Electromagnetic detection and in-situ regulation and control integrated method for residual stress of additive high-entropy alloy
Through the integrated method of residual stress electromagnetic detection and in-situ regulation of additive high-entropy alloys, multi-point detection and in-situ regulation are used to perform multi-point detection and in-situ regulation of components in additive manufacturing, the low efficiency and high cost of residual stress regulation of components in additive manufacturing are solved. The problem of this has achieved efficient and low-cost detection and regulation effects.
Patent Information
- Application Number
- CN202411385499.2
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2024-09-30
- Publication Date
- 2025-01-10
AI Technical Summary
During the additive manufacturing process, there are large residual stresses inside metal-type high-entropy alloy parts, resulting in reduced cracking, deformation and mechanical properties. The existing heat treatment methods have high energy consumption, serious pollution and high cost. Electromagnetic residual stress control is large The parts are costly and the inspection efficiency is low.
The integrated method of residual stress electromagnetic detection and in-situ regulation of additive high-entropy alloy is adopted. Multi-point synchronous detection and in-situ regulation of the sample is carried out through excitation and in-situ core groups, and electromagnetic detection and regulation technology is used to improve detection and regulation efficiency. Reduce costs.
It realizes efficient residual stress detection and regulation of large-scale additive manufacturing metal-type high-entropy alloy components, improves detection and regulation efficiency, reduces equipment complexity and energy consumption, and avoids the problem of poor regulation effect.
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Figure CN119282143A_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to the technical field of additive manufacturing, and in particular to an integrated method for electromagnetic detection and in-situ regulation of residual stress in additive high-entropy alloys. Background Art
[0002] A metallic high entropy alloy is an alloy composed of five or more main elements in roughly equal molar ratios. This unique composition leads to enhanced intermetallic chemical bonds and increased atomic structure complexity, making high entropy alloys exhibit an excellent combination of properties, such as high strength, high hardness, good wear resistance, excellent corrosion resistance, and low-temperature mechanical properties. Therefore, the demand for metallic high entropy alloys is also increasing rapidly with the rapid development of industries such as cryogenic pressure vessels, nuclear energy, deep space and deep sea exploration.
[0003] At present, the traditional metal mold high entropy alloy manufacturing methods, such as arc melting and casting, will cause uneven distribution of the alloy components (segregation) during the equilibrium solidification process, which poses a challenge to the control of high entropy alloys. However, the emergence of metal additive manufacturing technology provides another feasible solution for the efficient preparation of metal mold high entropy alloy parts. In addition, metal additive manufacturing technology also improves material utilization and reduces the manufacturing cost of complex structural parts.
[0004] However, in the process of additive manufacturing, there will inevitably be an increased temperature gradient inside the parts, which will cause some internal stress, namely residual stress, to remain inside the parts after they are manufactured. In addition, the greater material strength of metal-type high-entropy alloys will lead to greater residual stress inside the metal-type high-entropy alloys manufactured by additive manufacturing. The presence of residual stress will lead to cracking, deformation, and reduction of mechanical properties and service life of parts.
[0005] At present, the main way for additive manufacturing companies to control the residual stress of metal high entropy alloy mechanical parts is heat treatment. However, heat treatment consumes a lot of energy, causes serious pollution, and takes a long time. In addition, heat treatment can also lead to problems such as reduced material strength, oxidation, and changes in microstructure.
[0006] Electromagnetic residual stress control is a method that uses the magnetostrictive effect of materials during magnetization to control residual stress. It has the advantages of being green, efficient, easy to operate, low cost, and improving the mechanical properties of materials. However, for larger parts, residual stress control requires a larger external magnetic field, which will significantly increase costs.
[0007] In terms of residual stress detection, electromagnetic testing is an emerging non-destructive testing technology, which has the advantages of fast response, small size and low cost. Similarly, for larger parts, the detection efficiency will be low due to single-point detection.
[0008] In response to the above problems, this patent develops an integrated method for electromagnetic intelligent detection and in-situ regulation of residual stress in additively manufactured metal-type high-entropy alloys. This method can simultaneously detect multi-point residual stress of larger additively manufactured metal-type high-entropy alloy components without the need to take the equipment offline or replace equipment. The residual stress can be regulated in situ, thereby improving the detection and regulation efficiency and avoiding the problem of poor regulation effect caused by inconsistency between the detection position and the regulation position. Summary of the invention
[0009] In view of the shortcomings of the prior art, the present invention provides an integrated method for electromagnetic detection and in-situ regulation of residual stress in additive high-entropy alloys, which solves the problems raised in the above-mentioned background technology.
[0010] To solve the above technical problems, according to one aspect of the present invention, more specifically, an integrated method for electromagnetic detection and in-situ regulation of residual stress in additive high entropy alloys includes an excitation core, a sample, and an induction core group, characterized in that the following steps are performed:
[0011] S1. In order to improve the residual stress detection efficiency of additively manufactured metal high entropy alloys, the sample is divided into m rows and n columns of experimental areas according to the sample size, and they are recorded as A 11 ...A mn , arrange the excitation and induction core groups with m rows and n columns, and record them as M 11 ...M 1n M 21 ...M mn , perform multi-area synchronous detection on the tested sample, reset the direction of each core to zero, and make the direction of all cores uniform;
[0012] S2, set the detection distance l0 between the excitation and induction cores and the sample, the stress control distance l1 between the excitation core and the sample, the number a of residual stress directions to be detected, and the angle θ1…θ of the residual stress directions to be detected. a , residual stress detection magnetic field alternating frequency f1, residual stress detection magnetic field strength B1, detection angle α, angle between excitation core and induction core β, residual stress control threshold σ limit ;
[0013] S3, according to the first residual stress direction θ1 to be detected, rotate all the excitation cores so that the angle between them and the residual stress to be detected is θ1+α, and at the same time, rotate the induction core so that the minimum angle between it and the excitation core is β, and all experimental areas start detection at the same time;
[0014] S4, core group M 11 The inductive core, in M 11Under the action of the alternating magnetic field B1 of the excitation core, a corresponding induced electromotive force E1 is generated. The output voltage signal U1 is obtained through the signal processing circuit. U1 is substituted into the relationship model between the output voltage signal and the residual stress to obtain the corresponding residual stress value.
[0015] S5. Repeat step S4 to complete the detection of the remaining experimental areas, and write the absolute values of the residual stress values obtained by the detection into the matrix in sequence according to the experimental areas to form the residual stress distribution matrix [σ1] of the tested piece, and calculate the residual stress control change matrix [Δσ1] = [σ1] - [σ limit ], where the matrix [σ limit Each element in ] is σ limit , and record [σ1] and [Δσ1];
[0016] S6, repeating steps S3-S5 according to the next residual stress direction θ2 to be detected, until all residual stress directions to be detected are completed, and the residual stress distribution matrix and residual stress control change matrix of all residual stress directions to be detected are obtained;
[0017] S7, substitute the residual stress control variation matrix of the first residual stress direction θ1 to be detected into the residual stress control value and control parameter relationship model, and optimize the magnetic field frequency f used to control the residual stress of all excitation cores. mn1 , magnetic field strength B mn1 and control time t mn1 , where 1 represents the first residual stress direction to be detected;
[0018] S8, turn all the excitation cores parallel to the first residual stress direction θ1 to be detected, turn off all the induction cores and signal processing circuits, adjust the distance between all the excitation cores and the sample to l1, start regulating all the experimental areas at the same time, and time each excitation core separately for t' mn =0, when t' mn =t mn1 When the regulation ends;
[0019] S9, rotating all the excitation cores to be parallel to the next residual stress direction to be detected, and repeating step S8 until the residual stress regulation in all the residual stress directions to be detected is completed;
[0020] S10, repeat steps S3-S6 to determine whether all elements of the residual stress control variation matrix are less than zero. If not, repeat steps S7-S9 to correct the residual stress again. If yes, end.
[0021] Furthermore, for the same experimental area, the residual stress detection excitation core and the stress regulation excitation core are the same, only the working parameters are different, and the residual stress detection and regulation are carried out in situ, that is, the core targets the same area of the sample during detection and regulation.
[0022] Furthermore, the angle between the excitation coil and the residual stress to be detected during residual stress detection is different from the angle between the excitation coil and the residual stress to be detected during residual stress regulation, that is, the detection angle α≠0.
[0023] Furthermore, the output voltage signal and residual stress relationship model in step S4 includes the following steps:
[0024] S11. Perform electromagnetic detection experiments on the stress-free additively manufactured metal high-entropy alloy that has been stress-relieved and annealed, and calibrate the corresponding output voltage signal under stress-free conditions. Then, apply tension to the alloy once every 10 MPa, and perform electromagnetic detection experiments on the additively manufactured metal high-entropy alloy under each tension state, and calibrate the corresponding output voltage signal until the tensile yield strength σ corresponding to the alloy is loaded. s1 , and record all tensile stress and corresponding output voltage signal data;
[0025] S12, apply pressure once every -10MPa to the stress-free additively manufactured metal high-entropy alloy after stress relief annealing, conduct electromagnetic detection experiments on the additively manufactured metal high-entropy alloy under each pressure state, and calibrate the corresponding output voltage signal until the corresponding compressive yield strength σ is loaded. s2 , and record all compressive stress and corresponding output voltage signal data;
[0026] S13. Based on the data recorded in steps S11 and S12, a high-order function is used to fit the applied force and the output voltage signal to obtain a relationship model between the output voltage signal and the residual stress.
[0027] Furthermore, the residual stress control value and control parameter relationship model in step S7 includes the following steps:
[0028] S14, determine the residual stress control magnetic field intensity B interval as [a, b], determine the residual stress control magnetic field alternating frequency f interval as (0, f s ], determine the residual stress control time t interval as (0,t s ], determine the initial residual stress σ o The interval is [σ s1 ,σ s2 ], where the magnetic field intensity is determined by the hysteresis loop of the additively manufactured metal-type high entropy alloy, the initial residual stress is determined by the tensile and compressive yield strengths of the additively manufactured metal-type high entropy alloy, and the determined interval is used for orthogonal experimental design;
[0029] S15. Carry out multi-factor and multi-level orthogonal experimental design, and use 80% of the test data as the training set and the remaining 20% as the test set. Establish an electromagnetic residual stress control prediction model based on a neural network, and the nodes of the model input layer are magnetic field frequency f, magnetic field intensity B, aging time t and initial residual stress value σ o , the number of hidden layer units is determined according to design experience and test results, the output layer node is the residual stress change value Δσ, the model is trained using the training set to obtain the residual stress prediction model, and the model is tested using the test set;
[0030] S16. Combining the residual stress control model with the particle swarm algorithm, determine the optimal magnetic field frequency, magnetic field intensity, and aging time corresponding to each element in the residual stress control matrix.
[0031] The beneficial effects of the integrated method of electromagnetic detection and in-situ regulation of residual stress of additive high entropy alloy of the present invention are:
[0032] Compared with the prior art, the present invention solves the problems of residual stress reduction in large-scale additively manufactured metal-type high-entropy alloys affecting material properties, high pollution, and low efficiency, and realizes the integration of residual stress regulation and in-situ detection using electromagnetics, greatly improving the efficiency and effect of electromagnetic regulation and detection of residual stress in large-scale additively manufactured metal-type high-entropy alloys, and simplifying the complexity of the corresponding equipment. BRIEF DESCRIPTION OF THE DRAWINGS
[0033] The present invention is further described in detail below with reference to the accompanying drawings and specific implementation methods.
[0034] Figure 1 It is a structural schematic diagram of the present invention;
[0035] Figure 2 It is a schematic diagram of the process of the present invention.
[0036] In the figure: 1. Excitation core group; 2. Sample; 3. Induction core group. DETAILED DESCRIPTION
[0037] The present invention will be described in detail below with reference to the accompanying drawings and in combination with embodiments. It should be noted that the embodiments and features in the embodiments of the present application can be combined with each other without conflict.
[0038] like Figure 1 As shown, according to one aspect of the present invention, a method for integrating electromagnetic detection and in-situ regulation of residual stress of additive high entropy alloy is provided, comprising an excitation core 1, a sample 2, an induction core group 3, and the following steps:
[0039] S1. In order to improve the residual stress detection efficiency of additively manufactured metal high entropy alloys, sample 2 is divided into m rows and n columns of experimental areas according to the size of sample 2, and they are recorded as A 11 ...A mn , arrange the excitation and induction core groups 3 with m rows and n columns, and record them as M 11 ...M 1n M 21 ...M mn , perform multi-area synchronous detection on the test sample 2, reset the direction of each magnetic core to zero, and make the directions of all magnetic cores uniform;
[0040] S2, set the detection distance l0 between the excitation and induction cores and the sample 2, the stress control distance l1 between the excitation core 1 and the sample 2, the number a of the residual stress directions to be detected, and the angles θ1…θ of the residual stress directions to be detected. a , residual stress detection magnetic field alternating frequency f1, residual stress detection magnetic field strength B1, detection angle α, angle between excitation core 1 and induction core β, residual stress control threshold σ limit ;
[0041] S3, according to the first residual stress direction θ1 to be detected, rotate all the excitation cores 1 so that the angle between them and the residual stress to be detected is θ1+α, and at the same time, rotate the induction core so that the minimum angle between it and the excitation core 1 is β, and all experimental areas start detection at the same time;
[0042] S4, core group M 11 The inductive core, in M 11 Under the action of the alternating magnetic field B1 of the excitation core 1, a corresponding induced electromotive force E1 is generated. The output voltage signal U1 is obtained through the signal processing circuit, and U1 is substituted into the output voltage signal and residual stress relationship model to obtain the corresponding residual stress value.
[0043] S5. Repeat step S4 to complete the detection of the remaining experimental areas, and write the absolute values of the residual stress values obtained by the detection into the matrix in sequence according to the experimental areas to form the residual stress distribution matrix [σ1] of the tested piece, and calculate the residual stress control change matrix [Δσ1] = [σ1] - [σ limit ], where the matrix [σ limit Each element in ] is σ limit , and record [σ1] and [Δσ1];
[0044] S6, repeating steps S3-S5 according to the next residual stress direction θ2 to be detected, until all residual stress directions to be detected are completed, and the residual stress distribution matrix and residual stress control change matrix of all residual stress directions to be detected are obtained;
[0045] S7, substitute the residual stress control variation matrix of the first residual stress direction θ1 to be detected into the residual stress control value and control parameter relationship model, and optimize the magnetic field frequency f used to control the residual stress of all excitation cores 1. mn1 , magnetic field strength B mn1 and control time t mn1 , where 1 represents the first residual stress direction to be detected;
[0046] S8, rotate all the excitation cores 1 to be parallel to the first residual stress direction θ1 to be detected, turn off all the induction cores and signal processing circuits, adjust the distance between all the excitation cores 1 and the sample 2 to l1, start regulating all the experimental areas at the same time, and time each excitation core 1 individually for t' mn =0, when t' mn =t mn1 When the regulation ends;
[0047] S9, rotating all the excitation cores 1 to be parallel to the next residual stress direction to be detected, and repeating step S8 until the residual stress regulation in all the residual stress directions to be detected is completed;
[0048] S10, repeat steps S3-S6 to determine whether all elements of the residual stress control variation matrix are less than zero. If not, repeat steps S7-S9 to correct the residual stress again. If yes, end.
[0049] In this embodiment, for the same experimental area, the residual stress detection excitation core and the stress regulation excitation core are the same, only the working parameters are different, and the residual stress detection and regulation are performed in situ, that is, the core targets the same area of sample 2 during detection and regulation.
[0050] In this embodiment, the angle between the excitation coil and the residual stress to be detected during residual stress detection is different from the angle between the excitation coil and the residual stress to be detected during residual stress regulation, that is, the detection angle α≠0.
[0051] In this embodiment, the output voltage signal and residual stress relationship model in step S4 includes the following steps:
[0052] S11. Perform electromagnetic detection experiments on the stress-free additively manufactured metal high-entropy alloy that has been stress-relieved and annealed, and calibrate the corresponding output voltage signal under stress-free conditions. Then, apply tension to the alloy once every 10 MPa, and perform electromagnetic detection experiments on the additively manufactured metal high-entropy alloy under each tension state, and calibrate the corresponding output voltage signal until the tensile yield strength σ corresponding to the alloy is loaded. s1 , and record all tensile stress and corresponding output voltage signal data;
[0053] S12, apply pressure once every -10MPa to the stress-free additively manufactured metal high-entropy alloy after stress relief annealing, conduct electromagnetic detection experiments on the additively manufactured metal high-entropy alloy under each pressure state, and calibrate the corresponding output voltage signal until the corresponding compressive yield strength σ is loaded. s2 , and record all compressive stress and corresponding output voltage signal data;
[0054] S13. Based on the data recorded in steps S11 and S12, a high-order function is used to fit the applied force and the output voltage signal to obtain a relationship model between the output voltage signal and the residual stress.
[0055] In this embodiment, the residual stress control value and control parameter relationship model in step S7 includes the following steps:
[0056] S14, determine the residual stress control magnetic field intensity B interval as [a, b], determine the residual stress control magnetic field alternating frequency f interval as (0, f s ], determine the residual stress control time t interval as (0,t s ], determine the initial residual stress σ o The interval is [σ s1 ,σ s2 ], where the magnetic field intensity is determined by the hysteresis loop of the additively manufactured metal-type high entropy alloy, the initial residual stress is determined by the tensile and compressive yield strengths of the additively manufactured metal-type high entropy alloy, and the determined interval is used for orthogonal experimental design;
[0057] S15. Carry out multi-factor and multi-level orthogonal experimental design, and use 80% of the test data as the training set and the remaining 20% as the test set. Establish an electromagnetic residual stress control prediction model based on a neural network, and the nodes of the model input layer are magnetic field frequency f, magnetic field intensity B, aging time t and initial residual stress value σ o , the number of hidden layer units is determined according to design experience and test results, the output layer node is the residual stress change value Δσ, the model is trained using the training set to obtain the residual stress prediction model, and the model is tested using the test set;
[0058] S16. Combining the residual stress control model with the particle swarm algorithm, determine the optimal magnetic field frequency, magnetic field intensity, and aging time corresponding to each element in the residual stress control matrix.
[0059] Of course, the above description is not a limitation of the present invention, and the present invention is not limited to the above examples. Changes, modifications, additions or substitutions made by ordinary technicians in this technical field within the essential scope of the present invention also fall within the protection scope of the present invention.
Claims
1. An integrated method for electromagnetic detection and in-situ regulation of residual stress in additive high-entropy alloys, comprising an excitation core (1), a sample (2), and an induction core group (3), characterized in that: Follow these steps: S1. In order to improve the residual stress detection efficiency of additively manufactured metal high entropy alloy, the sample (2) is divided into m rows and n columns of experimental areas according to the size of the sample (2), and they are marked as A 11 ...A mn , arrange the excitation and induction core groups (3) with m rows and n columns, and record them as M 11 ...M 1n M 21 ...M mn , perform multi-region synchronous detection on the tested sample (2), reset the direction of each magnetic core to zero, and make the directions of all magnetic cores uniform; S2, setting the detection distance l0 between the excitation and induction cores and the sample (2), the stress control distance l1 between the excitation core (1) and the sample (2), the number a of the residual stress directions to be detected, and the angles θ1…θ of the residual stress directions to be detected a , residual stress detection magnetic field alternating frequency f1, residual stress detection magnetic field strength B1, detection angle α, angle β between the excitation core (1) and the induction core, residual stress control threshold σ limit ; S3, according to the first residual stress direction θ1 to be detected, all the excitation cores (1) are rotated so that the angle between them and the residual stress to be detected is θ1+α, and at the same time, the induction core is rotated so that the minimum angle between it and the excitation core (1) is β, and all experimental areas are tested at the same time; S4, core group M 11 The inductive core, in M 11 Under the action of the alternating magnetic field B1 of the excitation core (1), a corresponding induced electromotive force E1 is generated. The output voltage signal U1 is obtained through the signal processing circuit. U1 is substituted into the output voltage signal and residual stress relationship model to obtain the corresponding residual stress value. S5. Repeat step S4 to complete the detection of the remaining experimental areas, and write the absolute values of the residual stress values obtained by the detection into the matrix in sequence according to the experimental areas to form the residual stress distribution matrix [σ1] of the tested piece, and calculate the residual stress control change matrix [Δσ1] = [σ1] - [σ limit ], where the matrix [σ limit ] are all elements of σ limit , and record [σ1] and [Δσ1]; S6, repeating steps S3-S5 according to the next residual stress direction θ2 to be detected, until all residual stress directions to be detected are completed, and the residual stress distribution matrix and residual stress control change matrix of all residual stress directions to be detected are obtained; S7, substitute the residual stress control variation matrix of the first residual stress direction θ1 to be detected into the residual stress control value and control parameter relationship model, and optimize the magnetic field frequency f used to control the residual stress of all excitation cores (1) mn1 , magnetic field strength B mn1 and control time t mn1 , where 1 represents the first residual stress direction to be detected; S8, rotate all the excitation cores (1) to be parallel to the first residual stress direction θ1 to be detected, turn off all the induction cores and signal processing circuits, adjust the distance between all the excitation cores (1) and the sample (2) to l1, start regulating all the experimental areas at the same time, and each excitation core (1) is timed separately for t' mn =0, when t' mn =t mn1 When the regulation ends; S9, rotating all the excitation cores (1) to be parallel to the next residual stress direction to be detected, and repeating step S8 until the residual stress control in all the residual stress directions to be detected is completed; S10, repeat steps S3-S6 to determine whether all elements of the residual stress control variation matrix are less than zero. If not, repeat steps S7-S9 to correct the residual stress again. If yes, end.
2. The integrated method for electromagnetic detection and in-situ regulation of residual stress in additive high entropy alloy according to claim 1, characterized in that: For the same experimental area, the residual stress detection excitation core and the stress regulation excitation core are the same, only the working parameters are different, and the residual stress detection and regulation are carried out in situ, that is, the core targets the same area of the sample (2) during detection and regulation.
3. The integrated method for electromagnetic detection and in-situ regulation of residual stress in additive high entropy alloy according to claim 1, characterized in that: The angle between the excitation coil and the residual stress to be detected during residual stress detection is different from the angle between the excitation coil and the residual stress to be detected during residual stress regulation, that is, the detection angle α≠0.
4. The integrated method for electromagnetic detection and in-situ regulation of residual stress in additive high entropy alloy according to claim 1, characterized in that: The output voltage signal and residual stress relationship model in step S4 includes the following steps: S11. Perform electromagnetic detection experiments on the stress-free additively manufactured metal high-entropy alloy that has been stress-relieved and annealed, and calibrate the corresponding output voltage signal under stress-free conditions. Then, apply tension to the alloy once every 10 MPa, and perform electromagnetic detection experiments on the additively manufactured metal high-entropy alloy under each tension state, and calibrate the corresponding output voltage signal until the tensile yield strength σ corresponding to the alloy is loaded. s1 , and record all tensile stress and corresponding output voltage signal data; S12, apply pressure once every -10MPa to the stress-free additively manufactured metal high-entropy alloy after stress relief annealing, conduct electromagnetic detection experiments on the additively manufactured metal high-entropy alloy under each pressure state, and calibrate the corresponding output voltage signal until the corresponding compressive yield strength σ is loaded. s2 , and record all compressive stress and corresponding output voltage signal data; S13. Based on the data recorded in steps S11 and S12, a high-order function is used to fit the applied force and the output voltage signal to obtain a relationship model between the output voltage signal and the residual stress.
5. The integrated method for electromagnetic detection and in-situ regulation of residual stress in additive high entropy alloy according to claim 1, characterized in that: The residual stress control value and control parameter relationship model in step S7 includes the following steps: S14, determine the residual stress control magnetic field intensity B interval as [a, b], determine the residual stress control magnetic field alternating frequency f interval as (0, f s ], determine the residual stress control time t interval as (0,t s ], determine the initial residual stress σ o The interval is [σ s1 ,σ s2 ], where the magnetic field intensity is determined by the hysteresis loop of the additively manufactured metal-type high entropy alloy, the initial residual stress is determined by the tensile and compressive yield strengths of the additively manufactured metal-type high entropy alloy, and the determined interval is used for orthogonal experimental design; S15. Carry out multi-factor and multi-level orthogonal experimental design, and use 80% of the test data as the training set and the remaining 20% as the test set. Establish an electromagnetic residual stress control prediction model based on a neural network, and the nodes of the model input layer are magnetic field frequency f, magnetic field intensity B, aging time t and initial residual stress value σ o , the number of hidden layer units is determined according to design experience and test results, the output layer node is the residual stress change value Δσ, the model is trained using the training set to obtain the residual stress prediction model, and the model is tested using the test set; S16. Combining the residual stress control model with the particle swarm algorithm, determine the optimal magnetic field frequency, magnetic field intensity, and aging time corresponding to each element in the residual stress control matrix.