Based on the laser point heat source unsteady state transfer model, a novel method to gain thermo-physical parameters of isotropic solid materials is proposed. The enantiomorphous heat-source theory is introduced to calibrate the influence of adiabatic boundary on temperature rise of the measuring points, and a mathematical model is established. The thermal conductivity and thermal diffusivity of the material are calculated by numerical solution combined with computer programming, and a thermo-physical testing system is developed. The low vacuum environment in the sample container is obtained by using a vacuum pump. The laser generator emits a laser beam to heat a corner of the sample, and the variation of temperature on the upper surface of the sample measured by the temperature sensor is monitored by the wireless signal transmitting unit. The thermophysical properties of borosilicate glass (Pyrex7740), marble, diatomite firebrick, silica brick, and zirconium brick are comprehensively tested. The results show that the relative deviation between the test values of the first four samples with a relatively low thermal conductivity and the reference value is not more than 2.76%, and the test accuracy is higher. The relative deviation between the test values of the zirconium brick with a relatively large thermal conductivity and the reference value reaches 6.38%, and the test accuracy is lower. Uncertainty analysis of the test system shows that as the thermal conductivity of the tested sample increases, the credibility between the test value and the true value decreases, indicating that the device is more suitable for solid materials with a thermal conductivity less than 3.0W/(m·K).
The fracture toughness of in-service equipment and irradiation materials can be obtained from the ring-notched small punch specimen. The cohesive model was used to describe the ductile fracture behavior and crack propagation process of T91 steel, and the two parameters of material required by this model were calibrated by using the inverse finite element method. The successful implementation of this method requires that the load-displacement curve in the fracture damage stage is sensitive to the two model parameters, which can be optimized by the geometric design of the specimen and notch. The influence of the ratio of diameter to thickness, the depth of notch, and the presence or absence of prefabricated cracks on parameter sensitivity was studied, and the optimized design of the ring-notched specimen was obtained, based on which, a set of parameters was selected for finite element simulation to obtain the load-displacement curve. This curve was chosen as the target, and the genetic algorithm and the random walk algorithm were used for iterative fitting by using the inverse finite element method to extract the parameters of the cohesive model. The calculated results show that the error between the obtained parameters and the pre-selected parameters is less than 1%, which verifies the sensitivity of the specimen design and the accuracy of the inverse finite element method.
The release of compressive stress and atom diffusion have important influences on the growth of whiskers in 3D electronic packaging, and the compressive stress is also one of the main factors for dynamic recrystallization (DRX). By using the mathematical model of growth mechanism and the behavior of tin whisker based on the finite element method, the process of forming whiskers on silicon substrate by 3D electronic packaging tin layer with a typical physical size and structure was simulated. The qualitative analysis and growth of whiskers were realized. By controlling the key parameters such as gas pressure, thermal cycling temperature, and cycle of Ar in the background of the experiment, the external factors and plating process were constructed. The experimental system of accelerated test of internal pressure stress and whisker growth speed, length, and density in the film was constructed. The growth rate and density of whiskers were observed and detected by SEM. The effectiveness of the mathematical model of stress release, atom diffusion, and DRX in 3D electronic packaging tin whiskers was verified by SEM. The quantitative description of whiskers was realized, providing constructive suggestions for reducing whisker problems in future 3D packaging microstructure graphic design.
Carbon fiber-reinforced epoxy composites are widely used in the primary structure of aircraft, the compressive strength of which after impact is an important part in the evaluation of damage tolerance. At present, it mainly relies on a large number of tests to obtain compressive strength after impact in the engineering project. Therefore, it is necessary to develop a simple mathematical model to describe the compressive strength law after impact. A novel mathematical model for fitting compressive strength data of composite laminate after impact was proposed. Using the mathematical model and the initial model parameters, the compressive strength data after impact at different impact energy could be converted into some equivalent undamaged compressive strength data. Then, these equivalent undamaged compressive strength data were normally fitted using the maximum-likelihood estimate (MLE) method to obtain the standard deviation of normal distribution. The above steps was repeated until the minimum estimator of standard deviation was obtained. Hence, the best estimators of parameters for the mathematical model were determined. In order to further demonstrate the applicability of the mathematical model, post-impact compressive strength tests including different thicknesses, layup proportion, and material types were conducted, and the experimental data were fitted with the model. The results indicate that the mathematical model has a good applicability to the compressive strength test data after impact including different thicknesses, layup proportions, and material types.
