Method for determining critical thickness of protective layer of variable thickness sample based on three-dimensional strain field of dvc

Abstract

This invention discloses a method for defining the critical thickness of a protective layer based on a three-dimensional strain field (DVC) and a variable-thickness specimen. The method includes the following steps: preparing a composite specimen with an internal uniform cross-section matrix and an external gradient-thickness protective layer; extracting the three-dimensional strain field and microcrack damage evolution characteristics within the specimen using in-situ CT loading and digital volume correlation (DVC); introducing an interface synergy discrimination algorithm and a cross-sectional Poisson's ratio spatial inhomogeneity index; and applying targeted definition criteria for different protective mechanisms to obtain the critical effective thickness. This invention requires only a single specimen to achieve continuous targeted definition of the critical effective thickness of the protective layer, significantly reducing testing costs and providing scientific and quantitative theoretical support for the selection of protective materials in complex engineering environments.

Description

Technical Field

[0001] This invention belongs to the field of mechanical testing of engineering materials and structural engineering protection technology, specifically involving a method for defining the critical thickness of a protective layer based on a three-dimensional strain field (DVC) and a variable thickness specimen. Background Technology

[0002] In the fields of existing structural protection and modern civil engineering, applying protective materials (such as polyurea elastomers and epoxy resins) to the surface of load-bearing substrates (such as concrete, mortar, and rock) is an important means to improve the impact resistance, crack prevention, and durability of structures. In this process, scientifically determining the "effective thickness" of the surface protective material is the core key to balancing engineering protection effectiveness and economic costs.

[0003] Current methods for measuring and mechanically evaluating protective layer thickness suffer from the following significant technical bottlenecks:

[0004] First, traditional testing often relies on trial and error and discrete interpolation. This involves preparing a large number of uniform standard composite samples of varying thicknesses for macroscopic destructive comparative testing. This method is not only cumbersome in sample preparation and time-consuming in testing, but also, due to the discreteness of initial defects in different batches of samples, it easily masks the true influence of coating thickness. Furthermore, there are a large number of "interpolation blind spots" between discrete thickness nodes, making it difficult to accurately locate the critical thickness.

[0005] Second, testing methods are limited, lacking in-depth observation of physical mechanisms. While a few existing studies employ variable-thickness specimen designs, they largely rely on surface strain gauges or two-dimensional digital image correlation (2D-DIC) techniques to observe macroscopic load-displacement curves and surface strain fields. These methods can only obtain the mechanical response of the specimen surface, failing to reveal the development process of microcracks in the composite matrix or quantitatively identify the relative slippage of the interfacial transition zone (ITZ). Consequently, the final defined effective thickness lacks rigorous micromechanical data support.

[0006] Third, the evaluation criteria are too simplistic and fail to differentiate the fundamental differences in material properties based on their mechanical mechanisms. Protective materials exhibit drastically different mechanical properties: flexible materials, such as polyurea, rely on the high ductility of their coatings to provide strong lateral confinement, suppressing lateral expansion and instability of the internal matrix through large deformation; while rigid materials, such as epoxy resins, rely on high modulus to enhance the initial stiffness of components and prevent early brittle cracking. Existing technologies often employ a uniform macroscopic strength failure criterion for evaluation, lacking targeted mathematical models for different protective mechanisms. This leads to the risk of "uneconomical flexible coatings" or "early peeling of rigid coatings" in practical engineering applications. Summary of the Invention

[0007] The purpose of this invention is to provide a method for quantitatively determining and defining the optimal effective protective thickness of protective materials with different mechanical properties by using digital volume correlation (DVC) and in-situ CT scanning technology, through a single composite sample with gradient thickness variation characteristics, combined with microscopic damage evolution and stress correction algorithms.

[0008] The technical solution to achieve the objective of this invention is: a method for defining the critical thickness of the protective layer based on a three-dimensional strain field (DVC) and a variable thickness specimen, comprising the following steps:

[0009] Step S1: Prepare a continuously variable cross-section composite specimen with a protective layer gradient thickness. The composite specimen matrix is ​​a column with a uniform cross-section. The thickness of the protective layer of the composite specimen is continuously increased from the minimum value set at both ends of the specimen to the maximum value set at the midpoint of the specimen height.

[0010] Step S2: Perform in-situ CT multi-level loading test on the composite sample and simultaneously perform CT tomography to obtain three-dimensional grayscale data sequences under each loading state;

[0011] Step S3: Based on the three-dimensional grayscale data sequence from step S2, the degree of microscopic damage in the analysis layer is obtained according to the DVC algorithm, and the spatial non-uniformity index of Poisson's ratio of the cross section is defined and calculated.

[0012] Step S4: Based on the non-uniform stress normalization, stress mapping correction is performed on the macroscopic transverse strain of the substrate to obtain the circumferential tensile stress monitoring equation of the coating, and the circumferential tensile stress of the coating is calculated.

[0013] Step S5: Based on the circumferential tensile stress of the coating after correction in step S4, apply the target definition criteria for different protection mechanisms to obtain the critical effective thickness.

[0014] Furthermore, in step S1, the total axial height of the composite sample is H, and the matrix radius is... ;

[0015] The coating thickness t(z) of the protective layer is a set minimum value t at both ends of the sample. min The height is continuously increased towards the midpoint of the sample height until a set maximum value t is reached. max ;

[0016] The coating thickness varies continuously along the height z (z ∈ [0,H]) of the compression axis. The curvature of the thickness function t(z) must ensure that stress concentration failure is not caused by abrupt changes in interface geometry during uniaxial loading.

[0017] The total area distribution function of the composite section at height z is: .

[0018] Furthermore, step S2 specifically involves:

[0019] The composite specimen was placed in an in-situ CT mechanical loading system for uniaxial graded compression.

[0020] Set a series of discrete macroscopic loading displacement nodes (j=1, 2, 3...n);

[0021] Upon reaching each displacement node Displacement is maintained during operation, and CT tomography scans are performed simultaneously to acquire three-dimensional grayscale volume data sequences V under various loading conditions. j (x, y, z), where x, y, and z are nodes. The three-dimensional coordinates.

[0022] Furthermore, the in-situ CT mechanical loading system in step S2 is equipped with a servo-hydraulic lateral loading chamber, which is used to apply a constant confining pressure environment to the surface of the composite sample before performing uniaxial displacement loading, so as to simulate the actual underground or deep service stress boundary conditions of the engineering structure.

[0023] Furthermore, step S3 specifically includes:

[0024] Based on the acquired volume data sequence The internal matrix was discretized into i equal-height analytical layers along the axial direction using the digital volume correlation (DVC) method. The analysis was then performed using the matrix microcrack and pore volume ratio. The degree of microscopic damage in the analysis layer is obtained, which serves as the physical basis for characterizing the spatial non-uniformity ξ(z) of the cross-section Poisson's ratio. i , δ j The evolution of ) by comparing different loading stages; The correlation with ξ reveals the mechanical mechanism by which the internal damage evolution of the material leads to deformation localization;

[0025] Extracting the cross-sectional height z i The original axial compressive strain at each coordinate point (x,y) in the matrix plane With lateral expansion strain ;

[0026] Calculate the local Poisson's ratio at each point within each cross section. and the cross-sectional average Poisson's ratio :

[0027] ,

[0028] ,

[0029] Define and calculate the spatial non-uniformity exponent ξ(z) of the cross-section Poisson's ratio. i ,δ j ):

[0030] ,

[0031] In the formula, A base ξ represents the cross-sectional area of ​​the matrix; a larger ξ value indicates more asymmetrical lateral expansion and the occurrence of local instability; ξ approaching 0 indicates uniform and symmetrical lateral constraints.

[0032] Furthermore, in step S3, the proportion of matrix microcracks and pore volume... The calculation method is as follows: using a three-dimensional grayscale histogram and an adaptive threshold segmentation algorithm, the solid pixels of the substrate are separated from the pixels of microcracks and pores, and the corresponding analysis layer z is calculated. i The ratio of the total number of internal defect voxels to the total number of matrix voxels.

[0033] Furthermore, step S4 specifically involves:

[0034] By relative slip allowable threshold Remove failed analysis layers;

[0035] Calculate the equivalent composite modulus of each section. :

[0036] ,

[0037] Select the smallest cross section at the end of the specimen Using the normalized reference section, stress mapping correction is performed on the macroscopic transverse strain of the substrate, and the equation for monitoring the circumferential tensile stress of the coating is derived:

[0038] .

[0039] Furthermore, the relative slip allowable threshold in step S4 The definition criteria are:

[0040] When the relative slip of the interface Δu(z) i , δ j If the displacement of the uncoated substrate surface exceeds 15% of the ultimate elastic expansion displacement under the same displacement, then the height layer z is considered to be... i The interface coordination mechanism failed, and the section was removed from the sample library for effective thickness measurement.

[0041] Furthermore, step S5 specifically involves:

[0042] Regarding stiffness ratio R E =E m / E C Criterion A for flexible protective materials with a value <0.5: The core criterion is the "Poisson's ratio spatial non-uniform expansion threshold," specifically: the critical displacement nodes during the characterization of failure. At that time, the non-uniformity index ξ(z) is monitored along the height direction z. i), find the one that satisfies ξ(z) i ) ≤ ξ limit And the average Poisson's ratio Critical section for crack initiation falling back to the material's stable range , where ξ limit To allow for an asymmetric threshold, the critical section for crack initiation is extracted. Corresponding physical thickness This refers to the critical effective thickness that provides perfect symmetrical constraint for flexible protective materials;

[0043] Regarding stiffness ratio R E =E m / E C Criterion B for rigid protective materials with a stress >0.7: The core judgment is the "coupled boundary between material stress yield and stiffness degradation", specifically: finding the coating monitoring stress. Reaching the allowable tensile strength of the material Furthermore, the cross-sectional layers at the inflection point of overall stiffness degradation of the specimen Thickness corresponding to the cross section This refers to the optimal protective thickness to prevent the rigid coating from cracking due to its own brittleness.

[0044] Compared with the prior art, the significant advantages of this invention are:

[0045] 1. Breaking through the blind spots of traditional discrete testing, achieving continuous targeted analysis of critical thickness. Traditional methods rely on macroscopic damage comparison of a large number of homogeneous specimens of different thicknesses, resulting in significant sample discrete errors and interpolation blind spots in thickness ranges. This invention innovatively adopts a composite specimen design of a single "uniform cross-section matrix + gradient protective layer". By constructing the total area distribution function of the composite cross-section, it can obtain the full-domain continuous mechanical response from the smallest to the largest thickness in a single multi-level compression test. This improves the accuracy of defining the effective thickness from the traditional "millimeter-level discrete estimation" to "sub-millimeter-level continuous targeted optimization", significantly shortening the material evaluation cycle.

[0046] 2. A pioneering evaluation criterion for flexible material protection failure based on "Poisson's ratio spatial non-uniformity". For flexible, highly ductile materials such as polyurea, existing technologies cannot quantitatively assess their large deformation energy consumption and lateral confinement effect. This invention, based on high-resolution DVC full-field strain extraction, captures the phenomenon of "non-uniform expansion localized strain" caused by the development of microcracks in the internal matrix when the thickness is insufficient, and proposes for the first time the "cross-sectional Poisson's ratio spatial non-uniformity index ξ". By quantifying the local asymmetric expansion threshold, it accurately identifies the critical physical state at which the flexible coating degenerates from "effective symmetric constraint" to "lateral runaway," providing a physically meaningful criterion for flexible engineering protection design.

[0047] 3. Constructing interface collaborative identification and multi-dimensional coupling criteria to accurately quantify the effective constraints of rigid materials. Considering that the failure modes of rigid protective materials such as epoxy resin are mostly interface peeling or coating brittle fracture, this invention removes failure data by extracting the relative slip Δu between the substrate and the coating to ensure the authenticity of the test data; and, based on the characteristics of rigid materials, establishes a coupled evaluation boundary between material stress yielding and the degradation of macroscopic compressive stiffness of the component; this method avoids stiffness redundancy and cost waste caused by excessively thick coatings, and eliminates early brittle fracture failure caused by excessively thin coatings.

[0048] 4. In-situ CT combined with microscopic three-dimensional field to accurately map the service damage mechanism of complex structures. This invention overcomes the limitations of traditional surface strain gauges or two-dimensional DIC, which can only observe the macroscopic response of the material surface. By using in-situ CT tomography combined with DVC analysis, it penetrates the coating to directly observe the volume fraction evolution of microcracks and pores inside the substrate; it directly links the change in external coating thickness with the internal mesoscopic damage mechanism, and is suitable for the protection evaluation of underground space structures and explosion-proof components under complex three-dimensional stress environments. Attached Figure Description

[0049] Figure 1 This is a photograph of the test sample under polyurea coating in Example 1.

[0050] Figure 2 This is a schematic diagram showing the matching of the gradient thickness and the force mechanism of the sample in Example 1.

[0051] Figure 3 This is a grayscale CT slice image of the XY plane of the sample from Example 1.

[0052] Figure 4 This is a diagram showing the evolution of the Poisson's ratio along the height of a 16-layer polyurea structure under a displacement of 0.8 mm in Example 1.

[0053] Figure 5 This is a Poisson's ratio strain contour plot showing the change in specimen height along the displacement of 0.8 mm in Example 1. Detailed Implementation

[0054] The present invention will now be described in further detail with reference to the accompanying drawings.

[0055] This invention provides a method for determining the effective thickness of a protective layer using a single sample. The core of this method lies in: employing a sample morphology combining an internal cylindrical matrix with a uniform cross-section and an external protective layer with a gradient cross-section (thin at both ends and thick in the middle); simultaneously utilizing DVC (Differentiation of the Coefficient of Variation) technology during compression testing to capture the strain field and Poisson's ratio evolution of the matrix and protective layer at different cross-sections; and targeting rigid materials (such as epoxy resin, whose stiffness ratio R...). E =E m / E C >0.7, where E m To protect the elastic modulus of the material, EC The elastic modulus of concrete (R) and the stiffness ratio of flexible materials (such as polyurea) are R. E =E m / E C Based on the mechanical property differences of <0.5), a multi-dimensional thickness definition standard is established.

[0056] Example 1: Determination of the critical effective thickness of flexible, high-ductility protective coating polyurea elastomer

[0057] 1. Sample Preparation and Parameter Control: Standard cement mortar with a uniaxial compressive strength of 40 MPa was selected as the bearing substrate. Using precision core drilling and grinding equipment, the substrate was machined into a cylinder with a diameter of 10 mm (substrate radius r0 = 5 mm) and a total axial height of 12 mm (H = 12 mm). A polyurea elastic coating was sprayed onto the outer cylindrical surface of the substrate. The movement speed of the spraying robot was controlled to ensure that the coating thickness t(z) exhibited a symmetrical, continuous linear gradient along the height: the coating thickness was controlled to be 0 mm at the top and bottom ends of the cylinder (z = 0 mm and z = 12 mm), and linearly increased towards the midpoint of the height (z = 6 mm) to a maximum thickness of 4 mm. That is, within the interval z ∈ [0, 6], the thickness function t(z) = (2 / 3)z. The prepared sample is shown below. Figure 1 As shown.

[0058] 2. In-situ CT multi-stage loading test: The composite specimen was placed in a miniature in-situ CT mechanical loading stage (maximum range 100kN). After applying a preload of 50N, uniaxial graded compression was performed using displacement control mode, with the loading rate set at 0.1mm / min. A critical displacement node δ was defined as the macroscopic axial compressive deformation of the specimen reaching 0.8mm (corresponding to approximately 6.67% macroscopic compressive strain). crit During the displacement holding period, micron-level CT was activated for tomographic scanning. The X-ray tube voltage was set to 120 kV to acquire three-dimensional grayscale data, achieving a voxel resolution of 15 μm. The XY-plane CT grayscale slice image of the sample is shown below. Figure 2 As shown.

[0059] 3. DVC Analysis and Non-uniformity Extraction: Volume data is imported into DVC for calculation. The analysis sub-region (Subsetsize) is set to 31×31×31 voxels, and the step size is 15 voxels. The internal three-dimensional full-field strain is extracted, as shown below. Figure 4 As shown. When the displacement reaches 0.8 mm, the focus is on analyzing the z-section at each height. i Poisson's ratio field, such as Figure 3As shown. Observations revealed that in the extremely thin coating regions at both ends (e.g., z = 2.25 mm, where the coating thickness t = 1.5 mm), the Poisson's ratio of the cross section exhibited significant asymmetric polarization, with a high strain concentration region appearing on one side. The calculated spatial non-uniformity index ξ = 0.18, far exceeding the stable range; this indicates that polyurea at this thickness cannot suppress the propagation of asymmetric oblique cracks within the mortar matrix.

[0060] 4. Target definition based on criterion A: Thickness optimization is performed by substituting criterion A of this invention. A symmetry-allowed safety threshold ξ is set. limit = 0.05. Calculated by scanning along the specimen height, when positioned at the section height z fail When z = 3.9 mm, the average Poisson's ratio of the cross-section drops significantly and tends to a uniform and symmetrical distribution in the plane, while the non-uniformity index ξ just drops to 0.05 and remains stable. Substituting z = 3.9 mm into the thickness distribution function, the physical thickness t = 2.6 mm is calculated. Therefore, it is quantitatively determined that for this 40 MPa mortar matrix, the critical effective protective thickness for the polyurea coating to provide perfect triaxial uniform constraint during the large deformation compression stage is 2.6 mm.

[0061] Example 2: Determination of the optimal effective thickness of a rigid high-modulus protective coating (epoxy resin)

[0062] 1. Sample preparation and parameter control: The matrix material and geometry were completely consistent with Example 1 (40MPa mortar, Φ10mm×12mm). The external protective material was replaced with a high-modulus, low-ductility structurally modified epoxy resin (its measured elastic modulus E). coat = 3.5 GPa, allowable tensile strength [σ allow = 45 MPa). Using a mold casting method, the thickness of the outer epoxy resin protective layer also exhibits a linear gradient change with 0 mm at both ends and 4 mm in the middle.

[0063] 2. Loading Monitoring and Interface Slip Discrimination: The loading device and CT scan parameters are the same as in Example 1. During the compression process, step S4, "Interface Compatibility Discrimination," is performed first. Extract z i The displacement field between the outer edge of the cross-section mortar and the inner edge of the epoxy resin is extremely small in the early stage of loading (displacement < 0.2mm); however, in the later stage of loading, peeling occurs in the area near both ends where the thickness is less than 1.0mm, and the data of the peeling area are automatically removed from the optimization sample.

[0064] 3. Target definition based on criterion B: The main functions of epoxy resin are to improve stiffness and prevent cracking. The composite modulus E is calculated based on the effective cross-sectional data without peeling. eff The transverse strain of the substrate was extracted through mapping correction. The coating tensile stress monitoring equation was then used. The circumferential tensile state of the epoxy resin was continuously monitored. Simultaneously, the tangent modulus E was calculated from the macroscopic load-displacement curve. t , when E t When the first derivative of the curve is less than a set negative threshold, the corresponding displacement node is determined to be the inflection point of substantial stiffness degradation.

[0065] 4. Calculation result output: The system displays the results after optimization, synchronizing the overall stiffness degradation inflection point, and monitoring the internal stress σ of the coating. coat The safe section layer that just reaches the allowable tensile strength of the material (45 MPa) is located at z yield = 4.65mm. Substituting this coordinate into the thickness function t(z) = (2 / 3) × 4.65mm, the corresponding physical thickness of the section is 3.1mm. Therefore, it can be concluded that for this structural load-bearing system, when using epoxy resin for protection, to ensure that the protective layer does not experience brittle premature cracking and to maximize the initial compressive stiffness of the component, its optimal effective coating thickness should not be less than 3.1mm.

Claims

1. A method for defining the critical thickness of a protective layer based on a three-dimensional strain field (DVC) and a variable thickness specimen, characterized in that: Includes the following steps: Step S1: Prepare a continuously variable cross-section composite specimen with a protective layer gradient thickness. The composite specimen matrix is ​​a column with a uniform cross-section. The thickness of the protective layer of the composite specimen is continuously increased from the minimum value set at both ends of the specimen to the maximum value set at the midpoint of the specimen height. Step S2: Perform in-situ CT multi-level loading test on the composite sample and simultaneously perform CT tomography to obtain three-dimensional grayscale data sequences under each loading state; Step S3: Based on the three-dimensional grayscale data sequence from step S2, the degree of microscopic damage in the analysis layer is obtained according to the DVC algorithm, and the Poisson's ratio spatial non-uniformity index of the cross section is defined and calculated. Step S4: Based on the non-uniform stress normalization, stress mapping correction is performed on the macroscopic transverse strain of the substrate to obtain the circumferential tensile stress monitoring equation of the coating, and the circumferential tensile stress of the coating is calculated. Step S5: Based on the circumferential tensile stress of the coating after correction in step S4, apply the target definition criteria for different protection mechanisms to obtain the critical effective thickness.

2. The method according to claim 1, characterized in that, In step S1, the total axial height of the composite sample is H, and the matrix radius is... ; The coating thickness t(z) of the protective layer is a set minimum value t at both ends of the sample. min The height is continuously increased towards the midpoint of the sample height until a set maximum value t is reached. max ; The coating thickness varies continuously along the height z (z ∈ [0,H]) of the compression axis. The curvature of the thickness function t(z) must ensure that stress concentration failure is not caused by abrupt changes in interface geometry during uniaxial loading. The total area distribution function of the composite section at height z is: .

3. The method according to claim 2, characterized in that, Step S2 is as follows: The composite specimen was placed in an in-situ CT mechanical loading system for uniaxial graded compression. Set a series of discrete macroscopic loading displacement nodes (j=1, 2, 3...n); Upon reaching each displacement node Displacement is maintained during operation, and CT tomography scans are performed simultaneously to acquire three-dimensional grayscale volume data sequences V under various loading conditions. j (x, y, z), where x, y, and z are nodes. The three-dimensional coordinates.

4. The method according to claim 3, characterized in that, The in-situ CT mechanical loading system in step S2 is equipped with a servo-hydraulic lateral loading chamber, which is used to apply a constant confining pressure environment to the surface of the composite sample before performing uniaxial displacement loading, so as to simulate the actual underground or deep service stress boundary conditions of the engineering structure.

5. The method according to claim 4, characterized in that, Step S3 is as follows: Based on the acquired volume data sequence The internal matrix was discretized into i equal-height analytical layers along the axial direction using the digital volume correlation (DVC) method. The analysis was then performed using the matrix microcrack and pore volume ratio. The degree of microscopic damage in the analysis layer is obtained, which serves as the physical basis for characterizing the spatial non-uniformity ξ(z) of the cross-section Poisson's ratio. i , δ j The evolution of ) by comparing different loading stages; The correlation with ξ reveals the mechanical mechanism by which the internal damage evolution of the material leads to deformation localization; Extracting the cross-sectional height z i The original axial compressive strain at each coordinate point (x,y) in the matrix plane With lateral expansion strain ; Calculate the local Poisson's ratio at each point within each cross section. and the cross-sectional average Poisson's ratio : ， ， Define and calculate the spatial non-uniformity exponent ξ(z) of the cross-section Poisson's ratio. i ,δ j ): ， In the formula, A base ξ represents the cross-sectional area of ​​the matrix; a larger ξ value indicates more asymmetrical lateral expansion and the occurrence of local instability; ξ approaching 0 indicates uniform and symmetrical lateral constraints.

6. The method according to claim 5, characterized in that, The proportion of matrix microcracks and pore volume in step S3 The calculation method is as follows: using a three-dimensional grayscale histogram and an adaptive threshold segmentation algorithm, the solid pixels of the substrate are separated from the pixels of microcracks and pores, and the corresponding analysis layer z is calculated. i The ratio of the total number of internal defect voxels to the total number of matrix voxels.

7. The method according to claim 6, characterized in that, Step S4 is as follows: By relative slip allowable threshold Remove failed analysis layers; Calculate the equivalent composite modulus of each cross section. : ， Select the smallest cross section at the end of the specimen Using the normalized reference section, stress mapping correction is performed on the macroscopic transverse strain of the substrate, and the equation for monitoring the circumferential tensile stress of the coating is derived: 。 8. The method according to claim 7, characterized in that, relative slip allowable threshold in step S4 The definition criteria are: When the relative slip of the interface Δu(z) i , δ j If the displacement of the uncoated substrate surface exceeds 15% of the ultimate elastic expansion displacement under the same displacement, then the height layer z is considered to be... i The interface coordination mechanism failed, and the section was removed from the sample library for effective thickness measurement.

9. The method according to claim 8, characterized in that, Step S5 is as follows: Regarding stiffness ratio R E =E m / E C Criterion A for flexible protective materials with a value <0.5: The core criterion is the "Poisson's ratio spatial non-uniform expansion threshold," specifically: the critical displacement nodes during the characterization of failure. At that time, the non-uniformity index ξ(z) is monitored along the height direction z. i ), find the one that satisfies ξ(z) i ) ≤ ξ limit And the average Poisson's ratio Critical section for crack initiation falling back to the material's stable range , where ξ limit To allow for an asymmetric threshold, the critical section for crack initiation is extracted. Corresponding physical thickness This refers to the critical effective thickness that provides perfect symmetrical constraint for flexible protective materials; Regarding stiffness ratio R E =E m / E C Criterion B for rigid protective materials with a stress >0.7: The core judgment is the "coupled boundary between material stress yield and stiffness degradation", specifically: finding the coating monitoring stress. Reaching the allowable tensile strength of the material Furthermore, the cross-sectional layers at the inflection point of overall stiffness degradation of the specimen Thickness corresponding to the cross section This refers to the optimal protective thickness to prevent the rigid coating from cracking due to its own brittleness.

10. The method according to claim 9, characterized in that, In step S5, the flexible protective material in criterion A is polyurea elastomer or polyurethane, with an allowable asymmetric threshold ξ. limit The value range of ξ(z) is 0.03~0.

08. i Exceeding the threshold and accompanied by a pore volume ratio φ(z) i δ j When the coating exhibits exponential nonlinear growth, it is determined that the coating at that thickness has lost its uniform lateral confinement capability. In criterion B of step S5, the rigid protective material is epoxy resin or carbon fiber reinforced composite (CFRP). The mathematical criterion for the inflection point of the overall axial compressive stiffness degradation of the specimen is as follows: after smoothing and filtering the overall load-displacement curve obtained from in-situ loading (such as Savitzky-Golay filtering), the tangent modulus E is calculated. t (δ j ), when E t When the first derivative of the curve is less than a set negative threshold, the corresponding displacement node is determined to be the inflection point of stiffness degradation.

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