WAN Yin, WANG Huanran, CHU Guangxiang, REN Chunying. Spall Strength and Fracture Mechanism of Sintered Nd-Fe-B[J]. Chinese Journal of High Pressure Physics, 2019, 33(5): 054201. doi: 10.11858/gywlxb.20190746
Citation: MENG Yang, WEN He-Ming. Numerical Simulation of the Response of Reinforced Concrete Slabs to Projectile Impact or Explosive Loading[J]. Chinese Journal of High Pressure Physics, 2011, 25(4): 370-378 . doi: 10.11858/gywlxb.2011.04.014

Numerical Simulation of the Response of Reinforced Concrete Slabs to Projectile Impact or Explosive Loading

doi: 10.11858/gywlxb.2011.04.014
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  • Corresponding author: WEN He-Ming
  • Received Date: 17 Nov 2009
  • Rev Recd Date: 26 Jan 2010
  • Issue Publish Date: 15 Aug 2011
  • Numerical simulation is first conducted herein of the perforation of reinforced concrete slabs by an ogival-nosed projectile using LS-DYNA. The triaxial test data reported in this paper for the 48 MPa concrete are used to determine the values of the parameters employed in the Holmquist-Johnson-Cook (HJC) model. It is shown that the numerical simulations correlate well with the experimental observations in terms of ballistic limit, residual velocity, impact crater, penetration tunnel and scabbing crater. The response of reinforced concrete slabs to explosive loading is also studied numerically by the fluidsolid coupled method of LS-DYNA. The simulation reproduces the transient process of the shock wave and the main rupture process of the slabs. The numerically obtained pressure-time histories are found to be in reasonable agreement with those predicted by the empirical equations; the failure patterns obtained by the numerical simulation are found to be similar to those obtained experimentally.

     

  • 烧结钕铁硼永磁材料具有优越的磁性能,广泛应用于诸多领域,如航空航天、机械加工、电子计算机等。其中基于Nd2Fe14B合金的爆炸驱动脉冲电源被认为是最有效的紧凑型脉冲电源[1]。对于烧结钕铁硼永磁材料,人们关注的重点是其磁性能,对其力学性能的研究则相对较少,尤其是动态力学性能。然而,在现代精密仪器中经常用到烧结钕铁硼,如汽车、导弹制导、国防通讯设备,这些仪器在使用过程中常常承受外力作用,要求其具有一定的抗冲击性能,因此研究烧结钕铁硼在冲击压缩下的动态行为和断裂机理具有很高的学术意义和应用价值。李岩峰等[2]在一级轻气炮系统中对Nd-Fe-B磁体进行了冲击压缩实验,研究了退磁现象;李巧燕等[3]采用二级轻气炮,测量了钕铁硼永磁体在19~78 GPa压力范围内的冲击压缩特性。

    本课题组在前期工作中利用MTS万能试验机和分离式霍普金森压杆(Split Hopkinson Pressure Bar,SHPB)研究了烧结钕铁硼在准静态下的抗弯强度和弹性模量[4]以及在单轴压缩下的动态断裂[5];此外还开展了动态巴西圆盘试验[6],研究了烧结钕铁硼的断裂过程,根据弹性理论得到了其拉伸强度,并利用扫描电子显微镜(Scanning Electron Microscope,SEM)观察其微观结构。本研究将利用一级气体炮开展烧结钕铁硼在高应变率、一维平面冲击加载下的层裂实验,利用激光干涉测速技术VISAR(Velocity Interferometer System for Any Reflector)测量自由面粒子速度历史,确定其层裂行为,最后利用SEM观察断口微观形貌,分析烧结钕铁硼在冲击波作用下的断裂机理。

    采用宁波大学的一级气体炮进行冲击加载实验,图1为实验装置示意图。采用铝制弹托驱动飞片,飞片采用有机玻璃(PMMA)和铝合金(LY12)两种材料,直径均为42.5 mm。通过改变弹丸的速度和飞片的材质,实现较大范围的加载应力。利用测速探针测量飞片的撞击速度,利用VISAR测量样品自由面粒子速度历史。

    图  1  实验装置示意图
    Figure  1.  Schematic of experimental setup

    层裂是材料的一种动态失效形式,是由稀疏(膨胀)波相互作用产生拉应力而形成的[7]。层裂原理如图2所示。飞片以速度V撞击样品,在飞片和样品内产生冲击压缩波;压缩波到达飞片和样品自由面时反射稀疏波,随后稀疏波在样品内相遇,相互作用产生拉伸应力;当拉伸应力超过材料的强度极限时,样品发生破坏,即发生层裂;层裂形成后,从新产生的自由面上反射稀疏波,使拉伸应力降低;当稀疏波到达样品自由面时,下降的自由面粒子速度曲线立即回跳,这便是发生层裂行为的信号。根据带有层裂信号的自由面速度曲线,通过(1)式确定样品的层裂强度[8],即

    图  2  层裂原理示意图
    Figure  2.  Schematic illustration of spall process
    σsp=12ρ0cL(uf,maxuf,min)
    (1)

    式中:uf, maxuf, min是出现第1次回跳信号前自由面粒子速度的最大值和最小值,σsp为层裂强度,ρ0为样品的初始密度,cL为样品的弹性纵波声速。

    实验材料采用牌号为N42的烧结钕铁硼块状磁体,由宁波市三环钕铁硼磁业有限公司提供,采用未充磁的粉末冶金方法制备。通过电火花线切割方式,加工成直径为40 mm、厚度为4 mm的圆形样品,样品的厚度方向即磁化方向,也是冲击压缩方向,最后利用砂纸对样品表面进行打磨抛光。烧结钕铁硼的实测平均密度ρ0为7.544 g/cm3,泊松比 ν 取0.24,弹性模量E为155 GPa,根据

    cL=[1ν(1+ν)(12ν)Eρ0]1/2
    (2)

    可得一维应变下钕铁硼样品的弹性纵波声速cL=4.921 km/s[7]表1列出了两种飞片材料参数,其中c0iλi为Hugoniot关系常数,ρ0i为飞片的初始密度。

    表  1  飞片材料的Hugoniot参数[9]
    Table  1.  Hugoniot parameters of flyers[9]
    Materialρ0i/(gcm3)c0i/(kms1)λi
    PMMA1.1862.651.54
    LY122.7845.371.29
    下载: 导出CSV 
    | 显示表格

    烧结钕铁硼样品的层裂实验结果如表2所示,其中加载应力σ根据飞片和样品碰撞时的动量守恒及冲击界面上连续性条件计算得到。计算时,飞片采用流体力学模型,烧结钕铁硼样品采用线弹性模型[10]

    表  2  烧结钕铁硼层裂实验参数和结果
    Table  2.  Parameters and results of spall experiments for Nd-Fe-B
    Exp. No.Material of flyerThickness of flyer/mmV/(m·s–1)Thickness of sample/mmσ/GPaσsp/GPa
    01PMMA1.17122.673.990.3750.209
    02PMMA1.16173.993.990.5500.249
    03PMMA1.17230.723.960.7390.263
    04LY122.28146.333.951.5910.274
    05LY122.33161.903.901.7370.313
    06LY122.28190.893.942.0920.251
    07LY122.34230.733.952.5120.224
    下载: 导出CSV 
    | 显示表格
    σi=ρ0i(c0i+λiui)ui
    (3)
    σs=ρ0scLus
    (4)
    σs=σi=σ,us+ui=V
    (5)

    式中:u为粒子速度,V为飞片撞击速度,ρ0为初始密度,下标i和s分别表示飞片和样品。

    由自由面速度uf可以得到粒子速度,按忽略熵增的方法处理,则有[11]

    uf=u+ur2u
    (6)

    式中:ur表示由中心稀疏波引起的附加质点速度。

    层裂实验实测样品的自由面速度剖面如图3所示。可以看出,烧结钕铁硼在飞片撞击下发生了层裂破坏,所有实测曲线均有明显的层裂信号,如图3中黑色箭头所示。在冲击载荷下烧结钕铁硼的层裂强度与加载应力的关系如图4所示。可见:层裂强度随着加载应力的增加先增大后减小;存在一个明显的临界应力,约为1.7 GPa,当加载应力超过该临界应力时,材料的层裂强度就会减小。该临界应力值同时反映了冲击载荷下材料是否发生压缩损伤,如图3中06号实验所测自由面速度曲线所示,在速度上升过程中,接近峰值时速度突然变缓,说明材料在压缩过程中发生压缩损伤,材料开始由弹性向非弹性转化,导致材料的层裂强度减小。

    图  4  层裂强度与加载应力的关系
    Figure  4.  The relationship between spall strength and impact stress
    图  3  层裂实验样品的自由面速度剖面
    Figure  3.  Free surface velocity profile of the sample in the spall experiment

    通过SEM对冲击压缩实验后烧结钕铁硼样品的断口进行观察,如图5所示,可见晶粒表面非常光滑,断口比较平整,表现出脆性断裂的明显特征。另外,从图5(b)中可以看出,微裂纹处有明显的穿晶断裂。

    图  5  断口的SEM图像
    Figure  5.  SEM images of the fractured surface

    对比之前工作中烧结钕铁硼的断口形貌发现,在准静态下的三点弯曲实验中烧结钕铁硼主要是沿晶断裂[4],在动态巴西圆盘试验中出现穿晶断裂现象[6],而本实验中在微裂纹处出现多处穿晶断裂。准静态压缩下断口表面极不平整,充满了尖锐的边缘,这是由于晶界的强度较弱,裂纹沿着晶粒边界传播,说明在低加载速率下沿晶断裂在材料失效过程中占主导地位。随着加载速率的升高,穿晶断裂越来越明显,说明当加载速率小于某个临界值时,微裂纹沿晶界传播,导致断口不均匀,即沿晶断裂;当加载速率大于某个临界值时,由于裂纹尖端附近释放的应变能显著增大,导致其前面的单个晶粒分裂,这时断口非常平整、光滑,即穿晶断裂。因此,冲击波加载下烧结钕铁硼的失效过程是由两者共同控制下的沿晶断裂和穿晶断裂。

    在一级气体炮平面冲击压缩实验中,采用VISAR测量了烧结钕铁硼样品在冲击载荷下的自由面速度历史,得到了烧结钕铁硼在0.375~2.512 GPa范围内的层裂强度;分析了层裂强度与加载应力的关系,发现存在一个临界应力阈值(约1.7 GPa),当加载应力大于该阈值时,材料发生压缩损伤,导致烧结钕铁硼的层裂强度减小。观察烧结钕铁硼断口微观形貌发现,冲击波加载下烧结钕铁硼有明显的穿晶断裂,失效过程由沿晶断裂和穿晶断裂共同控制,而在准静态下则由沿晶断裂控制。研究结果有助于进一步了解烧结钕铁硼在冲击加载下的损伤和破坏。

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