Cylinder head high-cycle fatigue life partition prediction method based on defect size probability

Abstract

The application discloses a cylinder cover high-cycle fatigue life partition prediction method based on defect size probability and belongs to the field of engine cylinder covers. According to the yield strength difference degree of different positions of the cylinder cover, the application carries out area division, and according to the maximum pore size probability density distribution of different positions of the cylinder cover and different engineering reliability design requirements, the application calculates the crack initiation life of different reliability probabilities, and the small crack propagation life of different areas of the cylinder cover is predicted. The application can represent the influence of the multi-axial degree of the stress state of the complex structure of the cylinder cover on the fatigue life by calculating the maximum value of the multi-axial stress amplitude of each area through the dangerous cross-section method. The application can improve the high-cycle fatigue life calculation efficiency of different positions by constructing a Gerber type multi-axial stress amplitude calculation model which is simple in form and suitable for wide range traversal calculation and by solving the multi-axial stress amplitude of all sections of each unit through the Gerber type multi-axial stress amplitude solving model. The application has the advantages of high prediction accuracy, high prediction efficiency and wide prediction range.

Description

Technical Field

[0001] This invention relates to a method for predicting high-cycle fatigue life of cylinder heads based on defect size probability, belonging to the field of engine cylinder heads. Background Technology

[0002] The cylinder head of an automotive engine is the most critical load-bearing component, enduring high-cycle fatigue loads for extended periods during operation. The cylinder head's complex structure and function, coupled with significant differences in casting behavior such as cooling rates at different locations, result in high variability in internal characteristics, including microstructure and porosity defects, across different areas. Under high-cycle fatigue conditions, crack initiation life dominates the overall high-cycle fatigue life, and the dispersion of porosity defects at different locations leads to high dispersion in crack initiation life. Furthermore, the complex structure of the cylinder head and the high multiaxiality differences in loads at different locations also contribute to significant dispersion in high-cycle fatigue life. As a non-repairable component, the cylinder head is typically designed for unlimited life, with its service load conditions corresponding to the material's fatigue limit region. Fatigue behavior in this region is significantly influenced by the material's inherent porosity defects, exhibiting high dispersion related to both high defect rates and structural characteristics. These internal microstructure and external load characteristic dispersions result in low accuracy in assessing the high-cycle fatigue strength of the cylinder head.

[0003] Current high-cycle fatigue strength assessment of cylinder heads primarily relies on the macroscopic SN curve method. This method is unsuitable for assessing the strength of defective materials and struggles to couple the microstructure of the bulk material with defect characteristics, easily leading to non-conservative estimates of structural fatigue strength or redundant strength designs. Currently, patent CN 109598079 A predicts cylinder head fatigue life by zoning based on different fatigue failure modes at different locations, but it doesn't consider the probability distribution differences in porosity and microstructure characteristics at different locations. Patent CN 113434980 A calculates cylinder head stress dispersion using the Monte Carlo method, but it doesn't calculate the multiaxiality of cylinder head load stress. Furthermore, current cylinder head fatigue life prediction methods are all deterministic, lacking dispersion prediction methods corresponding to different reliability levels. Therefore, this invention establishes a high-cycle fatigue life zoning prediction method for cylinder heads based on defect size probability, based on the dispersion characteristics of cylinder head materials. This method is applicable to different engineering reliability evaluation design requirements and can improve the accuracy of high-cycle fatigue life prediction for different regions of the cylinder head. Summary of the Invention

[0004] To address the issues of high dispersion and low accuracy in high-cycle fatigue life prediction of cylinder heads in automotive internal combustion engines due to material porosity defects and microstructure differences, and the inability to meet varying reliability assessment requirements in engineering projects, this invention aims to provide a zoned prediction method for high-cycle fatigue life of cylinder heads based on defect size probability. This method characterizes the impact of microstructure differences in different regions of the cylinder head on small crack propagation life, and can predict crack initiation life under different engineering reliability probability requirements. Furthermore, it considers the influence of multiaxial stress states in the complex cylinder head structure on high-cycle fatigue crack initiation, small crack propagation, and long crack propagation using the critical section method. This invention improves the accuracy and applicability of high-cycle fatigue life prediction for cylinder heads.

[0005] The objective of this invention is achieved through the following technical solution.

[0006] This invention discloses a method for predicting the high-cycle fatigue life of cylinder heads based on defect size probability. First, the cylinder head structure is divided into zones according to the difference in yield strength of materials at different locations. Then, the pore size characteristics of each zone are extracted using a tomographic reconstruction method, and the probability density function of the maximum pore size distribution and the cumulative probability density function of each zone are fitted. Next, the maximum multiaxial stress amplitude of each zone is calculated using the critical section traversal method. Based on different reliability requirements in practical engineering applications, the maximum pore size corresponding to different reliability probabilities is calculated. Combined with the maximum multiaxial stress amplitude of each zone, a zoned probability crack initiation life model is constructed using a Manson-Coffin model driven by maximum plastic shear strain to calculate the crack initiation life of each zone corresponding to different reliability probabilities. Then, based on the yield strength of the materials in each zone and the maximum pore size corresponding to different reliability probabilities, a small crack propagation rate model is used to calculate the small crack propagation life of each zone corresponding to different reliability probabilities; and a long crack propagation rate model is used to calculate the long crack propagation life of the materials in each zone. Finally, based on the calculated crack initiation life, small crack propagation life, and long crack propagation life, the high-cycle fatigue life corresponding to different reliability probabilities in different areas of the cylinder head is obtained.

[0007] This invention discloses a method for predicting the high-cycle fatigue life of cylinder heads based on defect size probability, comprising the following steps:

[0008] Step 1: Considering the significant differences in microstructure and mechanical properties across different locations in the cylinder head, the microstructure characteristic size distribution of the material is obtained from the simulation results of the cylinder head casting process. Based on the microstructure-yield strength prediction formula, the yield strength distribution of the material at different locations in the cylinder head is obtained. The obtained yield strengths at different locations are also used as input for the subsequent step five, which predicts the small crack propagation rate at different locations, improving the accuracy of crack propagation rate prediction. The critical value for the degree of difference in the mechanical characteristics of the cylinder head structural material is determined according to engineering requirements. The degree of difference between the yield strength at different locations in the cylinder head and the average yield strength of the cylinder head is calculated using the yield strength difference calculation formula. When the degree of difference at a certain location exceeds the critical value, that location is designated as a new analysis region, thus obtaining several analysis regions for different locations in the cylinder head.

[0009] Step 1.1: Based on the material microstructure characteristic size distribution obtained from the simulation results of the cylinder head casting process, and using the microstructure-yield strength prediction formula, the yield strength distribution of the material at different locations in the cylinder head is obtained. The yield strength of the material at different locations is also used as input for the subsequent step five to predict the small crack propagation rate of the material at different locations.

[0010] The microstructure-yield strength prediction formula is expressed as:

[0011]

[0012] in, For the material's yield strength, Let be the characteristic size of the material's microstructure, and a and b be the fitting parameters of the formula.

[0013] Step 1.2: Calculate the difference between the yield strength of different positions in the cylinder head and the expected yield strength of the material. When the difference at a certain position is greater than the critical value of the difference, then that position is divided into a new analysis area, thereby obtaining several analysis areas at different positions in the cylinder head.

[0014] The formula for calculating the degree of yield strength difference is:

[0015]

[0016] in, The degree of difference in yield strength at position i. Let i be the yield strength value of the material at position i. This represents the expected yield strength of the material.

[0017] Step Two: Several small-sized samples are in-situ cut from each analysis region defined in Step One and reconstructed using 3D tomography to extract the pore volume of each sample. Based on the 3D equivalent size calculation method, the pore size of each sample is obtained, and the sizes are compared to determine the maximum pore size of each sample. A probability distribution is fitted to the maximum pore size of all samples in each analysis region to obtain the probability density function and cumulative probability density function of the maximum pore size for each analysis region. The inverse function of the cumulative probability density function of the maximum pore size for each analysis region is used to obtain the maximum pore size value corresponding to different reliability probabilities for each region. This value serves as the input for Step Four, which predicts the pore size for fatigue crack initiation at different reliability levels.

[0018] Step 2.1: Take several small-sized samples from each analysis area divided in Step 1 in situ and perform three-dimensional tomographic reconstruction to extract the pore volume of each sample. Based on the three-dimensional equivalent size calculation method, obtain the pore size of each sample and compare the sizes to obtain the maximum pore size of each sample.

[0019] The formula for calculating the three-dimensional equivalent size of pores is:

[0020]

[0021] in, and These are pore volume and pore size, respectively.

[0022] Step 2.2: Fit the probability distribution of the maximum pore size of all samples in each analysis region obtained in Step 2.1 to obtain the probability density function and cumulative probability density function of the maximum pore size in each analysis region. The probability distribution function is a normal distribution and a Gumbel distribution.

[0023] Step 2.3: Obtain the maximum pore size value corresponding to different reliability probabilities in each region based on the inverse function of the cumulative probability density function of the maximum pore size in each analysis region. This value will serve as the input for the subsequent step four, which aims to predict the pore size for fatigue crack initiation at different reliability levels.

[0024] Step 3: Calculate the maximum multiaxial stress amplitude in each region using the critical section traversal method. First, extract the stress tensors of the finite element elements before and after the high-cycle load step from the finite element calculation results of the cylinder head assembly structure. Calculate the stress amplitude tensor and average stress tensor of each element using the stress calculation formula. Then, determine all sections to be calculated using the traversal method. Any section direction is determined by two angular coordinates ( Within a 180° range, with a preset fixed angle δ as the rotation step, the coordinates in two directions are rotated respectively, with each direction divided into 180° / δ angle values. Each rotation determines a cross section to be calculated. Then, the amplitude and average value of the normal stress of the cross section are calculated using the normal stress calculation formula, the amplitude and average value of the shear stress of the cross section are calculated using the shear stress calculation formula, and the amplitude and average value of the equivalent stress of the cross section are calculated using the modified maximum shear strain energy criterion. Considering the complex structure and large number of finite element elements in the cylinder head assembly, a simple Gerber-type multiaxial stress amplitude calculation model suitable for large-scale traversal calculations is constructed. The multiaxial stress amplitude of each cross section is solved by traversing the Gerber-type multiaxial stress amplitude solution model, improving the efficiency of traversing multiaxial critical cross sections. Then, the multiaxial stress amplitudes of all cross sections of each finite element are compared, and the maximum value is taken as the maximum multiaxial stress amplitude of that element. Finally, the maximum multiaxial stress amplitudes of all finite element elements in each analysis region are compared, and the maximum value is taken as the maximum multiaxial stress amplitude of that region.

[0025] Step 3.1: Extract the stress tensor of the finite element before and after the high-cycle load step from the finite element calculation results of the cylinder head assembly structure. The stress amplitude tensor of each element is calculated using the stress calculation formula. and mean stress tensor .

[0026] Step 3.2: Determine all sections to be calculated using a traversal method. The direction of any section is determined by two angular coordinates (...). Within a 180° range, with a preset fixed angle δ as the rotation step, the coordinates are rotated in two directions respectively. Each direction is divided into 180° / δ angle values. Each rotation determines one cross section to be calculated, for a total of... One cross section.

[0027] Step 3.3: Calculate the multiaxial stress amplitude of all sections of each finite element element. The method for calculating the multiaxial stress amplitude at each cross-section is as follows:

[0028] First, calculate the amplitude of the normal stress at this cross section. and average value :

[0029]

[0030]

[0031] Then calculate the shear stress amplitude of that section. and average :

[0032]

[0033]

[0034] The equivalent stress amplitude of the cross section was calculated using the modified maximum shear strain energy criterion. and average :

[0035]

[0036]

[0037] in, and These are the tensile fatigue limit and tensile yield strength of the material, respectively. and These are the material's shear fatigue limit and shear yield strength, respectively.

[0038] To address the complex structure and large number of finite element elements in cylinder head assemblies, a simple Gerber-type multiaxial stress amplitude calculation model suitable for large-scale traversal calculations is constructed. This Gerber-type multiaxial stress amplitude solution model is then used to traverse and solve for the multiaxial stress amplitude of all sections of each element. This improves the efficiency of traversing multiaxial critical sections. The multiaxial stress amplitude of this section is calculated using Gerber-type formulas. :

[0039]

[0040] in, It is the ultimate tensile strength of the material.

[0041] Step 3.4: Compare the multiaxial stress amplitudes of all sections of each finite element element, and take the maximum value as the maximum multiaxial stress amplitude of that element. The maximum multiaxial stress amplitude of all finite element elements in each analysis region is compared, and the maximum value is taken as the maximum multiaxial stress amplitude of that region. .

[0042] Step 4: Using the maximum pore size corresponding to different reliability levels obtained in Step 2 and the maximum multiaxial stress amplitude of each partition region obtained in Step 3 as inputs, a partitioned probabilistic crack initiation life model is constructed by combining the Manson-Coffin model driven by maximum plastic shear strain. This model can characterize the distribution characteristics of pore defects in different regions of the cylinder head and the influence of the multiaxial characteristics of the cylinder head's high-cycle fatigue load on the high-cycle fatigue crack initiation life. It is applicable to life prediction under different engineering reliability requirements. Based on this model, the fatigue crack initiation life corresponding to different reliability probabilities is predicted. This improves the prediction accuracy of the probability of high-cycle fatigue crack initiation life.

[0043] The probabilistic crack initiation life model is based on the Manson-Coffin formula, which is determined by the maximum plastic shear strain around the pores. As the driving independent variable, the crack initiation life model is expressed as:

[0044]

[0045] in, Lifespan for crack initiation, and These are inherent parameters of the material; and These represent the maximum pore size and the maximum multiaxial stress amplitude corresponding to different reliability probabilities in steps two and three, respectively. Maximum plastic shear strain. The solution is obtained through simulation calculation using a two-dimensional representative finite element model containing pore size.

[0046] Step 5: Using the yield strength of the cylinder head material in different regions obtained in Step 1, the maximum porosity corresponding to different reliability levels obtained in Step 2, and the maximum multiaxial stress amplitude of each region obtained in Step 3 as inputs, a small crack propagation rate model driven by the cyclic plastic zone size at the crack tip is obtained. The critical crack size is calculated using the small crack propagation rate model and the long crack propagation rate model in Step 6. The critical crack size is the crack size corresponding to the equality of the small crack propagation rate and the long crack propagation rate. The small crack propagation rate model driven by the cyclic plastic zone size at the crack tip is integrated using an integral method to obtain the small crack propagation life corresponding to different reliability probabilities. The lower limit of integration is the maximum porosity corresponding to different reliability probabilities determined in Step 2, and the upper limit of integration is the critical crack size. This small crack propagation rate model can characterize the influence of the porosity defect distribution characteristics and material dispersion characteristics in different regions of the cylinder head on the high-cycle fatigue small crack propagation rate and life. Based on this small crack propagation rate model, the prediction accuracy of the high-cycle fatigue small crack propagation life of materials at different locations in the cylinder head is improved.

[0047] Step 5.1: Using the yield strength of the cylinder head material in different regions obtained in Step 1, the maximum pore size corresponding to different reliability levels obtained in Step 2, and the maximum multiaxial stress amplitude of each zone obtained in Step 3 as inputs, a small crack propagation rate model driven by the size of the cyclic plastic zone at the crack tip is obtained:

[0048]

[0049]

[0050] in, It is the rate of small crack propagation. and Define parameters for the model. By material yield strength Elastic modulus Maximum value of multiaxial stress amplitude and crack size calculate.

[0051] Step 5.2: Calculate the critical crack size using the small crack propagation rate model and the long crack propagation rate model in subsequent step six. Critical crack size This represents the crack size when the propagation rates of small cracks and long cracks are equal.

[0052] Step 5.3: By integrating the small crack propagation rate model driven by the cyclic plastic zone size at the crack tip using an integral method, the small crack propagation lifetime corresponding to different reliability probabilities is obtained, as shown in the equation. The lower limit of integration is the maximum pore size corresponding to different reliability probabilities determined in Step 2. The upper limit of integration is the critical crack size. .

[0053]

[0054] Step Six: Using the maximum multiaxial stress amplitude obtained in Step Three for each zone region As input, we obtain the effective stress intensity factor. A model for the driving long crack propagation rate. Based on the long crack propagation rate model and step five, the critical crack size is obtained. The long crack propagation life is obtained by integrating the long crack propagation rate model using an integral method. The lower limit of integration is the critical crack size obtained in step five. The upper limit of the integral is defined according to the actual failure criterion requirements. .

[0055] The long crack propagation rate model and the long crack propagation life are expressed as follows:

[0056]

[0057]

[0058] in, It is the rate of long crack propagation. and The parameters for the propagation of long cracks related to materials are defined.

[0059] Step 7: Based on the crack initiation life obtained in Step 4 Step 5 yields the small crack propagation life. And the long crack propagation life obtained in step six The total high-cycle fatigue life is calculated using an arithmetic summation method.

[0060] To address the issue of low high-cycle fatigue life prediction accuracy caused by the high variability of pore defects in different locations of the cylinder head, this invention performs tomographic reconstruction of pore sizes in different regions in step two, and obtains pore sizes corresponding to different reliability probabilities by fitting the probability distribution of the maximum pore size in different regions in step three. This is then used in step four. Based on the partitioned probability crack initiation life model in step four, the crack initiation life at different locations of the cylinder head under different engineering reliability requirements can be predicted, thereby improving the prediction accuracy and applicability of cracks at different locations of the cylinder head.

[0061] To address the issue of high dispersion and low prediction accuracy of high-cycle fatigue small crack propagation life caused by the high variability of microstructures in different locations of the cylinder head, this invention divides the cylinder head into multiple analysis regions based on the degree of microstructure variability in different locations in step one, and predicts the yield strength of each region using a microstructure-yield strength prediction formula. Furthermore, to address the issue of low fatigue life prediction accuracy caused by the multiaxial stress state of the complex cylinder head structure, this invention uses the critical section method to calculate the maximum multiaxial stress amplitude in each region in step three. Considering the large number of finite element elements in the cylinder head composite structure, a simple Gerber-type multiaxial stress amplitude calculation model suitable for large-scale traversal calculations is constructed. The Gerber-type multiaxial stress amplitude solution model is used to traverse and solve the multiaxial stress amplitude of all sections of each element, thereby improving the efficiency of traversing the multiaxial critical section. Using the results obtained from steps one, two, and three for predicting the small crack propagation rate in different regions of the cylinder head in step five can improve the prediction accuracy of high-cycle fatigue life of the cylinder head.

[0062] In summary, the high-cycle fatigue life obtained by summing steps four, five, and six can characterize the impact of microstructural differences in different regions of the cylinder head on the small crack propagation life. It can also predict crack initiation life under different engineering reliability probability requirements. Furthermore, the critical section method is used to consider the influence of the multiaxial stress state of the complex cylinder head structure on high-cycle fatigue crack initiation, small crack propagation, and long crack propagation. The aforementioned zoning evaluation method based on defect size probability can improve the accuracy and applicability of high-cycle fatigue life prediction for cylinder heads.

[0063] Step 8: Apply the processes from Step 1 to Step 7 to predict the high-cycle fatigue life of internal combustion engine cylinder heads under different materials and operating conditions, and apply them to life prediction for different reliability requirements. Based on the prediction results, improve and optimize the materials and structures at different locations of the cylinder head to increase the overall fatigue strength of the cylinder head and reduce material redundancy.

[0064] Beneficial effects:

[0065] 1. This invention discloses a crack initiation life prediction method based on pore size probability distribution. It calculates crack initiation life with different reliability probabilities based on the probability density distribution of the maximum pore size at different locations in the cylinder head and different engineering reliability requirements. Compared to traditional deterministic crack initiation life calculation methods, this method can predict crack initiation life under different engineering reliability requirements, improving the accuracy and applicability of cylinder head crack initiation life prediction.

[0066] 2. This invention discloses a crack initiation life prediction method based on pore size probability distribution. It divides the cylinder head into regions according to the degree of yield strength difference at different locations and predicts the small crack propagation life of different regions. Compared with traditional cylinder head small crack propagation life prediction methods, this method can characterize the influence of microstructure differences at different locations on small crack propagation life, improve the prediction accuracy of small crack propagation life at different locations of the cylinder head, and thus improve the optimization level of the strength of different structures in the cylinder head.

[0067] 3. The high-cycle fatigue life prediction method for cylinder head at different locations disclosed in this invention calculates the maximum value of multiaxial stress amplitude in each region using the critical section method. Compared with the traditional Mises stress method, this method can characterize the influence of multiaxial stress on fatigue life of the complex structure of the cylinder head, thereby improving the accuracy of high-cycle fatigue life prediction at different locations of the cylinder head.

[0068] 4. In view of the large number of finite element elements in the cylinder head assembly structure, this invention constructs a simple Gerber-type multiaxial stress amplitude calculation model that is suitable for large-scale traversal calculation. By traversing and solving the multiaxial stress amplitude of all sections of each element through the Gerber-type multiaxial stress amplitude solution model, the efficiency of traversing multiaxial critical sections is improved compared with the traditional Hager plot method, thereby improving the calculation efficiency of high-cycle fatigue life at different locations. Attached Figure Description

[0069] Figure 1 Flowchart of a method for predicting high-cycle fatigue life of cylinder heads based on defect size probability.

[0070] Figure 2 Finite element model of the intake manifold wall region of the cylinder head

[0071] Figure 3 Several small samples were cut from the in-situ of the intake wall for three-dimensional tomographic reconstruction.

[0072] Figure 4 The probability density function distribution of the normal distribution of the maximum pore size in the intake duct wall.

[0073] Figure 5 The cumulative probability density function distribution of the normal distribution of the maximum pore size in the intake duct wall.

[0074] Figure 6 The maximum multiaxial stress amplitude distribution of each element calculated for the intake manifold wall of the cylinder head.

[0075] Figure 7 Curves showing the propagation rates of small and long cracks in the intake manifold wall of the cylinder head.

[0076] Figure 8 Crack initiation life, small crack propagation life, long crack propagation life, and high-cycle fatigue life are defined for different reliability probabilities in the intake manifold wall region of the cylinder head. Detailed Implementation

[0077] The following is a detailed description of the present invention. Based on the technical solution of the present invention, this embodiment provides a detailed implementation method and operation process with reference to the accompanying drawings.

[0078] Figure 1 This is a flowchart of a high-cycle fatigue life zoning prediction method for cylinder heads based on defect size probability. The following section describes a high-cycle fatigue life zoning prediction method based on defect size probability for a cast aluminum-silicon alloy cylinder head for a diesel engine.

[0079] like Figure 1 As shown in the figure, this embodiment discloses a method for predicting the high-cycle fatigue life of cylinder heads based on defect size probability. The specific implementation steps are as follows:

[0080] Step 1: Based on the simulation results of the cylinder head casting process, the characteristic dimensions of the cast aluminum-silicon alloy, namely the secondary dendrite arm spacing (SDAS) distribution, are obtained. Based on the microstructure-yield strength, the yield strength and degree of difference at different locations of the cylinder head are obtained, as shown in Table 1. The microstructure-yield strength prediction formula is expressed as follows: The expected yield strength of the cast aluminum-silicon alloy is 260 nm, with a critical difference value of 20%. As shown in the table, the yield strength difference between the intake and exhaust manifold walls exceeds the critical value; therefore, these two locations are designated as analysis areas. The following section specifically predicts the high-cycle fatigue life of the cylinder head based on defect size probability within the intake manifold wall region.

[0081] Table 1 Yield strength at different locations in the cylinder head

[0082] SDAS / μm 24 43 22 65 72 Yield strength / MPa 247 216 253 201 194 Difference level / % 5.0 16.9 2.7 22.7 25.4

[0083] Step Two: As Figure 2 Finite element model of the intake manifold wall region of the cylinder head. Figure 3 To extract the pore volume of each sample by performing 3D tomographic reconstruction on several small-sized samples cut in situ from the intake wall, the maximum pore size of each sample was fitted with a normal distribution. The probability density function and cumulative probability density function are as follows: Figure 4 and Figure 5 As shown, the mean and standard deviation of the normal distribution of the maximum pore size in the intake duct wall are 395 μm and 98 μm, respectively.

[0084] Step 3: Calculate the maximum multiaxial stress amplitude at the intake location using the critical section traversal method, such as... Figure 6 The maximum multiaxial stress amplitude distribution of each unit of the cylinder head intake manifold wall is shown, and the maximum multiaxial stress amplitude in this region is 79.3 MPa.

[0085] Step 4: Typical reliability probabilities required in engineering are 90%, 95%, and 99%. Based on the cumulative probability density function fitted in Step 2, the maximum pore size corresponding to the above three reliability probabilities is calculated as shown in Table 2. At the same time, the maximum multiaxial stress amplitude obtained in Step 3 is used as input. Based on the Manson-Coffin type model driven by the maximum plastic shear strain, a partitioned probability crack initiation life model is constructed to calculate the crack initiation life under the three reliability probabilities, as shown in Table 2.

[0086] Table 2 Crack Initiation Life Corresponding to Different Reliability Probabilities in the Inlet Duct Wall Region

[0087] Maximum pore size / μm 522 558 625 Crack initiation lifespan <![CDATA[4.718×10 6 ]]> <![CDATA[2.665×10 6 ]]> <![CDATA[1.342×10 6 ]]>

[0088] Step 5: Using the yield strength of the intake duct wall material obtained in Step 1, the maximum pore size corresponding to the three reliability levels obtained in Step 2, and the maximum multiaxial stress amplitude of the intake duct obtained in Step 3 as inputs, the small crack propagation rate is obtained according to the small crack propagation rate model driven by the cyclic plastic zone size at the crack tip, as shown below. Figure 7 As shown in Table 3, the lower and upper limits of integration corresponding to different reliability probabilities are as shown in Table 3, and the small crack propagation lifetimes corresponding to different reliability probabilities obtained by integration are also shown in Table 3.

[0089] Table 3. Small Crack Propagation Life Corresponding to Different Reliability Probabilities in the Inlet Duct Wall Region

[0090] Lower limit of integration / μm 522 558 625 Upper limit of integration / μm 996 996 996 Small crack propagation lifespan <![CDATA[2.136×10 6 ]]> <![CDATA[1.242×10 6 ]]> <![CDATA[7.24×10 5 ]]>

[0091] Step Six: Using the maximum multiaxial stress amplitude in the intake region obtained in Step Three as input, the long crack propagation rate driven by the effective stress intensity factor is obtained as follows: Figure 7 As shown, the integral yields a corresponding long crack propagation lifetime of 2.52 × 10⁻⁶. 5 .

[0092] Step 7: Based on the crack initiation life of the intake area obtained in Step 4, the small crack propagation life obtained in Step 5, and the long crack propagation life obtained in Step 6, the total high-cycle fatigue life is calculated using an arithmetic summation method as follows: Figure 8 As shown.

Claims

1. A method for predicting the high-cycle fatigue life of cylinder heads based on defect size probability, characterized in that: Includes the following steps, Step 1: Considering the high differences in microstructure and mechanical properties at different locations in the cylinder head, based on the material microstructure characteristic size distribution obtained from the cylinder head casting process simulation results, and using the microstructure-yield strength prediction formula, the yield strength distribution of the material at different locations in the cylinder head is obtained. The obtained yield strength of the material at different locations is also used as the input for the subsequent step 5 to predict the small crack propagation rate of the material at different locations. The critical value of the degree of difference in mechanical characteristics of the cylinder head structural material is determined according to engineering requirements. The difference between the yield strength and the expected yield strength of the cylinder head at different locations is calculated according to the formula for calculating the difference in yield strength. When the difference at a certain location is greater than the critical value of the difference, that location is divided into a new analysis area, thereby obtaining several analysis areas at different locations of the cylinder head. Step 2: Several small-sized samples are cut in situ from each analysis region divided in Step 1 and reconstructed using three-dimensional tomographic scanning to extract the pore volume of each sample. Based on the three-dimensional equivalent size calculation method, the pore size of each sample is obtained, and the sizes are compared to obtain the maximum pore size of each sample. The probability distribution of the maximum pore size of all samples in each analysis region is fitted to obtain the probability density function and cumulative probability density function of the maximum pore size of each analysis region. The maximum pore size value corresponding to different reliability probabilities in each region is obtained from the inverse function of the cumulative probability density function of the maximum pore size in each analysis region. This value is used as the input for predicting the fatigue crack initiation pore size corresponding to different reliability levels in Step 4, and also as the lower limit input for the integral of the small crack propagation rate in different regions in Step 5. Step 3: Calculate the maximum multiaxial stress amplitude of each region using the dangerous section traversal method; first, extract the stress tensor of the finite element before and after the application of the burst pressure load step from the finite element calculation results of the cylinder head assembly structure, and calculate the stress amplitude tensor and average stress tensor of each element using the stress calculation formula; then, determine all sections to be calculated using the traversal method. Any cross-sectional direction is determined by two angular coordinates ( Within a 180° range, with a preset fixed angle δ as the rotation step, the coordinates in two directions are rotated respectively. Each direction is divided into 180° / δ angle values. Each rotation determines a section to be calculated. Then, the amplitude and average value of the normal stress of the section are calculated using the normal stress calculation formula, the amplitude and average value of the shear stress of the section are calculated using the shear stress calculation formula, and the amplitude and average value of the equivalent stress of the section are calculated using the modified maximum shear strain energy criterion. To address the complex structure and large number of finite element elements in cylinder head assemblies, a simple Gerber-type multiaxial stress amplitude calculation model suitable for large-scale traversal calculations is constructed. This Gerber-type multiaxial stress amplitude solution model is used to solve for the multiaxial stress amplitude of each cross-section, improving the efficiency of traversing critical multiaxial cross-sections. Then, the multiaxial stress amplitudes of all cross-sections of each finite element are compared, and the maximum value is taken as the maximum multiaxial stress amplitude of that element. Finally, the maximum multiaxial stress amplitudes of all finite element elements in each analysis region are compared, and the maximum value is taken as the maximum multiaxial stress amplitude of that region. Step 4: Using the maximum pore size corresponding to different reliability levels obtained in Step 2 and the maximum multiaxial stress amplitude of each partition region obtained in Step 3 as inputs, construct a partitioned probabilistic crack initiation life model by combining the Manson-Coffin model driven by the maximum plastic shear strain. The partitioned probabilistic crack initiation life model can characterize the distribution characteristics of pore defects in different regions of the cylinder head and the influence of the multiaxial characteristics of the cylinder head high-cycle fatigue load on the high-cycle fatigue crack initiation life. It is applicable to life prediction under different engineering reliability requirements. Based on the partitioned probabilistic crack initiation life model, predict the fatigue crack initiation life corresponding to different reliability probabilities, thereby improving the prediction accuracy of high-cycle fatigue crack initiation life probability prediction. Step 5: Using the yield strength of the cylinder head material in different regions obtained in Step 1, the maximum pore size corresponding to different reliability levels obtained in Step 2, and the maximum multiaxial stress amplitude of each region obtained in Step 3 as inputs, a small crack propagation rate model driven by the cyclic plastic zone size at the crack tip is obtained. The critical crack size is calculated using the small crack propagation rate model and the long crack propagation rate model in Step 6. The critical crack size is the crack size corresponding to the equality of the small crack propagation rate and the long crack propagation rate. The small crack propagation life corresponding to different reliability probabilities is obtained by integrating the small crack propagation rate model driven by the cyclic plastic zone size at the crack tip using an integral method. The lower limit of integration is the maximum pore size corresponding to different reliability probabilities determined in step two, and the upper limit of integration is the critical crack size. The small crack propagation rate model can characterize the influence of the distribution characteristics of pore defects in different regions of the cylinder head and the dispersion characteristics of the material mechanical properties in different regions of the cylinder head on the high-cycle fatigue small crack propagation rate and life. Based on the small crack propagation rate model, the prediction accuracy of the high-cycle fatigue small crack propagation life of materials in different locations of the cylinder head can be improved. Step 6: Using the maximum multiaxial stress amplitude of each region obtained in Step 3 as input, a long crack propagation rate model driven by the effective stress intensity factor is obtained; based on the long crack propagation rate model and the critical crack size obtained in Step 5, the long crack propagation life is obtained by integrating the long crack propagation rate model using the integration method. The lower limit of integration is the critical crack size obtained in step five, and the upper limit of integration is defined according to the actual failure criterion requirements. Step 7: Based on the crack initiation life obtained in Step 4, the small crack propagation life obtained in Step 5, and the long crack propagation life obtained in Step 6, the total high-cycle fatigue life is calculated by arithmetic summation, thus realizing the zonal prediction of cylinder head high-cycle fatigue life based on defect size probability.

2. The method for predicting high-cycle fatigue life of cylinder heads based on defect size probability as described in claim 1, characterized in that: It also includes step eight, which applies the processes of steps one to seven to the high-cycle fatigue life prediction of internal combustion engine cylinder heads with different materials and under different operating conditions, and applies them to the life prediction of different reliability requirements. Based on the prediction results, the materials and structures of different positions of the cylinder head are improved and optimized to improve the overall fatigue strength of the cylinder head and reduce material design redundancy.

3. A method for predicting high-cycle fatigue life of cylinder heads based on defect size probability as described in claim 1 or 2, characterized in that: The implementation method for step one is as follows: Step 1.1: Based on the material microstructure characteristic size distribution obtained from the simulation results of the cylinder head casting process, the yield strength distribution of the material at different locations of the cylinder head is obtained based on the microstructure-yield strength prediction formula; the yield strength of the material at different locations is also used as the input for the subsequent step five to predict the small crack propagation rate of the material at different locations. The microstructure-yield strength prediction formula is expressed as: in, For the material's yield strength, denoted as the characteristic size of the material's microstructure, and a, b, and c are the fitting parameters of the formula; Step 1.2: Calculate the difference between the yield strength at different locations of the cylinder head and the expected yield strength of the material. When the difference at a certain location is greater than the critical value of the difference, then that location is divided into a new analysis area, thereby obtaining several analysis areas at different locations of the cylinder head. The formula for calculating the degree of yield strength difference is: in, The degree of difference in yield strength at position i. Let i be the yield strength value of the material at position i. This represents the expected yield strength of the material.

4. The method for predicting high-cycle fatigue life of cylinder heads based on defect size probability as described in claim 3, characterized in that: The second step is implemented as follows: Step 2.1: Take several small-sized samples from each analysis area divided in Step 1 in situ and perform three-dimensional tomographic reconstruction to extract the pore volume of each sample. Based on the three-dimensional equivalent size calculation method, obtain the pore size of each sample and compare the sizes to obtain the maximum pore size of each sample. The formula for calculating the three-dimensional equivalent size of pores is: in, and These are pore size and pore volume, respectively. Step 2.2: Fit the probability distribution of the maximum pore size of all samples in each analysis region obtained in Step 2.1 to obtain the probability density function and cumulative probability density function of the maximum pore size in each analysis region; the probability distribution function is a normal distribution and a Gumbel distribution. Step 2.3: Obtain the maximum pore size value corresponding to different reliability probabilities in each region based on the inverse function of the cumulative probability density function of the maximum pore size in each analysis region. This value serves as the input for the subsequent step four, which aims to predict the fatigue crack initiation pore size corresponding to different reliability levels. It also serves as the lower limit input for the integral of the small crack propagation rate in different regions in the subsequent step five.

5. The method for predicting high-cycle fatigue life of cylinder heads based on defect size probability as described in claim 4, characterized in that: The method for implementing step three is as follows: Step 3.1: Extract the stress tensor of the finite element before and after the application of the burst load step from the finite element calculation results of the cylinder head assembly structure. The stress amplitude tensor of each element is calculated using the stress calculation formula. and mean stress tensor ; Step 3.2: Determine all sections to be calculated using a traversal method; the direction of any section is determined by two angular coordinates ( Within a 180° range, with a preset fixed angle δ as the rotation step, the coordinates are rotated in two directions respectively. Each direction is divided into 180° / δ angle values. Each rotation determines one cross section to be calculated, for a total of... One cross section; Step 3.3: Calculate the multiaxial stress amplitude of all sections of each finite element element. The calculation method for the multiaxial stress amplitude of each section is as follows: First, calculate the amplitude of the normal stress at this cross section. and average value : Then calculate the shear stress amplitude of that section. and average : The equivalent stress amplitude of the cross section was calculated using the modified maximum shear strain energy criterion. and average : in, and These are the material's tensile fatigue limit and tensile yield strength, respectively. and These are the material's shear fatigue limit and shear yield strength, respectively. To address the complex structure and large number of finite element elements in cylinder head assemblies, a simple Gerber-type multiaxial stress amplitude calculation model suitable for large-scale traversal calculations is constructed. This Gerber-type multiaxial stress amplitude solution model is then used to traverse and solve for the multiaxial stress amplitude of all sections of each element. This improves the efficiency of traversing multiaxial critical sections; the multiaxial stress amplitude of the section is calculated using Gerber-type formulas. : in, It is the ultimate tensile strength of the material; Step 3.4: Compare the multiaxial stress amplitudes of all sections of each finite element element, and take the maximum value as the maximum multiaxial stress amplitude of that element. Compare the maximum multiaxial stress amplitudes of all finite element elements in each analysis region, and take the maximum value as the maximum multiaxial stress amplitude for that region. .

6. The method for predicting high-cycle fatigue life of cylinder heads based on defect size probability as described in claim 5, characterized in that: In step four, The probabilistic crack initiation life model is based on the Manson-Coffin formula, which is determined by the maximum plastic shear strain around the pores. As the driving independent variable, the crack initiation lifetime model is expressed as: in, Lifespan for crack initiation, and These are inherent parameters of the material; and These represent the maximum pore size and the maximum multiaxial stress amplitude corresponding to different reliability probabilities in steps two and three, respectively; and the maximum plastic shear strain. The solution is obtained through simulation calculation using a two-dimensional representative finite element model containing pore size.

7. The method for predicting high-cycle fatigue life of cylinder heads based on defect size probability as described in claim 6, characterized in that: Step five is implemented as follows: Step 5.1: Using the yield strength of the cylinder head material in different regions obtained in Step 1, the maximum pore size corresponding to different reliability levels obtained in Step 2, and the maximum multiaxial stress amplitude of each zone obtained in Step 3 as inputs, a small crack propagation rate model driven by the size of the cyclic plastic zone at the crack tip is obtained: in, It is the rate of small crack propagation. and Define parameters for the model; By material yield strength Elastic modulus Maximum value of multiaxial stress amplitude and crack size calculate; Step 5.2: Calculate the critical crack size using the small crack propagation rate model and the long crack propagation rate model in subsequent step six. Critical crack size This represents the crack size when the small crack propagation rate and the long crack propagation rate are equal. Step 5.3: Integrate the small crack propagation rate model driven by the cyclic plastic zone size at the crack tip using the integration method to obtain the small crack propagation lifetime corresponding to different reliability probabilities, as shown in the equation; the lower limit of integration is the maximum pore size corresponding to different reliability probabilities determined in Step 2. The upper limit of integration is the critical crack size. ; 。 8. The method for predicting high-cycle fatigue life of cylinder heads based on defect size probability as described in claim 7, characterized in that: In step six, The long crack propagation rate model and the long crack propagation life are expressed as follows: in, It is the rate of long crack propagation. and Parameters related to the propagation of long cracks in materials were determined. It is the effective stress intensity factor of the crack.

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