梯度多胞金属材料的动态力学行为和多功能优化设计
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摘要
多胞金属材料具有优异的能量吸收和抗冲击性能,作为能量吸收器和耐撞性结构已广泛地应用于汽车、高速列车、航空航天等领域。最近,一种新型的固体组成相的力学性能渐变的多胞金属材料即梯度多胞金属材料被提出并受到了广泛的关注。已有的研究表明通过改变多胞金属材料的密度分布可以有效地帮助提高能量吸收和抗冲击等性能。但已有的文献中关于梯度多胞金属材料的研究均局限于由粘接不同均匀密度层形成的阶梯式、不连续的密度梯度多胞材料。目前,梯度多胞金属材料所表现出来的优异的动态力学性能还没有得到很好的解释,能量吸收和变形机理尚不清楚。阶梯式、不连续梯度的多胞材料具有不可控性,其在研究梯度多胞材料的变形机理及能量吸收机理时具有一定的困难。本文主要通过建立连续梯度多胞金属材料的细观有限元模型并深入研究其动态力学行为,揭示梯度多胞金属材料的能量吸收和变形机理,建立梯度多胞金属材料的冲击波传播的理论模型为其能量吸收和抗冲击等功能设计提供理论指导。
本文提出了变胞元尺寸分布法构建梯度多胞金属材料的细观有限元模型。根据规则蜂窝的局部相对密度与其相邻成核点之间距离的特征关系,由Voronoi技术生成了胞元尺寸渐进变化的二维梯度多胞金属材料的细观构型。通过对二维梯度多胞金属材料构型的细观参数统计对该变胞元尺寸分布法进行可靠性的验证,结果表明通过该方法生成的梯度蜂窝的一些参数与所设计的都很吻合。
通过数值模拟研究了梯度多胞金属材料的动态力学行为,并通过恒速冲击响应研究了梯度多胞金属材料的变形机理。在初始冲击速度不是很高的情况下,梯度多胞金属相比于质量相等的均匀多胞金属具有优异的能量吸收特性,且负梯度多胞金属的支撑端面上及正梯度的冲击端面上均有一稳定平缓的约束反力。冲击速度较高时,正梯度多胞金属可以有效地降低冲击力的初始峰值。通过恒速冲击时梯度多胞金属的变形图样、变形模式、局部工程应变及载荷响应等方面研究其变形机理。在中等恒速压溃时,负梯度多胞金属中出现了一个新的变形图样,即双‘I’形变形图样。提出了量化三种变形模式之间转变的两种临界冲击速度的应力均匀化指标和变形局部化指标。梯度多胞金属的能量吸收特性可由其变形机理加以理解。质量块冲击过程中,一个梯度多胞金属试件随着冲击速度的衰减可能会经历一个或多个变形模式。材料最终所吸收的总能量由这些不同变形机制之间的相互竞争所决定。
发展了梯度多胞金属材料在恒速冲击和质量块冲击时的冲击波传播的理论模型。恒速冲击时,考虑了两种冲击波传播情况：冲击波形成在冲击端处并向支撑端处传播和冲击波同时形成在冲击端与支撑端处并向着相反的方向传播。质量块冲击时,也考虑了两种冲击波传播模型,即单波模型和双波模型。单波模型适应于密度从冲击端到支撑端渐进增加的情形；双波模型适应于密度从冲击端到支撑端渐进降低的情形。恒速冲击和质量块冲击的双波传播模型中均存在冲击波传播模式的转变：模式转变之前,试件中存在两个冲击波且其传播的方向相反；模式转变之后,试件中只剩下单个冲击波朝着冲击端的方向传播。通过数值计算对恒速冲击和质量块冲击情形时的冲击波传播的理论模型进行验证,数值验证结果表明理论模型具有一定的可靠性和适应性。
本文还研究了温度梯度场中梯度多胞金属材料的动态力学行为。首先,通过数值方法研究了梯度多胞金属材料的热学性能,讨论了梯度多胞金属材料的热导率以及多胞金属的基体材料与温度相关的本构。其次,通过数值方法研究了温度梯度场中梯度多胞金属材料的动态冲击响应。温度梯度场中,梯度多胞金属材料的局部化变形依赖于温度梯度与密度梯度双重影响下的材料的强度分布。温度梯度场中梯度多胞金属材料在高速冲击时的能量吸收也经历了与无温度场中类似的三个特征阶段。最后,根据材料的变形特征发展了温度梯度场中的单波传播模型和双波传播模型。单波传播模型适应于材料的强度从冲击端到支撑端渐进增加的梯度多胞金属材料；双波传播模型适应于材料的强度从冲击端到支撑端渐进降低的梯度多胞金属材料。数值计算结果与理论模型预测的比较显示理论模型可以很好地对数值结果进行预估。
针对梯度多胞金属材料优异的力学和热学性能,对其进行耐撞性及隔热性能设计。通过能量吸收和冲击力初始峰值这两个指标对梯度多胞金属材料的耐撞性能进行分析,发现无论是无温度场还是温度梯度场中正梯度多胞金属材料不仅可以提高能量吸收还可以降低冲击物体所受到冲击力峰值。对于额定冲击动能可以设计出一个最优的梯度多胞金属材料满足高的能量吸收、平稳的抗冲击性能及低的应力峰值等耐撞性的要求。通过梯度多胞金属隔热构件的耐火性能参数研究发现改变多胞金属的密度分布可以提高结构整体的隔热性能。
Cellular metals have considerable excellent properties of energy absorption and shock resistance. They are widely used as energy absorbers and crashworthiness structures in the automotive, high-speed trains and aerospace industries. Recently, a novel class of cellular metals with a gradual change in mechanical properties of its constituent phases, namely a graded cellular metal (GCM), has attracted considerable research interests. Researchers have shown good properties of GCMs, and introducing a density gradient to cellular metals can help to improve their energy absorption capacity, shock resistance and other properties. However, the GCMs studied in the literature were limited to stepwise, discontinuous density gradients formed by joining different uniform-density layers. The excellent dynamic mechanical properties of GCMs have not been explored, but the energy absorption and deformation mechanisms of GCMs are not clear. GCMs with stepwise and discontinuous density gradients are uncontrollable and they are difficult to explore the energy absorption and deformation mechanisms. In order to explore the energy absorption and deformation mechanisms of GCMs, we conduct some numerical tests of GCMs with continuous density gradients to study their dynamic impact responses. For a deep understanding of the energy absorption and deformation mechanisms, shock wave models corresponding to two impact scenarios are presented to explore shock wave propagation mechanisms of GCMs.
A varying cell-size distribution method is newly developed to construct GCMs via using the Voronoi technique. The characteristic of the relation between the relative density and the distance between any two adjacent nuclei of a regular honeycomb when the cell-wall thickness is fixed enlightens us to design GCMs via changing cell-size distribution to change density distribution. To evaluate the varying cell-size distribution method, we compare the mesostructure parameters of constructed GCMs with that of the designed. Results show that they are fitted well.
Numerical simulations are performed to study the dynamic mechanical behaviors of GCMs under mass impact, and the dynamic responses of GCMs under constant-velocity are investigated to explore their deformation mechanisms. The results show that GCMs exhibit superior energy absorption characteristics than the equivalent uniform cellular metals under a not high initial velocity impact, but this superiority becomes indistinct with the increase of initial impact velocity. For a not high initial velocity impact, the reaction force at the support end of a negative gradient and that at the impact end of a positive gradient are much smooth. At a high initial velocity, GCMs with a positive gradient can mitigate effectively the peak impact stress. Deformation patterns, local strain distributions and load histories under constant-velocity impact have provided some insight to understand the energy absorption and deformation mechanisms of GCMs. A new deformation pattern named double "I"-shaped pattern is found. Two critical impact velocities of mode transitions are quantitatively determined by using the stress uniformity index and the deformation localization index. The deformation mechanisms well explain the energy absorption characteristics of GCMs. During the mass impact, a GCM may experience one or more deformation modes with the decrease of impact velocity. The total energy absorbed by the GCM is determined by the competition between different deformation mechanisms.
One-dimensional shock wave model is extended to GCMs for further understanding the energy absorption and deformation mechanisms of GCMs. Consider two shock wave propagation models of GCMs under constant-velocity impact:a shock wave is generated at the impact end and two shock waves are generated at the two ends simultaneously. Under mass impact, we also consider two shock models, namely single shock model and double shock model. Single shock model is suitable for the density increases gradually from the impact end to the support end and double shock model is suitable for the inverse density distribution. In the double shock model, there maybe exist two stages:stage1, two shock waves generated at the two ends simultaneously and propagate to the opposite directions; stage2, only one shock wave propagates from the support end to the impact end. Numerical verifications are carried out and the results are compared well with the predictions by shock models.
Dynamic mechanical behaviors of GCMs in a temperature field are also studied by finite element method. Numerical simulations of the steady heat conduction in GCMs are performed firstly and then a temperature-dependent constitutive of the cell-wall material of GCMs is discussed. Density and temperature distributions in GCMs may significantly affect the mechanisms of deformation and stress wave propagation, because the local strength of a graded cellular metal depends not only on the local relative density but also on the local temperature. The energy absorption of GCMs in a temperature field experiences three characteristic segments similar to that in room temperature. One-dimensional shock wave model is extended to study these shock wave propagations in GCMs in a temperature field. Here, single shock model is suitable for the material strength increases gradually along impact direction and double shock model is suitable for the inverse material strength distribution. Cell-based finite element models of GCMs are employed to verify the predictions of the shock models.
Based on the excellent mechanical properties and heat properties of GCMs, we design their crashworthiness and thermal insulation properties. In the crashworthiness design, energy absorption and impact resistance are two design objectives. The results show that a good choice of positive density gradient not only improves the energy absorption but also reduces the initial impact stress. Thus, there is an optimal value for the density-gradient parameter to meet the crashworthiness requirements of high energy absorption, stable impact resistance and low peak stress for an input kinetic energy. The analysis of the thermal insulation parameter of GCMs gives that changing the density distribution of cellular metals can improve their thermal insulation properties.
本文提出了变胞元尺寸分布法构建梯度多胞金属材料的细观有限元模型。根据规则蜂窝的局部相对密度与其相邻成核点之间距离的特征关系,由Voronoi技术生成了胞元尺寸渐进变化的二维梯度多胞金属材料的细观构型。通过对二维梯度多胞金属材料构型的细观参数统计对该变胞元尺寸分布法进行可靠性的验证,结果表明通过该方法生成的梯度蜂窝的一些参数与所设计的都很吻合。
通过数值模拟研究了梯度多胞金属材料的动态力学行为,并通过恒速冲击响应研究了梯度多胞金属材料的变形机理。在初始冲击速度不是很高的情况下,梯度多胞金属相比于质量相等的均匀多胞金属具有优异的能量吸收特性,且负梯度多胞金属的支撑端面上及正梯度的冲击端面上均有一稳定平缓的约束反力。冲击速度较高时,正梯度多胞金属可以有效地降低冲击力的初始峰值。通过恒速冲击时梯度多胞金属的变形图样、变形模式、局部工程应变及载荷响应等方面研究其变形机理。在中等恒速压溃时,负梯度多胞金属中出现了一个新的变形图样,即双‘I’形变形图样。提出了量化三种变形模式之间转变的两种临界冲击速度的应力均匀化指标和变形局部化指标。梯度多胞金属的能量吸收特性可由其变形机理加以理解。质量块冲击过程中,一个梯度多胞金属试件随着冲击速度的衰减可能会经历一个或多个变形模式。材料最终所吸收的总能量由这些不同变形机制之间的相互竞争所决定。
发展了梯度多胞金属材料在恒速冲击和质量块冲击时的冲击波传播的理论模型。恒速冲击时,考虑了两种冲击波传播情况：冲击波形成在冲击端处并向支撑端处传播和冲击波同时形成在冲击端与支撑端处并向着相反的方向传播。质量块冲击时,也考虑了两种冲击波传播模型,即单波模型和双波模型。单波模型适应于密度从冲击端到支撑端渐进增加的情形；双波模型适应于密度从冲击端到支撑端渐进降低的情形。恒速冲击和质量块冲击的双波传播模型中均存在冲击波传播模式的转变：模式转变之前,试件中存在两个冲击波且其传播的方向相反；模式转变之后,试件中只剩下单个冲击波朝着冲击端的方向传播。通过数值计算对恒速冲击和质量块冲击情形时的冲击波传播的理论模型进行验证,数值验证结果表明理论模型具有一定的可靠性和适应性。
本文还研究了温度梯度场中梯度多胞金属材料的动态力学行为。首先,通过数值方法研究了梯度多胞金属材料的热学性能,讨论了梯度多胞金属材料的热导率以及多胞金属的基体材料与温度相关的本构。其次,通过数值方法研究了温度梯度场中梯度多胞金属材料的动态冲击响应。温度梯度场中,梯度多胞金属材料的局部化变形依赖于温度梯度与密度梯度双重影响下的材料的强度分布。温度梯度场中梯度多胞金属材料在高速冲击时的能量吸收也经历了与无温度场中类似的三个特征阶段。最后,根据材料的变形特征发展了温度梯度场中的单波传播模型和双波传播模型。单波传播模型适应于材料的强度从冲击端到支撑端渐进增加的梯度多胞金属材料；双波传播模型适应于材料的强度从冲击端到支撑端渐进降低的梯度多胞金属材料。数值计算结果与理论模型预测的比较显示理论模型可以很好地对数值结果进行预估。
针对梯度多胞金属材料优异的力学和热学性能,对其进行耐撞性及隔热性能设计。通过能量吸收和冲击力初始峰值这两个指标对梯度多胞金属材料的耐撞性能进行分析,发现无论是无温度场还是温度梯度场中正梯度多胞金属材料不仅可以提高能量吸收还可以降低冲击物体所受到冲击力峰值。对于额定冲击动能可以设计出一个最优的梯度多胞金属材料满足高的能量吸收、平稳的抗冲击性能及低的应力峰值等耐撞性的要求。通过梯度多胞金属隔热构件的耐火性能参数研究发现改变多胞金属的密度分布可以提高结构整体的隔热性能。
Cellular metals have considerable excellent properties of energy absorption and shock resistance. They are widely used as energy absorbers and crashworthiness structures in the automotive, high-speed trains and aerospace industries. Recently, a novel class of cellular metals with a gradual change in mechanical properties of its constituent phases, namely a graded cellular metal (GCM), has attracted considerable research interests. Researchers have shown good properties of GCMs, and introducing a density gradient to cellular metals can help to improve their energy absorption capacity, shock resistance and other properties. However, the GCMs studied in the literature were limited to stepwise, discontinuous density gradients formed by joining different uniform-density layers. The excellent dynamic mechanical properties of GCMs have not been explored, but the energy absorption and deformation mechanisms of GCMs are not clear. GCMs with stepwise and discontinuous density gradients are uncontrollable and they are difficult to explore the energy absorption and deformation mechanisms. In order to explore the energy absorption and deformation mechanisms of GCMs, we conduct some numerical tests of GCMs with continuous density gradients to study their dynamic impact responses. For a deep understanding of the energy absorption and deformation mechanisms, shock wave models corresponding to two impact scenarios are presented to explore shock wave propagation mechanisms of GCMs.
A varying cell-size distribution method is newly developed to construct GCMs via using the Voronoi technique. The characteristic of the relation between the relative density and the distance between any two adjacent nuclei of a regular honeycomb when the cell-wall thickness is fixed enlightens us to design GCMs via changing cell-size distribution to change density distribution. To evaluate the varying cell-size distribution method, we compare the mesostructure parameters of constructed GCMs with that of the designed. Results show that they are fitted well.
Numerical simulations are performed to study the dynamic mechanical behaviors of GCMs under mass impact, and the dynamic responses of GCMs under constant-velocity are investigated to explore their deformation mechanisms. The results show that GCMs exhibit superior energy absorption characteristics than the equivalent uniform cellular metals under a not high initial velocity impact, but this superiority becomes indistinct with the increase of initial impact velocity. For a not high initial velocity impact, the reaction force at the support end of a negative gradient and that at the impact end of a positive gradient are much smooth. At a high initial velocity, GCMs with a positive gradient can mitigate effectively the peak impact stress. Deformation patterns, local strain distributions and load histories under constant-velocity impact have provided some insight to understand the energy absorption and deformation mechanisms of GCMs. A new deformation pattern named double "I"-shaped pattern is found. Two critical impact velocities of mode transitions are quantitatively determined by using the stress uniformity index and the deformation localization index. The deformation mechanisms well explain the energy absorption characteristics of GCMs. During the mass impact, a GCM may experience one or more deformation modes with the decrease of impact velocity. The total energy absorbed by the GCM is determined by the competition between different deformation mechanisms.
One-dimensional shock wave model is extended to GCMs for further understanding the energy absorption and deformation mechanisms of GCMs. Consider two shock wave propagation models of GCMs under constant-velocity impact:a shock wave is generated at the impact end and two shock waves are generated at the two ends simultaneously. Under mass impact, we also consider two shock models, namely single shock model and double shock model. Single shock model is suitable for the density increases gradually from the impact end to the support end and double shock model is suitable for the inverse density distribution. In the double shock model, there maybe exist two stages:stage1, two shock waves generated at the two ends simultaneously and propagate to the opposite directions; stage2, only one shock wave propagates from the support end to the impact end. Numerical verifications are carried out and the results are compared well with the predictions by shock models.
Dynamic mechanical behaviors of GCMs in a temperature field are also studied by finite element method. Numerical simulations of the steady heat conduction in GCMs are performed firstly and then a temperature-dependent constitutive of the cell-wall material of GCMs is discussed. Density and temperature distributions in GCMs may significantly affect the mechanisms of deformation and stress wave propagation, because the local strength of a graded cellular metal depends not only on the local relative density but also on the local temperature. The energy absorption of GCMs in a temperature field experiences three characteristic segments similar to that in room temperature. One-dimensional shock wave model is extended to study these shock wave propagations in GCMs in a temperature field. Here, single shock model is suitable for the material strength increases gradually along impact direction and double shock model is suitable for the inverse material strength distribution. Cell-based finite element models of GCMs are employed to verify the predictions of the shock models.
Based on the excellent mechanical properties and heat properties of GCMs, we design their crashworthiness and thermal insulation properties. In the crashworthiness design, energy absorption and impact resistance are two design objectives. The results show that a good choice of positive density gradient not only improves the energy absorption but also reduces the initial impact stress. Thus, there is an optimal value for the density-gradient parameter to meet the crashworthiness requirements of high energy absorption, stable impact resistance and low peak stress for an input kinetic energy. The analysis of the thermal insulation parameter of GCMs gives that changing the density distribution of cellular metals can improve their thermal insulation properties.
引文
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