采用有限元方法对倒装芯片的焊点进行数值模拟计算分析。结果表明,等效蠕变应变和等效塑性应变的最大值在芯片下的边缘焊点上表面;对焊点应力应变进行时间历程处理,在循环的开始阶段,应力松弛现象显著,同时塑性应变和蠕变应变都存在累...采用有限元方法对倒装芯片的焊点进行数值模拟计算分析。结果表明,等效蠕变应变和等效塑性应变的最大值在芯片下的边缘焊点上表面;对焊点应力应变进行时间历程处理,在循环的开始阶段,应力松弛现象显著,同时塑性应变和蠕变应变都存在累积叠加趋势;对应力应变迟滞回线研究,发现曲线呈现周期性变化,随着温度的循环加载并趋于稳定。凭借Solomon模型和Shine and Fox模型,基于塑性应变和蠕变应变的交互作用,计算焊点的疲劳寿命,模拟结果和实际情况基本接近。展开更多
Discrete element simulations of one-dimensional compression of breakable granular assemblies were performed to investigate the capability of the exponential compression equation suggested by Bauer.The relationship bet...Discrete element simulations of one-dimensional compression of breakable granular assemblies were performed to investigate the capability of the exponential compression equation suggested by Bauer.The relationship between the so-called solid hardness and the particle strength was studied so as to provide a physical background for the introduction of a time-dependent solid hardness.A hyperbolic flow rule,describing the relationship between the inclination of the strain path and the stress ratio during wetting,was proposed based on typical triaxial wetting experiments on two different rockfill materials.The flow rule was then extended and incorporated into the transformed stress based hypoplastic model to capture the direction of creep strains.Meanwhile,a new density factor was introduced to the extended model to take into account the dependence of the magnitude of creep strains on the packing density.The stiffness tensor given by the extended model was discussed and the flowchart for the integration of the constitutive equation was designed.The extended model was then embedded into a finite element program and used to simulate the triaxial compression and wetting experiments performed on the aforementioned rockfill materials.Good agreement between the model predictions and the measured results lends sufficient credibility to the extended model in reproducing the stress-stain behaviour under loading and the creep behaviour during wetting.The extended model and the finite element program were also used to investigate the deformation behaviour of an earth-rock dam at the end of construction and during first impounding.The familiar phenomena such as the wetting induced settlement of the upstream shell and the movement of the dam crest towards the upstream were successfully captured by the numerical model,which confirms the feasibility of applying the extended model to dam engineering in the future.展开更多
文摘采用有限元方法对倒装芯片的焊点进行数值模拟计算分析。结果表明,等效蠕变应变和等效塑性应变的最大值在芯片下的边缘焊点上表面;对焊点应力应变进行时间历程处理,在循环的开始阶段,应力松弛现象显著,同时塑性应变和蠕变应变都存在累积叠加趋势;对应力应变迟滞回线研究,发现曲线呈现周期性变化,随着温度的循环加载并趋于稳定。凭借Solomon模型和Shine and Fox模型,基于塑性应变和蠕变应变的交互作用,计算焊点的疲劳寿命,模拟结果和实际情况基本接近。
基金supported by the National Natural Science Foundation of China (Grant Nos. 51179059,90815024)the Fund for Young Scientists in Nanjing Hydraulic Research Institute (Grant No. Y312004)
文摘Discrete element simulations of one-dimensional compression of breakable granular assemblies were performed to investigate the capability of the exponential compression equation suggested by Bauer.The relationship between the so-called solid hardness and the particle strength was studied so as to provide a physical background for the introduction of a time-dependent solid hardness.A hyperbolic flow rule,describing the relationship between the inclination of the strain path and the stress ratio during wetting,was proposed based on typical triaxial wetting experiments on two different rockfill materials.The flow rule was then extended and incorporated into the transformed stress based hypoplastic model to capture the direction of creep strains.Meanwhile,a new density factor was introduced to the extended model to take into account the dependence of the magnitude of creep strains on the packing density.The stiffness tensor given by the extended model was discussed and the flowchart for the integration of the constitutive equation was designed.The extended model was then embedded into a finite element program and used to simulate the triaxial compression and wetting experiments performed on the aforementioned rockfill materials.Good agreement between the model predictions and the measured results lends sufficient credibility to the extended model in reproducing the stress-stain behaviour under loading and the creep behaviour during wetting.The extended model and the finite element program were also used to investigate the deformation behaviour of an earth-rock dam at the end of construction and during first impounding.The familiar phenomena such as the wetting induced settlement of the upstream shell and the movement of the dam crest towards the upstream were successfully captured by the numerical model,which confirms the feasibility of applying the extended model to dam engineering in the future.
