CN113094885A - Method for predicting strength of high-entropy alloy containing defect structure - Google Patents

Method for predicting strength of high-entropy alloy containing defect structure Download PDF

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CN113094885A
CN113094885A CN202110349228.1A CN202110349228A CN113094885A CN 113094885 A CN113094885 A CN 113094885A CN 202110349228 A CN202110349228 A CN 202110349228A CN 113094885 A CN113094885 A CN 113094885A
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李甲
方棋洪
彭静
陈阳
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Abstract

The invention relates to a method for predicting the strength of a high-entropy alloy containing a defect structure. And a related strength theoretical model is established by effectively combining a dislocation theory, a crystal plasticity theory and a defect theory. The influence of dislocation, dislocation loops and serious lattice distortion effect on the performance of the high-entropy alloy is considered, and the quantitative calculation of the strength of the high-entropy alloy with the defect structure is realized. The yield strength obtained by the prediction method provided by the invention is well consistent with the experimental result. The related deformation mechanism analyzed in the invention has important significance for researching and predicting the influence of the dislocation loop defect on the strength of the high-entropy alloy. By the prediction method provided by the invention, the element content of the alloy is regulated and controlled, and the influence on the yield strength under different element contents is researched, so that theoretical guidance is provided for the design of the high-performance high-entropy alloy. In the development process of new alloy, the method effectively avoids a large number of repeated tests, shortens the research and development period of the high-performance high-entropy alloy, saves the cost and has great engineering value.

Description

Method for predicting strength of high-entropy alloy containing defect structure
Technical Field
The invention relates to the field of prediction of strength of high-entropy alloy with a defect structure, in particular to a dislocation theory, a crystal plasticity theory and a defect theory.
Background
In recent years, with the demand of modern industry, high entropy alloys have been proposed and widely studied and used. Unlike most conventional alloys, high entropy alloys are composed of four or more equimolar or near equimolar amounts of elements. Therefore, it has many excellent properties such as high strength, high hardness, wear resistance, corrosion resistance, high temperature stability, etc. However, various microscopic defects may be generated during the processing and service thereof. For example, during the solidification of the material, the dislocation is generated due to the uneven distribution of the thermal stress gradient; the material undergoes mechanical working deformation (forging, rolling) and a large number of defect structures are generated inside the matrix under the action of force. Secondly, a large number of defects (interstitial atoms and vacancies) are created inside the material under irradiation conditions due to the impact of the energetic particles. The generation of the defect structures influences the movement and evolution of dislocation in the plastic deformation process of the high-entropy alloy, thereby causing the obvious change of macroscopic mechanical properties of the material. In addition, the high-entropy alloy has a serious lattice distortion effect due to the difference of the atomic size and the shear modulus of each main element, so that dislocation movement is more difficult than that of the traditional alloy. From previous experiments, the lattice distortion in the high-entropy alloy can improve the defect pinning capability and inhibit the accumulation of defects, which is one of the reasons for the reduction of the damage degree along with the increase of the complexity of the components. Compared with the traditional FeCrNi alloy, the FeNiMnCr high-entropy alloy has excellent performance, so the FeNiMnCr high-entropy alloy is selected as a research material of the invention. The main internal defects of the FeNiMnCr high-entropy alloy are dislocation, dislocation loops and grain boundaries.
In the previous researches, the influence of the high-entropy alloy microdefect on the strength of the material is mainly researched by adopting an experimental determination method, and a corresponding theoretical model of the high-entropy alloy microdefect strength is not established yet. In addition, the crystal plasticity theory has not been used for the research of the high-entropy alloy. Crystal plasticity theory is an effective method to combine atomic scale and dislocations and link them to macroscopic deformation processes. Based on experimental and simulation results, the invention analyzes related deformation mechanisms, establishes related micro defect strengthening theoretical models, and has important significance for researching quantitative hardening effect of defects and predicting influence of the defects on mechanical performance.
Disclosure of Invention
The invention aims to provide a method for quantitatively calculating and predicting the strength of a high-entropy alloy with a defect structure based on experimental data combined with a dislocation theory, a crystal plasticity theory and a defect theory. According to the invention, the dislocation loop strengthening model of the high-entropy alloy is considered, the strength quantitative prediction of the high-entropy alloy containing defects is realized, and meanwhile, the content of alloy elements can be regulated and controlled, and the high-entropy alloy with the optimal strength is predicted, so that the research and development period of the high-performance-resistant high-entropy alloy is greatly shortened, and the research and development cost is reduced.
The technical scheme of the invention is as follows:
determining material parameters of the high-entropy alloy, including element physical parameters and related parameters of defects. The material adopted by the invention is FeNiMnCr high-entropy alloy, and the material parameters are as follows:
table 1 physical parameters of each element.
Parameter(s) Fe Ni Mn Cr
Radius of atom (pm) 124 125 127 125
Shear modulus (GPa) 82 76 81 115
Volume fraction (at%) 27.1 29.5 26.6 16.8
According to the classical crystal plasticity theory, the critical component shear stress is constructed
Figure BDA0003001683610000021
And shear strain rate
Figure BDA0003001683610000022
The relationship between them.
Figure BDA0003001683610000023
In the formula
Figure BDA0003001683610000024
And m is the rate sensitivity coefficient for reference shear strain rate and slip, respectively.
The composition of the critical component shear stress is determined. In the general case of materials free of defects, the slip resistance to dislocation motion resulting from dislocation interactions
Figure BDA0003001683610000025
And slip resistance tau due to severe lattice distortion to dislocation motionsThe critical shear stress of the high-entropy alloy is formed. The present invention also takes into account the effect of dislocation loops, and therefore the critical shear stress also includes the slip resistance caused by dislocation loops
Figure BDA0003001683610000026
Then, the components of each critical component shear stress are calculated respectively.
Determining the contribution of the lattice distortion to the critical partial shear stress. Due to the difference of shear modulus and atomic radius among main elements of the high-entropy alloy, the randomness of lattice lattices enables the high-entropy alloy to have obvious lattice distortion effect, and the dislocation slip resistance is increased, so that the influence of serious lattice distortion of the high-entropy alloy on hardening cannot be ignored.
τs＝t-1σss (2)
Where t is the Taylor coefficient, which has a value of 3.06, σssFor the contribution of solid solution strengthening to yield strength, and according to Vegard's law, the lattice distortion strengthening of high entropy alloys is superimposed by the individual action of each element in the alloy:
Figure BDA0003001683610000027
n is the number of element types, ciIs the concentration of the i element(s),
Figure BDA0003001683610000028
is the independent contribution value of the ith element in the high-entropy alloy to the overall yield strength,
Figure BDA0003001683610000029
wherein A is a dimensionless parameter associated with the material and has a value of 0.04 and the material has a shear modulus of
Figure BDA0003001683610000031
In addition the mismatch parameter deltaiCan be expressed as:
Figure BDA0003001683610000032
for FCC high entropy alloys ξ ═ 1 and for BCC high entropy alloys ξ ═ 4. The value of beta depends on the dislocation type, when the screw dislocation dominates the plastic deformation, the beta is more than 2 and less than 4, when the edge dislocation dominates the plastic deformation, the beta is more than or equal to 16, and the size mismatch of the atom i is delta riAnd modulus mismatch δ μiAs shown in the following formula, assuming that the quaternary high-entropy alloy ijkl consists of ternary alloy ijk mixed l elements,
Figure BDA0003001683610000033
Figure BDA0003001683610000034
Figure BDA0003001683610000035
for the average size mismatch of the ijkl high entropy alloys,
Figure BDA0003001683610000036
for the average size mismatch of the ijk alloy,
Figure BDA0003001683610000037
for the average modulus mismatch of the ijkl high entropy alloy,
Figure BDA0003001683610000038
is the average modulus mismatch of the ijk alloy.
Figure BDA0003001683610000039
Figure BDA00030016836100000310
δrijAnd δ μijRepresenting the size mismatch and modulus mismatch between atom i and atom j.
δrij＝2(ri-rj)/(ri+rj) (10)
δμij＝2(μi-μj)/(μi+μj) (11)
The lattice distortion enhancement term can be finally obtained by the above derivation.
The contribution of dislocations to the critical partial shear stress is determined. The initial dislocation density measured from an experimental point of view is first obtained, the movement of dislocations on the slip system is hindered by other dislocations, and the contribution of dislocations to the critical component shear stress can be expressed as:
Figure BDA00030016836100000311
where b is the Berger vector, μ is the shear modulus, hnDislocation density considering dislocation propagation and annihilation for dislocation hardening coefficient
Figure BDA0003001683610000041
May be expressed as:
Figure BDA0003001683610000042
wherein
Figure BDA0003001683610000043
Is the loading strain rate. Multiplication factor k1And annihilation coefficient
Figure BDA0003001683610000044
The relationship between can be written as:
Figure BDA0003001683610000045
wherein epsilon0,Dα,gαK, and χ are the reference strain rate, drag stress, normalized activation energy, boltzmann constant, and interaction parameter, respectively, and equation (14) describes the nonlinear relationship between the propagation coefficient and the annihilation coefficient with respect to temperature and applied strain rate, and takes into account the annihilation mechanism of dislocation climbing and cross-slip.
The effect of dislocation loops on the shear stress of the interface was determined. The dislocation loops hinder the slip motion of dislocations, resulting in an increase in yield stress. Since FCC crystals have 12 slip systems, the defect-dislocation interaction model is used to characterize the spatial dependence of dislocation loops and dislocation interactions.
Figure BDA0003001683610000046
hdIs the hardening coefficient of dislocation loops, Nd4 is the number of dislocation feature planes 111.
Figure BDA0003001683610000047
nαIs the normal vector of the slip plane, HβIs a second order matrix describing dislocation loops.
Hβ＝ρ1·3d1·Mβ (16)
Figure BDA0003001683610000048
Wherein I(2)Is a unity second order matrix, nβIs the normal vector of the characteristic plane of the dislocation loop, p1And d1Respectively dislocation loop initial density and size.
And processing and data analysis are carried out on the calculation results of the three strengthening mechanisms.
Finally, the lattice distortion characteristics can be further regulated and controlled by regulating and controlling the element content, and meanwhile, the influence of the change of the element content on each hardening item is predicted.
Advantageous effects
The invention provides a method for predicting the strength of a high-entropy alloy containing a defect structure, which realizes the prediction of the strength of the high-entropy alloy by considering dislocation loop defects and severe lattice distortion effects and is based on a solid theoretical basis, a clear modeling process and a clear physical meaning.
The invention takes the high-entropy alloy with the basic component of FeNiMnCr as an example, adopts the experimental data of dislocation loop defects, calculates the qualitative and quantitative relation between the evolution of dislocation loops and the strength through a strength model in a prediction method, and has good result fit with the experiment, thereby quantifying the influence of the dislocation loop defects in the material on the performance and providing theoretical guidance for further service of the high-entropy alloy.
The invention can change the contribution ratio of three mechanisms by regulating the content of each element so as to carry out preliminary composition and performance prediction, take the high-entropy alloy taking the basic component of FeNiMnCr as an example, provide theoretical guidance for the design of other high-entropy alloys and have good application prospect.
Drawings
FIG. 1 is a schematic diagram of a high entropy alloy model that accounts for dislocations, dislocation loops, and lattice distortion effects.
Fig. 2 is (a) a tensile stress-strain curve of dislocation loops of different densities, (b) a relationship between work hardening rate and strain, (c) dislocation density evolution during stretching, (d) a comparison of strength values calculated by a strength model with experimental values, and the contribution of each strengthening mechanism in the model to strength.
FIG. 3 shows (a) the effect of different Cr element contents on the strengthening contribution of dislocations, dislocation loops and lattice distortion, and (b) the ratio of the contribution of the three strengthening mechanisms to yield strength.
Detailed Description
The technical scheme of the model schematic diagram and the specific example of the dislocation-ring-defect-containing high-entropy alloy considering three effects of dislocation, dislocation ring and lattice distortion are further explained in the following with reference to the attached drawing 1, and the invention is not limited to the following examples, and all the design ideas of the invention are within the protection scope of the invention.
Dislocation is mainly generated due to processing preparation, service and the like of the material and is used as the representation of plastic deformation of the material; the main defect dislocation loops generated by the FeNiMnCr high-entropy alloy in service are considered to be the main source of material hardening; lattice distortion is an inherent characteristic of the high-entropy alloy generated by the mismatch of the sizes and the moduli of the constituent elements and has an enhancement effect on the mechanical properties of the material.
The method comprises the following specific steps: by collecting dislocation loop experimental data of FeNiMnCr high entropy alloy, the characteristic parameters of dislocation loops are shown in Table 2.
TABLE 2 dislocation Loop size and Density under different services
Figure BDA0003001683610000061
The physical parameters involved in the process of the invention are shown in table 3.
TABLE 3 physical parameters of various types
Figure BDA0003001683610000062
For FeNiMnCr high-entropy alloy, the loading strain rate is 2.8 multiplied by 10-4s-1And simulating loading under the condition. The average grain size of the material was 35 μm and the initial dislocation density was 5X 1014m-2The lattice distortion effect in high entropy alloys is an important component of the strengthening mechanism. The intensity coefficient h of dislocation interaction is obtained by fitting the relevant experimental data of different dislocation loop sizes and densitiesn0.02, dislocation loop strength coefficient hd0.035. The stress-strain curves of the high-entropy alloy FeNiMnCr under different defect conditions in the figure 2(a) are obtained, and the fact that the sizes and the densities of dislocation loops become larger and the influence on yield stress and flow stress is increased along with the increase of irradiation dose is proved. As the dislocation loop size and density vary at different doses, the dislocation loops affect the evolution of the dislocation density and thus the hardening rate, as shown in fig. 2(b, c). On the other hand, this resultIt was shown that the resistance to plastic deformation in the case of defects was somewhat improved. Fig. 2(d) compares the yield stress results obtained from fig. 2(a) with the experimental results, and the predicted results and the experimental results agree well. Therefore, the method has better prediction precision on the strength of the FeNiMnCr high-entropy alloy containing dislocation loop defects.
In addition, the influence of the severe lattice distortion effect of the high-entropy alloy is related to different atomic radii and shear moduli and is closely related to the concentration of each principal element, so that the concentration change of different principal elements has a remarkable influence on the mechanical property of the FeNiMnCr high-entropy alloy, and the content of each element in the high-entropy alloy with better mechanical property needs to be predicted. Assuming that the concentrations of Cr are x, Fe, Ni and Mn are all (1-x)/3, three strengthening mechanisms for different dislocation loops at 293K are obtained to contribute to yield stress, as shown in FIG. 3 (a). It was found that when the Cr atomic concentration was increased from 0.1 to 0.85, δ r was found due to the average atomic size mismatchaveAnd mean modulus mismatch δ μaveThe contribution of the lattice distortion strengthening to the yield stress is very significant with the content of the Cr element being significantly changed. Since the shear modulus of Cr is larger than that of other elements in the alloy, the shear modulus of the alloy depends on the tendency of the Cr fraction to vary, and the lattice distortion strengthening contribution is largest at a Cr fraction of 0.65. As the Cr fraction increases, the contribution of dislocation strengthening and dislocation loop strengthening also gradually increases, as shown in fig. 3 (a). However, the contribution of dislocation loop strengthening to yield stress is different in the FeNiMnCrx high entropy alloys due to the different density and size of dislocation loops under different service conditions. The influence ratio of the three strengthening mechanisms on the yield stress of FeNiMnCrx is shown in FIG. 3 (b). Therefore, the method can predict the strength of the FeNiMnCr high-entropy alloy containing dislocation loop defects after the element content is changed, thereby providing guidance for the design of the FeNiMnCr high-entropy alloy and reducing the material preparation cost.

Claims (7)

1. A method for predicting the strength of a high-entropy alloy containing a defect structure is used for establishing a hardening model by combining a dislocation theory, a crystal plasticity theory and a defect theory, and is characterized in that:
the effect of the dislocation per se on the resistance to the slip in the high-entropy alloy is considered.
The interaction of dislocation loop defects with dislocation glide is considered.
The severe lattice distortion effect of the high-entropy alloy caused by atomic size and modulus difference is considered.
Defect structures in materials (dislocations, dislocation loops, grain boundaries, precipitates, etc.) are typically introduced by forces, heat, magnetism, etc. generated during processing or service. Dislocations generally enable the prediction of the strength of high entropy alloys containing dislocation loop defects. Meanwhile, guidance can be provided for the design of the high-entropy alloy with more excellent performance by regulating and controlling the content of the elements.
2. The method for predicting the strength of the high-entropy alloy with the defect structure according to claim 1, wherein the three strengthening mechanisms in the related strengthening model are accurately calculated by using intrinsic parameters of elements in the material and existing experimental data.
3. The use method according to any one of claims 1-2, wherein the treatment method comprises the following specific steps:
determining the basic material parameters needed in the model, and collecting the relevant physical parameters of the dislocation loop defects of the relevant materials.
According to the classical crystal plasticity theory, the critical component shear stress is constructed
Figure FDA0003001683600000011
And shear strain rate
Figure FDA0003001683600000012
The relationship between:
Figure FDA0003001683600000013
in the formula
Figure FDA0003001683600000014
And m is the reference shear strain rate and the rate of slip, respectivelyThe coefficient of sensitivity.
Determining the composition of critical shearing stress, wherein the high-entropy alloy critical shearing stress is generated by the slip resistance to dislocation motion due to the interaction of dislocations
Figure FDA0003001683600000015
Slip resistance tau of lattice distortion to dislocation motionsAnd defect-generated slip resistance
Figure FDA0003001683600000016
The three parts are combined.
Figure FDA0003001683600000017
And respectively calculating components of each critical component shearing stress.
The elemental content was varied and the contribution of each component was calculated again.
And analyzing and processing the simulation calculation result.
4. The specific step according to claim 3, characterized in that the effective material parameters are determined. The material adopted by the invention is FeNiMnCr high-entropy alloy, and the material parameters are shown in Table 1.
Table 1 physical parameters of each element.
Figure FDA0003001683600000021
5. The effect of lattice distortion on strength was calculated as claimed in claim 3, wherein the temperature on the shear modulus and atomic radius difference between the principal elements, as described in Table 1, is room temperature. If the influence at other temperatures needs to be calculated, material parameters at the corresponding temperatures should be used. The randomness of the lattice makes the high-entropy alloy have obvious lattice distortion effect, increases the dislocation slip resistance, and therefore, the influence of the lattice distortion of the high-entropy alloy on the strength of the material cannot be ignored.
τs＝t-1σss
Wherein t is Taylor coefficient 3.06, σssIs the contribution of lattice distortion to yield strength. According to Vegard's law, the total lattice distortion strengthening of the high-entropy alloy is formed by the superposition of the individual actions of each element in the alloy:
Figure FDA0003001683600000022
n is the number of element species, ciIs the concentration of the i element(s),
Figure FDA0003001683600000023
is the independent contribution value of the ith element in the high-entropy alloy to the overall yield strength.
6. A method as claimed in claim 3, characterized in that the dislocation interaction causes the material to be stress hardened. From the theory of dislocations, the contribution of dislocations to the critical shear stress can be expressed as:
Figure FDA0003001683600000024
where b is the Berger vector, μ is the shear modulus, hnIs the dislocation hardening coefficient. Considering dislocation propagation and annihilation, the evolution of dislocation density can be expressed as:
Figure FDA0003001683600000031
wherein
Figure FDA0003001683600000037
Is the strain rate, the multiplication coefficient k1And annihilation coefficient
Figure FDA0003001683600000032
The relationship between can be written as:
Figure FDA0003001683600000033
wherein epsilon0,Dα,gαK, and χ are the reference strain rate, drag stress, normalized activation energy, boltzmann constant, and interaction parameter, respectively.
7. A method as claimed in claim 3, characterized in that the dislocation loops hinder the gliding movement of dislocations, resulting in an increase of the yield stress. Since face-centered cubic crystals have 12 slip systems, the defect-dislocation interaction model is used to characterize the spatial dependence of dislocation loops and dislocation interactions
Figure FDA0003001683600000034
hdIs the hardening coefficient of dislocation loops, Nd4 is the number of dislocation feature planes 111.
Figure FDA0003001683600000035
nαIs the normal vector of the slip plane, HβIs a second order matrix describing dislocation loops.
Hβ＝ρ1·3d1·Mβ
Figure FDA0003001683600000036
Wherein I(2)Is a unity second order matrix, nβIs the normal vector of the characteristic plane of the dislocation loop, p1And d1Respectively dislocation loop initial density and size.
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