The flip chip package is a kind of advanced electri ca l packages. Due to the requirement of miniaturization, lower weight, higher dens ity and higher performance in the advanced electric package, it is expected that ...The flip chip package is a kind of advanced electri ca l packages. Due to the requirement of miniaturization, lower weight, higher dens ity and higher performance in the advanced electric package, it is expected that flip chip package will soon be a mainstream technology. The silicon chip is dir ectly connected to printing circuit substrate by SnPb solder joints. Also, the u nderfill, a composite of polymer and silica particles, is filled in the gap betw een the chip and substrate around the solder joints to improve the reliabili ty of solder joints. When flip chip package specimen is tested with thermal cycl ing, the cyclic stress/strain response that exists at the underfill interfaces and solder joints may result in interfacial crack initiation and propagation. Therefore, the chip cracking and the interfacial delamination between underfill and chip corner have been investigated in many studies. Also, most researches h ave focused on the effect of fatigue and creep properties of solder joint induce d by the plastic strain alternation and accumulation. The nuderfill must have lo w viscosity in the liquid state and good adhesion to the interface after solidif ying. Also, the mechanical behavior of such epoxy material has much dependen ce on temperature in its glass transition temperature range that is usually cove red by the temperature range of thermal cycling test. Therefore, the materia l behavior of underfill exists a significant non-linearity and the assumption o f linear elastic can lack for accuracy in numerical analysis. Through numerical analysis, this study had some comparisons about the effect of linear and non -linear properties of underfill on strain behaviors around the interface of fli p chip assembly. Especially, the deformation tendency inside solder bumps could be predicted. Also, it is worthily mentioned that we have pointed out which comp onent of plastic strain, thus, either normal or shear, has dominant influence to the fatigue and creep of solder bump, which have not brought up before. About the numerical analysis to the thermal plastic strain occurs in flip chip i nterconnection during thermal cycling test, a commercial finite element software , namely, ANSYS, was employed to simulate the thermal cycling test obeyed by MIL-STD-883C. The temperatures of thermal cycling ranged from -55 ℃ to 125 ℃ with ramp rate of 36 ℃/min and a dwell time of 25 min at peak temperature. T he schematic drawing of diagonal cross-section of flip chip package composed of FR-4 substrate, silicon chip, underfill and solder bump was shown as Fig.1. Th e numerical model was two-dimensional (2-D) with plane strain assumption and o nly one half of the cross-section was modeled due to geometry symmetry. The dim ensions and boundary conditions of numerical model were shown in Fig.2. The symm etric boundary conditions were applied along the left edge of the model, and the left bottom corner was additional constrained in vertical direction to prevent body motion. The finite element meshes of overall and local numerical model was shown as Fig.3. In this study, two cases of material model were used to describe the material behavior of the underfill: the case1 was linear elastic model that assumed Young’s Modulus (E) and thermal expansion coefficient (CTE) were consta nt during thermal cycling; the case2 was MKIN model (in ANSYS) that had nonlinea r temperature-dependent stress-strain relationship and temperature-dependent CTE. The material model applied to the solder bump was ANAND model (in ANSYS) th at described time-dependent plasticity phenomenon of viscoplastic material. Bot h the FR-4 substrate and silicon chip were assumed as temperature-independent elastic material; moreover, FR-4 substrate is orthotropic while silicon chip is isotropic. From the comparison between numerical results of linear and nonlinear material a ssumption of underfill, (i.e. case1 and case2), the quantities of plastic strain around the interconnection from case1 are higher than that in case2. Thus, the linear展开更多
Rock joint shape characteristics,waviness and unevenness play essential but distinct roles in shear mechanism of rock joints.This study presents a novel method to generate virtual rock joint profiles with realistic wa...Rock joint shape characteristics,waviness and unevenness play essential but distinct roles in shear mechanism of rock joints.This study presents a novel method to generate virtual rock joint profiles with realistic waviness and unevenness features.Firstly,joint profiles are obtained by 3D laser scanning device.Secondly,quantification of waviness and unevenness is conducted by traditional method,including digital filtering technique and roughness parameter RL.Thirdly,the discrete Fourier transform(DFT)method is employed to analyze the joint outlines.Two representative Fourier shape descriptors(D3,D8)for characterization of waviness and unevenness are suggested.Then,the inverse discrete Fourier transform(IDFT)is adopted to reconstruct the joint profiles with random values of phase angles but prescribed amplitudes controlled by D3 and D8.The traditional method is then applied to the reconstructed joint profiles to examine statistically the relationships between D3 and D8 and parameters RL of waviness and unevenness,respectively.The results show that larger D8 tends to result in larger waviness while higher D3 tends to increase unevenness.Reference charts for estimation of waviness and unevenness with different pairs of D3 and D8 are also provided to facilitate implementation of random joint reconstruction.展开更多
Large-scale genetic population used for genetic breeding researches covers a large area in the field experiment,and the effect of local control would be gradually weakened.The block in replication(BIR)design is suitab...Large-scale genetic population used for genetic breeding researches covers a large area in the field experiment,and the effect of local control would be gradually weakened.The block in replication(BIR)design is suitable for large population,which is applied to the field experiment of genetic population.The statistical methods of analysis of variance(ANOVA)and heritability estimation in single and multiple environments were derived and implemented using the statistical analysis system(SAS)program for the analysis of BIR.As a work example,a comparison of statistical analysis between BIR design and the completely random block(CRB)design were conducted for the protein content from a panel containing 455 soybean germplasms.The results indicated the different estimates of average heritability in multiple environments.The research results provided technical support for the application of BIR design in genetics and breeding studies.展开更多
文摘The flip chip package is a kind of advanced electri ca l packages. Due to the requirement of miniaturization, lower weight, higher dens ity and higher performance in the advanced electric package, it is expected that flip chip package will soon be a mainstream technology. The silicon chip is dir ectly connected to printing circuit substrate by SnPb solder joints. Also, the u nderfill, a composite of polymer and silica particles, is filled in the gap betw een the chip and substrate around the solder joints to improve the reliabili ty of solder joints. When flip chip package specimen is tested with thermal cycl ing, the cyclic stress/strain response that exists at the underfill interfaces and solder joints may result in interfacial crack initiation and propagation. Therefore, the chip cracking and the interfacial delamination between underfill and chip corner have been investigated in many studies. Also, most researches h ave focused on the effect of fatigue and creep properties of solder joint induce d by the plastic strain alternation and accumulation. The nuderfill must have lo w viscosity in the liquid state and good adhesion to the interface after solidif ying. Also, the mechanical behavior of such epoxy material has much dependen ce on temperature in its glass transition temperature range that is usually cove red by the temperature range of thermal cycling test. Therefore, the materia l behavior of underfill exists a significant non-linearity and the assumption o f linear elastic can lack for accuracy in numerical analysis. Through numerical analysis, this study had some comparisons about the effect of linear and non -linear properties of underfill on strain behaviors around the interface of fli p chip assembly. Especially, the deformation tendency inside solder bumps could be predicted. Also, it is worthily mentioned that we have pointed out which comp onent of plastic strain, thus, either normal or shear, has dominant influence to the fatigue and creep of solder bump, which have not brought up before. About the numerical analysis to the thermal plastic strain occurs in flip chip i nterconnection during thermal cycling test, a commercial finite element software , namely, ANSYS, was employed to simulate the thermal cycling test obeyed by MIL-STD-883C. The temperatures of thermal cycling ranged from -55 ℃ to 125 ℃ with ramp rate of 36 ℃/min and a dwell time of 25 min at peak temperature. T he schematic drawing of diagonal cross-section of flip chip package composed of FR-4 substrate, silicon chip, underfill and solder bump was shown as Fig.1. Th e numerical model was two-dimensional (2-D) with plane strain assumption and o nly one half of the cross-section was modeled due to geometry symmetry. The dim ensions and boundary conditions of numerical model were shown in Fig.2. The symm etric boundary conditions were applied along the left edge of the model, and the left bottom corner was additional constrained in vertical direction to prevent body motion. The finite element meshes of overall and local numerical model was shown as Fig.3. In this study, two cases of material model were used to describe the material behavior of the underfill: the case1 was linear elastic model that assumed Young’s Modulus (E) and thermal expansion coefficient (CTE) were consta nt during thermal cycling; the case2 was MKIN model (in ANSYS) that had nonlinea r temperature-dependent stress-strain relationship and temperature-dependent CTE. The material model applied to the solder bump was ANAND model (in ANSYS) th at described time-dependent plasticity phenomenon of viscoplastic material. Bot h the FR-4 substrate and silicon chip were assumed as temperature-independent elastic material; moreover, FR-4 substrate is orthotropic while silicon chip is isotropic. From the comparison between numerical results of linear and nonlinear material a ssumption of underfill, (i.e. case1 and case2), the quantities of plastic strain around the interconnection from case1 are higher than that in case2. Thus, the linear
基金Projects(51478477,51878668)supported by the National Natural Science Foundation of ChinaProjects(2014122006,2017-123-033)supported by the Guizhou Provincial Department of Transportation Foundation,ChinaProject(201722ts200)supported by the Fundamental Research Funds for the Central Universities,China
文摘Rock joint shape characteristics,waviness and unevenness play essential but distinct roles in shear mechanism of rock joints.This study presents a novel method to generate virtual rock joint profiles with realistic waviness and unevenness features.Firstly,joint profiles are obtained by 3D laser scanning device.Secondly,quantification of waviness and unevenness is conducted by traditional method,including digital filtering technique and roughness parameter RL.Thirdly,the discrete Fourier transform(DFT)method is employed to analyze the joint outlines.Two representative Fourier shape descriptors(D3,D8)for characterization of waviness and unevenness are suggested.Then,the inverse discrete Fourier transform(IDFT)is adopted to reconstruct the joint profiles with random values of phase angles but prescribed amplitudes controlled by D3 and D8.The traditional method is then applied to the reconstructed joint profiles to examine statistically the relationships between D3 and D8 and parameters RL of waviness and unevenness,respectively.The results show that larger D8 tends to result in larger waviness while higher D3 tends to increase unevenness.Reference charts for estimation of waviness and unevenness with different pairs of D3 and D8 are also provided to facilitate implementation of random joint reconstruction.
基金Supported by Key Research and Development Project of Heilongjiang Province(GA21B009-6)Heilongjiang Province Natural Science Foundation(C2015009)。
文摘Large-scale genetic population used for genetic breeding researches covers a large area in the field experiment,and the effect of local control would be gradually weakened.The block in replication(BIR)design is suitable for large population,which is applied to the field experiment of genetic population.The statistical methods of analysis of variance(ANOVA)and heritability estimation in single and multiple environments were derived and implemented using the statistical analysis system(SAS)program for the analysis of BIR.As a work example,a comparison of statistical analysis between BIR design and the completely random block(CRB)design were conducted for the protein content from a panel containing 455 soybean germplasms.The results indicated the different estimates of average heritability in multiple environments.The research results provided technical support for the application of BIR design in genetics and breeding studies.
