A stress-life model considering the influence of stress gradient and micro-slip at the edge of contact area under plane contact state

Abstract

The application discloses a stress-life model considering the influence of stress gradient and micro-sliding amount of the edge of a contact area in a plane contact state, designs a mathematical model for calculating the fatigue life of a component by using stress in the plane contact state considering the plane stress gradient and the influence of the micro-sliding of the contact area, and introduces the stress gradient of the edge of the contact area and the sliding displacement amount of the edge of the contact area for the plane contact problem on the basis of the most basic stress-life equation, and corrects the stress term on the left end of the equation, so that the stress-life model has good fitting effects on high-cycle fatigue and low-cycle fatigue and has good physical significance. When the stress-life model is applied, only the data of the stress change and the relative sliding amount of the structure are needed, and then the life prediction calculation can be performed, so that the process of the fatigue life prediction is simplified.

Description

Technical Field

[0001] This invention relates to a method for determining the fatigue life of a stress-life model that considers stress gradient correction and micro-slippage at the edge of the contact area under planar contact conditions. With this stress-life model, the fatigue life of a component can be determined by the component material parameters, the stress values ​​of the contact edge area, and the relative slippage of the micro-motion. Background Technology

[0002] The fatigue life of materials has always been a key topic of concern in engineering. Since the 19th century, researchers have proposed several mathematical models for predicting the fatigue life of materials. According to the type of independent variable, these models can be divided into two categories: strain life models and stress life models.

[0003] Fretting refers to a small-amplitude relative motion occurring between the surfaces of two approximately tightly fitted contacting objects. The presence of fretting results in a large stress gradient and stress concentration at the edge of the contact area between the two components. At low contact stresses, the wear caused by fretting has a significant impact on the fatigue life of the components. Most stress-life models only consider the effect of stress on life, and in the low-load, high-cyclic fatigue section (>10... 4 The fitting results (in cycles) were poor. As scientific research progresses, researchers need to explore more factors affecting fatigue life and obtain more accurate stress life prediction models. Summary of the Invention

[0004] To address the aforementioned issues, this invention proposes a fatigue life determination method based on a stress-life model that considers fretting wear under planar contact conditions. This method employs stress gradient correction, making it suitable for predicting the fatigue life of contact components. Furthermore, the model only requires data on stress changes and relative slippage of the structure, thus simplifying the fatigue life prediction process.

[0005] This invention provides a stress fatigue life prediction model that considers the plane stress gradient and the influence of fretting in the contact area under planar contact conditions. It includes a new stress-life model establishment part and a fatigue life determination part.

[0006] The new stress-life model establishment section specifically includes:

[0007] Step 1: Establish the stress-life prediction equation without considering stress gradient correction and fretting effects as follows:

[0008] Using the Busqin formula as the basic model, we obtain:

[0009] σ a =σ′ f (2N f ) b

[0010] In the formula, σ a Let σ′ be the stress amplitude. f N is the fatigue strength coefficient, b is the fatigue strength exponent, and N is the fatigue strength coefficient. f For fatigue life, where σ′ f and b are obtained by fitting the results of fatigue tests on smooth specimens (R = -1), where R is the stress ratio.

[0011] Step 2: Considering the impact of fretting on fatigue life, the stress-life prediction equation obtained in Step 1 is modified.

[0012] Introducing a characteristic length L and a small relative slip d, along with parameters σ0 and σ max After correcting the stress amplitude, the stress-life model considering the effects of fretting is obtained as follows:

[0013]

[0014] In the formula, L is the selected characteristic length of the contact area, σ0 is the minimum tangential normal stress within the characteristic length of the contact area, and σ max d represents the maximum tangential normal stress within the characteristic length of the contact area, and d represents the relative slip.

[0015] Step 3: Considering the influence of stress gradient on fatigue life, modify the stress-life prediction equation obtained in Step 2.

[0016] Introducing the stress gradient influence factor Y eq Further modifying the stress term on the left-hand side of the equation, we obtain the stress-life model that considers the stress gradient and fretting effects:

[0017]

[0018] Among them, Y eq This is the stress gradient factor.

[0019] Based on the newly established stress-life model, the fatigue life determination method is as follows:

[0020] Step A: Based on the fatigue test results of smooth specimens, the parameter σ′ in the stress-life model is calculated using fitting. f and b.

[0021] Step B: Select an appropriate characteristic length L, and calculate the relative slip d, tangential normal stress σ0, and σ in the contact area. max .

[0022] Step C: Calculate the stress gradient factor Y eq .

[0023] Step D: Set parameters L, σ0, σ max ,d,Yeq , σ′ f Substituting b into the stress-life model that considers stress gradient and fretting effects, the fatigue life of the fatigue test component is obtained.

[0024] The advantages of this invention are:

[0025] 1. This invention proposes a stress fatigue life prediction model that considers the plane stress gradient and the influence of fretting in the contact area under planar contact conditions. It uses only stress to calculate fatigue life and does not require strain.

[0026] 2. This invention proposes a stress fatigue life prediction model that considers the plane stress gradient and the influence of fretting in the contact area under planar contact conditions, which has good effect on fatigue life prediction under both high and low loads.

[0027] 3. This invention proposes a stress fatigue life prediction model that considers the plane stress gradient and the influence of fretting in the contact area under planar contact conditions. It is applicable to complex stress conditions, especially for fatigue life calculation of the highly stress-concentrated area at the contact edge of two components. Attached Figure Description

[0028] Figure 1 A fitting diagram of fatigue life parameters for high-quality TC4 alloy forgings.

[0029] Figure 2 This is a diagram showing the tangential normal stress distribution on the contact surface of a fatigued component.

[0030] Figure 3 This diagram shows the variation of tangential normal stress at the crack initiation location of a fatigued component.

[0031] Figure 4 Figure a shows the contact state of the component's contact area edge when no external load is applied.

[0032] Figure 4 b is a diagram showing the contact state of the component's contact area edge after applying a normal load.

[0033] Figure 4 c is a diagram showing the contact state of the component's contact area edge after applying both normal and tensile loads simultaneously.

[0034] Figure 5 This is a diagram showing the calculation path for the stress gradient factor.

[0035] Figure 6 a is the normalized curve of the tangential normal stress corresponding to path 1.

[0036] Figure 6 b is the normalized curve of the tangential normal stress corresponding to path 2.

[0037] Figure 6c is the normalized curve of the tangential normal stress corresponding to path 3.

[0038] Figure 7 a is a front view of the indenter component used in the fretting fatigue test.

[0039] Figure 7 b is a top view of the pressure head component used in the fretting fatigue test.

[0040] Figure 8 a is a top view of the plate component used in the fretting fatigue test.

[0041] Figure 8 b is a side view of the plate component used in the fretting fatigue test.

[0042] Figure 9 The loads and boundary conditions are defined for the finite element model.

[0043] Figure 10 This is a contour map of the tangential normal stress distribution (650MPa-40% test group).

[0044] Figure 11 The results of the stress life model prediction considering stress gradient and fretting effects are presented. Detailed Implementation

[0045] The present invention will now be described in further detail with reference to the accompanying drawings.

[0046] The stress-life model of this invention, which considers the influence of stress gradient and micro-slippage at the edge of the contact area under planar contact conditions, is designed as follows:

[0047] Step 1: Establish the stress-life prediction equation without considering stress gradient correction and fretting effects;

[0048] 101. Based on the Busqin formula, establish a basic stress-life equation.

[0049] The prototype of the Busqin formula is as follows:

[0050] σ a =σ′ f (2N f ) b (1)

[0051] In Equation 1, σ a Let σ′ be the stress amplitude. f N is the fatigue strength coefficient, b is the fatigue strength exponent, and N is the fatigue strength coefficient. f Let σ′ be the fatigue life, where σ′ is the fatigue life. f b is obtained by fitting the results of fatigue tests on smooth specimens (R = -1), where R is the stress ratio.

[0052] Based on the fatigue data of stress and life of high-quality TC4 alloy forgings in the Material Data Handbook for Aircraft Engine Design (Volume 3), in order to obtain more accurate results, the logarithm of the stress and life fatigue data was taken and then linearly fitted. The fitting equation is as follows:

[0053] lg(σ a )=lg(σ′ f )+b·lg(2N f (2)

[0054] The stress-life fitting curve of the fatigue test of the smooth specimen is obtained, as follows: Figure 1 As shown, the equation parameter σ′ is further obtained based on the curve fitting results. f and b.

[0055] Step 2: Considering the impact of fretting on fatigue life, the stress-life prediction equation obtained in Step 1 is modified.

[0056] The influence of fretting on fatigue life is considered. The effect of the relative slippage generated at the contact edge region of the two components after applying tensile and compressive loads on fatigue life is introduced into the stress-life equation. All introduced parameters can be obtained by finite element numerical simulation, as follows:

[0057] 201. Introduce the characteristic length L of the contact area.

[0058] like Figure 2 As shown, the variation of tangential normal stress on the surface of a fatigued component is given. It can be seen that there is a high tangential normal stress in the contact edge region between the two components. This location is also the location where cracks initiate. The characteristic length L is defined as twice the distance between the maximum stress point and the minimum stress point in the stress concentration region.

[0059] 202. Give the variation of tangential normal stress at the crack initiation location, such as... Figure 3 As shown, the magnitude of the tangential normal stress corresponding to the point of maximum stress is defined as σ. max The magnitude of the tangential normal stress corresponding to a point at a distance L from the point of maximum stress during the stress decrease process is defined as σ0.

[0060] 202. Calculate the relative slip between the two contacting components after applying tensile and compressive loads, denoted as d.

[0061] like Figure 4 Figure a shows the positional state of the edges of the contact area between the two components when no external load is applied. Node 19060 on the indenter component and node 3487 on the plate component are perfectly aligned, with a relative distance of 0 in the horizontal direction. Then, a normal load perpendicular to the contact surface is applied to the indenter, causing the indenter to contact the plate. Figure 4As shown in Figure b, the relative horizontal distance between node 19060 on the indenter component and node 3487 on the plate component is almost zero. Then, one end of the plate is fixed, and a tensile load is applied to the other end, causing relative slippage between the indenter and the plate. Figure 4 As shown in c, the relative distance in the horizontal direction between node 19060 on the pressure head component and node 3487 on the plate component is defined as the relative slip d.

[0062] Thus, the equation correction parameters considering the effect of fretting on fatigue were obtained through numerical simulation, and equation (1) was rewritten as follows:

[0063]

[0064] Equation (3) is the modified stress-life model proposed in this invention that takes into account the effects of fretting. If the effects of fretting are not considered, that is, d=0 is substituted into the equation, equation (3) can be degenerated into equation (1).

[0065] Step 3: Considering the influence of stress gradient on fatigue life, modify the stress-life prediction equation obtained in Step 2.

[0066] This invention is based on the stress gradient influence factor calculation method established in "Wang Yanrong, Li Hongxin, Yuan Shanhu, et al. A method for predicting fatigue life of notched surfaces considering stress gradient [J]. Journal of Aerospace Power, 2013, 28(6): 1208-1214". It presents a new method for calculating the stress gradient influence factor in the stress-life equation, applicable to stress states caused by unnotched planar contact. This invention introduces the stress gradient influence factor into unnotched planar components for the first time, and, combined with the characteristics of edge stress distribution in the planar contact area, provides a new method for calculating the stress gradient influence factor, as detailed below:

[0067] like Figure 5 As shown, three paths are selected for the calculation of stress gradient factors. Path 1 starts at σ. max The corresponding point, with the endpoint at the point corresponding to σ0, is parallel to the contact surface and has a length of L. Path 2 starts at σ. max The corresponding point is perpendicular to the contact surface and extends into the component body, with a length of L. The starting point of path 3 is the point corresponding to σ0, with a direction perpendicular to the contact surface and extending into the component body, and a length of L.

[0068] Figure 6 a gives the normalized curve of the tangential normal stress corresponding to path 1. Y1 is defined as the tangential stress gradient factor, and its calculation method is as follows:

[0069] Y1=S1 (4)

[0070] Where S1 is the area of ​​the normalized stress on path 1 within the normalized distance range of 0 to 1.

[0071] Figure 6 b gives the normalized tangential normal stress curve corresponding to path 2. Y2 is defined as the normal stress gradient factor at the point of maximum stress, and its calculation method is as follows:

[0072] Y2=S2 (5)

[0073] Where S2 is the area of ​​the normalized stress on path 2 within the normalized distance range of 0 to 1.

[0074] Figure 6 c provides the normalized tangential normal stress curve corresponding to path 3. Y2′ is defined as the normal stress gradient factor at the end of the characteristic length, and its calculation method is as follows:

[0075] Y2′=S3 (6)

[0076] Where S3 is the area of ​​the normalized stress on path 3 within the normalized distance range of 0 to 1.

[0077] Define the comprehensive stress gradient factor Y eq :

[0078]

[0079] Thus, the comprehensive stress gradient factor is obtained, and equation (3) is further modified and rewritten as follows:

[0080]

[0081] The stress fatigue life prediction model established above, which considers the plane stress gradient and the influence of fretting in the contact area under planar contact conditions, can be used to predict the fatigue life of components using existing material data and finite element numerical simulation results. The specific method is as follows:

[0082] Step A: Based on the fatigue test results of smooth specimens, the parameter σ′ in the stress-life model is calculated using fitting. f and b.

[0083] (1) Select fatigue life data.

[0084] Obtain fatigue data for a specific material from materials handbooks or other literature, selecting the following data:

[0085] ①Lifetime reverse number 2N f ;

[0086] ② Stress amplitude σ corresponding to the lifetime reverse number a (The minimum number of data pairs is 5).

[0087] (2) Substitute the data from ① and ② into equation (1) to perform linear fitting and obtain the parameter σ′. f and b.

[0088] Step B: Select an appropriate characteristic length L, and calculate the relative slip d, tangential normal stress σ0, and σ in the contact area. max .

[0089] (1) The stress state of the region to be checked under actual load was simulated using the finite element method to ensure that no plastic deformation would occur in the region to be checked, and the maximum tangential normal stress σ in the contact edge region was calculated. max The characteristic length L is selected as twice the distance between the maximum stress point and the minimum stress point in the contact area.

[0090] (2) Starting from the point of maximum tangential normal stress, select a path parallel to the direction of stress decrease on the contact surface, and take the point at a distance L from the point of maximum tangential normal stress along the path as the end point of the path, and denote the tangential normal stress at that point as σ0.

[0091] (3) Use the finite element method to calculate the displacement state of the two components under actual load.

[0092] When no load is applied, select two points at the same position on the two components at the edge of the contact area. After the load is applied, record the relative displacement between the two points as d.

[0093] Step C: Calculate the stress gradient factor Y eq .

[0094] (1) Select the stress on the contact surface of the fatigue component as σ max The point with stress σ0 is taken as the starting point, and the point with stress σ0 is taken as the ending point. The line connecting the two points is denoted as path 1. The stress on the contact surface of the fatigue component is selected as σ. max The point is taken as the starting point, and the point perpendicular to the contact surface into the component body at a distance L from the starting point is taken as the ending point. The line connecting the points is denoted as path 2. The point with stress σ0 on the contact surface of the fatigue component is selected as the starting point, and the point perpendicular to the contact surface into the component body at a distance L from the starting point is taken as the ending point. The line connecting the points is denoted as path 3.

[0095] (2) Draw the normalized curves of tangential normal stress-distance under the three paths and calculate the integral area of ​​the curves, denoted as Y1, Y2 and Y2′ respectively.

[0096] (3) Substitute Y1, Y2, and Y2′ into equation (7) to calculate the stress gradient factor Y. eq .

[0097] Step D: Set parameters L, σ0, σ max ,d,Y eq , σ′ fSubstituting b into the stress-life model that considers stress gradient and fretting effects, the fatigue life of the fatigue test component is obtained.

[0098] In the equation, the parameter σ′ f b is determined by step A, with parameters L, σ0, and σ max d is determined by step B, and parameter Y eq As determined in step C, each parameter is substituted into equation (8) to calculate the predicted life of the fatigue component.

[0099] Example

[0100] Existing fretting fatigue test indenter components ( Figure 7 a, Figure 7 b) and flat plate components ( Figure 8 (a) and (b) the model dimensions and test plan have been determined, and the model material is TC4. The indenter and the plate come into contact under load, and fretting wear occurs at the contact edge.

[0101] According to the test plan, multiple sets of tests were conducted on the two components under different tensile and compressive loads, and the fracture fatigue life of the plate component was recorded. Simultaneously, the fracture fatigue life of the plate component was calculated using the finite element method proposed in this invention, and compared with the experimental values.

[0102] (1) Fatigue parameter fitting. First, conventional fatigue tests were carried out on a single component to obtain fatigue performance data of the TC4 plate component under room temperature environment. The test results are shown in Table 1.

[0103] Table 1. Conventional fatigue test data for TC4 plate components

[0104]

[0105] Based on the above experimental results, fatigue parameters were fitted, and the fitting results are shown in Table 2.

[0106] Table 2. Fatigue parameter fitting results

[0107] Material Temperature / °C <![CDATA[σ′ f ]]> b TC4 20 24380.52163 -0.36454

[0108] (2) Stress and micromomentum calculation. Using a general finite element method, loads and boundary conditions are applied to the model, such as... Figure 9 As shown. The stress distribution of the experimental model was calculated. Figure 10 The figure shows the tangential normal stress distribution contour map when a tensile load of 650 MPa is applied and the stress on the contact surface of the indenter plate is 40% of the tensile load. Based on the stress calculation results, the characteristic length L = 50 μm is extracted, and σ0 and σ are further obtained. maxBased on the finite element analysis results, the relative slip d at the edge of the contact area is obtained. The test conditions for each group and the corresponding σ0 and σ... max d is shown in Table 3.

[0109] Table 3 Calculation results of the finite element model

[0110]

[0111] (3) Calculation of stress gradient factors. Based on the finite element results, the stress gradient distribution in the contact edge region is studied. Three paths of length L are selected, and Y1, Y2, Y2′ and Y are calculated. eq The results are shown in the table.

[0112] Table 4 Stress gradient factors

[0113]

[0114]

[0115] (4) Calculate the fatigue life. According to the stress life equation proposed in this invention, the stress gradient influence factor calculated according to (3), and the tangential normal stress and relative slip calculated according to (2), the fatigue life is calculated. The calculation results are shown in the table.

[0116] Table 5. Calculation results of fatigue life of plate indenter test specimens.

[0117]

[0118] (5) Analysis of calculation results, such as Figure 11 As shown, the prediction results of the stress-life model considering the effects of stress gradient and fretting are presented. The results show that the vast majority of lifetime points fall within the two-fold error band.

[0119] In summary, this invention presents a mathematical model for calculating the fatigue life of components under planar contact conditions, considering stress gradients and fretting effects. Based on the fundamental stress-life equation, this model introduces the stress gradient and sliding displacement at the contact edge for planar contact problems, correcting the stress term on the left-hand side of the equation. It exhibits good fitting results for both high-cyclic and low-cyclic fatigue, demonstrating significant physical meaning. In an application example, this invention provides a demonstration case using a head-plate model test. The life prediction results were calculated based on the stress-life equation presented in this invention, verifying the effectiveness of the prediction method.

Claims

1. A stress-life model considering the influence of stress gradient and edge micro-slip in the contact area under the plane contact condition, characterized in that: The creation method is as follows: Step 1: Establish the stress-life prediction equation without considering stress gradient correction and fretting effects as follows: s a =s f ′ (2N f ) b where σ a is the stress amplitude, σ f ′ is the fatigue strength coefficient, b is the fatigue strength exponent, N f is the fatigue life; Step 2: Considering the effect of fretting on fatigue life, the characteristic length L and the fretting relative slip d in the selected contact area are introduced, and the minimum tangential normal stress σ0 in the contact area characteristic length and the maximum tangential normal stress σ max The stress-life prediction equation obtained in Step 1 is corrected as follows: Step 3: Considering the influence of stress gradient on fatigue life, a stress gradient influence factor Y is introduced. eq The stress-life prediction equation obtained in step 2 is modified to obtain the stress-life model that considers the stress gradient and fretting effects: where Y eq is a stress gradient factor.

2. The stress-life model considering the effect of stress gradient and edge micro-slip in the contact area under the plane contact state according to claim 1, wherein: The method for determining fatigue life is as follows: Step A: Parameters σ and b in the stress-life model were fitted from the smooth specimen fatigue test results. f ′ and b; Step B: Choose a characteristic length L, calculate the relative slip d, the tangential normal stress σ0and σ max ; Step C: Calculate the stress gradient factor Y eq ; Step D: Set parameters L, σ0, σ max ,d,Y eq , σ f ′ Substituting b into the stress-life model that considers stress gradient and fretting effects, the fatigue life of the fatigue test component is obtained.

3. The stress-life model considering the influence of stress gradient and micro-slippage at the edge of the contact area under planar contact conditions as described in claims 1 and 2, characterized in that... The method for determining the relative slip d of the micro-motion is as follows: First, locate two points corresponding to the positions on the edge of the contact area between the pressure head component and the plate component. Then, apply a normal load perpendicular to the contact surface to the pressure head component, causing the pressure head component and the plate component to make contact and ensuring that the two points are aligned. At this time, the relative distance in the horizontal direction between the points on the pressure head component and the points on the plate component is 0. Finally, fix one end of the plate and apply a tensile load to the other end, causing relative slippage between the pressure head component and the plate component. At this time, the relative distance in the horizontal direction between the points on the pressure head component and the points on the plate component is the relative slippage amount d.

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