Material indentation depth calibration method and device based on nanoindentation simulation design, equipment and medium
By establishing finite element and constitutive models, indentation simulation was performed, the equivalent elastic modulus was calculated, and a quantitative mapping model was established. This solved the problem of the correspondence between test results and depth positions in continuous gradient thin film materials using nanoindentation technology, and achieved accurate characterization of mechanical properties.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- CENT SOUTH UNIV
- Filing Date
- 2026-03-31
- Publication Date
- 2026-07-21
Smart Images
Figure CN121938530B_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of materials mechanical characterization technology, and in particular to a method, apparatus, equipment and medium for calibrating the indentation depth of materials based on nanoindentation simulation design. Background Technology
[0002] Currently, when existing nanoindentation technology is applied to continuous gradient thin film materials, the equivalent mechanical properties obtained by testing generally correspond to the actual indenter depth, but cannot accurately correspond to a specific depth position inside the material. How to accurately map the nanoindentation test results to a specific depth position in a continuous gradient material is an urgent problem to be solved. Summary of the Invention
[0003] In view of this, the purpose of this invention is to provide a method, apparatus, device, and medium for calibrating material indentation depth based on nanoindentation simulation design, which can accurately map nanoindentation test results to specific depth positions of continuous gradient materials. The specific solution is as follows:
[0004] In a first aspect, this application discloses a method for calibrating the indentation depth of materials based on nanoindentation simulation design, including:
[0005] A finite element geometric model of a continuous gradient material corresponding to the Brinell indenter nanoindentation experiment was established, and a constitutive model of a continuous gradient material with continuously varying elastic modulus was constructed through a user-defined field subroutine.
[0006] The continuous gradient material finite element geometric model and the continuous gradient material constitutive model are combined to perform indentation simulation at several preset maximum indentation depths to obtain simulation results; the simulation results include load-displacement curves of the indenter tip corresponding to several preset maximum indentation depths;
[0007] The equivalent elastic modulus corresponding to the preset maximum indenter indentation depth is calculated based on the load-displacement curve, and the material indentation depth corresponding to the preset maximum indenter indentation depth is identified based on the equivalent elastic modulus, so as to determine the material indentation depth corresponding to several preset maximum indenter indentation depths respectively.
[0008] A quantitative mapping model between the preset maximum indenter indentation depth and the material indentation depth is established using a nonlinear regression algorithm. This model is used to determine the material indentation depth corresponding to any preset maximum indenter indentation depth, and the test results of the Brinell indenter nanoindentation experiment at the preset maximum indenter indentation depth are mapped to the corresponding material indentation depth.
[0009] Optionally, calculating the equivalent elastic modulus corresponding to the preset maximum indentation depth based on the load-displacement curve includes:
[0010] The unloading segment of the load-displacement curve is processed using the Oliver-Pharr method to obtain the equivalent elastic modulus corresponding to the preset maximum indentation depth.
[0011] Optionally, the step of processing the unloading segment curve of the load-displacement curve using the Oliver-Pharr method to obtain the equivalent elastic modulus corresponding to the preset maximum indentation depth includes:
[0012] The unloading segment of the load-displacement curve is fitted to a power law function, and the slope corresponding to the preset maximum indentation depth in the power law function is taken as the contact stiffness.
[0013] The contact projected area is calculated based on the contact stiffness, and the equivalent elastic modulus is calculated based on the contact stiffness and the contact projected area.
[0014] Wherein, the power-law function is ; Indicates load; and Indicates the fitted parameters; Indicates the depth of the indenter insertion; This indicates the final residual depth.
[0015] Optionally, the step of calculating the contact projected area based on the contact stiffness and calculating the equivalent elastic modulus based on the contact stiffness and the contact projected area includes:
[0016] The contact depth is calculated using the contact depth calculation formula and based on the contact stiffness; the contact projected area is calculated using the contact projected area calculation formula and based on the contact depth.
[0017] The equivalent elastic modulus is calculated using the formula for calculating the equivalent elastic modulus and based on the contact stiffness and the contact projected area.
[0018] The formula for calculating the contact depth is as follows: ;in, Indicates the contact depth; Indicates the preset maximum indentation depth; Indicates the strain value; Indicates the maximum load; This represents the contact stiffness; the formula for calculating the contact projected area is: ; The contact projection area is represented by the formula; the equivalent elastic modulus is calculated as follows: ;in, This represents the equivalent elastic modulus; This indicates the contact stiffness; This represents the projected contact area; This represents the geometric constant of the Burgh indenter.
[0019] Optionally, the step of constructing a continuous gradient material constitutive model with continuously varying elastic modulus through a user-defined field subroutine includes:
[0020] Establish a target correlation function to characterize the relationship between preset material properties and preset field variables of a continuous gradient material; the preset material properties include the elastic modulus.
[0021] The target correlation function is input into a user-defined field subroutine to construct a constitutive model of a continuously gradient material with a continuously varying elastic modulus.
[0022] Optionally, identifying the material indentation depth corresponding to the preset maximum indenter indentation depth based on the equivalent elastic modulus includes:
[0023] The material indentation depth corresponding to the equivalent elastic modulus is determined according to the preset modulus and depth correspondence, and the material indentation depth is used as the material indentation depth corresponding to the preset maximum indenter indentation depth.
[0024] Optionally, establishing the continuous gradient material finite element geometric model corresponding to the Brinell indenter nanoindentation experiment includes:
[0025] Based on the physical characteristics of the Brinell indenter nanoindentation experiment, a static finite element model was established in the Abaqus environment.
[0026] Based on the actual dimensions of the continuous gradient material, a temporary finite element geometric model is obtained by setting the finite element model parameters corresponding to the continuous gradient material for the static finite element model.
[0027] Adaptive meshing technology is used to locally refine the contact region of the temporary finite element geometric model to obtain a continuous gradient material finite element geometric model.
[0028] Secondly, this application discloses a material indentation depth calibration device based on nanoindentation simulation design, including:
[0029] The model building module is used to establish a continuous gradient material finite element geometric model corresponding to the Brinell indenter nanoindentation experiment. It constructs a continuous gradient material constitutive model with continuously changing elastic modulus through user-defined field subroutines.
[0030] The simulation module is used to perform indentation simulations at several preset maximum indentation depths by combining the finite element geometric model and the constitutive model of the continuous gradient material, respectively, to obtain simulation results; the simulation results include the load-displacement curves of the indenter tip corresponding to the several preset maximum indentation depths;
[0031] The material indentation depth determination module is used to calculate the equivalent elastic modulus corresponding to the preset maximum indentation depth based on the load-displacement curve, and to identify the material indentation depth corresponding to the preset maximum indentation depth based on the equivalent elastic modulus, so as to determine the material indentation depth corresponding to several preset maximum indentation depths respectively.
[0032] The depth mapping module is used to establish a quantitative mapping model between the preset maximum indenter indentation depth and the material indentation depth using a nonlinear regression algorithm, so as to determine the material indentation depth corresponding to any preset maximum indenter indentation depth according to the quantitative mapping model, and map the test results of the Brinell indenter nanoindentation experiment at the preset maximum indenter indentation depth to the corresponding material indentation depth.
[0033] Thirdly, this application discloses an electronic device, including:
[0034] Memory, used to store computer programs;
[0035] A processor is used to execute the computer program to implement the aforementioned disclosed method for calibrating material indentation depth based on nanoindentation simulation design.
[0036] Fourthly, this application discloses a computer-readable storage medium for storing a computer program; wherein, when the computer program is executed by a processor, it implements the aforementioned material indentation depth calibration method based on nanoindentation simulation design.
[0037] As can be seen, this application establishes a continuous gradient material finite element geometric model corresponding to the Brinell indenter nanoindentation experiment, and constructs a continuous gradient material constitutive model with continuously changing elastic modulus through a user-defined field subroutine; the continuous gradient material finite element geometric model and the continuous gradient material constitutive model are combined to perform indentation simulation at several preset maximum indenter indentation depths to obtain simulation results; the simulation results include load-displacement curves of the indenter tip corresponding to several preset maximum indenter indentation depths; the equivalent elastic modulus corresponding to the preset maximum indenter indentation depth is calculated based on the load-displacement curves, and the material indentation depth corresponding to the preset maximum indenter indentation depth is identified according to the equivalent elastic modulus to determine the material indentation depth corresponding to several preset maximum indenter indentation depths; a quantitative mapping model between the preset maximum indenter indentation depth and the material indentation depth is established using a nonlinear regression algorithm, so as to determine the material indentation depth corresponding to any preset maximum indenter indentation depth according to the quantitative mapping model, and the test results of the Brinell indenter nanoindentation experiment at the preset maximum indenter indentation depth are mapped to the corresponding material indentation depth. Therefore, this application establishes a quantitative mapping model between the preset maximum indenter depth and the material indentation depth to achieve the mapping of the test results corresponding to the preset maximum indenter depth to the material indentation depth, accurately mapping the nanoindentation test results to a specific depth position of the continuous gradient material. Specifically, this application calculates the equivalent elastic modulus of the preset maximum indenter depth and determines the material indentation depth corresponding to the preset maximum indenter depth based on the equivalent elastic modulus, thereby achieving the mapping between the preset maximum indenter depth and the material indentation depth, ensuring that the subsequent nanoindentation test results are accurately mapped to a specific depth position of the continuous gradient material. Attached Figure Description
[0038] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.
[0039] Figure 1 This is a flowchart of a material indentation depth calibration method based on nanoindentation simulation design disclosed in this application;
[0040] Figure 2 This is a schematic diagram of a two-dimensional finite element model of a continuous gradient thin film disclosed in this application;
[0041] Figure 3 This is a schematic diagram of the elastic modulus distribution of a continuous gradient thin film disclosed in this application;
[0042] Figure 4 This is a schematic diagram of a nanoindentation simulation stress cloud map disclosed in this application;
[0043] Figure 5 This is a schematic diagram of the load-displacement curve of a continuous gradient thin film nanoindentation experiment disclosed in this application;
[0044] Figure 6 This is a schematic diagram of a material indentation depth calibration device based on nanoindentation simulation design disclosed in this application;
[0045] Figure 7 This is a structural diagram of an electronic device disclosed in this application. Detailed Implementation
[0046] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. 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 are within the scope of protection of the present invention.
[0047] Currently, when existing nanoindentation technology is applied to continuous gradient thin film materials, the equivalent mechanical properties obtained by testing generally correspond to the actual indenter depth, but cannot accurately correspond to a specific depth position inside the material.
[0048] Therefore, this application proposes a material indentation depth calibration scheme based on nanoindentation simulation design, which can accurately map the nanoindentation test results to a specific depth position of a continuous gradient material.
[0049] This application discloses a method for calibrating material indentation depth based on nanoindentation simulation design. (See also...) Figure 1 As shown, the method includes:
[0050] Step S11: Establish a finite element geometric model of the continuous gradient material corresponding to the Brinell indenter nanoindentation experiment, and construct a constitutive model of the continuous gradient material with continuously changing elastic modulus through a user-defined field subroutine.
[0051] It should be noted that this application belongs to the interdisciplinary fields of surface modification of high-temperature components for aero-engines, micro / nano mechanical testing, and computational materials science. Hot-end components such as turbine blades of aero-engines operate for extended periods in extreme high-temperature, high-stress, and oxidative corrosion environments. To ensure reliability and improve efficiency, high-performance thin films, such as thermal barrier coatings (TBCs) or integrated thin-film sensors, are often fabricated on the surface of these components. Among these, continuous gradient structure thin films, through continuous and smooth changes in their composition or microstructure along the thickness direction, can effectively mitigate interfacial stress concentration and inhibit crack initiation, making them a key design for achieving high bonding strength and long lifespan. Functionally graded materials are high-performance materials whose composition, structure, and properties change continuously or stepwise with space or time. Gradient materials essentially eliminate macroscopic interfaces, effectively solving the problem of gradual functional changes within the material and achieving the goal of mitigating thermal stress. Functionally graded thin films are novel surface coating thin film structures based on gradient materials. By controlling deposition parameters and the ratio of deposition materials, the composition, microstructure, and properties of the gradient thin film change continuously from the substrate to the surface without interfaces. This unique structure endows gradient films with excellent stress relief and interfacial compatibility when subjected to external forces. Accurately characterizing the distribution of mechanical properties (such as elastic modulus) along the thickness direction of such gradient films is of decisive significance for material design, process optimization, and service safety assessment.
[0052] In this embodiment, establishing the finite element geometric model of the continuous gradient material corresponding to the Brinell indenter nanoindentation experiment includes: establishing a static finite element model in the Abaqus (Abaqus Finite Element Analysis (FEA) Software) environment based on the physical characteristics of the Brinell indenter nanoindentation experiment; setting the finite element model parameters corresponding to the continuous gradient material (continuous gradient film) for the static finite element model according to the actual size of the material to obtain a temporary finite element geometric model; and using adaptive meshing technology to locally refine the contact area of the temporary finite element geometric model to obtain the finite element geometric model of the continuous gradient material.
[0053] It should be noted that the continuous gradient film used in this application can be prepared by laser sintering of SiC-W hybrid particles (silicon carbide-tungsten hybrid particles) with a sintering power of 75W, a printing dot pitch of 0.04mm, and an annealing temperature of 600℃.
[0054] It should be noted that the continuous gradient material finite element geometric model can also be called the indenter-substrate finite element geometric model. Based on the traditional Brinell indenter nanoindentation experiment method, the indenter-substrate finite element geometric model is established. Specifically, based on the physical characteristics of the Brinell indenter nanoindentation experiment, a static finite element model is established in the Abaqus environment. According to the actual size of the continuous gradient film, the basic parameters of the continuous gradient film finite element model are set. Adaptive mesh technology is used to locally refine the mesh in the contact area to ensure the accuracy of the indentation stress field simulation while controlling the global computational scale. Details are described below: An axisymmetric finite element simulation benchmark model is constructed. Based on the axisymmetric physical characteristics of the Brinell indenter nanoindentation experiment, a two-dimensional axisymmetric static / dynamic finite element model is established in the Abaqus environment. The model uses a rigid shell to simulate the indenter, and its cone angle is defined according to standard geometric parameters. The substrate is defined as a deformable domain with dimensions much larger than the indentation influence area to eliminate boundary constraint effects. Corresponding displacement constraints are applied to the bottom of the substrate and the axis of symmetry. Adaptive mesh technology is used to locally refine the mesh in the contact area to ensure the accuracy of the indentation stress field simulation while controlling the global computational scale. See also... Figure 2 The image shown is a schematic diagram of a two-dimensional finite element model of a continuous gradient thin film, which will not be described in detail here.
[0055] It should be noted that the basic parameters (finite element model parameters) of the continuous gradient thin film finite element model include the substrate length, width, and height, the indenter cone angle, and the film thickness and width. It should also be noted that this application uses SEM (Scanning Electron Microscope) analysis to calculate the target volume fraction and spatial density of the continuous gradient thin film mechanical test specimen, and then determines the film thickness and width based on the target volume fraction and spatial density.
[0056] In this embodiment, the step of constructing a constitutive model of a continuously gradient material with a continuously changing elastic modulus through a user-defined field subroutine includes: establishing a target correlation function characterizing the relationship between preset material properties and preset field variables of the continuously gradient material; the preset material properties include the elastic modulus; and inputting the target correlation function into the user-defined field subroutine to construct a constitutive model of a continuously gradient material with a continuously changing elastic modulus.
[0057] It should be noted that the construction of the material constitutive model is as follows: This application establishes user-defined field variables, associates the elastic modulus with the field variables, establishes the functional dependency between material properties and field variables, and associates the field variables with predefined spatial continuous functions through the USDFLD (User-defined Field Variable) / VUSDFLD (Vectorized User-defined Field Variable) subroutines (user-defined field subroutines). The field variable values at the material integration points are dynamically calculated and updated, and the solver feeds the field variable values back to the material constitutive model, thereby accurately characterizing the essential properties of materials with continuous gradient structures. More specifically, this application implements spatial coupling of the material constitutive gradient based on user subroutines. In the material property definition, the elastic modulus parameter is associated with user-defined field variables, establishing the functional dependency between material properties and field variables. Furthermore, Abaqus user-defined field subroutines (USDFLD / VUSDFLD) are written and integrated. The subroutine is characterized by: at each material integration point, its spatial coordinates are read in real time, and the field variable values at that point are dynamically calculated and updated according to a predefined spatial continuity function. The field variable values are then fed back to the material constitutive model through the solver, thereby achieving a continuous and predetermined spatial distribution of parameters such as the elastic modulus, accurately characterizing the essential properties of continuous gradient structure materials.
[0058] In one specific embodiment, spatial coupling of the material constitutive gradient is implemented based on a user subroutine. Based on data obtained from continuous gradient thin film samples, the elastic modulus parameter of 13000MPa-25000MPa is associated with a user-defined field variable in the material property definition using a linear function, establishing a functional dependency between material properties and the field variable. ;in, Indicates the elastic modulus of a material. The spatial depth coordinates (z in three-dimensional coordinates) are represented. Then, Abaqus user-defined field subroutines (USDFLD / VUSDFLD) are written and integrated. The field variable values are fed back to the material constitutive model through the solver, thereby realizing the continuous and predetermined distribution of parameters such as elastic modulus in space, and performing nanoindentation simulations in the subsequent process.
[0059] See Figure 3The diagram shown is a schematic representation of the elastic modulus distribution of a continuous gradient thin film. Specifically, it is included in a constitutive model of a material with a continuous spatial distribution of elastic modulus, established using a user-defined field subroutine. In the diagram, FV1 (representing the first field variable) and 75% indicate that the value has been smoothed and averaged by 75%, achieving an average display of the field variable values. The color of the contour plot represents the magnitude of the elastic modulus at different spatial locations, and the corresponding values are the abbreviated form of the scientific notation of the elastic modulus. For example, +10016e+00 = 10016 × = 10016, indicating that the elastic modulus at this location is E = 10016 MPa. Other details are not specified.
[0060] Step S12: Combine the finite element geometric model of the continuous gradient material and the constitutive model of the continuous gradient material to perform indentation simulation at several preset maximum indentation depths to obtain simulation results; the simulation results include the load-displacement curves of the indenter tip corresponding to the several preset maximum indentation depths.
[0061] See Figure 4 The image shows a schematic diagram of a nanoindentation simulation stress cloud map, belonging to the cloud map corresponding to the simulated stress in the simulation results. In the figure, S Mises refers to the von Mises stress, which is the key equivalent stress for determining the plastic yield of a material. The average 75% is the numerical smoothing display parameter of the cloud map. Different colors correspond to the magnitude of the von Mises stress at different locations in space. For example, +6.955e+02 is the specific value of the von Mises stress at the corresponding location (expressed in scientific notation), +6.955e+02 = 6.955 × = 695.5.
[0062] See Figure 5 The figure shows a schematic diagram of the load-displacement curves of a continuous gradient thin film nanoindentation experiment; the horizontal axis represents the indentation depth (Pd, in nm), and the vertical axis represents the reaction load (Fn, in mN) on the indenter; in the figure, curve 1 represents the curve when the indenter is pressed in, at which point the film is compressed, curve 2 represents the curve when the indenter is unloaded, at which point the film rebounds, but the film has already undergone plastic deformation, so when the indenter is lifted by a small displacement, the film no longer rebounds, and curve 3 represents the curve when the indenter returns to its initial position.
[0063] Step S13: Calculate the equivalent elastic modulus corresponding to the preset maximum indentation depth based on the load-displacement curve, and identify the material indentation depth corresponding to the preset maximum indentation depth according to the equivalent elastic modulus, so as to determine the material indentation depth corresponding to several preset maximum indentation depths respectively.
[0064] In this embodiment, the step of calculating the equivalent elastic modulus corresponding to the preset maximum indentation depth based on the load-displacement curve includes: processing the unloading segment curve of the load-displacement curve using the Oliver-Pharr method to obtain the equivalent elastic modulus corresponding to the preset maximum indentation depth.
[0065] In this embodiment, the step of using the Oliver-Pharr method to process the unloading segment curve of the load-displacement curve to obtain the equivalent elastic modulus corresponding to the preset maximum indentation depth includes: fitting the unloading segment curve of the load-displacement curve to a power-law function, and using the slope corresponding to the preset maximum indentation depth in the power-law function as the contact stiffness; calculating the contact projected area based on the contact stiffness, and calculating the equivalent elastic modulus based on the contact stiffness and the contact projected area; wherein, the power-law function is... ; Indicates load; and The fitting parameters (Berkovic indenter) are typically between 1.2 and 1.6 for an ideal elastomer. =1.5), This represents a coefficient related to the elastic recovery of the material; Indicates the depth of the indenter insertion; The initial value can be assumed to be the final residual depth measured experimentally. The initial value can be assumed to be 1.5. It should be noted that the unloading segment curve of the load displacement curve is fitted with a power law function, specifically the 10%-25% portion of the unloading segment curve.
[0066] In this embodiment, the step of calculating the contact projected area based on the contact stiffness and calculating the equivalent elastic modulus based on the contact stiffness and the contact projected area includes: calculating the contact depth using the contact depth calculation formula and based on the contact stiffness; calculating the contact projected area using the contact projected area calculation formula and based on the contact depth; and calculating the equivalent elastic modulus using the equivalent elastic modulus calculation formula and based on the contact stiffness and the contact projected area; wherein, the contact depth calculation formula is: ;in, Indicates the contact depth; Indicates the preset maximum indentation depth; Indicates the strain value; Indicates the maximum load; This represents the contact stiffness; the formula for calculating the contact projected area is: ; The contact projection area is represented by the formula; the equivalent elastic modulus is calculated as follows: ;in, This represents the equivalent elastic modulus; This indicates the contact stiffness; This represents the projected contact area; This represents the geometric constant of the Brinell indenter. It should be noted that... The value can be set to 1;
[0067] In this embodiment, identifying the material indentation depth corresponding to the preset maximum indenter indentation depth based on the equivalent elastic modulus includes: determining the material indentation depth corresponding to the equivalent elastic modulus based on the preset modulus and depth correspondence, and using the material indentation depth as the material indentation depth corresponding to the preset maximum indenter indentation depth.
[0068] It should be noted that the preset modulus and depth correspondence can be calculated in advance through several analytical simulation results. By analyzing the spatial distribution of stress and strain energy density fields in several analytical simulation results, the key material region that plays a dominant role in the indentation response is identified. The weighted average value of the depth coordinates of the integration point in this region (with equivalent stress or strain energy as the weight) is calculated, and this value is defined as the effective characterization depth of this indentation test. This completes the traceability from macroscopic simulation output to microscopic material location, thereby realizing the correspondence between the indentation depth (preset maximum indenter indentation depth) and the characterization depth (material indentation depth), that is, obtaining the preset modulus and depth correspondence.
[0069] It should be noted that during the modeling stage, a correspondence is established between different depths of the thin film and the elastic modulus. At this point, the elastic modulus at all depths within the thin film is determined. After nanoindentation simulation, analyzing the load-displacement curve yields a definite elastic modulus, i.e., the equivalent elastic modulus. The depth at which this elastic modulus corresponds within the thin film is the effective characterization depth (material indentation depth) mentioned in this paper. For example, if the elastic modulus of the thin film is 10 GPa at 0.1 mm from top to bottom, 15 GPa at 0.2 mm, 20 GPa at 0.3 mm, and 30 GPa at 0.4 mm, then performing a nanoindentation simulation with an indentation depth of 0.2 mm yields an elastic modulus of 30 GPa, corresponding to the 0.4 mm position within the thin film. In this case, when the nanoindentation experiment indents to 0.2 mm, the measured material point is actually at 0.4 mm.
[0070] Step S14: Establish a quantitative mapping model between the preset maximum indenter indentation depth and the material indentation depth using a nonlinear regression algorithm, so as to determine the material indentation depth corresponding to any preset maximum indenter indentation depth according to the quantitative mapping model, and map the test results of the Brinell indenter nanoindentation experiment at the preset maximum indenter indentation depth to the corresponding material indentation depth.
[0071] It should be noted that the quantitative mapping model described in this application is the method for calculating the actual test depth of nanoindentation proposed in this invention. It enables the prediction of the actual internal depth of the material that can be characterized by a controllable indentation depth, or vice versa, providing a theoretical basis and simulation calibration tool for the accurate and quantitative characterization of the mechanical properties of gradient materials.
[0072] It should be noted that a quantitative mapping model between the preset maximum indenter depth and the material indentation depth is established. Under the premise of a fixed material gradient function, a series of nanoindentation simulations with different indentation depths are performed using the preset maximum indenter depth h as the control variable. Based on the obtained dataset, a nonlinear regression algorithm is used for fitting to construct a quantitative mapping model between the preset maximum indenter depth h (μm) and the material indentation depth H (μm) it can represent. .
[0073] It should be noted that, to verify the accuracy of the model, static load nanoindentation experiments were performed on continuous gradient thin film samples, with an indentation depth of h = 1.500 μm. Based on the load-displacement curves obtained from the experiment (see...), the model was validated. Figure 5 The Oliver-Pharr method was applied to fit and analyze the unloading section curve, and the equivalent elastic modulus was calculated to be Er = 20249 MPa. Substituting the indentation depth h into the above model, the effective depth was obtained as H = 6.045 μm. According to the above model, the actual location measured in this nanoindentation experiment is at a depth of H = 6.045 μm, and the elastic modulus at this location is Er = 20249 MPa. Next, it is only necessary to verify whether the elastic modulus at H of the film is the Er obtained by the model. A continuous stiffness nanoindentation experiment was performed on the film, and the elastic modulus at H = 6.045 μm was measured to be 20254 MPa, with a deviation of 0.0247% from the predicted result, proving that the model is reliable.
[0074] As can be seen, this application establishes a continuous gradient material finite element geometric model corresponding to the Brinell indenter nanoindentation experiment, and constructs a continuous gradient material constitutive model with continuously changing elastic modulus through a user-defined field subroutine; the continuous gradient material finite element geometric model and the continuous gradient material constitutive model are combined to perform indentation simulation at several preset maximum indenter indentation depths to obtain simulation results; the simulation results include load-displacement curves of the indenter tip corresponding to several preset maximum indenter indentation depths; the equivalent elastic modulus corresponding to the preset maximum indenter indentation depth is calculated based on the load-displacement curves, and the material indentation depth corresponding to the preset maximum indenter indentation depth is identified according to the equivalent elastic modulus to determine the material indentation depth corresponding to several preset maximum indenter indentation depths; a quantitative mapping model between the preset maximum indenter indentation depth and the material indentation depth is established using a nonlinear regression algorithm, so as to determine the material indentation depth corresponding to any preset maximum indenter indentation depth according to the quantitative mapping model, and the test results of the Brinell indenter nanoindentation experiment at the preset maximum indenter indentation depth are mapped to the corresponding material indentation depth. Therefore, this application establishes a quantitative mapping model between the preset maximum indenter depth and the material indentation depth to achieve the mapping of the test results corresponding to the preset maximum indenter depth to the material indentation depth, accurately mapping the nanoindentation test results to a specific depth position of the continuous gradient material. Specifically, this application calculates the equivalent elastic modulus of the preset maximum indenter depth and determines the material indentation depth corresponding to the preset maximum indenter depth based on the equivalent elastic modulus, thereby achieving the mapping between the preset maximum indenter depth and the material indentation depth, ensuring that the subsequent nanoindentation test results are accurately mapped to a specific depth position of the continuous gradient material.
[0075] Accordingly, this application also discloses a material indentation depth calibration device based on nanoindentation simulation design, see [link to relevant documentation]. Figure 6 As shown, the device includes:
[0076] Model building module 11 is used to establish a continuous gradient material finite element geometric model corresponding to the Brinell indenter nanoindentation experiment. It constructs a continuous gradient material constitutive model with continuously changing elastic modulus through a user-defined field subroutine.
[0077] Simulation module 12 is used to perform indentation simulation at several preset maximum indenter depths by combining the finite element geometric model and the constitutive model of the continuous gradient material, respectively, to obtain simulation results; the simulation results include load-displacement curves of the indenter tip corresponding to several preset maximum indenter depths;
[0078] The material indentation depth determination module 13 is used to calculate the equivalent elastic modulus corresponding to the preset maximum indentation depth based on the load displacement curve, and to identify the material indentation depth corresponding to the preset maximum indentation depth according to the equivalent elastic modulus, so as to determine the material indentation depth corresponding to several preset maximum indentation depths respectively.
[0079] The depth mapping module 14 is used to establish a quantitative mapping model between the preset maximum indenter indentation depth and the material indentation depth using a nonlinear regression algorithm, so as to determine the material indentation depth corresponding to any preset maximum indenter indentation depth according to the quantitative mapping model, and map the test results of the Brinell indenter nanoindentation experiment at the preset maximum indenter indentation depth to the corresponding material indentation depth.
[0080] The more specific working process of each of the above modules can be found in the corresponding content disclosed in the foregoing embodiments, and will not be repeated here.
[0081] As can be seen, this application establishes a continuous gradient material finite element geometric model corresponding to the Brinell indenter nanoindentation experiment, and constructs a continuous gradient material constitutive model with continuously changing elastic modulus through a user-defined field subroutine; the continuous gradient material finite element geometric model and the continuous gradient material constitutive model are combined to perform indentation simulation at several preset maximum indenter indentation depths to obtain simulation results; the simulation results include load-displacement curves of the indenter tip corresponding to several preset maximum indenter indentation depths; the equivalent elastic modulus corresponding to the preset maximum indenter indentation depth is calculated based on the load-displacement curves, and the material indentation depth corresponding to the preset maximum indenter indentation depth is identified according to the equivalent elastic modulus to determine the material indentation depth corresponding to several preset maximum indenter indentation depths; a quantitative mapping model between the preset maximum indenter indentation depth and the material indentation depth is established using a nonlinear regression algorithm, so as to determine the material indentation depth corresponding to any preset maximum indenter indentation depth according to the quantitative mapping model, and the test results of the Brinell indenter nanoindentation experiment at the preset maximum indenter indentation depth are mapped to the corresponding material indentation depth. Therefore, this application establishes a quantitative mapping model between the preset maximum indenter depth and the material indentation depth to achieve the mapping of the test results corresponding to the preset maximum indenter depth to the material indentation depth, accurately mapping the nanoindentation test results to a specific depth position of the continuous gradient material. Specifically, this application calculates the equivalent elastic modulus of the preset maximum indenter depth and determines the material indentation depth corresponding to the preset maximum indenter depth based on the equivalent elastic modulus, thereby achieving the mapping between the preset maximum indenter depth and the material indentation depth, ensuring that the subsequent nanoindentation test results are accurately mapped to a specific depth position of the continuous gradient material.
[0082] Furthermore, embodiments of this application also provide an electronic device. Figure 7 This is a structural diagram of an electronic device 20 according to an exemplary embodiment. The content of the diagram should not be construed as limiting the scope of this application.
[0083] Figure 7 This is a schematic diagram of the structure of an electronic device 20 provided in an embodiment of this application. The electronic device 20 may specifically include: at least one processor 21, at least one memory 22, a display screen 23, an input / output interface 24, a communication interface 25, a power supply 26, and a communication bus 27. The memory 22 stores a computer program, which is loaded and executed by the processor 21 to implement the relevant steps in the material indentation depth calibration method based on nanoindentation simulation design disclosed in any of the foregoing embodiments. Alternatively, the electronic device 20 in this embodiment may specifically be an electronic computer.
[0084] In this embodiment, the power supply 26 is used to provide operating voltage for each hardware device on the electronic device 20; the communication interface 25 can create a data transmission channel between the electronic device 20 and external devices, and the communication protocol it follows can be any communication protocol applicable to the technical solution of this application, and is not specifically limited here; the input / output interface 24 is used to acquire external input data or output data to the outside world, and its specific interface type can be selected according to specific application needs, and is not specifically limited here.
[0085] Furthermore, the memory 22, as a carrier for resource storage, can be a read-only memory, random access memory, disk, or optical disk, etc. The resources stored thereon may include computer programs 221, and the storage method may be temporary storage or permanent storage. In addition to including a computer program capable of performing the material indentation depth calibration method based on nanoindentation simulation design executed by the electronic device 20 as disclosed in any of the foregoing embodiments, the computer program 221 may further include computer programs capable of performing other specific tasks.
[0086] Furthermore, embodiments of this application also disclose a computer-readable storage medium for storing a computer program; wherein, when the computer program is executed by a processor, it implements the aforementioned material indentation depth calibration method based on nanoindentation simulation design.
[0087] The specific steps of this method can be found in the corresponding content disclosed in the foregoing embodiments, and will not be repeated here.
[0088] The various embodiments in this application are described in a progressive manner, with each embodiment focusing on the differences from other embodiments. For the same or similar parts between the various embodiments, refer to each other. As for the apparatus disclosed in the embodiments, since it corresponds to the method disclosed in the embodiments, the description is relatively simple, and relevant parts can be referred to in the method section.
[0089] Those skilled in the art will further recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, computer software, or a combination of both. To clearly illustrate the interchangeability of hardware and software, the components and steps of the various examples have been generally described in terms of functionality in the foregoing description. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of this application.
[0090] The steps of the methods or algorithms described in conjunction with the embodiments disclosed herein can be implemented directly by hardware, a software module executed by a processor, or a combination of both. The software module can be located in random access memory (RAM), main memory, read-only memory (ROM), electrically programmable ROM, electrically erasable programmable ROM, registers, hard disk, removable disk, CD-ROM, or any other form of storage medium known in the art.
[0091] Finally, it should be noted that in this document, relational terms such as "first" and "first" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.
[0092] The foregoing has provided a detailed description of a material indentation depth calibration method, apparatus, device, and storage medium based on nanoindentation simulation design provided in this application. Specific examples have been used to illustrate the principles and implementation methods of this application. The descriptions of the above embodiments are only for the purpose of helping to understand the method and core ideas of this application. At the same time, for those skilled in the art, there will be changes in the specific implementation methods and application scope based on the ideas of this application. Therefore, the content of this specification should not be construed as a limitation of this application.
Claims
1. A method for calibrating material indentation depth based on nanoindentation simulation design, characterized in that, include: A finite element geometric model of a continuous gradient material corresponding to the Brinell indenter nanoindentation experiment was established, and a constitutive model of a continuous gradient material with continuously varying elastic modulus was constructed through a user-defined field subroutine. The continuous gradient material finite element geometric model and the continuous gradient material constitutive model are combined to perform indentation simulation at several preset maximum indentation depths to obtain simulation results; the simulation results include load-displacement curves of the indenter tip corresponding to several preset maximum indentation depths; The equivalent elastic modulus corresponding to the preset maximum indenter indentation depth is calculated based on the load-displacement curve, and the material indentation depth corresponding to the preset maximum indenter indentation depth is identified based on the equivalent elastic modulus, so as to determine the material indentation depth corresponding to several preset maximum indenter indentation depths respectively. A quantitative mapping model between the preset maximum indenter indentation depth and the material indentation depth is established using a nonlinear regression algorithm. This model is used to determine the material indentation depth corresponding to any preset maximum indenter indentation depth, and the test results of the Brinell indenter nanoindentation experiment at the preset maximum indenter indentation depth are mapped to the corresponding material indentation depth.
2. The material indentation depth calibration method based on nanoindentation simulation design according to claim 1, characterized in that, The calculation of the equivalent elastic modulus corresponding to the preset maximum indentation depth based on the load-displacement curve includes: The unloading segment of the load-displacement curve is processed using the Oliver-Pharr method to obtain the equivalent elastic modulus corresponding to the preset maximum indentation depth.
3. The material indentation depth calibration method based on nanoindentation simulation design according to claim 2, characterized in that, The step of processing the unloading segment curve of the load-displacement curve using the Oliver-Pharr method to obtain the equivalent elastic modulus corresponding to the preset maximum indentation depth includes: The unloading segment of the load-displacement curve is fitted to a power law function, and the slope corresponding to the preset maximum indentation depth in the power law function is taken as the contact stiffness. The contact projected area is calculated based on the contact stiffness, and the equivalent elastic modulus is calculated based on the contact stiffness and the contact projected area. Wherein, the power-law function is ; Indicates load; and Indicates the fitted parameters; Indicates the depth of the indenter insertion; This indicates the final residual depth.
4. The material indentation depth calibration method based on nanoindentation simulation design according to claim 3, characterized in that, The step of calculating the contact projected area based on the contact stiffness and calculating the equivalent elastic modulus based on the contact stiffness and the contact projected area includes: The contact depth is calculated using the contact depth calculation formula and based on the contact stiffness; the contact projected area is calculated using the contact projected area calculation formula and based on the contact depth. The equivalent elastic modulus is calculated using the formula for calculating the equivalent elastic modulus and based on the contact stiffness and the contact projected area. The formula for calculating the contact depth is as follows: ;in, Indicates the contact depth; Indicates the preset maximum indentation depth; Indicates the strain value; Indicates the maximum load; This represents the contact stiffness; the formula for calculating the contact projected area is: ; The contact projection area is represented by the formula; the equivalent elastic modulus is calculated as follows: ;in, This represents the equivalent elastic modulus; This indicates the contact stiffness; This represents the projected contact area; This represents the geometric constant of the Burgh indenter.
5. The material indentation depth calibration method based on nanoindentation simulation design according to claim 1, characterized in that, The construction of a continuous gradient material constitutive model with continuously varying elastic modulus through a user-defined field subroutine includes: Establish a target correlation function to characterize the relationship between preset material properties and preset field variables of a continuous gradient material; the preset material properties include the elastic modulus. The target correlation function is input into a user-defined field subroutine to construct a constitutive model of a continuously gradient material with a continuously varying elastic modulus.
6. The method for calibrating material indentation depth based on nanoindentation simulation design according to claim 1, characterized in that, The step of identifying the material indentation depth corresponding to the preset maximum indenter indentation depth based on the equivalent elastic modulus includes: The material indentation depth corresponding to the equivalent elastic modulus is determined according to the preset modulus and depth correspondence, and the material indentation depth is used as the material indentation depth corresponding to the preset maximum indenter indentation depth.
7. The method according to any one of claims 1 to 6, characterized in that, The establishment of the continuous gradient material finite element geometric model corresponding to the Brinell indenter nanoindentation experiment includes: Based on the physical characteristics of the Brinell indenter nanoindentation experiment, a static finite element model was established in the Abaqus environment. Based on the actual dimensions of the continuous gradient material, a temporary finite element geometric model is obtained by setting the finite element model parameters corresponding to the continuous gradient material for the static finite element model. Adaptive meshing technology is used to locally refine the contact region of the temporary finite element geometric model to obtain a continuous gradient material finite element geometric model.
8. A material indentation depth calibration device based on nanoindentation simulation design, characterized in that, include: The model building module is used to establish a continuous gradient material finite element geometric model corresponding to the Brinell indenter nanoindentation experiment. It constructs a continuous gradient material constitutive model with continuously changing elastic modulus through user-defined field subroutines. The simulation module is used to perform indentation simulations at several preset maximum indentation depths by combining the finite element geometric model and the constitutive model of the continuous gradient material, respectively, to obtain simulation results; the simulation results include the load-displacement curves of the indenter tip corresponding to the several preset maximum indentation depths; The material indentation depth determination module is used to calculate the equivalent elastic modulus corresponding to the preset maximum indentation depth based on the load-displacement curve, and to identify the material indentation depth corresponding to the preset maximum indentation depth based on the equivalent elastic modulus, so as to determine the material indentation depth corresponding to several preset maximum indentation depths respectively. The depth mapping module is used to establish a quantitative mapping model between the preset maximum indenter indentation depth and the material indentation depth using a nonlinear regression algorithm, so as to determine the material indentation depth corresponding to any preset maximum indenter indentation depth according to the quantitative mapping model, and map the test results of the Brinell indenter nanoindentation experiment at the preset maximum indenter indentation depth to the corresponding material indentation depth.
9. An electronic device, characterized in that, include: Memory, used to store computer programs; A processor for executing the computer program to implement the material indentation depth calibration method based on nanoindentation simulation design as described in any one of claims 1 to 7.
10. A computer-readable storage medium, characterized in that, Used to store computer programs; wherein, when the computer programs are executed by a processor, they implement the material indentation depth calibration method based on nanoindentation simulation design as described in any one of claims 1 to 7.