A high-thermal-conductivity gel life prediction method based on multi-stress coupling failure mechanism

Abstract

The application is suitable for the field of thermal interface material reliability evaluation, and provides a high-thermal-conductivity gel life prediction method based on a multi-stress coupling failure mechanism, which is characterized by comprising the following steps: S1: determining key failure characteristic parameters of the high-thermal-conductivity gel, and setting a performance critical threshold for judging the failure; S2: designing and implementing a multi-stress cross-coupling accelerated aging test, and collecting degradation data of the key failure characteristic parameters of the high-thermal-conductivity gel under different stress level combinations in real time; and S3: based on the degradation data, calculating and extracting pseudo-failure life characteristic values of the high-thermal-conductivity gel under each accelerated stress combination condition. In the application, by designing a thermal-mechanical double-stress cross-coupling accelerated aging test and adopting a full-factor test design, at least three temperature levels and three mechanical shear stress levels are covered, so that the nonlinear interactive coupling effect between temperature stress and mechanical shear stress can be effectively captured.

Description

Technical Field

[0001] This invention belongs to the field of reliability assessment of thermal interface materials, and in particular relates to a method for predicting the lifetime of high thermal conductivity gels based on a multi-stress coupling failure mechanism. Background Technology

[0002] High thermal conductivity gels, as thermal interface materials filling the space between chip heat sources and heat sinks, play a crucial role in heat dissipation in 5G communications, new energy vehicles, and high-power electronic devices. Their service environment typically involves the combined effects of multiple stress factors such as high temperature, mechanical vibration, and thermal cycling. As the service time increases, the internal matrix of the gel gradually ages, and the filler interface debonds, leading to continuous degradation of thermal conductivity until failure.

[0003] Currently, the industry primarily uses a single stress-accelerated aging test method to assess the lifespan of high thermal conductivity gels. For example, this involves obtaining the thermal resistance degradation curve over time solely through high-temperature baking tests, and then extrapolating it to actual operating conditions using the Arrhenius model. This method has the following significant shortcomings:

[0004] First, single stress tests cannot reflect the interactive coupling effect between temperature and mechanical vibration. In actual service, temperature rise will accelerate interface fatigue caused by mechanical stress. The degradation rate under the combined effect of the two is much higher than the linear superposition of single stress.

[0005] Secondly, traditional life models (such as the Arrhenius model and the inverse power law model) have different physical dimensions and mathematical forms, making them difficult to use directly. Engineers often rely on experience to make simple calculations, lacking a strict dimensionless unified framework.

[0006] Third, existing methods typically use a fixed value for degradation as the failure criterion, failing to extract pseudo-failure lifetimes based on the stochastic process characteristics of the degradation trajectory, and lacking robustness to individual differences and measurement noise.

[0007] Therefore, there is an urgent need for a method to predict the lifetime of high thermal conductivity gels that can design accelerated tests with multi-stress cross-coupling, establish a dimensionless lifetime prediction model that considers stress interaction effects, and extract pseudo-failure lifetimes based on random degradation processes. Summary of the Invention

[0008] The purpose of this invention is to provide a method for predicting the lifetime of high thermal conductivity gels based on a multi-stress coupling failure mechanism, in order to solve the above-mentioned problems.

[0009] This invention is implemented as follows: a method for predicting the lifetime of high thermal conductivity gels based on a multi-stress coupling failure mechanism, comprising the following steps:

[0010] S1: Determine the key failure characterization parameters of the high thermal conductivity gel and set the performance critical threshold for judging its failure;

[0011] S2: Design and implement accelerated aging tests with multi-stress cross-coupling to collect degradation data of key failure characterization parameters of high thermal conductivity gel under different stress level combinations in real time;

[0012] S3: Based on the degradation data, calculate and extract the pseudo-failure lifetime characteristic values ​​of the high thermal conductivity gel under various accelerated stress combinations;

[0013] S4: Establish a dimensionless lifetime prediction model that considers the interactive coupling effect of multiple environmental stresses;

[0014] S5: Use the pseudo-failure lifetime characteristic values ​​obtained in step S3 to perform parameter fitting on the dimensionless lifetime prediction model and solve for the unknown coefficients in the model.

[0015] S6: Obtain real-time multiphysics stress data of the high thermal conductivity gel under actual service conditions, substitute it into the fitted dimensionless life prediction model, and calculate the predicted remaining service life of the high thermal conductivity gel.

[0016] In a further technical solution, in step S1, the key failure characterization parameter is the equivalent thermal resistance or in-situ shear strength of the high thermal conductivity gel, and the performance critical threshold is defined as a preset threshold within the range of 20% to 50% increase in equivalent thermal resistance compared to the initial state, or a threshold limit of 30% decrease in in-situ shear strength compared to the initial state.

[0017] In a further technical solution, in step S2, the accelerated aging test with multi-stress cross-coupling is a thermo-mechanical dual-stress coupling accelerated test, and the applied stress includes temperature stress and mechanical shear stress.

[0018] In a further technical solution, the test matrix of the thermo-mechanical dual-stress coupling accelerated test adopts a full factorial test design, which includes at least three discrete temperature levels and at least three discrete mechanical shear stress levels.

[0019] A further technical solution is that, in step S4, the specific modeling method of the dimensionless lifetime prediction model is as follows:

[0020] The natural logarithm of the predicted lifetime equals the unknown coefficient of the first model, plus the unknown coefficient of the second model multiplied by the normalized dimensionless temperature parameter, plus the unknown coefficient of the third model multiplied by the normalized dimensionless mechanical shear stress parameter, plus the unknown coefficient of the fourth model multiplied by the normalized dimensionless temperature parameter and the normalized dimensionless mechanical shear stress parameter.

[0021] The predicted lifespan is in hours; the unknown coefficients of the first model, the second model, the third model, and the fourth model are all unknown coefficients of the model to be fitted; the product of the normalized dimensionless temperature parameter and the normalized dimensionless mechanical shear stress parameter represents the nonlinear coupling effect between temperature stress and mechanical shear stress.

[0022] A further technical solution is that both the dimensionless temperature parameter and the dimensionless mechanical shear stress parameter must be processed through the following normalization method to ensure dimensional consistency:

[0023] The dimensionless temperature parameter is equal to the difference between the reciprocal of the reference temperature and the reciprocal of the absolute temperature under any operating condition, divided by the difference between the reciprocal of the reference temperature and the reciprocal of the highest limit temperature.

[0024] The dimensionless mechanical shear stress parameter is equal to the difference between the natural logarithm of the mechanical shear stress under any working condition and the natural logarithm of the reference stress, divided by the difference between the natural logarithm of the maximum ultimate stress and the natural logarithm of the reference stress.

[0025] The unit of absolute temperature under any working condition is Kelvin; the reference temperature and the maximum limit temperature are the reference temperature and the maximum limit temperature within the evaluation range, respectively, and the unit of both is Kelvin; the unit of mechanical shear stress under any working condition is MPa; the reference stress and the maximum limit stress are the reference stress and the maximum limit stress within the evaluation range, respectively, and the unit of both is MPa.

[0026] A further technical solution is that when the absolute temperature under any working condition is between the reference temperature and the maximum limit temperature, and the mechanical shear stress under any working condition is between the reference stress and the maximum limit stress, the dimensionless temperature parameter and the dimensionless mechanical shear stress parameter after transformation are both pure values ​​strictly within the range of zero to one, thereby eliminating the influence of the different physical dimensions of the Arrhenius model and the inverse power law model.

[0027] In a further technical solution, in step S3, a degradation trajectory model is established using a nonlinear Wiener process. The degradation amount of the key failure characterization parameter over time satisfies the following relationship: the degradation amount is equal to the drift coefficient characterizing the degradation rate multiplied by the time raised to the power of α, plus the diffusion coefficient characterizing individual differences and measurement noise multiplied by the time-transformed Brownian motion.

[0028] Among them, the drift coefficient characterizing the degradation rate is called the drift coefficient, the time scale parameter reflecting the nonlinear characteristics is called the time scale parameter, the diffusion coefficient characterizing individual differences and measurement noise is called the diffusion coefficient, the Brownian motion after time transformation represents the Brownian motion after time transformation, whose increment is independent and follows a normal distribution with a mean of zero and a variance of the time interval to the power of α; the probability density function is calculated by the first arrival time principle, and the time corresponding to the cumulative failure probability reaching 50% is extracted as the pseudo-failure lifetime feature value.

[0029] A further technical solution, in step S6, is as follows: The specific process of obtaining real-time multiphysics stress data of the high thermal conductivity gel under actual service conditions is as follows:

[0030] By deploying a miniature sensor array at the chip's heat source and heat dissipation interface, the ambient temperature time series and vibration stress time series are dynamically acquired in real time. The temperature time series is equivalent based on the Arrhenius model, and the mechanical shear stress time series is equivalent based on the Miner's rule. The dynamically fluctuating time series stress is converted into steady-state constant stress, and then substituted into the dimensionless lifetime prediction model for iterative calculation.

[0031] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0032] In this invention, by designing a thermo-mechanical dual-stress cross-coupling accelerated aging test and adopting a full-factor experimental design to cover at least three temperature levels and three mechanical shear stress levels, the nonlinear interactive coupling effect between temperature stress and mechanical shear stress can be effectively captured, overcoming the shortcomings of traditional single stress tests and simple linear superposition that cannot truly reflect complex service conditions.

[0033] In this invention, a dimensionless life prediction model considering the interactive coupling effect of multiple environmental stresses is established. The temperature parameter is normalized by the reciprocal temperature based on the Arrhenius model, and the mechanical shear stress parameter is normalized by logarithmic normalization, so that both are converted into pure values ​​in the interval [0,1], eliminating the influence of the different physical dimensions between the Arrhenius model and the inverse power law model. The product term of temperature and mechanical shear stress is used as the coupling effect term to improve the model fitting accuracy and engineering applicability.

[0034] In this invention, a degradation trajectory model is established using a nonlinear Wiener process. The degradation rate, nonlinear characteristics, individual differences, and measurement noise are characterized by the drift coefficient, time scale parameter, and diffusion coefficient, respectively. The probability density function is calculated using the first-arrival time principle, and the time corresponding to when the cumulative failure probability reaches 50% is extracted as the pseudo-failure lifetime feature value, thereby reducing the influence of random fluctuations and individual differences and obtaining a more robust median lifetime feature value.

[0035] In this invention, a miniature sensor array deployed at the chip's heat source and heat dissipation interface is used to collect real-time environmental temperature time series and vibration stress time series. Based on the Arrhenius model and Miner's rule, the dynamically fluctuating time series stress is equivalently converted into steady-state constant stress, which is then substituted into the already fitted dimensionless lifetime prediction model for iterative calculation. This bridges the gap between the dynamic actual working conditions and the static model input, enabling real-time and dynamic assessment of the remaining lifetime of the high thermal conductivity gel. Attached Figure Description

[0036] Figure 1 This is a schematic diagram illustrating the steps of a lifespan prediction method.

[0037] Figure 2 The structural logic diagram of the dimensionless lifetime prediction model;

[0038] Figure 3 This is a logic diagram for dynamic stress acquisition and equivalent conversion. Detailed Implementation

[0039] 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 and not intended to limit the invention.

[0040] The specific implementation of the present invention will be described in detail below with reference to specific embodiments.

[0041] like Figures 1-3 As shown, an embodiment of the present invention provides a method for predicting the lifetime of a high thermal conductivity gel based on a multi-stress coupling failure mechanism, comprising the following steps:

[0042] S1: Determine the key failure characterization parameters of the high thermal conductivity gel and set the performance threshold for judging its failure.

[0043] Specifically, before predicting the lifetime of high thermal conductivity gels, it is necessary to first identify which parameters can effectively characterize their performance degradation. For example, the thermal conductivity of the high thermal conductivity gel can be chosen as a key failure characterization parameter, because a decrease in thermal conductivity reflects a weakening of its heat dissipation capacity. Once the key failure characterization parameter is determined, a performance critical threshold also needs to be set. This threshold can be the parameter value reaching a certain absolute value, such as the thermal conductivity falling below a specific value; or it can be the change in the parameter value relative to its initial state, such as the thermal conductivity decreasing by a certain fixed percentage.

[0044] S2: Design and implement accelerated aging tests with multi-stress cross-coupling to collect degradation data of key failure characterization parameters of the high thermal conductivity gel under different stress level combinations in real time.

[0045] Specifically, to simulate the complex operating conditions faced by high thermal conductivity gels in actual service, an accelerated aging test needs to be designed that can simultaneously apply multiple stresses and consider their interactions. For example, a test could be designed to simultaneously apply high temperature and humidity stresses. During the test, the high thermal conductivity gel sample is placed under different combinations of temperature and humidity conditions, and its key failure characterization parameters, such as thermal conductivity, are measured periodically. Another design could be to simultaneously apply temperature and voltage stresses, observing changes in the gel's dielectric properties or thermal resistance by varying the combination of temperature and voltage. These tests require the use of sensors and data acquisition systems to ensure real-time recording of degradation data for key failure characterization parameters.

[0046] S3: Based on the degradation data, calculate and extract the pseudo-failure lifetime characteristic values ​​of the high thermal conductivity gel under various accelerated stress combinations.

[0047] Specifically, after obtaining degradation data of high thermal conductivity gels under different stress combinations, this data needs to be processed to extract lifetime information. One approach is to record the time when a key failure characterization parameter first reaches a preset performance threshold as the failure lifetime. For example, if a 20% decrease in thermal conductivity is set as the failure threshold, then when a sample under a specific stress combination experiences its thermal conductivity decrease by 20% for the first time, the test time at that moment is recorded as its failure lifetime. These failure times, obtained directly or through fitting of experimental data, can serve as pseudo-failure lifetime characteristic values.

[0048] S4: Establish a dimensionless lifetime prediction model that considers the interactive coupling effect of multiple environmental stresses.

[0049] Specifically, to predict the lifetime of highly thermally conductive gels, a mathematical model reflecting the interactions of multiple stresses is needed. This model should unify different types of stress (such as temperature, mechanical stress, and humidity) and consider their nonlinear coupling effects. For example, a lifetime model based on empirical formulas can be constructed, where lifetime is a polynomial function of temperature and mechanical stress, including temperature terms, mechanical stress terms, and the product of temperature and mechanical stress, to characterize their interactions. When constructing the model, it is necessary to ensure that the stress parameters in the model are transformed to eliminate the influence of different physical dimensions.

[0050] S5: Use the pseudo-failure lifetime characteristic values ​​obtained in step S3 to perform parameter fitting on the dimensionless lifetime prediction model and solve for the unknown coefficients in the model.

[0051] Specifically, after establishing a dimensionless lifetime prediction model, it is necessary to use pseudo-failure lifetime characteristic values ​​obtained from accelerated aging tests to determine the specific parameters in the model. For example, if the model contains multiple unknown coefficients, statistical regression techniques such as least squares can be used to substitute the pseudo-failure lifetime characteristic values ​​under each stress combination into the model to solve for the coefficients that make the model prediction results match the actual data. This may involve iterative optimization of the model to find the parameter combination. Through parameter fitting, the established lifetime prediction model can describe the lifetime characteristics of high thermal conductivity gels under different stress conditions.

[0052] S6: Obtain real-time multiphysics stress data of the high thermal conductivity gel under actual service conditions, substitute it into the fitted dimensionless life prediction model, and calculate the predicted remaining service life of the high thermal conductivity gel.

[0053] Specifically, once the high thermal conductivity gel is put into practical use, it is necessary to monitor the environmental stress it is exposed to. For example, temperature and vibration sensors can be installed inside the equipment to periodically or continuously collect environmental temperature and mechanical vibration data. This data can be instantaneous or averaged over a period of time. These stress data under actual service conditions are then transformed according to model requirements (e.g., temperature is converted to its reciprocal, and mechanical stress is converted to its logarithm), and then substituted into the dimensionless life prediction model that has already been fitted in step S5. The model will output the predicted life or remaining service life of the high thermal conductivity gel based on the input stress data.

[0054] In this embodiment, through the above steps, the method can systematically consider the multi-stress coupling effect, use a dimensionless model to uniformly process stresses of different dimensions, and extract lifetime feature values ​​based on actual degradation data, ultimately achieving the prediction of the lifetime of high thermal conductivity gels.

[0055] In a preferred embodiment of the present invention, in step S1, the key failure characterization parameter is the equivalent thermal resistance of the high thermal conductivity gel. Or the in-situ shear strength τ, the critical performance threshold is defined as the equivalent thermal resistance. A preset threshold that increases by 20% to 50% from the initial state, or a threshold that decreases the in-situ shear strength τ by 30% from the initial state.

[0056] In this embodiment, the equivalent thermal resistance Thermal conductivity is an important indicator for evaluating the heat transfer performance of high thermal conductivity gels, representing the temperature difference generated when a unit heat flow passes through the gel. When high thermal conductivity gels undergo aging, degradation, or interfacial debonding, their internal structure may change, leading to a decrease in thermal conductivity, which manifests as equivalent thermal resistance. The increase in equivalent thermal resistance. Changes in τ can directly reflect the thermal conductivity failure of the gel. In-situ shear strength τ refers to the ability of a high thermal conductivity gel to withstand shear forces in practical application environments.

[0057] The solution in this application explicitly specifies the equivalent thermal resistance of the high thermal conductivity gel as the key failure characterization parameter in step S1 above. Or the in-situ shear strength τ, and specifically defined the performance critical threshold, thus providing a clear and quantitative standard for judging the failure state of high thermal conductivity gels. Equivalent thermal resistance The in-situ shear strength τ directly reflects the thermal conductivity of the gel, while its mechanical stability and interfacial bonding ability are characterized. These two parameters comprehensively and objectively capture the degradation process of high thermal conductivity gels from two key dimensions: thermal and mechanical. By setting the equivalent thermal resistance... The preset thresholds, ranging from 20% to 50% above the initial state, or the threshold limit of a 30% decrease in in-situ shear strength τ compared to the initial state, provide clear termination conditions and judgment criteria for data acquisition in the accelerated aging test in step S2 and calculation of pseudo-failure lifetime characteristic values ​​in step S3. This specific definition ensures the consistency and repeatability of the failure criteria under different test conditions, thus laying a solid foundation for establishing an accurate lifetime prediction model.

[0058] In a preferred embodiment of the present invention, in step S2, the accelerated aging test involving multi-stress cross-coupling is a thermo-mechanical dual-stress coupling accelerated test. This test involves simultaneously or alternately applying temperature stress and mechanical stress to simulate the complex environments that highly thermally conductive gels may encounter in practical applications. This test design can more realistically reflect the degradation behavior of materials under multiple stresses, because the failure of many materials is not the result of a single stress, but rather the result of the interaction and synergistic acceleration of multiple stresses. For example, it can be achieved using integrated testing equipment with temperature control and mechanical loading functions, or by subjecting samples to cyclic testing under different stress environments.

[0059] The applied stress includes thermal stress T and mechanical shear stress S.

[0060] Temperature stress (T) refers to the internal stress of a material caused by changes in ambient temperature or sustained high / low temperatures. For highly thermally conductive gels, temperature changes can lead to the breakage, cross-linking, or rearrangement of their internal polymer chains, thereby altering their physicochemical properties, such as thermal conductivity and viscoelasticity. Temperature stress can be applied by placing the sample in a constant temperature chamber, a high / low temperature cycling chamber, or a thermal shock test chamber.

[0061] Mechanical shear stress (S) refers to the force acting on the surface of a material and causing it to undergo shear deformation. High thermal conductivity gels are often used as interface materials, subjected to shear forces caused by thermal expansion coefficient mismatch or external vibration between chips and heat sinks. This shear stress can lead to damage to the internal structure of the gel, interfacial debonding, or creep, thereby affecting its thermal conductivity and mechanical stability. Mechanical shear stress can be applied using a universal testing machine with shear fixtures, a rheometer, or a custom shear loading device.

[0062] In this embodiment, the solution of this application specifically defines the generalized multi-stress cross-coupling accelerated aging test in step S2 as a thermo-mechanical dual-stress coupling accelerated test, and clearly applies temperature stress T and mechanical shear stress S, thereby solving the above-mentioned problems.

[0063] As a preferred embodiment of the present invention, the test matrix of the thermo-mechanical dual-stress coupling accelerated test adopts a full factorial design, which includes at least three discrete temperature levels and at least three discrete mechanical shear stress levels.

[0064] In this embodiment, the solution of this application ensures that all preset discrete level combinations of temperature stress and mechanical shear stress can be fully tested in the thermo-mechanical dual-stress coupling accelerated test by adopting a full factorial experimental design.

[0065] Specifically, by setting at least three discrete temperature levels and at least three discrete mechanical shear stress levels, the experimental matrix can cover a broader stress space. This comprehensive experimental design allows researchers not only to independently assess the individual effects of temperature and mechanical shear stress on the degradation of highly thermally conductive gels, but more importantly, to accurately capture and quantify the nonlinear interactive coupling effect between these two stresses. Under multi-stress coupled failure mechanisms, the effects of a single stress or simple superposition of stresses often cannot fully explain the degradation behavior of materials, while a full factorial design can reveal the synergistic or antagonistic effects that stress combinations may produce. The degradation data obtained in this way are more comprehensive and representative, providing a solid data foundation for the subsequent establishment of a dimensionless lifetime prediction model that considers the interactive coupling effect of multi-environment stresses, thereby significantly improving the accuracy and reliability of the model.

[0066] In a preferred embodiment of the present invention, in step S4, the specific model formula of the dimensionless lifetime prediction model is as follows:

[0067]

[0068] in, The predicted lifetime of the high thermal conductivity gel is given in hours. , , , These are all unknown coefficients of the model to be fitted; This is the normalized dimensionless temperature parameter; This is the normalized dimensionless mechanical shear stress parameter; The term characterizes the nonlinear coupling effect between temperature stress and mechanical shear stress.

[0069] In this embodiment, the dimensionless lifetime prediction model aims to describe the lifetime performance of high thermal conductivity gels under different stress conditions through mathematical expressions and transform it into a dimensionless form to eliminate the influence of different physical dimensions on model fitting and prediction. Its core function is to provide a unified framework for quantifying the relationship between stress and lifetime, thereby achieving accurate prediction of product lifetime. This model can be derived based on physical failure mechanisms or constructed using data-driven statistical methods. The specific model formula uses a logarithmic transformation to correlate lifetime L with the stress parameter. and Connect them.

[0070] in, For the intercept term, it represents the logarithm of the baseline life when all stress parameters are zero; and These represent the independent linear effects of temperature stress and mechanical shear stress parameters on lifetime, respectively; while The key interaction term is used to capture the nonlinear coupling effect between temperature stress and mechanical shear stress. This model structure can effectively reflect the complexity of material failure under multiple stresses; for example, high temperature may accelerate fatigue damage caused by mechanical stress, and vice versa. The predicted lifetime L is the core indicator of the model output, directly reflecting the expected service life of the high thermal conductivity gel under specific stress conditions, expressed in hours, ensuring the practicality and operability of the prediction results. , , , These are all unknown coefficients in the model to be fitted. These coefficients are the model parameters, and their values ​​need to be determined through statistical regression analysis of accelerated aging test data. They quantify the degree of influence of different stress factors and their interactions on lifespan. For example, The magnitude of this reflects the sensitivity of lifespan to temperature changes, while This quantifies the strength and direction of the coupling effect between temperature and mechanical shear stress. Accurate fitting of these coefficients is fundamental to the model's predictive accuracy.

[0071] The This is the normalized dimensionless temperature parameter, a temperature variable that has undergone a specific mathematical transformation to eliminate the physical dimensions of temperature, making it numerically comparable to other stress parameters and fitting into the structure of the model formula. For example, it could be a temperature transformation based on the reciprocal of the Arrhenius equation, followed by normalization.

[0072] The This is a normalized dimensionless mechanical shear stress parameter, similar to a dimensionless temperature parameter. It is a mechanical shear stress variable that has undergone mathematical transformation to eliminate its physical dimensions and make it consistent with other parameters in the model. For example, it could be a logarithmic transformation of the mechanical shear stress followed by normalization.

[0073] The The nonlinear coupling effect between temperature stress and mechanical shear stress is one of the core innovations of this model. It explicitly introduces a product term between the two stress factors to capture the nonlinear effects generated when they act together. In many material failure processes, the effects of a single stress factor are not simply additive, but rather mutually reinforcing or weakening, forming complex interactions. For example, at high temperatures, even lower mechanical shear stress may lead to faster failure, or temperature sensitivity may change under specific mechanical stress. The introduction of this interaction term allows the model to more accurately describe this complex failure mechanism.

[0074] As a preferred embodiment of the present invention, the dimensionless temperature parameter With dimensionless mechanical shear stress parameter All must be processed using the following normalization formula to ensure dimensional consistency:

[0075]

[0076]

[0077] Where T is the absolute temperature under any operating condition, and the unit is K; and These represent the reference temperature and the maximum limit temperature within the evaluation range, both in K; S represents the mechanical shear stress under any working condition, in MPa. and These represent the reference stress and the maximum ultimate stress within the evaluation interval, respectively, both in MPa.

[0078] In this embodiment, the dimensionless temperature parameter The normalization formula aims to transform different absolute temperature values ​​into a dimensionless value between 0 and 1 to reflect the impact of temperature stress on material lifetime. Its form borrows from the relationship between the reciprocal of temperature and the reaction rate in the Arrhenius model, allowing the temperature effect to be incorporated into lifetime prediction models in a physically more reasonable way. Besides this Arrhenius-based normalization, other methods such as linear or exponential normalization can also be used, depending on the material's temperature response characteristics.

[0079] Dimensionless mechanical shear stress parameter The normalization formula is used to transform mechanical shear stress into a dimensionless value between 0 and 1. It uses a logarithmic form, corresponding to the relationship between the logarithm of stress and life in the inverse power-law model, thus more accurately capturing the nonlinear effect of mechanical shear stress on material degradation. Besides this logarithmic normalization, other methods such as linear or power-law normalization can also be used, depending on the material's response characteristics to mechanical stress. Represents the absolute temperature measured under any specific operating condition, in Kelvin (K), and is one of the model inputs.

[0080] It is a reference temperature used to define the normalization range, usually chosen as the lowest temperature in the evaluation range or a certain stable operating temperature, and is expressed in Kelvin (K). It is the highest limiting temperature within the evaluation range, expressed in Kelvin (K), and... Together, we determine the upper and lower limits of temperature normalization. Similarly, S represents the mechanical shear stress measured under any specific operating condition, in megapascals (MPa), and is another model input. It is a reference stress used to define the normalization range, usually chosen as the lowest stress in the evaluation interval or a certain stable working stress, and is expressed in megapascals (MPa). It is the highest ultimate stress within the evaluation range, expressed in megapascals (MPa), compared with... Together, we determine the upper and lower limits of the normalization of mechanical shear stress. The setting of these parameters is crucial to ensuring the validity of the normalization results and the applicability of the model.

[0081] As a preferred embodiment of the present invention, when and At that time, after transformation and All values ​​are pure values ​​strictly within the interval [0,1], thus eliminating the influence of the different physical dimensions between the Arrhenius model and the inverse power law model.

[0082] In this embodiment, the solution of this application ensures the dimensionless temperature parameter by performing specific normalization processing on the temperature stress T and mechanical shear stress S and limiting them within a preset evaluation range. and dimensionless mechanical shear stress parameters All are strictly within the interval [0,1]. Specifically, for the dimensionless temperature parameter... When the absolute temperature T changes from the reference temperature Gradually rise to the highest limit temperature When, its corresponding reciprocal Will from Gradually decrease to According to the normalization formula, when hour, The molecule is 0, therefore ;when hour, Since the numerator and denominator are equal, therefore For dimensionless mechanical shear stress parameters When the mechanical shear stress S changes from the reference stress Gradually increase to the maximum ultimate stress When, its logarithm Will from Gradually increase to According to the normalization formula, when hour, The molecule is 0, therefore ;when hour, Since the numerator and denominator are equal, therefore Through this design, regardless of the physical dimensions and numerical range of the original stresses T and S, the transformed values... and It is always a pure numerical value between 0 and 1, thus mathematically achieving a unified scale representation of different stress parameters. This unified scale representation allows stress effects with different physical dimensions, originally based on the Arrhenius model and the inverse power law model, to be seamlessly integrated into the same dimensionless lifetime prediction model, effectively avoiding the increase in model complexity or prediction errors caused by inconsistent dimensions.

[0083] In a preferred embodiment of the present invention, in step S3, a degradation trajectory model is established using a nonlinear Wiener process, and the degradation amount of the key failure characterization parameter with time t is... Satisfy the equation:

[0084]

[0085] in, The drift coefficient characterizes the degradation rate. The time-scale parameter reflects the nonlinear characteristics. To characterize individual differences and measure the diffusion coefficient of noise, This represents the Brownian motion after time transformation, whose increments are independent and follow a mean of 0 and a variance of . The normal distribution is obtained; the probability density function is calculated by the first arrival time principle, and the time corresponding to when the cumulative failure probability reaches 50% is extracted as the pseudo-failure lifetime feature value.

[0086] In this embodiment, the nonlinear Wiener process is a mathematical model that can effectively describe a degradation process with nonlinear trends and random fluctuations. By introducing a nonlinear time scale or drift term, it can better capture the nonlinear and random degradation behavior of key failure characterization parameters of highly thermally conductive gels under multi-stress coupling, which varies with time. This process can be implemented by introducing a time function as a parameter of the Wiener process, or by performing a nonlinear transformation on time; for example, a power-law function can be used. This is used to transform time to reflect the nonlinear characteristics of the degradation rate as it changes over time.

[0087] Degeneracy trajectory model It is a specific mathematical expression used to quantify and predict the degradation path of highly thermally conductive gels. This model estimates its parameters by fitting degradation data collected in accelerated aging tests. , and The parameters can be solved using statistical methods such as maximum likelihood estimation, least squares method, or Bayesian method.

[0088] Drift coefficient The deterministic component characterizing the degradation rate, i.e., the average trend of degradation over time without random fluctuations, reflects the inherent degradation rate of highly thermally conductive gels under specific stress conditions. This coefficient can be estimated through regression analysis of the average trend of the degradation data.

[0089] Time scale parameters This reflects the nonlinear characteristics and controls the degree of nonlinearity in the effect of time on the degradation process. When When, the degradation is linear; when At this time, degradation is nonlinear. This parameter allows the model to flexibly adapt to the acceleration or deceleration of degradation rates under different materials or stress conditions. For example, when the degradation rate increases with time, When the degradation rate slows down over time, .

[0090] diffusion coefficient Characterizing individual differences and the randomness of measurement noise, this coefficient reflects the degree of fluctuation in the degradation path around the average trend. It quantifies the randomness and uncertainty of the degradation process in highly thermally conductive gels, making the model more realistic. It can be estimated by analyzing the residual distribution of degradation data points relative to the fitted curve.

[0091] This represents the Brownian motion after time transformation, whose increments are independent and follow a mean of 0 and a variance of . The Brownian motion follows a normal distribution. This introduces randomness, allowing the model to simulate unpredictable fluctuations and individual differences present in actual degradation processes. In numerical simulations, the increments of Brownian motion can be simulated by generating a sequence of random numbers that conforms to a normal distribution.

[0092] The first-reach time principle refers to the time when a random process first reaches a predetermined threshold. In degradation modeling, it represents the time when the degradation amount first reaches the failure threshold. This principle is used to calculate the failure time probability distribution of highly thermally conductive gels, thereby accurately extracting pseudo-failure lifetime characteristic values. Its implementation typically involves mathematical derivation and numerical calculation in stochastic process theory to solve the probability density function of the degradation trajectory model reaching the failure threshold.

[0093] The probability density function describes the probability of a random variable taking a specific value or falling within a certain interval. By analyzing the probability density function, we can gain a comprehensive understanding of the probability distribution of failure of highly thermally conductive gels at different time points. Based on the first-arrival time theory of the Wiener process, the probability density function of the inverse Gaussian distribution or other related distributions of failure time can be derived.

[0094] The time when the cumulative failure probability (CDF) reaches 50% is extracted as the pseudo-failure lifetime feature value. This refers to the time point when the CDF reaches 50%, commonly known as the median lifetime or B50 lifetime, representing the time when half of the samples have failed. This method provides a statistically significant and robust lifetime feature value, effectively avoiding the randomness of a single failed sample and more accurately reflecting the overall lifetime performance of the high thermal conductivity gel. After obtaining the probability density function of the failure time, it is integrated to obtain the cumulative distribution function, and then the time point corresponding to the cumulative distribution function value of 0.5 is found.

[0095] In a preferred embodiment of the present invention, the specific process of obtaining real-time multiphysics stress data of the high thermal conductivity gel under actual service conditions in step S6 is as follows: A micro-sensor array deployed at the interface between the chip heat source and the heat dissipation interface dynamically acquires the ambient temperature time series in real time. With vibration stress time series The temperature time series is equivalent to the Arrhenius model, and the mechanical shear stress time series is equivalent to the Miner's rule. The dynamically fluctuating time series stress is converted into steady-state constant stress, and then substituted into the dimensionless life prediction model for iterative calculation.

[0096] In this embodiment, the array of miniature sensors deployed at the interface between the chip's heat source and heat dissipation is designed to achieve accurate, real-time monitoring of key stress parameters in the actual service environment of the highly thermally conductive gel. This array can consist of multiple miniature thermocouples or thermistors for acquiring ambient temperature time-series data, or miniature piezoelectric sensors or MEMS accelerometers for acquiring vibration stress time-series data. These sensors are strategically positioned near the gel layer between the chip and the heat sink to ensure that the acquired data accurately reflects the local stress state experienced by the gel.

[0097] Real-time dynamic acquisition of ambient temperature time series With vibration stress time series This refers to sensors continuously acquiring and recording temperature and vibration stress data that change over time at a preset sampling frequency, forming a continuous time series. These time series can capture the instantaneous fluctuations and periodic changes in stress under actual working conditions. Equivalent temperature time series based on the Arrhenius model refers to using the relationship between chemical reaction rates and temperature described by the Arrhenius equation to equate the fluctuating temperature history over a period of time to a constant temperature with the same damage effect at a specific reference temperature. For example, the damage contribution of different temperature ranges can be calculated, then summed to obtain the total damage, and then the equivalent constant temperature can be derived.

[0098] Equivalent mechanical shear stress time series based on Miner's rule refers to using Miner's linear cumulative damage theory to accumulate the damage caused by mechanical shear stress cycles of different amplitudes and frequencies. This equates the complex vibration stress time series to a constant mechanical shear stress with the same cumulative damage under a specific reference stress. For example, the damage fraction of each stress cycle can be calculated based on the SN curve, and then all damage fractions can be added together to obtain the total damage, from which the equivalent constant stress can be derived. Converting dynamically fluctuating time-series stress into steady-state constant stress is a combined result of the above two equivalent methods. Its purpose is to transform the complex and variable stress history under actual service conditions into a simplified constant stress value with the same damage effect that conforms to the input requirements of the life prediction model.

[0099] The subsequent substitution into the dimensionless lifetime prediction model for iterative calculation refers to using the steady-state constant temperature and mechanical shear stress values ​​obtained through equivalent processing as input parameters, periodically or under the trigger of specific events, into the pre-fitted dimensionless lifetime prediction model to continuously update the predicted remaining lifetime of the high thermal conductivity gel.

[0100] This application utilizes a micro-sensor array to achieve real-time dynamic monitoring of ambient temperature and vibration stress in high thermal conductivity gels under actual service conditions. Given the dynamic fluctuations in stress data under actual conditions and the fact that life prediction models are typically based on constant stress conditions, this application cleverly introduces the Arrhenius model and Miner's rule. Specifically, the Arrhenius model is used to equate complex temperature time series to steady-state constant temperatures with the same damage effect, while Miner's rule is used to equate dynamic mechanical shear stress time series to steady-state constant mechanical shear stress with the same cumulative damage. This equivalence mechanism effectively bridges the gap between dynamic actual conditions and static model inputs, enabling the dimensionless life prediction model based on accelerated aging test data to be accurately applied to actual service environments. Subsequently, these equivalent steady-state constant stress values ​​are substituted into the life prediction model for iterative calculations, thereby continuously and accurately assessing the predicted remaining service life of the high thermal conductivity gel. The synergistic effect of this series of steps ensures the accuracy and real-time nature of life prediction, greatly enhancing the practical value of the prediction method.

[0101] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for predicting the lifetime of high thermal conductivity gels based on a multi-stress coupling failure mechanism, characterized in that, Includes the following steps: S1: Determine the key failure characterization parameters of the high thermal conductivity gel and set the performance critical threshold for judging its failure; S2: Design and implement accelerated aging tests with multi-stress cross-coupling to collect degradation data of key failure characterization parameters of high thermal conductivity gel under different stress level combinations in real time; S3: Based on the degradation data, calculate and extract the pseudo-failure lifetime characteristic values ​​of the high thermal conductivity gel under various accelerated stress combinations; S4: Establish a dimensionless lifetime prediction model that considers the interactive coupling effect of multiple environmental stresses; S5: Use the pseudo-failure lifetime characteristic values ​​obtained in step S3 to perform parameter fitting on the dimensionless lifetime prediction model and solve for the unknown coefficients in the model. S6: Obtain real-time multiphysics stress data of the high thermal conductivity gel under actual service conditions, substitute it into the fitted dimensionless life prediction model, and calculate the predicted remaining service life of the high thermal conductivity gel.

2. The method according to claim 1, characterized in that, In step S1, the key failure characterization parameter is the equivalent thermal resistance or in-situ shear strength of the high thermal conductivity gel. The performance critical threshold is defined as a preset threshold in which the equivalent thermal resistance increases by 20% to 50% from the initial state, or a threshold limit in which the in-situ shear strength decreases by 30% from the initial state.

3. The method according to claim 1, characterized in that, In step S2, the accelerated aging test with multi-stress cross-coupling is a thermo-mechanical dual-stress coupling accelerated test, and the applied stress includes temperature stress and mechanical shear stress.

4. The method according to claim 3, characterized in that, The experimental matrix of the thermo-mechanical dual-stress coupling accelerated test adopts a full factorial design, which includes at least three discrete temperature levels and at least three discrete mechanical shear stress levels.

5. The method according to claim 3, characterized in that, In step S4, the specific modeling method of the dimensionless lifetime prediction model is as follows: The natural logarithm of the predicted lifetime equals the unknown coefficient of the first model, plus the unknown coefficient of the second model multiplied by the normalized dimensionless temperature parameter, plus the unknown coefficient of the third model multiplied by the normalized dimensionless mechanical shear stress parameter, plus the unknown coefficient of the fourth model multiplied by the normalized dimensionless temperature parameter and the normalized dimensionless mechanical shear stress parameter. The predicted lifespan is in hours; the unknown coefficients of the first model, the second model, the third model, and the fourth model are all unknown coefficients of the model to be fitted; the product of the normalized dimensionless temperature parameter and the normalized dimensionless mechanical shear stress parameter represents the nonlinear coupling effect between temperature stress and mechanical shear stress.

6. The method according to claim 5, characterized in that, Both the dimensionless temperature parameter and the dimensionless mechanical shear stress parameter must be processed using the following normalization method to ensure dimensional consistency: The dimensionless temperature parameter is equal to the difference between the reciprocal of the reference temperature and the reciprocal of the absolute temperature under any operating condition, divided by the difference between the reciprocal of the reference temperature and the reciprocal of the highest limit temperature. The dimensionless mechanical shear stress parameter is equal to the difference between the natural logarithm of the mechanical shear stress under any working condition and the natural logarithm of the reference stress, divided by the difference between the natural logarithm of the maximum ultimate stress and the natural logarithm of the reference stress. The unit of absolute temperature under any working condition is Kelvin; the reference temperature and the maximum limit temperature are the reference temperature and the maximum limit temperature within the evaluation range, respectively, and the unit of both is Kelvin; the unit of mechanical shear stress under any working condition is MPa; the reference stress and the maximum limit stress are the reference stress and the maximum limit stress within the evaluation range, respectively, and the unit of both is MPa.

7. The method according to claim 6, characterized in that, When the absolute temperature under any operating condition is between the reference temperature and the maximum limit temperature, and the mechanical shear stress under any operating condition is between the reference stress and the maximum limit stress, the dimensionless temperature parameter and the dimensionless mechanical shear stress parameter after transformation are both pure values ​​strictly within the range of zero to one, thereby eliminating the influence of the different physical dimensions of the Arrhenius model and the inverse power law model.

8. The method according to claim 1, characterized in that, In step S3, a degradation trajectory model is established using a nonlinear Wiener process. The degradation amount of the key failure characterization parameter over time satisfies the following relationship: the degradation amount is equal to the drift coefficient characterizing the degradation rate multiplied by the time raised to the power of α, plus the diffusion coefficient characterizing individual differences and measurement noise multiplied by the time-transformed Brownian motion. Among them, the drift coefficient is used to characterize the degradation rate, the time scale parameter is used to reflect nonlinear characteristics, the diffusion coefficient is used to characterize individual differences and measurement noise, and the time-transformed Brownian motion represents the Brownian motion after time transformation. Its increment is independent and follows a normal distribution with a mean of zero and a variance equal to the power of the time scale parameter of the time interval. The probability density function is calculated by the first arrival time principle, and the time corresponding to the cumulative failure probability reaching 50% is extracted as the pseudo-failure lifetime feature value.

9. The method according to claim 1, characterized in that, In step S6, the specific process of obtaining real-time multiphysics stress data of the high thermal conductivity gel under actual service conditions is as follows: By deploying a miniature sensor array at the chip's heat source and heat dissipation interface, the ambient temperature time series and vibration stress time series are dynamically acquired in real time. The temperature time series is equivalent based on the Arrhenius model, and the mechanical shear stress time series is equivalent based on the Miner's rule. The dynamically fluctuating time series stress is converted into steady-state constant stress, and then substituted into the dimensionless lifetime prediction model for iterative calculation.

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