细观结构对多孔金属材料力学性能的影响及多目标优化设计
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摘要
多孔金属材料具有轻质、高强韧、吸能性能优异、高效散热、隔热等特性,是一种兼具功能和结构双重作用的新型工程材料,已经广泛应用于航空航天、汽车、海洋采油等领域。多孔金属材料的力学性能与其细观结构密切相关,研究多孔金属材料细观结构与其宏观力学性能之间的关系,深入分析材料变形的细观力学机制并在此基础上进行材料细观结构的优化设计,对促进多孔金属材料的设计开发和工程应用具有重大意义,也是本文工作的主要目的。本文研究了含有细观结构缺陷的二维蜂窝结构动态力学行为,对渗流法制备的开孔泡沫金属进行了细观结构优化设计,并进一步探讨了多孔金属材料多目标优化设计的方法。
本文首先对胞壁随机移除的二维蜂窝结构动态力学行为进行有限元模拟,研究了不同胞壁移除比的蜂窝结构在动态冲击下的变形模式,发现蜂窝结构变形模式是由两种机制,即惯性效应引起的变形局部化和缺陷引起的多个变形带随机分布(变形分散化),共同作用所决定的。本文还研究了随机移除胞壁对蜂窝结构模式转换临界速度的影响,给出了临界速度的近似公式。对蜂窝结构平台应力速度效应的研究发现,当变形模式为过渡模式和动态模式时,平台应力与冲击速度的平方成正比。相同密度下,低缺陷蜂窝结构的平台应力在由过渡模式向动态模式转变的临界速度附近高于规则蜂窝结构,较高的随机缺陷则使蜂窝结构的平台应力在由准静态模式向过渡模式转变的临界速度附近显著下降。
本文还研究了含随机固体填充孔蜂窝结构的动态力学行为。通过对不同孔洞填充比的蜂窝结构动态变形过程进行有限元模拟,发现含固体填充孔蜂窝结构与相同密度的规则蜂窝结构具有相同的变形模式和临界速度。准静态模式下,随孔洞填充比的增加,蜂窝结构压缩应力显著下降。蜂窝结构变形为过渡模式或动态模式时,固体填充孔将导致蜂窝结构冲击面应力出现尖峰,在应力尖峰以外的区域,蜂窝结构压缩应力可通过具有相同壁厚的规则蜂窝结构平台应力估算。蜂窝结构的平台应力表现出明显的速度效应,与冲击速度的平方成线性关系。低速冲击下,含固体填充孔的蜂窝结构平台应力随孔洞填充比的增大而显著降低,随着冲击速度的提高,一方面固体填充孔导致蜂窝结构应力应变曲线中出现应力尖峰,提高了蜂窝结构的吸能能力,另一方面含固体填充孔蜂窝结构中的崩塌变形耗散能高于规则蜂窝结构中的逐层剪切变形耗散能,含固体填充孔蜂窝结构平台应力在较高的冲击速度下可以比规则蜂窝结构平台应力提高10%以上。
对渗流法制备开孔泡沫金属时盐粒的几何堆积方式进行了讨论,提出了引入二级孔洞,通过细观结构的设计来优化泡沫金属宏观力学性能的设想,并设计了优化的三维开孔泡沫金属绌观几何构型。建立了球形孔面心立方密排(FCC)堆积的双重孔径泡沫金属单胞有限元模型,并进行了单轴压缩过程的数值模拟。计算结果表明引入二级孔洞的泡沫金属弹性模量和压缩强度均明显高于相同密度的单一孔径泡沫金属,通过计算还获得了使材料性能最优的孔径比。对泡沫金属压缩变形机理的分析表明,单一孔径泡沫金属变形主要为斜杆的弯曲变形,引入二级孔洞后,更多的实体材料参与变形,泡沫金属中同时存在胞杆的轴向压缩与弯曲变形,提高了泡沫金属的强度,并使材料表现出与单一孔径泡沫金属不同的塑性流动特性。对双重孔径泡沫金属的实验研究验证了细观结构设计对材料性能的优化作用,材料弹性模量和屈服强度分别比单一孔径泡沫金属提高48%及19%,最优的孔径比和孔洞体积比分别为0.4和0.07～0.1。
本文对单一孔径和双重孔径泡沫金属的稳态热传导过程进行了有限元模拟,得到不同相对密度和孔径比的开孔泡沫金属等效热传导系数。通过最小二乘法获得了双重孔径泡沫金属的屈服应力和隔热参数的拟合函数式,建立了包含强度、隔热和轻质三个目标函数的多目标优化设计数学模型,在构件质量一定的情况下,采用约束法将多目标优化问题转化为单目标优化问题进行求解,得到满足强度要求,同时使隔热性能最优的泡沫金属细观参数。最后,求得了相同质量的泡沫金属板构件隔热参数—屈服应力关系图,对单一孔径泡沫金属板和双重孔径泡沫金属板性能进行了比较,发现双重孔径泡沫金属板综合性能要显著优于单一孔径泡沫金属板。
Cellular metals exhibit low densities, high specific stiffness and strength, high energy-absorbing capabilities and novel thermal properties comparing to fully-dense metals. They have been widely used in many fields for their multi-functionality, such as aircraft, spacecraft, automobile and offshore oil production platforms. The strong connections between mechanical behavior and cell structures of cellular metals are generally acknowledged, but not complete and in-depth. In the present work, the influences of cell structure defects on the macroscopic mechanical properties of 2-D honeycombs are investigated, optimization design of cell structure for open-cell metal foams is developed, and further more, the multi-objective optimization design are carried out for specified metal foam structures.
Finite element simulations are performed to study the effect of randomly removing cell walls on the dynamic crushing behaviour of honeycomb structures. The influences of the imperfection and impact velocity on the deformation mode and plateau stress are investigated. Simulation results reveal that both imperfection and impact velocity affect the deformation modes as well as the critical velocities of mode transition. It is found that the deformation mode of imperfect honeycomb is determined by the combined action of two mechanisms, i.e. the deformation localization caused by inertia effect and deformation bands dispersion introduced by random distributed defects. The plateau stress is found to be proportional to the square of the impact velocity when the imperfect honeycombs are deformed at transitional mode or dynamic mode. When the impact velocity is near the critical velocity between transitional mode and dynamic mode, honeycombs with small fraction of imperfection exhibit higher plateau stress, comparing to those of regular honeycombs having the same relative density. However, when the imperfection further increases, the plateau stress decreases obviously near the critical velocity between quasi-static mode and transitional mode.
The dynamic crushing behavior of honeycombs with randomly distributed solid inclusions is studied. Simulation results reveal that the deformation mode and critical velocities remain the same as regular honeycombs after introduction of solid inclusions. The plateau stress of honeycombs with solid inclusions is found to be proportional to the square of impact velocity. Comparing to regular honeycombs with same density, the compression strength of honeycombs with solid inclusion is found to decrease significantly under low velocity impact. However, as the impact velocity increases, inertia effects would result in spinous stress protuberances in the stress-strain curves of honeycombs with solid inclusions, moreover, the cell wall crushing of honeycombs with solid inclusions dissipates more energy than shear bands of regular honeycombs, accordingly, plateau stress of honeycomb with solid inclusions can be 10% higher than that of regular honeycomb.
A dual-size cellular structure design is proposed and used to improve the mechanical properties of open-cell metal foams fabricated by the infiltration technique. Assuming a spherical shape of cells and idealized face-centered cubic (FCC) arrangement of cells, numerical simulations on the axial compression of open-cell foams with dual-size cellular structure are performed. The results show that the stiffness and strength of metal foam with secondary cells are much higher than those of uniform cell foams. The analysis on the deformation mechanism reveals that cell wall bending is the dominated mechanism in uniform cell foams, however, In dual-size foams, larger proportion of solid materials deforms, lead to an increase on mechanical properties, the combined action of cell wall bending and axial compression also lead to a different flow behavior compared with uniform cell foams. According to the numerical results, optimal dual-size open-cell aluminum foams are then manufactured. Their mechanical properties are tested. The stiffness and yield strength of dual-size foams are 48% and 19% higher than uniform cell foam, respectively. The optimized radius ratio and volume ratio of secondary cells to large cells are acquired. The experimental results fit with numerical prediction qualitatively.
The geometric model of dual-size foams is further used for steady heat conduction simulations. The effective thermal conductivity of open-cell foams having various density and cell radius ratios are calculated by FEA method. The fitting functions of yield stress and thermal insulation parameter of dual-size foams are constructed by least square method. The multi-objective optimization design model including three objective functions, i.e. yield stress, thermal insulation parameter and structure weight, is proposed for metal foam plate. Solving the model with restriction method, the optimized density, cell radius ratio and plate thickness are acquired. Finally, the relationship graph of thermal insulation parameter and yield stress of metal foam plate is provided. It reveals that the comprehensive performance of dual-size foam plate is much better than that of uniform cell foam plate.
本文首先对胞壁随机移除的二维蜂窝结构动态力学行为进行有限元模拟,研究了不同胞壁移除比的蜂窝结构在动态冲击下的变形模式,发现蜂窝结构变形模式是由两种机制,即惯性效应引起的变形局部化和缺陷引起的多个变形带随机分布(变形分散化),共同作用所决定的。本文还研究了随机移除胞壁对蜂窝结构模式转换临界速度的影响,给出了临界速度的近似公式。对蜂窝结构平台应力速度效应的研究发现,当变形模式为过渡模式和动态模式时,平台应力与冲击速度的平方成正比。相同密度下,低缺陷蜂窝结构的平台应力在由过渡模式向动态模式转变的临界速度附近高于规则蜂窝结构,较高的随机缺陷则使蜂窝结构的平台应力在由准静态模式向过渡模式转变的临界速度附近显著下降。
本文还研究了含随机固体填充孔蜂窝结构的动态力学行为。通过对不同孔洞填充比的蜂窝结构动态变形过程进行有限元模拟,发现含固体填充孔蜂窝结构与相同密度的规则蜂窝结构具有相同的变形模式和临界速度。准静态模式下,随孔洞填充比的增加,蜂窝结构压缩应力显著下降。蜂窝结构变形为过渡模式或动态模式时,固体填充孔将导致蜂窝结构冲击面应力出现尖峰,在应力尖峰以外的区域,蜂窝结构压缩应力可通过具有相同壁厚的规则蜂窝结构平台应力估算。蜂窝结构的平台应力表现出明显的速度效应,与冲击速度的平方成线性关系。低速冲击下,含固体填充孔的蜂窝结构平台应力随孔洞填充比的增大而显著降低,随着冲击速度的提高,一方面固体填充孔导致蜂窝结构应力应变曲线中出现应力尖峰,提高了蜂窝结构的吸能能力,另一方面含固体填充孔蜂窝结构中的崩塌变形耗散能高于规则蜂窝结构中的逐层剪切变形耗散能,含固体填充孔蜂窝结构平台应力在较高的冲击速度下可以比规则蜂窝结构平台应力提高10%以上。
对渗流法制备开孔泡沫金属时盐粒的几何堆积方式进行了讨论,提出了引入二级孔洞,通过细观结构的设计来优化泡沫金属宏观力学性能的设想,并设计了优化的三维开孔泡沫金属绌观几何构型。建立了球形孔面心立方密排(FCC)堆积的双重孔径泡沫金属单胞有限元模型,并进行了单轴压缩过程的数值模拟。计算结果表明引入二级孔洞的泡沫金属弹性模量和压缩强度均明显高于相同密度的单一孔径泡沫金属,通过计算还获得了使材料性能最优的孔径比。对泡沫金属压缩变形机理的分析表明,单一孔径泡沫金属变形主要为斜杆的弯曲变形,引入二级孔洞后,更多的实体材料参与变形,泡沫金属中同时存在胞杆的轴向压缩与弯曲变形,提高了泡沫金属的强度,并使材料表现出与单一孔径泡沫金属不同的塑性流动特性。对双重孔径泡沫金属的实验研究验证了细观结构设计对材料性能的优化作用,材料弹性模量和屈服强度分别比单一孔径泡沫金属提高48%及19%,最优的孔径比和孔洞体积比分别为0.4和0.07～0.1。
本文对单一孔径和双重孔径泡沫金属的稳态热传导过程进行了有限元模拟,得到不同相对密度和孔径比的开孔泡沫金属等效热传导系数。通过最小二乘法获得了双重孔径泡沫金属的屈服应力和隔热参数的拟合函数式,建立了包含强度、隔热和轻质三个目标函数的多目标优化设计数学模型,在构件质量一定的情况下,采用约束法将多目标优化问题转化为单目标优化问题进行求解,得到满足强度要求,同时使隔热性能最优的泡沫金属细观参数。最后,求得了相同质量的泡沫金属板构件隔热参数—屈服应力关系图,对单一孔径泡沫金属板和双重孔径泡沫金属板性能进行了比较,发现双重孔径泡沫金属板综合性能要显著优于单一孔径泡沫金属板。
Cellular metals exhibit low densities, high specific stiffness and strength, high energy-absorbing capabilities and novel thermal properties comparing to fully-dense metals. They have been widely used in many fields for their multi-functionality, such as aircraft, spacecraft, automobile and offshore oil production platforms. The strong connections between mechanical behavior and cell structures of cellular metals are generally acknowledged, but not complete and in-depth. In the present work, the influences of cell structure defects on the macroscopic mechanical properties of 2-D honeycombs are investigated, optimization design of cell structure for open-cell metal foams is developed, and further more, the multi-objective optimization design are carried out for specified metal foam structures.
Finite element simulations are performed to study the effect of randomly removing cell walls on the dynamic crushing behaviour of honeycomb structures. The influences of the imperfection and impact velocity on the deformation mode and plateau stress are investigated. Simulation results reveal that both imperfection and impact velocity affect the deformation modes as well as the critical velocities of mode transition. It is found that the deformation mode of imperfect honeycomb is determined by the combined action of two mechanisms, i.e. the deformation localization caused by inertia effect and deformation bands dispersion introduced by random distributed defects. The plateau stress is found to be proportional to the square of the impact velocity when the imperfect honeycombs are deformed at transitional mode or dynamic mode. When the impact velocity is near the critical velocity between transitional mode and dynamic mode, honeycombs with small fraction of imperfection exhibit higher plateau stress, comparing to those of regular honeycombs having the same relative density. However, when the imperfection further increases, the plateau stress decreases obviously near the critical velocity between quasi-static mode and transitional mode.
The dynamic crushing behavior of honeycombs with randomly distributed solid inclusions is studied. Simulation results reveal that the deformation mode and critical velocities remain the same as regular honeycombs after introduction of solid inclusions. The plateau stress of honeycombs with solid inclusions is found to be proportional to the square of impact velocity. Comparing to regular honeycombs with same density, the compression strength of honeycombs with solid inclusion is found to decrease significantly under low velocity impact. However, as the impact velocity increases, inertia effects would result in spinous stress protuberances in the stress-strain curves of honeycombs with solid inclusions, moreover, the cell wall crushing of honeycombs with solid inclusions dissipates more energy than shear bands of regular honeycombs, accordingly, plateau stress of honeycomb with solid inclusions can be 10% higher than that of regular honeycomb.
A dual-size cellular structure design is proposed and used to improve the mechanical properties of open-cell metal foams fabricated by the infiltration technique. Assuming a spherical shape of cells and idealized face-centered cubic (FCC) arrangement of cells, numerical simulations on the axial compression of open-cell foams with dual-size cellular structure are performed. The results show that the stiffness and strength of metal foam with secondary cells are much higher than those of uniform cell foams. The analysis on the deformation mechanism reveals that cell wall bending is the dominated mechanism in uniform cell foams, however, In dual-size foams, larger proportion of solid materials deforms, lead to an increase on mechanical properties, the combined action of cell wall bending and axial compression also lead to a different flow behavior compared with uniform cell foams. According to the numerical results, optimal dual-size open-cell aluminum foams are then manufactured. Their mechanical properties are tested. The stiffness and yield strength of dual-size foams are 48% and 19% higher than uniform cell foam, respectively. The optimized radius ratio and volume ratio of secondary cells to large cells are acquired. The experimental results fit with numerical prediction qualitatively.
The geometric model of dual-size foams is further used for steady heat conduction simulations. The effective thermal conductivity of open-cell foams having various density and cell radius ratios are calculated by FEA method. The fitting functions of yield stress and thermal insulation parameter of dual-size foams are constructed by least square method. The multi-objective optimization design model including three objective functions, i.e. yield stress, thermal insulation parameter and structure weight, is proposed for metal foam plate. Solving the model with restriction method, the optimized density, cell radius ratio and plate thickness are acquired. Finally, the relationship graph of thermal insulation parameter and yield stress of metal foam plate is provided. It reveals that the comprehensive performance of dual-size foam plate is much better than that of uniform cell foam plate.
引文
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