boundary. However, this method not only requires the additional definition of complex dislocation motion rules, increasing the complexity of the model, but also fails to consider the real dynamic interaction between matrix dislocations and the evolving twin interface. In essence, it is still an equivalent representation method.

[0004] Therefore, existing methods are unable to accurately describe the structure of actual twin boundaries and their continuous migration behavior under external forces, making it difficult to accurately reflect the coupled effects of twin evolution on crystal plastic deformation in dislocation dynamics models. Due to the inability to accurately describe the entire process from twin nucleation to growth, the fine structure of twin boundaries, and their continuous migration mechanism, the models struggle to capture how twins affect dislocation motion in real time, and how dislocations react to twin evolution. This significantly limits the accuracy and reliability of simulations of the material's macroscopic plastic behavior. Summary of the Invention

[0005] The purpose of this section is to summarize some aspects of the embodiments of the present invention and briefly introduce some preferred embodiments. Some simplifications or omissions may be made in this section and the abstract and title of this application to avoid obscuring the purpose of this section, the abstract and the title of the invention, and such simplifications or omissions should not be used to limit the scope of the present invention.

[0006] The embodiments of the present invention provide a discrete dislocation dynamics modeling method that takes twin evolution into consideration, which can achieve cross-scale simulation from nanoscale twin nucleation to micron-scale dynamic growth, thereby improving the authenticity of material plastic deformation simulation.

[0007] The present invention provides a discrete dislocation dynamics modeling method considering twin evolution, comprising:

[0008] Construct a discrete dislocation dynamics geometric model based on the material constants of the target material and the computational information required for simulation;

[0009] Within the preset dislocation dynamics solution time step, the preset plastic deformation boundary conditions are applied to the target material at a constant time increment to determine the microstructural changes of the target material during the plastic deformation process;

[0010] When it is determined that the target material has twin nuclei, the growth rate of the twins is calculated and the twin evolution size in the current time step cycle is determined based on the growth rate;

[0011] In the geometric model, an elliptical twin boundary is defined based on the determined twin evolution size within the current time step cycle. A slip plane orientation reconstruction algorithm is implemented within the twin domain to update the crystal orientation and dislocation source location in real time to simulate twin growth. The twin growth process involves driving the twin boundary to rapidly expand longitudinally along the long axis of the ellipse and slowly grow laterally along the short axis.

[0012] After the twin growth is completed, the evolution of dislocations in the target material is iteratively corrected according to the twin growth state under the current time step cycle.

[0013] In some possible implementations, after constructing the discrete dislocation dynamics geometric model, the method further includes:

[0014] In the geometric model, the slip plane is defined according to the crystallographic characteristics of the target material, and dislocation sources and obstacles are randomly distributed on the slip plane;

[0015] Initialize the matrix used to store dislocation motion trajectories, stress-strain data, and dislocation nucleation and escape time data.

[0016] In some possible implementations, the twin boundary of the elliptical structure satisfies the following formula:

[0017] ;

[0018] in 、 is a coordinate variable used to describe the twin boundary of the elliptical structure, ( , ) are the coordinates of the ellipse center, and are the semi-axis lengths of the major axis and minor axis respectively, and 、 as well as 、 It is dynamically updated as the twin grows and is used to characterize the twin boundary extension.

[0019] In some possible implementations, the slip plane direction reconstruction algorithm includes:

[0020] Real-time division of twin domain and matrix domain based on elliptical boundary expansion;

[0021] Rotate the slip system in the twinning domain around the material twin axis by a preset angle;

[0022] Remap the dislocation source coordinates to the new slip plane and reset the critical shear stress.

[0023] In some possible implementations, the method further includes: when a matrix dislocation contacts a twin boundary, changing the interaction mechanism between the dislocation and the interface by setting properties of the twin boundary, and updating the type and size of the dislocation.

[0024] One or more technical solutions provided in the embodiments of the present invention have at least the following technical effects or advantages:

[0025] The present invention provides a discrete dislocation dynamics modeling method considering twin evolution, the method comprising: constructing a discrete dislocation dynamics geometric model based on the material constants of the target material and the computational information required for simulation; applying preset plastic deformation boundary conditions to the target material at a constant time increment within a preset dislocation dynamics solution time step to determine the microstructural changes of the target material during the plastic deformation process; when it is determined that twin nuclei exist in the target material, calculating the growth rate of the twins and determining the size of the twin growth within the current time step cycle based on the growth rate; in the geometric model, defining a twin boundary of an elliptical structure according to the determined size of the twin growth within the current time step cycle, implementing a slip plane direction reconstruction algorithm within the twin domain, and updating the crystal orientation and dislocation source position in real time to simulate the growth of twins; wherein the twin growth process comprises: driving the twin boundary to rapidly expand longitudinally along the major axis direction of the ellipse and slowly grow laterally along the minor axis direction; after the twin growth is completed, iteratively correcting the evolution of dislocations in the target material according to the twin growth state under the current time step cycle. In this way, the dynamic migration of elliptical boundaries solves the problem that twins cannot grow substantially. The two-stage growth mechanism of twins reproduces the growth path of twins, which can realize cross-scale simulation from nanoscale twin nucleation to micron-scale dynamic growth, and thereby realize the correction of dislocation evolution, thereby improving the authenticity of material plastic deformation simulation. BRIEF DESCRIPTION OF THE DRAWINGS

[0026] In order to more clearly illustrate the embodiments of the present invention, the following briefly introduces the drawings required for use in the embodiments of the present invention. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0027] Figure 1 A schematic flow chart of an embodiment of a discrete dislocation dynamics modeling method considering twin evolution provided by an embodiment of the present invention;

[0028] Figure 2 is a schematic diagram of simulating twin evolution in an embodiment of the present invention;

[0029] Figure 3 This is a flowchart of discrete dislocation dynamics modeling considering twin evolution in an embodiment of the present invention. DETAILED DESCRIPTION

[0030] The following will be combined with the accompanying drawings in the embodiments of this application to clearly and completely describe the technical solutions in the embodiments of this application. Obviously, the described embodiments are part of the embodiments of this application, not all of the embodiments. Based on the embodiments in this application, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of this application.

[0031] In the relevant description of this embodiment, the terms "including, containing, having" and the like are open terms and are generally understood to include but not be limited to; the term "at least one" is generally understood to mean one or more, where "plurality" refers to two or more; the term "at least one of the following" or similar expressions refers to any combination of these items, including any combination of single or plural items, for example, "at least one of a, b or c", or "at least one of a, b and c", can all represent: a, b, c, ab (i.e., a and b), ac, bc, or abc, where a, b, c can be single or multiple respectively; the symbol "A / B" is used to describe the selection relationship of associated objects, generally indicating an "or" relationship before and after.

[0032] In the following description of the present embodiment, the terms used in the embodiments of the present application are only for the purpose of describing specific embodiments and are not intended to limit the present application. The singular forms "a", "an" and "the" used in the embodiments of the present application and the appended claims are also intended to include plural forms unless the context clearly indicates otherwise.

[0033] Those skilled in the art should understand that in the following description of the embodiments of the present application, the order of serial numbers does not mean the order of execution, some or all of the steps can be executed in parallel or sequentially, and the execution order of each process should be determined by its function and internal logic, and should not constitute any limitation on the implementation process of the embodiments of the present application.

[0034] It will be understood by those skilled in the art that the numerical ranges in the examples of the present application are to be understood as also specifically disclosing each intermediate value between the upper and lower limits of the ranges. Each smaller range between the intermediate value in any stated value or stated range and any other stated value or intermediate value in the range is also included in the present invention. The upper and lower limits of these smaller ranges may be independently included or excluded in the scope.

[0035] Unless otherwise indicated, the technical / scientific terms used herein have the same meanings as those commonly understood by those skilled in the art to which this application belongs. Although this application describes only preferred methods and materials, any methods and materials similar or equivalent to those herein may also be used in the implementation or testing of this application. All documents mentioned in this specification are incorporated by reference to disclose and describe the methods and / or materials related to the documents. In the event of any conflict with any incorporated document, the content of this specification shall prevail.

[0036] In order to illustrate the technical solution of the present invention, specific embodiments are provided below.

[0037] In the study of plastic deformation in metals, twin evolution significantly influences the mechanical behavior of materials, such as the strong anisotropy of magnesium / titanium alloys. Its ability to coordinate strain through crystallographic reorientation is directly related to the material's strength, toughness, and anisotropy. Discrete dislocation dynamics (DDD), which can directly track dislocation motion and interactions, is widely used to reveal the deformation mechanisms of twinning.

[0038] However, the prior art usually relies on the preset twin interface properties, and regards the twin boundary as a fixed rigid boundary, and its migration behavior can only be approximately characterized by equivalent or indirect means. A common equivalent method is to utilize the dissociation reaction of dislocations on the twin boundary, and induce plastic strain by presetting the slip of twin dislocations on the interface, thereby indirectly reflecting the migration of the twin boundary. Although it can characterize the competitive relationship between twin growth and size effect to a certain extent, it completely ignores the natural starting process of twins spontaneously nucleating and evolving from nano-embryos driven by external forces, and the growth mechanism of the entire early evolution is simplified or directly skipped. Another approximate solution is to use a discrete twin dislocation array to simulate the twin boundary. However, this method not only requires the additional definition of complex dislocation motion rules, increasing the complexity of the model, but also fails to consider the real dynamic interaction between matrix dislocations and the evolving twin interface. In essence, it is still an equivalent representation method.

[0039] Therefore, existing methods are unable to accurately describe the structure of actual twin boundaries and their continuous migration behavior under external forces, making it difficult to accurately reflect the coupled effects of twin evolution on crystal plastic deformation in dislocation dynamics models. Due to the inability to accurately describe the entire process from twin nucleation to growth, the fine structure of twin boundaries, and their continuous migration mechanism, the models struggle to capture how twins affect dislocation motion in real time, and how dislocations react to twin evolution. This significantly limits the accuracy and reliability of simulations of the material's macroscopic plastic behavior.

[0040] Based on this, an embodiment of the present invention provides a discrete dislocation dynamics modeling method that takes into account twin evolution, which can achieve cross-scale simulation from nanoscale twin nucleation to micron-scale dynamic growth, and thereby realize the correction of dislocation evolution, thereby improving the authenticity of material plastic deformation simulation.

[0041] Figure 1 A schematic diagram of an embodiment of a discrete dislocation dynamics modeling method considering twin evolution provided by an embodiment of the present invention is provided. Figure 1 As shown, the above method may include:

[0042] S101, constructing a discrete dislocation dynamics geometric model based on the material constants of the target material and the computational information required for simulation;

[0043] In some embodiments, the target crystal material is the crystal material to be studied. The target crystal material can be any material capable of plastic deformation, such as metals (e.g., magnesium alloys, zirconium alloys), semiconductors, etc. The material constants of the target material include, but are not limited to, geometric information, elastic modulus, Poisson's ratio, and dislocation mobility; the computational information required for the simulation includes, but is not limited to, deformation amount, load type, and accuracy requirements;

[0044] Among them, geometric information can include the overall shape and size specifications of the target material, and can also include the geometric characteristics of the internal microstructure of the material, such as the size, shape and distribution of the grains. Micro-geometric characteristics can provide a deeper characterization of the stress transfer and dislocation movement path within the material. The elastic modulus is an indicator of the material's ability to resist elastic deformation. The elastic modulus of different materials determines the ease with which the material undergoes elastic deformation under the same external force. Poisson's ratio reflects the proportional relationship between the lateral strain and the longitudinal strain of the material when it is subjected to stress. The numerical value of the dislocation mobility reflects the speed and ease with which dislocations move in the material lattice, which directly affects the rate and degree of plastic deformation of the material.

[0045] Furthermore, within the calculation information, deformation refers to the quantitative representation of the change in shape, size, or structure of the target material under the influence of external forces or the environment. Common load types include tension, compression, bending, and shear. Accuracy requirements can be flexibly set based on the specific application scenario and research depth of the simulation.

[0046] When constructing the initial discrete dislocation dynamics geometric model, the model can be finely meshed based on the material's geometric information. For materials with complex shapes, adaptive meshing technology can be used to increase mesh density in stress concentration areas or critical locations, such as notches and corners, to improve computational accuracy. In areas where stress changes more gently, the mesh density can be appropriately relaxed to balance computational efficiency and accuracy. Elastic modulus and Poisson's ratio, as parameters of the material's constitutive relationship, can be embedded in the mechanical calculation module of the dislocation dynamics geometric model to describe the material's elastic deformation behavior when subjected to stress, ensuring that the model can accurately simulate the material's elastic response.

[0047] In some embodiments, after constructing the discrete dislocation dynamics geometric model, the method further comprises:

[0048] In the geometric model, the slip plane is defined according to the crystallographic characteristics of the target material, and dislocation sources and obstacles are randomly distributed on the slip plane;

[0049] Initialize the matrix used to store dislocation motion trajectories, stress-strain data, and dislocation nucleation and escape time data.

[0050] Specifically, after constructing the geometric model, slip planes can be defined based on the crystallographic characteristics of the target material. Crystallographic characteristics reflect the regularity of the atomic arrangement within a material, and different crystal structures have specific slip planes. By precisely analyzing the crystal structure of the target material, its slip planes are determined, and this information is accurately input into the constructed dislocation dynamics geometric model.

[0051] After defining the slip plane, dislocation sources and obstacles can be randomly distributed on the slip plane to more realistically simulate the complexity of the material's internal microstructure. Dislocation sources are the source of dislocations, and the randomness of their distribution simulates the uncertainty of dislocation generation locations during the actual production and processing of materials. Obstacles are used to simulate various factors within the material that hinder dislocation movement, such as impurity atoms, second-phase particles, and grain boundaries. By properly setting parameters such as the distribution density and size of dislocation sources and obstacles, the finite element model can be made closer to the microstructure of the actual material, thereby improving the reliability of the simulation results. For example, for materials containing a large number of impurities, the distribution density of obstacles can be appropriately increased; for materials that have undergone special treatment and have relatively concentrated dislocation sources, the distribution range and frequency of dislocation sources can be adjusted.

[0052] During initialization, a two-dimensional matrix is ​​created for the dislocation trajectory. The number of rows is preset to the maximum number of possible dislocations, and the number of columns is determined based on the total simulation time step. Each matrix element records the 3D coordinates of the corresponding dislocation at each time step, allowing accurate tracking of the dislocation's movement path.

[0053] The matrix storing stress and strain data can be constructed as a three-dimensional matrix. The first dimension corresponds to the nodes or elements of the finite element model, used to distinguish different locations within the material. The second and third dimensions represent the components of the stress-strain tensor, respectively. During the simulation process, the stress and strain data calculated at each time step can be stored in the corresponding position of this matrix, thus recording the changes in stress and strain at each location in the material over time.

[0054] Two one-dimensional matrices can be initialized for dislocation nucleation and escape time data, respectively. The matrix lengths are set based on the estimated maximum number of dislocations. During the simulation, whenever a dislocation nucleation or escape event is detected, the corresponding time is recorded at the corresponding dislocation position in each matrix, providing time series data for subsequent investigations of the microscopic mechanisms of plastic deformation.

[0055] S102, applying preset plastic deformation boundary conditions to the target material at constant time increments within a preset dislocation dynamics solution time step, and determining microstructural changes of the target material during the plastic deformation process;

[0056] The dislocation dynamics solution time step can be the total duration of applying boundary conditions to the target material. This can be set based on experience and a combination of algorithm accuracy and efficiency. A constant time increment divides the total solution time step into a number of equal-length time intervals, with the length of each time interval representing the constant time increment. The constant time increment can be an empirical value or determined based on the twin growth state during actual application.

[0057] Preset plastic deformation boundary conditions are external constraints or loads applied to the target material to drive the material's plastic deformation. Boundary conditions include, but are not limited to, displacement / strain-controlled boundary conditions, stress / load-controlled boundary conditions, and mixed boundary conditions.

[0058] S103, when it is determined that twin nuclei exist in the target material, calculating the growth rate of the twins and determining the twin evolution size within the current time step cycle based on the growth rate;

[0059] It should be noted that after determining the presence of twin nucleation in the target material, twin growth is affected by physical mechanisms such as dislocation slip, atomic diffusion and interface migration, and parameters such as stress state, temperature, material properties and twin orientation will significantly affect these mechanisms. A physical model can be constructed based on these parameters. If dislocation slip dominates the evolution and growth of twins, the slip rate of dislocations on the twin boundaries can be calculated through dislocation dynamics simulation, and the growth rate can be estimated by combining stress and material properties; if diffusion is the controlling factor, the diffusion coefficient and concentration gradient can be used to calculate the atomic migration rate with the help of equations such as Fick's law to estimate the growth rate.

[0060] After determining the twin growth rate, the twin evolution size can be calculated based on the growth rate and time according to the time of the current time step cycle.

[0061] S104, in the geometric model, based on the determined twin evolution size within the current time step cycle, defining a twin boundary of an elliptical structure, and implementing a slip plane direction reconstruction algorithm within the twin domain to update the crystal orientation and dislocation source position in real time to simulate the growth of the twin;

[0062] The twin growth process includes: driving the twin boundary to expand rapidly longitudinally along the long axis of the ellipse and slowly grow laterally along the short axis;

[0063] In some embodiments, the twin boundaries of the elliptical structure satisfy the following formula:

[0064] ;

[0065] in 、 is a coordinate variable used to describe the twin boundary of the elliptical structure, ( , ) are the coordinates of the ellipse center, and are the semi-axis lengths of the major axis and minor axis respectively, and 、 as well as 、 It is dynamically updated as the twin grows and is used to characterize the twin boundary extension.

[0066] The major axis of the ellipse is aligned with the longitudinal growth direction of the twin, while the minor axis is aligned with the lateral growth direction of the twin. The Euler angle transformation matrix can be used to map the ellipse equation in the Cartesian coordinate system to the crystallographic coordinate system, thus achieving an orientation correlation with the lattice.

[0067] Specifically, after the initial nucleation is completed, the twin boundary begins to expand rapidly longitudinally along the major axis of the ellipse, while slowly growing laterally along the minor axis. Since the twins expand extremely quickly in the longitudinal direction, the growth process of the twins can be roughly described as: first, they expand rapidly along the major axis, and according to the constraints of the above-mentioned ellipse equation, the minor axis radius of the ellipse is fixed (that is, the twin thickness remains unchanged), and only the major axis radius is increased. Once the twin boundary reaches a preset length threshold, or encounters a grain boundary or other obstacle, its expansion mode changes. At this point, the evolution process of the twins becomes a fixed major axis radius, and only the minor axis radius is increased. The rate of lateral expansion of the twins is slower than the longitudinal expansion, and the higher the density of grain boundaries or other obstacles, the slower the expansion rate.

[0068] It should be noted that during the lateral expansion phase, the simulation focuses on accurately capturing the complex interactions between twin boundaries and obstacles. These interactions include, but are not limited to, dislocation accumulation, stress concentration, and localized plastic deformation. To achieve this, the simulation algorithm must incorporate appropriate physical models to describe these effects. For example, discrete dislocation dynamics methods can be used to accurately simulate the clustering behavior of dislocations near twin boundaries and their impact on the expansion process.

[0069] A key goal throughout the expansion process is to maintain consistent crystal orientation across the entire twin domain. This means that as the twin boundary expands, the newly formed domains must have the same crystallographic orientation as the existing domains. To achieve this, the simulation program continuously adjusts the orientation of the new domains based on the crystallographic symmetry of the twinning deformation to ensure consistency with the overall twin domain. This not only helps maintain the overall homogeneity of the material but also improves its mechanical properties.

[0070] Furthermore, an explicit time integration algorithm can be used in the rapid longitudinal expansion stage, and the time step is dynamically adjusted according to the curvature radius of the twin boundary; an implicit time integration algorithm is used in the slow lateral growth stage, and the interface migration driving force is calculated through the dislocation density gradient.

[0071] Specifically, after twin nucleation, when the twin boundary rapidly expands along the long axis, an explicit time integration algorithm is used for simulation. This algorithm first calculates the radius of curvature of the twin boundary and dynamically adjusts the time step based on this calculation. A smaller time step is suitable for regions of high curvature to ensure numerical stability; in regions of low curvature, the time step can be appropriately increased to improve computational efficiency. In practice, the time step can be adjusted by monitoring the morphological changes of the twin boundary in real time, ensuring both efficient and accurate simulation.

[0072] The advantage of explicit algorithms is their ability to quickly respond to local changes, making them particularly well-suited for describing rapidly growing twin boundaries. For example, under high temperature or high pressure conditions, the atomic diffusion rate accelerates, leading to rapid expansion of the twin boundary. Explicit algorithms are well-suited to capturing these rapid changes.

[0073] When the twin boundary reaches a predetermined length and encounters an obstacle, it enters a phase of slow lateral growth, during which the implicit time integration algorithm is employed. The key to this phase is the accurate calculation of the driving force for interface migration, which relies primarily on the analysis of dislocation density gradients. The implicit algorithm determines the interface migration velocity by solving a system of nonlinear equations, ensuring simulation stability and accuracy.

[0074] In the embodiment of the present invention, a method combining explicit and implicit time integration algorithms is adopted to improve the accuracy and efficiency of simulation, especially in processing complex microstructure evolution processes.

[0075] For example, see Figure 2 As shown, Figure 2 is a schematic diagram of simulating twin evolution in an embodiment of the present invention, Figure 2 The paper dynamically demonstrates the evolution of twins in metallic materials through four stages: from left to right, nucleation (local stress triggers the formation of nanoscale twin nuclei), expansion (twins rapidly extend along crystallographic directions into thin lamellar structures), growth (twin thickness continues to increase, achieving plastic deformation), and lattice reorientation (grid lines in the figure represent twin lattice orientation). The gray area represents the original crystal, while black annotations and diagonal lines highlight the initiation of twin nuclei, the interface migration path, and the direction of shear deformation. The terminal grid structure reveals the mirror symmetry of the lattices on both sides of the twin boundary, concisely presenting the complete mechanism of twinning from nanoscale twin nucleation to dynamic growth at the micron level.

[0076] In some embodiments, in the above step S104, the sliding surface direction reconstruction algorithm includes:

[0077] S1041, real-time division of the twin domain and the matrix domain according to the elliptical boundary expansion;

[0078] S1042, rotating the slip system in the twin domain around the material twin axis by a preset angle;

[0079] S1043, remap the dislocation source coordinates to the new slip plane and reset the critical shear stress.

[0080] It should be noted that twinning deformation is an important plastic deformation mechanism in metal materials. When twinning deformation occurs, the crystal orientation between the matrix and the twin domain changes, resulting in the reorientation of the slip plane direction. This reorientation not only affects the direction of dislocation motion and the Burgers vector, but also changes the location and effectiveness of pinning barriers and dislocation sources. Therefore, in order to accurately simulate the microstructural changes during twin evolution, it is necessary to implement a slip plane direction reconstruction algorithm. This algorithm determines the direction of the slip plane based on the crystallographic symmetry of twin deformation, adjusts the dislocation motion rules according to the new crystal orientation, and updates the distribution of pinning barriers and dislocation sources.

[0081] Each time the ellipse boundary expands outward, the simulation space is divided into two regions, the twin domain and the matrix domain, using the current ellipse equation as a criterion. The twin domain includes all regions within the ellipse boundary, while the matrix domain includes the original matrix region outside the ellipse. Adaptive meshing technology can be used to locally refine the mesh near the ellipse boundary to ensure that the position error between the partition boundary and the physical twin boundary is within a preset value.

[0082] For all dislocation nodes, slip systems, and defects within the twinning domain, the slip direction and slip plane normal of the original slip system are rotated by a preset angle around the material-specific twinning axis. This rotation updates the slip direction from the original crystal orientation to the twinning orientation, and the slip plane normal from the original crystal plane to the twinning plane. The direction vectors of the dislocation segments are also rotated by the same angle to ensure they remain within the new slip plane.

[0083] Updating the spatial coordinates and slip properties of dislocation sources involves recalculating the spatial coordinates of dislocation sources to match the rotated slip plane and dynamically adjusting the critical shear stress based on the crystallographic orientation of the new slip system. Updating the spatial coordinates and slip properties of obstacles involves updating the spatial coordinates of pinning points in real time with lattice rotation and adjusting the obstacle strength proportionally to the critical stress of the new slip system.

[0084] In this way, the growth process of twins can be simulated through the constructed geometric model.

[0085] S105, after the twin growth is completed, iteratively correcting the evolution of dislocations in the target material according to the twin growth state in the current time step cycle.

[0086] The dislocation evolution correction includes, but is not limited to, modifying dislocation velocities, updating dislocation positions, and eliminating dislocations that disappear due to annihilation or escape from the free surface. After the dislocations are corrected based on the state of twin growth, the next time increment is entered and the above process is repeated until the preset dislocation dynamics solution time step is reached.

[0087] It is understandable that the movement of dislocations inside the material is not unconstrained free movement, but is affected by various factors, among which the interaction with the previous dislocation, the obstacles encountered, and the twins encountered have a limiting effect on its movement trajectory. Since in actual materials, there are mutually repulsive or attractive forces between dislocations, skipping or overlapping the previous dislocation is physically inconsistent with the actual situation. Once a dislocation is detected that violates this rule, the movement speed of the dislocation can be reduced according to the preset rules. The preset rules can be formulated based on the physical principles of dislocation interaction and a large amount of simulation experimental experience. The unreasonable movement of dislocations can be corrected by reducing the speed, so that its movement state is more in line with the actual situation. For example, according to the theoretical model of dislocation interaction, when it is detected that a dislocation has a tendency to skip or overlap, a new, lower speed value is calculated according to the formula related to the current speed and dislocation spacing, thereby ensuring the rationality of the dislocation movement.

[0088] When dislocations move within a material, it's also important to consider their arrival at the specimen's free surface. In real materials, dislocations' behavior changes upon reaching the free surface, impacting the material's overall properties. To accurately simulate this process, the algorithm can specify that dislocations are moved to an effective infinity away from the sample upon reaching the free surface. This eliminates interference from dislocations that disappear due to annihilation or escape from the free surface. By removing dislocations that reach the free surface, the behavior of dislocations within the material can be more clearly observed and analyzed, ensuring that the simulation results accurately reflect the material's internal conditions.

[0089] The following combination Figure 3 The above steps S101 to S105 are described in detail.

[0090] Figure 3 This is a flowchart of discrete dislocation dynamics modeling considering twin evolution in an embodiment of the present invention, see Figure 3 As shown in the figure, first, the material constants of the target material and the computational information required for the simulation are input to construct a discrete dislocation dynamics geometric model. In the constructed combined model, a slip plane is defined and dislocation sources and obstacles are randomly distributed on the slip plane. Then, a matrix is ​​initialized to store dislocation motion trajectories, stress-strain data, and dislocation nucleation and escape time data, where Figure 3 middle is the current time, is the total time that the plastic boundary conditions are applied (i.e., the preset dislocation dynamics solution time step).

[0091] First of all, Initialize, Figure 3 In Chinese it is represented as: ;judge When , the plastic deformation time step cycle is entered. Within the time step cycle, the pinning and release of dislocations at obstacles are simulated with constant time increments. For example, represents a constant time increment in the time step cycle, expressed as:

[0092] ;

[0093] In each cycle of the time step cycle, the target material is subjected to the preset boundary conditions that produce plastic deformation, and the presence of twin nucleation is checked in real time. If twin nucleation exists, the growth rate of the twin is calculated first, and then the time increment step is combined with the time increment step. The size to which the twins can grow (twin size) is calculated. Then, within the constructed geometric model, the process of twin growth to the calculated twin evolution size is simulated, i.e., the process described in step S104 above. If twin nucleation is not detected, or if twin nucleation is detected and the twin growth process is complete, the presence of dislocation nucleation is detected. If dislocation nucleation is determined, the dislocation evolution state in the target material is corrected in real time through the process described in step S105 above.

[0094] In some embodiments, the above method further includes: when a matrix dislocation contacts a twin boundary, changing the interaction mechanism between the dislocation and the interface by setting the properties of the twin boundary, and updating the type and size of the dislocation.

[0095] It should be noted that when a dislocation moves to a twin boundary, its slip behavior is terminated and transformed into an interface dislocation due to the special structure of the interface. By adjusting the properties of the twin boundary, such as the elastic modulus and the symmetry of the atomic arrangement, the interaction mechanism between the dislocation and the interface can be changed. For example, at low interface energy, dislocations are more easily absorbed, a high elastic modulus gradient may lead to dislocation reflection, and an incoherent interface may promote dislocation transmission. At the same time, the type of dislocation will change accordingly. For example, a screw dislocation may be transformed into an edge dislocation, and a partial dislocation may be reorganized into a full dislocation. Its size will also be adjusted due to decomposition, reorganization, or changes in line length. Ultimately, these dynamic adjustments will affect the growth behavior of the twin.

[0096] For example, the dislocation absorption mechanism is used as an example: the model detects contact between a dislocation segment and a twin boundary through spatial position judgment, and then triggers the preset interface reaction rules. Through the dislocation-interface interaction mechanism, the matrix slip properties of the dislocation (such as the direction of the Burgers vector and the direction of the dislocation line) are eliminated, and it is redefined as an interface dislocation anchored to the twin boundary. The type and size of the interface dislocation are also updated. This process can simulate the loss of dislocation mobility caused by interface coherence or stacking fault energy differences when dislocations interact with twin boundaries in physical reality.

[0097] In the above embodiments, the core physical basis of the dislocation absorption mechanism is that the twin boundary, as a low-energy stable structure, hinders the movement of dislocations. When a dislocation attempts to penetrate the twin boundary, the periodic interruption of the atomic arrangement at the interface will break the energy conditions for continuous slip of the dislocation, prompting the dislocation to be converted into an interface defect through decomposition or recombination. This transformation can not only directly terminate the matrix plasticity contribution of the dislocation, but also affect the subsequent interaction mode between dislocations and twin boundaries through the accumulation of interfacial dislocation density. This mechanism can effectively reproduce the experimentally observed twin boundary strengthening effect, that is, as deformation proceeds, the twin boundary forms a dislocation barrier by continuously absorbing dislocations, resulting in an increase in the rheological stress of the material. At the same time, the dynamic evolution of the interfacial dislocation network also provides a numerical carrier for understanding the twin-dislocation cooperative deformation.

[0098] In an embodiment of the present invention, a discrete dislocation dynamics geometric model is constructed based on the material constants of the target material and the computational information required for simulation; within a preset dislocation dynamics solution time step, preset plastic deformation boundary conditions are applied to the target material at a constant time increment to determine the microstructural changes of the target material during the plastic deformation process; when it is determined that twin nuclei exist in the target material, the growth rate of the twins is calculated and the twin evolution size within the current time step cycle is determined based on the growth rate; in the geometric model, according to the determined twin evolution size within the current time step cycle, an elliptical structure twin boundary is defined, and a slip plane direction reconstruction algorithm is implemented in the twin domain to update the crystal orientation and dislocation source position in real time to simulate the growth of twins; wherein, the twin growth process includes: driving the twin boundary to expand rapidly longitudinally along the major axis direction of the ellipse and to grow slowly laterally along the minor axis direction; after the twin growth is completed, the evolution of dislocations in the target material is iteratively corrected according to the twin growth state under the current time step cycle. In this way, the dynamic migration of elliptical boundaries solves the problem that twins cannot grow substantially. The two-stage growth mechanism of twins reproduces the growth path of twins, which can realize cross-scale simulation from nanoscale twin nucleation to micron-scale dynamic growth, and thereby realize the correction of dislocation evolution, thereby improving the authenticity of material plastic deformation simulation.

[0099] The various embodiments in this specification are described in a progressive manner, and the same or similar parts between the various embodiments can be referenced to each other. Each embodiment focuses on the differences from other embodiments.

[0100] The above embodiments are only used to illustrate the technical solutions of the present application, rather than to limit the present application. Although the present application has been described in detail with reference to the aforementioned embodiments, a person of ordinary skill in the art should understand that the technical solutions described in the aforementioned embodiments can still be modified, or some or all of the technical features therein can be replaced by equivalents. However, these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the present application.

Claims

1. A discrete dislocation dynamics modeling method considering twin evolution, characterized in that: include: Construct a discrete dislocation dynamics geometric model based on the material constants of the target material and the computational information required for simulation; Applying preset plastic deformation boundary conditions to the target material at constant time increments within a preset dislocation dynamics solution time step to determine microstructural changes of the target material during the plastic deformation process; When it is determined that twin nuclei exist in the target material, calculating the growth rate of the twins and determining the evolution size of the twins in the current time step cycle based on the growth rate; In the geometric model, based on the determined twin evolution size within the current time step cycle, an elliptical twin boundary is defined, and a slip plane direction reconstruction algorithm is implemented within the twin domain to update the crystal orientation and dislocation source position in real time to simulate the growth of twins. The twin growth process includes: driving the twin boundary to rapidly expand longitudinally along the major axis of the ellipse and slowly grow laterally along the minor axis. The slip plane direction reconstruction algorithm includes: Real-time division of twin domain and matrix domain based on elliptical boundary expansion; Rotate the slip system in the twin domain around the material twin axis by a preset angle to achieve lattice reorientation; Remap the dislocation source coordinates to the new slip plane and reset the critical shear stress; After twin growth is completed, the evolution of dislocations in the target material is iteratively corrected according to the twin growth state under the current time step cycle; wherein, when the matrix dislocation contacts the twin boundary, the interaction mechanism between the dislocation and the interface is changed by setting the properties of the twin boundary, and the type and size of the dislocation are updated.

2. The method according to claim 1, characterized in that After constructing the discrete dislocation dynamics geometric model, the method further includes: defining a slip plane in the geometric model according to the crystallographic characteristics of the target material, and randomly distributing dislocation sources and obstacles on the slip plane; Initialize the matrix used to store dislocation motion trajectories, stress-strain data, and dislocation nucleation and escape time data.

3. The method according to claim 2, characterized in that The twin boundary of the elliptical structure satisfies the following formula: ； in 、 is a coordinate variable used to describe the twin boundary of the elliptical structure, ( , ) are the coordinates of the ellipse center, and are the semi-axis lengths of the major axis and minor axis respectively, and 、 as well as 、 It is dynamically updated as the twin grows and is used to characterize the twin boundary extension.

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