A method for probabilistic fatigue strength assessment considering random features of defects

Abstract

The application discloses a kind of probability fatigue strength evaluation methods considering defect random characteristics, applied to strength checking and fatigue strength evaluation field.For the fatigue dispersion problem generally existing under the influence of random defect characteristics of target material, the application adopts the thought of Monte Carlo to combine the fatigue strength model considering defect size, shape and position and other characteristics, establishes a kind of probability fatigue strength evaluation technology considering random uncertainty of defect characteristics;The method is based on stress intensity factor and fatigue strength model in fracture mechanics, by correlating the relationship between defect characteristics and defect geometry correction coefficient, the influence of defect characteristics on stress concentration and fatigue performance can be better presented;At the same time, based on the random variable in fatigue strength model, probability K-T diagram can be drawn, which can effectively quantify the defect tolerance distribution under different design stresses;Finally, the failure probability of target material under different design stresses is calculated based on the proposed defect tolerance interference model.

Description

Technical Field

[0001] This invention belongs to the field of strength verification and fatigue strength assessment, and specifically relates to a probabilistic fatigue strength prediction technology. Background Technology

[0002] Fatigue is one of the most common failure modes of engineering components. In mechanical structure design, strength verification is often the final hurdle before actual production and use. For a considerable period in the past, structural strength design was mainly based on static strength design, using the allowable stress method. Currently, a complete set of mature methods for structural strength analysis, design, and testing has been established in this area. However, with increasingly harsh service environments for mechanical structures and a growing number of random influencing factors due to increased system complexity, fatigue caused by alternating stress has become the main failure mode of mechanical structures, accounting for 50-90% of all failures. The fatigue process is the accumulation of internal damage to the material of a component due to repeated loading. Fatigue phenomena are extremely complex, with numerous influencing factors. Despite more than a century of research and exploration, the fatigue problem has not yet been completely solved.

[0003] Early analyses of the fatigue performance and reliability of mechanical structures often employed design methods that considered the absence of internal material defects. Safety factors were used to account for factors such as multi-source dispersion and size effects. This overly conservative approach resulted in excessively high costs and overstrength in the structure. Modern mechanical structure design has evolved from simple static strength-based infinite-life design and safe-life design to design based on fracture mechanics and defect tolerance (i.e., the allowable defect size without fatigue fracture). This approach considers initial defects, cracks, or other damage present in the structure. Through analysis and experimental verification, strict crack growth limits are proposed to ensure that the structure, within a given lifespan, avoids catastrophic accidents caused by the uncontrolled propagation of undetected initial defects.

[0004] Common forms of defects include porosity, microcracks, and inclusions. Due to the irregular geometry of defects, localized stress concentrations occur, significantly impacting the fatigue life of components under cyclic loading. This poses a significant challenge to the integrity and service reliability of mechanical structures. Surface defects, in particular, cause greater damage to the structure and are often the location of fatigue initiation, exhibiting higher stress levels and a tendency for cracks to initiate and propagate in these areas. Due to factors such as manufacturing processes, inherent defects in materials are unavoidable. Early design methods that considered the absence of internal defects and assumed infinite life were overly conservative, leading to excessive costs and overstrength in the structure. Furthermore, traditional fatigue analysis typically involves fatigue testing on small specimens to obtain basic fatigue performance and component fatigue assessment. However, due to size effects, even under similar loads, the fatigue life of components differs from that of specimens. For example, the fatigue strength of a material decreases with increasing material volume, which is related to the distribution of critical defects within the material. Therefore, establishing a fatigue life prediction method that comprehensively considers defect size, location, and shape is particularly necessary. Defect tolerance assessment of structures that takes into account the inherent internal defects of materials, and obtaining the allowable defect or microcrack sizes of structures under different stress levels, is of great significance for structural design and integrity assessment. Summary of the Invention

[0005] To address the aforementioned technical problems, this invention proposes a probabilistic fatigue strength assessment method that considers the random characteristics of defects. It comprehensively considers the influence of defect size, shape, and location on the fatigue performance of materials, and proposes a fatigue strength prediction model that comprehensively considers multiple defect characteristics. Based on this fatigue strength model, a defect tolerance assessment and failure probability calculation method under random defects is established. The method of this invention has a simple calculation process, strong universality, and high accuracy in fatigue strength prediction results.

[0006] The technical solution adopted in this invention is: a probabilistic fatigue strength assessment method considering the random characteristics of defects, comprising:

[0007] S1. Determine the distribution of defect characteristics and randomly sample the main defect characteristics;

[0008] S2. Substitute the randomly sampled results obtained in S1 into the fatigue strength prediction model to perform probabilistic fatigue strength assessment.

[0009] S3. Based on the model parameter variables obtained in S2, construct the probability KT diagram; KT diagram is short for Kitagawa–Takahashi diagram, which is a diagram showing the relationship between fatigue strength and defect size.

[0010] S4. Based on the probability KT diagram, obtain the target defect tolerance distribution dataset; then calculate the defect tolerance distribution.

[0011] S5. Using the defect tolerance interference model, based on the defect tolerance distribution, calculate the failure probability under different design stresses.

[0012] The beneficial effects of this invention are as follows: This invention considers the influence of defect characteristics on the stress intensity factor, establishes a fatigue strength assessment model that comprehensively considers the effects of multiple defect characteristics, and establishes a probabilistic fatigue strength assessment framework under random defects based on the Model Calo method. Specifically, this invention first conducts fatigue tests and defect information statistics, then obtains numerical information on defect size, shape, and location through random sampling as input, substitutes it into the fatigue strength model to perform probabilistic fatigue strength prediction, and plots a probability KT diagram. Based on the proposed defect tolerance interference model, a failure probability curve is drawn. Finally, after experimental verification, the fatigue strength prediction model of this invention can comprehensively characterize the combined effect of multiple defect characteristics on fatigue performance, with high prediction accuracy and simple operation. Specifically, the method of this invention has the following advantages:

[0013] (1) The relationship between the defect characteristics and the defect geometric correction coefficient Y was quantified. Based on this, a fatigue strength prediction model that comprehensively considers the effects of multiple defect characteristics was established, and a set of general calculation and analysis procedures were given. Finally, the defect shape and location factors were incorporated into the traditional KT diagram (only considering the relationship between defect size and strength) to form a probability KT diagram that can be used to quantify the defect tolerance and calculate the failure probability curve under different design stresses.

[0014] (2) The fatigue strength prediction model proposed in this invention has a simple calculation process and considers all defect characteristics. Moreover, the influence of defect characteristics on stress intensity factor and fatigue strength is calculated by polynomial, without the need to repeatedly obtain it through finite element analysis. It has the characteristics of universality, simple operation and wide applicability in the evaluation of materials with defects.

[0015] (3) In this invention, through random variable Y and The probabilistic KT curve is constructed, which breaks through the shortcomings of the traditional deterministic KT curve that only considers the defect size, and directly establishes the relationship between design stress and defect tolerance; the proposed defect tolerance interference model can intuitively present the failure probability under different design stresses.

[0016] (4) This invention comprehensively considers the main characteristic parameters of defects such as size, shape and location, and realizes the quantification of fatigue dispersion based on Monte Carlo simulation. Attached Figure Description

[0017] Figure 1 The present invention provides two gauge length dimensions for smooth Al-Si-10Mg additive fatigue test specimens.

[0018] Figure 2 The flowchart provided in the embodiments of the present invention;

[0019] Figure 3 Schematic diagram of the defect tolerance interference model provided in this embodiment of the invention;

[0020] Figure 4 The probability KT diagram of the smooth specimen of additive Al-Si-10Mg(P1) fatigue test provided in the embodiments of the present invention, and the schematic diagram comparing the simulated points and the test points;

[0021] Figure 5 The probability KT diagram of the smooth specimen of additive Al-Si-10Mg(P2) fatigue test provided in the embodiments of the present invention, and the schematic diagram comparing the simulated points and the test points;

[0022] Figure 6 The failure probability diagrams of P1 and P2 under different design stresses based on the defect tolerance interference model provided in this embodiment of the invention. Detailed Implementation

[0023] To facilitate understanding of the technical content of this invention by those skilled in the art, the following description, in conjunction with the accompanying drawings, further illustrates the invention.

[0024] This embodiment takes the probabilistic fatigue strength assessment and failure probability calculation process of an additively smoothed specimen with defects as an example. By establishing the relationship between fatigue strength and defect characteristics, and based on the proposed probabilistic fatigue prediction model and defect tolerance interference model, the probability KT diagram of the additively smoothed specimen with defects and the failure probability curves under different design stresses are plotted. The specific steps include:

[0025] 1. Conduct random sampling based on defect feature distribution

[0026] 11. Regarding such Figure 1 The smooth specimens shown were subjected to uniaxial tensile fatigue tests and fatigue limit tests under different stress levels. Figure 1 The paper specifically provides additive Al-Si-10Mg(P1) and additive Al-Si-10Mg(P2).

[0027] 12. Defect information in the gauge length segments of some specimens was reconstructed using computed tomography (xCT). The defect size, shape, and location information are shown in Table 1. Since defect characteristics are correlated, and defect size is the most critical factor in fatigue assessment, defect shape data were obtained from defects above the Pareto distribution threshold u for the critical defect size, rather than all defect information obtained from xCT scans. Defects causing final fatigue failure after fatigue testing, as determined by cross-sectional analysis, are mostly surface defects. Assuming the defect is an ideal elliptical defect with a major axis of 2a, a minor axis of 2b, and a depth of h, the defect location parameter (a / h) was selected within the range of 0.8-1 (a / h > 0.8 is considered a surface defect). Random sampling was performed based on the defect characteristic distribution in Table 1, with a sample size of n (taking n = 100 as an example).

[0028] Table 1. Main Defect Characteristics and Distribution

[0029]

[0030] In Table 1, u and σ represent position and scale parameters, respectively.

[0031] Note: For irregularly shaped defects, the shape ratio b / a is taken as the width-to-length ratio of the rectangle enclosing the defect.

[0032] 2. Conduct probabilistic fatigue strength assessment based on random defect information.

[0033] 21. The impact of quantified defect characteristics on stress concentration

[0034] The expression for the stress intensity factor ΔK is:

[0035]

[0036] Where Δσ is the nominal stress range applied in the fatigue test, Let be the Murakami parameter (i.e., the square root of the projected area of ​​the defect perpendicular to the load plane), and Y be the defect geometry correction factor (related to uncertain parameters such as defect shape and location). The expression is:

[0037]

[0038]

[0039] Where M is the stress intensity magnification factor, and E is a parameter related to the defect shape (b / a is the shape ratio, for a perfectly circular defect it is...). Generally, the Y-value is often taken as 0.65 for surface defects and 0.5 for internal defects. These parameters are average values ​​obtained from extensive experiments and analyses, ensuring the prediction results are within a certain error range. Representing different defect shapes and locations using a constant is a deterministic method. This invention, through specific analysis of multiple defect characteristics, provides a stress intensity amplification factor M in polynomial form for a more convenient and accurate consideration of the relationship between defect characteristics and Y:

[0040] M=1.276+0.1319x-1.188y+0.1427x 2 -0.6815xy+1.649y 2

[0041] x = b / a is the defect shape ratio in Table 1, and y = a / h is the defect location parameter. Since the influencing factors of the Y value are mainly the defect shape and location (compared to microstructure, mechanical properties, etc.), the M-polynomial calculation in this invention has universality and is not limited to the materials used in this invention.

[0042] 22. Probabilistic Fatigue Strength Assessment

[0043] This invention uses the El-Haddad model, and its specific formula is as follows:

[0044]

[0045] Where Δσ w0 For the fatigue strength of defect-free materials, The El-Haddad parameter is calculated using the following formula:

[0046]

[0047] Where ΔK th，lc This is the threshold for long crack propagation. In this invention, it is used... With ΔK th,lc The parameter data are shown in Table 2 (the test method for obtaining material parameters is existing technology and will not be described in detail here).

[0048] Table 2 Crack propagation parameters of test samples

[0049]

[0050] Substituting the sample set of Y values ​​obtained in step 21 into the above formula, we can calculate... The set of values, and then the fatigue strength numerical set and its distribution can be calculated based on the El-Haddad model, such as... Figure 4 , 5 The simulated data points are shown in the figure.

[0051] 3. Based on the probability parameters obtained in step 2, plot the probability KT diagram to quantify the defect tolerance distribution under different design stresses.

[0052] Based on the above El-Haddad model and the known Δσ w0 ΔK th,lc and Plot the probability KT curve for the set (e.g.) Figure 4 and 5 To obtain the defect tolerance distribution under different design stresses, such as... Figure 3 As shown, with a certain design stress Δσ w For example, the intersection of the design stress and the KT curve family is the target defect tolerance distribution dataset. This data is then summarized. Given the convenience of the Weibull distribution, this invention uses Matlab (wblfit command) to perform Weibull distribution (two-parameter maximum distribution) parameter fitting on this dataset to obtain the defect tolerance distribution (probability density) under the design stress:

[0053]

[0054] Where σ and γ are the scale and shape parameters, respectively. The subscript 't' in this context is an abbreviation for tolerance. The above process is repeated to obtain different design stresses Δσ. w The corresponding defect tolerance distribution is calculated in this invention, with Δσ covering the range of 100-280 MPa. w Distribution (select an appropriate range based on material properties to ensure that subsequent calculations cover the 0-100% failure range), with different design stress intervals of 1 MPa.

[0055] 4. The failure probability under different design stresses is calculated using a defect tolerance interference model.

[0056] To calculate the failure probability of specimens under different design stresses, this invention proposes a defect-tolerant interference model, whose limit state function is:

[0057]

[0058] in, For defect tolerance, For actual defects, when When this occurs, the sample can be considered to have failed (the principle is as follows). Figure 3 As shown), therefore, the failure probability of this sample is:

[0059]

[0060] in For the defect tolerance distribution (obtained in step 3), The measured defect distribution of the sample is given. When calculating the failure probability, the ranges of two distribution variables need to be considered. In the above formula, the ranges of the independent variables for both distributions are [-∞, +∞]. However, the lower limits of the actual defect sizes of the two sets of samples P1 and P2 used in this invention are 0.1 mm and 0.15 mm, respectively, while the lower limit of the defect tolerance in the Weibull form is 0. Therefore, the failure probability P... f The calculation needs to be performed in the form of a piecewise function, as shown in the following formula:

[0061]

[0062] Generally, in defect-tolerant design, the area within the traditional KT envelope is considered safe and reliable, and fatigue fracture is unlikely to occur. However, the KT envelope also exhibits dispersion; within this family of KT curves, the failure probability of the target structure needs to be calculated and evaluated. For example... Figure 6 As shown, the obtained failure probability is defined as the probability that the target structure will experience fatigue failure under the design stress. For materials without a fatigue limit, it is defined as the probability that the target structure will fail at a specific fatigue cycle (e.g., 10 cycles) under the design stress. 6 The probability of fatigue failure occurring in cycles.

[0063] This invention validated the model using uniaxial fatigue test data of additive Al-Si-10Mg material, and the specimen dimensions are as follows. Figure 1 As shown. Figure 2 The flowchart provided in this embodiment of the invention includes the defect size, location and shape, M, Y, It is a random variable. Figure 3 This is a schematic diagram of the defect tolerance interference model. Figure 4 , 5 The figure shows a comparison between simulated data and actual experimental data of additive Al-Si-10Mg smooth specimens subjected to uniaxial loads using the method of this invention; from Figure 4 , 5 It can be seen that the method proposed in this invention can simultaneously characterize the influence of defect feature dispersion on fatigue performance. Most test points fall within the range of the plotted probability KT curve (due to the existence of size effect, the actual defect size is larger), and it has high accuracy. Figure 6 The failure probability curves of P1 and P2 based on the defect tolerance interference model under different design stresses are presented, which more intuitively demonstrates the reliability of the sample under different design stresses.

[0064] Those skilled in the art will recognize that the embodiments described herein are intended to help the reader understand the principles of the invention, and should be understood that the scope of protection of the invention is not limited to such specific statements and embodiments. Various modifications and variations can be made to the invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the invention should be included within the scope of the claims of the invention.

Claims

1. A probabilistic fatigue strength assessment method considering the random characteristics of defects, characterized in that, include: S1. Determine the defect feature distribution of the additive smoothing specimen with defects to be analyzed, and randomly sample the main defect features; S2. Substitute the randomly sampled results obtained in S1 into the fatigue strength prediction model to perform probabilistic fatigue strength assessment; the fatigue strength prediction model expression is: ； in, For the fatigue strength of defect-free materials, For El-Haddad parameters, , For long crack propagation threshold, Y represents the square root of the projected area of ​​the defect perpendicular to the load plane, and Y is the defect geometric correction factor; the formula for calculating Y is: ； Where M is the stress intensity amplification factor, x represents the defect shape ratio, and y represents the defect location parameter. For parameters relating to the shape of the defect, The major axis of the elliptical defect is 2a, and the minor axis is 2b. S3. Based on the model parameter variables obtained in S2, plot the probability KT diagram; step S3 specifically depends on the fatigue strength prediction model and known parameters. , and Plot the probability KT curve for the set; S4. Based on the probability KT diagram, obtain the target defect tolerance distribution dataset; then calculate the defect tolerance distribution; the expression for the defect tolerance distribution mentioned in step S4 is: ； in, For scale parameters, For shape parameters, For defect tolerance, The subscript 't' in the text is an abbreviation for tolerance. S5. Using a defect tolerance interference model, and based on the defect tolerance distribution, calculate the failure probability under different design stresses; the formula for calculating the failure probability in step S5 is: ； in, , () represents the defect tolerance distribution. The measured defect distribution of the sample.

2. The probabilistic fatigue strength assessment method considering the random characteristics of defects according to claim 1, characterized in that, Step S1 specifically includes the following sub-steps: S11. Conduct uniaxial tensile fatigue tests and fatigue limit tests under different stress levels on the additive smooth specimens with defects to be analyzed. S12. The defect information of the additive smoothing specimen with defects to be analyzed after processing in step S1 is reconstructed using computed tomography (CT) technology; the main defect features are obtained, including: defect size, shape and location. S13. Random sampling is performed based on the distribution of defect size, shape, and location.

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