Construction method of sintered nano-silver constitutive model based on nanoindentation test

Abstract

The invention discloses a construction method of a sintered nano-silver constitutive model based on a nanoindentation test. The construction method comprises the following steps: preparing a sintered nano-silver sample; carrying out a nanoindentation experiment at different loading rates, and recording a load-displacement curve; establishing a unified creep-plasticity constitutive model; establishing a finite element model, embedding the constitutive model into the finite element model through a user-defined material subprogram, simulating the nanoindentation process at different loading rates, and recording a load-displacement curve; and comparing and analyzing the obtained load-displacement curve, and verifying the accuracy of the model. According to the method, by accurately describing the mechanical behaviors of the sintered nano-silver at different loading rates, the data blank of the mechanical properties of the sintered nano-silver at a high loading rate is filled, and the constitutive model capable of capturing the micro-mechanical behaviors of the sintered nano-silver is established; and an effective simulation means and theoretical support are provided for reliability evaluation of the electronic packaging material.

Description

Technical Field

[0001] This invention belongs to the field of mechanical property testing and constitutive modeling, specifically relating to a method for constructing a constitutive model of sintered nanosilver based on nanoindentation testing. Background Technology

[0002] As microelectronic devices continue to evolve towards higher integration and smaller dimensions, the size of solder joints and interfaces in packaging structures is constantly decreasing, placing increasingly stringent demands on the mechanical properties of materials at the microscale. Sintered nanosilver, as a high-performance lead-free interconnect material, exhibits great application potential in high-temperature, high-power electronic packaging due to its excellent thermal conductivity, electrical conductivity, high melting point, and good mechanical properties.

[0003] However, current research on its mechanical behavior under high loading rates is insufficient, mainly due to the limitations of traditional experimental methods. Quasi-static testing equipment cannot cover the high strain rate range in actual working conditions, and the size effect, interface effect, and porous structure of micro-welds prevent direct extrapolation of macroscopic test results. Furthermore, there is a lack of constitutive models that can accurately describe its viscoplastic deformation over a wide strain rate and temperature range, and correlate it with microstructural characteristics. Therefore, systematically studying its dynamic mechanical response and establishing accurate constitutive models has become a key challenge for promoting its reliable application. Summary of the Invention

[0004] To address the above problems, the purpose of this invention is to provide a testing and constitutive modeling method that can accurately characterize the mechanical behavior of sintered nanosilver under various loading rate conditions.

[0005] A method for constructing a constitutive model of sintered silver nanoparticles based on nanoindentation experiments includes the following steps:

[0006] Step 1: Prepare sintered silver nanoparticle samples;

[0007] Step 2: Perform nanoindentation experiments at different loading rates and record the load-displacement curves;

[0008] Step 3: Establish a unified creep-plastic constitutive model;

[0009] Step 4: Establish a finite element model and embed the constitutive model into the finite element model through a user-defined material subroutine to simulate the nanoindentation process under different loading rates and record the load-displacement curves.

[0010] Step 5: Compare and analyze the load-displacement curves obtained in Step 2 and Step 4 to verify the accuracy of the model.

[0011] Compared with the prior art, the beneficial effects of this invention are as follows: (1) By obtaining the mechanical properties of sintered nanosilver under different loading rates through the nanoindentation experimental system, a unified creep-plastic constitutive model is established, which can accurately describe its viscoplastic behavior; (2) By combining finite element simulation, the nanoindentation process can be accurately simulated. By comparing the load-displacement curve obtained by the nanoindentation experiment under laboratory conditions, it can be obtained that the viscoplastic deformation behavior of sintered nanosilver under various loading conditions can be accurately captured. It can be used to predict the mechanical response and reliability in electronic packaging, and provide theoretical support for engineering applications. Attached Figure Description

[0012] Figure 1 This is a flowchart illustrating the constitutive model construction method in a specific embodiment of the present invention.

[0013] Figure 2 This is the sintering temperature curve of the nano-silver paste in a specific embodiment of the present invention.

[0014] Figure 3 This is a schematic diagram of the Berkovich indenter, a triangular pyramid, used in a specific implementation of the present invention.

[0015] Figure 4 This is a schematic diagram of mesh generation for a finite element model in a specific embodiment of the present invention.

[0016] Figure 5 This is a schematic diagram of the boundary condition constraints of the finite element model in a specific embodiment of the present invention.

[0017] Figure 6 This is a comparison diagram of the load-displacement in the nanoindentation experiment and simulation in a specific embodiment of the present invention. Detailed Implementation

[0018] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings.

[0019] The method for constructing a constitutive model of sintered nanosilver based on nanoindentation testing, as described in this embodiment, is illustrated in the flowchart below. Figure 1 As shown, the specific steps are as follows.

[0020] Step 1: Prepare sintered nano-silver samples. High-purity (99.9%) commercially available nano-silver paste is used. The sample is heated in a furnace according to a pre-set temperature curve. Figure 2 The sample was heated to prepare a high-density cylindrical silver sample, and the prepared nano-silver was then pre-ground, polished, and ion-polished.

[0021] First, using a metallographic pre-grinding machine, silicon carbide wet sandpaper of progressively finer grits (180 grit, 400 grit, 800 grit, 1200 grit, and 2000 grit) was used to quickly smooth the sample surface and remove macroscopic unevenness. Then, a short-pile, stiff polishing cloth was used, kept moist, for coarse polishing, significantly reducing visible scratches. A fine polishing cloth with long, fine pile was then used for fine polishing until no obvious scratches were visible under an optical microscope. Finally, the sample surface was ion-polished using a GATANPIPS II 695 precision ion polishing system, achieving stress-free polishing through physical sputtering ablation.

[0022] Step 2: Nanoindentation experiments were conducted at room temperature using a Berkovich diamond indenter. The load was increased from 0 to a maximum load of 40 mN at a constant loading rate, held at the maximum load for 20 s, and then unloaded to 0 at the same rate. Four loading rates of 1 mN / s, 2 mN / s, 4 mN / s, and 8 mN / s were selected for comparative testing. Under each loading rate condition, data were recorded to obtain load-displacement curves, hardness, and Young's modulus at different loading rates. Each rate was repeated five times to obtain the average value to ensure the repeatability and representativeness of the data.

[0023] Step 3: Establish a unified creep-plastic constitutive model and describe the viscoplastic deformation behavior of sintered nanosilver. In this model, the total strain rate... Decomposed into elastic strain rate, inelastic strain rate, and thermal strain rate, the formula is as follows: ,in Represents elastic strain rate. Indicates inelastic strain rate. The thermal strain rate is represented by the value of . In this embodiment, the experiment is conducted at room temperature, and the thermal strain rate can be ignored. Therefore, the total strain rate consists only of elastic and inelastic components.

[0024] elastic strain rate Defined as: ,in It is the stress tension component. It is the elastic modulus. It is Poisson's ratio. For different UCP models, the formula proposed by McDowell et al. is used to describe the development of inelastic strain. The formula is:

[0025]

[0026] in , , For material constants, To activate energy, It is a universal gas constant. Absolute temperature For resistance strength, For viscous overstress, In the direction of deformation load, This is the stress index.

[0027] Viscous overstress Defined as:

[0028]

[0029] in For the deviatoric stress tensor, Where is the radius of the yield surface. The brackets for Macaulay indicate that the value inside the brackets is taken if it is greater than zero, otherwise it is zero.

[0030] The behavior formula using the isotropic hardening criterion is as follows:

[0031]

[0032] in The initial yield stress, This is the saturation value. For material constants, To accumulate equivalent plastic strain.

[0033] Step 4: Using the finite element software Abaqus, a nanoindentation model is created. Component one is created by establishing a three-dimensional deformable solid. An equilateral triangle with a side length of 0.03 mm is drawn and then vertically stretched to obtain a triangular prism with a stretched thickness of 0.04 mm. This prism is then cut to obtain a triangular pyramid indenter component. Figure 3 As shown. A second component is created by constructing a three-dimensional deformable solid, drawing a square with a side length of 0.1 mm, and then vertically stretching it to obtain a cuboid sintered silver nanoparticle component with a stretched thickness of 0.1 mm. The two component models are created independently and placed in the same spatial coordinate system. A triangular pyramid indenter is moved to the apex of the sintered silver nanoparticle component, with the distance between the indenter and the vertex being 1 micrometer, providing the indenter with a pre-contact downward pressing motion. Considering the geometric and boundary symmetry of the sample and loading conditions, a 1 / 4 symmetry model is used for simulation. The indenter is modeled as a Berkovich triangular pyramid, and the sintered silver nanoparticle sample is modeled as a rectangular block, as shown. Figure 4 A schematic diagram of the finite element model mesh generation. The contact interaction between the indenter and the specimen was precisely defined during the modeling process.

[0034] During the modeling process, the contact interaction between the indenter and the sample was precisely defined, and appropriate boundary conditions were applied. The contact type was defined as tangential and normal, and the friction coefficient was set to 0.15. The normal behavior of the two contact surfaces was hard contact, ensuring that the two components could only transmit normal pressure when compressed. This resulted in the bottom surface of the sintered nanosilver sample being constrained only in the Z direction; symmetrical boundary conditions were applied to the surface perpendicular to the Y-axis, restricting its displacement in the Y direction and rotation about the X and Z axes; symmetrical boundary conditions were also applied to the surface perpendicular to the X-axis, restricting its displacement in the X direction and rotation about the Y and Z axes; complete constraints were applied at the corners where the bottom surface intersects with the two symmetrical planes, such as... Figure 5 Schematic diagram of boundary conditions for a finite element model.

[0035] The creep-plasticity constitutive model (UCP) is implemented through a user-defined material subroutine (UMAT).

[0036] The experimentally measured indenter displacement data were embedded as displacement loads in the finite element model to simulate the nanoindentation process at four rates: 1 mN / s, 2 mN / s, 4 mN / s, and 8 mN / s. The load-displacement curves from the software were then exported.

[0037] Step 5: Compare and analyze the load-displacement curves obtained in Step 2 and Step 4, such as... Figure 5 Comparison of load-displacement between nanoindentation experiments and simulations. At four loading rates of 1 mN / s, 2 mN / s, 4 mN / s, and 8 mN / s, the simulated and experimental curves show a high degree of agreement in the loading, holding, and unloading phases. This indicates that the UCP constitutive model of this invention can accurately capture the complex mechanical behaviors of sintered nanosilver, including elasticity, yielding, creep, and plastic recovery, and can be used for predicting the mechanical response and reliability assessment of sintered nanosilver materials under a wide range of loading conditions in electronic packaging. Figure 6 As shown, the simulated curves agree well with the experimental curves at all loading rates. During the loading phase, the upward trend of the simulated curve almost coincides with that of the experimental curve, indicating that the model correctly captures the stiffness response and yielding behavior of sintered nanosilver at different loading rates. During the constant load holding phase, the simulated curve also shows a trend of gradually increasing indentation depth, consistent with the creep deformation observed experimentally. During the unloading phase, the simulated curve and the experimental curve show a very good agreement in their trends, exhibiting similar recovery characteristics. Furthermore, the final residual indentation depth is almost the same.

[0038] The above description is only a preferred embodiment of the present invention. The scope of protection of the present invention is not limited to the above embodiments. Any equivalent modifications or changes made by those skilled in the art based on the content disclosed in the present invention should be included within the scope of protection set forth in the claims.

Claims

1. A method for constructing a constitutive model of sintered nanosilver based on nanoindentation experiments, characterized in that: The steps are as follows: Step 1: Prepare sintered silver nanoparticle samples; Step 2: Perform nanoindentation experiments at different loading rates and record the load-displacement curves; Step 3: Establish a unified creep-plastic constitutive model; Step 4: Establish a finite element model and embed the constitutive model into the finite element model through a user-defined material subroutine to simulate the nanoindentation process under different loading rates and record the load-displacement curves. Step 5: Compare and analyze the load-displacement curves obtained in Step 2 and Step 4 to verify the accuracy of the model.

2. The method for constructing a constitutive model of sintered nanosilver based on nanoindentation testing according to claim 1, characterized in that: The sintered nano-silver sample in step 1 is prepared by a gradient temperature sintering process using high-purity nano-silver paste.

3. The method for constructing a constitutive model of sintered nanosilver based on nanoindentation testing according to claim 1, characterized in that: The loading rates in step 2 include 1 mN / s, 2 mN / s, 4 mN / s and 8 mN / s, and each rate is repeated five times to obtain the average value.

4. The method for constructing a constitutive model of sintered nanosilver based on nanoindentation testing according to claim 1, characterized in that: In step 3, the unified creep-plastic constitutive model is based on the UCP model, in which the total strain rate... Decomposed into elastic strain rate Inelastic strain rate and thermal strain rate The relationship is as follows: .

5. The method for constructing a constitutive model of sintered nanosilver based on nanoindentation testing according to claim 4, characterized in that: elastic strain rate Defined as: ,in It is the stress tension component. It is the elastic modulus. It is Poisson's ratio.

6. The method for constructing a constitutive model of sintered nanosilver based on nanoindentation testing according to claim 4, characterized in that: In step 3, the inelastic strain rate follow: ,in , , For material constants, To demonstrate activation energy, It is a universal gas constant. Absolute temperature For resistance strength, In the direction of deformation load, For viscous overstress, This is the stress index.

7. The method for constructing a constitutive model of sintered nanosilver based on nanoindentation testing according to claim 6, characterized in that: Viscous overstress ,in For the deviatoric stress tensor, The radius of the yield surface is denoted as .

8. The method for constructing a constitutive model of sintered nanosilver based on nanoindentation testing according to claim 7, characterized in that: Yield surface radius ,in The initial yield stress, This is the saturation value. For material constants, To accumulate equivalent plastic strain.

9. The method for constructing a constitutive model of sintered nanosilver based on nanoindentation testing according to claim 1, characterized in that: In step 4, a nanoindentation model is established using the finite element software Abaqus. The constitutive model is then embedded into the finite element model through a user-defined material subroutine to simulate the nanoindentation process under different loading rates. The simulated loading rates include four loading rates: 1 mN / s, 2 mN / s, 4 mN / s, and 8 mN / s. The load-displacement curves are recorded.

10. The method for constructing a constitutive model of sintered nanosilver based on nanoindentation testing according to claim 1, characterized in that: In step 5, the accuracy of the established UCP constitutive model is evaluated by comparing the load-displacement curves obtained from simulation and experiment in steps 2 and 4, thus proving the effectiveness of the model and obtaining a UCP model that is effective and applicable in describing the viscoplastic deformation behavior of sintered nanosilver.

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