Dislocation Dynamics and Single‐Crystal Constitutive Relations: Shock‐Wave Propagation and Precursor Decay
Dislocation Dynamics and Single‐Crystal Constitutive Relations: Shock‐Wave Propagation and Precursor Decay
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位错动力学和单晶本构关系：冲击波传播和前体衰变
DOI：
10.1063/1.1659227
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发表时间：
1970
影响因子：
3.2
通讯作者：
T. Michaels
中科院分区：
文献类型：
--
作者：
J. N. Johnson;O. Jones;T. Michaels
用位错动力学方法推导了单晶的率相关本构关系。各个滑动面上滑移的贡献被假定为线性叠加，从而得到总的塑性应变。作为理论的应用，建立了沿[100]、[110]和[111]方向传播的面心立方、体心立方和岩盐结构中纵向平面波传播的弹性前兆衰减方程。此外，还导出了平行和垂直于c轴传播的波在锌(hcp结构)中的前驱衰变表达式。对单晶铜(FCC)、钨(BCC)、氯化钠(岩盐)和LiF(岩盐)的前驱体振幅进行了理论计算，并与实验数据进行了比较。在这些计算中使用了通过直接观察位错而确定的位错迁移率。一般而言，该理论预测了不同传播方向的前兆振幅的适当相对顺序。比较表明，为了使理论确定的振幅与实验数据相吻合，初始移动位错密度必须比冲击加载前在材料中测量的初始总密度大两到三个数量级。对这种差异的可能解释进行了讨论。
Rate‐dependent constitutive relations for single crystals are derived in terms of dislocation dynamics. Contributions from slip on the individual glide planes are assumed to superpose linearly to give the total plastic strain. As an application of the theory, equations describing elastic precursor decay are developed for longitudinal plane‐wave propagation in fcc, bcc, and rocksalt structures with wave propagation in the [100], [110], and [111] directions. In addition, expressions for precursor decay in zinc (hcp structure) are derived for wave propagation both parallel and perpendicular to the c‐axis. Calculated theoretical results are compared with experimental data on precursor amplitudes for single‐crystal copper (fcc), tungsten (bcc), NaCl (rocksalt), and LiF (rocksalt). Dislocation mobilities determined from direct observation of dislocations are used in these calculations. In general the theory predicts the proper relative order of the precursor amplitudes for different propagation directions. The comparisons show that in order for theoretically determined amplitudes to agree with experimental data, initial mobile dislocation densities must be two or three orders‐of‐magnitude greater than initial total densities which are measured in the material prior to shock loading. Possible explanations for this discrepancy are discussed.