Dynamic response and energy absorption properties of sinusoidally curved three-dimensional negative Poissonʼs ratio sandwich panels subjected to blast loading
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摘要: 具有优异能量吸收特性的负泊松比结构在抗爆炸冲击防护领域有广阔的应用前景。为进一步提升夹芯板的抗爆性能,提出了一种在X、Y方向力学特性相同的正弦曲边三维负泊松比夹芯板用于防爆保护。采用数值模拟方法,对夹芯板在空爆载荷下的动态响应和吸能特性进行了研究,分析了夹芯板塑性拉伸和弯曲对背面板变形模式和轴向偏转分布的影响,并探究了爆炸距离、炸药质量、面板厚度和芯层关键结构参数对夹芯板变形和能量吸收的影响。结果表明,在空爆载荷下,夹芯板的动态响应过程可分为芯层压缩、整体变形和自由振动3个阶段。后面板在纵向(X方向)和横向(Y方向)上的抗变形能力无明显差异。随着炸药质量增加和爆炸距离减小,夹芯板的后面板中心位移增加,芯层吸能占比减小。此外,采用薄前面板和厚后面板的夹芯板可以提高芯层的吸能占比。当分别增加相同的前、后面板厚度时,前面板厚度对减小后面板中心位移的影响更显著。当芯层厚度从0.6 mm减小至0.2 mm时,后面板中心位移减小49.0%,总能量吸收增加86.7%;芯层振幅从0.2 mm增大至1.0 mm时,后面板中心位移减小20.7%,总能量吸收大致不变;芯层高度从10 mm增大至18 mm时,后面板中心位移减小88.3%,总能量吸收增加56.9%;芯层宽长比从0.56减小至0.2时,后面板中心位移减小39%,总能量吸收增加47.4%。Abstract: The remarkable energy absorption properties of the negative Poissonʼs ratio structure offer extensive prospects for applications in blast protection. However, the existing in-plane configurations of two-dimensional auxetic honeycomb cores always represent anisotropic behavior. To further enhance the blast resistance of sandwich panels, a three-dimensional sinusoidal curved-edge sandwich panel with a negative Poissonʼs ratio effect in both the X and Y directions for blast protection was proposed. The dynamic response and energy absorption characteristics under air blast load were studied by numerical simulation. Deformation modes and axial deflection distribution caused by plastic stretching and bending of the back face sheet were investigated in detail. The effects of stand-off distance (SOD), explosive mass, panel thickness, and key geometric parameters of the core layer on deformation and energy absorption were discussed. The results show that the dynamic response process of the sandwich panel can be divided into three stages: core compression, overall deformation, and free vibration. Moreover, it is found that there is no significant difference in the ability to resist deformation of the sandwich structure along the longitudinal (X) and transverse (Y) directions. As the TNT mass increases and the SOD decreases, the central displacement of the back face sheet of the sandwich panel increases, leading to a decrease in the energy absorption ratio of the core layer. Furthermore, utilizing a sandwich panel with a thin front panel and a thick back panel can increase the energy absorption proportion of the core layer. When increasing the thickness of the front and back panels by the same amount, the thickness of the front panel has a more significant effect on reducing the center displacement of the back panel. When the core thickness decreases from 0.6 mm to 0.2 mm, the back panel center displacement decreases by 49.0%, and the total energy absorption increases by 86.7%. As the core amplitude increases from 0.2mm to 1.0mm, the back panel center displacement decreases by 20.7%, with the total energy absorption remaining roughly constant. With an increase in core height from 10mm to 18mm, the back panel center displacement decreases by 88.3%, and the total energy absorption increases by 56.9%. Furthermore, a decrease in core aspect ratio from 0.56 to 0.2 results in a 39% reduction in back panel center displacement and a 47.4% increase in total energy absorption. The results of this study can guide the design of energy-absorbing protection for sandwich panels.
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泡沫金属及其复合结构在实际工程应用[1-6]中往往承受复杂的动态冲击荷载,发生拉伸破坏和剪切破坏以及坍塌失稳等典型的破坏行为。然而,拉伸条件下泡沫金属的变形模式和破坏机理均与压缩条件下存在显著差异,因此,泡沫金属冲击压缩的本构模型将无法准确地表征其动态拉伸破坏性能。泡沫金属动态拉伸破坏性能及破坏机理亟待研究与解决。
目前,准静态加载条件下泡沫金属力学性能研究相对完善[6-11],但动态加载,特别是高应变率拉伸实验数据稀缺。目前,动态性能测试主要基于霍普金森杆装置和高速拉伸试验机。Yang等[12]采用霍普金森压杆(SHPB)装置实现了泡沫铝冲击试验,观察到加载过程中泡沫铝受惯性效应的影响,其变形集中在试样的一端或两端附近。李忠献等[13]采用高速试验机实现了1000 s−1应变率下闭孔泡沫铝的动态压缩试验,发现试件越厚,高速压缩时惯性效应越明显,通过选取合适的试件厚度可以削弱泡沫铝高速压缩试验中惯性效应的影响。常白雪等[14]开展了恒定冲击加载条件下梯度泡沫金属力学行为的数值模拟。与冲击压缩试验相比,泡沫金属动态拉伸试验更难以实现。习会峰等[15]采用高速拉伸试验机实现了泡沫金属中低应变率(50 s−1以内)拉伸,采用数字图像相关方法(DIC)测量变形,并提出了合理确定泡沫金属拉伸过程中应力和应变数据的处理方法。然而,采用试验机拉伸主要存在两个难以解决的问题:(1) 试验机拉伸时初始段为加速过程,对于泡沫金属这类脆性材料而言,材料在加速过程中将发生断裂,因此,泡沫金属破坏过程为非恒定应变率拉伸破坏;(2) 试验机拉伸的最大速度有限,高应变率拉伸试验难以实现。为了实现中高应变率条件下材料的动态拉伸试验测试,霍普金森拉杆(SHTB)装置被广泛使用[15-20],该装置的主要机理是通过撞击产生拉伸应力波,通过入射杆传递到试件和透射杆,通过应变信号测得材料的动态拉伸力学性能,该试验方法需要满足一维应力波[21]和应力均匀性条件[22]。对于泡沫金属,满足应力均匀性需要减小试件厚度,而薄试件会导致夹持困难,且该方法无法实现恒定应变率的动态拉伸,因此,该方法尚未用于泡沫金属材料的动态拉伸性能测试。如何合理地获得恒定高应变率动态拉伸条件下泡沫金属的力学性能仍是尚未解决的难题。
当前泡沫金属动态拉伸实验面临的主要技术难题包括:如何实现高速拉伸的加载装置,如何实现加载过程中恒定应变率,如何避免试件边缘局部破坏,如何满足应力均匀性和变形均匀性条件等。谢倍欣等[22]提出了泡沫金属冲击试件的应力不均匀性指标和变形均匀性指标,试件高度越小,变形均匀性越好,采用有效高度为一个胞孔等效直径的试件,实现了6000 s−1应变率冲击压缩试验。这些动态冲击压缩的应力均匀性和变形均匀性指标将有助于指导泡沫金属材料动态拉伸力学性能的研究。
本文基于3D Voronoi模型,对恒定高应变率动态拉伸条件下泡沫金属宏观拉伸力学性能进行数值模拟,分析试件高度对泡沫金属动态拉伸的破坏位置、应力均匀性和破坏性能的影响,探讨动态拉伸变形过程;在满足破坏位置合理、应力均匀性和变形均匀性以及重复性等要求的条件下,采用高度为1.55倍胞孔等效直径的泡沫金属试件,进行5000 s−1应变率动态拉伸性能计算,分析应变率对泡沫铝拉伸动态力学性能的影响。
1. 动态拉伸加载方案设计
采用Voro++程序建立长宽高分别为
l0 、w0 、h0 的长方体3D Voronoi泡沫金属模型,建模过程详见文献[23]。3D Voronoi模型的平均等效直径与真实试件的平均等效直径相同,即d0=3.25mm 。构建了高度分别为30和5 mm的A和B两个3D Voronoi 模型,如图1所示,用于探究试件高度对泡沫金属动态拉伸实验应力均匀性、变形均匀性和破坏形态的影响。网格类型包括四边形(S4R)和三角形(S3R)的混合网格,网格尺寸为0.13 mm。设置模型平均相对密度ρf 均为20%,模型的胞壁厚度为t=V0ρf/S0 (1) 其中:
V0=l0w0h0 为长方体体积;S0 为泡沫金属胞孔的总表面积,本文两个高度分别为30和5 mm的模型对应的S0 分别为27525.74和4077.72 mm2。根据式(1)确定3D Voronoi模型A和B的胞壁厚度分别为0.196和0.221 mm。基于3D Voronoi细观模型,通过赋予基体材料纯铝的材料参数,模拟泡沫金属材料的力学性能。基体材料为纯铝,不考虑基体材料的应变率效应,采用如下的基体材料参数:弹性模量70 GPa,泊松比0.33,密度2.7×103 kg/m3,屈服强度80 MPa,线性硬化模量30 MPa,剪切破坏和延性破坏参考文献[24]。这些基体材料参数被泡沫金属单、多轴准静态试验结果验证了其合理性[25-26]。
动态拉伸技术方案如图2所示,沿加载方向上施加一对解析刚体模拟实验中的压头。为减弱高速拉伸过程中在试件两端产生的惯性效应的影响,采取双向拉伸的方式进行加载,即正负向解析刚体以相同加载速度同时反向移动(
vf=vz=v/2 )。泡沫金属之间采用通用接触,摩擦因数为0.02[26],允许接触后分离;解析刚体与泡沫金属采用面面接触,摩擦因素为0.02[26],接触后不允许分离,模拟拉伸过程。此外,为避免泡沫金属动态拉伸时试件端部的胞孔发生局部单元破坏断裂现象,在不影响材料拉伸性能的基础上,对模型A试件加载边缘1 mm区域内的单元胞壁单元厚度参数进行了连续线性加厚处理,最大胞壁厚度为非加厚胞壁厚度的1.3倍;模型B采用均匀的胞壁厚度,不做加厚处理。动态拉伸应变率(
˙ε=v(t)/h0 )时程曲线设置如图3所示。首先,以0.5 s−1的应变率预压1×10−4 s,确保解析刚体与泡沫金属单元节点接触,为后续动态拉伸做准备,且预压过程中产生的变形极小,模型始终处于弹性阶段,因此,不影响后续的恒速动态加载过程;然后,以0.5 s−1的应变率拉伸1×10−4 s,使得模型整体位移为零;这两步预加载为后续的恒定高应变率动态拉伸做准备。最后,以恒定的应变率进行拉伸直至破坏断裂。本文采用质量缩放方法,保证数值模拟较好的计算效率且兼顾较高的计算精度,整个动态拉伸过程的质量缩放时间增量设置为1×10−9 s。为了评估数值模拟结果的合理性,需要采用以下四个方面的指标:
(1) 伪应变能与内能的比值不应超过10%,数值越小,说明结果越合理;
(2) 应力和变形的不均匀性指标
I1 和I2 [22]应满足:I1=|σL(t)−σR(t)[σL(t)+σR(t)]/2| (2) I2=1ˉε√1nn∑k=1(εk−ˉε)2 (3) 式中:
σL(t) 与σR(t) 分别对应某时刻负向与正向两端的应力;模型在拉伸轴方向被均分为n份,如图4所示,本文两个模型均按1 mm均分,模型A和B的n取值分别为30和5;第k份(k=1,2,…,n)在y方向上的厚度为Δyk ;εk 为第k份的应变;ˉε 试件整体的平均应变;为了满足应力均匀性要求,I1≤5% ;应力和变形的不均匀性指标数值越小,说明应力和变形越均匀,结果越合理;(3) 破坏位置,破坏位置越集中在试件端部,结果越不合理;
(4) 重复性检验,避免该数值模拟结果的偶然性。
采用这四个指标,评估试件高度和加载方式对泡沫金属动态拉伸结果的影响,最终确定适合泡沫金属的高应变率动态拉伸实验方案。
2. 试件高度对动态拉伸结果的影响
2.1 动态拉伸变形过程分析
为探究试件高度对泡沫金属拉伸结果的影响,对两模型进行中低应变率(300 s−1)拉伸模拟。如图5所示,模型A、B在单向拉伸数值模拟过程中的伪应变能与内能的比值(
η=Eas/U ),在整个加载过程中均小于10%,说明两个模型的结果均合理。在模型A、B的同一位置所取z=0截面在加载过程中的应力变化如图6所示,在加载初期,由于高速拉伸所产生的惯性效应使得模型加载端应力骤增,相比于模型A,高度较小的模型B能够更好地消减惯性效应对拉伸加载的影响。随着加载的进行,各模型内部单元发生断裂破坏,如图7所示,模型A内部单元的变形主要出现在局部区域,破坏时只产生一条贯穿裂缝,表现出较为明显的脆性拉伸断裂,因此,采用模型A的动态拉伸数据去表征其动态拉伸力学性能是不准确的;相对而言,模型B内部单元出现了多条断裂带,模型整体变形均匀,且破坏位置相较模型B离端部更远,结果更合理。2.2 模型应力均匀性与变形均匀性对比
模型A和B的名义应力-应变曲线以及应力不均匀性指标对比如图8所示。两个模型破坏时的峰值应力相差不大,且在达到峰值状态之前应力均匀性条件均满足
I1≤5% ,但模型A的I1 值在应力达到峰值之后便发生了振荡,且超出了5%,此时,模型A内部单元并未完全断裂,所测数据无法准确表征泡沫金属动态拉伸性能。相比于模型A,模型B在整个拉伸过程中的I1 值较小,说明模型B两拉伸端在发生破坏之前阶段结果更为可靠。因此,降低高度对于提高应力均匀性具有非常显著的效果。模型A、B在相同区间宽度(
Δy1=Δy2=⋯=Δyn=1mm )的情况下,计算得到拉伸过程中泡沫金属的局部应变,由式(3)计算得出各不均匀性指标I2 的数值,对比模型A、B加载过程变形不均匀指标I2 的变化如图9所示,表明降低试件的高度也能有效地降低I2 的值,同时也验证了图6模型A内部大部分单元在整个动态拉伸过程中变形较小或并未参与变形,因此,模型B动态拉伸过程的应力均匀性与变形均匀性都优于模型A。2.3 模型B重复性检验
模型B拉伸方向高度为5 mm(
h0/d0=1.55 ),如果模型拉伸方向的高度太小,可能导致实验结果具有偶然性,因此,需要对模型B进行重复性检验。采用原模型B的模型参数生成另外两个Voronoi模型,分别记为模型B1、B2。采用相同的加载方式分别对模型B1与模型B2进行300 s−1的拉伸加载。经检验,模型B与其衍生的模型B1、B2正负向应力-应变曲线基本重合,如图10所示,说明模型重复性良好。综上所述,降低试件的高度能有效地提高泡沫金属动态拉伸实验的应力均匀性和应变均匀性,改善试件破坏位置,说明降低高度有利于提高结果的合理性,实现高应变率动态拉伸。
3. 模型B最大拉伸应变率探究
为探究模型B所能实现的最大拉伸应变率,以1000 s−1为增量逐步增加应变率进行拉伸加载。结果表明,随着加载应变率的增加,模型B的破坏位置逐渐移向两加载端位置,在5000 s−1应变率拉伸时,试件破坏位置合理,如图11所示,且此时应力不均匀性指标满足I1≤5%;然而,当加载应变率达到6000 s−1时,模型呈边缘局部破坏,模型破坏位置不合理,如图11所示。因此,模型B所能实现的最大拉伸应变率为5000 s−1。
模型B在5000 s−1拉伸加载下的应力-应变曲线如图12所示。模型在高应变率拉伸瞬时,因接触与惯性效应共同的影响,产生异常大的应力,此时泡沫铝单元并未发生破坏;随着拉伸加载的持续进行,应力逐渐下降,试件断裂时对应的应力-应变曲线无明显峰值状态。因此,以模型应力-应变曲线的“峰值状态”作为模型的破坏时刻已不再适用,需要找出适合泡沫金属动态拉伸加载的破坏准则。
4. 应变率对泡沫铝动态拉伸力学性能的影响
模型B不同应变率(0.5~5000 s−1)动态拉伸时的名义应力-名义应变曲线如图13所示,随着加载拉伸应变率的增大,受惯性效应的影响,初始应变段对应的应力逐渐增大,曲线变化趋势出现明显变化,当应变率为5000 s−1拉伸时,模型破坏时对应的名义应力-名义应变曲线无明显的峰值特征。定义图13中的峰值应力状态为破坏状态,泡沫金属动态拉伸的破坏应力和破坏应变随应变率变化曲线如图14所示,拉伸破坏应变几乎不受加载速率的影响;破坏应力在应变率较小时(500 s−1 及以下)时受应变率的影响不大,当应变率超过一定范围(大于500 s−1)后,拉伸破坏应力随着应变率增大而显著增大,近似线性关系。因此,即使基体材料无应变率效应,但泡沫金属高应变率拉伸时,仍需要考虑应变率效应。
5. 结 论
(1) 开展了对泡沫金属模型A(30 mm×30 mm×30 mm)及模型B(30 mm×30 mm×5 mm)的动态拉伸数值模拟,通过对模型进行预压后再进行单轴反向拉伸的加载方式,研究了泡沫金属试件高度对动态拉伸加载的影响,结果表明降低试件拉伸方向的高度不仅能有效地避免泡沫金属边缘局部破坏,而且能够显著地改善泡沫金属动态拉伸实验的应力均匀性和变形均匀性。
(2) 采用高度为1.55 倍胞孔等效直径的泡沫金属试件能够合理地实现最高应变率为5000 s−1的恒定应变率动态拉伸加载数值模拟;高应变率动态拉伸时瞬时,因接触与惯性效应的共同影响,产生异常大的应力,此时泡沫铝单元并未发生破坏,随着拉伸加载的持续进行,应力逐渐下降,试件断裂时对应的应力-应变曲线无明显峰值状态。
(3) 泡沫铝恒定应变率动态拉伸时,破坏应变几乎不受拉伸应变率的影响,破坏应力在中低应变率(500 s−1及以下)时基本不受拉伸应变率的影响,但在高应变拉伸时破坏应力随应变率增大而近似线性增加。
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表 1 数值模拟中采用的铝合金主要材料参数[37]
Table 1. Main material parameters of aluminum alloy used in numerical simulation[37]
部件 材料 屈服应力/MPa 拉伸强度/MPa 杨氏模量/GPa 密度/(g·cm−3) 泊松比 面板 AL1200 140 160 70 2.7 0.3 芯层 AL5052 70 210 70 2.7 0.3 表 2 爆炸载荷下三维负泊松比夹芯板设计方案
Table 2. Designs of 3D negative Poisson’s ratio sandwich panels subjected to blast loading
编号 Tf/mm Tb/mm A/mm L2/mm 爆炸距离/mm Q/g 拉伸宽度L4/mm A-1 1.2 1.2 1 10 100 20 5 Q-30 1.2 1.2 1 10 100 30 5 Q-40 1.2 1.2 1 10 100 40 5 S-80 1.2 1.2 1 10 80 20 5 S-120 1.2 1.2 1 10 120 20 5 表 3 4组夹芯板的几何参数和爆炸参数[37]
Table 3. Geometric and explosion parameters for four sets of sandwich panels[37]
夹芯板 L2/mm 蜂窝边长L1/mm Tc/mm Q/g 爆炸距离/mm S4-1 18.4 5 0.04 10 150 S4-2 18.4 5 0.04 10 100 S3-1 18.4 3 0.04 15 100 S3-2 18.4 3 0.04 20 130 表 4 3种夹芯板的几何信息和模拟结果
Table 4. Geometric information and simulation results for three sandwich panels
编号 胞元长度
L1/mm胞元高度
L2/mm胞元夹角
θ/(°)胞元厚度
Tc/mm夹芯板总质量
M/g背面板中心最终
位移Db/mm结构总能量
吸收E/J比吸能
e/(J·g−1)C-1 10 10 − 0.2 211.64 6.58 382.6 1.81 C-2 10 10 120 0.2 257.66 8.67 316.1 1.23 C-3 5.77 10 120 0.2 229.13 10.4 256.6 1.12 C-4 5.77 10 120 0.2 226.20 11.4 236.3 1.04 -
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