Packaging system reliability evaluation method and device considering viscoplastic behavior

Abstract

The invention discloses a packaging system reliability evaluation method and device considering viscoplastic behaviors, and relates to the technical field of electronic packaging reliability simulation analysis, and the method comprises the steps: converting an original impact response spectrum into a power spectrum based on a stable random vibration process hypothesis; generating an initial time domain signal according to the power spectrum and a randomly generated phase spectrum; performing iterative correction on the initial time domain signal to obtain a time domain impact vibration signal consistent with the original impact response spectrum in energy distribution; establishing a finite element model of the packaging system, and describing viscoplastic mechanical behaviors of a welding spot material in the finite element model by adopting a unified creep-plastic constitutive model; according to the method, the time-domain impact vibration signal is used as a load to be input into the finite element model, time-domain nonlinear dynamic simulation is carried out, the mechanical response of the packaging system under impact vibration is obtained, the uncertainty of a nonlinear simulation result caused by inaccurate input is reduced, and therefore the impact vibration reliability of the packaging system is accurately evaluated.

Description

Technical Field

[0001] This invention relates to the field of electronic packaging reliability simulation and analysis technology, specifically to a method and apparatus for reliability assessment of packaging systems that considers viscoplastic behavior. Background Technology

[0002] As electronic packaging technology advances towards higher density and miniaturization, the reliability of multi-chip packaging systems under dynamic loads becomes increasingly prominent. Traditional frequency domain vibration analysis methods rely on the principle of linear superposition, which cannot accurately describe the nonlinear viscoplastic behavior of solder joints in the package structure. Solders such as SAC305 exhibit significant time-dependent stress relaxation and plastic accumulation during impact and random vibration, leading to overestimation of reliability results by frequency domain methods and hindering reliability assessment. Therefore, a simulation calculation method capable of characterizing the nonlinear mechanical properties of materials in the time domain is needed to accurately evaluate the impact vibration reliability of packaging systems. Summary of the Invention

[0003] The technical problem to be solved by the present invention is how to accurately assess the shock and vibration reliability of a packaging system. The purpose is to provide a method and apparatus for assessing the reliability of a packaging system that takes into account viscoplastic behavior, thereby solving the above-mentioned problem.

[0004] This invention is achieved through the following technical solution:

[0005] In a first aspect, the present invention provides a reliability assessment method for a packaging system considering viscoplastic behavior, comprising:

[0006] Based on the frequency domain design standard of the packaging system, the original impulse response spectrum is obtained;

[0007] Based on the assumption of a stationary random vibration process, the original impact response spectrum is converted into a power spectrum;

[0008] An initial time-domain signal is generated based on the power spectrum and the randomly generated phase spectrum;

[0009] The initial time-domain signal is iteratively corrected to obtain a time-domain impact vibration signal that is consistent with the original impact response spectrum in terms of energy distribution;

[0010] A finite element model of the packaging system is established, and a unified creep-plastic constitutive model is used to describe the viscoplastic mechanical behavior of the solder joint material in the finite element model.

[0011] The time-domain impact vibration signal is used as a load input to the finite element model to perform time-domain nonlinear dynamic simulation, obtain the mechanical response of the packaging system under impact vibration, and evaluate the impact vibration reliability of the packaging system based on the mechanical response.

[0012] Optionally, the conversion of the original impact response spectrum into a power spectrum based on the assumption of a stationary random vibration process includes:

[0013] Based on the frequency response function of a single-degree-of-freedom system, and assuming that the power near the natural frequency is constant, a first relationship expression is established between the variance of the original impact response spectrum and the power spectrum.

[0014] Based on the extremum theory of Gaussian processes, a second relationship expression between the variance and the original impact response spectrum is established;

[0015] By combining the first relational expression and the second relational expression, the power spectrum can be obtained.

[0016] Optionally, the power spectrum is calculated using the following formula:

[0017]

[0018] in, The power spectrum at frequency The value at; The damping ratio; The original impact response spectrum at frequency The value at; Indicates the duration of the impact vibration. This indicates the probability that the peak value does not exceed a given amplitude.

[0019] Optionally, generating the initial time-domain signal based on the power spectrum and the randomly generated phase spectrum includes:

[0020] Based on the power spectrum, the corresponding Fourier amplitude spectrum is calculated;

[0021] Based on the Fourier amplitude spectrum and the randomly generated phase spectrum, construct a frequency domain signal in complex form;

[0022] The frequency domain signal is subjected to an inverse fast Fourier transform to generate the initial time domain signal.

[0023] Optionally, the formula for calculating the Fourier amplitude spectrum is as follows:

[0024]

[0025] in, Δf is the value of the Fourier amplitude spectrum at frequency f; Δf is the sampling frequency interval of the original impulse response spectrum; The number of transformation points is the power of 2 that is closest to and not less than the length of the sampled signal.

[0026] Optionally, the iterative correction of the initial time-domain signal to obtain a time-domain impact vibration signal with an energy distribution consistent with the original impact response spectrum includes:

[0027] Step a: Calculate the computational response spectrum generated by the single-degree-of-freedom system excited by the initial time-domain signal;

[0028] Step b: Compare the calculated response spectrum with the original impulse response spectrum, and correct the Fourier amplitude spectrum used to generate the initial time-domain signal based on the comparison result;

[0029] Step c: Repeat steps a and b until the energy distribution of the calculated response spectrum is consistent with that of the original impact response spectrum, and obtain the time-domain impact vibration signal.

[0030] Optionally, calculating the computational response spectrum generated by the single-degree-of-freedom system excited by the initial time-domain signal includes:

[0031] Calculate the impulse response generated by the initial time-domain signal excitation of the single-degree-of-freedom system, and perform a Fourier transform on the impulse response to obtain the corresponding frequency domain transfer function;

[0032] Perform a Fourier transform on the initial time-domain signal to obtain the corresponding frequency-domain representation;

[0033] The frequency domain representation is multiplied point by point with the frequency domain transfer function to obtain the frequency domain response of the single-degree-of-freedom system.

[0034] Perform an inverse Fourier transform on the frequency domain response to obtain the time domain response of the single-degree-of-freedom system;

[0035] Extract the maximum absolute value of the time-domain response at each frequency point to generate the calculated response spectrum.

[0036] Optionally, the formula for the iterative correction is as follows:

[0037]

[0038] in, This is the Fourier amplitude spectrum of the current iteration; The Fourier amplitude spectrum for the next iteration; The original impact response spectrum; This is the calculated response spectrum obtained in the current iteration.

[0039] Optionally, the total strain rate of the unified creep-plastic constitutive model is decomposed into elastic strain rate and inelastic strain rate. The inelastic strain rate is jointly controlled by viscous overstress and back stress, and the back stress is decomposed into short-range back stress and long-range back stress.

[0040] In a second aspect, the present invention provides a reliability evaluation apparatus for a packaging system considering viscoplastic behavior, comprising:

[0041] The acquisition module is used to obtain the original impulse response spectrum based on the frequency domain design standards of the packaging system.

[0042] The signal generation module is used to convert the original impact response spectrum into a power spectrum based on the assumption of a stationary random vibration process; generate an initial time-domain signal according to the power spectrum and a randomly generated phase spectrum; and iteratively correct the initial time-domain signal to obtain a time-domain impact vibration signal that is consistent with the original impact response spectrum in terms of energy distribution.

[0043] A module is established to build a finite element model of the packaging system and to describe the viscoplastic mechanical behavior of the solder joint material in the finite element model using a unified creep-plastic constitutive model.

[0044] The simulation evaluation module is used to input the time-domain impact vibration signal as a load into the finite element model, perform time-domain nonlinear dynamic simulation, obtain the mechanical response of the packaging system under impact vibration, and evaluate the impact vibration reliability of the packaging system based on the mechanical response.

[0045] Compared with the prior art, the present invention has the following advantages and beneficial effects:

[0046] This application provides a reliability assessment method for packaging systems considering viscoplastic behavior. Using spectral transformation theory based on the assumption of stationary random vibration, the original impact response spectrum directly given in engineering is inversely derived into a power spectrum conforming to the statistical laws of random vibration. A random phase is assigned to each frequency component, simulating the uncertain phase relationship of each frequency component in a real impact vibration environment. This results in an initial time-domain signal with a nondeterministic random waveform, more closely resembling physical reality. Iterative correction of the initial time-domain signal yields a time-domain impact vibration signal with an energy distribution consistent with the original impact response spectrum. This time-domain impact vibration signal serves as the input load for finite element analysis. By introducing a unified creep-plastic constitutive model and time-domain nonlinear dynamic simulation, the linear assumptions of traditional methods are fundamentally eliminated, significantly reducing the uncertainty of nonlinear simulation results caused by inaccurate input. This allows the simulation results to accurately reflect the core nonlinear process of stress relaxation and continuous accumulation of plastic strain in solder joint materials such as SAC305 during impact vibration. Therefore, based on the simulation results, the impact vibration reliability of the packaging system can be accurately assessed. Attached Figure Description

[0047] To more clearly illustrate the technical solutions of the exemplary embodiments of the present invention, the accompanying drawings used in the embodiments will be briefly described below. It should be understood that the following drawings only show some embodiments of the present invention and should not be considered as a limitation of the scope. For those skilled in the art, other related drawings can be obtained based on these drawings without creative effort. In the drawings:

[0048] Figure 1 A schematic flowchart illustrating the reliability assessment method for a packaging system considering viscoplastic behavior provided in this application embodiment;

[0049] Figure 2 A comparison diagram of frequency domain and time domain vibration stress distribution provided for embodiments of this application;

[0050] Figure 3 This is a schematic diagram of the structure of the BGA package model provided in the embodiments of this application;

[0051] Figure 4 This is a frequency domain modal diagram of the BGA packaging model provided in the embodiments of this application;

[0052] Figure 5 This is a logic block diagram of the time-domain conversion algorithm provided in the embodiments of this application;

[0053] Figure 6 A schematic diagram showing the frequency domain and time domain vibration calculation results of the BGA package model provided in the embodiments of this application;

[0054] Figure 7 A schematic diagram of stress distribution of a BGA after being excited by three sets of random time-domain shock vibration signals, provided in an embodiment of this application;

[0055] Figure 8 Stress-strain contour plots of each model at the end of vibration, provided in the embodiments of this application;

[0056] Figure 9 A schematic diagram showing the evolution of maximum stress and cumulative equivalent plastic strain over time for embodiments of this application;

[0057] Figure 10 This is a schematic diagram of the structure of a packaging system reliability evaluation device that takes into account viscoplastic behavior, provided in an embodiment of this application. Detailed Implementation

[0058] To make the objectives, technical solutions, and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the embodiments and accompanying drawings. The illustrative embodiments and descriptions of the present invention are only used to explain the present invention and are not intended to limit the present invention.

[0059] This application provides a method for reliability assessment of a packaging system that considers viscoplastic behavior. Please refer to... Figure 1 This is a flowchart illustrating the reliability assessment method for a packaging system considering viscoplastic behavior provided in this application embodiment. The following is a further explanation. Figure 1 The reliability assessment method for packaging systems that takes into account viscoplastic behavior is introduced.

[0060] S1. Obtain the original impulse response spectrum based on the frequency domain design standard of the packaging system.

[0061] In practical implementation, the original shock response spectrum can be acquired based on the frequency domain design standards of the packaging system (such as GB / T2423.10-2008). This shock response spectrum defines the maximum acceleration response that a single-degree-of-freedom system can withstand at different frequencies, and serves as the basis for shock-resistant design.

[0062] S2. Based on the assumption of a stationary random vibration process, the original impact response spectrum is converted into a power spectrum.

[0063] In one possible embodiment, based on the frequency response function of a single-degree-of-freedom system and assuming that the power spectrum is constant near the natural frequency, a first relational expression between the variance of the original impact response spectrum and the power spectrum is established; based on the extremum theory of Gaussian processes, a second relational expression between the variance and the original impact response spectrum is established; the power spectrum is obtained by combining the first and second relational expressions.

[0064] In practical implementation, the mathematical derivation and implementation steps of this power spectrum conversion method are as follows:

[0065] S2.1 Establish frequency domain response relationship.

[0066] Based on the assumption of a stationary random vibration process, the original shock response spectrum of the encapsulation system can be calculated from the input power spectrum and the frequency response function of the single-degree-of-freedom system:

[0067]

[0068] in, For frequency; This is the original impact response spectrum; Power spectrum; The frequency response function of a single-degree-of-freedom system is expressed as the square of its modulus:

[0069]

[0070] in, The damping ratio; The natural frequency. When the excitation frequency... Approaching the natural frequency And when the damping ratio is less than 1, It will reach its maximum value.

[0071] S2.2 Establish the relationship between variance and power spectrum.

[0072] Variance of the original impact response spectrum It can be obtained by integrating the frequency response function over the entire frequency domain:

[0073]

[0074] Because a single-degree-of-freedom system's frequency response function peaks near its natural frequency and decays rapidly away from it, the energy from the vibrational load is mainly concentrated near the natural frequency, and the integration range can be concentrated near the resonance peak. Assuming the power spectrum... It is constant near its natural frequency, that is ,available:

[0075]

[0076] Calculate this integral to obtain the variance of the original impact response spectrum. The approximate relationship between the power spectrum and the first relation expression is as follows:

[0077]

[0078] S2.3. Establish the relationship between variance and impact response spectrum based on extreme value theory.

[0079] For a zero-mean Gaussian stationary process, its peak distribution follows an extreme value statistical law. The second relationship between the original impact response spectrum and its variance is expressed as follows:

[0080]

[0081] in, The duration of the impact vibration is indicated by , and p represents the probability that the peak value does not exceed the given amplitude.

[0082] S2.4, Solve the power spectrum together.

[0083] By combining the first and second relational expressions, the variance term is eliminated. The input power spectrum required to generate the original impact response spectrum can be obtained by solving the problem. The calculation formula is as follows:

[0084]

[0085] in, The power spectrum at frequency The value at; The damping ratio; For frequency; The original impact response spectrum at frequency The value at that location.

[0086] Traditional designs directly use the shock response spectrum (SRS) as the frequency domain input. However, the shock response spectrum is the envelope of the system response, not a true physical description of the environmental excitation. In the embodiments of this application, a shock response spectrum is established through rigorous mathematical derivation. With input power spectrum The quantitative relationship between these factors enables the reliability assessment of packaging systems based on engineering standards (SRS) to be directly integrated with time-domain simulation based on physical excitations (power spectrum), solving the long-standing industry problem of mismatch between "design input" and "analysis input".

[0087] S3. Generate the initial time-domain signal based on the power spectrum and the randomly generated phase spectrum.

[0088] In one possible embodiment, the corresponding Fourier amplitude spectrum is calculated based on the power spectrum; a complex frequency domain signal is constructed based on the Fourier amplitude spectrum and the randomly generated phase spectrum; and an inverse fast Fourier transform is performed on the frequency domain signal to generate an initial time domain signal.

[0089] In the specific implementation process, the initial time-domain signal The calculation formula is as follows:

[0090]

[0091] in, It is a complex number; Indicates the inverse Fourier transform; Fourier amplitude spectrum; For phase spectrum, Defined as 0 to 2 Random values ​​between.

[0092] Since shocks and random vibrations in real-world environments are inherently non-periodic and non-deterministic, in this embodiment, each frequency component is independently generated between 0 and 2... By using random phases within the time domain to simulate real vibration environments, the "energy statistical distribution" characteristics described by the power spectrum are transformed into time-domain signals with "random waveform" features, providing a rich "phase search space" for subsequent iterative correction processes. Different initial values ​​of random phases will produce time-domain signals with different waveforms but the same energy spectrum, which increases the possibility of finding signals that also meet the impact response spectrum requirements in the time domain through iteration.

[0093] In one possible embodiment, the Fourier amplitude spectrum The calculation formula is as follows:

[0094]

[0095] in, Δf is the value of the Fourier amplitude spectrum at frequency f; Δf is the sampling frequency interval of the original impulse response spectrum; This represents the number of transform points in the Fast Fourier Transform. The design takes advantage of the Fast Fourier Transform (FFT) algorithm's optimal computational efficiency for power-of-2 length sequences, finding the closest power to the sampled signal length, and reducing the algorithm's complexity to O(n). It has a much lower complexity than the Direct Discrete Fourier Transform (DFT) algorithm. This improves computational efficiency.

[0096] S4. Iteratively correct the initial time-domain signal to obtain a time-domain impact vibration signal that is consistent with the original impact response spectrum in terms of energy distribution.

[0097] In one possible embodiment, the specific steps of S4 are as follows:

[0098] Step a: Calculate the computational response spectrum of the single-degree-of-freedom system excited by the initial time-domain signal;

[0099] Step b: Compare the calculated response spectrum with the original impulse response spectrum, and correct the Fourier amplitude spectrum used to generate the initial time-domain signal based on the comparison results;

[0100] Step c: Repeat steps a and b until the energy distribution of the calculated response spectrum matches that of the original impact response spectrum, thus obtaining the time-domain impact vibration signal.

[0101] In this embodiment, the time-domain signal generated in each iteration is applied to a standard single-degree-of-freedom system to calculate the actual generated impact response spectrum, which is then compared point-by-point with the original impact response spectrum. This feedback mechanism, based on physical response (rather than simple frequency domain error), ensures that the correction direction always points to make the actual dynamic response of the generated signal consistent with the target. This fundamentally solves the problem that signals generated by traditional methods are "similar in form but not in essence," ultimately achieving a high degree of consistency between the energy distribution of the time-domain signal and the original impact response spectrum.

[0102] In one possible embodiment, the formula for iterative correction is as follows:

[0103]

[0104] in, This is the Fourier amplitude spectrum of the current iteration; The Fourier amplitude spectrum for the next iteration; This is the original impact response spectrum; This is the calculated response spectrum obtained in the current iteration.

[0105] In this embodiment of the application, at frequency point f, if the response spectrum is calculated... Below the original shock response spectrum Then proportionally Increase the amplitude at this frequency point Conversely, if the response spectrum is calculated... Higher than the original shock response spectrum Then proportionally Reduce the amplitude at that frequency point The correction for each frequency point f is independent, the formula can be highly vectorized and calculated in parallel, resulting in extremely high computational efficiency. Furthermore, it uses multiplicative correction instead of additive correction, avoiding numerical instability caused by differences in signal amplitude magnitude.

[0106] In one possible embodiment, step a specifically involves the following steps:

[0107] S4.1 Calculate the impulse response generated by the initial time-domain signal excitation of the single-degree-of-freedom system, and perform a Fourier transform on the impulse response to obtain the corresponding frequency domain transfer function.

[0108] Initial time domain signal The impulse response value of each frequency to a single-free system for:

[0109]

[0110] in, Let be the natural angular frequency of the system, expressed as: ; Let be the damping angular frequency of the system, expressed as: ; is the damping ratio.

[0111] Impulse response value Perform a Fourier transform to convert it into a frequency domain transfer function. :

[0112]

[0113] S4.2, For the initial time domain signal Perform a Fourier transform to obtain the corresponding frequency domain representation. :

[0114]

[0115] in, Includes the initial time-domain signal The amplitude and phase information of all frequency components.

[0116] S4.3, Representing the frequency domain With frequency domain transfer function By multiplying point by point, we obtain the frequency domain response of the single-degree-of-freedom system. :

[0117]

[0118] S4.4 Frequency Domain Response Performing the inverse Fourier transform yields the time-domain response of the single-degree-of-freedom system. :

[0119]

[0120] S4.5 Extract the maximum absolute value of the time-domain response at each frequency point to generate the calculated response spectrum. :

[0121]

[0122] Please refer to Figure 2 This is a comparison diagram of frequency domain and time domain vibration stress distribution provided in an embodiment of this application; wherein, Figure 2 (a) in the figure is a schematic diagram of the original impact response spectrum and the calculated response spectrum provided in the embodiment of this application. It can be seen that the original impact response spectrum and the calculated response spectrum are basically overlapping. Figure 2 (b) is a schematic diagram of the time-domain impact vibration signal provided in the embodiment of this application.

[0123] S5. Establish a finite element model of the packaging system and use a unified creep-plastic constitutive model to describe the viscoplastic mechanical behavior of the solder joint material in the finite element model.

[0124] In one possible embodiment, the total strain rate of the unified creep-plastic constitutive model is decomposed into elastic strain rate and inelastic strain rate. The inelastic strain rate is jointly controlled by viscous overstress and back stress, and the back stress is decomposed into short-range back stress and long-range back stress.

[0125] In practical implementation, within the framework of viscoplastic theory, the constitutive models of solder materials are generally divided into non-unified models and unified models. Non-unified models are based on the assumption that creep and plastic deformation are independent phenomena, while the unified creep-plastic constitutive model (UCP) attributes both creep and plastic deformation to inelastic deformation controlled by dislocation motion.

[0126] Because the solder material has a relatively low melting point, creep and plastic deformation must be considered simultaneously in this modeling. Under a viscoelastic framework, the total strain rate... It can be decomposed into elastic strain rate Inelastic strain rate : .

[0127] The formation of inelastic strain is a key characteristic of UCP models, and different UCP models differ in this respect. This application adopts the following formula:

[0128]

[0129]

[0130]

[0131] in, ρ is viscous overstress; d is resistive strength; A, B, and n are material constants; Q is apparent activation energy; T is absolute temperature; v is universal gas constant. (Symbols) Indicates Macaulay brackets (if H>0, ,otherwise N represents the direction of the deformation load; S represents the deviatoric stress tensor. .

[0132] Here, is an internal state variable representing the deviatoric stress, which determines the center of the yield surface, and R is the radius of the yield space. Isotropic hardening behavior is described as follows:

[0133]

[0134] in, It is the initial yield stress; is the saturation value; b is the material constant. It is the cumulative equivalent plastic strain:

[0135]

[0136] in, This represents the inelastic strain rate tensor.

[0137] Back stress can be decomposed into two variables: short-range back stress and long-range back stress. Short-range back stress represents a fast dynamic process, while long-range back stress represents a slower dynamic process.

[0138] Finally, the above-mentioned UCP model is used to describe the viscoplastic behavior of the weld joint material in the finite element model.

[0139] S6. Using the time-domain impact vibration signal as the load input to the finite element model, perform time-domain nonlinear dynamic simulation to obtain the mechanical response of the packaging system under impact vibration, and evaluate the impact vibration reliability of the packaging system based on the mechanical response.

[0140] In the specific implementation process, time-domain shock vibration signals are applied to the finite element model of the packaging system as a basic excitation. A unified creep-plastic constitutive model is activated in the finite element model, and time-domain nonlinear dynamic simulation is performed. Then, from the simulation results, core mechanical response data for reliability assessment are extracted, including the curve of the maximum stress of the packaging system during shock vibration as a function of time, and the curve of the cumulative equivalent plastic strain of the solder joint material at the location of maximum stress as described by the UCP model as a function of time.

[0141] Finally, based on the extracted mechanical response, the shock vibration reliability of the packaging system is evaluated. The main evaluation criteria include: comparing and analyzing the curves of maximum stress evolution over time to determine whether its peak value exceeds the yield strength or allowable stress of the solder joint material; assessing the degree of cumulative plastic deformation based on the curves of cumulative equivalent plastic strain evolution over time; and quantifying the mitigation effect of viscoplastic deformation on stress concentration by comparing the simulation results (such as peak maximum stress and stress distribution) of the purely elastic model and the viscoplastic (UCP) model under the same load, thereby verifying the necessity and accuracy of the UCP model in reliability assessment.

[0142] The following section uses a typical ball grid array (BGA) package structure finite element model (hereinafter referred to as BGA package model) as an example to explain in detail the specific implementation process of the package system reliability assessment method considering viscoplastic behavior provided in this application.

[0143] Please refer to Figure 3 This is a schematic diagram of the structure of the BGA packaging model provided in the embodiments of this application, wherein... Figure 3 Image (a) is a perspective view of the BGA package model provided in the embodiment of this application. Figure 3 (b) in the figure is a cross-sectional view of the BGA package model provided in the embodiment of this application.

[0144] First, a finite element model of the BGA package structure (referred to as the BGA package model) is established, such as... Figure 3 As shown, the BGA array consists of two PCB substrates and an 8×8 SAC305 solder ball array. The upper substrate is 20mm wide and 1mm thick; the lower substrate is 18mm wide and 0.8mm thick; and the solder ball radius is 0.5mm. In the BGA package model, the substrate grid is 0.4mm, the solder ball grid is 0.2mm, and the solder balls are defined as bonded contacts to the substrate. Table 1 shows the material properties of the BGA package model.

[0145] Table 1

[0146] Apply boundary conditions for vibration acceleration in the Z direction. During the calculation, apply fixed constraints to the surface of the bottom substrate in the negative X direction, such as... Figure 3As shown in (a) above. Simulations were performed using both the purely elastic and viscoplastic models, as detailed below:

[0147] In the frequency domain calculation process, the modes of the BGA package system are first calculated, such as... Figure 4 As shown, the modal frequencies of each order represent the natural frequencies of the BGA package structure. Frequency domain vibration calculations are based on the linear superposition of the system's natural frequency response characteristics in the Z direction. The original shock response spectrum is used as the input for the shock vibration frequency domain analysis, employing methods such as... Figure 5 The time-domain transformation algorithm shown obtains the time-domain impact vibration signal. In the time-domain impact calculation, Z-direction acceleration control is applied to the boundary condition constraint surface, and the input is the time-domain vibration signal.

[0148] Please refer to Figure 6 This is a schematic diagram showing the frequency domain and time domain shock vibration calculation results of the BGA package model provided in this application embodiment, wherein... Figure 6 (a) in the figure represents the frequency domain shock vibration calculation results of the BGA package model provided in the embodiments of this application. Figure 6 (b) shows the time-domain shock vibration calculation results of the BGA package model provided in the embodiment of this application. It can be seen that the equivalent stress distribution obtained by the two calculation methods is basically the same, and the maximum stress is distributed on the bottom surface of the top corner solder ball. The maximum stress value obtained by frequency domain shock vibration calculation is 0.053955MPa, and the maximum stress value obtained by time domain shock vibration calculation is 0.05026MPa, with an error within 7%.

[0149] Since a random phase distribution is introduced in the vibration signal conversion algorithm, in order to verify the effectiveness of the conversion algorithm under different time histories, time-domain signals with total durations of 0.1s, 0.2s and 0.4s were generated and calculated respectively.

[0150] Please refer to Figure 7 The diagram shows the stress distribution of the BGA after being excited by three sets of random time-domain impact vibration signals according to the embodiments of this application. Each set was tested three times. It can be seen that the equivalent stress is rapidly excited to the peak value in the first half of the impact vibration cycle and then begins to decrease. In the second half of the cycle, it shows an oscillating downward trend. This phenomenon is affected by the damping in the time-domain transformation algorithm, which enables the impact vibration simulation to restore the energy oscillation attenuation process of the real system to the greatest extent.

[0151] The maximum equivalent stresses of the three sets of random signal impact vibrations over the entire period were 0.05047 MPa, 0.05323 MPa, and 0.05582 MPa, respectively. The errors between these values ​​and the frequency domain calculation results were all kept within 7%, indicating that the algorithm is effective in converting impact signals over different time histories.

[0152] The material parameters of the UCP model were determined experimentally, as shown in Table 2. This enables a description of the viscoplastic behavior of BGA solder joints during impact vibration calculations.

[0153] Table 2

[0154]

[0155] right Figure 2 The time-domain shock vibration signal shown is amplified by 1000 times and then input into the BGA package model for shock vibration verification calculations of viscoplastic and pure elastic models.

[0156] Please refer to Figure 8 , is the stress-strain contour plot of each model at the end of vibration provided in the embodiments of this application, wherein, Figure 8 (a) is the stress cloud diagram of the pure elastic model at the end of vibration provided in the embodiment of this application. It can be seen that the pure elastic model showed obvious stress concentration at the end of vibration, and a steep stress gradient appeared at the node on the right side of the welding ball. Figure 8 (b) is the stress cloud diagram of the viscoplastic model at the end of vibration provided in the embodiment of this application. It can be seen that the viscoplastic model (i.e., the UCP model) also exhibits a certain stress concentration phenomenon, but its concentration degree is significantly less than that of the pure elastic model, and the stress gradient is smaller.

[0157] Figure 8 (c) in the figure is the strain contour plot of the pure elastic model at the end of vibration provided in the embodiment of this application; Figure 8 (d) in the figure shows the strain contour plot of the viscoplastic model at the end of vibration according to the embodiment of this application. It can be seen that the strain concentration phenomenon is more obvious in the viscoplastic model, and the region of strain concentration is different from the region of stress concentration, which indicates that the viscoplastic model absorbs local stress through plastic deformation. In contrast, in the purely elastic model, stress and strain concentrate at the same node.

[0158] Please refer to Figure 9 This is a schematic diagram showing the evolution of maximum stress and cumulative equivalent plastic strain over time, as provided in an embodiment of this application. Figure 9 (a) is a schematic diagram showing the maximum stress evolution over time during impact vibration of the BGA package model provided in this application embodiment. The maximum impact stress of the purely elastic model is 62.1 MPa, while the maximum impact stress of the viscoplastic model is 34.7 MPa. The stress level is lower than and close to the yield strength (40.8 MPa) of the industrial solder SAC305-CLF5013.

[0159] Figure 9(b) is a schematic diagram showing the evolution of the cumulative equivalent plastic strain of the weld joint at the location of maximum stress over time in the viscoplastic model provided in this application embodiment. The influence of the viscoplastic effect on the stress-strain relationship of the weld ball under impact vibration load is manifested as follows:

[0160] The BGA package model experienced a phase of rising and stabilizing vibration amplitude from 0 to 0.25 s, during which the solder joints bore the maximum stress, leading to a rapid increase in cumulative plastic strain. In the subsequent low-amplitude phase from 0.25 to 0.4 s, the cumulative plastic strain remained essentially unchanged, indicating that the solder joint stress was much lower than the yield stress.

[0161] Comparing the simulation results, it was found that the maximum stress of the viscoplastic model was 44% lower than that of the purely elastic model, and it more realistically reflected the energy dissipation process. The calculation results show that the viscoplastic behavior exhibited by the SAC305 solder joint during impact vibration can absorb local stress and generate a high level of strain, indirectly indicating that frequency domain vibration analysis based on purely elastic behavior is unreliable. In the embodiments of this application, the stress level of the purely elastic solder joint is much higher than the yield strength of SAC305, with a difference of up to 44% compared to the viscoplastic model. In contrast, time-domain viscoplastic analysis provides a more accurate prediction for the reliability assessment of the packaging system under impact vibration.

[0162] In summary, this application provides a reliability assessment method for packaging systems considering viscoplastic behavior. Simulation verification based on the BGA packaging model shows that the maximum equivalent stress calculated using the time-domain method is very close to the frequency-domain result (error <7%), and can accurately capture the dynamic process of vibration energy decay, further confirming its engineering feasibility. Based on the time-domain calculation method, a description of the viscoplastic behavior of the SAC305 solder joint is implemented. Comparison between the purely elastic BGA model and the viscoplastic BGA model shows that the SAC305 solder joint reduces stress concentration through plastic deformation, with the maximum stress level reduced by 44% compared to the purely elastic case, while maintaining consistency with the material's yield strength.

[0163] In summary, this application provides a reliability assessment method for packaging systems that considers viscoplastic behavior. This method effectively addresses a key limitation in current industrial frequency domain design standards: vibration failure in packaging systems exhibits strong spatiotemporal nonlinear characteristics, while also providing a more accurate numerical solution. Therefore, it provides theoretical support and practical methods for vibration-resistant structure design. This method can be used for dynamic reliability prediction of structures such as ball grid array (BGA), chip-scale package (CSP), and wafer-level package (WLP) in electronic packaging, and is suitable for packaging structure designs that consider material size effects and nonlinear time-dependent behavior.

[0164] Based on the same inventive concept, please refer to Figure 10This application also provides a reliability evaluation device for a packaging system considering viscoplastic behavior, the device comprising:

[0165] In a second aspect, the present invention provides a reliability evaluation apparatus for a packaging system considering viscoplastic behavior, comprising:

[0166] The acquisition module is used to obtain the original impulse response spectrum based on the frequency domain design standards of the packaging system.

[0167] The signal generation module is used to convert the original impact response spectrum into a power spectrum based on the assumption of a stationary random vibration process; generate an initial time-domain signal based on the power spectrum and a randomly generated phase spectrum; and iteratively correct the initial time-domain signal to obtain a time-domain impact vibration signal that is consistent with the original impact response spectrum in terms of energy distribution.

[0168] A module is established to build the finite element model of the packaging system, and a unified creep-plastic constitutive model is used to describe the viscoplastic mechanical behavior of the solder joint material in the finite element model.

[0169] The simulation evaluation module is used to input the time-domain impact vibration signal as a load into the finite element model, perform time-domain nonlinear dynamic simulation, obtain the mechanical response of the packaging system under impact vibration, and evaluate the impact vibration reliability of the packaging system based on the mechanical response.

[0170] Optionally, the signal generation module is specifically used for:

[0171] Based on the frequency response function of a single-degree-of-freedom system, and assuming that the power is constant near the natural frequency, a first relationship expression between the variance of the original impulse response spectrum and the power spectrum is established.

[0172] Based on the extremum theory of Gaussian processes, a second relational expression between variance and the original impact response spectrum is established.

[0173] By combining the first and second relational expressions, the power spectrum can be obtained.

[0174] Alternatively, the power spectrum can be calculated using the following formula:

[0175] ;

[0176] in, The power spectrum at frequency The value at; The damping ratio; The original impact response spectrum at frequency The value at; Indicates the duration of the impact vibration. This indicates the probability that the peak value does not exceed a given amplitude.

[0177] Optionally, the signal generation module is specifically used for:

[0178] Based on the power spectrum, the corresponding Fourier amplitude spectrum is calculated;

[0179] Construct a frequency domain signal in complex form based on the Fourier amplitude spectrum and the randomly generated phase spectrum;

[0180] Perform an inverse fast Fourier transform on the frequency domain signal to generate the initial time domain signal.

[0181] Optionally, the formula for calculating the Fourier amplitude spectrum is as follows:

[0182] ;

[0183] in, Fourier amplitude spectrum at frequency The value at the specified location; Δf is the sampling frequency interval of the original impulse response spectrum; The number of transformation points is the power of 2 that is closest to and not less than the length of the sampled signal.

[0184] Optionally, the signal generation module is specifically used for:

[0185] Step a: Calculate the computational response spectrum of the single-degree-of-freedom system excited by the initial time-domain signal;

[0186] Step b: Compare the calculated response spectrum with the original impulse response spectrum, and correct the Fourier amplitude spectrum used to generate the initial time-domain signal based on the comparison results;

[0187] Step c: Repeat steps a and b until the energy distribution of the calculated response spectrum matches that of the original impact response spectrum, thus obtaining the time-domain impact vibration signal.

[0188] Optionally, the signal generation module is specifically used for:

[0189] Calculate the impulse response generated by the initial time-domain signal excitation of the single-degree-of-freedom system, and perform a Fourier transform on the impulse response to obtain the corresponding frequency domain transfer function;

[0190] Perform a Fourier transform on the initial time-domain signal to obtain the corresponding frequency-domain representation;

[0191] Multiplying the frequency domain representation by the frequency domain transfer function point by point yields the frequency domain response of a single-degree-of-freedom system.

[0192] Perform an inverse Fourier transform on the frequency domain response to obtain the time domain response of the single-degree-of-freedom system;

[0193] Extract the maximum absolute value of the time-domain response at each frequency point to generate the calculated response spectrum.

[0194] Optional, the formula for iterative correction is as follows:

[0195] ;

[0196] in, This is the Fourier amplitude spectrum of the current iteration; The Fourier amplitude spectrum for the next iteration; This is the original impact response spectrum; This is the calculated response spectrum obtained in the current iteration.

[0197] Optionally, the total strain rate of the unified creep-plastic constitutive model is decomposed into elastic strain rate and inelastic strain rate. The inelastic strain rate is jointly controlled by viscous overstress and back stress, and the back stress is decomposed into short-range back stress and long-range back stress.

[0198] It should be noted that each module in the packaging system reliability assessment device considering viscoplastic behavior in this embodiment corresponds one-to-one with each step in the packaging system reliability assessment method considering viscoplastic behavior in the aforementioned embodiment. Therefore, the specific implementation of this embodiment can refer to the implementation of the aforementioned packaging system reliability assessment method considering viscoplastic behavior, and will not be repeated here.

[0199] Based on the same inventive concept, this application also provides a computer device, which includes a processor, a memory, and a computer program stored in the memory. The computer program is executed by the processor to implement the aforementioned method for evaluating the reliability of a packaging system that takes into account viscoplastic behavior.

[0200] Based on the same inventive concept, this application also provides a computer storage medium storing a computer program, which is executed by a processor to implement the aforementioned reliability assessment method for a packaging system considering viscoplastic behavior.

[0201] In some embodiments, the computer-readable storage medium may be a memory such as FRAM, ROM, PROM, EPROM, EEPROM, flash memory, magnetic surface memory, optical disk, or CD-ROM; or it may be a device including one or any combination of the above-mentioned memories. The computer may be a variety of computing devices, including smart terminals and servers.

[0202] In some embodiments, executable instructions may take the form of a program, software, software module, script, or code, written in any form of programming language (including compiled or interpreted languages, or declarative or procedural languages), and may be deployed in any form, including as a standalone program or as a module, component, subroutine, or other unit suitable for use in a computing environment.

[0203] As an example, executable instructions may, but do not necessarily, correspond to files in the file system. They may be stored as part of a file that holds other programs or data, for example, in one or more scripts in a Hyper Text Markup Language (HTML) document, in a single file dedicated to the program in question, or in multiple collaborative files (e.g., a file that stores one or more modules, subroutines, or code sections).

[0204] As an example, executable instructions can be deployed to execute on a single computing device, or on multiple computing devices located in one location, or on multiple computing devices distributed across multiple locations and interconnected via a communication network.

[0205] It should be noted that, in this document, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or system that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or system. Unless otherwise specified, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or system that includes that element.

[0206] The sequence numbers of the embodiments in this application are for descriptive purposes only and do not represent the superiority or inferiority of the embodiments.

[0207] The above specific embodiments further illustrate the purpose, technical solution, and beneficial effects of the present invention. It should be understood that the above are merely specific embodiments of the present invention and are not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A reliability assessment method for a packaging system considering viscoplastic behavior, characterized in that, include: Based on the frequency domain design standard of the packaging system, the original impulse response spectrum is obtained; Based on the assumption of a stationary random vibration process, the original impact response spectrum is converted into a power spectrum; An initial time-domain signal is generated based on the power spectrum and the randomly generated phase spectrum; The initial time-domain signal is iteratively corrected to obtain a time-domain impact vibration signal that is consistent with the original impact response spectrum in terms of energy distribution; A finite element model of the packaging system is established, and a unified creep-plastic constitutive model is used to describe the viscoplastic mechanical behavior of the solder joint material in the finite element model. The time-domain impact vibration signal is used as a load input to the finite element model to perform time-domain nonlinear dynamic simulation, obtain the mechanical response of the packaging system under impact vibration, and evaluate the impact vibration reliability of the packaging system based on the mechanical response.

2. The reliability assessment method for a packaging system considering viscoplastic behavior according to claim 1, characterized in that, The conversion of the original impact response spectrum into a power spectrum based on the assumption of a stationary random vibration process includes: Based on the frequency response function of a single-degree-of-freedom system, and assuming that the power near the natural frequency is constant, a first relationship expression is established between the variance of the original impact response spectrum and the power spectrum. Based on the extremum theory of Gaussian processes, a second relationship expression between the variance and the original impact response spectrum is established; By combining the first relational expression and the second relational expression, the power spectrum can be obtained.

3. The reliability assessment method for a packaging system considering viscoplastic behavior according to claim 2, characterized in that, The formula for calculating the power spectrum is as follows: ； in, The power spectrum at frequency The value at; The damping ratio; The original impact response spectrum at frequency The value at; Indicates the duration of the impact vibration. This indicates the probability that the peak value does not exceed a given amplitude.

4. The reliability assessment method for a packaging system considering viscoplastic behavior according to claim 1, characterized in that, The step of generating an initial time-domain signal based on the power spectrum and the randomly generated phase spectrum includes: Based on the power spectrum, the corresponding Fourier amplitude spectrum is calculated; Based on the Fourier amplitude spectrum and the randomly generated phase spectrum, construct a frequency domain signal in complex form; The frequency domain signal is subjected to an inverse fast Fourier transform to generate the initial time domain signal.

5. The reliability assessment method for a packaging system considering viscoplastic behavior according to claim 4, characterized in that, The formula for calculating the Fourier amplitude spectrum is as follows: ； in, The Fourier amplitude spectrum at frequency The value at the specified location; Δf is the sampling frequency interval of the original impact response spectrum; The number of transformation points is the power of 2 that is closest to and not less than the length of the sampled signal.

6. The reliability assessment method for a packaging system considering viscoplastic behavior according to claim 1, characterized in that, The iterative correction of the initial time-domain signal to obtain a time-domain impact vibration signal with an energy distribution consistent with the original impact response spectrum includes: Step a: Calculate the computational response spectrum generated by the single-degree-of-freedom system excited by the initial time-domain signal; Step b: Compare the calculated response spectrum with the original impulse response spectrum, and correct the Fourier amplitude spectrum used to generate the initial time-domain signal based on the comparison result; Step c: Repeat steps a and b until the energy distribution of the calculated response spectrum is consistent with that of the original impact response spectrum, and obtain the time-domain impact vibration signal.

7. The reliability assessment method for a packaging system considering viscoplastic behavior according to claim 6, characterized in that, The calculation of the computational response spectrum generated by the single-degree-of-freedom system excited by the initial time-domain signal includes: Calculate the impulse response generated by the initial time-domain signal excitation of the single-degree-of-freedom system, and perform a Fourier transform on the impulse response to obtain the corresponding frequency domain transfer function; Perform a Fourier transform on the initial time-domain signal to obtain the corresponding frequency-domain representation; The frequency domain representation is multiplied point by point with the frequency domain transfer function to obtain the frequency domain response of the single-degree-of-freedom system. Perform an inverse Fourier transform on the frequency domain response to obtain the time domain response of the single-degree-of-freedom system; Extract the maximum absolute value of the time-domain response at each frequency point to generate the calculated response spectrum.

8. The reliability assessment method for a packaging system considering viscoplastic behavior according to claim 6, characterized in that, The formula for the iterative correction is as follows: ； in, This is the Fourier amplitude spectrum of the current iteration; The Fourier amplitude spectrum for the next iteration; The original impact response spectrum; This is the calculated response spectrum obtained in the current iteration.

9. The reliability assessment method for a packaging system considering viscoplastic behavior according to claim 1, characterized in that, The total strain rate of the unified creep-plastic constitutive model is decomposed into elastic strain rate and inelastic strain rate. The inelastic strain rate is jointly controlled by viscous overstress and back stress, and the back stress is decomposed into short-range back stress and long-range back stress.

10. A reliability assessment device for a packaging system considering viscoplastic behavior, characterized in that, include: The acquisition module is used to obtain the original impulse response spectrum based on the frequency domain design standards of the packaging system. The signal generation module is used to convert the original impact response spectrum into a power spectrum based on the assumption of a stationary random vibration process; generate an initial time-domain signal according to the power spectrum and a randomly generated phase spectrum; and iteratively correct the initial time-domain signal to obtain a time-domain impact vibration signal that is consistent with the original impact response spectrum in terms of energy distribution. A module is established to build a finite element model of the packaging system and to describe the viscoplastic mechanical behavior of the solder joint material in the finite element model using a unified creep-plastic constitutive model. The simulation evaluation module is used to input the time-domain impact vibration signal as a load into the finite element model, perform time-domain nonlinear dynamic simulation, obtain the mechanical response of the packaging system under impact vibration, and evaluate the impact vibration reliability of the packaging system based on the mechanical response.

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