A method for constructing a calculation model of dislocation resistance coefficient caused by phonon wind and its application

Abstract

The present invention relates to a method for constructing a calculation model of the dislocation resistance coefficient caused by phonon wind and its application. The calculation of the dislocation resistance coefficient B of phonon wind mainly includes three parts: calculating the average value of elastic constants; calculating the steady-state displacement gradient field of dislocations at any characteristic angle in any crystal structure; calculating the dislocation resistance coefficient B of phonon wind for any type of dislocation at any velocity; by considering the crystal and slip plane geometries, the influence of crystal anisotropy on dislocation resistance is emphasized, and the relationship between different dislocation characteristic angles (the angle between the dislocation line and the slip direction) and the dislocation resistance coefficient is analyzed; this innovative mechanical constitutive calculation model has a guiding role in predicting the mechanical behavior of metallic materials under high strain rates and high loads.

Description

Technical Field

[0001] The present invention belongs to the technical field of condensed matter physics, and relates to a method for constructing a calculation model of dislocation resistance coefficient caused by phonon wind and its application, in particular to the application of a method for constructing a calculation model of dislocation resistance coefficient caused by phonon wind in the material design and development. Background Art

[0002] Mechanical properties are important indicators reflecting whether a material can work stably under specific environments with different loads. Traditional mechanical property tests mainly apply corresponding loads to the material by experimental means, and then measure the maximum stress it can withstand to obtain different mechanical moduli. However, testing the mechanical properties of materials by experimental means requires destroying the specimen, resulting in unnecessary waste, and it is more difficult to implement the experimental approach for samples with tiny volumes. With the increasing perfection of the computational materials discipline system, it has been possible to accurately predict various physical properties of materials by means of computer simulation, including the accurate prediction of the mechanical properties of materials.

[0003] In materials science, a fundamental issue in the dynamic response of solid metals is the mechanism contributing to the dislocation resistance coefficient under high stress and strain: mobile dislocations (linear defects in the metal crystal structure) are resisted due to their interaction with the crystal structure, which is an important factor for understanding material strength. Under high stress conditions, when the stress level becomes "critical", that is, high enough to easily overcome the highest potential barrier, the dislocation resistance becomes viscous, and the stress-velocity dependence changes significantly. The typical dislocation velocity is within a few percent of the transverse sound velocity. The main contribution to the dislocation resistance coefficient (near and above the Debye temperature) is the dissipative effect of phonon scattering ("phonon wind"). Accurately evaluating the resistance coefficient at high strain rates is crucial for single-crystal volume plasticity, polycrystalline plasticity, and ductile fracture models applicable under high stress and strain rates.

[0004] In early studies, the resistance coefficient B was only calculated and experimentally determined for dislocation velocities far below the transverse sound velocity. However, there is currently no theoretical framework in the literature for accurately calculating the velocity dependence of the resistance coefficient B until approaching the transverse sound velocity. Therefore, establishing a dislocation resistance model for the action of phonon wind at high strain rates has become an urgent problem to be solved. Summary of the Invention

[0005] In view of this, the present invention provides a method for constructing a calculation model of dislocation resistance coefficient caused by phonon wind and its application to solve the problem that the current research methods only calculate and experimentally determine the dislocation velocity far below the transverse sound velocity, cannot accurately calculate the velocity dependence of the resistance coefficient B, and are not conducive to the study of the mechanical behavior of metal materials under high strain rate loading environments.

[0006] To achieve the above object, the present invention provides the following technical solutions:

[0007] A method for constructing a calculation model of the dislocation resistance coefficient caused by phonon wind, comprising the following steps:

[0008] S1. Calculate the average value of the elastic coefficient

[0009] To study the interaction between phonons and a single mobile dislocation in a crystal, considering the harmonic approximation and taking the limit of the continuum, the Hamiltonian expression of the continuum is:

[0010] (1)

[0011] (2)

[0012] (3)

[0013] Hamiltonian consists of the kinetic part of phonons and the interaction between phonons and dislocations The Hamiltonian describes the interaction of phonons along edge and screw dislocations and depends on the two-dimensional wave vector of the dislocation , and the displacement gradient field in the Fourier space caused by the dislocation is represented by ;

[0014] The wave vector is located in the first Brillouin zone. Due to momentum conservation, the dislocation wave vector satisfies ; represents the radius of a sphere whose volume is equal to the volume of the unit cell in the Fourier space, that is , where represents the volume of the unit volume, represents the material density, and the average value of the elastic coefficient depends on the second-order elastic constant and the third-order elastic constant , and the average value of the elastic coefficient is obtained by the following formula:

[0015] (4);

[0016] S2. Calculate the steady-state displacement gradient field of dislocations at any characteristic angle in any crystal structure

[0017] The displacement gradient field is obtained by solving the equations of motion (e.o.m) and the stress-strain relationship (Hooke's law):

[0018] (5)

[0019] Here, for the displacement field a sign is introduced for the gradient , and is the time derivative of the displacement field, which is expressed in terms of its gradient as: , in which case the e.o.m equation simplifies to:

[0020] (6)

[0021] The "effective" elastic constants

[0022] are usually defined. According to the theory of A.N. Stroh, the displacement gradient field is calculated by the formula:

[0023] (7)

[0024] (8)

[0025] We use the shorthand notation , where the value of is determined by the following formula:

[0026] (9)

[0027] (10)

[0028] where is the normal vector of the slip plane, is perpendicular to both and the dislocation direction. The value of in equation (8) is determined by the following formula:

[0029] (11)

[0030] (12)

[0031] Finally, the Fourier transform of the displacement gradient field is performed:

[0032] (13);

[0033] S3. Calculate the dislocation resistance coefficient B of the phonon wind for any type of dislocation at any velocity

[0034] The resistance coefficient of the dislocation is defined as the proportionality coefficient of the force required to maintain the dislocation velocity , related to the dissipation per unit length passing through , which in turn is directly determined by the phonons transitioning from state per unit time to the state scattering probability obtain, by multiplying by the equilibrium phonon distribution function to obtain the number of transitions per unit time; considering that each transition transfers an energy, i.e., the energy is , then for the dissipation per unit time and unit dislocation length:

[0035] (14)

[0036] second-order elastic constant and third-order elastic constant are both anisotropic. To maintain the isotropy of the phonon spectrum, spherical coordinates of the phonon wave vector are introduced, and the sum of these vectors is approximated by an integral over the first Brillouin zone. The drag coefficient of the phonon wind in the continuum is:

[0037] (15)

[0038] where , the main contribution to B is due to the interaction with transverse phonons, and the Debye spectrum of transverse phonons in the isotropic limit is given by:

[0039] (16)

[0040] For the high-frequency part, due to consistency with the continuum approximation, a variable substitution is introduced:

[0041] (17)

[0042] (18)

[0043] (19)

[0044] Furthermore, if the dislocation core effect is neglected, the radial dependence of the dislocation field in the continuum limit is always ; is the Fourier transform of . Considering these factors and introducing the unit vector , , the expression for the dislocation drag coefficient of isotropic transverse phonons is:

[0045]

[0046] (20)

[0047] Among them, removing q supports the dimensionless variable t defined by Equation (17), so that:

[0048] (21)

[0049] Furthermore, for the isotropic Debye phonon spectrum in step S2, the effective Lame constants of polycrystals are used, that is, the "transverse" phonon hypothesis is based on the effective polycrystalline shear modulus to calculate the motion of the transverse sound velocity.

[0050] Furthermore, in step S3, although the maximum contribution of the phonon wind to the dislocation resistance comes from the interaction with the transverse phonons, other branches cannot be completely ignored: the combined contribution of pure longitudinal phonons ( ), and mixed transverse / longitudinal phonons ( ) can increase the resistance coefficient by 20%; as can be seen from Equation (20), at low speeds and high temperatures, is proportional to the fifth power of the transverse sound velocity.

[0051] Furthermore, in step S3, on the one hand, the two or all of the powers of the mixed transverse / longitudinal phonon and pure longitudinal phonon branches are replaced by a larger longitudinal sound velocity, thereby reducing the of these branches; on the other hand the different combinations of elastic constants in result in different branches, making the

[0052] exact ratio depend on the material; for the mixed branch (i.e., input transverse phonons, output longitudinal phonons, and vice versa), different variable substitutions are selected: The Debye spectrum of longitudinal phonons in the isotropic limit is given by , for dislocations interacting with pure longitudinal phonons, a simple substitution is made, that is

[0053] (22)

[0054] (23)

[0055] where is the transition function after , and it simplifies to when a linear expression of , where the integration range of

[0056] (24)

[0057] Therefore, becomes a function that has finite minimum / maximum values at all corners; the expressions for the dislocation resistance coefficients of mixed transverse / longitudinal phonons and mixed longitudinal / transverse phonons are:

[0058] (25)

[0059]

[0060] (26)

[0061]

[0062]

[0063] For these two mixed branches, where is determined by (22); the two variables and are discretized into points (with higher precision at higher speeds), and then integrated using the trapezoidal method, requiring to be more accurate than .

[0064] Furthermore, when the dislocation velocity is greater than the minimum critical velocity in step S3, at this time the dislocation resistance coefficient approaches infinity, so in the program we default to infinity at this time. Conversely, when the dislocation velocity is less than the minimum critical velocity , then continue to iteratively calculate the dislocation resistance coefficient at higher speeds until the dislocation velocity is greater than the minimum critical velocity , and the specific calculation steps are shown in Figure 1 .

[0065] The application of the method for constructing a calculation model of the dislocation resistance coefficient caused by phonon wind in the study of the mechanical behavior of materials under high strain rate loading environments and the design and development of high-precision materials.

[0066] The beneficial effects of the present invention are as follows:

[0067] The method for constructing a calculation model of the dislocation resistance coefficient caused by phonon wind disclosed in the present invention re-studies the dislocation resistance coefficient of phonon scattering ("phonon wind") at different temperatures in the continuous approximation, and then generalizes the model to include the anisotropic effect of single crystal grains in polycrystalline metals. To establish the anisotropic model, the interaction between the dislocations and elastic constants of anisotropic single crystal grains and the polycrystalline isotropic Debye phonon spectrum is considered. The Debye approximation greatly simplifies the theory, and the dislocations are modeled according to crystal symmetries (bcc, fcc, hcp, etc.). The present invention emphasizes the influence of crystal anisotropy on dislocation resistance by considering the crystal and slip plane geometries, and analyzes the relationship between different dislocation characteristic angles (the angle between the dislocation line and the slip direction) and the dislocation resistance coefficient. This innovative mechanical constitutive model calculation method has a guiding role in predicting the mechanical behavior of metal materials under high strain rates and high loads.

[0068] Other advantages, objectives, and features of the present invention will be described to some extent in the subsequent specification, and to some extent, will be obvious to those skilled in the art based on the study of the following text, or can be taught from the practice of the present invention. The objectives and other advantages of the present invention can be achieved and obtained through the following specification. Brief Description of the Drawings

[0069] In order to make the objectives, technical solutions, and advantages of the present invention clearer, the present invention will be described in detail preferably with reference to the accompanying drawings, where:

[0070] Figure 1 is the calculation flow chart of the method for constructing a calculation model of the dislocation resistance coefficient caused by phonon wind according to the present invention;

[0071] Figure 2 is the curve graph of the dislocation resistance coefficient B of different velocity average dislocation characteristic angles output by the embodiment of the present invention;

[0072] Figure 3 is the curve graph of the dislocation resistance coefficient B of different velocity screw dislocations output by the embodiment of the present invention;

[0073] Figure 4 is the curve graph of the dislocation resistance coefficient B of different velocity edge dislocations output by the embodiment of the present invention. Detailed Embodiment

[0074] The following illustrates the embodiments of the present invention through specific specific examples. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and various details in this specification can also be modified or changed based on different viewpoints and applications without departing from the spirit of the present invention.

[0075] A method for constructing a calculation model of the dislocation resistance coefficient caused by phonon wind, comprising the following steps:

[0076] S1. Calculate the average value of the elastic constants:

[0077] To study the interaction between phonons and a single mobile dislocation in a crystal, consider the harmonic approximation and take the limit of the continuum, where the Hamiltonian expression of the continuum is:

[0078] (1)

[0079] (2)

[0080] (3)

[0081] Hamiltonian consists of the kinetic part of phonons and the interaction between phonons and dislocations For the isotropic Debye phonon spectrum, use the effective lame constant of polycrystals, that is, the "transverse" phonon hypothesis is used for the motion of the transverse sound velocity calculated by the effective polycrystalline shear modulus The Hamiltonian describes the interaction of phonons along edge and screw dislocations and depends on the two-dimensional wave vector of the dislocation The displacement gradient field in the Fourier space caused by the dislocation is represented by ;

[0082] The wave vector is located in the first Brillouin zone. Due to momentum conservation, the dislocation wave vector satisfies ; represents the radius of the sphere with a volume equal to the unit cell volume in the Fourier space, that is , where represents the volume of the unit cell, represents the material density, and the average value of the elastic coefficient depends on the second-order elastic constant and the third-order elastic constant The average value of the elastic coefficient is obtained by the following formula:

[0083] (4);

[0084] S2. Calculate the steady-state displacement gradient field of dislocations at any characteristic angle in any crystal structure

[0085] The displacement gradient field is obtained by solving the equations of motion (e.o.m) and the stress-strain relationship (Hooke's law):

[0086] (5)

[0087] We introduce a sign for the gradient of the displacement field and, where is the time derivative of the displacement field, which can be expressed in terms of its gradient as: In this case, the e.o.m equation can be simplified to:

[0088] (6)

[0089] The "effective" elastic constants are usually defined

[0090] According to the theory of A.N. Stroh, the displacement gradient field is calculated as:

[0091] (7)

[0092] (8)

[0093] We use the shorthand notation , where the value of is determined by the following formula:

[0094] (9)

[0095] (10)

[0096] where is the normal vector to the slip plane, is perpendicular to both and the dislocation direction, and the value of in equation (8) is determined by the following formula:

[0097] (11)

[0098] (12)

[0099] Finally, we perform a Fourier transform on the displacement gradient field:

[0100] (13);

[0101] S3. Calculate the dislocation resistance coefficient B of the phonon wind for any type of dislocation at any velocity

[0102] The resistance coefficient of a dislocation is defined as the proportionality coefficient of the force required to maintain the dislocation velocity to the dissipation per unit length through ​ is related to which, in turn, is directly determined by the probability of phonon scattering from state to state per unit time. Multiply by the equilibrium phonon distribution function to obtain the number of transitions per unit time; considering that each transition transfers an energy, i.e., the energy is , then for the dissipation per unit time and unit dislocation length:

[0103] (14)

[0104] The second-order elastic constant and the third-order elastic constant are both anisotropic. To maintain the isotropy of the phonon spectrum, spherical coordinates of the phonon wave vector are introduced, and the sum of these vectors is approximated by an integral over the first Brillouin zone. The drag coefficient of the phonon wind in the continuum is:

[0105]

[0106] (15)

[0107] where the main contribution to B is due to the interaction with transverse phonons. The Debye spectrum of transverse phonons in the isotropic limit is given by:

[0108] (16)

[0109] For the high-frequency part, due to consistency with the continuum approximation, a variable substitution is introduced:

[0110] (17)

[0111] (18)

[0112] (19) Furthermore, if the dislocation core effect is ignored, the radial dependence of the dislocation field in the continuum limit is always ; is the Fourier transform of . Taking these factors into account and introducing the unit vectors and

[0113] , the expression for the dislocation drag coefficient of isotropic transverse phonons is:

[0114]

[0115] ​​ (20)

[0116] Among them, removing q supports the dimensionless variable t defined by formula (17), so that:

[0117] (21)

[0118] Although the largest contribution of the phonon wind to the dislocation resistance comes from the interaction with transverse phonons, other branches cannot be completely ignored: the combined contribution of pure longitudinal phonons ( ) and mixed transverse / longitudinal phonons ( ) can increase the resistance coefficient by 20%; as can be seen from formula (20), at low speeds and high temperatures, is proportional to the fifth power of the transverse sound speed.

[0119] On the one hand, the two or all of the mixed transverse / longitudinal phonon and pure longitudinal phonon branches powers are replaced by a larger longitudinal sound speed, thereby reducing these branches ; on the other hand in different combinations of elastic constants lead to different branches, making the exact proportion depend on the material; for the mixed branch (i.e., input transverse phonons, output longitudinal phonons, and vice versa), different variable substitutions are selected:

[0120] The Debye spectrum of longitudinal phonons in the isotropic limit is given by , for dislocations interacting with pure longitudinal phonons, a simple substitution is made, that is ;

[0121] (22)

[0122] (23)

[0123] where is the transition function after , only when , is simplified to a linear expression of where the integration range of

[0124] (24)

[0125] Therefore, becomes The function has finite minimum / maximum values at all corners; the expressions for the dislocation resistance coefficients of mixed transverse / longitudinal phonons and mixed longitudinal / transverse phonons are as follows:

[0126] (25)

[0127]

[0128] (26)

[0129]

[0130]

[0131] For these two mixed branches, where is determined by (22); the two variables and are discretized into points (with higher precision at higher speeds), and then integrated using the trapezoidal method, requiring to be more accurate than . Additionally, when the dislocation velocity is greater than the minimum critical velocity , at this time the dislocation resistance coefficient approaches infinity, so in the program we default to infinity at this time. Conversely, when the dislocation velocity is less than the minimum critical velocity , the dislocation resistance coefficient at higher speeds is calculated iteratively, and the specific calculation steps are shown in Figure 1 .

[0132] The above details the mathematical and physical modeling process of the calculation method for the dislocation resistance coefficient of phonon wind .

[0133] Examples

[0134] The following details Cu and Al as examples

[0135] Figures 2 to 4 where the abscissa is the normalized velocity of the dislocation , and the ordinate is the dislocation resistance coefficient , with the unit of . Figure 2 is a graph of the dislocation resistance coefficient B of the average dislocation characteristic angle at different speeds for Cu and Al. It can be seen from the graph that as the normalized dislocation velocity increases, the dislocation resistance coefficient B of both Cu and Al decreases slowly. For Cu, it rises steeply around approaching 0.67 and then approaches infinity. For Al, at There is a sharp rise when approaching about 0.88, and then it approaches infinity; Figure 3 It is a graph of the dislocation resistance coefficient B of different velocity screw dislocations of Cu and Al. Similar to when the dislocation is the average dislocation characteristic angle, as the velocity increases, the dislocation resistance coefficient B of both Cu and Al decreases slowly. Cu has a sharp rise when approaching about 0.62, and then it approaches infinity. Al has a sharp rise when approaching about 0.85, and then it approaches infinity; Figure 4 It is a graph of the dislocation resistance coefficient B of different velocity edge dislocations of Cu and Al. It can be seen from the figure that as the velocity increases, the dislocation resistance coefficient B of both Cu and Al decreases slowly. Cu has a sharp rise when approaching about 0.67, and then it approaches infinity. Al has a sharp rise when approaching about 0.88, and then it approaches infinity. Among them, the direct comparison of the dislocation resistance coefficient B with the experiment is only limited to the low-velocity state ( ).

[0136] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not restrictive. Although the present invention has been described in detail with reference to the preferred embodiments, those of ordinary skill in the art should understand that the technical solutions of the present invention can be modified or equivalently replaced without departing from the purpose and scope of the present technical solution, and they should all be covered by the scope of the claims of the present invention.

Claims

1. A method for constructing a calculation model for dislocation resistance coefficient caused by phonon wind, characterized in that: The following steps are involved: S1. Calculate the average value of elastic modulus In order to study the interaction between phonons and a single mobile dislocation in a crystal, the harmonic approximation is considered and the limit of a continuous medium is taken, where the Hamiltonian of the continuum is expressed as: (1) (2) (3) Hamiltonian By phonon The dynamic part and phonons and dislocations The Hamiltonian describes the interaction of phonons along the edge and the screw dislocation and depends on the two-dimensional wave vector of the dislocation , the displacement gradient field in Fourier space caused by the dislocation is expressed as express; The wave vector is located in the first Brillouin zone. Due to the conservation of momentum, the dislocation wave vector satisfies ; represents the radius of a sphere whose volume is equal to the unit cell volume in Fourier space, that is, ,in represents the volume of the unit volume, Indicates material density, average value of elastic modulus Depends on the second-order elastic constant and the third-order elastic constant , the average value of elastic coefficient Obtained by the following formula: (4)； S2. Calculate the steady-state displacement gradient field of dislocations of any characteristic angle in any crystal structure The displacement gradient field is obtained by solving the equation of motion (eom) and the stress-strain relationship (Hooke's law): (5) Here is the displacement field The gradient of ,and is the time derivative of the displacement field, expressed as its gradient: , in this case the eom formula simplifies to: (6) The "effective" elastic constant is usually defined According to ANStroh's theory, the calculation formula of the displacement gradient field is: (7) (8) Use shorthand notation , in the above formula The value of is determined by the following formula: (9) (10) In the formula is the normal vector of the sliding surface, and and the dislocation direction are perpendicular to each other, and in (8) The value of is determined by the following formula: (11) (12) Finally, the displacement gradient field is Fourier transformed: (13)； S3. Calculate the dislocation drag coefficient B of the phonon wind of any type of dislocation at any speed Dislocation resistance coefficient is defined as maintaining the dislocation velocity Required force The proportionality coefficient is Dissipation per unit length This in turn is directly related to the phonon switching from the state To status The probability of scattering Get, will Multiply by the equilibrium phonon distribution function The number of transitions per unit time is obtained; considering that each transition transfers an energy, that is, the energy is , then for the dissipation per unit time and per unit dislocation length: (14) Second-order elastic constants and the third-order elastic constant In order to maintain the isotropy of the phonon spectrum, the spherical coordinates of the phonon wave vector are introduced, and the sum of these vectors is approximated by the integral of the first Brillouin zone. The drag coefficient is: (15) in , the main contribution to B is due to the interaction with transverse phonons, whose Debye spectrum in the isotropic limit is given by: (16) For the high frequency part, variable substitution is introduced because it is consistent with the continuum approximation: (17) (18) (19) Furthermore, if dislocation nucleation effects are neglected, the radial dependence of the dislocation field in the continuum limit is always ; for The Fourier transform of , , the expression of dislocation resistance coefficient of isotropic transverse phonon is: (20) where q is removed to support the dimensionless variable t defined in equation (17), thus: (21)。 2. The method for constructing a calculation model for the dislocation resistance coefficient caused by phonon wind according to claim 1, characterized in that: The isotropic Debye phonon spectrum in step S2 uses the effective lame constant of the polycrystal, i.e., the "transverse" phonons are assumed to be determined by the effective polycrystal shear modulus Calculated transverse sound velocity motion.

3. The method for constructing a calculation model for the dislocation resistance coefficient caused by phonon wind according to claim 1, characterized in that: Although the largest contribution of the phonon wind to the dislocation drag in step S3 comes from the interaction with transverse phonons, other branches cannot be completely ignored: the combined contribution of pure longitudinal phonons and mixed transverse / longitudinal phonons Can increase the drag coefficient 20% share; From formula (20), we can see that at low speed and high temperature, Proportional to the fifth power of the transverse speed of sound.

4. The method for constructing a calculation model for the dislocation resistance coefficient caused by phonon wind according to claim 3, characterized in that: In step S3, two or all of the mixed transverse / longitudinal phonon branches and the pure longitudinal phonon branches are The second power is replaced by a greater longitudinal sound velocity, which reduces the ;on the other hand Different combinations of elastic constants in lead to different branches, making The exact ratio depends on the material; for mixed branches, i.e. transverse phonons in and longitudinal phonons out, or vice versa, different variable substitutions are chosen: The Debye spectrum of longitudinal phonons in the isotropic limit is given by Given that, for a dislocation interacting with purely longitudinal phonons, a simple substitution ,Right now ; (22) (23) in yes The subsequent transition function is only hour, Simplified to The linear expression of The integral range of is limited to a finite interval by the following conditions: (24) therefore, become The function has finite minimum / maximum values ​​at all angles; the dislocation resistance coefficient expressions for mixed transverse / longitudinal phonons and mixed longitudinal / transverse phonons are: (25) (26) For these two mixed branches, Determined by (22); Two variables and is discretized into points, with higher accuracy at higher speeds, and subsequently integrated using the trapezoidal method, requiring Compare With higher precision.

5. The method for constructing a calculation model for the dislocation resistance coefficient caused by phonon wind according to claim 4, characterized in that: In step S3, when the dislocation velocity is greater than the minimum critical velocity When the dislocation velocity is less than the minimum critical velocity, the dislocation resistance coefficient approaches infinity. The dislocation resistance coefficient at a higher speed is calculated iteratively until the dislocation speed is greater than the minimum critical speed. .

6. Application of the method for constructing a calculation model for dislocation resistance coefficient caused by phonon wind as described in any one of claims 1 to 5 in the study of mechanical behavior of materials under high strain rate loading environment, and in the design and development of high-precision materials.

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