【作者】 刘耀东；

【导师】 虞吉林；

【作者基本信息】 中国科学技术大学 ， 工程力学， 2010， 博士

【摘要】 多孔金属材料由于其微结构的特殊性和多样性,从而具有相当优异的力学特性和能量吸收能力。因此,多孔材料作为功能结构材料已在众多的工程实践中得到了广泛的应用。关于多孔金属材料的静态及准静态力学行为已经有了大量的研究和系统的认识,而对其动态力学行为的研究却相对较少。目前文献中对泡沫金属的动态行为和率敏感性效应有了较多的实验研究,但在对泡沫金属的应变率效应和惯性效应的相关认识中,尚存在着一些矛盾的结果。本论文中,为弄清多孔金属材料的率效应,我们通过数值模拟的手段,揭示了惯性效应、基体材料的应变强化效应和应变率效应对泡沫金属动态力学行为的影响。另外,为进一步理解多孔材料的变形传播行为,我们还提出了两种对应于不同变形模式下的理论模型来说明其中出现的冲击波现象。利用二维随机Voronoi技术,我们建立了不规则蜂窝的有限元模型。当蜂窝基体材料为弹性理想塑性时,有限元模拟的结果表明,蜂窝在不同的冲击速度之下将会发生三种变形模式。当冲击速度比较低时,蜂窝剪切变形带随机分布,其整体的宏观变形基本均匀,我们称之为准静态模式。当冲击速度足够高时,蜂窝的胞元几乎是逐层崩塌,在冲击面一侧形成很窄的剪切带,我们称之为动态模式或冲击模式。而当冲击速度介于准静态模式和冲击模式之间时,蜂窝的剪切变形带相对来说集中于冲击侧,形成较为局部的变形,并在整体上表现出梯度化,此时我们称之为过渡模式。经研究表明,当改变蜂窝的密度和基体材料的力学属性时,蜂窝仍然会发生上述三种变形模式,有所不同的是,对应不同变形模式的临界冲击速度将发生变化。为了揭示惯性效应对多孔金属材料力学行为的影响,我们人为地改变了蜂窝试件基体材料的密度。数值试验的结果表明,当蜂窝的变形模式处于准静态均匀模式时,对于不同的冲击速度和基体材料密度,试件的名义应力应变曲线基本上是一致的。因此惯性效应并没有导致蜂窝应力应变关系的应变率敏感性。而在过渡模式和冲击模式之下,蜂窝平台应力将随着冲击速度的增大而显著增加。当降低蜂窝基体材料的密度时,三种变形模式之间的临界速度将明显提高,相对来说均匀的变形容易发生。此时在过渡模式和冲击模式下,蜂窝平台应力强度的增长会明显减小。由此可知,在中高冲击速度之下,惯性导致了蜂窝变形出现明显的局部化,促使平台应力的提高。因此多孔金属材料出现的率效应主要是由惯性引起的。与此同时,我们还研究了微惯性的影响,结果表明蜂窝微惯性的影响相对来说是可以忽略不计的。为了进一步认清多孔金属材料的力学行为,我们还考察了基体材料属性对蜂窝动态压缩响应的影响,其中包括基体材料的应变强化效应和两种强度不同的应变率强化效应。基体材料的应变率效应对变形模式之间的临界速度影响不大,其引起的增幅大约在10%之内,但对蜂窝的平台应力会有所提高。在相同的应变率之下,蜂窝平台应力的相对增长要小于蜂窝基体材料屈服应力的相对增长。不同冲击速度下的平台应力的相对增长变化基本不大,且随着冲击速度的提高有减小的趋势。因此相对于惯性效应来说,应变率效应是可以忽略不计的。同时我们也考虑了基体材料应变强化效应对压缩行为的影响,相对于基体材料为弹性理想塑性的蜂窝来说,在不同冲击速度之下,由应变强化效应引起的平台应力的相对增长大约在5%左右,可见应变强化对蜂窝动态力学行为的影响是很微弱的。最后关于不同变形模式之间的临界速度也做了讨论,并且我们也估算了蜂窝在压缩时变形传播的冲击波波速。本文还探讨了多孔材料在冲击压缩时变形会出现类似冲击波传播的现象。一方面,在众多的有关多孔金属材料高速冲击下的动态力学响应的研究中,都存在着一个共同的现象,即在试件的压缩波前处会出现大约只有一个胞元宽度大小的不连续区域,在此区域的两侧,应力、应变和质点速度都有明显地跳跃。此时多孔材料试件的冲击部分逐渐地被压垮几乎达到密实状态。另一方面,当多孔材料在中等速度冲击下,同样也在试件中压缩波前处存在一不连续区域,此刻多孔材料试件被压缩部分的名义应变会逐渐变小。为了能更好的解释这种现象存在的内在机理,基于应力波理论中的刚性卸载假设,对应于上述两种情况,我们建立了两个理论模型,分别为冲击模式模型和过渡模式模型。利用模型中冲击面处的位移连续条件,我们给出了两个模型的显式解。理论解结果表明,当多孔材料处于冲击模式时,模型中泡沫杆冲击端处的初始应力大小与冲击速度的平方成比例关系,而当多孔材料处于过渡模式时,初始应力将随着冲击速度成线性增长。根据理论模型,我们还给出了冲击模式发生的临界速度和从冲击模式到过渡模式的转变时间。最后,为了验证理论模型的正确性,我们进行了相关的数值验证,数值计算的结果与理论预测值符合得很好。更多还原

【Abstract】 Cellular metals have considerably excellent mechanical properties and energy absorption capacity because of the specialty and variability of their micro structures. Therefore, cellular metals are widely used as advanced structural components in many engineering applications. The static and quasi-static mechanical behaviors of cellular metals have been studied substantially and systematically while the dynamic mechanical responses of them are relatively less researched. Although many experimental researches on the dynamic behavior and rate sensitivity of cellular metals have been reported in the literature, there are some conflicting conclusions on the strain-rate effect and the inertia effect of metallic foams. In order to know the role of rate effect in this paper, we conduct some numerical tests to explore the influence of inertia effect and strain hardening, strain-rate hardening of metal matrix on the behavior of cellular metals under impact compression. Moreover, for a deep understanding of the deformation propagating behavior, two theoretical models corresponding to different deformation modes are presented to reveal the inherent mechanism of this shock wave phenomenon.Finite element model of irregular honeycomb samples is constructed using the 2D random Voronoi technique. When elastic-perfectly plastic model is adopted for the cell wall material, numerical simulations show that three types of deformation modes are observed. At a low impact velocity, the deformation of the honeycomb is macroscopically homogeneous with multiple random weak shear bands (the quasi-static mode). At a high impact velocity, the deformation mode is layer wise collapse near the impact surface (the shock or dynamic mode). A transition mode with gradual change of macroscopic strain exists for an intermediate impact velocity. It is also shown that when the density and cell-wall material properties of the honeycomb are changed, these three types of deformation modes are still happened, but the corresponding critical velocities are different.To explore the effect of inertia, the density of the wall material is artificially reduced and it is found that when the honeycomb deformed in quasi-static mode, the stress-strain curves are nearly the same, regardless of the impact velocity and the matrix density. Hence the inertia effect will not cause strain-rate sensitivity of the stress-strain relation of the honeycomb. Nevertheless, the plateau stress in transition mode and shock mode increase significantly with the increase of impact velocity. As the matrix density decreases, the critical impact velocities of mode transition increase significantly, and the increase in plateau stress under the same impact velocity for both transition mode and shock mode reduces remarkably. It will be seen form this that due to the inertial effect, the deformation becomes inhomogeneous and localized, and the plateau stress on the impact interface increases rapidly when the impact velocity is moderate or high. So the rate effect of the cellular metals exhibited under high-velocity impact is mainly because of an inertia effect, rather than the strain-rate effect. Meanwhile, the effect of micro inertia is also studied and the results show that this effect is almost neglectable.In order to further understand the mechanical behavior of cellular metals, we also study the influence of cell-wall material properties on their dynamic responses, including strain hardening effect and strain-rate hardening effect. It is found that strain-rate hardening effect of base metal has little influence to the mode transition velocities (increasing about 10%), and will cause a slight increase in the plateau stress. The relative increase in the plateau stress is less than the relative increase in yield stress of the matrix under the same strain rate. The increase in the plateau stress for different impact velocity is nearly the same, and usually decreases gradually with the increasing velocity, thus the influence at high impact velocities is neglectable, in comparison with the inertia effect. Meanwhile, the strain hardening effect of metal matrix is taken into account. In comparison with the elastic-perfectly plastic material, the relative increase in the plateau stress caused by the strain hardening effect is about 5%, so it is found that this effect has minor influence on the plateau stress under dynamic cases. Finally, the critical velocities between the three different deformation modes are discussed and we also evaluate the shock front propagation velocity during the compaction process.On the one hand, among extensive studies of the dynamic responses of cellular materials under high impact velocity, there is a common phenomenon that a zone almost only one single-layer width of cell at the compaction front exists, across which the physical quantities such as stress, strain and velocity are apparently discontinuous. In this case, the compressed part of the cellular material is progressively crushed and almost densified. On the other hand, when the impact velocity is moderate, there also exists a discontinuity at the compaction front while the nominal strain of the compressed portion of the cellular metal is gradually getting smaller. To explore the inherent mechanism of this phenomenon, two models, viz. Transition-Mode model and Shock-Mode model, based on stress wave theory with a’rigid unloading’ assumption are established, and their explicit solutions are obtained by using a supplemental relationship of the continuous condition at impact interface. The theoretical results show that the initial stress at the impact end of the foam rod is proportional to the square of the impact velocity when the cellular metal is deformed in Shock Mode but increases linearly with the increasing impact velocity in Transition Mode. The critical velocity for the occurrence of Shock Mode and the transition time when the deformation mode transformed from Shock Mode to Transition Mode are presented. Finally, numerical verifications based on finite element method were carried out and the results are compared well with the theoretical predictions by both the models.更多还原