A composite material digital modeling and simulation method

Abstract

The application discloses a composite material digital modeling and simulation method, comprising the following steps: S1, constructing an anisotropic parameterized reference twin model containing layer information, and associating a material database containing specific failure criteria of the composite material; S2, configuring a special interface for receiving quantitative data of defects of the composite material component in the manufacturing stage and monitoring data of structural response in the service stage; S3, constructing a damage dynamic evolution rule library based on composite material damage mechanics; S4, in response to new data input, automatically triggering corresponding rule to update the model, performing progressive damage analysis of the composite material on the updated model, and predicting the post-impact compression strength; S5, based on the prediction result, generating a maintenance decision suggestion for the composite material component. The application realizes high-fidelity simulation of the whole process of the composite material structure by constructing the reference twin model containing the layer information and constructing the damage dynamic evolution rule library based on the composite material damage mechanics.

Description

Technical Field

[0001] This application relates to the field of dynamic modeling technology, specifically a method for digital modeling and simulation of composite materials. Background Technology

[0002] Fiber-reinforced resin matrix composites are widely used in aerospace, transportation and other fields due to their advantages such as high specific strength, high specific modulus and strong designability.

[0003] However, the mechanical behavior and failure mechanisms of composite material structures are complex, and their performance and reliability are significantly affected by manufacturing processes and service environments, specifically in the following two stages: During the manufacturing stage, defects such as pores, delamination, and fiber bending are inevitably introduced into the interior of composite components. These defects have random spatial distribution, which can significantly degrade the local properties of the material and become weak points for damage initiation and propagation during service. Traditional deterministic modeling methods are usually based on perfect performance data from material handbooks or only consider the impact of defects in a general way through safety factors. They are difficult to accurately reflect the true mechanical state of components with defects, resulting in large deviations in performance prediction (especially residual strength and fatigue life).

[0004] During service, composite structures may be subjected to complex loads and environmental factors, leading to the initiation and evolution of various damage modes such as matrix cracking, fiber breakage, and delamination. In existing technologies, monitoring of structural health status and simulation-based damage prediction are often separate. Monitoring data is mostly used for qualitative or semi-qualitative damage alarms, while simulation models are usually initialized with ideal conditions and lack the ability to be dynamically updated based on measured data. This makes it impossible to construct a high-fidelity digital twin model that can evolve synchronously with the physical structure, thus restricting the prediction of remaining service life and condition-based maintenance decisions based on accurate condition awareness.

[0005] Therefore, it is necessary to provide a method for digital modeling and simulation of composite materials to solve the above problems.

[0006] It should be noted that the information disclosed in this background section is only for understanding the background technology of this application concept, and therefore may include information that does not constitute prior art. Summary of the Invention

[0007] Based on the aforementioned problems in the existing technology, the problem to be solved by this application is to provide a digital modeling and simulation method for composite materials, which can achieve high-fidelity simulation of the entire process of composite material structure from micro-defect initiation to macro-failure.

[0008] The technical solution adopted by this application to solve its technical problem is: a digital modeling and simulation method for composite materials, comprising the following steps: S1. Construct an anisotropic parameterized benchmark twin model containing layup information and associate it with a material database containing specific failure criteria for composite materials. The model supports the insertion of interface elements to characterize delamination damage. S2. Configure a dedicated interface for receiving quantitative data on defects in composite material components during the manufacturing stage and structural response monitoring data during the service stage. S3. Based on the damage mechanics of composite materials, a damage dynamic evolution rule base is constructed. This rule base includes at least the following: rules for converting porosity distribution data during the manufacturing stage into spatially variable material property fields in the benchmark twin model, and rules for inverting acoustic emission or guided wave monitoring signals during the service stage into internal damage states and driving the model to update interface units or material failure parameters. S4. In response to new data input, the corresponding rules are automatically triggered to update the model, and progressive damage analysis of composite materials is performed on the updated model. Post-impact compressive strength prediction is also performed to predict the remaining compressive strength or fatigue life. S5. Based on the prediction results, generate maintenance decision recommendations for composite material components.

[0009] Furthermore, the parameterization dimensions of the anisotropic parameterized benchmark twin model include ply angle, ply sequence, and single-layer thickness; the specific failure criteria include two-dimensional or three-dimensional failure criteria for judging fiber and matrix failure, and criteria based on energy release rate or stress for judging delamination initiation and propagation.

[0010] Furthermore, the manufacturing stage defect quantification data includes quantitative information on porosity distribution, delamination location and size, and fiber curvature obtained by ultrasonic C-scan or industrial CT; the structural response monitoring data includes distributed optical fiber strain, acoustic emission signal characteristic parameters, guided wave propagation signal, and service environment temperature and humidity data.

[0011] Furthermore, the rule for converting porosity distribution data into a spatially variable material property field is as follows: based on a micromechanical model or empirical formula, a quantitative relationship is established between porosity and the transverse elastic modulus, shear modulus, and corresponding strength of the composite single-layer plate. Based on this relationship and the input porosity distribution map, differentiated material properties are assigned to the units at different locations in the benchmark twin model.

[0012] Furthermore, the rule for inverting acoustic emission monitoring signals into internal damage states specifically involves: establishing a mapping database of characteristic parameters of acoustic emission events and typical damage modes of composite materials, wherein the characteristic parameters include amplitude, energy, rise time, and frequency center, and the damage modes include matrix cracking, fiber breakage, and delamination; identifying and locating active damage modes based on the monitored acoustic emission signals, and initializing or updating the corresponding damage state variables at the corresponding positions in the benchmark twin model.

[0013] Furthermore, the damage dynamic evolution rule library also includes a damp and heat environment performance coupling degradation rule. This rule is embedded with a physical model of composite material performance degradation that considers moisture absorption and thermo-oxidative aging. Based on the input historical temperature and humidity data, the material performance parameters related to the resin matrix in the benchmark twin model are dynamically updated.

[0014] Furthermore, in the coupled degradation rules for performance in humid and hot environments, the updated material performance parameters include at least the elastic modulus of the resin matrix, the glass transition temperature, and the strength parameters dominated by the matrix; the degradation physical model is constructed based on the diffusion reaction kinetic equation or the time-temperature and time-humidity equivalence principle.

[0015] Furthermore, the progressive damage analysis of the composite material includes: under static or fatigue loads, progressively calculating the stress / strain state at each integration point in the updated model, determining the damage initiation and evolution based on the updated failure criteria, and simulating damage propagation through stiffness reduction or element deletion until the structure reaches final failure, thereby obtaining the remaining strength or fatigue life.

[0016] Furthermore, the prediction of its remaining strength specifically includes the prediction of post-impact compressive strength, which is achieved by first introducing impact simulation into the model to generate initial damage, and then performing compressive stability analysis on the damaged model.

[0017] Furthermore, the maintenance decision recommendations include repair solutions for delamination damage in composite materials, specifically including recommendations on the dimensions and layup sequence for stepped patching or adhesive bonding repairs.

[0018] The beneficial effects of this application are: This application provides a digital modeling and simulation method for composite materials, which achieves high-fidelity simulation of the entire process of composite material structure from micro-defect initiation to macro-failure by constructing a benchmark twin model containing layup information and building a damage dynamic evolution rule library based on composite material damage mechanics.

[0019] In addition to the purposes, features, and advantages described above, this application has other purposes, features, and advantages. A further detailed description of this application will be provided below with reference to the figures. Attached Figure Description

[0020] The accompanying drawings, which form part of this application, are used to provide a further understanding of this application. The illustrative embodiments and descriptions of this application are used to explain this application and do not constitute an undue limitation of this application. In the drawings: Figure 1 This is a schematic diagram of an overall method for digital modeling and simulation of composite materials according to this application. Detailed Implementation

[0021] It should be noted that, unless otherwise specified, the embodiments and features described in this application can be combined with each other. This application will now be described in detail with reference to the accompanying drawings and embodiments.

[0022] To enable those skilled in the art to better understand the present application, the technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present application, and not all embodiments. Based on the embodiments in the present application, all other embodiments obtained by those of ordinary skill in the art without creative effort should fall within the scope of protection of the present application.

[0023] like Figure 1 As shown, this application provides a digital modeling and simulation method for composite materials. This method is applied to the whole life cycle performance prediction and maintenance decision support of composite structures, and can achieve high-precision simulation and real-time mapping of the damage evolution process of composite material structures under complex load environments. Specifically, the method includes the following steps: S1. Construct an anisotropic parameterized benchmark twin model containing layup information and associate it with a material database containing specific failure criteria for composite materials. The model supports the insertion of interface elements to characterize delamination damage. A twin model is a virtual entity that can dynamically map and synchronously evolve the state of a physical composite structure. Therefore, it can simulate and predict different states of composites in real time. Specifically, based on the design drawings of composite components, a parametric baseline twin model can be built in finite element analysis software such as Abaqus and ANSYS. On this baseline twin model, a material database containing specific failure criteria for composite materials can be linked to ensure that the model can accurately reflect the damage initiation and propagation behavior of actual materials under different stress states. The baseline twin model also embeds information about each ply, thus forming an anisotropic parameterized baseline twin model. For example, the ply information includes the ply angle of each ply, the ply sequence of all plies, and the thickness of a single layer, thereby enabling accurate characterization of the anisotropic mechanical behavior of the composite structure.

[0024] It should be noted that layup information refers to the set of geometric and physical parameters such as the layup direction, sequence, and thickness of each fiber layer in the composite material during the manufacturing process. This information directly affects the overall stiffness, strength, and damage tolerance characteristics of the composite structure.

[0025] For example, specific failure criteria include two-dimensional or three-dimensional failure criteria for judging fiber and matrix failure, and criteria based on energy release rate or stress for judging delamination initiation and propagation. For example, the criteria may include single-layer plate failure criteria: used to judge fiber and matrix failure, which can be two-dimensional (such as the Hashin criterion, Puck criterion) or three-dimensional, and its general form can be expressed as a function containing stress or strain components. For example, a simple criterion for fiber tensile failure (σ11>0) is (σ11 / XT)² + (τ12 / S12)² ≥ 1, where XT is the tensile strength in the fiber direction, S12 is the in-plane shear strength, and τ12 is the in-plane shear stress; when this criterion is satisfied, fiber tensile failure is determined to have occurred. And, delamination failure criteria: used to determine the debonding or delamination behavior of interlayer interfaces. Usually, a criterion based on energy release rate or a stress-based criterion is adopted. For example, the criterion based on energy release rate can be GIC + GIIC ≥ Gc, where GIC and GIIC are the type I and type II energy release rates, respectively, and Gc is the interfacial fracture toughness. When this inequality is true, it is determined that delamination initiation has occurred at the interface.

[0026] In addition, the model also supports the dynamic insertion of interface elements, that is, zero-thickness interface elements are inserted at the positions automatically activated by the damage criteria during the simulation based on the damage evolution, in order to simulate the delamination propagation process. For example, cohesive elements are pre-arranged in the region where delamination may be initiated. When the energy release rate exceeds the critical value, the element is automatically activated and the crack propagation path is simulated, thereby realizing continuous simulation of the entire process from damage initiation to failure.

[0027] S2. Configure a dedicated interface for receiving quantitative data on defects in composite material components during the manufacturing stage and structural response monitoring data during the service stage. Since defects such as porosity, fiber buckling, and interlaminar debonding are inevitably introduced during the manufacturing process, and fatigue damage and cumulative degradation will occur due to environmental loads during service, it is necessary to access defect and damage data from different periods in real time through a dedicated interface in order to achieve dynamic correction of model parameters and continuous improvement of simulation accuracy. For example, the dedicated interface includes at least: a manufacturing data interface for receiving defect quantification data of composite component from the manufacturing stage, which is typically acquired by non-destructive testing techniques, including porosity distribution cloud maps, delamination location and size information, and fiber curvature quantification information acquired by ultrasonic C-scan or industrial CT; and a service monitoring interface for receiving monitoring data from a sensor network attached to the component in real time or periodically, including strain fields measured by distributed fiber optic sensors, event signals acquired by acoustic emission systems, guided wave excitation and reception signals, and environmental data recorded by temperature and humidity sensors.

[0028] It should be noted that all of the above interfaces must have data format compatibility and timestamp alignment functions to ensure that multi-source heterogeneous data from different devices and monitoring systems can be uniformly accessed and accurately mapped to the spatial location and physical time in the model, thereby supporting the temporal consistency requirements of damage evolution analysis and remaining life prediction.

[0029] S3. Based on the damage mechanics of composite materials, a damage dynamic evolution rule base is constructed. This rule base includes at least the following: rules for converting porosity distribution data during the manufacturing stage into spatially variable material property fields in the benchmark twin model, and rules for inverting acoustic emission or guided wave monitoring signals during the service stage into internal damage states and driving the model to update interface units or material failure parameters. Damage mechanics of composite materials is a nonlinear mechanical theory system that reflects the initiation, propagation, and coalescence of internal microcracks in materials under the coupled action of complex loads and environment. Its core lies in establishing the mapping relationship between damage variables and constitutive degradation.

[0030] In this embodiment, based on the damage mechanics of composite materials, a damage dynamic evolution rule base is constructed. This rule base includes at least rules for converting porosity distribution data from the manufacturing stage into a spatially variable material property field in a benchmark twin model. Specifically, based on micromechanical models or empirical formulas, a quantitative relationship is established between porosity and the transverse elastic modulus, shear modulus, and corresponding strength of the composite single-layer plate. Based on this relationship and the input porosity distribution map, differentiated material properties are assigned to units at different locations in the benchmark twin model. For example, the quantitative relationship between porosity and material properties can be expressed as: E_p = E_0 (1 - αφ), where E_p is the effective modulus of the porous material, E_0 is the modulus of the ideal dense material, φ is the local porosity, and α is the degradation coefficient determined by the fiber arrangement and matrix properties; In the specific implementation process, the input porosity distribution map is first read, and the effective modulus at the corresponding position is calculated by substituting the porosity value of each pixel position on the map into the above formula. A material property field is then generated in the benchmark twin model to replace the original uniform properties, thereby achieving accurate characterization of the spatial variability of material properties caused by manufacturing defects; The rule base also includes rules for inverting acoustic emission monitoring signals into internal damage states. Specifically, it establishes a mapping database between acoustic emission event characteristic parameters and typical damage modes. For example, high-amplitude, high-energy burst signals are often associated with fiber fracture; low-amplitude, continuous signals may be associated with matrix cracking or interfacial friction; specific frequency components may point to layered expansion. By processing real-time acoustic emission signals using pattern recognition algorithms, active damage modes can be identified, and their spatial locations can be determined using acoustic emission source localization technology. Subsequently, at the corresponding location in the baseline twin model, the corresponding damage state variables are initialized or updated. For example, the matrix damage variable is initialized to a non-zero value at the corresponding cell, or the interfacial cells in that region are activated to introduce initial softening. Among them, pattern recognition algorithms can use support vector machines, random forests or deep neural networks to classify acoustic emission events based on feature parameters in the training set, such as amplitude, duration, rise time, energy, frequency spectrum, etc.

[0031] The rule base also includes performance coupling degradation rules for humid and hot environments to address the impact of service environments, and embeds physical models of composite material performance degradation that consider moisture absorption and thermo-oxidative aging into the rule base. For example, based on diffusion reaction kinetics, the performance degradation of the resin matrix is ​​related to temperature and humidity history. A simplified model uses the time-temperature-humidity equivalence principle to construct the master curve of performance over time, temperature, and humidity. The updated material performance parameters include at least the elastic modulus of the resin matrix, the glass transition temperature, and the matrix-dominant strength parameters (such as transverse tensile strength and in-plane shear strength). Then, based on the input temperature and humidity history data, the model dynamically calculates the performance retention rate at the current moment and updates all material parameters related to the resin matrix in the baseline twin model, thereby achieving the synergistic prediction of material performance evolution and structural response under service environments. Furthermore, the rule base integrates the evolution logic of cumulative damage under fatigue loading. By introducing an improved Miner linear cumulative damage theory and a nonlinear damage coupling model, it comprehensively considers the load sequence effect and residual performance degradation under different stress levels. Based on the measured load spectrum, it calculates the damage increment for each cycle and dynamically updates the fatigue damage variables at the unit level in the benchmark twin model. For example, when a unit experiences a high load amplitude cycle, its resin matrix microcrack density increases, and the corresponding fatigue damage variables accumulate accordingly. At the same time, a nonlinear correction factor is introduced to reflect the damage acceleration effect.

[0032] S4. In response to new data input, the corresponding rules are automatically triggered to update the model, and progressive damage analysis of composite materials is performed on the updated model. Post-impact compressive strength prediction is also performed to predict the remaining compressive strength or fatigue life. The system is equipped with an automatic triggering mechanism. When a new batch of manufacturing defect data or service monitoring data is input through a dedicated interface, the system automatically matches and triggers the corresponding rules in the aforementioned process, driving the update of the reference twin model. The update content may include: remapping of material property fields, initialization of damage state variables, modification of interface element properties, application of environmental loads, etc.; Subsequently, perform progressive damage analysis of the composite material on the updated model. This damage analysis is carried out step by step under static or fatigue loads, specifically including: At a given load step, calculate the stress / strain state of each integration point in the model; Call the updated failure criterion in the material database to judge whether damage starts; Once damage starts, adopt a preset stiffness reduction scheme (such as multiplying the elastic modulus in the damage direction by a reduction factor d (0 < d < 1)) or element deletion technique to simulate the degradation of material properties; After equilibrium iteration, enter the next load increment step and repeat the above process until the structure reaches final failure (such as load divergence, displacement mutation). Finally, obtain the remaining strength or fatigue life of the structure.

[0033] It should be noted that for predicting the compressive strength after impact, the specific implementation process is as follows: First, introduce low-energy impact simulation (such as using impactor contact analysis) in the reference model to generate initial damage (including matrix damage, delamination); Subsequently, use this damaged model as input to perform compressive stability analysis (such as applying in-plane compressive displacement load and performing nonlinear buckling analysis) to predict its remaining bearing capacity.

[0034] In addition, for fatigue life prediction, the system extracts the cyclic characteristics in the load history based on the updated damage evolution path in combination with the rainflow counting method, and then accumulates the damage increments of each cycle until the total damage value reaches the critical threshold. At this time, it is determined that the structure fails, and the corresponding number of cycles is recorded as the predicted life. This critical threshold is usually 1.0. Therefore, the damage increment of each cycle is expressed as ΔD_i = (N_f / N_i)^(-β) · f(σ_max, R, T), where N_f is the remaining life in the current damage state, N_i is the number of load cycles corresponding to this cycle, β is the fatigue index dependent on the material, and f(σ_max, R, T) is a nonlinear correction function based on the maximum stress σ_max, stress ratio R, and temperature T; The ΔD_i of all cycles is accumulated to the total damage D = ΣΔD_i. When D ≥ 1.0, it is determined that the structure fails, and the corresponding total number of cycles is the predicted fatigue life.

[0035] Rainflow counting is an effective method for statistically analyzing stress cycles in complex load histories. By identifying loading-unloading inflection points and tracing them chronologically, irregular load histories are decomposed into a series of closed stress-strain cycles. This method first extracts extreme points in the load time series, and then matches them according to the four-point or three-point criteria to form complete cycles. Each cycle corresponds to a stress amplitude and mean. The obtained cycle parameters are input into Miner's linear cumulative damage theory or the aforementioned nonlinear fatigue model for damage increment calculation. Its advantage lies in its ability to accurately capture the damage contribution under multi-amplitude and random loads in actual service, and it is particularly suitable for life prediction of composite material structures such as aircraft and wind turbines.

[0036] S5. Based on the prediction results, generate maintenance decision recommendations for composite material components.

[0037] Based on the remaining strength and fatigue life prediction results, and in conjunction with safety margin requirements, it is determined whether the component needs to be immediately taken out of service, operated under limited load, or undergo preventive maintenance. Maintenance decision recommendations include repair schemes for delamination damage in composite materials, which specifically include recommendations on the dimensions and layup sequence for stepped patching or adhesive bonding repairs, as well as resin injection repair process parameters for matrix cracks, such as injection pressure, curing temperature, and holding time. For components nearing their lifespan threshold, it is recommended to increase the frequency of health monitoring or install strain sensors to track damage development in real time, and to combine digital twin models for dynamic evaluation when necessary.

[0038] The above description is merely a preferred embodiment of this application and is not intended to limit this application. Various modifications and variations can be made to this application by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this application should be included within the protection scope of this application.

Claims

1. A method for digital modeling and simulation of composite materials, characterized in that: Includes the following steps: S1. Construct an anisotropic parameterized benchmark twin model containing layup information and associate it with a material database containing specific failure criteria for composite materials. The model supports the insertion of interface elements to characterize delamination damage. S2. Configure a dedicated interface for receiving quantitative data on defects in composite material components during the manufacturing stage and structural response monitoring data during the service stage. S3. Based on the damage mechanics of composite materials, a damage dynamic evolution rule base is constructed. This rule base includes at least the following: rules for converting porosity distribution data during the manufacturing stage into spatially variable material property fields in the benchmark twin model, and rules for inverting acoustic emission or guided wave monitoring signals during the service stage into internal damage states and driving the model to update interface units or material failure parameters. S4. In response to new data input, the corresponding rules are automatically triggered to update the model, and progressive damage analysis of composite materials is performed on the updated model. Post-impact compressive strength prediction is also performed to predict the remaining compressive strength or fatigue life. S5. Based on the prediction results, generate maintenance decision recommendations for composite material components.

2. The method for digital modeling and simulation of composite materials according to claim 1, characterized in that: The parameterization dimensions of the anisotropic parameterized reference twin model include ply angle, ply sequence, and single-layer thickness; the specific failure criteria include two-dimensional or three-dimensional failure criteria for judging fiber and matrix failure, and criteria based on energy release rate or stress for judging delamination initiation and propagation.

3. The method for digital modeling and simulation of composite materials according to claim 1, characterized in that: The manufacturing stage defect quantification data includes quantitative information on porosity distribution, delamination location and size, and fiber curvature obtained by ultrasonic C-scan or industrial CT; the structural response monitoring data includes distributed optical fiber strain, acoustic emission signal characteristic parameters, guided wave propagation signal, and service environment temperature and humidity data.

4. The method for digital modeling and simulation of composite materials according to claim 3, characterized in that: The rule for converting porosity distribution data into a spatially variable material property field is as follows: based on a micromechanical model or empirical formula, a quantitative relationship is established between porosity and the transverse elastic modulus, shear modulus, and corresponding strength of the composite single-layer plate. Based on this relationship and the input porosity distribution map, differentiated material properties are assigned to the units at different locations in the benchmark twin model.

5. The method for digital modeling and simulation of composite materials according to claim 3, characterized in that: The rule for inverting acoustic emission monitoring signals into internal damage states specifically involves: establishing a mapping database of characteristic parameters of acoustic emission events and typical damage modes of composite materials, wherein the characteristic parameters include amplitude, energy, rise time, and frequency center, and the damage modes include matrix cracking, fiber breakage, and delamination; identifying and locating active damage modes based on the monitored acoustic emission signals, and initializing or updating the corresponding damage state variables at the corresponding positions in the benchmark twin model.

6. The method for digital modeling and simulation of composite materials according to claim 3, characterized in that: The damage dynamic evolution rule library also includes a damp and heat environment performance coupling degradation rule. This rule is embedded with a physical model of composite material performance degradation that considers moisture absorption and thermo-oxidative aging. Based on the input historical temperature and humidity data, the material performance parameters related to the resin matrix in the benchmark twin model are dynamically updated.

7. The method for digital modeling and simulation of composite materials according to claim 6, characterized in that: In the aforementioned damp and hot environment performance coupling degradation rule, the updated material performance parameters include at least the elastic modulus of the resin matrix, the glass transition temperature, and the strength parameters dominated by the matrix; the degradation physical model is constructed based on the diffusion reaction kinetic equation or the time-temperature and time-humidity equivalence principle.

8. The method for digital modeling and simulation of composite materials according to claim 1, characterized in that: The progressive damage analysis of the composite material includes: under static or fatigue loads, progressively calculating the stress / strain state at each integration point in the updated model, determining the damage initiation and evolution based on the updated failure criteria, and simulating damage propagation through stiffness reduction or element deletion until the structure reaches final failure, thereby obtaining the remaining strength or fatigue life.

9. The method for digital modeling and simulation of composite materials according to claim 8, characterized in that: The prediction of its remaining strength specifically includes the prediction of post-impact compressive strength, which is achieved by first introducing an impact simulation into the model to generate initial damage, and then performing compressive stability analysis on the damaged model.

10. The method for digital modeling and simulation of composite materials according to claim 1, characterized in that: The maintenance decision recommendations include repair solutions for delamination damage in composite materials, specifically including recommendations on dimensions and layup sequence for stepped patching or adhesive bonding repairs.

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