Finite element model-based method for predicting fatigue propagation of volute composite structure crack

Abstract

The invention provides a method for predicting volute composite structure crack fatigue extension based on a finite element model, and relates to the field of volute composite structure concrete fatigue life prediction. The method comprises the following steps: establishing a volute composite structure plane axial symmetry finite element model; after internal water pressure and static load are applied to the volute composite structure in the model, trial calculation is conducted, the distribution area of initial cracks of the concrete structure under the effect of the designed internal water pressure is obtained, and the distribution area of the initial cracks is marked as a cracking sensitive area; encrypting a grid region in the cracking sensitive region to obtain an encrypted model; a load is applied to a volute combination structure in the encryption model, the water pressure in the steel volute is increased to the maximum value so as to obtain an initial crack formed in the concrete structure, and the contact pressure of all nodes on the contact face of concrete and the steel volute is extracted; and applying the contact pressure to the inner surface of the concrete as a cyclic load to obtain concrete crack fatigue expansion data. And an effective technical means is provided for evaluation of the overall durability of the volute combined structure.

Description

Technical Field

[0001] The present application relates to the field of fatigue life prediction of concrete of a volute combination structure, and in particular to a method for predicting fatigue propagation of cracks in a volute combination structure based on a finite element model. Background Art

[0002] The lower structure of the hydropower plant building is composed of the steel volute of the turbine and the large volume of concrete wrapped around it. During the operation of the unit, the steel volute and the concrete form a combined structure called the volute composite structure, which bears the external load together. In specific practice, the steel volute of the turbine is generally designed according to the full head, but due to the contact force transmission between the steel volute and the concrete, the concrete will inevitably bear part of the internal water pressure, thereby forming a hoop tensile stress around the steel volute at the meridian section of the volute. Under the action of this hoop tensile stress, due to the low tensile strength of the concrete material, local cracking will occur at the contact point between the concrete and the volute in most cases.

[0003] In the design of the volute composite structure, for the sake of structural durability, the volute concrete is generally designed according to the limited crack design. The specific method is generally to establish a three-dimensional finite element numerical model of the steel volute and concrete composite structure. The steel volute is simulated by shell elements and the concrete is simulated by solid elements. At the same time, the material nonlinearity of the concrete and the contact nonlinearity between the steel volute and the concrete are considered, and the crack width or steel stress is verified according to the load effect standard combination. Although the above method has been widely used, it has at least the following problems:

[0004] The above method only considers the case of single loading of internal water pressure and cannot obtain the fatigue extension data of concrete cracks. Summary of the invention

[0005] The purpose of the present application is to provide a method for predicting fatigue expansion of cracks in a volute composite structure based on a finite element model, which can obtain the expansion process of the initial crack, that is, the fatigue expansion data of the concrete crack.

[0006] This application is implemented as follows:

[0007] The present application provides a method for predicting fatigue expansion of cracks in a volute assembly structure based on a finite element model, comprising:

[0008] A plane axisymmetric finite element model of the volute composite structure is established; after applying internal water pressure and static load to the volute composite structure in the model, a trial calculation is performed to obtain the distribution area of ​​the initial cracks in the concrete structure under the design internal water pressure, and the distribution area of ​​the initial cracks is marked as the crack-sensitive area; the mesh area in the crack-sensitive area is encrypted to obtain an encrypted model, and each encrypted mesh area is assigned with extended finite element properties, wherein on the basis of a given material fracture initiation stress, the judgment criterion for the development of the initial fracture is described by defining the material limit strain energy release rate, and the fatigue expansion behavior of the initial crack is described by defining the material fatigue crack initiation and development parameters; a load is applied to the volute composite structure in the encrypted model and the water pressure in the steel volute is increased to the maximum value to obtain the initial cracks formed in the concrete structure, and the contact pressure of each node on the contact surface between the concrete and the steel volute is extracted; the contact pressure is applied to the inner surface of the concrete as a cyclic load to obtain the fatigue expansion data of the concrete crack.

[0009] Furthermore, the establishment of a plane axisymmetric finite element model of the volute combined structure includes: the steel volute is simulated using solid units, and the outer surface of the connection between steel plates of different thicknesses in the steel volute is locally sloped according to the weld structure to establish a non-smooth contact surface between the steel volute and the surrounding concrete.

[0010] Furthermore, the initial stress of concrete fracture is taken as 0.77MPa-2.04MPa, and the ultimate strain energy release rate is taken as 5N / m-85N / m, that is, when the strain energy release rate at the tip of the initial crack exceeds the ultimate strain energy release rate, the marked initial crack will expand; the fatigue crack initiation parameter c1 is taken as 0.001~1.854×10-3, and c2 is taken as -2.1316~-1, that is, when the number of cycles exceeds c1△Gc2, the fatigue crack begins to expand; the fatigue crack development parameter c3 is taken as 10.017~18.017, and c4 is taken as 1~2.1316, that is, the development length of a single cycle fatigue crack is c3△Gc4, and △G represents the change value of the strain energy release rate of a single cycle.

[0011] Furthermore, the initial stress of concrete fracture is taken as 1.27MPa, and the ultimate strain energy release rate is taken as 45N / m, that is, when the strain energy release rate at the tip of the initial crack exceeds 45N / m, the marked initial crack will expand; the fatigue crack initiation parameters c1 and c2 are taken as 1.427×10-3 and -1.5658 respectively, that is, when the number of cycles exceeds c1△Gc2, the fatigue crack begins to expand; the fatigue crack development parameters c3 and c4 are taken as 14.017 and 1.5658 respectively, that is, the development length of a single cycle fatigue crack is c3△Gc4, and △G represents the change value of the strain energy release rate of a single cycle.

[0012] Furthermore, applying load to the volute combination structure in the encrypted model includes: applying structural deadweight, turbine layer load, stator and lower frame foundation load and internal water pressure to the volute combination structure in the encrypted model, and increasing the water pressure in the steel volute to a maximum value.

[0013] Compared with the prior art, the present invention has at least the following advantages or beneficial effects:

[0014] This application proposes a method for predicting fatigue expansion of cracks in a volute composite structure based on a finite element model. By extracting the contact pressure of each node on the contact surface between the concrete and the steel volute in the static calculation results, the cyclic internal water pressure is directly applied to the inner surface of the concrete, effectively overcoming the problem that the contact conditions of a single cycle in fatigue analysis based on the direct cycle method cannot be changed. This method can simulate the phenomenon of reduced stiffness of concrete structures as the number of internal water pressure cycles increases, making it possible to dynamically predict the fatigue life of the steel volute under the condition of considering the degradation of the concrete wrapping effect on the steel volute, providing an effective technical means for evaluating the overall durability of the volute composite structure. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] In order to more clearly illustrate the technical solutions of the embodiments of the present application, the drawings required for use in the embodiments will be briefly introduced below. It should be understood that the following drawings only show certain embodiments of the present application and therefore should not be regarded as limiting the scope. For ordinary technicians in this field, other related drawings can be obtained based on these drawings without paying creative work.

[0016] Figure 1 This is a flow chart of an embodiment of a method for predicting fatigue expansion of cracks in a volute assembly structure based on a finite element model of the present application;

[0017] Figure 2 A flowchart of another embodiment of the method for predicting fatigue expansion of cracks in a volute assembly structure based on a finite element model of the present application;

[0018] Figure 3 This is a schematic diagram of a local slope cutting of a steel volute weld structure of a hydropower station in an embodiment of the present application;

[0019] Figure 4 This is a plane axisymmetric finite element model of a 0° meridian section of a volute combination structure of a hydropower station in an embodiment of the present application (before local encryption);

[0020] Figure 5 It is a plane axisymmetric finite element model of a 0° meridian section of a volute combination structure of a hydropower station in an embodiment of the present application (after partial encryption);

[0021] Figure 6The pressure distribution on the contact surface between the steel volute and the concrete of a volute combination structure of a hydropower station under static load in an embodiment of the present application;

[0022] Figure 7 The cyclic load application range of the inner surface of the concrete of the volute composite structure of a hydropower station in the embodiment of the present application;

[0023] Figure 8a-8e The calculation result of fatigue expansion of concrete cracks around the steel volute of a hydropower station in the embodiment of the present application;

[0024] Figure 9a-9c This is the calculation result of fatigue expansion of concrete cracks at the junction of the turbine layer and the pier of a hydropower station in the embodiment of the present application.

[0025] Icon: 1-Welding seam. DETAILED DESCRIPTION

[0026] In order to make the purpose, technical solution and advantages of the embodiments of the present application clearer, the technical solution in the embodiments of the present application will be clearly and completely described below in conjunction with the drawings in the embodiments of the present application. Obviously, the described embodiments are part of the embodiments of the present application, rather than all the embodiments. The components of the embodiments of the present application described and shown in the drawings here can be arranged and designed in various different configurations.

[0027] In conjunction with the accompanying drawings, some embodiments of the present application are described in detail below. In the absence of conflict, the following embodiments and features in the embodiments can be combined with each other.

[0028] Example 1

[0029] After long-term research and practice, the applicant found that in the design of the volute composite structure, for the sake of structural durability, the volute concrete is generally designed according to the limited crack design. The specific practice of the prior art is generally to establish a three-dimensional finite element numerical model of the steel volute and concrete composite structure, the steel volute is simulated by shell units, and the concrete is simulated by solid units. At the same time, the material nonlinearity of the concrete and the contact nonlinearity between the steel volute and the concrete are considered, and the crack width (or steel stress) is verified according to the load effect standard combination. Although the above method has been widely used, it still has the following problems:

[0030] The method adopted in the existing technology only considers the case of single loading of internal water pressure, but in fact, the steel volute will be subjected to the cyclic loading of internal water pressure as the hydropower station operates. In particular, as the functional positioning of hydropower has gradually extended from simply providing energy to the power grid to new directions such as energy storage and tempering that adapt to the new energy structure in recent years, the start and stop of hydropower generating units have become more frequent, and the characteristics of the steel volute bearing the cyclic internal water pressure have become more significant. Therefore, the fatigue expansion of concrete cracks should be considered in the calculation.

[0031] In view of this, please refer to Figure 1 The embodiment of the present application provides a method for predicting fatigue expansion of cracks in a volute combination structure based on a finite element model, comprising:

[0032] S101: Establish a plane axisymmetric finite element model of the volute combined structure;

[0033] In this step, the volute combination structure generally refers to a structure composed of concrete and steel volutes, which is commonly found in hydropower stations and is used to convert water flow energy into mechanical energy or electrical energy. In this embodiment, the method for establishing the plane axisymmetric finite element model of the volute combination structure is not limited.

[0034] S102: After applying internal water pressure and static load to the volute combined structure in the model, a trial calculation is performed to obtain the distribution area of ​​the initial cracks of the concrete structure under the design internal water pressure, and the distribution area of ​​the initial cracks is marked as a cracking sensitive area;

[0035] For ease of understanding, internal water pressure: usually the pressure generated by the presence of fluid inside the volute, this pressure acts on the inner wall of the volute and may be transmitted to the entire structure. Static load: refers to external forces that do not change with time, such as the deadweight of the structure, turbine layer load, stator and lower frame foundation load, etc. In this step, after applying internal water pressure and static load to the volute combination structure in the model, cracks will appear in the areas of the volute combination structure that are more susceptible to damage or destruction. These areas are marked to facilitate subsequent processing of the area.

[0036] S103: Encrypting the mesh area in the crack sensitive area to obtain an encrypted model, and assigning extended finite element properties to each encrypted mesh area, wherein on the basis of a given material fracture initiation stress, the material limit strain energy release rate is defined to describe the judgment criterion for the initial fracture development, and the material fatigue crack initiation and development parameters are defined to describe the fatigue extension behavior of the initial crack;

[0037] In this step, in order to increase the analysis accuracy of the volute combination structure, the crack-sensitive area is encrypted. It should be noted that in finite element analysis, the density and quality of the grid (or unit) have a great influence on the accuracy of the analysis results. Mesh encryption means adding more grid units in a specific area (here is the crack-sensitive area) to more finely simulate the changes in physical quantities such as stress and strain in the area. For crack-sensitive areas, the encrypted grid can more accurately capture the initial formation and expansion process of cracks. Further, for ease of understanding, the extended finite element attribute (XFEM, Extended Finite Element Method) is a finite element technique for simulating discontinuity problems (such as cracks, holes, etc.). It allows discontinuities (such as cracks) to be introduced in specific areas without re-dividing the grid. In this embodiment, assigning extended finite element attributes to the encrypted grid area means enabling XFEM technology in these areas so that the formation and expansion of cracks can be simulated. Furthermore, the fracture initiation stress of a material is the stress threshold at which cracks begin to form in the material under specific conditions. The ultimate strain energy release rate is another important parameter related to the material fracture process, which describes the energy released per unit area when the crack expands. By defining these parameters, the criterion for the development of initial fracture can be established, that is, when the stress in the structure reaches the fracture initiation stress and the energy released by the crack expansion reaches or exceeds the ultimate strain energy release rate, it is considered that the crack will begin to expand. In addition to crack expansion under static load, the volute composite structure is also subjected to cyclic loads (such as vibration, alternating stress, etc.), which may lead to the formation and expansion of fatigue cracks. The fatigue crack initiation and development parameters describe the formation and expansion characteristics of cracks in materials under cyclic loads. By defining these parameters, the expansion behavior of initial cracks under fatigue loads can be simulated. After the above steps, the original finite element model is encrypted in the crack-sensitive area, and these areas are assigned extended finite element properties, and the material parameters related to the initial formation and expansion of cracks are defined. The encrypted model can more accurately simulate the crack behavior of the structure under complex loading conditions.

[0038] S104: Apply load to the volute composite structure in the encrypted model and increase the water pressure in the steel volute to the maximum value to obtain the initial cracks formed in the concrete structure and extract the contact pressure of each node on the contact surface between the concrete and the steel volute;

[0039] In this step, in order to be closer to the actual working conditions of the volute combination structure and to test the bearing capacity and stability of the structure under extreme working conditions, the volute combination structure in the encrypted model is loaded and the water pressure in the steel volute is increased to the maximum value. For example, the structure deadweight, turbine layer load, stator and lower frame foundation load and internal water pressure are applied to the volute combination structure in the encrypted model. During the simulation, the water pressure inside the steel volute is gradually increased until it reaches or approaches its maximum value in design or operation. As the water pressure increases, cracks begin to form in the concrete structure because the stress exceeds its tensile strength. The appearance of these initial cracks is an important indicator for evaluating structural performance, indicating further damage or failure of the structure. In the simulation, the strength and durability of the structure can be evaluated by observing and recording the formation location, morphology and expansion path of the cracks. For ease of understanding, contact pressure refers to the pressure generated by extrusion between two surfaces in contact with each other. In the volute combination structure, the contact surface between the concrete and the steel volute is the key force transmission path, and the size and distribution of its contact pressure directly affect the overall performance of the structure. Extracting the contact pressure of each node means obtaining the contact pressure values ​​of all nodes on the contact surface in the numerical simulation results. These data can be used to analyze the stress state of the contact surface and evaluate the stability of the structure.

[0040] S104: Apply contact pressure as a cyclic load to the inner surface of the concrete to obtain concrete crack fatigue growth data.

[0041] In this step, the contact pressure is periodically applied as a load to the inner surface of the concrete to simulate the dynamic loading process under actual working conditions. The impact of cyclic loads on concrete structures is reflected in fatigue damage, that is, long-term exposure to cyclic loads will cause the material properties to gradually degrade, and eventually cause the expansion of cracks and the destruction of the structure. In concrete structures, the formation and expansion of cracks are direct manifestations of fatigue damage. When concrete is subjected to cyclic loads, its internal microstructure will gradually change, such as the generation and expansion of microcracks, plastic deformation of materials, etc. As the number of cycles increases, these microscopic changes will gradually accumulate and lead to the formation and expansion of macroscopic cracks. In this embodiment, the fatigue performance of the concrete structure is evaluated by simulating the dynamic loading process under actual working conditions, and the relevant data of crack expansion are collected for subsequent analysis. This method is of great significance for improving the safety and durability of engineering structures.

[0042] Example 2

[0043] The inventors also found that the prior art uses a three-dimensional finite element numerical model of a steel volute and concrete composite structure to simulate the volute composite structure. The steel volute is simulated using shell units and the concrete is simulated using solid units. Although the method has been widely used, it still has the following problems: the use of shell units to simulate the steel volute cannot take into account the local structure of the non-smooth transition area of ​​the outer surface of the steel volute at the weld of steel plates of different thicknesses. In these non-smooth areas, contact force transmission is often prone to sudden increase or decrease (local de-energization), thereby causing excessive local stress (cracking) in the concrete. Under the cyclic action of such large stress, the expansion of local fatigue cracks in the structure needs to be paid attention to. Therefore, the non-smooth characteristics of the outer surface of the steel volute should be considered in the calculation to achieve accurate prediction of fatigue expansion of concrete cracks.

[0044] In view of this, please refer to Figure 2 and Figure 3 ,The difference between this embodiment and embodiment 1 is that the following steps are adopted in the process of establishing the plane axisymmetric finite element model of the volute combination structure,S201: the steel volute is simulated by solid units, and the outer surface of the connection of steel plates of different thicknesses in the steel volute is locally sloped according to the weld structure to establish a non-smooth contact surface between the steel volute and the surrounding concrete.

[0045] Figure 3The steel volute weld structure details of a hydropower station in this embodiment are shown in Figure 1. The steel volute in this embodiment is formed by connecting different steel plates of different thicknesses. The outer surface of the steel volute is not smooth due to the transition of the thickness of the steel plate (such as from thick to thin or the splicing of steel plates of different thicknesses). This unevenness has an important impact on the overall performance and durability of the structure. The cross section of the steel volute in this embodiment is formed by welding a steel plate with a thickness of t1, two steel plates with a thickness of t2 and two steel plates with a thickness of t3. t1<t2<t3. Due to the different thicknesses of the steel plates, this embodiment performs slope cutting at the weld 1 of the two steel plates of different thicknesses, and cuts the slope of the steel plate with a higher thickness. After the slope cutting, a slope is formed. The outer surface of the steel plate with a lower thickness forms an angle α with the slope, and the thickness of the steel plate and the size of the angle α are recorded. This embodiment takes into account the uneven characteristics caused by the transition of the thickness of the steel plate. Instead of simply regarding the contact between the steel volute and the concrete as a completely smooth or idealized contact, the uneven contact state between them is simulated closer to the actual situation. When the water flow pressure acts on the steel volute, concentrated force transmission behavior will occur at the uneven contact point, that is, the pressure is not evenly distributed on the entire contact surface, but concentrated in certain local areas. This concentrated force transmission behavior further causes the structure to have stress concentration phenomenon in these local areas, that is, the stress level in these areas is much higher than the average level. This embodiment can effectively simulate this complex force transmission behavior and stress concentration phenomenon. It provides a more reliable premise and basis for predicting and calculating the fatigue expansion of concrete cracks. It is of great significance to ensure the safety and durability of similar engineering structures such as hydropower stations. This step is followed by the following steps:

[0046] S202: After applying internal water pressure and static load to the volute combination structure in the model, a trial calculation is performed to obtain the distribution area of ​​the initial cracks in the concrete structure under the design internal water pressure, and the distribution area of ​​the initial cracks is marked as the crack-sensitive area; S203: The grid area in the crack-sensitive area is encrypted to obtain an encrypted model, and each encrypted grid area is assigned with extended finite element properties, wherein on the basis of a given material fracture initiation stress, the judgment criterion for the development of the initial fracture is described by defining the material limit strain energy release rate, and the fatigue extension behavior of the initial crack is described by defining the material fatigue crack initiation and development parameters; S204: A load is applied to the volute combination structure in the encrypted model and the water pressure in the steel volute is increased to the maximum value to obtain the initial cracks formed in the concrete structure, and the contact pressure of each node on the contact surface between the concrete and the steel volute is extracted; S205: The contact pressure is applied to the inner surface of the concrete as a cyclic load to obtain the fatigue extension data of the concrete crack.

[0047] Among them, the value ranges of concrete fracture initial stress, ultimate strain energy release rate, fatigue crack initiation parameters c1, c2, fatigue crack development parameters c3, c4 are as follows:

[0048] The initial stress of concrete fracture is 0.77MPa-2.04MPa, and the ultimate strain energy release rate is 5N / m-85N / m, that is, when the strain energy release rate at the tip of the initial crack exceeds the ultimate strain energy release rate, the marked initial crack will expand; the fatigue crack initiation parameter c1 is 0.001~1.854×10-3, c2 is -2.1316~-1, that is, when the number of cycles exceeds c1△Gc2, the fatigue crack begins to expand; the fatigue crack development parameter c3 is 10.017~18.017, c4, is 1~2.1316, that is, the development length of a single cycle fatigue crack is c3△Gc4, △G represents the change value of the strain energy release rate of a single cycle.

[0049] Preferably, the initial stress of concrete fracture is 1.27MPa, and the ultimate strain energy release rate is 45N / m, that is, when the strain energy release rate at the tip of the initial crack exceeds 45N / m, the marked initial crack will expand; the fatigue crack initiation parameters c1 and c2 are 1.427×10-3 and -1.5658 respectively, that is, when the number of cycles exceeds c1△Gc2, the fatigue crack begins to expand; the fatigue crack development parameters c3 and c4 are 14.017 and 1.5658 respectively, that is, the development length of a single cycle fatigue crack is c3△Gc4, and △G represents the change value of the strain energy release rate of a single cycle.

[0050] Taking a hydropower station as an example, six 700MW turbine generator sets are installed in the main powerhouse, the turbine volute inlet section diameter is 6.8m, and the designed internal water pressure value is 2.76MPa.

[0051] The plane axisymmetric finite element model of the 0° meridian section of the volute combined structure of a hydropower station is established. The steel volute is simulated using solid elements. The details of the weld structure are shown in Figure 3 In addition, the steel volute of the hydropower station is formed by welding a steel plate with a thickness of t1, two steel plates with a thickness of t2, and two steel plates with a thickness of t3. t1<t2<t3. Due to the different thicknesses of the steel plates, this embodiment performs slope cutting at the weld 1 of the two steel plates of different thicknesses. The steel plate with a higher thickness is sloped. After slope cutting, a slope is formed. The outer surface of the steel plate with a lower thickness forms an angle α with the slope. The thickness of the steel plate and the size of the angle α are recorded. See the finite element model. Figure 4 , Figure 4 In the figure, t1 = 47 mm, t2 = 68 mm, t3 = 100 mm, α = 15°. The length of the concrete grid side is controlled at 20 cm.

[0052] Static loads (structural deadweight, turbine layer load, stator and lower frame foundation load) and internal water pressure were applied to the volute composite structure in the model. It was found that the initial cracks in the concrete structure were mainly distributed in four locations of the steel volute thickness transition, the waist of the steel volute, and the junction of the turbine layer and the pier, a total of six areas.

[0053] According to the above results, the meshes near the six initial crack distribution areas are encrypted, and the encryption range is 50cm×50cm. The mesh side length within the encryption range is controlled at 2cm, and the mesh side length outside the encryption range is appropriately increased. The finite element model after local encryption is shown in Fig. Figure 5 The extended finite element properties are assigned to the six encrypted mesh areas. The concrete fracture initial stress is 1.27MPa, and the ultimate strain energy release rate is 45N / m. That is, when the strain energy release rate calculated at the initial crack tip exceeds 45N / m, the initial crack will extend. The fatigue crack initiation parameters c1 and c2 are 1.427×10 -3 and -1.5658, that is, when the number of cycles exceeds c1△Gc2, the fatigue crack begins to expand; the fatigue crack development parameters c3 and c4 are 14.017 and 1.5658 respectively, that is, the development length of a single cycle fatigue crack is c3△Gc4, △G represents the change value of the strain energy release rate of a single cycle.

[0054] The structural deadweight, turbine layer load, stator and lower frame foundation load, and internal water pressure are applied to the mesh encryption model to extract the pressure distribution on the contact surface between the steel volute and the concrete, such as Figure 6 , and then remove the water pressure in the volute.

[0055] Will Figure 6 The contact pressure in the concrete is cyclically applied to the inner surface of the concrete in the form of sinusoidal loading and unloading. Figure 7 , concrete crack fatigue expansion calculation is carried out, and the calculation results are shown in Figure 8a-8e and Figure 9a-9c . Figure 8a It means that the crack depth of the concrete outside the steel volute is 6.75cm after the number of cycles reaches 300202. Figure 8b It means that the crack depth of the concrete outside the steel volute is 14.10cm after the number of cycles reaches 465963. Figure 8c It means that the crack depth of the concrete outside the steel volute is 17.62cm after the number of cycles reaches 622463. Figure 8d It means that the crack depth of the concrete outside the steel volute is 22.78cm after the number of cycles reaches 797171 times. Figure 8e It means that the crack depth of the concrete outside the steel volute is 26.71cm after the number of cycles reaches 975458. Figure 9aIt means that the crack depth of the concrete at the junction of the turbine layer and the pier is 6 cm after the number of cycles reaches 355628. Figure 9b It means that the crack depth of the concrete at the junction of the turbine layer and the pier is 8cm after the number of cycles reaches 465963. Fig.9c It means that the crack depth of the concrete at the junction of the turbine layer and the pier is 10cm after the cycle number reaches 924990 times.

[0056] The calculation results show that in 10 6 Under the action of internal water pressure cycles, the fatigue expansion of the initial cracks in the volute concrete was significant in the lower half away from the transition of the thickness of the steel plate on the seat ring side and at the junction of the turbine layer and the pier. The crack depth of the former reached 26.71 cm after 975,458 load cycles, and the crack depth of the latter reached 10 cm after 724,990 load cycles. The crack depths at both locations reached or even exceeded the thickness of the steel bar protective layer, which is very unfavorable to the durability of the structure.

[0057] In summary, the method proposed in the present invention, firstly, takes into account the unevenness of the outer surface of the steel volute caused by the transition of the steel plate thickness, and can effectively simulate the concentrated force transmission behavior at the uneven contact between the steel volute and the concrete and the local stress concentration phenomenon of the structure caused by it, which provides a reliable premise for the calculation of fatigue expansion of concrete cracks;

[0058] Second, by extracting the contact pressure of each node on the contact surface between concrete and steel volute from the static calculation results, the cyclic internal water pressure is directly applied to the inner surface of the concrete, which effectively overcomes the problem that the contact conditions of a single cycle cannot be changed in fatigue analysis based on the direct cycle method.

[0059] Thirdly, the calculation method proposed in the present invention can simulate the phenomenon of reduced stiffness of concrete structures as the number of internal water pressure cycles increases, making it possible to dynamically predict the fatigue life of the steel volute under the condition of degradation of the concrete wrapping effect on the steel volute, and providing an effective technical means for evaluating the overall durability of the volute composite structure.

[0060] It will be apparent to those skilled in the art that the present application is not limited to the details of the exemplary embodiments described above, and that the present application can be implemented in other specific forms without departing from the spirit or essential features of the present application. Therefore, the embodiments should be considered exemplary and non-limiting in all respects, and the scope of the present application is defined by the appended claims rather than the above description, and it is intended that all changes falling within the meaning and scope of the equivalent elements of the claims be included in the present application. Any reference numeral in a claim should not be considered as limiting the claim to which it relates.

Claims

1. A method for predicting fatigue growth of cracks in volute composite structures based on finite element model. It is characterized in that include: Establish a plane axisymmetric finite element model of the volute combined structure; After applying internal water pressure and static load to the volute combined structure in the model, a trial calculation is performed to obtain the distribution area of ​​the initial cracks of the concrete structure under the design internal water pressure, and the distribution area of ​​the initial cracks is marked as the cracking sensitive area; The mesh area in the crack-sensitive area is encrypted to obtain an encrypted model, and each encrypted mesh area is assigned with extended finite element properties. On the basis of a given material fracture initiation stress, the material limit strain energy release rate is defined to describe the criterion for the development of initial fracture, and the material fatigue crack initiation and development parameters are defined to describe the fatigue extension behavior of the initial crack. Apply load to the volute composite structure in the encrypted model and increase the water pressure in the steel volute to the maximum value to obtain the initial cracks formed in the concrete structure and extract the contact pressure of each node on the contact surface between the concrete and the steel volute. The contact pressure is applied to the inner surface of the concrete as a cyclic load, and the fatigue growth data of concrete cracks are obtained.

2. The method according to claim 1, It is characterized in that The establishment of the plane axisymmetric finite element model of the volute combined structure comprises: The steel volute is simulated by solid elements. The outer surface of the connection between steel plates of different thicknesses in the steel volute is locally sloped according to the weld structure to establish a non-smooth contact surface between the steel volute and the surrounding concrete.

3. The method according to claim 1, It is characterized in that The initial stress of concrete fracture is 0.77MPa-2.04MPa, and the ultimate strain energy release rate is 5N / m-85N / m, that is, when the strain energy release rate at the tip of the initial crack exceeds the ultimate strain energy release rate, the marked initial crack will expand; the fatigue crack initiation parameter c1 is 0.001~1.854×10-3, c2 is -2.1316~-1, that is, when the number of cycles exceeds c1△Gc2, the fatigue crack begins to expand; the fatigue crack development parameter c3 is 10.017~18.017, c4, is 1~2.1316, that is, the development length of a single cycle fatigue crack is c3△Gc4, △G represents the change value of the strain energy release rate of a single cycle.

4. The method according to claim 3, It is characterized in that The initial stress of concrete fracture is 1.27MPa, and the ultimate strain energy release rate is 45N / m, that is, when the strain energy release rate at the tip of the initial crack exceeds 45N / m, the marked initial crack will expand; the fatigue crack initiation parameters c1 and c2 are 1.427×10-3 and -1.5658 respectively, that is, when the number of cycles exceeds c1△Gc2, the fatigue crack begins to expand; the fatigue crack development parameters c3 and c4 are 14.017 and 1.5658 respectively, that is, the development length of a single cycle fatigue crack is c3△Gc4, and △G represents the change value of the strain energy release rate in a single cycle.

5. The method according to claim 1, It is characterized in that The load applied to the volute combined structure in the encrypted model includes: The self-weight of the structure, the turbine layer load, the stator and lower frame foundation load and the internal water pressure are applied to the volute combined structure in the encrypted model, and the water pressure inside the steel volute is increased to the maximum value.

Images