Failure prediction method for blade crown with wear-resistant block
Through partition design and finite element analysis, the problem of inaccurate blade crown failure prediction in the existing technology is solved, accurate failure assessment of blade crowns with wear-resistant blocks is achieved, and prediction accuracy and safety are improved.
Patent Information
- Application Number
- CN202511171151.8
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-08-21
- Publication Date
- 2025-10-28
AI Technical Summary
The existing blade shroud failure calculation method is based on the point stress method, which cannot accurately evaluate the fracture reserve of the blade shroud with a wear-resistant layer. It also has large errors under high temperature and vibration environments and cannot effectively predict the risk of blade shroud failure caused by initial defects.
A zonal design approach was adopted, taking into account the influence of wear-resistant blocks and heat-affected zones on blade crown failure. The stress distribution was obtained through finite element analysis, and extrusion strength and damage tolerance analyses were performed to assess the failure risk of the blade crown.
The accuracy of blade shroud failure prediction with wear-resistant blocks is improved, and the failure risk of the blade shroud in different areas can be accurately assessed, errors can be reduced, and the safety of the wear-resistant block contact surface under working conditions can be ensured.
Smart Images
Figure CN120850683A_ABST
Abstract
Description
Technical Field
[0001] This application belongs to the field of engine turbine blade technology, and in particular relates to a method for predicting the failure of blade crowns with wear-resistant blocks. Background Art
[0002] Current methods for calculating leaf crown failure are mainly based on the point stress method, which states that the maximum stress σ at a single local point during leaf crown operation is greater than the tensile strength of the leaf crown matrix.
[0003] This failure calculation method is applicable to homogeneous materials. A schematic diagram of a blade canopy with a wear-resistant layer is shown below. Figure 1 If the existing method is used directly for calculation, taking the tensile limit value of the leaf canopy matrix, the calculated leaf canopy fracture reserve will be inaccurate. This is because: 1. Because the blade crown wear-resistant block needs to be constructed using a weld overlay method, a heat-affected zone will exist between the weld overlay and the blade crown substrate. See Figure 2 The tensile properties of the matrix and the weld overlay material cannot represent the material properties of the heat-affected zone. 2. Under working conditions, the temperature in some areas of the blade crown is relatively high. After entering the plastic stage, the stress in local areas of the blade crown is redistributed, and the point stress method will have a large error in assessing the fracture reserve. 3. Initial defects may exist at the weld overlay location, and the blade crown is simultaneously subjected to steady-state stress and vibration stress, resulting in a high risk of crack initiation. Summary of the Invention
[0004] The purpose of this application is to overcome the problems of the prior art by disclosing a method for predicting the failure of a blade crown with wear-resistant blocks. This method considers the influence of wear-resistant blocks and heat-affected zones on the failure analysis of the blade crown and conducts extrusion strength and damage tolerance analysis based on the normal pressure of the contact surface of the wear-resistant blocks, which can improve the accuracy of blade crown failure prediction.
[0005] The objective of this application is achieved through the following technical solution: A method for predicting the failure of a blade canopy with wear-resistant blocks, the method comprising: S1: Acquisition of leaf crown material properties and stress analysis; S2: Conduct failure analysis of different regions of the blade crown, and predict blade crown failure when the contact surface compressive strength requirement is not met; S3: Conduct compressive strength analysis of the contact surface between the leaf crowns, and predict leaf crown failure when the tensile and / or compressive strength requirements are not met; S4: Conduct blade crown damage tolerance analysis to predict blade crown failure when the crack propagation threshold value is not met.
[0006] According to a preferred embodiment, step S1 includes: S11: Obtain the material properties of the leaf crown matrix and the weld overlay material at different temperatures; S12: Obtain the dimensions of the heat-affected zone and the relationship between the heat-affected zone and the thickness of the wear-resistant block; S13: Based on the properties of the weld overlay material and the relationship between the heat-affected zone and the thickness of the wear-resistant block obtained in S11 and S12, obtain the material properties of the heat-affected zone; S14: Establish a blade crown model with wear-resistant blocks, perform partitioned modeling of the wear-resistant blocks, and assign different material properties to the matrix, heat-affected zone and wear-resistant blocks respectively. Obtain the blade crown stress distribution through finite element analysis.
[0007] According to a preferred embodiment, the material properties obtained in step S11 include elastic modulus E, coefficient of linear expansion θ, and tensile strength. Compressive strength ; Step S12 includes: designing several sets of calibration parts with different wear-resistant block thicknesses, with no less than 5 samples in each set; measuring the size of the heat-affected zone of the wear-resistant block through metallographic analysis; and obtaining the relationship between the heat-affected zone H2 and the thickness of the wear-resistant block.
[0008] Where: H2 is the thickness of the heat-affected zone, H1 is the thickness of the wear-resistant block, and k is the welding influence coefficient.
[0009] According to a preferred embodiment, step S13 specifically includes: Elastic modulus E2 of the heat-affected zone at a certain temperature:
[0010] Wherein, E3 is the elastic modulus of the matrix at this temperature, and E1 is the elastic modulus of the weld overlay material at this temperature; The coefficient of linear expansion of the heat-affected zone at a certain temperature:
[0011] Where: θ3 is the linear expansion coefficient of the substrate at this temperature, and θ1 is the linear expansion coefficient of the weld overlay material at this temperature; Tensile strength of the heat-affected zone at a certain temperature:
[0012] in, The tensile strength of the matrix at this temperature. denoted as the tensile strength of the weld overlay material at this temperature, and x as the vertical distance from the heat-affected zone to the substrate boundary. Compressive strength of the heat-affected zone at a certain temperature:
[0013] in, The compressive strength of the matrix at this temperature. The compressive strength of the weld overlay material at this temperature.
[0014] According to a preferred embodiment, step S2 includes: S21: Matrix failure prediction, including: starting from the maximum first principal stress point and the maximum third principal stress point of the matrix, obtaining the critical section of the matrix along the stress gradient direction, and obtaining the average first principal stress of the critical section. With the average third principal stress ,when or At that time, the leaf canopy matrix was predicted to fail; S22: Failure prediction in the heat-affected zone, including: taking the maximum first principal stress point and the maximum third principal stress point in the heat-affected zone as starting points, obtaining the critical section of the blade crown perpendicular to the wear-resistant block, with a section thickness of H2. In the critical section of the heat-affected zone, when x=x1... Take the average value from the top to the bottom of the dangerous section of the leaf crown, until the result is obtained. and curve, The first principal stress in the heat-affected zone, This is the third principal stress in the heat-affected zone; when and When any position on the curve is above the x-tensile / compressive strength curve, the heat-affected zone is considered to have failed.
[0015] S23: Failure prediction of wear-resistant block, obtaining the maximum first principal stress of the wear-resistant block. With the maximum third principal stress ,when or At that time, the wear-resistant block of the leaf crown is predicted to fail.
[0016] According to a preferred embodiment, step S3 includes: S31: Through the design of the blade crown damping, the upper limit of the normal pressure on the contact surface of the wear-resistant block that satisfies the vibration reduction effect of the blade crown damping is obtained. and lower limit value Combined with the nominal contact area A 名义 The upper and lower limits of the contact surface compressive strength that satisfy the crown damping and vibration reduction effect are obtained:
[0017] S32: Based on finite element analysis, obtain the stress distribution on the contact surface of the blade crown wear-resistant block, and extract the total normal force on the contact surface. When the mesh element compressive stress When the contact state is considered invalid, the areas of the effective contact elements are summed:
[0018] Average compressive stress on the contact surface of the wear-resistant block:
[0019] when At that time, the compressive strength of the contact surface of the wear-resistant block of the blade crown met the requirements.
[0020] According to a preferred embodiment, step S4 includes: S41: Upper limit of normal pressure at the blade crown contact surface obtained from S31 and lower limit value When the positive pressure is at [ , Within the specified range, the maximum first principal stress of the leaf crown was obtained through finite element analysis. The relationship curve between the normal force F and the normal force F; S42: Through crown damping vibration reduction design and testing, when the normal pressure is [ , Within the range, the leaf crown vibration is obtained. The relationship curve between stress and normal force F; S43: Assume that an initial crack a0 appears in the weld seam of the wear-resistant block of the blade crown, and at the maximum first principal stress... Superimposed vibration stress Stress intensity factor amplitude under action : When the stress intensity factor amplitude Crack propagation threshold ,Right now At that time, the initial crack in the leaf crown will expand and fail.
[0021] According to a preferred embodiment, the stress intensity factor amplitude in step S43 Obtained through the following formula:
[0022] Among them, K max K represents the maximum value of the stress intensity factor. min λ is the minimum stress intensity factor, and λ is the shape factor.
[0023] The aforementioned main solution and its various further alternative solutions can be freely combined to form multiple solutions, all of which are solutions that can be adopted and are claimed in this application. Those skilled in the art, after understanding the solution of this application, will realize that there are many combinations based on the prior art and common general knowledge, all of which are technical solutions to be protected in this application, and will not be exhaustively listed here.
[0024] The beneficial effects of this application are: This application establishes a failure prediction method for blade crowns with wear-resistant blocks based on a zonal design. Considering the influence of the wear-resistant blocks and the heat-affected zone (HAZ) on crown failure, failure predictions are performed separately for the substrate, HAZ, and wear-resistant layer. This method improves the accuracy of failure prediction for blade crowns with wear-resistant blocks. Simultaneously, the compressive stress at the wear-resistant block contact surface and the crown damage tolerance are analyzed to determine whether the normal pressure at the wear-resistant block contact surface during operation meets the requirements for crown damping, compressive strength, and damage tolerance. This method further improves the accuracy of failure prediction for blade crowns with wear-resistant blocks. Attached Figure Description
[0025] Figure 1 This is a schematic diagram of a blade crown structure with wear-resistant blocks; Figure 2 This is a schematic diagram of the leaf crown partition structure; Figure 3 This is a schematic diagram of the critical section of the leaf crown matrix; Figure 4 This is a schematic diagram of the dangerous section of the heat-affected zone of the leaf crown; Figure 5 It is the stress curve of the heat-affected zone; Figure 6 It is the stress curve of the heat-affected zone; Figure 7 This is a schematic diagram of the contact state of the wear-resistant block contact surface of the blade crown; Figure 8 It is a stress curve that varies with normal pressure; Figure 9 It is the stress intensity factor curve that varies with normal pressure; Figure 10 This is a schematic diagram of the failure prediction method for blade crowns with wear-resistant blocks in this application. Detailed Implementation
[0026] The following specific examples illustrate the implementation of this application. Those skilled in the art can easily understand other advantages and effects of this application from the content disclosed in this specification. This application can also be implemented or applied through other different specific embodiments, and various details in this specification can also be modified or changed based on different viewpoints and applications without departing from the spirit of this application. It should be noted that, unless otherwise specified, the following embodiments and features in the embodiments can be combined with each other.
[0027] It should be noted that similar reference numerals and letters denote similar items in the following drawings, and therefore, once an item is defined in one drawing, it does not need to be further defined or explained in subsequent drawings.
[0028] In the description of this application, it should be noted that the terms "center," "upper," "lower," "left," "right," "vertical," "horizontal," "inner," and "outer," etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings, or the orientation or positional relationship commonly used when the product of this application is in use. They are only for the convenience of describing this application and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation on this application. In addition, the terms "first," "second," and "third," etc., are only used to distinguish descriptions and should not be construed as indicating or implying relative importance.
[0029] Furthermore, terms such as "horizontal," "vertical," and "sag" do not imply that components must be absolutely horizontal or suspended, but rather that they can be slightly tilted. For example, "horizontal" simply means that its direction is more horizontal relative to "vertical," and does not mean that the structure must be completely horizontal, but can be slightly tilted.
[0030] It should also be noted that, in the description of this application, unless otherwise expressly specified or limited, the terms "disposed," "installed," "connected," and "connected" should be understood in a broad sense. For example, they can refer to fixed connections, detachable connections, or integral connections; they can refer to mechanical connections or electrical connections; they can refer to direct connections or indirect connections through an intermediate medium; and they can refer to internal connections between two components. Those skilled in the art will understand the specific meanings of the above terms in this application based on the specific circumstances.
[0031] Furthermore, it should be noted that unless otherwise specified in this application, the specific structures, connections, positions, power sources, etc. involved are all things that a person skilled in the art can know without creative effort based on the prior art.
[0032] Example 1 refer to Figures 1 to 10 As shown, this application discloses a method for predicting blade crown failure with wear-resistant blocks, which includes the following steps.
[0033] Step 1: Obtaining the material properties and stress analysis of the blade canopy with wear-resistant blocks Step 1-1: Design standard specimens for the leaf crown substrate and weld overlay material. Obtain material properties at different temperatures through experiments, including elastic modulus E, coefficient of linear expansion θ, and tensile strength. Compressive strength wait.
[0034] Steps 1-2: Design calibration parts for substrate weld overlay. Design 10 sets of calibration parts with different wear-resistant block thicknesses H1(i) (i=1~10), with no less than 5 samples in each set. Measure the size of the heat-affected zone of the wear-resistant block through metallographic analysis. Figure 2 (H2), obtain the relationship between the heat-affected zone (H2 is the average value of each group of samples) and the thickness of the wear-resistant block: (1) Where k is the welding impact coefficient.
[0035] Step 1-3: Obtain the material properties of the heat-affected zone. Based on the weld overlay material properties obtained in Step 1-1 and Step 1-2 and the relationship between the heat-affected zone and the wear-resistant block thickness, i.e., Formula (1), the material properties of the heat-affected zone are obtained.
[0036] Elastic modulus of the heat-affected zone at a certain temperature: (2) Where: E3 is the elastic modulus of the matrix at this temperature; E1 is the elastic modulus of the weld overlay material at this temperature.
[0037] The coefficient of linear expansion of the heat-affected zone at a certain temperature: (3) Where: θ3 is the linear expansion coefficient of the substrate at this temperature; θ1 is the linear expansion coefficient of the weld overlay material at this temperature.
[0038] Tensile strength of the heat-affected zone at a certain temperature: (4) in: The tensile strength of the matrix at this temperature; ρ represents the tensile strength of the weld overlay material at this temperature; x represents the vertical distance from the heat-affected zone to the substrate boundary, in mm, see [reference needed]. Figure 2 .
[0039] Compressive strength of the heat-affected zone at a certain temperature: (5) in: The compressive strength of the matrix at this temperature; The compressive strength of the weld overlay material at this temperature.
[0040] Steps 1-4: Blade Crown Stress Analysis. A blade crown model with wear-resistant blocks is established. The wear-resistant blocks are modeled in sections, and different material properties are assigned to the matrix, heat-affected zone, and wear-resistant blocks respectively. The blade crown stress distribution is obtained through finite element analysis.
[0041] Step 2: Failure Prediction in Different Regions of the Leaf Canopy Step 2-1: Matrix Failure Prediction. Starting from the maximum first principal stress point and the maximum third principal stress point of the matrix, obtain the critical section of the matrix along the stress gradient direction (the section extends to the rounded transition between the blade crown and the blade body). Figure 3 At point M (with a cross-sectional width of H3), the average first principal stress of the critical section is obtained. With the average third principal stress ,when or At that time, the leaf crown matrix prediction failed.
[0042] Step 2-2: Failure Prediction in the Heat-Affected Zone. Starting from the point of maximum first principal stress and maximum third principal stress in the heat-affected zone, obtain the critical section of the blade crown (section depth H2) perpendicular to the wear-resistant block. See... Figure 4 In the critical section of the heat-affected zone, when x = x1, Pick and The average value along the path (i.e., the average value along the path from the top to the bottom of the dangerous section of the leaf crown). This process is repeated to obtain... and Curves, such as Figure 5 , Figure 6 .
[0043] when and When any position on the curve is above the x-tensile / compressive strength curve, the heat-affected zone is considered to have failed.
[0044] Steps 2-3: Wear-resistant block failure prediction. Obtain the maximum first principal stress of the wear-resistant block. With the maximum third principal stress ,when or At that time, the wear-resistant block of the leaf crown is predicted to fail.
[0045] Step 3: Analysis of the compressive strength of the contact surface between the leaf crowns Step 3-1: Through the design of the blade crown damping scheme, obtain the upper limit value of the normal pressure on the contact surface of the wear-resistant block that satisfies the vibration reduction effect of the blade crown damping. and lower limit value Combined with the nominal contact area A 名义 The upper and lower limits of the contact surface compressive strength that satisfy the crown damping and vibration reduction effect are obtained: (6) Step 3-2: Based on finite element analysis, obtain the stress distribution on the contact surface of the blade crown wear-resistant block, such as... Figure 7 Simultaneously extract the total normal force of the contact surface. When the mesh element compressive stress When this occurs, the contact state is considered invalid. For valid contact units ( Figure 7Summing the areas of the Central African (×) units: (7) Average compressive stress on the contact surface of the wear-resistant block: (8) when At that time, the compressive strength of the contact surface of the wear-resistant block of the blade crown met the requirements.
[0046] Step 4: Leaf crown damage tolerance analysis Step 4-1: Based on the upper limit value of the normal pressure on the blade crown contact surface obtained in Step 3-1 and lower limit value When the positive pressure is at [ , Within the specified range, the maximum first principal stress of the leaf crown was obtained through finite element analysis. The relationship curve between the normal force F and the normal force F is shown in the figure. Figure 8 .
[0047] Step 4-2: Through crown damping vibration reduction design and testing, when the normal pressure is [ , Within the range, the leaf crown vibration is obtained. The stress versus normal force F curve is shown in the figure. Figure 8 .
[0048] Step 4-3: Assume that an initial crack a0 appears in the weld seam of the wear-resistant block of the blade crown, and at the maximum first principal stress... Superimposed vibration stress Stress intensity factor amplitude under action : (8) (9) (10) Where λ is the shape factor, see Figure 9 .
[0049] When the stress intensity factor amplitude Crack propagation threshold ,Right now At this time, the initial crack in the leaf crown will rapidly expand and fail.
[0050] This application presents a method for predicting the failure of blade crowns with wear-resistant blocks. It considers the influence of the wear-resistant blocks and the heat-affected zone (HAZ) on crown failure, and performs failure predictions separately for the substrate, HAZ, and wear-resistant layer, thus improving the accuracy of failure prediction for blade crowns with wear-resistant blocks. Simultaneously, it analyzes the compressive stress at the wear-resistant block contact surface and the crown damage tolerance to determine whether the normal pressure at the wear-resistant block contact surface during operation meets the requirements for crown damping, compressive strength, and damage tolerance. This method improves the accuracy of predicting the failure of blade crowns with wear-resistant blocks.
[0051] The above description is merely a preferred embodiment of this application and is not intended to limit this application. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of this application should be included within the protection scope of this application.
Claims
1. A method for predicting blade crown failure with wear-resistant blocks, characterized in that, The method for predicting blade crown failure with wear-resistant blocks includes: S1: Acquisition of leaf crown material properties and stress analysis; S2: Conduct failure analysis of different regions of the leaf crown, and predict leaf crown failure when the tensile and / or compressive strength requirements are not met; S3: Conduct compressive strength analysis of the contact surface between the blades and the crown, and predict the failure of the blades and the crown when the compressive strength requirement of the contact surface is not met; S4: Conduct blade crown damage tolerance analysis to predict blade crown failure when the crack propagation threshold value is not met.
2. The method for predicting blade crown failure with wear-resistant blocks as described in claim 1, characterized in that, Step S1 includes: S11: Obtain the material properties of the leaf crown matrix and the weld overlay material at different temperatures; S12: Obtain the dimensions of the heat-affected zone and the relationship between the heat-affected zone and the thickness of the wear-resistant block; S13: Based on the properties of the weld overlay material and the relationship between the heat-affected zone and the thickness of the wear-resistant block obtained in S11 and S12, obtain the material properties of the heat-affected zone; S14: Establish a blade crown model with wear-resistant blocks, perform partitioned modeling of the wear-resistant blocks, and assign different material properties to the matrix, heat-affected zone and wear-resistant blocks respectively. Obtain the blade crown stress distribution through finite element analysis.
3. The method for predicting blade crown failure with wear-resistant blocks as described in claim 2, characterized in that, The material properties obtained in step S11 include elastic modulus E, coefficient of linear expansion θ, and tensile strength. Compressive strength ; Step S12 includes: designing several sets of calibration parts with different wear-resistant block thicknesses, with no less than 5 samples in each set; measuring the size of the heat-affected zone of the wear-resistant block through metallographic analysis; and obtaining the relationship between the heat-affected zone H2 and the thickness of the wear-resistant block. Where: H2 is the thickness of the heat-affected zone, H1 is the thickness of the wear-resistant block, and k is the welding influence coefficient.
4. The method for predicting blade crown failure with wear-resistant blocks as described in claim 3, characterized in that, Step S13 specifically includes: Elastic modulus E2 of the heat-affected zone at a certain temperature: Wherein, E3 is the elastic modulus of the matrix at this temperature, and E1 is the elastic modulus of the weld overlay material at this temperature; The coefficient of linear expansion of the heat-affected zone at a certain temperature: Where: θ3 is the linear expansion coefficient of the substrate at this temperature, and θ1 is the linear expansion coefficient of the weld overlay material at this temperature; Tensile strength of the heat-affected zone at a certain temperature: in, The tensile strength of the matrix at this temperature. denoted as the tensile strength of the weld overlay material at this temperature, and x as the vertical distance from the heat-affected zone to the substrate boundary. Compressive strength of the heat-affected zone at a certain temperature: in, The compressive strength of the matrix at this temperature. The compressive strength of the weld overlay material at this temperature.
5. The method for predicting blade crown failure with wear-resistant blocks as described in claim 4, characterized in that, Step S2 includes: S21: Matrix failure prediction, including: starting from the maximum first principal stress point and the maximum third principal stress point of the matrix, obtaining the critical section of the matrix along the stress gradient direction, and obtaining the average first principal stress of the critical section. With the average third principal stress ,when or At that time, the leaf canopy matrix was predicted to fail; S22: Failure prediction in the heat-affected zone, including: taking the maximum first principal stress point and the maximum third principal stress point in the heat-affected zone as starting points, obtaining the critical section of the blade crown perpendicular to the wear-resistant block, with a section thickness of H2. In the critical section of the heat-affected zone, when x=x1... Take the average value from the top to the bottom of the dangerous section of the leaf crown, until the result is obtained. and curve, The first principal stress in the heat-affected zone, This is the third principal stress in the heat-affected zone; when and When any position on the curve is above the x-tensile / compressive strength curve, the heat-affected zone is considered to have failed. S23: Failure prediction of wear-resistant block, obtaining the maximum first principal stress of the wear-resistant block. With the maximum third principal stress ,when or At that time, the wear-resistant block of the leaf crown is predicted to fail.
6. The method for predicting blade crown failure with wear-resistant blocks as described in claim 4, characterized in that, Step S3 includes: S31: Through the design of the blade crown damping, the upper limit of the normal pressure on the contact surface of the wear-resistant block that satisfies the vibration reduction effect of the blade crown damping is obtained. and lower limit value Combined with the nominal contact area A 名义 The upper and lower limits of the contact surface compressive strength that satisfy the crown damping and vibration reduction effect are obtained: S32: Based on finite element analysis, obtain the stress distribution on the contact surface of the blade crown wear-resistant block, and extract the total normal force on the contact surface. When the mesh element compressive stress When the contact state is considered invalid, the areas of the effective contact elements are summed: Average compressive stress on the contact surface of the wear-resistant block: when At that time, the compressive strength of the contact surface of the wear-resistant block of the blade crown met the requirements.
7. The method for predicting blade crown failure with wear-resistant blocks as described in claim 6, characterized in that, Step S4 includes: S41: Upper limit of normal pressure at the blade crown contact surface obtained from S31 and lower limit value When the positive pressure is at [ , Within the specified range, the maximum first principal stress of the leaf crown was obtained through finite element analysis. The relationship curve between the normal force F and the normal force F; S42: Through crown damping vibration reduction design and testing, when the normal pressure is [ , Within the range, the leaf crown vibration is obtained. The relationship curve between stress and normal force F; S43: Assume that an initial crack a0 appears in the weld seam of the wear-resistant block of the blade crown, and at the maximum first principal stress... Superimposed vibration stress Stress intensity factor amplitude under action : When the stress intensity factor amplitude Crack propagation threshold ,Right now At that time, the initial crack in the leaf crown will expand and fail.
8. The method for predicting blade crown failure with wear-resistant blocks as described in claim 7, characterized in that, Stress intensity factor amplitude in step S43 Obtained through the following formula: Among them, K max K represents the maximum value of the stress intensity factor. min λ is the minimum stress intensity factor, and λ is the shape factor.