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    Theme Articles on "Thermal Stress"

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    Zhu Zhenhua, Shao Baijun, Wang Jun, Shao Yu, Chen Jiankang, Zhang Minghua
    Chinese Journal of Theoretical and Applied Mechanics    2018, 50 (3): 517-526.   DOI: 10.6052/0459-1879-18-080
    Abstract375)   HTML3)    PDF(pc) (590KB)(437)       Save

    Conductive polymer composites, with good flexibility, adjustable conductivity, easy forming and low production cost, can be used as functional material in many fields for its antistatic properties, electromagnetic shielding/microwave absorbing properties, and pressure/temperature sensitivity. However, in the process of processing, storage and use, due to comprehensive influence of many factors, aging will inevitably occur which will lead to deterioration of the properties. In this paper, PP/SSFs (stainless steel fibers) conductive composites were prepared by melt-blending and injection molding. The specimens were subjected to accelerated hygrothermal aging and UV aging. Stress relaxation curves, resistivity and crystallinity were experimentally measured. Micromorphology and elemental distribution of specimens before and after aging have been observed and dectected by scanning electron microscope (SEM) and energy spectrometer (EDS). The results show that the stress relaxation curves display three-stages in characteristics. And the stress reduces after hygrothermal aging due to the breaking and cross-linking of molecular chain caused by aging. The initial resistivity of PP/SSFs composites decreases with the increase of filler content, while it will increased with aging time. Due to the piezoresistive effect of the conductive polymer, the resistivity of the specimens decreases significantly with the increase of initial load, and then it tends to a stable value and fluctuation in a smaller range. The results of SEM/EDS analysis show that with the increase of aging time, the oxygen content on the specimens surface increases, and it will decreases with distance (depth) to the surface of specimen. XRD results show that the crystallinity of composites decreased with the increase of SSFs content and aging time. The present research will provide an experimental basis for the study of aging properties of conductive polymer composites.

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    Zhang Pei, He Tianhu
    Chinese Journal of Theoretical and Applied Mechanics    2018, 50 (3): 508-516.   DOI: 10.6052/0459-1879-18-079
    Abstract565)   HTML1)    PDF(pc) (1370KB)(599)       Save

    The existing generalized thermoelastic theory is mainly applicable to obtain the dynamic responses of the problems in which the time scale is extremely short while the spatial scale is still macro-scale. Nevertheless, when the characteristic length scale of elastic body is also of micro-scale, the dynamic responses of the elastic body will take on intense size-dependent effect, and the existing generalized thermoelastic theory will be no longer suitable for such problems. In present work, based upon the generalized thermoelasticity with nonlocal effect and memory-dependent derivative, the dynamic response of a finite thermoelastic rod fixed at both ends and subjected to a moving heat source is investigated. The corresponding governing equations of the problem are formulated and the initial conditions as well as the boundary conditions are specified. Then, the governing equations are solved by means of Laplace transform and its numerical inversion. In calculation, first, the influence of the time-delay factor on the distributions of the considered physical quantity was examined. Then, the influence of the time-delay factor on the distributions of the considered variables under two kinds of kernel functions (i.e. normalized form and unmodified form) was compared. Last, the influence of the nonlocal factor on the dimensionless temperature, displacement and stress is considered and illustrated graphically. The results show that: with the increase of the time-delay factor, the heat wave propagation velocity becomes smaller, the peak values of the physical quantities become larger, and the influence of the time delay factor on the considered variables is more significant in the case with the kernel function modified by normalized condition than that with unmodified kernel function; The non-local parameter barely affects the distribution of the dimensionless temperature, slightly affects the distribution of the dimensionless displacement, while markedly affects the peak values of the dimensionless stress.

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    Fei Qingguo, Jiang Dong, Chen Sufang, Qin Furong
    Chinese Journal of Theoretical and Applied Mechanics    2018, 50 (3): 497-507.   DOI: 10.6052/0459-1879-18-078
    Abstract369)   HTML0)    PDF(pc) (10640KB)(246)       Save

    To obtain accurate elastic parameters and coefficient of thermal expansion (CTE) of braided composites at high temperature, An approach for identifying thermal-related parameters based on homogenization theory is proposed. Firstly, on the basis of the finite element model of unit cell, the thermo-elastic parameters of the braided composites are predicted, basing on the theory of homogenization and thermos elasticity, and by applying the periodic displacement and temperature boundary conditions. Secondly, considering the errors in the equivalent process causing by the uneven distributed stress, the thermal modal frequencies of the refined model are taken as the supplementary information to further identify the thermo-elastic parameters, as a calibration of the predicted parameters. Based on the finite element unit cell model of two-dimensional braided structure, this paper carries out equivalent prediction and identification, to verify the validity and accuracy of the proposed method. after comparing the error of the thermal mode of equival model and identification model, it is shown that the proposed method based on equivalent prediction and parameter identification can accurately identify the macro-thermo-elasticity related parameters of braided composites at high temperature.

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    Zhang Yuanxiang, Liang Lihua, Zhang Jicheng, Chen Junjun, Sheng Yufeng
    Chinese Journal of Theoretical and Applied Mechanics    2018, 50 (3): 487-496.   DOI: 10.6052/0459-1879-18-077
    Abstract382)   HTML3)    PDF(pc) (24128KB)(264)       Save

    With the rapid development of microelectronics packaging technology, more attention has been paid to the electromigration (EM) failure on solder bump. The electric-thermal-structural multi-physical coupled analysis for flip chip ball grid array (FCBGA) packaging is performed in this paper based on FEM and submodeling technique. The simplified method of package model is introduced in detail. The current density distribution, temperature distribution and stress distribution of the key solder bump is investigated. It is found that the current crowding effect is easily generated at the location where electrons enter the bump from Cu metal layer, and the temperature gradient of the whole key solder bump is small. This paper presents the atomic density integral (ADI) method which considers four driving forces for electromigration such as electron wind force, stress gradient, temperature gradient and atomic density gradient. According to ADI method and the failure rule on void formation and diffusion, the electromigration void evolution process of the key solder bump is simulated with different mesh density. In can be found that the ADI method is stable and almost independent on the mesh density. The EM void location and time to failure (TTF) of key solder bump in FCBGA package is also simulated in the real service condition by ADI method. And the effect of solder material and Cu metal layer on EM failure is investigated in detail. We can see that the TTF of lead-free solder (Sn3.5Ag) is about 2.5 times than leaded solder (63Sn37Pb) because the TTF is determined to increase exponentially with the activation energy. And the EM failure is also influenced by the effective charge number. The adjustment of Cu metal layer structure will change the current flow direction and the stress distribution of the solder bump, which will affect the time to failure of solder bump.

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    Yu Yuanfeng, Li Zewei, Zheng Xiaoya
    Chinese Journal of Theoretical and Applied Mechanics    2018, 50 (3): 479-486.   DOI: 10.6052/0459-1879-18-076
    Abstract380)   HTML4)    PDF(pc) (1346KB)(468)       Save

    When two solid surfaces are in contact, it leads to non-uniform contact because of surfaces roughness. This causes constriction of heat flux and forms thermal contact resistance. The theoretical research is mainly focused on the positive problem, but there are few studies on the inverse problem. The inverse problem of thermal contact resistance is to obtain thermal contact resistance by a part of the boundary temperature, heat flux and some of the measured point temperature. The research has been applied in many fields, such as aerospace, mechanical manufacturing, microelectronics and other fields. It is a fast and effective method to determine thermal contact resistance in engineering field. In this paper, the inverse problem of thermal contact resistance with 2-D coordinate variation was solved by the boundary element method (BEM) and the conjugate gradient method (CGM). In order to verify the accuracy and feasibility of the method, according to the measured point temperature and the assumed thermal contact resistance, the temperature and the heat flux of the interface could be obtained, and then calculated and compared with the value of actual thermal contact resistance. The results show that the actual thermal contact resistance can be accurately obtained by using the BEM and CGM without the measurement error. But there exists the measurement error, the calculated result will be extremely sensitive to the measurement error, and the error of inversion result will be amplified due to the measurement error. In order to deal with this ill-posed problem, the least-squares method (LSM) was used to correct the calculated results. The results show that it can avoid some points deviating from the actual value in the inverse problem, and obviously improve the accuracy of calculations.

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