CN112926213B - Method, system, medium, equipment and terminal for measuring thermal damage boundary element - Google Patents
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Abstract
The invention belongs to the technical field of special steel processing, and discloses a method, a system, a medium, equipment and a terminal for measuring thermal damage boundary elements, which are used for analyzing structural fatigue fracture failure process caused by a heat treatment process in the manufacturing process of special steel. Based on the achievement of the existing boundary element method, the temperature, displacement, strain, stress field distribution and crack problems in a special steel structure are taken as objects, the high-precision advantage of the boundary element method relative to the finite element method is fully utilized, and the key theories and algorithms such as near singular integration, singular integration and super singular integration algorithms, unit decomposition methods, reinforcement functions, NURBS algorithms and the like are subjected to system deep research. The invention can accurately obtain accurate displacement, stress field and corresponding fracture mechanical property parameters near the internal cracks of the special steel structure, and reveal the defect generation mechanism in the special steel forming process.
Description
Technical Field
The invention belongs to the technical field of special steel processing, and particularly relates to a method, a system, a medium, equipment and a terminal for measuring thermal damage boundary elements.
Background
At present, in the manufacturing and forming process of special steel blanks, heat treatment processes such as quenching, tempering and the like are often adopted to improve the surface hardness. And in the process of repeated heating, quenching and tempering, the temperature distribution in the structure is uneven to cause thermal stress, under the effect of the thermal stress, the weak part easily initiates cracks, and the cracks further evolve and expand under the cyclic thermal load of repeated heating and cooling of the structure, so that the damage of the structure is finally caused. Of course, the generation of cracks under alternating heat load is inevitable, and the size and scale of the cracks have a great influence on the service performance of the special steel structure. Therefore, it is necessary to accurately analyze and calculate the crack growth level of the special steel structures under the quenching and tempering heat treatment working condition, so as to guide and optimize the heat treatment process and improve the yield.
To analyze crack propagation, it is extremely critical to accurately calculate the stress field distribution near the crack tip. The current structural analysis software mainly adopts a Finite Element Method (FEM), and the simulation of the FEM on physical quantities mainly adopts conventional entity units, so that the conventional finite element method needs to use extremely dense grids near cracks to ensure the calculation accuracy of crack tip opening displacement (COD) and Stress Intensity Factor (SIF) near the cracks. The requirement of dense grids brings great difficulty to grid division, on the other hand, the calculation scale is greatly increased, and when microcracks are initiated at a plurality of positions in the structure, the finite element grid division becomes extremely difficult and automatic division cannot be achieved. To solve this problem, the international authority t.belyschko of the finite element method developed an extended finite element (X-FEM) technique based on conventional unit-based techniques, which was dedicated to analyzing crack growth problems. In the X-FEM, a step function term is introduced into the shape function of the unit by introducing a reinforcing unit (EE) for simulating the discontinuity of displacement fields at two sides of the internal crack of the unit; meanwhile, crack propagation is controlled inside the units, and cracks among the units are not affected, so that calculation becomes efficient. However, the introduction of EE in X-FEM also deteriorates the coefficient matrix behavior of the finite element equation set, the condition number becomes large, and stability of numerical solution becomes a new challenge. The Boundary Element Method (BEM) is a semi-analytic numerical method, and the advantage of the same-order precision of the surface force and displacement solved by the BEM is utilized, so that the structural thermal strain and stress calculation precision can be improved. BEM is therefore of great advantage in structural thermal strain, stress field analysis. The singular nature of the BEM base solution is more suitable for stress singularities such as crack problems during structural thermal coupling fatigue fracture failure.
However, the middle and outer students basically only pay attention to the residual stress after the special steel is formed or the temperature distribution under the working condition, or simply analyze the structural crack problem by using BEM, and rarely relate to the analysis of internal crack development under the repeated quenching and tempering working condition in the manufacturing process of the special steel, which is mainly attributed to the following reasons: (1) When the cast forging blank contains cracks or defects, singular integration, super singular integration and near super singular integration in a double boundary integral equation under thermal coupling are required to be processed. The mathematical sum algorithm implementation of singular integration, super singular integration and near singular integration is quite difficult to process, and the calculation accuracy of the singular integration, super singular integration and near singular integration directly influences the temperature, strain and stress accuracy of the BEM analysis special steel structure and the corresponding fracture mechanical property parameters, so that the analysis of the fatigue fracture and damage process of the BEM analysis special steel structure is further influenced. (2) The vicinity of the crack tip belongs to a high gradient stress region (stress singularity), and special units capable of reflecting the stress singularity are required to be used for improving the calculation accuracy of stress intensity factors and improving the accuracy of the fatigue fracture and damage process of the special steel structure. In addition, due to the special shape of the crack, especially the non-penetrating crack, grids (triangle and quadrilateral grids) with various shapes are needed in discrete time, and terms reflecting the singularities are needed to be added into the conventional unit shape function. While high quality triangular shaped split tip units are yet to be developed. (3) For the problem of crack extension in the fatigue fracture and damage process of the cutter structure under repeated quenching and tempering, whether a finite element method, an extended finite element method or a boundary element method is used, triangular units or quadrilateral units are used for dispersing crack surfaces in the fatigue fracture process, C0 continuity is kept, when the crack front is simulated to be extended in the next step, linear segments of the crack front are obtained, the crack front is difficult to accurately capture in actual calculation, the calculation precision of stress intensity factors in the next step is low, and simulation distortion is further accumulated along with the crack extension errors. In addition, it is difficult to construct a local coordinate system of the crack front, and the deflection angle in the process of obtaining the crack extension is discontinuous, so that the problem of multi-crack crossing in the fatigue fracture and destruction process of the special steel structure is difficult to analyze.
While BEM is a serious difficulty in its application in this field, it is worth noting that some criticality has achieved a series of important advances in recent years. The specific expression is as follows: first, singular integration, super singular integration and near singular integration algorithms are continuously perfected. After the singular integral, the super singular integral and the near singular integral are accurately processed, BEM can be based on the fatigue fracture and destruction process of the three-dimensional entity structure without introducing deformation assumptions such as plate shell theory. Of course, the existing singular integration, super singular integration and near singular integration algorithms have some problems, such as that various near singular integration nonlinear transformations excessively depend on the position of a projection point, and the calculation accuracy of the projection point seriously affects the calculation accuracy of the near singular integration; the analytical method and the semi-analytical method are difficult to implement on curved surfaces; the indirect method has poor effect of calculating the corner points and the stress concentration areas; the unit subdivision method can cause excessive operand; for the larger size difference between the microcrack area and the matrix unit, the calculation accuracy of the near singular integral on the units can be also influenced; in addition, when the crack problem is analyzed, singular integral, super singular integral and near super singular integral are also arranged on the crack surface, and the shapes of the units can influence the calculation precision of the singular integral, the super singular integral and the near super singular integral. Of these methods, nonlinear transformation is an ideal method for solving near singular integration. The invention aims to reduce the dependence of various near singular integral nonlinear transformations on the position of the projection point and overcome the grid size effect of singular integral, super singular integral and near singular integral.
Secondly, the special unit of the crack tip displacement and the high gradient stress field is reflected. However, the current reinforcement unit or crack front unit is only suitable for cracks of a specific shape and specific location. Because the displacement and crack tip stress singular regions expand along with the expansion of the crack, the size of the expansion region is limited by the special units, and the real crack expansion scale is difficult to reflect. For cracks and multi-crack crossing problems with complex geometries, such units are more difficult to accurately simulate. The crack problem is a strong discontinuity (displacement discontinuities on both sides of the crack).
The crack problem is solved, and firstly, displacement and stress singularity of the crack tip can be captured. Based on a unit decomposition method, the idea of adding a strengthening function (reflecting the main singular terms and possible displacement states of the crack tip) function capable of reflecting the existence of discontinuity into a conventional unit shape function can be used as a reference.
Third, the non-uniform rational B-spline (NURBS) algorithm was proposed and continually improved. The NURBS parameter curved surface is used for simulating a new crack expansion area, so that the crack expansion front can be obtained based on the NURBS curved surface sheet, a crack tip stress singular unit is constructed, a local coordinate system of the crack front is naturally established, the next step of crack front stress intensity factor solving precision is improved, the continuity of a crack expansion angle can be maintained, the problem of multi-crack cross expansion is solved, and the fatigue fracture damage process of the special steel structure is accurately simulated.
Through the above analysis, the problems and defects existing in the prior art are as follows:
(1) In the prior art, the singular integration, super singular integration and near singular integration technologies have the problems that various near singular integration nonlinear transformations excessively depend on the position of a projection point, and the calculation accuracy of the projection point seriously influences the calculation accuracy of the near singular integration; the analytical method and the semi-analytical method are difficult to implement on curved surfaces; the indirect method has poor effect of calculating the corner points and the stress concentration areas; the unit subdivision method can cause excessive operand; for the larger size difference between the microcrack area and the matrix unit, the calculation accuracy of the near singular integral on the units can be also influenced; in addition, when the crack problem is analyzed, singular integral, super singular integral and near super singular integral are also arranged on the crack surface, and the shapes of the units can influence the calculation precision of the singular integral, the super singular integral and the near super singular integral.
(2) The current strengthening unit or the crack front unit is only suitable for cracks with specific shapes and specific positions; along with the expansion of the crack, the displacement and crack tip stress singular area also expands, and the special units limit the size of the expansion area, so that the real crack expansion scale is difficult to reflect. For cracks and multi-crack crossing problems with complex geometries, such units are more difficult to accurately simulate.
The difficulty of solving the problems and the defects is as follows:
(1) When solving the crack problem, a large number of singular integrals, super singular integrals and near singular integrals influence the calculation accuracy of the coefficient matrix, and at present, no general high-efficiency high-accuracy calculation method is used for processing, so that the numerical calculation is relatively difficult to implement.
(2) And in the fatigue fracture and destruction process of the special steel structure, the geometric model of the crack surface needs to be updated continuously along with the crack propagation. There are great difficulties in accurately characterizing newly formed crack surfaces.
The meaning of solving the problems and the defects is as follows:
(1) And (3) accurately calculating singular integral, super singular integral and near singular integral to obtain an accurate coefficient matrix, wherein the accurate coefficient matrix directly relates to the calculation stability of the BEM analysis special steel structure and the accuracy of stress and displacement, and influences the final fatigue fracture analysis result.
(2) The new expansion crack surface is accurately represented, so that the stress singularity near the crack tip can be accurately simulated, the geometric shape of each step of expansion of the crack and the accurate fracture mechanical parameters can be successfully obtained, and the accurate fatigue expansion life of the special steel can be obtained.
Disclosure of Invention
Aiming at the problems existing in the prior art, the invention provides a method, a system, a medium, equipment and a terminal for measuring thermal damage boundary elements. The invention develops accurate and efficient singular integration, super singular integration and near singular integration algorithms, can accurately simulate the temperature, displacement, strain and stress field distribution in the special steel structure, and predicts the stress intensity factor of the tip after crack initiation in the structure. By constructing a universal crack tip unit and combining with a NURBS algorithm, the crack growth of the special steel structure is accurately simulated, and the fatigue crack damage process and damage degree of the cutting tool caused by quenching and tempering in the forming process are analyzed and predicted.
The invention is realized in that a method for measuring a thermal injury boundary element comprises the following steps:
considering thermal coupling boundary conditions, adding a crack tip singular unit and a near singular integration algorithm to obtain a thermal coupling boundary element method for solving key parts of the special steel structure, and accurately predicting crack initiation positions;
After crack initiation, a near singular integration algorithm, a super singular integration algorithm and a crack tip singular unit based on a unit decomposition method and a strengthening function idea are added to realize a thermal coupling double-boundary element method, so that accurate displacement, thermal stress, strain and stress intensity factors near the crack can be accurately solved;
adding a crack expansion criterion, and judging whether the crack is expanded or not; the NURBS is utilized to represent a newly-expanded crack surface and a crack front, a crack tip singular unit is constructed based on a NURBS shape function, and the crack tip singular unit is realized in a double-boundary element method frame in a numerical mode, is used for accurately solving displacement, thermal stress and strain fields, and is convenient for establishing a crack tip local coordinate system;
obtaining a crack tip stress intensity factor by using J integral and M integral, judging whether a crack is expanded, calculating a crack expansion angle and an expansion amount, solving by using an incremental double-boundary element method, accurately simulating a crack expansion process, and predicting the effective life;
and comparing the analysis solution, the numerical solution and the corresponding test results to verify the correctness of the algorithm in the invention.
Further, the method for determining the crack boundary element of the special steel structure under thermal coupling comprises the following steps: and a double-boundary integral equation under thermal coupling is adopted, a thermal cracking tip singular unit deduced based on a unit decomposition method and a strengthening function is combined, a new format is formed by the double-boundary integral equation under thermal coupling, and numerical implementation is performed.
Further, the thermal crack tip singular units are identified and determined by using a level set method and the like, corresponding integral criteria are established, integral blocks and integral point control criteria are established, the stress intensity factors are solved by using J integral or M integral, and the crack propagation direction is obtained by using an energy release rate criterion or a strain energy density factor criterion.
Further, when the thermodynamic coupling double-boundary integral equation is used, singular integral and super singular integral are generated on a crack surface, and singular value decomposition technology with integral blocks and local polar coordinates according to source point positions approximately unfolded as cores is utilized; while singular value decomposition is employed, a conformal transformation is used.
Further, the thermal stress of the special steel structure is accurately calculated, and the specific process is as follows: based on the existing thermal problem and elastic mechanical boundary element program, aiming at key areas including cracks and the like, numerical implementation is carried out by adopting a thermodynamic coupling boundary integral equation formula, and stress concentration of the areas is considered to construct corresponding crack tips, and improved distance transformation, exponential transformation and shape preserving transformation are carried out;
reasonably partitioning the integration unit according to the position of the projection point in the integration unit, and formulating an integration point distribution control criterion to obtain a balance between the number of the integration points and the integration precision;
For singular integration, integrating block, local coordinate transformation technology and conformal transformation are adopted according to the position of a source point.
Further, the simulation of the fatigue crack growth process of the special steel structure specifically comprises the following steps: deducing a new combination format of a double boundary integral equation under NURBS and thermal coupling, judging whether a crack is expanded or not by using an energy release rate criterion or a strain energy density factor criterion, and obtaining a crack expansion direction;
using NURBS to represent a new crack surface and a crack front after expansion, constructing a crack tip unit under a NURBS basis function according to the singular nature of the crack tip, establishing a crack tip local coordinate system, and solving a stress intensity factor by using J integral or M integral;
a series of sampling points are taken from the front edge of the crack, a NURBS surface fitting is used for newly obtaining a crack expansion surface, the crack expansion surface is discrete, an incremental boundary element method is adopted for carrying out iterative solution, simulation of the crack expansion process is realized, and the service life of the special steel structure is predicted by using a pair formula;
the verification proposes the specific process of correctness and reliability of the numerical algorithm as follows: aiming at the accurate determination of the thermal stress of the special steel structure, the simulation of the special steel structure crack boundary element and the special steel structure fatigue crack expansion process under the thermal coupling, a large number of typical calculation examples are combined after each step is completed, and the verification is repeatedly carried out;
After the completion of the method, the result of the fatigue crack damage test of the special steel structure is compared and analyzed by adopting a calculation program, and compared with classical analytical solutions, numerical results or test results, the numerical algorithm is comprehensively verified, and the data structure of the improved program is continuously optimized;
the calculation accuracy and stability of the thermal stress of the special steel structure, the theoretical deduction accuracy of singular integral, super singular integral and near singular integral, and the calculation accuracy and efficiency of the program module;
the accuracy of the thermal coupling boundary integral equation form of the thermal crack tip unit based on the unit decomposition method and the strengthening function idea is adopted, the high precision of the temperature field, displacement, thermal stress, strain and stress intensity factors is verified, and the calculation precision and the numerical stability of the program module are verified;
and verifying the correctness of the new format by combining the NURBS and a double-boundary integral equation under thermal coupling, performing numerical simulation on a crack propagation process, and comparing the service life prediction of the special steel structure with a test result.
It is a further object of the present invention to provide a computer device comprising a memory and a processor, the memory storing a computer program which, when executed by the processor, causes the processor to perform the steps of:
Considering thermal coupling boundary conditions, adding a crack tip singular unit and a near singular integration algorithm to obtain a thermal coupling boundary element method for solving key parts of the special steel structure, and predicting crack initiation;
after crack initiation, a near singular integration algorithm, a super singular integration algorithm and a crack tip singular unit based on a unit decomposition method and a strengthening function idea are added to realize a thermal coupling double-boundary element method, and accurate displacement, thermal stress, strain and stress intensity factors near the crack are solved;
adding a crack expansion criterion, and judging whether the crack is expanded or not; representing a newly-expanded crack surface and a crack front by using NURBS, constructing a crack tip singular unit based on NURBS shape functions, carrying out numerical implementation in a double-boundary element method frame, solving displacement, thermal stress and strain fields, and establishing a crack tip local coordinate system;
obtaining a crack tip stress intensity factor by using J integral and M integral, judging whether a crack is expanded, calculating a crack expansion angle and an expansion amount, and solving by using an incremental double-boundary element method;
by comparison with analytical solutions, numerical solutions and corresponding test results.
Another object of the present invention is to provide a computer readable storage medium storing a computer program which, when executed by a processor, causes the processor to perform the steps of:
Considering thermal coupling boundary conditions, adding a crack tip singular unit and a near singular integration algorithm to obtain a thermal coupling boundary element method for solving key parts of the special steel structure, and predicting crack initiation;
after crack initiation, a near singular integration algorithm, a super singular integration algorithm and a crack tip singular unit based on a unit decomposition method and a strengthening function idea are added to realize a thermal coupling double-boundary element method, and accurate displacement, thermal stress, strain and stress intensity factors near the crack are solved;
adding a crack expansion criterion, and judging whether the crack is expanded or not; representing a newly-expanded crack surface and a crack front by using NURBS, constructing a crack tip singular unit based on NURBS shape functions, carrying out numerical implementation in a double-boundary element method frame, solving displacement, thermal stress and strain fields, and establishing a crack tip local coordinate system;
obtaining a crack tip stress intensity factor by using J integral and M integral, judging whether a crack is expanded, calculating a crack expansion angle and an expansion amount, and solving by using an incremental double-boundary element method;
by comparison with analytical solutions, numerical solutions and corresponding test results.
The invention further aims to provide a special steel structure thermal process information data processing terminal which is used for realizing the thermal damage boundary element measuring method.
Another object of the present invention is to provide a thermal damage boundary element measurement system for performing the thermal damage boundary element measurement method, the thermal damage boundary element measurement system comprising:
the crack initiation prediction module 1 is used for considering thermal coupling boundary conditions, adding a crack tip singular unit and a near singular integration algorithm to obtain a thermal coupling boundary element method for solving key parts of the special steel structure, and predicting crack initiation;
the crack information processing module is used for adding a near singular integration algorithm, a super singular integration algorithm and a crack tip singular unit based on a unit decomposition method and a strengthening function idea after crack initiation to realize a thermal coupling double-boundary element method and solve accurate displacement, thermal stress, strain and stress intensity factors near the crack;
the crack tip local coordinate system building module is used for adding a crack expansion criterion to judge whether the crack is expanded or not; representing a newly-expanded crack surface and a crack front by using NURBS, constructing a crack tip singular unit based on NURBS shape functions, carrying out numerical implementation in a double-boundary element method frame, solving displacement, thermal stress and strain fields, and establishing a crack tip local coordinate system;
the incremental double-boundary element method solving module is used for obtaining a crack tip stress intensity factor by using J integral and M integral, judging whether a crack is expanded, calculating a crack expansion angle and expansion quantity, and solving by using the incremental double-boundary element method;
And the result comparison module is used for comparing the analysis solution, the numerical solution and the corresponding test results.
By combining all the technical schemes, the invention has the advantages and positive effects that: the invention develops accurate and efficient singular integration, super singular integration and near singular integration algorithms, can accurately simulate the temperature, displacement, strain and stress field distribution in the special steel structure, and predicts the stress intensity factor of the tip after crack initiation in the structure. By constructing a universal crack tip unit and combining with a NURBS algorithm, the crack growth of the special steel structure is accurately simulated, and the fatigue crack damage process and the damage degree of the special steel in the forming process due to quenching and tempering are analyzed and predicted. Based on the achievement of the existing boundary element method, the invention takes the problems of temperature, displacement, strain, stress field distribution and cracks in a special steel structure as objects, fully utilizes the high precision advantage of the boundary element method relative to the finite element method, carries out system penetration on critical theories and algorithms such as near singular integration, singular integration and super singular integration algorithms, unit decomposition methods, strengthening functions, NURBS algorithms and the like, and builds a fatigue fracture destruction process analysis boundary element algorithm with high precision and strong universality in the quenching and tempering manufacturing process. The invention can accurately obtain accurate displacement and stress field near the internal crack of the special steel structure, corresponding fracture mechanical property parameters, reveal the defect generation mechanism in the cutter forming process, and provide an important calculation method for optimizing the technological parameters of the special steel structure.
Meanwhile, the invention aims to reduce the dependence of various near singular integral nonlinear transformations on the position of the projection point and overcome the grid size effect of singular integral, super singular integral and near singular integral. The invention starts from the progressive property of the crack tip stress, utilizes the unit decomposition method and the strengthening function idea to construct the shape function and the thermal crack tip unit which can reflect the thermal crack tip displacement, the stress singularity and the strong discontinuity, and combines with the thermal coupling double-boundary element method to establish a new solving format, thereby being universal and convenient for analyzing the crack expansion problem. The invention develops accurate and efficient singular integration, super singular integration and near singular integration algorithms, can accurately simulate the temperature, displacement, strain and stress field distribution in the special steel structure, and predicts the stress intensity factor of the tip after crack initiation in the structure. By constructing a universal crack tip unit and combining with a NURBS algorithm, the crack growth of the special steel structure is accurately simulated, and the fatigue crack damage process and the damage degree of the special steel in the forming process due to quenching and tempering are analyzed and predicted.
Drawings
In order to more clearly illustrate the technical solutions of the embodiments of the present application, the following description will briefly explain the drawings needed in the embodiments of the present application, and it is obvious that the drawings described below are only some embodiments of the present application, and that other drawings can be obtained according to these drawings without inventive effort for a person skilled in the art.
FIG. 1 is a flow chart of a method for determining thermal damage boundary elements according to an embodiment of the present invention.
Fig. 2 is a schematic diagram of a technical route of a fatigue fracture failure boundary element method of a special steel structure provided by the embodiment of the invention.
Fig. 3 is a schematic diagram of a structure of a near singular integration, singular integration and super singular integration algorithm provided by the embodiment of the invention.
Fig. 4 is a flowchart of implementation of the numerical values of the singular units of the split tip provided by the embodiment of the invention.
Fig. 5 is a schematic diagram of a simulation technical route of a fatigue crack growth process of a special steel structure provided by the embodiment of the invention.
Detailed Description
The present invention will be described in further detail with reference to the following examples in order to make the objects, technical solutions and advantages of the present invention more apparent. It should be understood that the specific embodiments described herein are for purposes of illustration only and are not intended to limit the scope of the invention.
Aiming at the problems existing in the prior art, the invention provides a method, a system, a medium, equipment and a terminal for measuring thermal damage boundary elements, and the invention is described in detail below with reference to the accompanying drawings.
As shown in fig. 1, the method for measuring thermal damage boundary elements provided by the embodiment of the invention includes:
s101: based on the existing thermal problem and elastic mechanical boundary element program, considering thermal coupling boundary conditions, adding a newly proposed crack tip singular unit and a near singular integration algorithm to obtain a thermal coupling boundary element method capable of accurately solving key parts of a special steel structure and predicting crack initiation.
S102: after crack initiation, a near singular integration algorithm, a super singular integration algorithm and a crack tip singular unit based on a unit decomposition method and a strengthening function idea are added, so that a thermal coupling double-boundary element method is realized, accurate displacement, thermal stress, strain and stress intensity factors near the crack are accurately solved, and a foundation is laid for simulating crack propagation in the next step.
S103: adding a crack expansion criterion, and judging whether the crack is expanded or not; and (3) representing a newly-expanded crack surface and a crack front by utilizing NURBS, constructing a crack tip singular unit based on NURBS shape functions, realizing numerical values in a double-boundary element method frame, accurately solving displacement, thermal stress and strain fields, and establishing a crack tip local coordinate system.
S104: and (3) obtaining a crack tip stress intensity factor by using J integral and M integral, further judging whether the crack is expanded, calculating a crack expansion angle and expansion quantity, and solving by using an incremental double-boundary element method.
S105: the method adopts theory, algorithm programming, programming and verification to carry out work, and verifies the correctness and reliability of the proposed numerical algorithm by comparing with the analytic solution, the numerical solution and the corresponding test results.
Other steps may be performed by those skilled in the art of the method for determining thermal damage boundary elements provided by the present invention, and the method for determining thermal damage boundary elements provided by the present invention of fig. 1 is merely one specific example.
In S101 provided by the embodiment of the present invention, a method for determining a crack boundary element of a special steel structure under thermal coupling includes:
and a double-boundary integral equation under thermal coupling is adopted, a thermal cracking tip singular unit deduced based on a unit decomposition method and a strengthening function is combined, a new format is formed by the double-boundary integral equation under thermal coupling, and numerical implementation is performed.
The thermal crack tip singular units are identified and determined by using a level set method and the like, corresponding integral criteria are established, integral blocks and integral point control criteria are established, the stress intensity factors are solved by using J integral or M integral, and the crack propagation direction is obtained by using an energy release rate criterion or a strain energy density factor criterion.
When the thermodynamic coupling double-boundary integral equation is used, singular integral and super singular integral are generated on a crack surface, and singular value decomposition technology with a core formed by approximate expansion of integral blocks and local polar coordinates according to the position of a source point is utilized; while singular value decomposition is employed, a conformal transformation is required.
In S102 provided by the embodiment of the present invention, the specific steel structure thermal stress is accurately calculated, and the specific process is:
based on the existing thermal problem and elastic mechanical boundary element program, aiming at key areas such as a weld joint transition area, cracks and the like, numerical implementation is carried out by adopting a thermodynamic coupling boundary integral equation formula, and the stress concentration of the areas is considered to construct corresponding crack tips, and improved distance transformation, index transformation and shape preservation transformation are carried out;
And reasonably partitioning the integration unit according to the position of the projection point in the integration unit, and formulating an integration point distribution control criterion to ensure that the integration point distribution control criterion obtains a balance between the number of the integration points and the integration precision.
For singular integration, integrating block, local coordinate transformation technology and conformal transformation are adopted according to the position of a source point.
In S103 provided by the embodiment of the present invention, simulation of a fatigue crack growth process of a special steel structure specifically includes:
and deducing a new combined format of the NURBS and a double-boundary integral equation under thermal coupling, and judging whether the crack is expanded or not by using an energy release rate criterion or a strain energy density factor criterion to obtain the crack expansion direction.
The NURBS is used for representing a new crack surface and a crack front after expansion, a crack tip unit under a NURBS basis function is constructed according to the singular nature of the crack tip, a crack tip local coordinate system is established, and a stress intensity factor is solved by J integral or M integral.
A series of sampling points are taken from the crack front edge, NURBS surface fitting is used for newly obtaining a crack expansion surface, the crack expansion surface is discrete, an incremental boundary element method is adopted for carrying out iterative solution, simulation of a crack expansion process is realized, and a pair formula is used for predicting the service life of a special steel structure.
In S105 provided by the embodiment of the present invention, the specific process of verifying and proposing the correctness and reliability of the numerical algorithm is:
aiming at the accurate determination of the thermal stress of the special steel structure, the simulation of the special steel structure crack boundary element and the special steel structure fatigue crack expansion process under the thermal coupling, a large number of typical calculation examples are combined after each step is completed, and the verification is repeatedly carried out. And after the completion, the result of the fatigue crack damage test of the special steel structure is compared and analyzed by adopting a calculation program, and compared with classical analytical solutions, numerical results or test results, the validity and the accuracy of the numerical algorithm provided by the invention are comprehensively verified. Meanwhile, the program data structure is continuously optimized and improved, and the calculation efficiency is improved.
The calculation accuracy and stability of the thermal stress of the special steel structure, the theoretical deduction accuracy of singular integral, super singular integral and near singular integral, and the calculation accuracy and efficiency of the program module;
the accuracy of the thermal coupling boundary integral equation form of the thermal crack tip unit based on the unit decomposition method and the strengthening function idea is adopted, the high precision of the temperature field, displacement, thermal stress, strain and stress intensity factors is verified, and the calculation precision and the numerical stability of the program module are verified.
And verifying the correctness of the new format by combining the NURBS and a double-boundary integral equation under thermal coupling, performing numerical simulation on a crack propagation process, and comparing the service life prediction of the special steel structure with a test result.
The technical scheme of the invention is further described below with reference to specific embodiments.
The method solves the problems in the analysis of the fatigue fracture and damage process to different degrees by using a boundary element method, fully references and improves the results, and is used for analyzing the structural fatigue fracture and damage process caused by the processes of quenching tempering and the like in the cutting tool process of the W18CrMoV material. Based on the achievement of the existing boundary element method, the problems of temperature, displacement, strain, stress field distribution and cracks in a W18CrMoV material cutter structure are taken as objects, the high-precision advantage of the boundary element method relative to the finite element method is fully utilized, and key theories and algorithms such as near singular integration, singular integration and super singular integration algorithms, a unit decomposition method, a strengthening function and a NURBS algorithm are systematically and deeply implemented, so that the boundary element algorithm is constructed in the fatigue fracture failure process analysis in the quenching and tempering manufacturing process with high precision and strong universality. The algorithm can accurately obtain accurate displacement and stress field near the internal crack of the cutter structure, corresponding fracture mechanical property parameters, reveal a defect generation mechanism in the cutter forming process, and provide an important calculation method for optimizing the technological parameters of the W18CrMoV material manufacturing cutter.
(1) Accurate calculation of thermal stress in quenching and tempering process of special steel structure
The thermal stress and mechanical stress generated by the special steel structure under the gradient temperature and alternating load can cause the high concentration of stress in key areas such as a welding seam transition area, cracks and the like, crack initiation can be caused, and the fatigue strength is reduced, which is an important cause of fatigue fracture and damage of the W18CrMoV special steel structure. The method is used for accurately solving the temperature, strain and stress field of the special steel structure. The method comprises the step of deriving a thermodynamic coupling boundary element algorithm formula, constructing a special steel structure weld joint transition region stress concentration unit and a unit capable of reflecting crack front stress singularities, and a method capable of accurately calculating near singular integral and singular integral, solving nonlinear transformation (distance transformation, exponential transformation and the like) of the near singular integral and integral point distribution control criteria, improving, balancing calculation accuracy and calculation efficiency, reducing sensitivity to projection points and overcoming unit shape effects of the projection points.
(2) Crack boundary element algorithm under special steel structure thermal coupling
The method is characterized by comprising the following steps of aiming at special steel structure crack initiation, deducing a double boundary integral equation formula under thermal coupling, deducing a thermal crack tip singular unit based on a unit decomposition method and an enhancement function idea, establishing a new double boundary element method solving format by combining with the double boundary integral equation under thermal coupling, and realizing a numerical value, wherein the method comprises the steps of deducing the formula, identifying and determining a thermal crack tip singular unit area, constructing a thermal crack tip singular unit function, integrating a criterion of the thermal crack tip singular unit, implementing a scheme for improving the calculation accuracy of displacement stress and stress intensity factors near a crack tip, and judging a crack expansion criterion (whether the crack is expanded, the direction of expansion and the like). The method also comprises the steps of developing a set of algorithms for singular integration and super singular integration on the crack surface when a thermodynamic coupling double boundary integral equation is used, overcoming the shape effect of singular integration and super singular integration units, and improving the calculation precision and calculation efficiency.
(3) Simulation of crack propagation process of special steel structure
The method comprises the steps of crack extension criterion, characterization of new crack surfaces and crack fronts after extension, NURBS and boundary method solving format derivation, crack tip unit structure under NURBS basis function and special steel structure service life prediction. Because crack propagation is a dynamic process, displacement, stress and stress intensity factors in each crack propagation process need to be solved iteratively, wherein the method comprises the steps of obtaining sampling points, fitting a crack propagation surface, realizing a crack tip unit based on a NURBS basis function, calculating the stress intensity factors in the propagation process and judging a crack next-step propagation criterion.
(4) The invention provides a numerical algorithm and verification of algorithm program
Aiming at a typical special steel structure, the accuracy, efficiency and robustness of a calculation program are verified by comparing and analyzing a numerical calculation result and a test result through a typical calculation example comparison and physical model test method.
The invention aims to develop a set of special steel structure thermal damage boundary element algorithm in the quenching and tempering process: the method can realize the accurate calculation of the thermal stress in the quenching and tempering process of the special steel structure, accurately simulate the structure to generate concentrated thermal stress and thermal strain under the severe heat load, and predict crack initiation at the weak part of the structure by combining the microstructure crystalline phase structure of the microscopic material; developing a crack boundary element algorithm under the thermal coupling of the special steel structure, accurately solving thermal stress, displacement and stress intensity factors of the crack front, and judging whether the crack is expanded and possibly has a trend; accurately simulating the crack expansion process of the special steel structure and predicting the thermal fatigue failure life of the structure. The crack propagation level under the quenching tempering heat treatment working condition of the special steel structure is accurately analyzed and calculated, the heat treatment process is guided to be optimized, and the yield is improved.
The key technology solved by the invention is as follows:
(1) Efficient and accurate singular integration, super singular integration and near singular integration algorithm
The efficient and accurate calculation of near singular integral is the key to successfully implement the thermal stress analysis of the special steel structure. In addition, when the thermodynamic coupling double-boundary integral equation is used, the accurate calculation of the grid size effect on the singular integral, the super singular integral and the near singular integral is considered in the microcrack area, the corresponding fracture mechanical property parameter calculation is also influenced, and the simulation of the special steel structure damage process is directly related.
(2) Boundary element algorithm for simulating special steel structure crack propagation process by combining NURBS function
The NURBS and the boundary element method are combined with a new solving format to represent the generation and expansion process of crack surfaces in the special steel structure damage, incremental step solving is carried out, the stress intensity factor precision of the crack front in the next step is improved, a local coordinate system of the crack front is naturally established, and the simulation of the special steel structure crack evolution process is a key point of the invention.
The invention is designed to work by adopting methods of theory, algorithm programming, programming and verification, and verifies the correctness and reliability of the numerical algorithm by comparing with analytical solutions, numerical solutions and corresponding test results.
As shown in fig. 2, the invention considers the thermal coupling boundary condition on the basis of the existing thermal problem and elastic mechanics boundary element program, and adds a newly proposed crack tip singular unit and near singular integration algorithm (fig. 2) to obtain a thermal coupling boundary element method capable of accurately solving the key parts of the special steel structure and predicting crack initiation. After crack initiation, a near singular integration algorithm, a super singular integration algorithm and a crack tip singular unit (figure 4) based on a unit decomposition method and a strengthening function idea are added, so that a thermal coupling double-boundary element method is realized, accurate displacement, thermal stress, strain and stress intensity factors near the crack are accurately solved, and a foundation is laid for simulating crack propagation in the next step. And adding a crack expansion criterion, and judging whether the crack is expanded or not. The method comprises the steps of representing a newly-expanded crack surface and a crack front by utilizing NURBS, constructing a crack tip singular unit based on NURBS shape functions, realizing numerical values in a double-boundary element method frame, accurately solving displacement, thermal stress and strain fields, establishing a crack tip local coordinate system, obtaining a crack tip stress intensity factor by utilizing J integral and M integral, further judging whether a crack is expanded, calculating a crack expansion angle and expansion quantity, and solving by using an incremental double-boundary element method (a specific flow can be seen in figure 5).
The thermal stress and mechanical stress generated by the special steel structure under the gradient temperature and alternating load can cause the high concentration of stress in key areas such as a welding seam transition area, cracks and the like, crack initiation can be caused, and the fatigue strength is reduced, which is an important cause of the fatigue fracture and destruction of the special steel structure. The invention relates to a method for accurately solving the temperature, displacement, stress and strain field distribution of a special steel structure. The method comprises the steps of deriving a thermodynamic coupling boundary element algorithm formula, constructing a unit of crack front singularity in a welding seam transition region, and accurately calculating near singular integral and singular integral, solving nonlinear transformation (distance transformation, exponential transformation and the like) of the near singular integral and integral point distribution control criteria, improving, balancing calculation accuracy and calculation efficiency, reducing sensitivity to projection points and overcoming unit shape effects of the projection points.
The scheme of the invention is as follows
(1) Accurate calculation of special steel structure thermal stress
Based on the existing thermal problem and elastic mechanical boundary element program, aiming at key areas such as a weld joint transition area, a crack and the like, numerical implementation is carried out by adopting a thermodynamic coupling boundary integral equation formula, and the stress concentration of the area is considered to construct a corresponding crack tip stress singular unit and a transition unit capable of reflecting the stress concentration. Aiming at the problems of singular integration and near singular integration caused by the grid size effect, aiming at the problems of near singular integration and singular integration caused by the grid size effect of key areas such as a weld transition zone, cracks and the like, nonlinear transformation (improved distance transformation and exponential transformation) and conformal transformation are prepared, and the problem of reasonably partitioning an integration unit according to the position of the projection point in the integration unit is solved, so that the sensitivity of the near singular integration nonlinear transformation to the projection point is reduced, an integration point distribution control criterion is formulated, so that the balance is obtained between the number of the integration points and the integration precision, and the unit shape effect of the near singular integration is overcome; for singular integration, the set of entries will employ integration blocks, local coordinate transformation techniques, and conformal transformations based on the source point locations.
(2) Crack boundary element algorithm for special steel structure under thermal coupling
Aiming at the problem of thermal cracking of a special steel structure, a double-boundary integral equation under thermal coupling is adopted, a thermal cracking tip singular unit deduced based on a unit decomposition method and an enhanced function idea is combined, a new format is solved by the double-boundary integral equation under thermal coupling, and numerical implementation is performed. The thermal crack tip singular units are identified and determined by using a level set method and the like, corresponding integration criteria (an integration block and an integration point control criterion) are established, a stress intensity factor is solved by using J integration or M integration, and a crack propagation direction is obtained by using an energy release rate criterion or a strain energy density factor criterion. It is noted that when using the thermodynamic coupling double boundary integral equation, singular and super singular integrals are generated on the crack surface, and the singular and super singular integral unit shape effect needs to be overcome. To this end, a singular value decomposition technique is to be adopted in which a term set is to be expanded as a core using integral blocks and local polar coordinate approximation according to source point positions, and in order to overcome the element effect thereof, a conformal transformation is required to be used while singular value decomposition is adopted.
(3) Simulation of fatigue crack propagation process of special steel structure
And (3) determining whether the crack is expanded or not by using an energy release rate criterion or a strain energy density factor criterion to obtain a crack expansion direction according to a new combination format of a double-boundary integral equation under NURBS and thermal coupling. The NURBS is used for representing a new crack surface and a crack front after expansion, a crack tip unit under a NURBS basis function is constructed according to the singular nature of the crack tip, a crack tip local coordinate system is established, and a stress intensity factor is solved by J integral or M integral. A series of sampling points are taken from the crack front edge, NURBS surface fitting is used for newly obtaining a crack expansion surface, the crack expansion surface is discrete, an incremental boundary element method is adopted for carrying out iterative solution, simulation of a crack expansion process is realized, and a pair formula is used for predicting the service life of a special steel structure.
(4) The invention provides a numerical algorithm and verification of algorithm program
For the three parts, after each step is completed, a large number of typical examples are combined, and verification is repeatedly performed to ensure the accuracy and the effectiveness of the program modules. This mainly includes the following three parts: the accuracy and stability of the calculation of the thermal stress of the special steel structure, the accuracy of theoretical deduction of singular integral, super singular integral and near singular integral, and the calculation accuracy and efficiency of the program module; the accuracy of the thermal coupling boundary integral equation form of the thermal crack tip unit based on the unit decomposition method and the strengthening function idea is ensured theoretically, the high precision of the temperature field, displacement, thermal stress, strain and stress intensity factors is ensured, and the calculation precision and the numerical stability of the program module are verified. And (3) verifying the correctness of a new format by combining a NURBS and a double-boundary integral equation under thermal coupling, and comparing the numerical simulation of the crack propagation process with the service life prediction and test results of the special steel structure. After all the above works are completed, the calculation program developed by the invention is applied to carry out comparison analysis on the fatigue crack failure test result of the special steel structure, and the comparison is carried out with classical analysis solutions, numerical results or test results, so that the validity and the accuracy of the numerical algorithm provided by the invention are comprehensively verified. Meanwhile, the program data structure is continuously optimized and improved, and the calculation efficiency is improved.
The foregoing is merely illustrative of specific embodiments of the present invention, and the scope of the invention is not limited thereto, but any modifications, equivalents, improvements and alternatives falling within the spirit and principles of the present invention will be apparent to those skilled in the art within the scope of the present invention.
Claims (9)
1. A method for determining a thermal damage boundary element, the method comprising:
based on a thermal conduction and elastic mechanical boundary element method, considering thermal coupling boundary conditions, adding a crack tip singular unit and a near singular integration algorithm to obtain a thermal coupling boundary element method for solving key parts of the special steel structure, and predicting crack initiation;
after crack initiation, a near singular integration algorithm, a super singular integration algorithm and a crack tip singular unit based on a unit decomposition method and a strengthening function idea are added to realize a thermal coupling double-boundary element method, and accurate displacement, thermal stress, strain and stress intensity factors near the crack are solved;
adding a crack expansion criterion, and judging whether the crack is expanded or not; representing a newly-expanded crack surface and a crack front by using NURBS, constructing a crack tip singular unit based on NURBS shape functions, carrying out numerical implementation in a double-boundary element method frame, solving displacement, thermal stress and strain fields, and establishing a crack tip local coordinate system;
Obtaining a crack tip stress intensity factor by using J integral and M integral, judging whether a crack is expanded, calculating a crack expansion angle and an expansion amount, and solving by using an incremental double-boundary element method;
by comparing with the analytic solution, the numerical solution and the corresponding test results;
the special steel structure thermal stress is accurately calculated, and the specific process is as follows: based on the existing thermal problem and elastic mechanical boundary element program, aiming at a weld joint transition zone and a crack key zone, adopting a thermodynamic coupling boundary integral equation formula to carry out numerical implementation, and taking the stress concentration of the zone into consideration to construct a corresponding crack tip, and carrying out improved distance transformation, exponential transformation and shape preserving transformation;
reasonably partitioning the integration unit according to the position of the projection point in the integration unit, and formulating an integration point distribution control criterion to obtain a balance between the number of the integration points and the integration precision;
for singular integration, integrating block, local coordinate transformation technology and conformal transformation are adopted according to the source point position.
2. The method for determining the thermal damage boundary element according to claim 1, wherein the method for determining the crack boundary element of the special steel structure under thermal coupling comprises the following steps: and a double-boundary integral equation under thermal coupling is adopted, a thermal cracking tip singular unit deduced based on a unit decomposition method and a strengthening function is combined, a new format is formed by the double-boundary integral equation under thermal coupling, and numerical implementation is performed.
3. The method of claim 2, wherein the thermal crack tip singular units are identified and determined using a level set method, corresponding integration criteria are formulated, integration blocks and integration point control criteria, J-integration or M-integration is used to solve for stress intensity factors, and energy release rate criteria or strain energy density factor criteria are used to obtain crack propagation directions.
4. The method for determining thermal damage boundary element according to claim 2, wherein when using a thermally coupled double boundary integral equation, singular integral and super singular integral are generated on the crack surface, and singular value decomposition technique using integral blocks and local polar coordinates according to the source point position to be approximately developed as a core is utilized; while singular value decomposition is employed, a conformal transformation is used.
5. The method for determining thermal damage boundary elements according to claim 1, wherein the simulation of the fatigue crack propagation process of the special steel structure is as follows: deducing a new combination format of a double boundary integral equation under NURBS and thermal coupling, judging whether a crack is expanded or not by using an energy release rate criterion or a strain energy density factor criterion, and obtaining a crack expansion direction;
Using NURBS to represent a new crack surface and a crack front after expansion, constructing a crack tip unit under a NURBS basis function according to the singular nature of the crack tip, establishing a crack tip local coordinate system, and solving a stress intensity factor by using J integral or M integral;
a series of sampling points are taken from the crack front edge, a NURBS surface fitting is used for newly obtaining a crack expansion surface, the crack expansion surface is discrete, an incremental boundary element method is adopted for carrying out iterative solution, simulation of a crack expansion process is realized, and a pair formula is used for predicting the service life of a special steel structure.
6. A computer device comprising a memory and a processor, the memory storing a computer program which, when executed by the processor, causes the processor to perform the thermal damage boundary element measurement method of any one of claims 1 to 5.
7. A computer readable storage medium storing a computer program which, when executed by a processor, causes the processor to perform the thermal damage boundary element measurement method of any one of claims 1 to 5.
8. The special steel structure thermal process information data processing terminal is characterized in that the special steel structure thermal process information data processing terminal is used for realizing the thermal damage boundary element measuring method according to any one of claims 1-5.
9. A thermal damage boundary element measurement system for performing the thermal damage boundary element measurement method of any one of claims 1 to 5, the thermal damage boundary element measurement system comprising:
the crack initiation prediction module is used for considering thermal coupling boundary conditions, adding a crack tip singular unit and a near singular integration algorithm to obtain a thermal coupling boundary element method for solving key parts of the special steel structure, and predicting crack initiation;
the crack information processing module is used for adding a near singular integration algorithm, a super singular integration algorithm and a crack tip singular unit based on a unit decomposition method and a strengthening function idea after crack initiation to realize a thermal coupling double-boundary element method and solve accurate displacement, thermal stress, strain and stress intensity factors near the crack;
the crack tip local coordinate system building module is used for adding a crack expansion criterion to judge whether the crack is expanded or not; representing a newly-expanded crack surface and a crack front by using NURBS, constructing a crack tip singular unit based on NURBS shape functions, carrying out numerical implementation in a double-boundary element method frame, solving displacement, thermal stress and strain fields, and establishing a crack tip local coordinate system;
the incremental double-boundary element method solving module is used for obtaining a crack tip stress intensity factor by using J integral and M integral, judging whether a crack is expanded, calculating a crack expansion angle and expansion quantity, and solving by using the incremental double-boundary element method;
The result comparison module is used for comparing the result with the analytic solution, the numerical solution and the corresponding test results;
the special steel structure thermal stress is accurately calculated, and the specific process is as follows: based on the existing thermal problem and elastic mechanical boundary element program, aiming at key areas such as a weld joint transition area, cracks and the like, numerical implementation is carried out by adopting a thermodynamic coupling boundary integral equation formula, and the stress concentration of the areas is considered to construct corresponding crack tips, and improved distance transformation, index transformation and shape preservation transformation are carried out;
reasonably partitioning the integration unit according to the position of the projection point in the integration unit, and formulating an integration point distribution control criterion to obtain a balance between the number of the integration points and the integration precision;
for singular integration, integrating block, local coordinate transformation technology and conformal transformation are adopted according to the position of a source point.
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