A method for modeling residual strength of a composite laminate

Abstract

The application discloses a kind of composite material laminate residual strength modeling methods, the method comprises the following steps: obtaining the residual strength test data of test piece of different damage degree;According to the damage degree and residual strength test data of each test piece, determine residual strength calculation parameter and equivalent undamaged residual strength;According to residual strength calculation parameter and equivalent undamaged residual strength, construct the relationship of residual strength and damage degree as residual strength calculation model;Wherein, residual strength calculation model is: ε=ε unc ·(1+α·L) ‑β ;ε is residual strength, L is the damage size of piece to be measured, α and β are first calculation parameter and second calculation parameter respectively, ε unc Equivalent undamaged residual strength is used.The above scheme is used, and the calculation result of residual strength is closer to the real situation, and the deviation caused by the strain singularity of residual strength calculation model is reduced;Model is relatively simple, and the calculation step is less, and the requirement to technical personnel is lower, and it is suitable for general structure design and strength analysis.

Description

Technical Field

[0001] This invention relates to the field of mathematical models for residual strength of composite material structures, and more particularly to a method for modeling the residual strength of composite laminates. Background Technology

[0002] Penetration damage is a common form of damage in composite material structure design. Technicians usually use refined finite element methods and simplified engineering calculation methods. However, the modeling process of refined finite element calculation methods is complex, the damage evolution calculation cycle based on fracture mechanics is long and not easy to converge, and it also has high requirements for operators. Therefore, its application among engineering technicians is limited. At present, simplified engineering calculation methods are usually the main ones used in engineering applications.

[0003] Simplified engineering calculation methods typically involve simplifying the damage shape, such as reducing it to an ideal circle or ellipse, to find an analytical solution, or establishing an empirical mathematical model based on experimental data. However, analytical solutions are extremely complex; the analytical solution for an elliptical notch involves solving a large number of complex variables, requiring computer programming for computation. This is acceptable for engineers specializing in strength or damage tolerance analysis, but poses a significant challenge for general structural designers. When calculating the residual strength of composite structures, empirical mathematical models based on experimental data, such as the Mar-Lin model, are most commonly used. However, the Mar-Lin model is a negative exponential model. When the penetrating notch length or the diameter of the circular hole is small, the calculated allowable strain will exhibit singularities, resulting in unsatisfactory results. Furthermore, the fitting parameters of the Mar-Lin model must be obtained by combining experimental data with larger-sized damage; fitting Mar-Lin model parameters using experimental data with small-sized damage will produce non-conservative calculation results. Therefore, the application of the Mar-Lin model also has certain limitations. Summary of the Invention

[0004] This invention provides a method for modeling the residual strength of composite laminates to overcome the limitations of existing residual strength models for composite laminates with penetrating damage.

[0005] According to one aspect of the present invention, a method for modeling the residual strength of composite laminates is provided, comprising:

[0006] Obtain residual strength test data for specimens with different degrees of damage;

[0007] Based on the degree of damage to each test piece and the remaining strength test data, the remaining strength calculation parameters and the equivalent undamaged remaining strength are determined.

[0008] Based on the remaining strength calculation parameters and the equivalent undamaged remaining strength, a relationship between the remaining strength and the degree of damage is constructed as a remaining strength calculation model.

[0009] Optionally, the residual strength calculation model is: ε = ε unc ·(1+α·L) -β ε represents the residual strength, L represents the damage size of the test piece, and α and β are the first and second calculation parameters for the residual strength calculation, respectively. unc This is the equivalent undamaged residual strength.

[0010] Optionally, the residual strength calculation parameters include a first calculation parameter α and a second calculation parameter β. Based on the damage degree of each test piece and the residual strength test data, the residual strength calculation parameters and the equivalent undamaged residual strength are determined, including:

[0011] The second calculation parameter β is determined by the first calculation formula;

[0012] The first calculation parameter α is determined by the second calculation formula;

[0013] The first calculation formula is: β=(lnε all,a -lnε all,b ) / (lnL b -lnL a The second calculation formula is: α=((ε) UNC / ε all,a ) 1 / β -1) / L a ;ε all,a The residual strength corresponding to the test specimen with the first degree of damage; ε all,b The residual strength corresponding to the test specimen with the second degree of damage; L a The damage size of the test specimen with the first degree of damage; L b The damage size of the test specimen with the second degree of damage; ε UNC The undamaged residual strength is the residual strength corresponding to the specimen with a damage size of 0.

[0014] Optionally, the test specimens with different damage degrees include m types of test specimens with different damage degrees; the number of test specimens for each damage degree is n; m≥3, and m is an integer; n≥3, and n is an integer;

[0015] Among them, the residual strength ε corresponding to the test piece with the first degree of damage all,a The average residual strength of n test specimens with the first degree of damage;

[0016] The residual strength ε corresponding to the test piece with the second degree of damage all,b It is the average residual strength of n test specimens with the second degree of damage;

[0017] Undamaged residual strength ε UNC It is the average of the residual strength of the n test specimens with a damage size of 0.

[0018] Optionally, determining the remaining strength test data and the equivalent undamaged remaining strength based on the damage degree of each test piece and the remaining strength test data further includes:

[0019] The equivalent undamaged residual strength ε is determined using the third calculation formula. unc ;

[0020] The third calculation formula is: ε unc,ij =ε all,ij ·(1+α·L i ) β , ε unc,ij L represents the residual strength of the j-th test specimen under theoretical conditions when the damage size is 0, representing the i-th damage level. i Let ε be the damage size of the test specimen for the i-th damage level, 1≤i≤m, where m is an integer, 1≤j≤n, where m is an integer, and ε unc,ij >0.

[0021] Optionally, based on the residual strength calculation model, the equivalent undamaged residual strength ε of each of the test specimens is calculated. unc,x ;ε unc,x Let N be the equivalent undamaged residual strength of the x-th test specimen, 1≤x≤N, where N is the total number of test specimens and N is an integer;

[0022] Based on the normal distribution model and the maximum likelihood estimation method, the equivalent undamaged residual strength ε of each test specimen is determined. unc,x The standard deviation σ;

[0023] Based on the LM iterative method, the residual strength calculation parameters of the residual strength calculation model are redefined. Then, based on these redefined parameters, the equivalent undamaged residual strength ε of each test specimen is determined using a normal distribution model and maximum likelihood estimation. unc,x The standard deviation σ;

[0024] Determine whether the difference between the current standard deviation σ and the previously determined standard deviation σ is within a preset range;

[0025] If so, the redefined residual strength calculation parameters will be used as the residual strength calculation parameters of the residual strength calculation model.

[0026] If not, then return to the LM iteration method to redetermine the residual strength calculation parameters of the residual strength calculation model. Based on the redetermined residual strength calculation parameters, determine the equivalent undamaged residual strength ε of each of the test specimens by fitting a normal distribution model and the maximum likelihood estimation method. unc,x The steps for determining the standard deviation σ.

[0027] Optionally, based on the residual strength calculation model, the equivalent undamaged residual strength ε of each of the test specimens is calculated. unc,x ;ε unc,x Let N be the equivalent undamaged residual strength of the x-th test specimen, 1≤x≤N, where N is the total number of test specimens and N is an integer;

[0028] Based on the normal distribution model and the maximum likelihood estimation method, the equivalent undamaged residual strength ε of each test specimen is determined. unc,x The standard deviation σ;

[0029] Based on the LM iterative method, the residual strength calculation parameters of the residual strength calculation model are redefined. Then, based on these redefined parameters, the equivalent undamaged residual strength ε of each test specimen is determined using a normal distribution model and maximum likelihood estimation. unc,x The standard deviation σ;

[0030] Determine whether the number of times the residual strength calculation parameters of the residual strength calculation model are re-determined based on the LM iteration method has reached the preset number;

[0031] If so, the redefined residual strength calculation parameters will be used as the residual strength calculation parameters of the residual strength calculation model.

[0032] If not, return to the step of redetermining the residual strength calculation parameters of the residual strength calculation model based on the LM iteration method, and determining the standard deviation σ of the equivalent undamaged residual strength ε_(unc,x) of each test specimen based on the redefined residual strength calculation parameters, fitting the model with a normal distribution and the maximum likelihood estimation method.

[0033] Optionally, the B-benchmark reduction factor can be determined using the fourth calculation formula;

[0034] The B-benchmark reduction factor is used as the model coefficient of the residual strength calculation model;

[0035] The fourth calculation formula is: B = 1 - kB·s;

[0036] B is the B benchmark reduction factor;

[0037] The equivalent undamaged residual strength ε of each of the test specimens with N-1 degrees of freedom. unc,x p-quantiles of non-central t-distribution, ε unc,x Let x be the equivalent undamaged residual strength of the x-th test specimen, 1 ≤ x ≤ N, where N is the total number of test specimens and N is an integer. For non-central parameters, zB represents the equivalent undamaged residual strength ε of each test specimen. unc,x The q quantiles of the standard normal distribution;

[0038]

[0039] The technical solution of this invention determines the residual strength calculation parameters and the equivalent undamaged residual strength based on the damage degree and residual strength test data of each test piece. It then combines the residual strength with the corresponding data on damage degree to obtain the residual strength calculation parameters, making the calculated residual strength results closer to reality. Based on the residual strength calculation parameters and the equivalent undamaged residual strength, a relationship between residual strength and damage degree is constructed. The calculation of residual strength uses the equivalent undamaged residual strength as an intermediate parameter, which can reduce the deviation caused by strain singularities in the residual strength calculation model. Furthermore, this residual strength calculation model is relatively simple in form, has few calculation steps, and requires less expertise from technical personnel, making it well-suited for general structural design and strength analysis.

[0040] It should be understood that the description in this section is not intended to identify key or essential features of the embodiments of the present invention, nor is it intended to limit the scope of the invention. Other features of the invention will become readily apparent from the following description. Attached Figure Description

[0041] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0042] Figure 1 A flowchart of a residual strength modeling method is provided in Embodiment 1 of the present invention;

[0043] Figure 2 This is a flowchart of a residual strength modeling method provided in Embodiment 2 of the present invention;

[0044] Figure 3 This is a flowchart of a residual strength modeling method provided in Embodiment 3 of the present invention;

[0045] Figure 4This is a flowchart of a residual strength modeling method provided in Embodiment 4 of the present invention;

[0046] Figure 5 This is a flowchart of a residual strength modeling method provided in Embodiment 5 of the present invention;

[0047] Figure 6 A flowchart of a residual strength modeling method provided in Embodiment Six of the present invention.

[0048] Figure 7 A residual strength calculation model curve is provided for an embodiment of the present invention. Detailed Implementation

[0049] To enable those skilled in the art to better understand the present invention, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of the present invention.

[0050] It should be noted that the terms "first," "second," etc., in the specification, claims, and accompanying drawings of this invention are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate so that the embodiments of the invention described herein can be implemented in orders other than those illustrated or described herein. Furthermore, the terms "comprising" and "having," and any variations thereof, are intended to cover a non-exclusive inclusion; for example, a process, method, system, product, or apparatus that comprises a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or apparatus.

[0051] Example 1

[0052] Figure 1 This is a flowchart illustrating a method for modeling the residual strength of composite laminates according to Embodiment 1 of the present invention. This embodiment is applicable to calculating the residual strength of composite laminates with penetrating damage. This method can be executed by a residual strength modeling device, which can be implemented in hardware and / or software. Figure 1 As shown, the method includes:

[0053] S110. Obtain residual strength test data for test specimens with different degrees of damage.

[0054] The degree of damage includes damage size, damage area, and damage volume. The degree of damage can be determined using data such as damage size, damage area, and damage volume. Damage size can be parameters such as the length of a cut or the diameter of a circular hole. Residual strength refers to the maximum load-bearing capacity of a damaged structure, which is also the maximum stress value (allowable strain) that a part or component can withstand. Since damage often occurs during the manufacturing or service of engineering structures, the actual maximum load-bearing capacity of an engineering structure often depends on its residual strength. The residual strength test data for test specimens with different degrees of damage refers to the residual strength data of test specimens with different degrees of damage (including no damage). For example, the residual strength data of test specimens can be obtained using a material stress testing machine, residual stress analyzer, etc. This embodiment of the invention does not specifically limit how to obtain the residual strength test data of test specimens with different degrees of damage.

[0055] S120. Based on the damage degree and residual strength test data of each test piece, determine the residual strength calculation parameters and the equivalent undamaged residual strength.

[0056] The residual strength calculation parameter refers to the calculation parameter used when calculating the residual strength. This parameter is related to the material properties of the test specimen but independent of the degree of damage. It is a relatively fixed constant. It should be noted that the residual strength calculation parameter includes at least one parameter, but is not limited to one. The equivalent undamaged residual strength refers to the residual strength of a damaged test specimen obtained after calculation, under theoretically undamaged conditions. This equivalent undamaged residual strength is also a calculation parameter used when calculating the residual strength. It is related to the material properties of the test specimen but independent of the degree of damage.

[0057] S130. Based on the residual strength calculation parameters and the equivalent undamaged residual strength, construct the relationship between residual strength and damage degree as the residual strength calculation model.

[0058] The residual strength calculation model is: ε=ε unc ·(1+α·L) -β ε represents the residual strength, L represents the damage size of the test specimen, the material and structure of the test specimen are the same as those of the test specimen, α and β are the first and second calculation parameters of the residual strength calculation parameters, respectively. unc The equivalent undamaged residual strength is the residual strength when the damage size of the test specimen is assumed to be 0.

[0059] Specifically, residual strength is negatively correlated with the degree of damage and positively correlated with the equivalent undamaged residual strength. Based on the residual strength test data of test pieces with different degrees of damage, there is a specific relationship between residual strength, degree of damage, equivalent undamaged residual strength, and residual strength calculation parameters, which is the relationship between residual strength and degree of damage.

[0060] For example, by performing curve fitting on the residual strength test data of test specimens with different degrees of damage, the residual strength ε can be obtained with respect to the damage size L of the test specimen and the equivalent undamaged residual strength ε. unc The curve, i.e., ε = ε unc ·(1+α·L) -β .

[0061] For example, firstly, several test specimens with different degrees of damage are prepared. These test specimens are identical in material, size, and structure. The degree of damage and residual strength of each test specimen are obtained by calculation and / or measurement, resulting in multiple data pairs regarding residual strength and degree of damage. The equivalent undamaged residual strength is calculated based on the data pairs of residual strength and degree of damage of the test specimens. Curve fitting is performed on the residual strength test data of test specimens with different degrees of damage to obtain the residual strength ε with respect to the damage size L of the test specimen and the equivalent undamaged residual strength ε. unc The curve, i.e., the residual strength calculation model ε=ε unc ·(1+α·L) -β .

[0062] In this embodiment of the invention, by determining the residual strength calculation parameters and the equivalent undamaged residual strength based on the damage degree and residual strength test data of each test piece, and combining the residual strength with the data corresponding to the damage degree to obtain the residual strength calculation parameters, the calculation results of the residual strength are closer to the actual situation. Based on the residual strength calculation parameters and the equivalent undamaged residual strength, a relationship between the residual strength and the damage degree is constructed. The calculation of the residual strength uses the equivalent undamaged residual strength as an intermediate parameter, which can reduce the deviation caused by the strain singularity of the residual strength calculation model. Moreover, the residual strength calculation model is relatively simple in form, has few calculation steps, and requires less technical personnel, making it well applicable to general structural design and strength analysis.

[0063] Example 2

[0064] Figure 2 This is a flowchart of a method for modeling the residual strength of a composite laminate according to Embodiment 2 of the present invention. Compared with the above embodiments, this embodiment refines the details regarding how to determine the first calculation parameter α and the second calculation parameter β. Figure 2 As shown, the method includes:

[0065] S210. Obtain residual strength test data for test specimens with different degrees of damage.

[0066] S220. Determine the second calculation parameter β using the first calculation formula.

[0067] S230. Determine the first calculation parameter α using the second calculation formula.

[0068] S240. Based on the damage level and residual strength test data of each test piece, the equivalent undamaged residual strength is obtained.

[0069] S250. Based on the residual strength calculation parameters and the equivalent undamaged residual strength, construct the relationship between residual strength and damage degree as the residual strength calculation model.

[0070] The first calculation formula is: β=(lnε all,a -lnε all,b ) / (lnL b -lnL a The second calculation formula is: α=((ε) UNC / ε all,a ) 1 / β -1) / L a ;ε all,a The residual strength corresponding to the test specimen with the first degree of damage; ε all,b The residual strength corresponding to the test specimen with the second degree of damage; L a The damage size of the test specimen with the first degree of damage; L b The damage size of the test specimen with the second degree of damage; ε UNC The undamaged residual strength is the residual strength corresponding to the specimen with a damage size of 0.

[0071] For example, the first degree of damage can be the minimum degree of damage, and the second degree of damage can be the maximum degree of damage. The magnitude of the damage can be represented by the damage size. First, several test specimens with different degrees of damage are prepared. These test specimens are identical in material, size, and structure. The degree of damage and residual strength of each test specimen are obtained by calculation and / or measurement. Then, the first and second calculation parameters for calculating the residual strength can be obtained using the first and second calculation formulas. Based on the obtained first and second calculation parameters, the residual strength ε with respect to the damage size L of the test specimen and the equivalent undamaged residual strength ε can be obtained. unc By finding the curve and its coordinates, the specific residual strength calculation model ε=ε can be obtained. unc ·(1+α·L) -βIt is understandable that the residual strength of a test specimen with any damage size can be calculated using the strength calculation model. It should be noted that the test specimen with the minimum damage level does not include specimens with a damage size of 0; however, specimens with a damage size of 0 can be included when obtaining test specimens with different damage levels.

[0072] Optionally, the test specimens with different damage levels include m types of damage levels; the number of test specimens for each damage level is n; m ≥ 3, and m is an integer; n ≥ 6, and n is an integer. For example, residual strength test data for m groups of test specimens are obtained, each group including n test specimens, and the damage level of the test specimens in each group is the same, i.e., the damage size of the test specimens in the same group is the same. Obtaining residual strength test data for m groups of test specimens is equivalent to obtaining residual strength test data for test specimens with m types of damage, and for each type of damage, residual strength test data is obtained n times (obtaining residual strength test data for the n test specimens in each group).

[0073] Optionally, when determining the first calculation parameter α and the second calculation parameter β, the residual strength ε corresponding to the test piece with the first degree of damage is... all,a The residual strength is the average of n test specimens with the first degree of damage; the residual strength ε of the test specimen with the second degree of damage is... all,b The average residual strength of n test specimens with the second degree of damage; the residual strength ε without damage. UNC This is the average residual strength of the n test specimens with a damage size of 0. Thus, by obtaining residual strength test data n more times for each damage level of the test specimens, the randomness of the residual strength test data can be reduced, errors can be decreased, and the accuracy of the residual strength calculation parameters, equivalent undamaged residual strength, and residual strength calculation model obtained in subsequent steps can be improved.

[0074] For example, taking X850 / IM+ composite laminate as an example, this residual strength modeling method is illustrated, where the layup ratio of the test specimens is [45 / 0 / -45 / 90]. 3S The test specimens included five damage levels (one of which was no damage, i.e., damage size of 0). Six specimens were produced for each damage level, and each damage level contained six duplicate specimens, resulting in six sets of residual strength data. The residual strength test data for the specimens with different damage levels are shown in Table 1.

[0075] Table 1. Residual strength test data of specimens with different damage levels.

[0076]

[0077]

[0078] The damage size L of the test specimen with the least damage a =6.35mm, the residual strength corresponding to the test specimen with the least damage. The damage size L of the test specimen with the greatest degree of damage b =50mm, the residual strength corresponding to the test piece with the greatest degree of damage Undamaged residual strength At this point, the first calculation parameter α and the second calculation parameter β are respectively:

[0079] β=(lnε all,a -lnε all,b ) / (lnL b -lnL a )

[0080] =(ln5109-ln3011) / (ln50-ln6.35)≈0.26

[0081] α=((ε UNC / ε all,a ) 1 / β -1) / L a

[0082] =((9980 / 5109) 1 / 0.26 -1) / 6.35≈2

[0083] At this point, the constructed residual strength calculation model is: ε=ε unc ·(1+2·L) -0.26 .

[0084] Example 3

[0085] Figure 3 This is a flowchart of a method for modeling the residual strength of a composite laminate according to Embodiment 3 of the present invention. Compared with the above embodiments, this embodiment refines the content on how to determine the equivalent undamaged residual strength portion. Figure 3 As shown, the method includes:

[0086] S310. Obtain residual strength test data for test specimens with different degrees of damage.

[0087] S320. Determine the second calculation parameter β using the first calculation formula.

[0088] S330. Determine the first calculation parameter α using the second calculation formula.

[0089] S340. Determine the equivalent undamaged residual strength ε using the third calculation formula. unc .

[0090] S350. Based on the residual strength calculation parameters and the equivalent undamaged residual strength, construct the relationship between residual strength and damage degree as the residual strength calculation model.

[0091] The third calculation formula is: ε unc,ij =ε all,ij ·(1+α·L i ) β , ε unc,ij L represents the residual strength of the j-th test specimen under theoretical conditions when the damage size is 0, representing the damage level of the i-th damage condition. i Let ε be the damage size of the test specimen for the i-th damage level, 1≤i≤m, where m is an integer, 1≤j≤n, where n is an integer, and ε unc,ij >0.

[0092] For example, taking the residual strength test data of test specimens with different damage degrees as an example, the damage size L of the test specimen with the smallest damage degree is... a =6.35mm, the residual strength ε corresponding to the specimen with the least damage. all,a ≈5109, the damage size L of the test piece with the greatest degree of damage. b =50mm, the residual strength ε corresponding to the test piece with the greatest damage. all,b ≈3011, according to the first formula β=(lnε all,a -lnε all,b ) / (lnL b -lnL a The second calculation parameter β≈0.26 was determined; then, the undamaged residual strength ε was determined by averaging the residual strengths of the six specimens with damage size 0. UNC ≈9980.5; calculated using the second formula α=((ε) UNC / ε all,a ) 1 / β -1) / L a The first calculation parameter was determined to be α≈2; based on the residual strength test data of 30 test specimens (L... i , ε unc,ij The first calculation parameter α and the second calculation parameter β are used to calculate the third calculation formula ε. unc,ij =ε all,ij ·(1+α·L i ) β =ε all,ij ·(1+2·L i ) 0.26 Determine the equivalent undamaged residual strength ε of 30 test specimens unc,ij The equivalent undamaged residual strength data of test specimens with different degrees of damage are shown in Table 2:

[0093] Table 2. Equivalent undamaged residual strength data of test specimens with different damage levels.

[0094]

[0095] Equivalent undamaged residual strength of the test specimen By obtaining the equivalent undamaged residual strength data ε of all test specimens unc,ij Then, the equivalent undamaged residual strength ε of the test specimen is determined by averaging the values. unc This allows for obtaining a more accurate equivalent undamaged residual strength ε. unc This makes the calculation results of residual strength more accurate and can reflect the true relationship between residual strength and damage degree.

[0096] For example, the damage size L of the test piece with the known minimum damage level. a =6.35mm, the residual strength ε corresponding to the specimen with the least damage. all,a ≈5109, the damage size L of the test piece with the greatest degree of damage. b =50mm, the residual strength ε corresponding to the test piece with the greatest damage. all,b When ≈3011, and the second calculation parameter β≈0.26; assuming initial ε UNC =ε unc,ij It can be calculated using the second formula α=((ε) UNC / 5109) 1 / 0.26 -1) / 6.35 and the third calculation formula ε unc,ij =ε all,ij ·(1+α·L i ) 0.26 Determine ε unc,ij ;final (actual situation ε) UNC and ε unc They are also approximately equal); α can be calculated using the second formula α=((ε) UNC / ε all,a ) 1 / β -1) / L a Sure.

[0097] Example 4

[0098] Figure 4 This is a flowchart of a method for modeling the residual strength of a composite laminate according to Embodiment 4 of the present invention. Compared with the above embodiments, this embodiment further estimates (or optimizes) the residual strength calculation parameters of the residual strength calculation model. Figure 4 As shown, the method includes:

[0099] S410. Obtain residual strength test data for test specimens with different degrees of damage.

[0100] S420. Based on the damage degree and residual strength test data of each test piece, determine the residual strength calculation parameters and the equivalent undamaged residual strength.

[0101] S430. Based on the residual strength calculation parameters and the equivalent undamaged residual strength, construct the relationship between residual strength and damage degree as the residual strength calculation model.

[0102] S440. Based on the residual strength calculation model, calculate the equivalent undamaged residual strength ε of each test specimen. unc,x .

[0103] Where, ε unc,x Let N be the equivalent undamaged residual strength of the x-th test specimen, 1≤x≤N, where N is the total number of test specimens and N is an integer.

[0104] S450. Based on the normal distribution model and the maximum likelihood estimation method, determine the equivalent undamaged residual strength ε of each test piece. unc,x The standard deviation σ.

[0105] S460. Based on the LM iterative method, redetermine the residual strength calculation parameters of the residual strength calculation model. Based on the redetermined residual strength calculation parameters, determine the equivalent undamaged residual strength ε of each test piece by fitting the normal distribution model and the maximum likelihood estimation method. unc,x The standard deviation σ.

[0106] S470. Determine whether the difference between the current standard deviation σ and the previously determined standard deviation σ is within the preset range. If yes, proceed to S480; otherwise, return to S460.

[0107] S480. The redefined residual strength calculation parameters are used as the residual strength calculation parameters of the residual strength calculation model.

[0108] For example, by acquiring residual strength test data of test specimens with different damage degrees, the initial residual strength calculation parameters and the initial equivalent undamaged residual strength can be obtained based on the damage degree and residual strength test data of each test specimen. Based on the initial residual strength calculation parameters, the initial equivalent undamaged residual strength, the damage size of each test specimen, and the residual strength calculation model, the initial equivalent undamaged residual strength distribution of each test specimen can be determined, thus determining the initial equivalent undamaged residual strength ε of each test specimen. unc,x Then, based on the normal distribution model and the maximum likelihood estimation method, the equivalent undamaged residual strength ε is fitted. unc,x The fitting process can be edited and calculated using professional statistical software (such as Origin). After fitting, the equivalent undamaged residual strength ε of each test specimen can be obtained. unc,xThe standard deviation σ is used to obtain new residual strength calculation parameters using the Levenberg-Marquardt (LM) iterative algorithm. After fitting, the equivalent undamaged residual strength ε of each specimen after the iteration can be obtained. unc,x And its standard deviation σ, calculate the difference between the currently determined standard deviation σ and the previously determined standard deviation σ, and determine whether the difference is within the preset range. Assume the preset range can be [-10]. -9 10 -9 If the difference is within the preset range, it is considered that the residual strength calculation model obtained based on the current residual strength calculation parameters can realistically reflect the relationship between the actual residual strength and damage size, and the current residual strength calculation parameters and the theoretical undamaged residual strength are the best estimates. If the difference is not within the preset range, it is considered that the residual strength calculation model obtained based on the current residual strength calculation parameters deviates significantly from the relationship between the actual residual strength and damage size, and the current residual strength calculation parameters and the theoretical undamaged residual strength are not the best estimates. It is necessary to continue iterating to obtain new residual strength calculation parameters until the difference between the currently determined standard deviation σ and the previously determined standard deviation σ is within the preset range. Taking the equivalent undamaged residual strength data of test pieces with different damage degrees in Table 1 of the above embodiment as an example, the final best estimates are α≈1.79, β≈0.27, and ε. UNC =ε unc ≈9980.

[0109] In this embodiment of the invention, the equivalent undamaged residual strength ε of each test specimen is determined using a normal distribution model and the maximum likelihood estimation method. unc,x The standard deviation δ is used to redetermine the residual strength calculation parameters of the residual strength calculation model based on the LM iterative method, until the difference between the currently determined standard deviation σ and the previously determined standard deviation σ is within a preset range. This allows the final determined residual strength calculation model to more realistically reflect the relationship between residual strength and damage size, improving the accuracy of the residual strength calculation model.

[0110] Example 5

[0111] Figure 5 This is a flowchart of a method for modeling the residual strength of a composite laminate according to Embodiment 5 of the present invention. Compared with the above embodiments, this embodiment optimizes the estimation process of the residual strength calculation parameters for the residual strength calculation model. Figure 5 As shown, the method includes:

[0112] S510. Obtain residual strength test data for test specimens with different degrees of damage.

[0113] S520. Based on the damage degree and residual strength test data of each test piece, determine the residual strength calculation parameters and the equivalent undamaged residual strength.

[0114] S530. Based on the residual strength calculation parameters and the equivalent undamaged residual strength, construct the relationship between residual strength and damage degree as the residual strength calculation model.

[0115] S540. Based on the residual strength calculation model, calculate the equivalent undamaged residual strength ε of each test specimen. unc,x .

[0116] Where, ε unc,x Let N be the equivalent undamaged residual strength of the x-th test specimen, 1≤x≤N, where N is the total number of test specimens and N is an integer.

[0117] S550. Based on the normal distribution model and the maximum likelihood estimation method, determine the equivalent undamaged residual strength ε of each test piece. unc,x The standard deviation σ.

[0118] S560. Based on the LM iterative method, redetermine the residual strength calculation parameters of the residual strength calculation model. Based on the redetermined residual strength calculation parameters, determine the equivalent undamaged residual strength ε of each test piece by fitting the normal distribution model and the maximum likelihood estimation method. unc,x The standard deviation σ.

[0119] S570. Determine whether the number of times the residual strength calculation parameters of the residual strength calculation model based on the LM iteration method has been redefined has reached the preset number. If yes, proceed to S480; otherwise, return to S460.

[0120] S480. The redefined residual strength calculation parameters are used as the residual strength calculation parameters of the residual strength calculation model.

[0121] For example, based on the damage degree and residual strength test data of each test piece, the initial residual strength calculation parameters and the initial equivalent undamaged residual strength can be obtained. Based on the initial residual strength calculation parameters, the initial equivalent undamaged residual strength, the damage size of each test piece, and the residual strength calculation model, the initial equivalent undamaged residual strength distribution of each test piece can be determined, thus determining the initial equivalent undamaged residual strength ε of each test piece. unc,x Then, based on the normal distribution model and the maximum likelihood estimation method, the equivalent undamaged residual strength ε of each test specimen is determined. unc,x The standard deviation σ is used to select a new set of residual strength calculation parameters using the LM iterative algorithm, and the equivalent undamaged residual strength and its standard deviation σ of all test specimens are recalculated until the number of iterations reaches the preset number. The residual strength calculation parameters obtained in the last iteration are the best fitting parameters of the residual strength model.

[0122] Understandably, after iterating using the LM iterative algorithm to select new residual strength calculation parameters and recalculating the equivalent undamaged residual strength and its standard deviation σ for all test specimens, if the number of iterations has not reached the preset number, but the difference between the currently determined standard deviation σ and the previously determined standard deviation σ is within the preset range, then the residual strength calculation parameters obtained in the current iteration can be used as the residual strength calculation parameters of the residual strength model, i.e., the best-fit parameters of the residual strength model. If the difference between the currently determined standard deviation σ and the previously determined standard deviation σ is not within the preset range, but the number of iterations has reached the preset number, then the residual strength calculation parameters obtained in the current iteration can also be used as the residual strength calculation parameters of the residual strength model. Regardless of which condition is met first (whether the difference between the current standard deviation σ and the previously determined standard deviation σ is within the preset range, and whether the number of times the residual strength calculation parameters of the residual strength calculation model has been re-determined based on the LM iterative method has reached the preset number), the iteration process can be terminated, and the residual strength calculation obtained in the last iteration can be used as the residual strength calculation parameters of the residual strength model.

[0123] Example 6

[0124] Figure 6 This is a flowchart of a method for modeling the residual strength of a composite laminate according to Embodiment 5 of the present invention. Compared with the above embodiments, this embodiment adds content about model coefficients. Figure 6 As shown, the method includes:

[0125] S610. Obtain residual strength test data for test specimens with different degrees of damage.

[0126] S620. Based on the damage degree and residual strength test data of each test piece, determine the residual strength calculation parameters and the equivalent undamaged residual strength.

[0127] S630. Based on the residual strength calculation parameters and the equivalent undamaged residual strength, construct the relationship between residual strength and damage degree as the residual strength calculation model.

[0128] S640. Determine the B benchmark reduction factor using the fourth calculation formula.

[0129] S650. Use the B-benchmark reduction factor as the model coefficient for the residual strength calculation model.

[0130] The fourth calculation formula is: B = 1 - K B ·s; B is the B benchmark reduction factor; The equivalent undamaged residual strength ε of each of the aforementioned test specimens with N-1 degrees of freedom. unc,x p-quantiles of non-central t-distribution, ε unc,xLet be the equivalent undamaged residual strength of the x-th test specimen, 1 ≤ x ≤ N, where N is the total number of test specimens and N is an integer. For non-central parameters, z B The equivalent undamaged residual strength ε of each of the aforementioned test specimens unc,x The q quantiles of the standard normal distribution;

[0131] For example, based on the damage degree and residual strength test data of each test piece, the determined residual strength calculation parameters and equivalent undamaged residual strength still have a certain mean deviation (the equivalent undamaged residual strength of each test piece deviates from the mean in an unequal distribution). Therefore, the confidence and reliability of the residual strength calculation model obtained by using the mean of the equivalent undamaged residual strength of each test piece are low, and it cannot truly reflect the relationship between residual strength and damage size. Therefore, a non-central t-distribution is used to calculate the B-benchmark reduction factor, that is, the B-benchmark reduction factor is determined by the fourth calculation formula. Taking p as 95% and q as 90% as an example, after multiplying the residual strength calculation model by the model coefficient (B-benchmark reduction factor), its confidence can reach 95% or above, and its reliability can reach 90% or above. Using the equivalent undamaged residual strength data and residual strength calculation model ε=ε of the test pieces with different damage degrees in Table 1 of the above embodiment, unc ·(1+α·L) -β =9980·(1+1.79·L) -0.27 For example, the calculation result is B = 0.87. Figure 6 This invention provides a residual strength calculation model curve, taking X850 / IM+ composite laminate as an example. The residual strength calculation model curve includes residual strength test data of multiple test specimens, residual strength calculation model curve constructed based on residual strength calculation parameters and equivalent non-destructive residual strength, and B-baseline residual strength calculation model curve (residual strength calculation model multiplied by model coefficients).

[0132] In this embodiment of the invention, the model coefficients of the residual strength calculation model are obtained by calculating the B-benchmark reduction factor through a non-central t-distribution. This reduces the mean deviation of the residual strength calculation parameters and the equivalent undamaged residual strength determined based on the damage degree and residual strength test data of each test piece, thereby improving the confidence and reliability of the residual strength calculation model and further enhancing its accuracy.

[0133] It should be understood that the various forms of processes shown above can be used, with steps reordered, added, or deleted. For example, the steps described in this invention can be executed in parallel, sequentially, or in different orders, as long as the desired result of the technical solution of this invention can be achieved, and this is not limited herein.

[0134] The specific embodiments described above do not constitute a limitation on the scope of protection of this invention. Those skilled in the art should understand that various modifications, combinations, sub-combinations, and substitutions can be made according to design requirements and other factors. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of this invention should be included within the scope of protection of this invention.

Claims

1. A method for modeling the residual strength of composite laminates, characterized in that, include: Obtain residual strength test data for specimens with different degrees of damage; The second calculation parameter is determined by the first calculation formula. ; The first calculation parameter is determined by the second calculation formula. ; The equivalent undamaged residual strength is determined using the third calculation formula; The first calculation formula is: The second calculation formula is: The third calculation formula is: , ; The remaining strength corresponding to the test specimen with the first degree of damage; The remaining strength corresponding to the test specimen with the second degree of damage; The damage size of the test specimen with the first degree of damage; The damage size of the test specimen with the second degree of damage; The undamaged residual strength is the residual strength corresponding to a test specimen with a damage size of 0. The residual strength of the j-th test specimen under theoretical conditions when the damage size is 0, for the i-th damage level. Let be the damage size of the test specimen with the i-th damage level. m is an integer. n is an integer. ; Based on the damage size L of the test piece, the first calculation parameter α, the second calculation parameter β, and the equivalent undamaged residual strength, a relationship between residual strength and damage degree is constructed as a residual strength calculation model; wherein, the residual strength calculation model is: .

2. The method for modeling the residual strength of composite laminates according to claim 1, characterized in that, The test specimens with different damage levels include m types of test specimens with different damage levels; the number of test specimens for each type of damage level is n. And m is an integer; And n is an integer; Among them, the residual strength corresponding to the test piece with the first degree of damage. The average residual strength of n test specimens with the first degree of damage; Residual strength corresponding to the test piece with the second degree of damage It is the average residual strength of n test specimens with the second degree of damage; Undamaged residual strength It is the average of the residual strength of the n test specimens with a damage size of 0.

3. The method for modeling the residual strength of composite laminates according to claim 1, characterized in that, Also includes: Based on the residual strength calculation model, the equivalent undamaged residual strength of each test specimen is calculated. ; The equivalent undamaged residual strength of the xth test specimen. N is the total number of test pieces, and N is an integer; Based on the normal distribution model and the maximum likelihood estimation method, the equivalent undamaged residual strength of each test specimen is determined. Standard deviation ; Based on the LM iterative method, the residual strength calculation parameters of the residual strength calculation model are redefined. Then, based on these redefined parameters, the equivalent undamaged residual strength of each test specimen is determined using a normal distribution model and maximum likelihood estimation. The standard deviation σ; Determine the standard deviation mentioned above. Compared with the previously determined standard deviation Is the difference within the preset range? If so, the redefined residual strength calculation parameters will be used as the residual strength calculation parameters of the residual strength calculation model. If not, then return to the LM iteration method to redetermine the residual strength calculation parameters of the residual strength calculation model. Based on the redetermined residual strength calculation parameters, determine the equivalent undamaged residual strength of each of the test specimens by fitting a normal distribution model and the maximum likelihood estimation method. Standard deviation The steps.

4. The method for modeling the residual strength of composite laminates according to claim 1, characterized in that, Also includes: Based on the residual strength calculation model, the equivalent undamaged residual strength of each test specimen is calculated. ; The equivalent undamaged residual strength of the xth test specimen. N is the total number of test pieces, and N is an integer; Based on the normal distribution model and the maximum likelihood estimation method, the equivalent undamaged residual strength of each test specimen is determined. Standard deviation ; Based on the LM iterative method, the residual strength calculation parameters of the residual strength calculation model are redefined. Then, based on these redefined parameters, the equivalent undamaged residual strength of each test specimen is determined using a normal distribution model and maximum likelihood estimation. Standard deviation ; Determine whether the number of times the residual strength calculation parameters of the residual strength calculation model are re-determined based on the LM iteration method has reached the preset number; If so, the redefined residual strength calculation parameters will be used as the residual strength calculation parameters of the residual strength calculation model. If not, then return to the LM iteration method to redetermine the residual strength calculation parameters of the residual strength calculation model. Based on the redetermined residual strength calculation parameters, determine the equivalent undamaged residual strength of each of the test specimens by fitting a normal distribution model and the maximum likelihood estimation method. Standard deviation The steps.

5. The method for modeling the residual strength of composite laminates according to claim 1, characterized in that, Also includes: The B-benchmark reduction factor is determined using the fourth calculation formula; The B-benchmark reduction factor is used as the model coefficient of the residual strength calculation model; The fourth calculation formula is as follows: ; B is the B benchmark reduction factor; , The equivalent undamaged residual strength of each of the aforementioned test specimens with N-1 degrees of freedom. p quantiles of noncentral t-distribution The equivalent undamaged residual strength of the xth test specimen. N is the total number of test specimens, and N is an integer. For non-central parameters, The equivalent undamaged residual strength of each of the aforementioned test specimens The q quantiles of the standard normal distribution; , ,in, The equivalent undamaged residual strength of each of the aforementioned test specimens The mean.

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