A method for analyzing residual stress and deformation in ultrasonic shot peening

Abstract

The present invention discloses a method for analyzing residual stress and deformation in ultrasonic shot peening strengthening. A coupled ultrasonic shot peening model is established by combining the finite element method (FEM) and the discrete element method (DEM). Based on the established coupled ultrasonic shot peening model, the residual stress curves along the depth direction under different process parameters are obtained through simulation calculation, and the correlation coefficients are regressed according to the corresponding equations of the residual stress curves to complete the construction of the initial stress function. The constructed initial stress function is imported into the component through the user subroutine SIGINI of the finite element software ABAQUS in the form of a Fortran program, and the component is analyzed and solved by using the ABAQUS static solver to obtain the deformation conditions under different ultrasonic shot peening process parameters. This method can save calculation time, realize the rapid evaluation of the internal residual stress of the workpiece, complete the prediction of the initial stress deformation, and obtain a reasonable deformation amount on the premise of ensuring strengthening.

Description

Technical Field

[0001] The present invention relates to the technical field of ultrasonic shot peening process, and particularly relates to a method for analyzing residual stress and deformation in ultrasonic shot peening strengthening. Background Technique

[0002] Ultrasonic shot peening is a metal surface treatment process mainly used to improve the fatigue strength of components, inhibit the initiation of fatigue cracks, and increase the fatigue life of components. At present, most numerical simulations of ultrasonic shot peening strengthening use the finite element method to build models. The modeling process is complex and the mutual collision relationship between shot particles is not fully considered during the analysis process. There are differences between the simulated residual stress field and the stress field under actual working conditions. The numerical simulation of ultrasonic shot peening deformation is mainly completed by the equivalent load method. The equivalent load method mainly includes the in-plane extrusion method, the equivalent thermal load method, and the direct stress method.

[0003] Among them, the in-plane extrusion method and the equivalent thermal load method have certain limitations and complexities when dealing with large-sized workpieces, and the solution calculation amount is large. The direct stress method uses statics to directly apply the shot-induced stress obtained from finite element simulation in the form of initial stress to the integration points of finite element units. After stress equilibrium calculation, the shot peening deformation result is obtained. The direct stress method needs to perform function characterization on the obtained residual stress curve. The residual stress curve after ultrasonic shot peening includes a shot peening stress layer and a bending deformation layer, and a single function cannot accurately characterize the residual stress field. Summary of the Invention

[0004] The purpose of the present invention is to provide a method for analyzing residual stress and deformation in ultrasonic shot peening strengthening. Based on explicit dynamics, a discrete element DEM - finite element FEM (Discrete Element Method - Finite Element Method) ultrasonic shot peening coupling model is established. By introducing the discrete element particle model, the influences of shot particle size, contact properties, and the number of shot particles are taken into account. This method can obtain a more realistic residual stress field and save calculation time, perform parametric characterization on the obtained residual stress curve, realize the rapid assessment of internal residual stress of the workpiece, complete the prediction of initial stress deformation, and further coordinate the relationship between ultrasonic shot peening process parameters and stress and deformation, and obtain a reasonable deformation amount on the premise of ensuring strengthening.

[0005] The purpose of the present invention is achieved through the following technical solutions:

[0006] A method for analyzing residual stress and deformation in ultrasonic shot peening strengthening, the method comprising:

[0007] Step 1: Establish an ultrasonic shot peening coupling model by combining finite element FEM and discrete element DEM;

[0008] Step 2: Based on the established ultrasonic shot peening coupling model, obtain the residual stress curves in the depth direction under different process parameters through simulation calculation, and regress the correlation coefficients according to the corresponding equations of the residual stress curves to complete the construction of the initial stress function;

[0009] Step 3: Import the constructed initial stress function into the component through the user subroutine SIGINI of the finite element software ABAQUS in the form of a Fortran program, and use the ABAQUS static solver to analyze and solve the component to obtain the deformation conditions under different ultrasonic shot peening process parameters;

[0010] Among them, the ultrasonic shot peening process parameters include: amplitude, frequency, and pellet diameter.

[0011] It can be seen from the technical solutions provided by the present invention described above that the above method can save calculation time, realize the rapid evaluation of the residual stress inside the workpiece, complete the prediction of the initial stress deformation, further coordinate the relationship between the ultrasonic shot peening process parameters and the stress and deformation, and obtain a reasonable deformation amount on the premise of ensuring strengthening. Brief Description of the Drawings

[0012] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the following will briefly introduce the drawings required for the description of the embodiments. Obviously, the following drawings are only some embodiments of the present invention. For those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative efforts.

[0013] Figure 1 It is a schematic flow chart of the method for analyzing the residual stress and deformation of ultrasonic shot peening strengthening provided by the embodiment of the present invention;

[0014] Figure 2 It is a schematic diagram of the ultrasonic shot peening DEM-FEM coupling model in the example of the present invention;

[0015] Figure 3 It is a comparison diagram of the residual stress fitting curve and the simulation curve under the parameter of amplitude 40 - 100 μm in the example of the present invention;

[0016] Figure 4 It is a finite element model of the A-type Almen strip in the example of the present invention;

[0017] Figure 5 It is a cloud diagram of the simulation result of the ultrasonic shot peening strengthening deformation of the A-type Almen strip in the example of the present invention; Detailed Embodiments

[0018] Combined with the accompanying drawings in the embodiments of the present invention, the technical solutions in the embodiments of the present invention are clearly and completely described. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments, which does not constitute a limitation to the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts belong to the protection scope of the present invention.

[0019] As Figure 1 is a schematic flow chart of the method for analyzing the residual stress and deformation of ultrasonic shot peening provided by the embodiment of the present invention, and the method includes:

[0020] Step 1: Establish an ultrasonic shot peening coupling model by combining the finite element method (FEM) and the discrete element method (DEM);

[0021] In this step, as Figure 2 shown is a schematic diagram of the ultrasonic shot peening DEM-FEM coupling model in the example of the present invention. Specifically, the workpiece in the ultrasonic shot peening strengthening process is regarded as a continuous medium, and the shot peening particles are regarded as a discrete system. The entire strengthening process is regarded as the combination of a continuous system and a discrete system. The particle system is generated by a static method. An additional shot peening particle generation component needs to be established in the preprocessing. The mesh is divided to generate unit nodes, and the inp keyword is modified to convert the unit nodes of the shot peening particle generation component into PD3D particle units. Each particle represents a shot peening particle, and each particle unit has the same size. The deformation of the particle unit is not considered, and the particle unit is set as a rigid body;

[0022] The Johnson-Cook model is used to describe the dynamic mechanical behavior of the workpiece in the ultrasonic shot peening strengthening process, and the expression is as follows:

[0023]

[0024] In the formula, σ is the material stress; A is the static yield stress of the material; B is the material strain power exponent coefficient; ε is the equivalent plastic strain of the material; n is the strain hardening index; C is the strain rate sensitivity coefficient; is the strain influence factor; T * is the temperature influence factor; m is the temperature sensitivity coefficient;

[0025] The workpiece adopts the principle of local mesh refinement. The center of the workpiece is selected as the research area, and the mesh of the research area is set to be no more than one-tenth of the shot peening particle diameter to obtain a good stress gradient. The mesh size of other areas except the research area is increased; other components except the workpiece are set with rigid body constraints, and deformation is not considered. The workpiece selects three-dimensional variable solid elements and uses eight-node reduced integration elements (C3D8R). This element has a hourglass control mode, and the element will not produce serious distortion phenomena after simulation, which is suitable for simulation analysis of large strain and high strain rate;

[0026] The amplitude is loaded using a Fourier function. Since the waveform of ultrasonic vibration is a sine wave, a sine displacement load is applied. In the ultrasonic peening coupling model, the contact is divided into two parts:

[0027] The Hertz contact model is used between particles, and hard contact is used between particles and other components. The friction coefficient is 0.3, and an explicit dynamic solver is selected for ultrasonic peening coupling simulation analysis.

[0028] Step 2: Based on the established ultrasonic peening coupling model, stress nephograms under different process parameters are obtained through simulation calculation. The residual stress curves along the depth direction are extracted and curve-fitted, and the correlation coefficients are regressed according to the corresponding equations of the residual stress curves to complete the construction of the initial stress function;

[0029] In this step, based on the established ultrasonic peening coupling model, Python script programs are used to extract the residual stress data of multiple paths of the workpiece along the depth direction. The residual stress data at the same depth are averaged, and an S-shaped residual stress curve is constructed with the average value. As Figure 3 is the comparison chart of residual stress fitting and simulation curves under the parameter of amplitude 40 - 100 μm in the example of the present invention;

[0030] According to the distribution law of residual stress inside the workpiece after ultrasonic peening strengthening, the residual stress curve is divided into a peening stress layer and a bending deformation layer; among them, the stress distribution law of the peening stress layer along the thickness direction of the workpiece is similar to that of a cosine function, so it is approximately represented by a cosine function; the stress distribution law of the bending deformation layer is approximately represented by a polynomial function, and the best correlation coefficient is obtained through piecewise fitting and multiple iterations. The fitting formula is as follows:

[0031]

[0032] In the formula, A i , ω i , a, b, c, d, e, f are control parameters; z represents the depth of a certain layer of the workpiece; e i represents the depth of the peening stress layer; h represents the thickness of the workpiece;

[0033] The expressions of control parameters ω i and are:

[0034]

[0035]

[0036] Among them, control parameters ω i and can be expressed by the stress layer depth e iAnd the maximum depth m of the compressive stress layer i is represented by

[0037] Step 3: Import the constructed initial stress function into the component in the form of a Fortran program through the user subroutine SIGINI of the finite element software ABAQUS, and use the ABAQUS static solver to analyze and solve the component to obtain the deformation conditions under different ultrasonic shot peening process parameters; wherein, the ultrasonic shot peening process parameters include: amplitude, frequency, and shot diameter.

[0038] In this step, based on the initial stress function constructed in Step 2, the initial stress function is imported into the finite element model in the form of a Fortran program by modifying the keywords of the user subroutine SIGINI of the finite element software ABAQUS.

[0039] The user subroutine SIGINI defines the distance of the finite element model along the thickness direction to distinguish the initial stress functions corresponding to different thickness regions, and completes the editing of the initial stress function with the node coordinates or integration points as variables.

[0040] Since the directly imported ultrasonic shot peening residual stress cannot fully meet the initial conditions of the finite element model, it is necessary to perform a stress equilibrium static analysis on it, and then the strengthening deformation amount of the workpiece is characterized by the maximum displacement amount of the simulation result.

[0041] For example, taking the Type A Almen strip as an example, simulate the deformation condition after its ultrasonic shot peening strengthening. Use three-dimensional solid elements to create a Type A Almen strip model, as Figure 4 shown in the schematic diagram of the finite element model of the Type A Almen strip in the embodiment of the present invention. The workpiece is a Type A Almen strip, and the material is spring steel. The piecewise function is imported into the deformed part in the form of a Fortran program by editing the user subroutine SIGINI to complete the assignment of the initial stress, and use the static solver to perform analysis and calculation on it to obtain the deformation condition of the strip under a specific stress state.

[0042] (1) Pretreatment: Create a Type A Almen strip model with dimensions of 76*32*1.32 mm. Set the material properties. The density of spring steel is 7.8e-9 g / mm3, the Poisson's ratio is 0.29, and the elastic modulus is 205 GPa. For the Johnson-Cook equation, the relevant parameters are A = 1408 MPa, B = 600.8 MPa, c = 0.0134, and n = 0.234. Use the eight-node reduced integration element C3D8R. The mesh size is required to be no more than one-tenth of the shot size to ensure good convergence of the model calculation. Set two analysis steps. In the first analysis step, fully fix the bottom surface of the strip for stress equilibrium calculation. In the second analysis step, release the stress. Constrain the degrees of freedom in the x, y, and z directions at one point on the bottom surface of the strip, constrain the degrees of freedom in the y and z directions at the second point, and constrain the degree of freedom in the z direction at the third point;

[0043] (2) Solution: Select a static solver for solution. Create a job, call the SIGINI subroutine, and perform the solution calculation;

[0044] (3) Post-processing: Complete the calculation and view the deformation amount of the workpiece after ultrasonic shot peening. Further coordinate the relationship between strengthening and deformation based on the deformation amount, as Figure 5 shown in the contour map of the simulation results of the deformation of the Type A Almen strip after ultrasonic shot peening in the example of the present invention.

[0045] It should be noted that the content not described in detail in the embodiments of the present invention belongs to the prior art well-known to those skilled in the art.

[0046] In addition, those of ordinary skill in the art can understand that all or part of the steps in implementing the above-described embodiment methods can be completed by instructing relevant hardware through a program. The corresponding program can be stored in a computer-readable storage medium. The above-mentioned storage medium can be a read-only memory, a disk, or an optical disc, etc.

[0047] The above is only a preferred specific embodiment of the present invention, but the protection scope of the present invention is not limited thereto. Any changes or substitutions that can be easily thought of by those skilled in the art within the technical scope disclosed by the present invention should be covered by the protection scope of the present invention. Therefore, the protection scope of the present invention should be subject to the protection scope of the claims. The information disclosed in the background art section of this article is only intended to deepen the understanding of the overall background art of the present invention, and should not be regarded as an admission or any form of implication that this information constitutes the prior art already known to those skilled in the art.

Claims

1. A method for analyzing residual stress and deformation in ultrasonic shot peening strengthening, characterized in that, the method includes: Step 1: Establish an ultrasonic shot peening coupling model by combining the finite element method (FEM) and the discrete element method (DEM); The process of Step 1 is specifically as follows: Regarding the workpiece during the ultrasonic shot peening strengthening process as a continuous medium and the shot peening particles as a discrete system, and regarding the entire strengthening process as the combination of a continuous system and a discrete system. Use the Johnson-Cook model to describe the dynamic mechanical behavior of the workpiece during ultrasonic shot peening strengthening. The expression is as follows: Wherein, σ is the material stress; A is the static yield stress of the material; B is the power exponent coefficient of the material strain; ε is the equivalent plastic strain of the material; n is the strain hardening index; C is the strain rate sensitivity coefficient; is the strain influence factor; T * is the temperature influence factor; m is the temperature sensitivity coefficient; For the workpiece, adopt the principle of local mesh refinement. Select the center of the workpiece as the research area, and set the mesh size of the research area to not be greater than one-tenth of the shot peening particle diameter to obtain a good stress gradient. Increase the mesh size for other areas except the research area; The amplitude is loaded using a Fourier function. Since the waveform of ultrasonic vibration is a sine wave, a sine displacement load is applied. The contact in the ultrasonic shot peening coupling model is divided into two parts: Adopt the Hertz contact model between particles and hard contact between particles and other components, with a friction coefficient of 0.3; Step 2: Based on the established ultrasonic shot peening coupling model, obtain the residual stress curves along the depth direction under different process parameters through simulation calculations, and regress the correlation coefficients according to the corresponding equations of the residual stress curves to complete the construction of the initial stress function; Step 3: Import the constructed initial stress function into the component in the form of a Fortran program through the user subroutine SIGINI of the finite element software ABAQUS, and use the ABAQUS static solver to analyze and solve the component to obtain the deformation conditions under different ultrasonic shot peening process parameters; Among them, the ultrasonic shot peening process parameters include: amplitude, frequency, and shot peening particle diameter.

2. The method for analyzing residual stress and deformation in ultrasonic shot peening strengthening according to claim 1, characterized in that, In Step 2, based on the established ultrasonic shot peening coupling model, use a Python script program to extract the residual stress data along the depth direction of multiple paths of the workpiece, perform averaging processing on the residual stress data at the same depth, and construct an S-shaped residual stress curve with the average value; According to the distribution law of the internal residual stress of the workpiece after ultrasonic shot peening strengthening, divide the residual stress curve into a shot peening stress layer and a bending deformation layer; among them, the stress distribution law of the shot peening stress layer along the thickness direction of the workpiece is similar to that of a cosine function, so it is approximately represented by a cosine function; the stress distribution law of the bending deformation layer is approximately represented by a polynomial function; Obtain the best correlation coefficient through piecewise fitting after multiple iterations. The fitting formula is as follows: Where, A i , ω i , a, b, c, d, e, f are control parameters; z represents the depth of a certain layer of the workpiece; e i represents the depth of the shot-peening stress layer; h represents the thickness of the workpiece; Control parameter ω i and The expression of is as follows: Among them, the control parameters ωi and can be expressed by the stress layer depth ei and the maximum compressive stress layer depth mi.

3. The method for analyzing residual stress and deformation in ultrasonic shot peening strengthening according to claim 1, characterized in that, In Step 3, based on the initial stress function constructed in Step 2, import the initial stress function into the finite element model in the form of a Fortran program by modifying the keywords of the user subroutine SIGINI of the finite element software ABAQUS; The user subroutine SIGINI defines the distance along the thickness direction of the finite element model to distinguish the initial stress functions corresponding to different thickness regions, and completes the editing of the initial stress function with the node coordinates or integration points as variables; Since the directly imported ultrasonic peening residual stress cannot fully meet the initial conditions of the finite element model, it is necessary to perform a static analysis of stress balance on it, and then the maximum displacement of the simulation results is used to characterize the strengthening deformation of the workpiece.

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