A method for predicting mechanical properties of coal modified by nanofluid

Abstract

The application provides a method for predicting mechanical properties of nanofluid modified coal body, and relates to the technical field of coal mine safety engineering and material characterization. The method comprises the following steps: constructing a coal molecule initial model, obtaining a coal molecule model through geometric optimization and annealing treatment, constructing a coal molecule box through Monte Carlo random reconstruction and optimizing to obtain a coal pore model; constructing an AES-SiO2 nanofluid model; assembling the coal pore model and the nanofluid model at an interface to obtain a coal-nanofluid fluid-solid coupling interface model; performing molecular dynamics relaxation simulation to obtain a stable configuration; performing molecular dynamics nanoindentation simulation to extract a force-displacement curve; performing data processing based on the force-displacement curve to calculate mechanical parameters, and realizing the prediction of mechanical properties of the modified coal body. The application can predict the mechanical properties of the coal body after nanofluid modification from the molecular level, and provides a theoretical basis for deep coal seam mining.

Description

Technical Field

[0001] This application relates to the fields of coal mine safety engineering and materials characterization technology, and in particular to a method for predicting the mechanical properties of coal modified by nanofluids. Background Technology

[0002] In coal mining, the stability and safety of deep coal seams are crucial research topics. As mining depth increases, the geological environment of the coal seam becomes more complex, with frequent occurrences of harsh conditions such as high temperature, high pressure, and high gas content. These factors significantly affect the physical and mechanical properties of the coal body, thus posing severe challenges to borehole stability, gas extraction efficiency, and the prevention and control of coal and gas outbursts.

[0003] Traditionally, methods to improve the stability of coal seams have relied heavily on physical reinforcement techniques, such as grouting and anchor bolting. While these methods have improved the overall stability of coal seams to some extent, their effectiveness is often limited under deep and complex geological conditions, and they are also costly and difficult to implement. Meanwhile, chemical modification methods, as an emerging technology, are gradually attracting the attention of researchers because they can alter the structural properties of coal seams at the microscopic level.

[0004] Nanofluid technology, as a cutting-edge field in chemical modification, effectively enhances the water absorption capacity of coal by injecting fluids containing nanoparticles into coal seam fissures. This leads to efficient softening of the coal body, increased plastic fracturing, and reduced elastic energy release, thereby eliminating stress concentration effects around the coal seam and reducing the occurrence of coal and gas outbursts. However, existing research largely focuses on the macroscopic experimental characterization of nanofluid-modified coal, lacking a systematic methodology to reveal the interaction mechanism between nanofluids and coal and the evolution of their mechanical properties at the molecular level.

[0005] Currently, although some studies have involved the application of nanofluids in coal modification, most of them focus on macroscopic experimental characterization and lack a systematic approach to reveal the interaction mechanism between nanofluids and coal and the evolution of mechanical properties at the molecular level. Summary of the Invention

[0006] This application provides a method for predicting the mechanical properties of coal modified by nanofluids. Addressing the shortcomings of existing research, which largely focuses on macroscopic experimental characterization of nanofluid-modified coal and lacks a systematic approach to revealing the interaction mechanism and mechanical property evolution of nanofluids and coal at the molecular level, this method constructs a coal-nanofluid composite structure model and combines it with molecular dynamics nanoindentation simulation to obtain the mechanical parameters of the modified coal at the molecular level. This fills the technological gap in predicting the microscopic mechanical properties of nanofluid-modified coal and provides a theoretical basis for stabilizing deep coal seam drilling, improving gas extraction efficiency, and preventing coal and gas outbursts.

[0007] To achieve the above objectives, this application adopts the following technical solution: This application provides a method for predicting the mechanical properties of coal modified by nanofluids, the method comprising: An initial model of coal molecules is constructed, and the initial model of coal molecules is geometrically optimized and annealed to obtain an optimized coal molecule model. A coal molecule box composed of coal molecules in the optimized coal molecule model is constructed by Monte Carlo random reconstruction, and the coal molecule box is geometrically optimized and annealed to obtain a coal pore model. AES molecule and SiO2 molecule models were constructed, and the AES molecule and SiO2 molecule models were subjected to geometric optimization and annealing, respectively. Based on the optimized SiO2 molecule model, a SiO2 cluster model was constructed. The optimized AES molecule was grafted onto the SiO2 cluster through a hydrolysis-condensation reaction. After geometric optimization and annealing, a composite cluster model of AES activator molecules and SiO2 nanoparticles was obtained. A composite cluster box composed of the composite clusters in the composite cluster model was constructed by Monte Carlo random reconstruction. The composite cluster box was subjected to geometric optimization and annealing to obtain an AES-SiO2 nanofluid model. The coal pore model and the AES-SiO2 nanofluid model are interfacially assembled to generate an initial interlayer composite structure, and a vacuum layer is added at the top of the system to obtain a coal-nanofluid fluid-solid coupling interface model. Based on the aforementioned coal-nanofluid fluid-structure interaction interface model, molecular dynamics relaxation simulations were performed to bring the system to thermodynamic equilibrium, thereby obtaining a stable configuration of the modified coal-nanofluid composite structure. Based on the stable configuration of the modified coal-nanofluid composite structure, molecular dynamics nanoindentation simulation was performed. A virtual indenter load was applied and the atomic force and displacement response during the indentation process were recorded, and the force-displacement curve was extracted. Based on the force-displacement curve, the mechanical parameters are calculated using the Oliver-Pharr method or the atomic stress integral method, thereby enabling the prediction of the mechanical properties of the modified coal.

[0008] Preferably, in the above-mentioned method for predicting the mechanical properties of coal modified by nanofluids, the step of constructing a coal molecule box composed of coal molecules in the optimized coal molecule model through Monte Carlo random reconstruction includes: Based on the optimized coal molecule model, coal molecules are filled within a three-dimensional periodic box using a Monte Carlo method of random insertion and energy screening. After each attempt to insert a coal molecule, the total energy change of the system caused by the insertion is calculated. The acceptance probability of this insertion event is calculated using the following formula. : ; in, Boltzmann's constant, For temperature; each time an insertion attempt is made, a uniformly random number within the interval [0,1] is generated independently. If this uniformly random number is less than or equal to the acceptance probability... If the result is positive, the insertion is accepted; otherwise, the insertion is rejected, and the coal molecule is not placed in the box. The above random insertion and judgment process is repeated until the target density is reached, and the coal molecule box is obtained.

[0009] Preferably, in the above-mentioned method for predicting the mechanical properties of coal modified by nanofluids, the step of constructing a composite cluster box composed of composite clusters in the composite cluster model through Monte Carlo random reconstruction, and performing geometric optimization and annealing on the composite cluster box to obtain the AES-SiO2 nanofluid model includes: Based on the AES-SiO2 composite clusters in the composite cluster model, the system is filled in a three-dimensional periodic box using a Monte Carlo method of random insertion and energy screening. After each attempt to insert a composite cluster, the total energy change of the system caused by the insertion is calculated, and the acceptance probability of the insertion event is calculated. For each insertion attempt, a uniform random number in the interval [0,1] is generated independently. If the uniform random number is less than or equal to the acceptance probability, the insertion is accepted; otherwise, the insertion is rejected, and the composite cluster is not placed in the box. The above random insertion and judgment process is repeated until the target density is reached. After filling, the system undergoes geometric optimization and annealing to obtain the AES-SiO2 nanofluid model.

[0010] Preferably, in the above-mentioned method for predicting the mechanical properties of coal modified by nanofluids, the coal pore model and the AES-SiO2 nanofluid model are interfacially assembled to generate an initial interlayer composite structure, and a vacuum layer is added at the top of the system to obtain a coal-nanofluid fluid-structure interaction interface model, including: The coal pore model and the AES-SiO2 nanofluid model are assembled at the interface. An initial interlayer spacing is set and the minimum strain lattice matching mode is enabled. The maximum strain of the interface lattice is controlled to not exceed 2%. At the same time, layered geometric constraints are applied to fix all atoms of the coal pore substrate in the coal pore model, release the triaxial motion degrees of freedom of the layer where the AES-SiO2 nanofluid model is located, and set the minimum atomic distance constraint at the interface to avoid atomic overlap. An initial interlayer composite structure is generated, and a vacuum layer is added at the top of the system to obtain the coal-nanofluid fluid-structure interaction interface model.

[0011] Preferably, in the above-mentioned method for predicting the mechanical properties of coal modified by nanofluids, molecular dynamics relaxation simulation is performed based on the coal-nanofluid fluid-structure interaction interface model to bring the system to thermodynamic equilibrium and obtain a stable configuration of the modified coal-nanofluid composite structure, including: Molecular dynamics relaxation simulations were performed on the coal-nanofluid fluid-structure interaction interface model. The initial configuration of the coal-nanofluid fluid-structure interaction interface model was minimized using the conjugate gradient method until the maximum force on the system was less than 10. -4  eV / A˚; Simulated annealing is performed in the NVT ensemble, heating from a first temperature to a second temperature at a set target heating rate, holding for a set time, and then cooling back to the first temperature at the target heating rate; Equilibrium relaxation is performed in the NPT ensemble, with the first temperature as the target temperature, setting the damping coefficient and isotropic pressure, and the system temperature fluctuates within ±5% of the target temperature while the energy convergence parameter Δ E When the value is less than 0.001, thermodynamic equilibrium is considered to have been reached, and the final configuration after equilibrium is recorded as the stable configuration of the modified coal-nanofluid composite structure.

[0012] Preferably, in the above-mentioned method for predicting the mechanical properties of nanofluid-modified coal, based on the stable configuration of the modified coal-nanofluid composite structure, molecular dynamics nanoindentation simulation is performed, a virtual indenter load is applied and the atomic force and displacement response during the indentation process is recorded, and the force-displacement curve is extracted, including: The composite structure model corresponding to the stable configuration of the modified coal-nanofluid composite structure is divided into three regions: the bottom 1 / 6 of the model is a boundary layer, where atoms are fixed to prevent overall rigid body displacement; the atoms above the boundary layer are a isothermal layer, which is maintained at a constant temperature using the Nose-Hoover heat bath method to dissipate the heat generated during the indentation process; the remaining 2 / 3 of the model is a Newtonian layer, where motion follows the classical Newton's second law. A virtual spherical rigid indenter with a radius of 4-5 nm is used as the virtual indenter. The initial position is above the sample surface. After the virtual indenter contacts the sample surface, it is loaded at a constant rate along the negative Z-axis. After reaching the set peak load, the load is maintained and then unloaded. Data on the depth change of the virtual indenter in the coal body are collected. Combined with the set load, the force-displacement curve is obtained.

[0013] Preferably, in the above-mentioned method for predicting the mechanical properties of coal modified by nanofluids, the mechanical parameters include elastic recovery rate. Contact stiffness Equivalent elastic modulus True elastic modulus Nano hardness The proportion of plastic deformation Total loading power Elastic rebound function Plastic dissipation work Plastic dissipation coefficient Stress relaxation amount Stress relaxation rate Interface critical failure load F c Critical depth of interface failure h c .

[0014] Preferably, in the above-mentioned method for predicting the mechanical properties of coal modified by nanofluids, the elastic recovery rate is calculated. Contact stiffness Equivalent elastic modulus True elastic modulus ,include: Extract the maximum indentation depth corresponding to the peak load at the loading endpoint from the force-displacement curve. and the depth of residual indentation after unloading The elastic recovery rate is calculated using the following formula. : ; The contact stiffness is calculated using the following formula. : ; in, This represents the load change during the initial stage of the unloading phase. This represents the corresponding displacement change; Based on the Hertz contact model between a spherical rigid indenter and an elastic matrix, the equivalent elastic modulus of the composite system is calculated using the following formula. : ; in, The pressure head exhibits Z-axis repulsive force; For effective indentation depth; Based on the elastic modulus of the virtual rigid indenter → The true elastic modulus of the specimen is calculated using the following formula. : ; in, The Poisson's ratio for a coal-based composite system.

[0015] Preferably, in the above-mentioned method for predicting the mechanical properties of coal modified by nanofluids, the nanohardness is calculated. The proportion of plastic deformation Total loading power Elastic rebound function Plastic dissipation work and plastic dissipation coefficient ,include: The contact radius is calculated using the spherical indentation contact projected area method and the following formula. : ; According to the contact radius The contact projected area is calculated using the following formula. : ; Based on peak load With the contact projected area Nanohardness is calculated using the following formula. : ; Based on the maximum indentation depth and residual indentation depth The proportion of plastic deformation is calculated using the following formula. : ; Integrating the loading and unloading segments of the force-displacement curve respectively, the total loading work is calculated using the following formula. Elastic rebound function and plastic dissipation work : ; ; ; in, The load on the loading segment is a function of the indentation depth. The unloading section load is a function of the indentation depth; According to the plastic dissipation work and the total loading power The plastic dissipation coefficient is calculated using the following formula. : .

[0016] Preferably, in the above-mentioned method for predicting the mechanical properties of coal modified by nanofluids, the stress relaxation amount is calculated. Stress relaxation rate Interface critical failure load F c Critical depth of interface failure h c ,include: Extracting the peak load during the load-holding phase With stable afterload The stress relaxation amount is calculated using the following formula. : ; According to the stress relaxation amount With the peak load The stress relaxation rate is calculated using the following formula. : The load value corresponding to the first sudden drop in load in the loading segment of the force-displacement curve is taken as the critical interface failure load. F c The indentation depth corresponding to this load value is taken as the critical indentation depth for interface failure. h c .

[0017] The method for predicting the mechanical properties of coal modified by nanofluids provided in this application has at least the following beneficial effects: This application constructs an initial model of coal molecules, and obtains a coal pore model with nanoscale pore structure through geometric optimization and annealing to accurately characterize the microstructure of coal. Simultaneously, an AES-SiO2 nanofluid model is constructed. By interfacially assembling the coal pore model and the AES-SiO2 nanofluid model and adding a vacuum layer at the top of the system, a coal-nanofluid fluid-solid coupling interface model is built that can realistically reflect the adsorption and spreading state of nanofluids on the coal surface. Molecular dynamics relaxation simulation is used to bring the system to thermodynamic equilibrium and obtain a stable configuration of the modified coal-nanofluid composite structure, ensuring that the simulated system is in a minimum energy equilibrium state. Based on this, molecular dynamics nanoindentation simulation is performed, recording the atomic force and displacement response through a virtual indenter loading-holding-unloading process and extracting force-displacement. The force-displacement curves are processed using the Oliver-Pharr method or atomic stress integral method to calculate a series of micromechanical parameters, including elastic recovery rate, contact stiffness, equivalent elastic modulus, true elastic modulus, nanohardness, plastic deformation ratio, loading work, elastic rebound work, plastic dissipation work, plastic dissipation coefficient, stress relaxation amount, stress relaxation rate, interface critical failure load, and interface failure critical depth. This allows for the quantitative evaluation of the mechanical properties of nanofluid-modified coal from multiple dimensions, including elastic response, plastic deformation, energy dissipation, and interfacial bonding strength. This fills the gap in existing technologies for predicting the mechanical properties of nanofluid-modified coal at the molecular level, providing theoretical support for the chemical-mechanical synergistic regulation of deep coal seam borehole stability control, gas extraction efficiency improvement, and coal and gas outburst disaster prevention. Attached Figure Description

[0018] The accompanying drawings, which are incorporated in and form part of this specification, illustrate embodiments consistent with this application and, together with the description, serve to explain the principles of this application.

[0019] Figure 1 A technical roadmap for a method to predict the mechanical properties of coal modified by nanofluids, provided for embodiments of this application; Figure 2 A flowchart illustrating a method for predicting the mechanical properties of coal modified by nanofluids, provided for embodiments of this application; Figure 3 Load-unloading curves for indentation testing provided in this application embodiment.

[0020] The accompanying drawings illustrate specific embodiments of this application, which will be described in more detail below. These drawings and descriptions are not intended to limit the scope of the concept in any way, but rather to illustrate the concepts of this application to those skilled in the art through reference to specific embodiments. Detailed Implementation

[0021] Exemplary embodiments will now be described in detail, examples of which are illustrated in the accompanying drawings. When the following description relates to the drawings, unless otherwise indicated, the same numbers in different drawings denote the same or similar elements. The embodiments described in the following exemplary embodiments do not represent all embodiments consistent with this application. Rather, they are merely examples of apparatuses and methods consistent with some aspects of this application as detailed in the appended claims.

[0022] The technical solution of this application and how the technical solution of this application solves the above-mentioned technical problems are described in detail below with specific embodiments. These specific embodiments can be combined with each other, and the same or similar concepts or processes may not be described again in some embodiments. The embodiments of this application will be described below with reference to the accompanying drawings.

[0023] This application provides a method for predicting the mechanical properties of coal modified by nanofluids, such as... Figure 1As shown, this method includes the following steps: constructing a coal pore model, constructing an AES-SiO2 nanofluid model, establishing a coal-nanofluid fluid-structure interaction model based on the constructed coal pore model and AES-SiO2 nanofluid model, conducting long-term molecular dynamics simulations to equilibrium based on this interaction model to obtain a modified coal-nanofluid composite structure model, constructing an indenter-sample system model based on this composite structure model, performing nanoindentation simulations, extracting force-displacement data, and predicting the mechanical properties of coal based on the extracted data results. This method is based on comprehensive and reliable data, has a clear design concept, and achieves accurate prediction of the mechanical properties of modified coal by compound nanofluids, providing a chemical-mechanical synergistic control method for drilling stability and outburst prevention in deep coal seams.

[0024] Specifically, such as Figure 2 As shown, the method for predicting the mechanical properties of coal modified by nanofluids includes the following steps S10-S60.

[0025] S10: Construct an initial coal molecule model, perform geometric optimization and annealing on the initial coal molecule model to obtain an optimized coal molecule model; construct a coal molecule box composed of coal molecules in the optimized coal molecule model through Monte Carlo random reconstruction, perform geometric optimization and annealing on the coal molecule box to obtain a coal pore model.

[0026] In this embodiment, step S10, by constructing an initial coal molecule model and performing geometric optimization and annealing, can eliminate unreasonable bond lengths, bond angles, and dihedral angle tensions within the molecules, allowing individual coal molecules to relax to the stable conformation with the lowest energy, thus providing an accurate molecular structural basis for subsequent stacking modeling. Monte Carlo random reconstruction is used to construct a coal molecule box composed of coal molecules from the optimized coal molecule model. Geometric optimization and annealing are then performed on the coal molecule box under three-dimensional periodic boundary conditions, allowing coal molecules to fully slide and rearrange within a limited space, naturally forming nanoscale pore structures between molecules. This yields a coal pore model that reflects the microscopic morphology of raw coal, providing a reliable solid substrate for subsequent simulations of nanofluid adsorption, diffusion, and interfacial interactions.

[0027] In some embodiments, based on Materials Studio software, a coal molecular model is first constructed, followed by geometric optimization and annealing to obtain the coal molecular model. In this embodiment, the model is anthracite molecule with the molecular formula C2. 145 H 96 NO5. Next, using the AC module (Amorphous Cell) in the software, the Monte Carlo random reconstruction method is used to construct a coal molecule box, which is composed of coal molecules. After geometric optimization and annealing, a coal pore model is obtained.

[0028] Two types of computational models were constructed: a single anthracite molecule model and a coal molecule aggregate pore box model. Geometric optimization and molecular dynamics annealing relaxation were then performed sequentially to obtain the equilibrium coal pore structure. The modeling and structural relaxation were achieved throughout the process using the Build module, Forcite module, and Amorphous Cell (AC) module.

[0029] In this embodiment, the coal molecular model is the anthracite single-molecule model (C). 145 H 96 NO5), its expression is: Coal=Aromatic core +Alkyl side chains+Heteroatomgroups Where: Aromatic core Aromatic carbon skeleton; Alkyl side chains; Heteroatom groups (this model includes N and O functional groups).

[0030] The anthracite single-molecule model (C) 145 H 96 The construction process of NO5 is as follows: Step 1) Skeleton Construction: In MS, draw the aromatic ring matrix of anthracite, and sequentially add alkyl branches, oxygen-containing (hydroxyl, ether bond) and nitrogen-containing heteroatom groups, matching the molecular formula C 145 H 96 NO5, to fill all the saturated and unsaturated carbon sites of hydrogen atoms.

[0031] Step 2) Geometric optimization: (Initial structural relaxation) Select the Forcite module, set the Compass force field, and ensure that the energy, force, and displacement all reach the high-precision threshold of the software to eliminate unreasonable bond lengths, bond angles, and dihedral angle tensions within the molecule, thereby obtaining a preliminary stable unimolecular configuration.

[0032] Step 3) Annealing kinetics: NVT canonical ensemble annealing simulation is used: the temperature is raised to 1000 K for high-temperature isothermal relaxation, and then linearly cooled to 300 K for room temperature; local molecular stress is released in the high-temperature section, and stable low-energy conformation is locked in the low-temperature section. After annealing, the equilibrium anthracite single-molecule model is output.

[0033] The coal pore model is constructed using optimized annealed single anthracite molecules as basic units. A three-dimensional periodic box is constructed using the Monte Carlo random filling algorithm of the AC module. A large number of coal molecules are stacked randomly, and nanoscale pores are naturally formed between the molecules, which is the coal pore medium model, used for microscopic simulation of fluid adsorption, diffusion, and wettability.

[0034] The composition expression of the box system in the pore model: Coalbox =N*Coal; where N: the number of anthracite macromolecules filling the box; Coal: a single coal molecule that has been relaxed as described above.

[0035] Specifically, during construction, AC employs a random insertion + energy-screened Monte Carlo method, with a single-molecule insertion acceptance probability of: : in, Boltzmann's constant, For temperature; each time an insertion attempt is made, a uniformly random number within the interval [0,1] is generated independently. If this uniformly random number is less than or equal to the acceptance probability... If the result is positive, the insertion is accepted; otherwise, the insertion is rejected, and the coal molecule is not placed in the box. The above random insertion and judgment process is repeated until the target density is reached, and the coal molecule box is obtained.

[0036] The boundary conditions for the three-dimensional periodic box are: ; in, The x, y, and z axes represent the side lengths of the box, simulating an infinitely extending coal body and eliminating surface boundary effects.

[0037] This embodiment constructs a coal porosity model using AC module modeling and a two-step relaxation process. The specific steps are as follows: Step 1. After the first step of annealing, the lowest energy anthracite single-molecule C 145 H 96 NO5 is imported into the AmorphousCell module as a filler component.

[0038] Step 2. Set the target box size, number of filling molecules, and density. The software uses a Monte Carlo random algorithm to batch-dispense coal molecules, generating an initial disordered stack of coal molecule boxes.

[0039] Step 3. The Compass force field of the Forcite module is used for global geometry optimization to eliminate close-range repulsion and unreasonable stacking between molecules, thereby reducing the initial total potential energy of the system.

[0040] Step 4. Utilize the NVT ensemble for high-temperature relaxation to release the internal stress of molecular stacking, and slowly cool down to room temperature to allow coal molecules to fully slide and rearrange, forming naturally developed intermolecular nanopores; after relaxation, an equilibrium coal pore box model is obtained, which can be directly used for subsequent simulations of adsorption, molecular diffusion, and fluid wetting.

[0041] S20: Construct AES and SiO2 molecular models, and perform geometric optimization and annealing on the AES and SiO2 molecular models respectively; construct a SiO2 cluster model based on the optimized SiO2 molecular model, and graft the optimized AES molecules onto the SiO2 clusters through a hydrolysis-condensation reaction, and obtain a composite cluster model of AES activator molecules and SiO2 nanoparticles through geometric optimization and annealing; construct a composite cluster box composed of composite clusters in the composite cluster model through Monte Carlo random reconstruction, and perform geometric optimization and annealing on the composite cluster box to obtain an AES-SiO2 nanofluid model.

[0042] In this embodiment, step S20 constructs AES molecule and SiO2 molecule models respectively and performs geometric optimization and annealing to obtain their respective energy-stable molecular configurations, ensuring the structural rationality of the monomer molecules before the grafting reaction. Based on the optimized SiO2 molecule model, a SiO2 cluster model is constructed, and the optimized AES molecules are grafted onto the SiO2 clusters through a hydrolysis-condensation reaction. This can simulate the chemical modification state of surfactants on the surface of nanoparticles in nanofluids. By controlling the grafting density, graft chain length, and terminal functional group type of AES molecules, the dispersion stability of nanofluids can be flexibly adjusted to adapt to different simulation requirements. After geometric optimization and annealing, a composite cluster model of AES surfactant molecules and SiO2 nanoparticles is obtained. Then, a composite cluster box composed of composite clusters in the composite cluster model is constructed through Monte Carlo random reconstruction and geometric optimization and annealing are performed to make the composite clusters uniformly dispersed in three-dimensional space and achieve energy balance, thereby obtaining an AES-SiO2 nanofluid model corresponding to the experimental system, accurately characterizing the aggregation state and dispersion characteristics of nanofluids.

[0043] In some embodiments, step S20 involves first constructing AES molecule and SiO2 molecule models, with molecular formulas C0 and C2 respectively. 14 H 29 O5NaS and SiO2 were used, and their geometry was optimized and annealed to obtain a processed molecular model for later use. Then, a SiO2 cluster model was constructed based on the SiO2 molecular model, and AES molecules were grafted onto the SiO2 clusters through a hydrolysis-condensation reaction, controlling the grafting density of AES molecules to be 1-8 molecules / nm. 2The dispersion stability of the nanofluid was controlled by adjusting the graft chain length and the type of terminal functional groups. The binding state of AES activator and SiO2 nanoparticles in the nanofluid was simulated. The Forcite module was used for geometry optimization and annealing. The force field was selected as Compass. The composite cluster model of AES activator molecules and SiO2 nanoparticles was obtained by high-temperature relaxation using the NVT ensemble. Then, the AC module (AmorphousCell) in the software was used to construct the composite cluster box using the Monte Carlo random reconstruction method. After geometry optimization and annealing, the AES-SiO2 nanofluid model was obtained.

[0044] S30: The coal pore model and the AES-SiO2 nanofluid model are assembled at the interface to generate an initial interlayer composite structure. A vacuum layer is added at the top of the system to obtain the coal-nanofluid fluid-solid coupling interface model.

[0045] In this embodiment, step S30 involves assembling the coal pore model and the AES-SiO2 nanofluid model at the interface, setting the initial interlayer spacing, and activating the minimum strain lattice matching mode. This allows for a smooth transition of the lattice parameters between the two models at the interface, reducing the artificial stress introduced by lattice mismatch. By applying layered geometric constraints, all atoms of the coal pore substrate are fixed, the triaxial motion degrees of freedom of the nanofluid layer are released, and minimum atomic distance constraints are set at the interface to avoid atomic overlap, ensuring the physical rationality of the interatomic forces at the interface. A vacuum layer is added at the top of the system to eliminate the interference of periodic boundaries on the interface interaction, thereby constructing a coal-nanofluid fluid-structure interaction interface model that can reflect the adsorption and spreading state of the nanofluid on the coal surface, providing an accurate initial configuration for subsequent relaxation simulations.

[0046] In some embodiments, step S30 involves using the Build Layers tool in Materials Studio software to perform interface assembly. The coal pore skeleton model (coal pore model) that has undergone geometric optimization and surface saturation treatment, and the AES-SiO2 nanofluid thin-layer model that has undergone molecular dynamics pre-equilibrium treatment. The coal pore substrate is first imported as the bottom solid phase, and the AES-SiO2 nanofluid monolayer is imported as the upper liquid phase. An initial interlayer spacing of 3.0 Å is set, and the minimum strain lattice matching mode is enabled. The maximum strain of the interface lattice is controlled to not exceed 2% to weaken the artificial stress introduced by lattice mismatch. At the same time, layered geometric constraints are applied to fix all atoms of the coal pore substrate, and the triaxial motion degrees of freedom of the nanofluid layer are released. The minimum atomic distance constraint of the interface is set to avoid atomic overlap. After completing lattice matching and interlayer constraints, an initial interlayer composite structure is generated. Then, a vacuum layer is added at the top of the system to eliminate periodic boundary interference, and a preliminary coal-nanofluid fluid-structure interaction interface model is obtained.

[0047] S40: Based on the coal-nanofluid fluid-solid coupling interface model, molecular dynamics relaxation simulation is performed to bring the system to thermodynamic equilibrium and obtain a stable configuration of the modified coal-nanofluid composite structure.

[0048] In this embodiment, step S40 performs molecular dynamics relaxation simulation on the coal-nanofluid fluid-structure interaction interface model. The conjugate gradient method is used to minimize the energy of the initial configuration, which can quickly eliminate the high-energy configuration introduced by atomic overlap and reduce the system force to below the convergence threshold. Simulated annealing is performed under the NVT ensemble. High-temperature isothermal relaxation allows the AES molecular chains to obtain sufficient kinetic energy to overcome the rotational energy barrier and achieve reorientation. Then, the temperature is slowly cooled to room temperature to lock the molecular chains in a lower-energy conformation, optimizing the adsorption configuration and arrangement of the nanofluid layer on the coal surface. Long-term equilibrium relaxation is performed under the NPT ensemble to stabilize the temperature and pressure of the system near the target values ​​and to converge the total energy of the system to a minimum, obtaining a stable configuration of the modified coal-nanofluid composite structure in thermodynamic equilibrium. This ensures that the mechanical response data of the subsequent nanoindentation simulation has statistical reliability and physical authenticity.

[0049] In some embodiments, step S40, in its specific implementation, involves using the Dynamics function in the Forcite module of Materials Studio software, based on the constructed coal-nanofluid fluid-structure interaction model, to perform molecular dynamics relaxation simulation on the multi-scale fluid-structure interaction model. Under the NPT ensemble, the system reaches thermodynamic equilibrium, obtaining a stable configuration of the modified coal-nanofluid composite structure. First, the conjugate gradient method is used to minimize the energy of the initial configuration, eliminating unreasonable atomic overlap, until the maximum force on the system is less than 10. -4 eV / Å, and then simulated annealing was performed in the NVT ensemble: the temperature was increased from 300 K to 600 K (heating rate 50 K / ps), held for 100 ps, ​​and then cooled to 300 K at 50 K / ps. This process helps to reorient the AES molecular chains and optimize the interface structure. Next, long-term equilibrium relaxation was performed in the NPT ensemble, with the target temperature set at 300 K, the damping coefficient at 100 fs, and the isotropic pressure at 0.1 MPa. When the system temperature fluctuates within ±5% of the target temperature and the energy convergence parameter ΔE < 0.001, it is considered to have reached thermodynamic equilibrium. The final configuration after equilibrium was recorded as the stable configuration of the modified coal-nanofluid composite structure. At this time, the AES-SiO2 composite clusters should be fully dispersed and bound to the coal pores to simulate the coal body modified by nanofluid, which will be used as the sample for subsequent prediction of the mechanical properties of the coal body.

[0050] S50: Based on the stable configuration of the modified coal-nanofluid composite structure, molecular dynamics nanoindentation simulation was performed. A virtual indenter load was applied and the atomic force and displacement response during the indentation process were recorded to extract the force-displacement curve.

[0051] In this embodiment, step S50 divides the composite structure model corresponding to the stable configuration of the modified coal-nanofluid composite structure into a boundary layer, an isothermal layer, and a Newtonian layer. The fixed atoms in the boundary layer can effectively eliminate the interference of the overall rigid body displacement on the indentation data. The isothermal layer uses the Nose-Hoover hot bath method to maintain a constant temperature, which can dissipate the Joule heat generated during the indentation process to avoid the system temperature drift affecting the measurement accuracy. The Newtonian layer, as the main area of ​​indentation deformation, ensures that all the mechanical responses collected come from the target deformation area. A virtual spherical rigid indenter is used to load along the negative Z-axis at a constant rate. After reaching the set peak load, the load is held and then unloaded. During the entire loading-holding-unloading process, the indenter depth data and the corresponding atomic force data are continuously collected, thereby obtaining a force-displacement curve containing complete mechanical information of the loading segment, the holding segment, and the unloading segment, providing a comprehensive data foundation for subsequent mechanical parameter calculations.

[0052] In some embodiments, step S50, based on the nanofluid-modified coal model obtained in step S40, employs a molecular dynamics nanoindentation simulation method to apply a virtual indenter load to simulate the process of the indenter pressing into the coal body under a set load. The simulation is an ideal scenario; the load on the indenter should be consistent with the load set in the program. Data on the depth change of the virtual indenter pressing into the coal body is collected, and combined with the load set in the program, force-displacement curve data is obtained. The balanced coal-nanofluid composite model is divided into three regions: the bottom 1 / 6 thickness is the boundary layer, with atoms fixed to prevent overall rigid body displacement; the upper 1 / 6 thickness is the isothermal layer, maintained at 300 K using the Nosé-Hoover thermal bath method to dissipate heat generated during indentation; the remaining 2 / 3 thickness is the Newtonian layer, where motion follows the classical Newton's second law and is the main area for indentation deformation. A virtual spherical rigid indenter with a radius R = 4-5 nm is used, initially positioned 0.5 mm above the sample surface. At a distance of nm, after the nanoindenter contacts the test surface of the sample, the indenter is loaded at a constant rate v along the negative Z-axis. After reaching the set peak load, the load is held, and then unloaded, resulting in the load-unload curve of the indentation test, i.e., the force-displacement curve, as shown below. Figure 3 As shown.

[0053] S60: Based on the force-displacement curve, the mechanical parameters are calculated using the Oliver-Pharr method or the atomic stress integral method to predict the mechanical properties of modified coal.

[0054] In this embodiment, step S60 is based on the force-displacement curve, using the Oliver-Pharr method or atomic stress integral method for data processing. Key characteristic parameters are extracted from the curve, including the maximum indentation depth corresponding to the peak load at the loading endpoint, the residual indentation depth after unloading, the initial slope of the unloading section, the peak load, the load attenuation during the load holding phase, and the location of the first sudden drop in load during the loading section. The equivalent elastic modulus is calculated using the Hertz contact model and corrected for Poisson's ratio to obtain the true elastic modulus. Nanohardness is calculated using the spherical indentation contact projection area method. The loading and unloading sections are then processed separately. The total loading work, elastic rebound work, and plastic dissipation work are obtained by integration, and then the plastic dissipation coefficient is obtained. The load attenuation during the holding stage is extracted to calculate the stress relaxation amount and stress relaxation rate to characterize the viscous rheological properties of the nanofluid layer. The load value and indentation depth corresponding to the first sudden drop in load during the loading stage are taken as the critical failure load and critical indentation depth of the interface to evaluate the solid-liquid interface bonding strength. Thus, the micromechanical properties of the coal modified by nanofluid are quantitatively characterized from multiple dimensions such as elastic recovery, resistance to indentation, energy dissipation, rheological behavior and interface bonding, so as to achieve a comprehensive prediction and evaluation of the modification effect.

[0055] In some embodiments, step S60 is based on, for example Figure 3 The loading-unloading curves of the indentation test shown are used to calculate mechanical parameters such as nanoscale hardness, elastic modulus, and fracture toughness based on the Oliver-Pharr method, thus predicting the mechanical properties of the modified coal. Depending on the type of indenter used, the values ​​of constants ε and η, and the projected area A are selected. c With contact depth h c The value of the relationship coefficient, next, the slope of the initial tangent of the unloading section is the contact stiffness S, combined with the residual indentation depth h that can be directly obtained from the data. r and maximum depth h m The contact projected area A can be calculated. c Combined with the maximum load F m The nanoscale hardness number H can be calculated. Given the contact stiffness and the projected contact area, the reduced modulus E can be calculated. r For coal and pressure head, the Poisson's ratio of coal and the elastic modulus of pressure head can both be approximated as constants, thus allowing the calculation of the elastic modulus E. By extracting the data from the loading and holding sections and integrating F from 0 to hm, the sum of the elastic energy Ue and the plastic property Up can be obtained. This, combined with the creep depth h obtained from the data, further yields the result. k The total energy U can be calculated. t The fracture energy U can then be calculated. c Then, the critical energy release rate G is obtained. c Combined with the reduced modulus E r The fracture toughness K can then be calculated. cWhere F: Z-axis repulsive force of the indenter, nN; h: effective indentation depth, nm; R: radius of the spherical indenter, nm; h max Maximum indentation depth; F ma x: peak load; h r : Depth of residual indentation after unloading.

[0056] Specifically, the mechanical parameters used to reflect the mechanical properties of modified coal include elastic-related mechanical parameters, plasticity and hardness parameters, energy-dimensional evaluation parameters of interfacial mechanical stability, interfacial bonding strength-related characteristic parameters, and load-holding stage force relaxation parameters; among them, the load-holding stage force relaxation parameters characterize the interfacial viscous rheological properties and are unique to nanofluids.

[0057] Elastic-related mechanical parameters include elastic recovery rate. Contact stiffness Equivalent elastic modulus and true elastic modulus .

[0058] elastic recovery rate The calculation formula is: in, : The indentation depth corresponding to the peak load at the end of the loading process; The depth of permanent residual deformation on the surface of the Newtonian layer after the indenter is completely unloaded and detached from the specimen; elastic recovery rate. The larger the value, the better the elasticity of the modified coal-nanofluid interface and the smaller the residual plastic deformation after unloading; the hydrogen bond network formed by AES and nanoparticles can improve the elastic recovery rate.

[0059] Unloading elastic stiffness or contact stiffness The calculation formula is: in, This represents the load change during the initial stage of the unloading phase. This represents the corresponding displacement change; a negative sign indicates that the displacement decreases upwards and the force decreases simultaneously, with the output being positive. The unit of S is nN / nm, which serves as the basic parameter for calculating the elastic modulus.

[0060] Equivalent elastic modulus and true elastic modulus The calculation derivation is as follows: based on the Hertz contact formula for a spherical rigid indenter and an elastic matrix. Determine the equivalent modulus by deformation : ; Engineering modifications were made, taking into account both the indenter and specimen deformation, and a virtual rigid indenter was constructed. The formula for the equivalent modulus above can be simplified to: Virtual rigid pressure head → The second term is 0, therefore we can obtain: ; in, : The true elastic modulus of the sample; Poisson's ratio for coal-based composite systems (typically taken as 0.30 in MD simulations of coal systems); peak load is used for all calculation values. , and the corresponding maximum pressure depth By substituting the values ​​into the calculation, the modulus can also be calculated in segments at different pressing depths to observe the evolution of the modulus with the pressing depth.

[0061] Plasticity and hardness parameters include contact radius Contact projection area and the proportion of plastic deformation η p .

[0062] The contact radius is calculated using the spherical indentation contact projected area method. : ; Contact Projection Area The calculation formula is: ; Nano hardness Defined as the ratio of peak load to the projected contact area: ; Nano hardness The higher the value, the stronger the resistance to indentation and plastic damage of the coal-nanofluid composite structure; the hardness differences of the three groups can be compared: raw coal, single AES modification, and SiO2-AES composite modification.

[0063] Plastic deformation ratio η p The calculation formula is: Plastic deformation ratio η It characterizes the proportion of irreversible plastic deformation after indentation. The higher the value, the easier it is for the interface to slip, hydrogen bond breakage, and nanoparticle extrusion and rearrangement, resulting in more significant plastic failure.

[0064] The energy dimension evaluates the interface mechanical stability parameters, including the total applied work. Elastic rebound function Plastic dissipation work and plastic dissipation coefficient .

[0065] Integrating the loading and unloading segments of the force-displacement curve separately, the total loading work is calculated using the following formula. Elastic rebound function and plastic dissipation work : ; ; ; in, The load on the loading segment is a function of the indentation depth. The unloading section load is a function of the indentation depth; Based on plastic dissipation work and the total loading power The plastic dissipation coefficient is calculated using the following formula. : .

[0066] Plastic dissipation coefficient The larger the value, the more energy is consumed during deformation processes such as interfacial hydrogen bond breaking, molecular slippage, and particle rearrangement, resulting in better material buffering and impact resistance.

[0067] Interface bond strength related characteristic parameters include the critical failure load of the interface. F c Critical depth of interface failure h c .

[0068] Interface critical failure load F c It is the load value corresponding to the first sudden drop in the slope of the loading curve and the sudden drop in load; reaching the critical failure load at this interface. F c At this time, a large number of hydrogen bond networks between the coal surface and AES / nanofluid break, and desorption and delamination occur at the solid-liquid interface. This is the critical load for interface failure and directly characterizes the interfacial bonding strength.

[0069] Critical depth of interface failure h c It is the indentation depth corresponding to the point of sudden load drop. h c The larger the surface area, the greater the deformation the interface can withstand before peeling occurs, resulting in stronger interface stability.

[0070] The stress relaxation parameters during the load holding phase include the stress relaxation amount. and stress relaxation rate .

[0071] During the load holding phase, the pressure head is fixed at As the load remains constant, it decreases over time, resulting in stress relaxation. The amount of stress relaxation... for: ; in, To stabilize the back load.

[0072] Stress relaxation rate .

[0073] Nanofluids exhibit viscous flow characteristics; during the load maintenance process, SiO2 particles and AES molecules slowly slide and rearrange, resulting in a continuous decrease in load; stress relaxation rate It can quantitatively evaluate the laminar rheological behavior of nanofluids.

[0074] With the calculation of each parameter clearly defined, the micromechanical parameters of the composite system are quantitatively calculated based on the loading-holding-unloading force-displacement curves output by nanoindentation simulation: with the maximum indentation depth as the starting point. Residual indentation depth after unloading Calculate elastic recovery rate With the proportion of plastic deformation The equivalent elastic modulus was solved using the Hertz contact model with a spherical indenter, and the true elastic modulus of the sample was obtained by combining it with the Poisson's ratio ν correction of the coal matrix. ; through peak load Calculation of nanoscale hardness based on the projected contact area with the spherical indenter By integrating piecewise sections of the force-displacement curve, the total loading work can be obtained. Elastic rebound function With plastic dissipation work Further solve for the plastic dissipation coefficient ; Extract the load attenuation during the holding phase to calculate the stress relaxation rate and characterize the viscous rheological properties of the nanofluid; Take the interface critical failure load corresponding to the first sudden drop in load on the loading curve. F c Critical compressive depth at interface failure h c The bonding strength between coal and nanofluid solid-liquid interface was evaluated. All mechanical parameter calculations used only the effective mechanical response data generated by the Newtonian deformation layer. The bottom fixed layer eliminated rigid body displacement interference, and the isothermal layer stabilized the simulation temperature, ensuring the accuracy and reliability of parameter calculations.

[0075] The above embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit them. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features therein. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of this application.

Claims

1. A method for predicting the mechanical properties of coal modified by nanofluids, characterized in that, The method includes: An initial model of coal molecules is constructed, and the initial model of coal molecules is geometrically optimized and annealed to obtain an optimized coal molecule model. A coal molecule box composed of coal molecules in the optimized coal molecule model is constructed by Monte Carlo random reconstruction, and the coal molecule box is geometrically optimized and annealed to obtain a coal pore model. AES molecule and SiO2 molecule models were constructed, and the AES molecule and SiO2 molecule models were subjected to geometric optimization and annealing, respectively. Based on the optimized SiO2 molecule model, a SiO2 cluster model was constructed. The optimized AES molecule was grafted onto the SiO2 cluster through a hydrolysis-condensation reaction. After geometric optimization and annealing, a composite cluster model of AES activator molecules and SiO2 nanoparticles was obtained. A composite cluster box composed of the composite clusters in the composite cluster model was constructed by Monte Carlo random reconstruction. The composite cluster box was subjected to geometric optimization and annealing to obtain an AES-SiO2 nanofluid model. The coal pore model and the AES-SiO2 nanofluid model are interfacially assembled to generate an initial interlayer composite structure, and a vacuum layer is added at the top of the system to obtain a coal-nanofluid fluid-solid coupling interface model. Based on the aforementioned coal-nanofluid fluid-structure interaction interface model, molecular dynamics relaxation simulations were performed to bring the system to thermodynamic equilibrium, thereby obtaining a stable configuration of the modified coal-nanofluid composite structure. Based on the stable configuration of the modified coal-nanofluid composite structure, molecular dynamics nanoindentation simulation was performed. A virtual indenter load was applied and the atomic force and displacement response during the indentation process were recorded, and the force-displacement curve was extracted. Based on the force-displacement curve, the mechanical parameters are calculated using the Oliver-Pharr method or the atomic stress integral method, thereby enabling the prediction of the mechanical properties of the modified coal.

2. The method according to claim 1, characterized in that, The method of constructing a coal molecule box composed of coal molecules in the optimized coal molecule model through Monte Carlo random reconstruction includes: Based on the optimized coal molecule model, coal molecules are filled within a three-dimensional periodic box using a Monte Carlo method of random insertion and energy screening. After each attempt to insert a coal molecule, the total energy change of the system caused by the insertion is calculated. The acceptance probability of this insertion event is calculated using the following formula. : ； in, Boltzmann's constant, For temperature; each time an insertion attempt is made, a uniformly random number within the interval [0,1] is generated independently. If this uniformly random number is less than or equal to the acceptance probability... If the result is positive, the insertion is accepted; otherwise, the insertion is rejected, and the coal molecule is not placed in the box. The above random insertion and judgment process is repeated until the target density is reached, and the coal molecule box is obtained.

3. The method according to claim 1, characterized in that, The process involves constructing a composite cluster box composed of composite clusters from the composite cluster model through Monte Carlo random reconstruction, and then performing geometric optimization and annealing on the composite cluster box to obtain an AES-SiO2 nanofluid model, including: Based on the AES-SiO2 composite clusters in the composite cluster model, the system is filled in a three-dimensional periodic box using a Monte Carlo method of random insertion and energy screening. After each attempt to insert a composite cluster, the total energy change of the system caused by the insertion is calculated, and the acceptance probability of the insertion event is calculated. For each insertion attempt, a uniform random number in the interval [0,1] is generated independently. If the uniform random number is less than or equal to the acceptance probability, the insertion is accepted; otherwise, the insertion is rejected, and the composite cluster is not placed in the box. The above random insertion and judgment process is repeated until the target density is reached. After filling, the system undergoes geometric optimization and annealing to obtain the AES-SiO2 nanofluid model.

4. The method according to claim 1, characterized in that, The coal pore model and the AES-SiO2 nanofluid model are interfacially assembled to generate an initial interlayer composite structure. A vacuum layer is then added to the top of the system to obtain a coal-nanofluid fluid-structure interaction interface model, including: The coal pore model and the AES-SiO2 nanofluid model are assembled at the interface. An initial interlayer spacing is set and the minimum strain lattice matching mode is enabled. The maximum strain of the interface lattice is controlled to not exceed 2%. At the same time, layered geometric constraints are applied to fix all atoms of the coal pore substrate in the coal pore model, release the triaxial motion degrees of freedom of the layer where the AES-SiO2 nanofluid model is located, and set the minimum atomic distance constraint at the interface to avoid atomic overlap. An initial interlayer composite structure is generated, and a vacuum layer is added at the top of the system to obtain the coal-nanofluid fluid-structure interaction interface model.

5. The method according to claim 1, characterized in that, Based on the aforementioned coal-nanofluid fluid-structure interaction interface model, molecular dynamics relaxation simulations were performed to bring the system to thermodynamic equilibrium, thereby obtaining a stable configuration of the modified coal-nanofluid composite structure, including: Molecular dynamics relaxation simulations were performed on the coal-nanofluid fluid-structure interaction interface model. The initial configuration of the coal-nanofluid fluid-structure interaction interface model was minimized using the conjugate gradient method until the maximum force on the system was less than 10. -4  eV / A˚; Simulated annealing is performed in the NVT ensemble, heating from a first temperature to a second temperature at a set target heating rate, holding for a set time, and then cooling back to the first temperature at the target heating rate; Equilibrium relaxation is performed in the NPT ensemble, with the first temperature as the target temperature, setting the damping coefficient and isotropic pressure, and the system temperature fluctuates within ±5% of the target temperature while the energy convergence parameter Δ E When the value is less than 0.001, thermodynamic equilibrium is considered to have been reached, and the final configuration after equilibrium is recorded as the stable configuration of the modified coal-nanofluid composite structure.

6. The method according to claim 1, characterized in that, Based on the stable configuration of the modified coal-nanofluid composite structure, molecular dynamics nanoindentation simulation was performed. A virtual indenter load was applied, and the atomic force and displacement responses during the indentation process were recorded. Force-displacement curves were extracted, including: The composite structure model corresponding to the stable configuration of the modified coal-nanofluid composite structure is divided into three regions: the bottom 1 / 6 of the model is a boundary layer, where atoms are fixed to prevent overall rigid body displacement; the atoms above the boundary layer are a isothermal layer, which is maintained at a constant temperature using the Nose-Hoover heat bath method to dissipate the heat generated during the indentation process; the remaining 2 / 3 of the model is a Newtonian layer, where motion follows the classical Newton's second law. A virtual spherical rigid indenter with a radius of 4-5 nm is used as the virtual indenter. The initial position is above the sample surface. After the virtual indenter contacts the sample surface, it is loaded at a constant rate along the negative Z-axis. After reaching the set peak load, the load is maintained and then unloaded. Data on the depth change of the virtual indenter in the coal body are collected. Combined with the set load, the force-displacement curve is obtained.

7. The method according to claim 1, characterized in that, The mechanical parameters include elastic recovery rate. Contact stiffness Equivalent elastic modulus True elastic modulus Nano hardness The proportion of plastic deformation Total loading power Elastic rebound function Plastic dissipation work Plastic dissipation coefficient Stress relaxation amount Stress relaxation rate Interface critical failure load F c Critical depth of interface failure h c .

8. The method according to claim 7, characterized in that, Calculate the elastic recovery rate Contact stiffness Equivalent elastic modulus True elastic modulus ,include: Extract the maximum indentation depth corresponding to the peak load at the loading endpoint from the force-displacement curve. and the depth of residual indentation after unloading The elastic recovery rate is calculated using the following formula. : ； The contact stiffness is calculated using the following formula. : ； in, This represents the load change during the initial stage of the unloading phase. This represents the corresponding displacement change; Based on the Hertz contact model between a spherical rigid indenter and an elastic matrix, the equivalent elastic modulus of the composite system is calculated using the following formula. : ； in, The pressure head exhibits Z-axis repulsive force; For effective indentation depth; Based on the elastic modulus of the virtual rigid indenter → The true elastic modulus of the specimen is calculated using the following formula. : ； in, The Poisson's ratio for a coal-based composite system.

9. The method according to claim 8, characterized in that, Calculate the nanohardness The proportion of plastic deformation Total loading power Elastic rebound function Plastic dissipation work and plastic dissipation coefficient ,include: The contact radius is calculated using the spherical indentation contact projected area method and the following formula. : ； According to the contact radius The contact projected area is calculated using the following formula. : ； Based on peak load With the contact projected area Nanohardness is calculated using the following formula. : ； Based on the maximum indentation depth and residual indentation depth The proportion of plastic deformation is calculated using the following formula. : ； Integrating the loading and unloading segments of the force-displacement curve respectively, the total loading work is calculated using the following formula. Elastic rebound function and plastic dissipation work : ； ； ； in, The load on the loading segment is a function of the indentation depth. The unloading section load is a function of the indentation depth; According to the plastic dissipation work and the total loading power The plastic dissipation coefficient is calculated using the following formula. : 。 10. The method according to claim 7, characterized in that, Calculate the stress relaxation amount Stress relaxation rate Interface critical failure load F c Critical depth of interface failure h c ,include: Extracting the peak load during the load-holding phase With stable afterload The stress relaxation amount is calculated using the following formula. : ； According to the stress relaxation amount With the peak load The stress relaxation rate is calculated using the following formula. : The load value corresponding to the first sudden drop in load in the loading segment of the force-displacement curve is taken as the critical interface failure load. F c The indentation depth corresponding to this load value is taken as the critical indentation depth for interface failure. h c .

Images