A method for determining high stress volume under notch-defect interaction

Abstract

The present invention discloses a method for determining high stress volume under notch-defect interaction, which belongs to the technical field of damage tolerance assessment and fatigue strength prediction, comprising: calculating stress distribution data of the notch root in a component structure containing a defect notch by finite element analysis, and outputting the ratio of axial stress to nominal stress; calculating the virtual defect size of the notch component structure; using the critical distance method, combined with the ratio, calculating the stress concentration parameter of the notch root in the component structure containing the defect notch; and calculating the high stress volume area by analyzing the competitive effect of the notch and the defect, combined with the virtual defect size and stress concentration parameter. The present invention comprehensively considers the interaction between the notch and the defect, accurately calculates the high stress volume of the structure, helps to predict the fatigue failure site, and thus improves the accuracy of fatigue assessment. It is universal for structural parts with notches of any size and shape, is easy to operate, and has a wide range of applications.

Description

Technical Field

[0001] The present invention relates to the technical field of damage tolerance assessment and fatigue strength prediction, and more particularly to a method for determining high stress volume under notch-defect interaction. Background Art

[0002] In mechanical structure design, strength verification is often the last hurdle before it is put into actual production and application. In the early days, structural strength design was mainly based on static strength design, and the entire set of methods for structural strength analysis, design and testing has matured. Since the end of the 20th century, with the application and promotion of computer-aided design technology, in-depth research on structural optimization algorithms, iterative upgrades of material manufacturing processes, and continuous improvement of basic testing levels, the basic design capabilities of the mechanical industry have been significantly improved. At this stage, structural failures due to insufficient static strength can basically be avoided. As the service environment of mechanical structures becomes increasingly harsh and complex, fatigue caused by alternating stress has become one of the most common failure modes of engineering structures.

[0003] Fatigue failure often occurs at geometric discontinuities (such as machined holes and notches) or defects. The actual failure mechanism can be driven by a combination of both defect (local stress concentration) and notch (global stress concentration) failure modes. Global geometric discontinuities and defects both negatively impact the fatigue performance of materials, and these effects can act synergistically. The coupled effect of the two is more pronounced than either effect alone. Previous studies have investigated fatigue assessment of global geometric discontinuities (notches) and local (defect) stress concentrations using stress concentration factors and stress intensity factors, respectively. However, the mechanisms underlying these coupled effects remain under investigation. Fatigue assessment of real structures first requires identifying the structural weak points, i.e., areas prone to fatigue failure. These areas are typically characterized by high stress values. Through the continuous efforts of researchers, the high-stress volume method (also known as the control volume or risk volume) has been continuously refined and developed. Simply using 80-90% of the high-stress area for failure analysis is not realistic, and the same high-stress volume value for different structures is unreliable. The selection of the high-stress volume should be individualized for each structure, rather than a single, general percentage.

[0004] Therefore, the existing fatigue assessment methods have certain limitations, which are mainly manifested in the lack of comprehensive and personalized analysis of the structure, especially the lack of in-depth research on geometric discontinuities and defect coupling effects, which may lead to inaccurate and unreliable fatigue failure predictions.

[0005] Based on the critical distance method and fracture mechanics, this paper conducts notch-defect competition analysis, comprehensively considers factors such as geometric structure, material properties and defect distribution to determine the high stress volume stress threshold of complex structures, proposes a method for determining the high stress volume of structural parts with notches of any size, and clarifies the key areas for complex structures to be applied in life assessment and reliability analysis. Summary of the Invention

[0006] In light of this, and building on the advantages of the critical distance method and fracture mechanics in addressing notch and defect issues, this paper provides a method for determining the high-stress volume under notch-defect interaction. This method addresses the problem that traditional fatigue assessment methods often consider the effects of notches and defects separately, resulting in inaccurate assessments. By comprehensively considering the interaction of notches and defects, this paper accurately calculates the high-stress volume of a structure, helping to predict fatigue failure locations and thus improving the accuracy of fatigue assessments.

[0007] In order to achieve the above object, the present invention adopts the following technical solutions:

[0008] A method for determining a high stress volume under notch-defect interaction comprises the following steps:

[0009] S1. Calculate the stress distribution data of the notch root in the defective notch component structure through finite element analysis, and output the ratio of axial stress to nominal stress K t,S ;

[0010] S2. Calculate the virtual defect size of the notched component structure

[0011] S3, using the critical distance method, combined with the ratio K t,S , calculate the stress concentration parameter K at the root of the notch in the structure containing the defect notch t,0.5L ;

[0012] S4. By analyzing the competitive effect of gaps and defects, combined with the virtual defect size and stress concentration parameter K t,0.5L , calculate the high stress volume area.

[0013] It can be seen from the above technical solutions that compared with the prior art, the present invention has the following technical advantages:

[0014] (1) The present invention compares the degree of weakening of structural fatigue strength by notches and defects and conducts competitive failure analysis, comprehensively considers factors such as geometric structure, material properties and defect distribution to determine the high stress volume of complex structures, establishes a high stress volume calculation process based on notch-defect interaction, clarifies the key areas for complex structures to be applied in life assessment and reliability analysis, and has reference significance for the control volume used for size effect extrapolation and the judgment of failure locations of actual engineering structures. It has a wide range of applications, ranging from traditional casting and forging (a small number of processing defects or service defects) to emerging additive manufacturing technology (a large number of processing defects).

[0015] (2) The notch-defect competition model proposed in the present invention has a relatively simple calculation process; the required parameters can be directly determined by finite element analysis or directly obtained through a small number of experiments. It is universal for structural parts with notches of any geometric shape, easy to operate, and has a wide range of applicability;

[0016] (3) In the present invention, the high stress volume threshold stress varies with the defect and notch geometry, compared with the general use of 80% or 90% high stress volume concept (V 80％ or V 90％ , that is, the volume of the material where the stress exceeds 80% or 90% of the maximum stress), comprehensively considering the actual geometry of the structure, stress and defect distribution, and providing a practical method for calculating high-stress volume;

[0017] (4) The application of the proposed notch-defect competition model is not limited to the materials used in the present invention. The high stress volume of the notch structure is calculated through failure competition analysis and probabilistic methods. It is suitable for evaluating the failure site of the notch structure under random defect distribution or a small number of processing / service defects, and the prediction results are highly accurate. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are merely embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on the provided drawings without paying any creative work.

[0019] Figure 1 A flow chart of a method for determining high stress volume under notch-defect interaction provided by an embodiment of the present invention;

[0020] Figure 2 A schematic diagram of the dimensions of a notched specimen for a GH4169 fatigue test according to an embodiment of the present invention;

[0021] Figure 3 Schematic diagram of critical distances for different notched parts;

[0022] Figure 4 Schematic diagram of the high stress volume threshold stress of GH4169 notched specimen changing with defect size and the comparison of test results;

[0023] Figure 5 Schematic diagram of the comparison between the failure position and high stress volume of the notched specimen in the GH4169 fatigue test using the method of the present invention. DETAILED DESCRIPTION

[0024] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0025] The embodiment of the present invention discloses a method for determining high stress volume under notch-defect interaction, referring to Figure 1 As shown, the following steps are included:

[0026] S1. Calculate the stress distribution data of the notch root in the defective notch component structure through finite element analysis, and output the ratio of axial stress to nominal stress K t,S ;

[0027] S2. Calculate the virtual defect size of the notched component structure

[0028] S3, using the critical distance method, combined with the ratio K t,S , calculate the stress concentration parameter K at the root of the notch in the structure containing the defect notch t,0.5L ;

[0029] S4. By analyzing the competitive effect of gaps and defects, combined with the virtual defect size and stress concentration parameter K t,0.5L , calculate the high stress volume area.

[0030] The present invention addresses the problem that the weak parts of a structure under the action of defects (inclusions, holes, scratches and corrosion points) are difficult to determine and the fatigue failure location (notch or defect). Based on the notch-defect competition relationship (the notch-defect relationship is not only competition, but also mutually promoting - stress concentration superposition, and the failure location judgment depends more on competition, so the present invention is generally referred to as competition, and the actual proposed model also takes the promotion relationship into account), a method for calculating the high stress volume under the coupling of defects and notch effects is proposed, and the key areas for complex structures to be applied to life assessment and reliability analysis are clarified. The present invention quantifies the notch effect with the critical distance method and the equivalent stress concept, quantifies the influence of defects through the fatigue strength model based on the stress intensity factor and defect size, conducts a competitive failure analysis of the degree of weakening of the fatigue strength of the structure by notches and defects, and determines the high stress volume of the complex structure by comprehensively considering factors such as geometric structure, material properties and defect distribution. The proposed method flow is universal for structural parts with notches of any size and shape, is easy to operate, and has a wide range of applicability.

[0031] Take the failure location prediction process of the component with defect notch to be analyzed as an example. The specimen is made of GH419 material. Figure 2 As shown in the figure, three different geometric shapes are included: quasi-smooth parts, C-notches, and V-notches, as well as their respective dimensional data. The specimen size is analyzed through the competitive failure analysis between notches and defects, with the critical distance and virtual defect size (El Haddad parameter) as the main parameters to realize the failure location prediction process of the defective notch component to be analyzed. The specific steps include:

[0032] 1. Calculate the stress distribution at the notch root based on finite element analysis and output the ratio of axial stress to nominal stress K t,S

[0033] Perform linear elastic finite element analysis on the component to be analyzed (in this invention, the Young's modulus of GH4169 is 182GPa and the Poisson's ratio is 0.325), determine the stress distribution at the root of the notch, and output the stress value of the notch root with the distance from the notch (maximum stress gradient direction). In this invention, the maximum stress gradient direction of the notch is the direction of the line connecting the notch roots on both sides. Output axial stress (fatigue test and finite element analysis are both uniaxial tensile load) and nominal stress ratio K t,S , as shown in Table 1, and the data in Table 1 is used as input for step 3. Among them, K t Represents the stress concentration factor.

[0034] Table 1 Stress gradient of specimens with different notches

[0035]

[0036]

[0037] 2. Fatigue strength assessment of defective materials and output of virtual defect size (i.e., El Haddad parameter)

[0038] The present invention adopts the El Haddad model to calculate the fatigue strength of materials under the action of defects, and its specific formula is as follows:

[0039]

[0040] where Δσ w0 is the fatigue strength of defect-free material, square root of the defect projected area Indicates the defect size, is the El-Haddad parameter, which is calculated using the following formula:

[0041]

[0042] Where ΔK th,lc is the crack growth threshold, and Y is the defect geometry correction coefficient (related to uncertain parameters such as defect shape and location). Generally, the Y value for surface defects is 0.65, while that for internal defects is 0.5. Experimental results show that both low- and high-cycle failures originate from surface defects. In this invention, the Y value is 0.65. th,lc and Δσ w0 The parameter data are shown in Table 2 (the material parameter acquisition test method is the existing technology and will not be repeated here). Due to the existence of material dispersion, ΔK th,lc and Δσ w0 The parameter values ​​are all within the range and not fixed. As shown in Table 2.

[0043] It is worth noting that in step 2 only The calculation result is used as the input of step 4, and the fatigue strength Δσ in formula (1) w This is a non-essential calculation item. It is listed to introduce and derive formula (2) on the one hand, and to derive the final notch-defect competition model in step 4 on the other hand, reflecting the degree of weakening of notch fatigue strength by defects.

[0044] Table 2 Parameters related to high stress volume calculation

[0045]

[0046] 3. Calculate the fatigue strength of the notched part based on the critical distance method and output the stress concentration parameter K at the notch root t,0.5L

[0047] The critical distance is an effective tool to solve the effect of the notch. The stress at a point a certain distance from the notch root (the half length of the critical distance L / 2) is taken as the effective stress Δσeff , expressed as:

[0048] Δσ eff =Δσ(L / 2) (3)

[0050] Δσ represents the stress magnitude, and L is the critical distance. For high cycle fatigue problems, the calculation of the critical distance is the same as the virtual crack length in the El Haddad model. The parameter Y is also considered. The calculation is based on the surface defect Y = 0.65, that is, the critical distance L is equal to the El Haddad parameter When Δσ eff =Δσ w0 , Δσ w0 is the fatigue strength of defect-free material. It is assumed that the notched part has reached the fatigue failure condition. The fatigue limit Δσ of the notched part without defect is w '(the minimum nominal stress for fatigue failure of notched parts) can be expressed as:

[0051]

[0052] K t,0.5L is the ratio of the maximum (tensile) stress to the nominal stress at the half-length critical distance (K t Only the stress concentration at the root of the notch is described. The present invention expands its concept, such as K t,n％ , K t,0.5L With K t,L , convenient for high stress volume calculation), K t,0.5L According to Table 1 and the critical distance half length L / 2, specifically, through the software tool The K value is obtained by fitting the data in Table 1 using interpolation. t,S As the distance S from the root of the notch changes, the K corresponding to the critical distance L / 2 calculated in this step is obtained. t,0.5L Values, as shown in Table 2 and Figure 3 As shown, Figure 3 Schematic diagram of critical distance of different notch parts. t,0.5L The calculation result is used as the input of step 4, and the fatigue strength of the notched part Δσ w 'Reflects the degree of weakening of notch fatigue strength caused by the notch, and is not a necessary calculation item.

[0053] 4. Perform notch-defect competition analysis and calculate the K corresponding to the high stress volume t,n％ With high stress volume V n％ Based on the above analysis, the competition between defects uses extreme value statistics to screen out larger defects, while the competition between defects and notches requires a comparative analysis of the degree to which each weakens the material strength. In summary, assuming that the fatigue strength of the material is the same under the influence of defects (step 2) and notches (step 3), the following formula can be obtained:

[0054] Δσ w =Δσ w ' (5)

[0056]

[0057] Among them, Δσ w ' is the fatigue limit of the part without defect notch, K t,n％ Defined as the stress concentration factor K t The nth percentile value (K t ×n%), which is related to the notch shape and critical defect characteristics and is used to represent the high stress volume V n％ Boundary stress conditions.

[0058] Combining equation (4) in step 3 and equation (6) in step 4, the stress concentration factor threshold for determining the high stress volume (the product of this threshold and the nominal stress is the high stress volume threshold stress) is:

[0059]

[0060] The result of step 2 and K obtained in step 3 t,0.5L (as shown in Table 2) into formula (7), we can get K t,n％ With defects Functional relationship between them, it is worth noting that K t,0.5L and The function relationship should be a family of curves, not a single curve. Substitute the boundary values ​​of the range into the calculation, take the upper and lower boundary curves and the middle range, and the boundary and the middle shaded part are as follows. Figure 4 As shown. The expression of high stress volume (percentage) of notched parts is:

[0061]

[0062] Through finite element software Screen out the element set with stress exceeding the maximum stress n% ​​(select the maximum defect size of 0.2mm and Figure 4 Intersection point K of the lower boundary of the middle dispersion zone t,n％ used for n% calculation), which is the high stress volume V of the structure n％ Based on the high stress volume V n％ The fatigue failure location of structures containing defect notches can be predicted.

[0063] The present invention uses the uniaxial fatigue test data of the additive GH4169 material to verify the above method. The specimen size is as follows: Figure 2 As shown; Figure 4 and Figure 5The comparison chart of the predicted results and actual test data of the additive GH4169 specimens with different notches under uniaxial load is given in FIG. Figure 4 It can be seen that the maximum defect value and the ultimate failure position obtained by computed tomography (CT) as the experimental data points fall within the dispersion band, indicating that the proposed model achieves accurate evaluation. In addition, the failure positions of the quasi-smooth part obtained by scanning electron microscopy (SEM) cross-sectional analysis are 1mm and 2.5mm away from the root, respectively, both located at the V 95％ It is far from the predicted smooth part dispersion zone. But it is worth noting that Figure 4 The middle dispersion zone is caused by the dispersion of the material itself. The stress concentration factor threshold of the high stress volume should fall within this range, and the actual test point position should fall on the upper right side of the lower boundary of the range. Because not all test sample points (when the high stress volume is selected) can reach the limit state, as the sample size increases, the maximum point of the high stress volume range of all samples should gradually approach Figure 4 The lower boundary of each dispersion zone. Figure 5 It can be seen that the predicted high stress volume (i.e., the range where fatigue failure may occur) covers all failure locations obtained from the test, and the predicted boundary is close to the farthest point of the failure location, making an accurate judgment on the failure location boundary.

[0064] Based on the competitive relationship between notches and defects, this paper proposes a new method for calculating high-stress volumes. This method comprehensively considers the impact of notches and defects on structural fatigue performance, and quantitatively analyzes them using the critical distance method and fatigue strength model to ultimately determine the threshold stress of the high-stress volume. This method has the following advantages:

[0065] Targeted: It can determine the high stress volume according to the actual conditions of different structures, avoiding the limitations of the fixed percentage method.

[0066] Accuracy: Competitive failure analysis allows for more accurate prediction of the size and location of high stress volumes.

[0067] Versatility: This method can be applied to fatigue life assessment of different materials and structures.

[0068] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on the differences from other embodiments. Reference can be made to the common and similar parts between the various embodiments. For the devices disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the description is relatively simple, and the relevant parts can be referred to the method description.

[0069] The above description of the disclosed embodiments is intended to enable one skilled in the art to implement or use the present invention. Various modifications to these embodiments will be readily apparent to one skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the present invention. Therefore, the present invention is not limited to the embodiments shown herein but is intended to conform to the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for determining high stress volume under notch-defect interaction, characterized in that: The following steps are involved: S1. Calculate the stress distribution data of the notch root in the defective notch component structure through finite element analysis, and output the ratio of axial stress to nominal stress K t，S ; The notch component structure includes: quasi-smooth parts, C-shaped notches and V-shaped notches; S2. Calculate the virtual defect size of the notched component structure S3, using the critical distance method, combined with the ratio K t,S , calculate the stress concentration parameter K at the root of the notch in the structure containing the defect notch t,0.5L ; The step S3 comprises: Based on the critical distance method, the critical distance L is set as the El Haddad parameter When the effective stress Δσ at the critical distance eff Equal to the fatigue strength of defect-free material Δσ w0 When the fatigue limit of the notched part is w ′ is expressed as: K t，0.5L is the ratio of the maximum stress to the nominal stress at the critical distance half length L / 2; through the ratio K t，S Obtained with the critical distance half length L / 2; S4. By analyzing the competitive effect of gaps and defects, combined with the virtual defect size and stress concentration parameter K t，0.5L , calculate the high stress volume area; the step S4 specifically includes: Assuming that the fatigue strength of the material under the influence of defects and notches is the same, the formula is as follows: Board w =Ds w ' (5) Among them, Δσ w ' is the fatigue limit of the notched part without defects, K t，n％ Defined as the stress concentration factor K t The nth percentile value is related to the notch shape and critical defect characteristics; is the actual defect size; Formula (4) and formula (6) are combined to obtain the stress concentration factor threshold for judging high stress volume: The result of step S2 and K obtained in step S3 t，0.5L Substitute into formula (7) to obtain K t,n％ With defects Functional relationship between them; among them, K t,0.5L and All are ranges, and the resulting function relationship is a family of curves. Substitute the range boundary values ​​into the calculation and take the upper and lower boundary curves and the middle range; The high stress volume expression of the notched part is: By screening out the unit set whose stress exceeds n% of the maximum stress, the high stress volume V of the structure is obtained. n％ .

2. The method for determining high stress volume under notch-defect interaction according to claim 1, characterized in that: The step S2 comprises: The virtual defect size of the component structure is calculated by the following formula Where ΔK th,lc is the long crack growth threshold, Δσ w0 is the fatigue strength of defect-free material, and Y is the defect geometry correction factor.

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