CN115470672A - Spatial residual stress reconstruction method - Google Patents
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Abstract
The invention discloses a spatial residual stress reconstruction method, which comprises the following steps of firstly, obtaining residual stress data of a component to be measured by a traditional residual stress measurement technology; then, fitting calculation is performed on the measured experimental data by means of a least square method and a radial basis function. And finally, reconstructing the spatial multidimensional residual stress field by using the intrinsic strain theory under a finite element frame. In the reconstruction process, the intrinsic strain is introduced into the finite element frame in a thermal strain mode, and the requirements of relevant mechanical conditions are also ensured while calculation is carried out by means of finite element software. The method provided by the invention can reflect more complete multi-dimensional space residual stress field information by using limited experimental data. The method has the advantages that the residual stress with a complex distribution form under the multidimensional condition is effectively and accurately predicted by adopting the radial basis function, the defects of the traditional residual stress measurement technology are overcome, and the method has important significance in further research on the residual stress problem in the key fields of advanced manufacturing and the like.
Description
Technical Field
The invention belongs to the field of residual deformation field measurement, and particularly relates to a spatial residual stress reconstruction method.
Background
The residual stress comes from the advanced material processing and manufacturing processes of plastic deformation, thermal mismatch, phase transformation and the like. The existence of residual stress can reduce the processing precision, increase the internal stress, reduce the bearing capacity and the fatigue strength, and easily cause cracks. Due to the significant influence of the residual stress on the long-term performance of the structure, the measurement, simulation and reconstruction of the residual stress are always the research hotspots of the engineering community.
The techniques for measuring residual stress mainly employ experimental methods, which can be divided into destructive and non-destructive methods. The traditional experimental method is direct and reliable, but the data quantity which can be obtained is limited, and certain economic cost and manpower input are required. The measurement result of a general experimental method is data of a limited number of measurement points, the values are discrete, the data are usually fitted to obtain approximate complete stress distribution, but the stress field distribution obtained by the method has certain limitations, for example, the stress cannot meet the self-balancing condition, and the stress cannot be conveniently input into a finite element program for analysis. Due to the limitation of the data quantity, most of the existing residual stress measuring methods cannot completely reflect the whole space residual stress distribution condition of the structural member.
Disclosure of Invention
In view of the above defects or improvement requirements of the prior art, the present invention provides a spatial residual stress reconstruction method, so as to solve the technical problem that the existing residual stress measurement is difficult to comprehensively reflect the spatial residual stress distribution of the whole component.
To achieve the above object, according to a first aspect of the present invention, there is provided a spatial residual stress reconstructing method, including:
s1, obtaining stress data t = [ t (x) of the component to be measured 1 ),t(x 2 ),…,t(x i ),…,t(x M )] T Wherein x is i As a measuring point of the component to be measured, t (x) i ) Is x i M is the number of measurement points;
s2, establishing a finite element model of the component to be measured, carrying out grid division, inputting the Young modulus and the Poisson ratio, setting temperature change, and sequentially setting xi 1 (x),ξ 2 (x),…,ξ k (x) Inputting the finite element model for the thermal expansion coefficient to obtain the stress value at each measuring point
Wherein, in order
Characterizing the unknown intrinsic strain distribution of the member to be measured, N being the total number of basis functions, c k For the coefficient to be solved, xi k (x) Is a basis function, N is less than or equal to M;
s3, according to the formula C = [ S = T S] -1 St solution of c k Obtaining intrinsic strain distribution of the component to be measured, and introducing the intrinsic strain distribution into the finite element model by taking the intrinsic strain distribution as a thermal expansion coefficient to obtain stress field distribution of the component to be measured; wherein, C = [ C = 1 ,c 2 ,…,c k ,…,c N ] T 。
Preferably, the basis functions employ radial basis functions.
Preferably, the radial basis function is any one of a gaussian radial basis function, an inverse quadratic function, or an inverse multi-quadratic function.
Preferably, the basis function is a modified radial basis function;
under the condition of two-dimensional space,
under the three-dimensional space, the device can be used,
wherein r is the radius of the radial basis function, x, y, z are the abscissa, ordinate and ordinate of any point in space, and x c ,y c ,z c The abscissa, ordinate and ordinate of the center point of the radial basis function, and alpha and beta are shape coefficients.
Preferably, the modified radial basis function is any one of a modified gaussian radial basis function, a modified inverse quadratic function, or a modified inverse multi-quadratic function.
Preferably, in step S1, the stress data of the member to be tested is acquired based on a priori method.
Preferably, the a priori method is any one of a drilling method, a ring core method, a slit method, an XRD method, a profiling method, a neutron diffraction method.
According to a second aspect of the present invention, there is provided a spatial residual stress reconstruction system comprising: a computer-readable storage medium and a processor;
the computer readable storage medium is used for storing executable instructions;
the processor is configured to read executable instructions stored in the computer-readable storage medium and execute the method according to the first aspect.
In general, compared with the prior art, the above technical solution contemplated by the present invention can achieve the following beneficial effects:
1. the method provided by the invention takes the defects of the traditional residual stress measurement technology into consideration, utilizes the limited residual stress measurement data of the component and the intrinsic strain theory to carry out complete reconstruction calculation on the residual stress of the component under multiple dimensions, effectively and accurately calculates the residual stress with a complex distribution form under the multi-dimensional condition based on the radial basis function, and has important significance on further research on the residual stress.
2. The method provided by the invention adopts finite element software to construct the integral space residual stress according to the limited residual stress value of the component to be tested, thereby solving and obtaining the residual stress field distribution of the component to be tested. The complex material parameters are not required to be considered, and the thermal expansion coefficient, the Young modulus and the Poisson ratio are only required to be input in finite element software.
Drawings
Fig. 1 is a schematic flow chart of a spatial residual stress reconstruction method according to an embodiment of the present invention;
FIG. 2 is a schematic representation of a Gaussian radial basis function in one and two dimensions;
FIG. 3 (a) is a schematic structural diagram of a complete finite element model of a component to be tested according to an embodiment of the present invention; FIG. 3 (b) is a schematic structural diagram of a 1/2 finite element model; FIG. 3 (c) is a schematic diagram of the selection of experimental measurement points;
fig. 4 (a) and (b) are schematic diagrams of the profiles of the three-dimensional gaussian radial basis function before and after modification according to the embodiment of the present invention;
fig. 5 (a) and (b) are graphs comparing the residual stress reconstruction results of the paths AB and BC in fig. 3 (b) with the target values, respectively, according to the embodiment of the present invention;
fig. 6 (a) is a target residual stress cloud, and fig. 6 (b) is a residual stress cloud reconstructed by the method provided by the embodiment of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention. In addition, the technical features involved in the respective embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other.
An embodiment of the present invention provides a method for reconstructing a spatial residual stress, as shown in fig. 1, including:
s1, obtaining stress data t = [ t (x) of the component to be measured 1 ),t(x 2 ),…,t(x i ),…,t(x M )] T Wherein x is i As measuring points of the component to be measured, t (x) i ) Is x i M is the number of measurement points.
Preferably, in step S1, the stress data of the member to be tested is obtained based on a drilling method, a ring core method or a slit method.
Specifically, stress data of the component to be measured is acquired by a conventional residual stress measurement technique, such as: drilling, ring core, slit, XRD, profile, neutron diffraction, etc.
S2, establishing a finite element model of the component to be measured, carrying out grid division, inputting the Young modulus and the Poisson ratio, setting temperature change, and sequentially setting xi 1 (x),ξ 2 (x),…,ξ k (x) Inputting the finite element model for the thermal expansion coefficient to obtain the stress value at each measuring point
Wherein, in order
Characterizing the unknown intrinsic strain distribution of the member to be measured, N being the total number of basis functions, c k For the coefficient to be solved, xi k (x) Is a basis function, N is less than or equal to M.
Specifically, a combination of a series of basis functions is used to assume an unknown intrinsic strain distribution of the component under test. The intrinsic strain represented by a single basis function is introduced into a finite element framework, and the residual stress caused by the intrinsic strain is calculated under the finite element framework.
The hypothetical form of the unknown intrinsic strain distribution is:
wherein N is the total number of basis functions, c k Is an unknown coefficient, ξ k (x) Is a basis function.
Further, the intrinsic strain induced into the finite element framework in the form of thermal strain will produce a corresponding distribution of residual stress fields. The thermal expansion coefficient changing along with the space is defined through a user subprogram, the thermal expansion coefficient is used as intrinsic strain distribution and is led into finite element software for calculation, the obtained stress distribution result is residual stress distribution caused by the intrinsic strain, and then the residual stress value at the position of a corresponding experimental measuring point is output.
When the method provided by the invention is used for establishing the finite element model, complex material parameters do not need to be considered, and only the thermal expansion coefficient, the Young modulus and the Poisson ratio need to be input.
S3, according to the formula C = [ S = T S] -1 St solution to c k Obtaining intrinsic strain distribution of the component to be measured, and introducing the intrinsic strain distribution into the finite element model by taking the intrinsic strain distribution as a thermal expansion coefficient to obtain stress field distribution of the component to be measured; wherein, C = [ C = 1 ,c 2 ,…,c k ,…,c N ] T 。
Specifically, since only the young's modulus, poisson's ratio, and thermal expansion coefficient are input to the material parameters in the model, the finite element calculation process of the present invention can be considered as a complete elastic process. Since the elasticity problem is a linear problem, the residual stress T (x) in the finite element model is the intrinsic strain ξ represented by the basis function in equation (1) k (x) Residual stress s generated k (x) Given by a linear combination of:
furthermore, the measured experimental data t is calculated and reconstructed by means of a least square method and basis functions to solve unknown coefficients c of the basis functions k . That is, to obtain a reconstruction solution that fits well with t, the least squares approximation constructor J:
in the formula, t (x) i ) For measuring points x obtained based on conventional residual stress measurement techniques i The stress value of (A), T (x) i ) Measurement points (also called experimental measurement points) x output for finite element model i Stress value of, w i Is a weighting factor.
In order to obtain a solution that fits well with the experimental values, we need to find a set of c k The target error function J is minimized. This is done by taking the function J versus the unknown parameter c k And is made equal to zero, i.e.:
equation (4) is further developed to yield:
to simplify the calculation, the following matrix is defined:
C＝[c 1 ,c 2 ,…,c k ,…,c N ] T (7)
t＝[t(x 1 ),t(x 2 ),…,t(x i ),…,t(x M )] T (8)
further, the residual stress reconstruction problem is finally simplified into a problem of solving unknown coefficients of basis functions, and in combination with formulas (6), (7) and (8), the formula (5) is simplified into a matrix form, and the specific form is as follows:
C＝[S T S] -1 St (9)
wherein C is an unknown coefficient C k Forming an Nx 1 array, S is a measuring point x in the finite element model i Is subject to intrinsic strain xi k (x) Induced residual stress s k (x i ) Forming an N multiplied by M array, wherein M is the number of the measuring points, and t is the measuring point x obtained based on the traditional residual stress measuring technology i The M x 1 array of stress values.
Further, an unknown coefficient c is obtained k And then, according to the formula (1), obtaining final complete intrinsic strain distribution, wherein the method for introducing the intrinsic strain distribution into a finite element is the same as that in the step S2, namely, the method for introducing the single radial basis function in the step S2 is changed into the method for introducing the final solution to obtain the complete intrinsic strain distribution. And then complete residual stress distribution information on the space can be obtained.
That is, the intrinsic strain distribution result obtained finally is introduced into the finite element frame, and then complete residual stress distribution information on the space can be obtained.
The method for introducing the intrinsic strain into the finite element frame comprises the following steps: in the form of thermal strain into a finite element frame.
Preferably, the basis functions are radial basis functions.
Specifically, the radial basis functions are used as basis function spaces, one-dimensional, two-dimensional or three-dimensional function forms are used for meeting the requirements of residual stress fields with different dimensions in the spaces, and meanwhile, the radial basis functions led into the finite element model are distributed in the spaces according to the density of experimental measuring points.
Preferably, the radial basis function is any one of a gaussian radial basis function, an inverse quadratic function, or an inverse multi-quadratic function.
Specifically, as shown in FIG. 2, ξ of the radial basis functions k (x) The basic form of (A) is as follows:
in the formula, X c The coordinate of the central point of the radial basis function is shown, X represents the coordinate of any point in the area to be measured, and r is the distance from one point X in the area to be measured to the center of the radial basis function.
Preferably, in the process of reconstructing the multi-dimensional space residual stress field, the radial basis function is considered to be corrected so as to improve the efficiency and accuracy of the reconstruction process, and the specific correction form is as follows:
in the two-dimensional space, the device can be used,
under the three-dimensional space, the device can be used,
wherein r is the radius of the radial basis function, x, y, z are the abscissa, ordinate of any point in space, x c ,y c ,z c The radial basis function is selected according to the ratio of the distribution space of the experimental measuring points in all directions of the space, wherein the radial basis function is the abscissa, the ordinate and the vertical coordinate of the central point of the radial basis function, and alpha and beta are shape coefficients.
The radial basis functions before and after correction are shown in fig. 4 (a) and (b), respectively.
Preferably, the modified radial basis function is any one of a modified gaussian radial basis function, a modified inverse quadratic function, or a modified inverse multi-quadratic function.
The method provided by the present invention is verified below with a specific example. The verification method is performed with the intrinsic strain of the member to be tested known.
The method is characterized in that the effectiveness of the method is verified by establishing a three-dimensional finite element model and taking a residual stress field obtained by finite element calculation as a reconstruction target, and the method comprises the following specific steps:
step 1: in this embodiment, since the intrinsic strain of the to-be-measured member is known, a residual stress field is constructed by finite element simulation, and stress data output from the measurement point position in fig. 3 (c) is used as stress data t = [ t (x) of the to-be-measured member 1 ),t(x 2 ),…,t(x i ),…,t(x M )] T The method comprises the following specific steps:
(1) A three-dimensional model is created, as shown in fig. 3 (a), and for the sake of easy calculation, a 1/2 model structure is taken here, as shown in fig. 3 (b), and mesh division is performed.
In this example, the original model has a length of 160mm, a width of 80mm and a thickness of 20mm; after taking 1/2 of the structure, the model size is 160mm long, 40mm wide and 20mm thick.
(2) Introducing intrinsic strain into the finite element model to generate residual stress;
the intrinsic strain introduced is in the specific form:
in the formula, x is a horizontal coordinate of one point in space, y is a vertical coordinate of one point in space, w is the width 80mm of the original model, and t is the thickness 20mm of the original model.
The intrinsic strain being introduced into the finite-element model as thermal strain, e.g. epsilon * = α Δ T, wherein ∈ * For the introduced intrinsic strain, α is a thermal expansion coefficient, Δ T is a temperature change value, and Δ T is set to be constant.
In the embodiment, complicated material parameters do not need to be considered, and only the thermal expansion coefficient, the Young modulus and the Poisson ratio need to be input. In this embodiment, the young's modulus is 210GPa, and the poisson ratio is 0.3.
(3) The above formula is used as an intrinsic strain distribution and is introduced into finite element software for calculation, the obtained stress distribution result is the residual stress distribution caused by the intrinsic strain, the stress result is shown in (a) and (b) in fig. 5, wherein Target represents t, and then the stress value t = [ t (x) at the corresponding measuring point position is output 1 ),t(x 2 ),…,t(x i ),…,t(x M )] T 。
The distribution of the target test points in this embodiment is shown in fig. 3 (c), and specifically includes: taking 7 groups of experimental measuring points along the z-axis direction, wherein the distance between every two groups of experimental measuring points in the z direction is 24mm; taking 4 groups of experimental measuring points from 0mm to 20mm along the y-axis direction, wherein the maximum distance between the measuring points is 8mm; points are taken at a distance of 4mm along the x-axis direction, and according to the ratio of the distribution distances of the experimental measurement points in the spatial directions, the radial basis function correction parameter alpha of the embodiment is taken as 6 and the radial basis function correction parameter beta is taken as 2.
Step 2: an unknown intrinsic strain distribution of the object to be measured in the member to be measured is assumed with a combination of a series of basis functions.
In this embodiment, the assumed form of the unknown intrinsic strain distribution in the member to be measured is:
wherein N is the total number of basis functions, c k Is an unknown coefficient, ξ k (x, y, z) are basis functions.
The basis function in this embodiment is a radial basis function, that is, the radial basis function is used as a basis function space, and further, the radial basis function is a three-dimensional gaussian radial basis function, and the specific form is as follows:
in the formula (I), the compound is shown in the specification,
r k is the distance from any point in space to the center point of the kth radial basis function, x is nullThe abscissa of any point in space, y is the ordinate of any point in space, z is the ordinate of any point in space, and x kc Is the abscissa of the central point of the kth radial basis function and is equal to the abscissa, y, of the kth experimental measuring point kc Is the ordinate of the center point of the radial basis function, z kc And alpha and beta are radial basis function correction coefficients which are vertical coordinates of the central point of the radial basis function, and are selected according to the ratio of the distribution distances of the experimental measuring points in all directions of the space.
The intrinsic strain represented by a single basis function is introduced into a finite element frame, and the residual stress generated by the single intrinsic strain is calculated under the finite element frame, which comprises the following steps:
(1) Establishing a three-dimensional model which is the same as the three-dimensional model in the step 1, and carrying out grid division;
(2) Imposing a predefined initial temperature field and temperature variation on a model
(3) Inputting material parameters;
just as in step 1, the coefficient of thermal expansion, young's modulus and Poisson's ratio also need to be input. Wherein, the Young modulus is 210GPa, and the Poisson ratio is 0.3. According to the formula (2), the distribution specific function form of the intrinsic strain is the three-dimensional Gaussian radial basis function in the step 1.
Since the material parameters in the model are only input with Young's modulus, poisson's ratio and thermal expansion coefficient, the finite element calculation process of the invention can be considered as a complete elastic process. Since the elasticity problem is a linear problem, the residual stress T (x) in the finite element model is the intrinsic strain ξ represented by the basis function in equation (1) k (x) Residual stress s generated k (x) Given by a linear combination of:
as can be seen from the formula (1), the N basis functions xi need to be distributed on the component to be measured in the embodiment k (x, y, z) and taking the position of the target experimental measuring point as the position of the central point of each radial basis function. Therefore, the total number of distribution of basis functions in this embodiment is the same as the total number of selected experimental measurement points, i.e., N = M =308.
(4) Guiding the three-dimensional Gaussian radial basis function as intrinsic strain distribution into finite element software for calculation, obtaining a stress distribution result which is residual stress distribution caused by the intrinsic strain, and then outputting a residual stress predicted value under the intrinsic strain in a single basis function distribution form, namely s in a formula k (x) And finally form the matrix S.
Since N basis functions are required in total, in step 2, gaussian radial basis functions at N different central point positions are respectively used as intrinsic strains to be introduced into a finite element model for calculation, and finally N groups of stress data are output to form a stress matrix:
and 3, step 3: taking the stress data t obtained in the step 1 as the target experiment data of the embodiment, and performing calculation reconstruction on the obtained target experiment data t by means of a least square method to solve the unknown coefficient c of the basis function k (ii) a In this step, a least square approximation is used to construct a function J, and [ S ] is finally obtained T S]C＝St。
The reconstruction problem of the residual stress is finally simplified into the problem of solving unknown coefficients of basis functions, and S and t are known, so that the residual stress is finally reduced according to the formula C = [ S ] T S] -1 St can be used to obtain the unknown coefficient c k 。
Finding the unknown coefficient c k And (3) finally obtaining complete intrinsic strain distribution according to the formula (1), wherein the method for introducing the intrinsic strain distribution into the finite element is the same as that in the step 2, namely, the method for introducing the single radial basis function in the step 2 is changed into the method for introducing the complete intrinsic strain distribution obtained by finally solving. And obtaining the complete residual stress distribution information of the component to be measured in space.
Fig. 5 (b) shows the residual stress field obtained after the final intrinsic strain is introduced and the finite element calculation is performed, and compared with the target residual stress field shown in fig. 5 (a), it can be seen that the three-dimensional residual stress field to be constructed is well reconstructed by the method provided by the present invention. Further selecting two paths AB and BC in fig. 3 (b) to perform the comparison of the residual stress results, and the comparison results are shown in fig. 6 (a) and (b), it can be seen that the predicted value of the residual stress reconstruction is well matched with the target value for the two selected paths, and the effectiveness of the invention is further verified.
The method provided by the invention considers the defects of the traditional residual stress measurement technology, utilizes limited experimental data and an intrinsic strain theory to carry out complete reconstruction prediction on the residual stress of the component under multiple dimensions, effectively carries out accurate prediction on the residual stress with a complex distribution form under the multi-dimensional condition based on the radial basis function, and has important significance on further research on the residual stress.
The embodiment of the invention provides a spatial residual stress reconstruction system, which comprises: a computer-readable storage medium and a processor;
the computer-readable storage medium is used for storing executable instructions;
the processor is used for reading the executable instructions stored in the computer readable storage medium and executing the method according to any one of the above embodiments.
It will be understood by those skilled in the art that the foregoing is only a preferred embodiment of the present invention, and is not intended to limit the invention, and that any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the scope of the present invention.
Claims (8)
1. A method for reconstructing spatial residual stress, comprising:
s1, obtaining stress data t = [ t (x) of the component to be measured 1 ),t(x 2 ),…,t(x i ),…,t(x M )] T Wherein x is i As measuring points of the component to be measured, t (x) i ) Is x i M is the number of measurement points;
s2, establishing a finite element model of the component to be measured, carrying out grid division, inputting the Young modulus and the Poisson ratio, setting temperature change, and sequentially setting xi 1 (x),ξ 2 (x),…,ξ k (x) Inputting the finite element model for the thermal expansion coefficient to obtainStress value at each measuring point
Wherein, in order
Characterizing the unknown intrinsic strain distribution of the member to be measured, N being the total number of basis functions, c k For the coefficient to be solved, xi k (x) Is a basis function, N is less than or equal to M;
s3, according to the formula C = [ S = T S] -1 St solution of c k Obtaining intrinsic strain distribution of the component to be measured, and introducing the intrinsic strain distribution into the finite element model by taking the intrinsic strain distribution as a thermal expansion coefficient to obtain stress field distribution of the component to be measured; wherein, C = [ C = 1 ,c 2 ,…,c k ,…,c N ] T 。
2. The method of claim 1, wherein the basis functions employ radial basis functions.
3. The method of claim 2, wherein the radial basis function is any one of a gaussian radial basis function, an inverse quadratic function, or an inverse multi-quadratic function.
4. The method of claim 1, wherein the basis functions employ modified radial basis functions;
in the two-dimensional space, the device can be used,
under the three-dimensional space, the device can be used,
wherein r is the radius of the radial basis function, x, y, z are the abscissa, ordinate and ordinate of any point in space, and x c ,y c ,z c The abscissa, ordinate and ordinate of the center point of the radial basis function, and alpha and beta are shape coefficients.
5. The method of claim 4, wherein the modified radial basis function is any one of a modified Gaussian radial basis function, a modified inverse quadratic function, or a modified inverse multi-quadratic function.
6. The method of claim 1, wherein in step S1, the stress data of the component under test is obtained based on a priori methods.
7. The method of claim 6, wherein the a priori method is any one of a drilling method, a ring-core method, a kerf method, an XRD method, a profilometry, and a neutron diffraction method.
8. A spatial residual stress reconstruction system, comprising: a computer-readable storage medium and a processor;
the computer-readable storage medium is used for storing executable instructions;
the processor is configured to read executable instructions stored in the computer-readable storage medium and execute the method according to any one of claims 1-7.
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| Publication number | Priority date | Publication date | Assignee | Title |
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| CN115629130A (en) * | 2022-12-21 | 2023-01-20 | 国网天津市电力公司电力科学研究院 | Imaging method and system for residual stress of basin-type insulator and test block preparation method |
| CN115979158A (en) * | 2023-01-29 | 2023-04-18 | 哈尔滨工业大学 | Inversion method of composite material curing intrinsic strain |
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Cited By (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN115629130A (en) * | 2022-12-21 | 2023-01-20 | 国网天津市电力公司电力科学研究院 | Imaging method and system for residual stress of basin-type insulator and test block preparation method |
| CN115979158A (en) * | 2023-01-29 | 2023-04-18 | 哈尔滨工业大学 | Inversion method of composite material curing intrinsic strain |
| CN115979158B (en) * | 2023-01-29 | 2023-07-04 | 哈尔滨工业大学 | Inversion method of composite material curing intrinsic strain |
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