A heterogeneous additive cross-scale interface constitutive mapping and damage assessment method

Abstract

The application discloses a heterogeneous additive cross-scale interface constitutive mapping and damage evaluation method, and belongs to the technical field of additive manufacturing mechanics simulation, and comprises the following steps: a micro-heterogeneous interface model of metal nanoparticles and a ceramic substrate is constructed, and the atoms at the bottom of the ceramic substrate are set as rigid body constraints; a thermodynamic sintering cycle simulation is performed on the model, and residual prestress is introduced; after ensemble relaxation to equilibrium, a quasi-static drawing is applied along the interface normal, and interface resultant force and normal separation displacement are collected, a traction force-displacement constitutive relationship is constructed, and mechanical parameters are extracted; the mechanical parameters are mapped to a macroscopic unit system, and then injected into a cohesive zone model of a macroscopic structure finite element model, damage evolution variables are calculated to determine interface cracking and failure. The application establishes a cross-scale physical mapping from micro-process to macro-failure, can realize high-precision quantitative evaluation of additive manufacturing film cracking and peeling, and is suitable for anti-peeling design and reliability evaluation of complex heterogeneous components such as high-performance radio frequency antenna covers.

Description

Technical Field

[0001] This invention belongs to the field of mechanical simulation technology of additive manufacturing, specifically involving a method for cross-scale interface constitutive mapping and damage assessment in heterogeneous additive manufacturing. Background Technology

[0002] With the rapid development of aerospace technology towards hypersonic and electromechanical-thermal integration, the service environment of complex conformal components such as high-frequency communication radomes is becoming increasingly demanding. To achieve highly integrated radio frequency functions, heterogeneous additive manufacturing technology, due to its extremely high degree of design freedom, is widely used to deposit in-situ conductive nanofilms of metals such as silver on the surface of amorphous silica and other ceramic substrates to construct surface conformal antenna arrays or frequency selective surfaces. However, after molding, the metal nanoparticle ink must undergo high-temperature sintering to achieve densification of the conductive network. Due to the huge difference in thermal expansion properties between metallic silver and silica ceramics, the free shrinkage of the silver layer during the cooling and curing stage after sintering is strongly restricted by the rigid ceramic substrate, thereby generating extremely large thermal mismatch residual stress at the heterogeneous interface. This multi-scale micro-prestress makes additively manufactured films highly susceptible to microcrack initiation and propagation in stress concentration areas when subjected to hypersonic aerodynamic pressure, severe mechanical vibration, or thermo-mechanical coupling bending loads during subsequent service. This can ultimately lead to the entire conductive film lifting, debonding, and large-area peeling failure, seriously threatening the communication link security of the aircraft.

[0003] To predict and suppress the aforementioned interfacial delamination phenomenon, existing macroscopic mechanical simulations widely employ cohesive region models to simulate the nonlinear damage evolution process of the interface. The accuracy of this model's calculations highly depends on the precise input of three core constitutive parameters: interfacial elastic stiffness, peak initiation strength, and interfacial fracture energy. Currently, the industry primarily relies on macroscopic physical experiments combined with numerical inversion to attempt to obtain these parameters. Specifically, macroscopic testing methods include scratch tests, tape peeling tests, and micro-bending tests. However, for ultrathin additive manufacturing conductive films with thicknesses typically on the micro-nano scale, traditional macroscopic testing methods and phenomenological simulation models suffer from insurmountable fundamental flaws: First, size effects severely interfere with testing. The responses measured by macroscopic delamination experiments are often a mixed superposition of substrate bending deformation, plastic dissipation of the metal film, and actual interfacial fracture, making it extremely difficult to mathematically and accurately extract the inherent constitutive parameters of the interface, resulting in significant dispersion and error in the obtained stiffness and fracture energy data. Second, there is a disconnect between microscopic physical mechanisms and macroscopic mechanics. Existing macroscopic cohesive region models treat heterostructures as idealized scenarios, completely ignoring the profound impact of micro-additive manufacturing processes on the atomic-level bonding strength of the interface. Specifically, these models fail to adequately consider underlying physical parameters such as sintering temperature, densification time, nanoparticle-scale characteristics, and the random atomic morphology of amorphous substrates.

[0004] In summary, due to the lack of support from underlying microscopic physical mechanisms, existing interface simulation methods based on macroscopic empirical parameters cannot accurately reflect the initial residual stress state caused by the process, and are even less capable of establishing multi-scale quantitative mapping relationships encompassing microscopic processes, inherent constitutive structures, and macroscopic evolution. This often leads to interface reliability assessments under extreme service environments becoming passive data fitting lacking forward-looking predictive capabilities, severely limiting the forward damage resistance design and process iteration optimization of high-performance heterogeneous additive manufacturing radomes. Therefore, a novel cross-scale interface constitutive extraction and damage assessment method is urgently needed to overcome this technical bottleneck. Summary of the Invention

[0005] In view of the above, in order to overcome the technical defects of existing macroscopic mechanical simulation methods that rely too much on empirical parameters, ignore the influence of microscopic processes, and cannot establish multi-scale physical mapping, the purpose of this invention is to provide a cross-scale interface constitutive mapping and damage assessment method for heterogeneous additive manufacturing. It adopts a multi-scale progressive architecture of microscopic atomic scale simulation, cohesive constitutive extraction, and macroscopic finite element injection. By constructing a heterogeneous interface model of metal nanoparticles and ceramic substrate at the microscopic level and performing a complete thermodynamic sintering cycle including heating, isothermal densification, and cooling solidification to introduce real thermal mismatch prestress, a quasi-static pull-out simulation is then performed to extract the traction force-displacement constitutive relationship. The interface elastic stiffness, peak strength, and critical fracture energy are obtained by combining adaptive window fitting and full displacement domain integration. Finally, the above parameters are mapped to macroscopic units and injected into the finite element cohesive model to calculate the damage evolution variables. This invention can establish a cross-scale physical mapping bridge from microscopic process evolution to macroscopic failure judgment, eliminate the dependence of the cohesive region model on empirical parameters, realize high-precision quantitative evaluation of cracking and peeling of additive manufacturing films, and is applicable to the anti-peeling design and reliability evaluation of complex heterogeneous components such as high-performance radio frequency antenna covers.

[0006] To achieve the above-mentioned objectives, the present invention provides the following technical solution: This invention provides a method for cross-scale interface constitutive mapping and damage assessment in heterogeneous additive manufacturing, comprising the following steps: A microscopic heterogeneous interface model containing metal nanoparticles and a ceramic substrate was constructed, and the atomic group at the bottom of the ceramic substrate was set as a non-integral absolute rigid body constraint state. Thermodynamic sintering cycle simulation was performed on the micro-heterogeneous interface model to enable metal nanoparticles to spread and form a film on the ceramic substrate and generate thermal mismatch residual prestress. The sintered micro-heterogeneous interface model was ensemble-relaxed to equilibrium, and then a quasi-static constant-rate displacement load was applied along the interface normal, and the resultant force of the interface and the normal separation displacement during the drawing process were collected. Based on the collected data, a traction force-displacement constitutive relationship was constructed, and mechanical parameters including interface elastic stiffness, interface peak strength and critical fracture energy were extracted. After the extracted mechanical parameters are mapped to the macroscopic unit system, they are injected as constitutive parameters into the cohesive region model of the macroscopic structural finite element model to calculate damage evolution variables in order to determine interface cracking and failure.

[0007] Preferably, the initial geometric diameter of the metal nanoparticles is set to 20~100Å, more preferably 40Å; when constructing the microscopic heterogeneous interface model, the thermodynamic relaxation temperature applied to the metal nanoparticles is 900~1500K, more preferably 1300K, and the duration of a single relaxation is 50~200ps, more preferably 100ps. Among them, (1) the initial diameter is set to 20~100Å: this size is highly consistent with the typical particle size of nano-metal inks used in real electrohydrodynamics or inkjet printing additive manufacturing processes. In molecular dynamics, particles of 20~100Å can ensure that they contain a sufficient number of atoms to eliminate statistical fluctuation errors caused by small size, and can also make their specific surface energy large enough to fully stimulate the melting point reduction characteristics caused by small size effect, so as to truly reproduce the surface melting and sintering spreading behavior of nanoparticles at a lower temperature; (2) The thermodynamic relaxation temperature is set to 900~1500K: For silver nanoparticles of 20~100Å, 900~1500K is just higher than their effective melting point at the nanoscale, but much lower than their violent vaporization temperature. This temperature can give the system sufficient kinetic energy, enabling metal atoms to cross local potential barriers, eliminate non-physical high-frequency initial stress caused by simply relying on geometric modeling and cutting, and make the particles spontaneously shrink into the most stable low-energy spherical state; (3) The duration is set to 50~200ps: This time window just meets the minimum convergence time required for the root mean square displacement and potential energy curve of the system to reach the horizontal asymptote, ensuring that the particles reach an absolute thermodynamic equilibrium state while avoiding the waste of computing power caused by excessive relaxation.

[0008] Preferably, the horizontal side length of the spatial model of the ceramic substrate is set to 80~200Å, and the thickness is set to 15~50Å. More preferably, the size is set to 100Å×100Å×20Å. When constructing the microscopic heterogeneous interface model, the thermodynamic relaxation evolution process of the ceramic substrate includes four stages: the first stage, raising the system temperature from the initial room temperature (e.g., 300K) to a high temperature of 2000~3000K (more preferably 2000K) within 20~100ps (more preferably 50ps); the second stage, maintaining the system isothermally at the high temperature for 50~200ps (more preferably 100ps); the third stage, uniformly cooling the system to the initial room temperature within 100~500ps (more preferably 200ps); and the fourth stage, continuing to maintain isothermally at the initial room temperature for 50~200ps (more preferably 100ps). Among them, (1) Spatial size design: The horizontal side length of 80~200Å is more than twice the diameter of the metal particles, which can completely avoid the particles from interacting with their own mirror image through periodic boundary conditions after spreading; the thickness of 15~50Å is strictly greater than the cutoff radius of 10Å of the Vashishta potential function and the LJ potential function, ensuring that the absolute rigid body constraint layer at the bottom will not interfere with the atomic interaction of the film spread on the surface; (2) The first stage is heated to 2000~3000K and is isothermal for 50~200ps in the second stage: The ultra-high temperature of 2000~3000K can completely break the original long-range ordered lattice bond of silicon dioxide, and the isothermal time of 50~200ps allows the silicon-oxygen tetrahedral network to achieve a completely randomized distribution in space, which is a necessary physical condition for obtaining a real amorphous glass liquid phase structure; (3) The third stage is cooled to the initial room temperature within 100~500ps: This stage defines the quenching cooling rate of the system by controlling the time. In molecular dynamics simulation, this specific cooling rate can perfectly suppress the secondary crystallization of silicon-oxygen network, so that it is frozen in the amorphous state during the cooling process. The generated topology is closest to the real world's high-fidelity amorphous silicon dioxide substrate in terms of short-range order and density; (4) The initial room temperature isothermal maintenance of the fourth stage is 50~200ps: used to release the high residual strain energy accumulated in the substrate during the rapid quenching process, so that it reaches the structural relaxation and energy minimum value at room temperature, thereby providing a stable and flat substrate environment without thermal wave interference for the subsequent deposition of heterogeneous nanoparticles and interface interaction.

[0009] Preferably, when constructing the microscopic heterogeneous interface model, its potential field calculation is described by a hybrid potential function, wherein the homogeneous interaction between metal atoms is calculated using the embedded atom method potential function, the heterogeneous interaction between metal and ceramic atoms is calculated using the Lennard-Jones potential function, and the interaction between ceramic atoms is calculated using the multinomial Vashishta potential function.

[0010] Preferably, the thermodynamic sintering cycle is performed under the NVT ensemble and includes three stages: the first stage is the heating and melting stage, in which the system temperature is uniformly raised from the initial room temperature (e.g., 300K) to the set sintering temperature of 900-1500K (more preferably 1300K) within 50-200ps (more preferably 100ps); the second stage is the isothermal densification stage, in which the system is kept isothermally running at the set sintering temperature for 50-300ps (more preferably 100ps); and the third stage is the cooling and solidification stage, in which the system is uniformly cooled to the initial room temperature within 50-200ps (more preferably 100ps). Among them, (1) NVT ensemble is adopted: the system volume and number of atoms are kept constant, which effectively avoids the non-physical deformation caused by the drastic volume fluctuation during the heating and cooling process of the substrate under rigid body constraint, and restores the boundary conditions of local constraint sintering in the most realistic way; (2) the first stage is heated to 900~1500K: the uniform heating avoids the numerical impact of temperature jump on the system, and the temperature of 900~1500K provides sufficient thermal activation energy, overcomes the surface diffusion barrier of nanoparticles, and promotes the metal atoms to undergo deep physical wetting and spreading deformation on the ceramic substrate; (3) the second stage isothermal densification for 50~300ps: gives the heterogeneous atoms at the interface sufficient time for movement and rearrangement to fill the local pores and grain boundary defects in the early stage of spreading, complete the complete densification of the conductive film, and establish a large area of ​​stable interface adsorption network; (4) the third stage isothermal curing for 50~200ps: this stage perfectly reproduces the real cooling history of additive manufacturing post-processing. Since the macroscopic thermal expansion coefficient of silver film is much greater than that of silicon dioxide substrate, during the shrinkage process of uniform cooling, the confinement effect of rigid substrate will spontaneously generate extremely high thermal mismatch pre-stress at the heterogeneous interface, thereby sealing the microscopic interface pre-damage caused by the actual manufacturing process into the model without damage, laying the physical fidelity foundation for subsequent mechanical evaluation.

[0011] Preferably, setting the atomic group at the bottom of the ceramic substrate as a non-integral, absolutely rigid body constraint state includes: setting the bottom atomic group of the ceramic substrate away from the interface as a non-integral, absolutely rigid body state, and canceling the time-step integral iteration solution of the interatomic internal forces in this region, so as to simplify the calculation of atomic interactions inside the ceramic substrate. This can improve the computational efficiency of the overall cross-scale model without affecting the accuracy of interface interaction calculation.

[0012] Preferably, the pull-out speed of the quasi-static constant velocity displacement load is 0.001~0.1 Å / ps, more preferably 0.01 Å / ps, and the data sampling output interval is set to 1~50 integration steps, more preferably no more than 10 integration steps. Among them, (1) the pull-out speed is set to 0.001~0.1 Å / ps: in molecular dynamics simulation, this speed is in the best quasi-static mechanical response window. If the pull-out speed is too fast, it will cause the system kinetic energy to surge, excite artificial dynamic stress waves, induce the illusion of dynamic hardening of the interface, and lead to an overestimation of the fracture energy; while the extremely low pull-out rate of 0.001~0.1 Å / ps can ensure that the system kinetic energy during the pull-out process is much less than the potential energy, so that the strain energy of the interface atoms can be fully transferred and relaxed and redistributed, ensuring that the measured constitutive response completely corresponds to the quasi-static anti-peeling performance under real environment; (2) the data sampling interval is set to 1~50 integration steps: the batch breaking of atomic bonds in heterogeneous interfaces is an extremely nonlinear transient avalanche event. On the pull-out curve, after the stress reaches its highest point, a sharp softening drop occurs. Using an extremely high-density sampling frequency of 1 to 50 integration steps, data aliasing and peak omission can be strictly prevented from the underlying logic. This ensures that the interface crack initiation peak and softening envelope area in the traction force-displacement curve are accurately recorded, providing an absolutely reliable and distortion-free discrete data source guarantee for subsequent integral calculation of interface fracture.

[0013] Preferably, the construction of the traction force-displacement constitutive relationship includes: defining the relative displacement change of the overall centroid of the metal nanoparticle along the pulling direction as the normal separation displacement, and defining the sum of the interaction forces experienced by all metal atoms in the metal nanoparticle in the pulling direction as the interfacial resultant force. By extracting the normal separation displacement and the interfacial resultant force under continuous relaxation time steps, the traction force-displacement curve is jointly constructed.

[0014] Preferably, the extraction of mechanical parameters including interfacial elastic stiffness, interfacial peak strength, and critical fracture energy includes: locating the point in the traction force-displacement constitutive relation where the stress reaches its global maximum value as the interfacial peak strength. s max Automatic stress interception at 15% s max Up to 75% s max For discrete points on the rising segment of the curve where the separation displacement is less than the peak displacement, a univariate linear fit is performed using the least squares method. The slope of the fitted line is the interface elastic stiffness. K The critical fracture energy is obtained by numerically integrating the traction force-displacement constitutive relation over the entire displacement domain from the initial stage to the critical failure displacement, where the normal traction stress at the positioning interface decays to zero with increasing normal separation displacement. G c .

[0015] Preferably, the cohesive region model calculates damage evolution variables based on constitutive parameters to determine interface cracking and failure, including: The cohesive region model is realized based on surface-based cohesive behavior. The initial elastic stiffness response of the cohesive region is established by the interfacial elastic stiffness. Damage initiation adopts the maximum nominal stress criterion and uses the peak interfacial strength as the basis for damage initiation. Damage evolution adopts a linear softening model controlled by the critical fracture energy. By extracting the stress distribution of the entire structural field, the stress concentration region at the interface is located, and the scalar stiffness degradation variable of the interface contact surface in the stress concentration region is extracted. The evolution of the scalar stiffness degradation variable to 1.0 is used as the quantitative basis for determining complete cracking and crack propagation at the interface.

[0016] Compared with the prior art, the beneficial effects of the present invention include at least the following: (1) A non-integral absolute rigid body constraint algorithm is proposed, which significantly improves the efficiency of cross-scale computation: In multi-scale simulation, the ceramic substrate contains a huge spatial atomic array, and its thermodynamic integral calculation occupies most of the microscopic computational resources. This invention establishes a non-integral absolute rigid body constraint group at the bottom of the microscopic heterogeneous interface model. The atoms in this group do not participate in the time step iteration solution of the complex internal force matrix during the system evolution. While perfectly preserving the accuracy of the short-range interaction potential energy between interface atoms, this algorithm greatly eliminates the redundant computation of high-frequency phonon vibrations inside the substrate, which improves the overall efficiency of molecular dynamics pulling and sintering calculations by several times, and successfully solves the high cost problem of excessive microscopic computational power consumption in cross-scale computational mechanics.

[0017] (2) A closed-loop digital twin prediction from manufacturing process to structural service performance has been achieved: Existing mechanical assessment methods simply equate heterogeneous interfaces to non-destructive black boxes, severing the connection between the front-end manufacturing process and the back-end mechanical service performance. This invention explicitly introduces a complete thermodynamic sintering cycle simulation, including heating melting, isothermal densification, and cooling solidification, at the microscopic level. It can sensitively capture multi-scale thermal mismatch residual pre-stress, adsorption displacement bias, and crystal domain distortion induced by process temperature changes and differences in material thermal expansion coefficients. The initial interface pre-damage caused by these microscopic process histories is seamlessly inherited into the macroscopic finite element analysis through strict dimensional transformation, making the prediction of film peeling behavior under hypersonic aerodynamic loads and bending loads highly process-dependent, directly empowering the process-structure positive integrated damage resistance design of high-performance radomes.

[0018] (3) A constitutive calibration paradigm driven by a purely physical mechanism was established, eliminating systematic errors in macroscopic experiments: The mechanical parameter input of the traditional finite element cohesive region model is highly dependent on macroscopic destructive experiments such as scratching, tape peeling, or micro-bending. The measured data inevitably contains interference from the macroscopic plastic deformation energy of the metal film, the elastic bending recovery energy of the substrate, and the flexibility of the testing machine fixture, making it impossible to extract pure interfacial mechanical properties. This invention directly calibrates constitutive parameters from the bottom up using the gradient of the interatomic potential function of molecular dynamics. It removes microscopic thermal noise through adaptive fitting of the 15%~75% peak stress window, thus providing a precise interfacial mechanical scale driven by pure physics that is not affected by size effects and multi-field coupling interference for ultrathin heterogeneous additive manufacturing films.

[0019] (4) The bottleneck of matching micro- and macro-scale feature lengths has been overcome, ensuring high fidelity and numerical convergence of macro-scale finite element methods: The cohesive feature length caused by the breaking of micro-atomic bonds is usually on the nanometer scale. If it is directly input into the macro-scale finite element model, the macro-scale mesh will need to be refined to the micro- and nano-scale, which will cause the computational resources of engineering-level structural simulation to collapse. If a coarse mesh is forcibly used, it will cause serious transient cracking and implicit dynamic non-convergence errors. This invention establishes a strict dimensional mapping and provides a dimensionality reduction algorithm that scales strength and stiffness proportionally while maintaining the conservation of critical fracture energy. This allows the adjusted cohesive feature length to smoothly span 3 to 5 macro-scale elements of 0.05 mm. With the addition of a small amount of viscosity regularization, it ensures both the high fidelity of macro-bending peeling limit load and cracking path and the robust convergence of large-scale engineering finite element solutions. Attached Figure Description

[0020] 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 some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0021] Figure 1 This is a flowchart illustrating the cross-scale interface constitutive mapping and damage assessment method for heterogeneous additive manufacturing provided in this embodiment of the invention. Figure 2 The standardized traction force-displacement curve is derived from the molecular dynamics quasi-static pull-out test provided in the embodiments of the present invention. Figure 3 This is a schematic diagram of the microscopic molecular dynamics sintering film formation model and rigid body constraint setting of heterogeneous materials provided in the embodiments of the present invention; Figure 4This is a von Mises stress concentration distribution cloud map of a heterogeneous interface region under a macroscopic finite element three-point bending load provided in an embodiment of the present invention. Detailed Implementation

[0022] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and do not limit the scope of protection of this invention.

[0023] like Figure 1 As shown in the embodiment, a method for constitutive mapping and damage assessment of cross-scale interfaces in heterogeneous additive manufacturing is provided, including the following steps: S1. Construct a microscopic heterogeneous interface model that includes metal nanoparticles and a ceramic substrate, and set the atomic group at the bottom of the ceramic substrate as a non-integral absolute rigid body constraint state.

[0024] In this embodiment, the metal nanoparticles are silver (Ag) nanoparticles used for additive manufacturing, and the ceramic substrate is an amorphous silica (SiO2) substrate. Using the molecular dynamics simulation platform LAMMPS, an amorphous silica substrate with a spatial topological size of 100 Å × 100 Å × 20 Å was first constructed. The two-body and three-body interactions of the atoms within this substrate were described using a polynomial Vashishta potential function. The substrate was then uniformly heated from room temperature to a high temperature of 2000 K within 50 ps, ​​held for 100 ps to melt, and then rapidly cooled to 300 K within 200 ps. This was followed by isothermal holding for 100 ps to obtain a fully relaxed amorphous substrate structure with a random atomic topological morphology. Silver nanoparticles with an initial geometric diameter of 40 Å were introduced at the geometric center of the substrate surface. Homogeneous interactions between metal atoms were described using the embedded atom normal potential function, while interactions between metal and ceramic heteroatoms were described using the Lennard-Jones hybridization potential function. The silver nanoparticles were subjected to a single unconstrained thermal equilibrium motion lasting 100 ps at a specific thermodynamic relaxation temperature of 1300 K to release their internal high-frequency initial stress.

[0025] After completing the overall spatial topology assembly, boundary constraints are set: a specific group of atoms from the bottommost layer of the silica ceramic substrate farthest from the interface is precisely selected. By forcibly shutting down the force and velocity calculations in the time step integration, it is set as a non-integral absolute rigid body constraint state. This completely eliminates the numerical interference of the macroscopic overall rigid slip of the substrate in the subsequent loading analysis step on the true constitutive response of the heterogeneous interface, thereby improving the computational efficiency without affecting the accuracy of the interface interaction calculation.

[0026] S2 performs thermodynamic sintering cycle simulation on the micro-heterogeneous interface model, causing metal nanoparticles to spread into a film on the ceramic substrate and generate thermal mismatch residual prestress.

[0027] In this embodiment, the microscopic heterogeneous interface model constructed in step S1 is placed under the NVT ensemble (i.e., constant particle number, constant volume, and constant temperature ensemble) for thermodynamic control and solution. The global initial temperature of the system is set to room temperature of 300K, and then the system is driven to perform a complete thermodynamic sintering cycle consisting of three consecutive stages with a total time span strictly controlled within 300ps. The first stage is the heating and melting stage. Within a 100ps time window, the system temperature is uniformly increased from 300K to the set densification sintering temperature of 1300K by adjusting the Nose-Hoover heat pump. During this period, the surface atoms of the silver nanoparticles overcome the potential barrier due to the increase in thermal activation energy, and spontaneously wet and physically spread on the surface of the amorphous silica substrate. The second stage is the isothermal densification stage, in which the system is kept isothermally at a supercritical temperature of 1300K for 100ps, driving silver atoms to fully diffuse and rearrange in three-dimensional space, eliminating the initial local porosity inside the particles and at the phase interface, and establishing a stable and strongly adsorbed interface network between the densified continuous metal film and the amorphous ceramic substrate. The third stage is the cooling and curing stage, in which the system is uniformly cooled from 1300K back to the calibration room temperature of 300K within 100ps. During this process, since the macroscopic thermal expansion coefficient of silver is significantly greater than that of silicon dioxide, the shrinkage caused by cooling is limited by the rigid constraint layer at the bottom, thereby spontaneously activating and retaining residual prestress caused by thermal mismatch induced by the thermal history of additive manufacturing within the heterogeneous film interface.

[0028] Throughout the sintering cycle, the rigid atomic group of the bottom layer of the ceramic substrate set in step S1 does not participate in the internal force time step iterative solution, thereby significantly reducing the dimension of the substrate atomic redundant calculation matrix without reducing the accuracy of heterogeneous interface interaction.

[0029] S3. The sintered micro-heterogeneous interface model is ensemble-relaxed to equilibrium, and then a quasi-static constant-velocity displacement load is applied along the interface normal, and the resultant force of the interface and the normal separation displacement are collected during the drawing process.

[0030] In this embodiment, after the sintering cycle, the true geometrically effective contact area A between the sintered silver thin film circuit and the ceramic substrate is extracted and recalibrated using an atomic coordinate recognition algorithm. Subsequently, additional equilibrium ensemble relaxation is performed on the system at standard room temperature (300K) until the total energy converges. At this point, due to residual stress, the interface spontaneously exhibits an initial equilibrium separation adsorption offset of approximately 0.3 Å, which is defined as the absolute physical zero point for subsequent mechanical pull-out tests. Next, the thermal coupling of the silver thin film layer in the pull-out direction is cancelled, and a quasi-static constant-velocity displacement load along the interface normal is applied to the entire silver nanolayer. The pull-out driving speed is strictly limited to 0.01 Å / ps to minimize the artificial dynamic wave oscillation and hardening effect caused by high transient strain rates. The data sampling output interval is set to no more than 10 time steps, and the change in height of the overall centroid of the silver nanoparticles along the Z direction is recorded in real time and continuously throughout the entire pull-out lifecycle, and this change is defined as the normal separation displacement. d Simultaneously, the interaction forces experienced by all silver atoms in the Z direction in the microscopic model are algebraically summed and defined as the interfacial resultant force. F This allows us to derive a high-density original discrete dataset of micromechanical responses.

[0031] S4. Based on the collected data, a traction force-displacement constitutive relationship is constructed, and mechanical parameters including interface elastic stiffness, interface peak strength, and critical fracture energy are extracted.

[0032] In this embodiment, based on the actual effective contact area A calibrated in step S3, the resultant force at the interface in the original discrete dataset is normalized to convert the force vector into the traction stress of the continuous medium at the interface, thereby constructing a standard traction force-displacement curve reflecting atomic-level bond breaking behavior. Based on this standard curve, the interface elastic stiffness is accurately located and extracted using an adaptive interval linear regression algorithm. K First, traverse the data across the entire displacement domain to retrieve the absolute maximum value of the traction stress, which is then defined as the interface peak strength. s max Record the x-coordinate corresponding to this point as the peak separation displacement. d 0 Subsequently, to avoid initial nonlinear disturbances caused by atomic thermal vibrations or short-range repulsion during the initial drawing stage, the script automatically truncates the stress value to 15%. s max Up to 75% s max Between and the separation displacement is strictly less than d 0 The discrete data points of the rising segment of the curve are used as the effective fitting window. A univariate linear fit is performed using the least squares method. The slope of the fitted line is then calibrated as the inherent elastic stiffness of the interface without artificial noise interference. KNext, the ultimate point of complete separation displacement is determined when the traction stress gradually decreases to zero with increasing pull-out distance. d f An integration calculation program based on the first-order trapezoidal rule is used to perform integration calculations over the entire displacement domain [0, ... d f The formula for calculating the global cumulative integral of the traction force-displacement curve envelope area within the range is as follows: , in, s For the interface normal traction stress, d For normal separation displacement, d f This represents the ultimate failure displacement at which the interface damage evolves until the stress completely drops to zero. Based on this, the critical fracture energy of the interface, a key energy dissipation characteristic of the entire process of heterogeneous interface damage evolution from linear damage initiation to later nonlinear softening and finally to complete fracture, can be accurately calculated. G c .

[0033] Table 1

[0034] Table 1 shows the statistical table of peak strength, interface stiffness, and damage evolution fracture energy parameters extracted in the embodiment.

[0035] S5, after mapping the extracted mechanical parameters to the macroscopic unit system, is injected as constitutive parameters into the cohesive region model of the macroscopic structural finite element model to calculate damage evolution variables in order to determine interface cracking and failure.

[0036] In this embodiment, the interfacial elastic stiffness extracted from the microscopic discrete atomic system in step S4 is used as the interfacial elastic stiffness. K Peak intensity of the interface s max and critical fracture energy G c The dimensional transformation was performed using a multi-scale dimensional law, uniformly mapping it to the millimeter-ton-second standard SI unit required for the macroscopic three-point bending finite element model. In the finite element software ABAQUS, a macroscopic three-point bending structure geometric model was established, consisting of a 2mm thick silica ceramic substrate and a 0.05mm thick silver conductive film circuit. The entire model was discretized using three-dimensional reduced integral solid elements, with the mesh density at the heterogeneous material contact interface region locally refined to the 0.05mm level. Surface-based cohesive behavior was configured on the spatial contact geometry of the two materials. The dimensional transformation parameters were filled into the elasticity matrix and damage behavior attributes, respectively, with the damage evolution control parameter specified as a linear softening bilinear model based on the energy method. A macroscopic three-point bending displacement load step was applied to the model, and a value of 1×10⁻⁶ was introduced into the damage evolution attribute.-5 The static viscous stability regularization coefficient is used to assist implicit nonlinear iterative convergence. In post-processing, the von Mises stress distribution cloud map of the entire structural field is extracted in real time to locate the high stress concentration singular region induced at the heterogeneous interface due to thermal mismatch and mechanical load. Then, the focus is on the interface contact surface of this weak region. After the local stress reaches the peak intensity and triggers damage evolution, the full-field cloud map of the scalar stiffness degradation variable of the interface is further extracted. The geometric boundary where the scalar stiffness degradation variable at the integration point evolves to 1.0 is used as the absolute quantitative criterion for the warping and complete cracking of the metal line and the dynamic propagation of macroscopic and microcracks along the interface.

[0037] like Figure 2 As shown in the figure, the embodiment demonstrates the standardized traction force-displacement curve derived from molecular dynamics quasi-static pull-out tests. As can be seen from the figure, this curve is constructed from a discrete dataset output by microscopic quasi-static pull-out tests, fully recording the entire lifecycle mechanical response of the interface from linear elastic tension and extreme damage initiation to nonlinear softening fracture. The curve first experiences a nearly linear elastic ascent segment, then reaches its peak value; the ordinate corresponding to this point is calibrated as the peak strength of the interface. Using an adaptive interval linear regression algorithm, the effective discrete points of the curve's ascent segment are accurately extracted for least-squares fitting; the slope represents the interface's elastic stiffness after eliminating initial thermal vibration noise. Furthermore, the total area enclosed by the curve from its peak descent until the stress completely returns to zero represents the critical fracture energy required for complete interface delamination. This figure demonstrates that this method can completely calibrate constitutive parameters from the bottom up using the physical potential function, completely eliminating the dependence of traditional macroscopic experiments on phenomenological empirical parameters.

[0038] like Figure 3 As shown in the figure, the embodiment illustrates the microscopic molecular dynamics sintering film formation model of heterogeneous materials and the schematic diagram of rigid body constraint settings. As can be seen from the figure, this embodiment realistically reproduces the microscopic morphological evolution history of metal nanoparticles (purple spheres) on a ceramic substrate (green spheres). At the bottom of the model, the lowest atomic group of the amorphous silica ceramic substrate is precisely selected and set as a non-integral absolute rigid body constraint state. This effectively prevents macroscopic overall system slippage and significantly reduces the redundant computational load on the substrate without affecting the surface interface interaction accuracy (three views are shown in the figure). Figure 3 As shown in (a), (b), and (c)). During the thermodynamic sintering heating and melting and isothermal densification stages (three views as shown in...), Figure 3As shown in (d), (e), and (f), the surface atoms of the silver nanoparticles acquire sufficient thermal activation energy, spontaneously undergoing physical wetting and spreading on the substrate surface, eliminating internal pores and forming a dense, continuous adsorption interface. During the subsequent cooling and curing stage, due to the order-of-magnitude difference in thermal expansion coefficients between the silver film and the ceramic substrate, and the rigid constraint of the substrate's bottom layer, the silver layer spontaneously generates extremely high thermal mismatch residual pre-stress and initial adsorption shift at the heterogeneous interface during volume shrinkage. This figure visually confirms that the microscopic sintering model of this method provides a high-fidelity initial configuration consistent with the actual manufacturing process history for subsequent mechanical evaluation.

[0039] like Figure 4 As shown in the figure, the embodiment illustrates the concentrated distribution of von Mises stress (i.e., S, Mises) in the heterogeneous interface region under a macroscopic finite element three-point bending load. This figure demonstrates that by injecting the microscopically extracted elastic stiffness, peak strength, and critical fracture energy into the cohesive model, the macroscopic structural finite element model can robustly perform implicit nonlinear solutions. During the application of the macroscopic three-point bending mechanical load, significant stress singularities are induced in the heterogeneous interface region, especially at the structural edges, due to the coupling effect of abrupt material property changes and large bending deformation. The figure clearly identifies the warm-toned high-order von Mises stress concentration region, which represents the initial physical weakness of the heterogeneous structure. As the displacement load continues to increase, this method focuses on tracking the stress evolution state of the interface contact surface in this stress concentration region. When the von Mises stress in this local area reaches the critical failure strength mapped to the input and triggers damage, combined with the evolution of the scalar stiffness degradation variable to 1.0, it can be definitively and quantitatively determined that physical warping and dynamic crack propagation have occurred in the metallic conductive lines in this region. This figure verifies the engineering practical value of the present invention in the anti-peeling design and failure threshold prediction of complex heterogeneous additive components.

[0040] The specific embodiments described above illustrate the technical solution and beneficial effects of the present invention in detail. It should be understood that the above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, additions, and equivalent substitutions made within the scope of the principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for constitutive mapping and damage assessment of cross-scale interfaces in heterogeneous additive manufacturing, characterized in that, Includes the following steps: A microscopic heterogeneous interface model containing metal nanoparticles and a ceramic substrate was constructed, and the atomic group at the bottom of the ceramic substrate was set as a non-integral absolute rigid body constraint state. Thermodynamic sintering cycle simulation was performed on the micro-heterogeneous interface model to enable metal nanoparticles to spread and form a film on the ceramic substrate and generate thermal mismatch residual prestress. The sintered micro-heterogeneous interface model was ensemble-relaxed to equilibrium, and then a quasi-static constant-rate displacement load was applied along the interface normal, and the resultant force of the interface and the normal separation displacement during the drawing process were collected. Based on the collected data, a traction force-displacement constitutive relationship was constructed, and mechanical parameters including interface elastic stiffness, interface peak strength and critical fracture energy were extracted. After the extracted mechanical parameters are mapped to the macroscopic unit system, they are injected as constitutive parameters into the cohesive region model of the macroscopic structural finite element model to calculate damage evolution variables in order to determine interface cracking and failure.

2. The method for cross-scale interface constitutive mapping and damage assessment in heterogeneous additive manufacturing according to claim 1, characterized in that, The initial geometric diameter of the metal nanoparticles is set to 20~100 Å; when constructing the microscopic heterogeneous interface model, the thermodynamic relaxation temperature applied to the metal nanoparticles is 900~1500 K, and the duration of a single relaxation is 50~200 ps.

3. The method for cross-scale interface constitutive mapping and damage assessment in heterogeneous additive manufacturing according to claim 1, characterized in that, The horizontal side length of the spatial model of the ceramic substrate is set to 80~200 Å, and the thickness is set to 15~50 Å. When constructing the microscopic heterogeneous interface model, the thermodynamic relaxation evolution process of the ceramic substrate includes four stages: the first stage is to raise the system temperature from the initial room temperature to a high temperature of 2000~3000 K within 20~100 ps; the second stage is to keep the system isothermally running at the high temperature for 50~200 ps; the third stage is to cool the system uniformly to the initial room temperature within 100~500 ps; and the fourth stage is to continue isothermally maintaining at the initial room temperature for 50~200 ps.

4. The method for cross-scale interface constitutive mapping and damage assessment in heterogeneous additive manufacturing according to claim 1, characterized in that, When constructing the microscopic heterogeneous interface model, the potential field calculation is described by a hybrid potential function. The homogeneous interaction between metal atoms is calculated using the embedded atom method potential function, the heterogeneous interaction between metal and ceramic atoms is calculated using the Lennard-Jones potential function, and the interaction between ceramic atoms is calculated using the multinomial Vashishta potential function.

5. The method for cross-scale interface constitutive mapping and damage assessment in heterogeneous additive manufacturing according to claim 1, characterized in that, The thermodynamic sintering cycle is performed under the NVT ensemble and includes three stages: the first stage is the heating and melting stage, in which the system temperature is uniformly raised from the initial room temperature to the set sintering temperature of 900~1500K within 50~200ps; the second stage is the isothermal densification stage, in which the system is kept isothermally at the set sintering temperature for 50~300ps; and the third stage is the cooling and solidification stage, in which the system is uniformly cooled to the initial room temperature within 50~200ps.

6. The method for cross-scale interface constitutive mapping and damage assessment in heterogeneous additive manufacturing according to claim 1, characterized in that, Setting the atomic group at the bottom of the ceramic substrate as a non-integral absolute rigid body constraint state includes: setting the bottom atomic group of the ceramic substrate away from the interface as a non-integral absolute rigid body state, and canceling the time-step integral iteration solution of the internal forces between atoms in this region, so as to simplify the calculation of atomic interactions inside the ceramic substrate.

7. The method for cross-scale interface constitutive mapping and damage assessment in heterogeneous additive manufacturing according to claim 1, characterized in that, The pull-out speed of the quasi-static constant velocity displacement load is 0.001~0.1 Å / ps, and the data sampling output interval is set to 1~50 integration steps.

8. The method for cross-scale interface constitutive mapping and damage assessment in heterogeneous additive manufacturing according to claim 1, characterized in that, The construction of the traction force-displacement constitutive relationship includes: defining the relative displacement change of the overall centroid of the metal nanoparticle along the pulling direction as the normal separation displacement, and defining the sum of the interaction forces experienced by all metal atoms in the metal nanoparticle in the pulling direction as the interface resultant force. By extracting the normal separation displacement and the interface resultant force under continuous relaxation time steps, the traction force-displacement curve is jointly constructed.

9. The method for cross-scale interface constitutive mapping and damage assessment in heterogeneous additive manufacturing according to claim 1, characterized in that, The extraction includes mechanical parameters such as interfacial elastic stiffness, interfacial peak strength, and critical fracture energy, including: identifying the point in the traction force-displacement constitutive relation where the stress reaches its global maximum value as the interfacial peak strength. σ max Automatic stress interception at 15% σ max Up to 75% σ max For discrete points on the rising segment of the curve where the separation displacement is less than the peak displacement, a univariate linear fit is performed using the least squares method. The slope of the fitted line is the interface elastic stiffness. K The critical fracture energy is obtained by numerically integrating the traction force-displacement constitutive relation over the entire displacement domain from the initial stage to the critical failure displacement, where the normal traction stress at the positioning interface decays to zero with increasing normal separation displacement. G c .

10. The method for cross-scale interface constitutive mapping and damage assessment in heterogeneous additive manufacturing according to claim 1, characterized in that, The cohesive region model calculates damage evolution variables based on constitutive parameters to determine interface cracking and failure, including: The cohesive region model is realized through surface-based cohesive behavior, constructing a traction-separation constitutive relationship. The initial elastic stiffness response of the cohesive region is established by constructing an elastic matrix using the interface elastic stiffness. Damage initiation adopts the maximum nominal stress criterion, and the interface peak strength is used as the basis for damage initiation determination. Damage evolution employs an energy-based linear softening model controlled by the critical fracture energy. The stress distribution across the entire structural field is extracted to locate the interface stress concentration region, and the scalar stiffness degradation variable of the interface contact surface in the interface stress concentration region is extracted. The evolution of the scalar stiffness degradation variable at the local integration point to 1.0 serves as the absolute quantitative basis for determining complete interface cracking and dynamic crack propagation.

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