Crystal Plasticity Finite Element Simulation of High-Rate Shock Deformation Process of <100> LiF
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摘要: 结合状态方程建立晶体塑性有限元模型，模拟高速冲击加载条件下<100> LiF的动态弹塑性大变形行为，得到应力波剖面特征、动态力学演化规律及其连续介质力学根源。结果表明：毫米级样品经约15 GPa以内的低压冲击，波剖面具有弹塑性双波响应、弹性前驱衰减和应力松弛现象，其决定性因素包括样品厚度、外加压力和材料本构；从连续介质力学角度分析得到,应力松弛本质上是由于黏性塑性流动，导致总应变增速小于塑性应变增速，从而使弹性应变减小、压力降低；提出用压力关于时间的三阶导数大于零作为判断条件，对应力波剖面上双波和单波响应的临界压力进行估测，发现随着样品掺杂浓度的增加，临界压力增大；高速冲击变形的温升效应不可忽略，且温升绝大部分来自弹性体积变形的贡献。Abstract: A crystal plasticity finite element model combined with equation of state was built to simulate the dynamic elastic-plastic large deformation behavior of <100> LiF under high-rate shock loading. The characterization of the stress wave profile, the patterns of the dynamic mechanical evolution and their essential causes in view of the continuum mechanics were obtained through simulations, with the following results achieved: (1) the wave profiles of millimeter-sized specimens exhibit elastic-plastic two-wave response, elastic precursor decay and stress relaxation below 15 GPa; (2) in view of continuum mechanics, the stress relaxation is essentially due to the viscous plastic flow which accounts for the increase rate of the total strain being less than that of the plastic strain, and which further reduces the elastic strain and pressure; (3) the third derivative of pressure to time being greater than zero was proposed as a criterion for estimating the critical pressure of the two-wave and the one-wave response of the stress wave profile, and the estimation result indicated that the critical pressure increased with the increase of the doping concentration in specimen; (4) the effect of temperature rise during the high-rate shock deformation is non-negligible, and the elastic volumetric deformation contributes to most of the temperature rise.
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Key words:
- LiF /
- crystal plasticity /
- equation of state /
- stress relaxation /
- two-wave response
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图 3 CPFEM模拟的<100> LiF波剖面与实验的比对结果
Figure 3. Comparison of wave profiles of <100> LiF from CPFEM simulations and experiments
图 4 加载条件和样品厚度相同、样品掺杂浓度不同（LiF11～LiF13，掺杂浓度依次减小）时模拟的应力波剖面
Figure 4. Stress wave profiles from models with same loading condition, specimen thickness and different doping concentrations (LiF11–LiF13, with doping concentration decreasing in order)
图 5 采用Johnson-Cook本构方程对LiF01、LiF02模型的模拟结果
Figure 5. Simulation results of LiF01 and LiF02 models using Johnson-Cook constitutive equation
图 6 LiF03、LiF04、LiF05和LiF12双波和 单波响应的临界压力
Figure 6. Critical pressure of two-wave and one-wave response of LiF03–LiF05 and LiF12 models
图 7 模拟LiF03、LiF04、LiF05和LiF12在13.4 GPa压力下的双波响应
Figure 7. Two-wave response of LiF03–LiF05 and LiF12 models under 13.4 GPa pressure by simulation
图 8 模拟LiF03、LiF04、LiF05、LiF12在0～40 GPa 冲击压力范围内温度随压力的响应
Figure 8. Temperature responding to pressure ranging from 0 to 40 GPa of LiF03–LiF05 and LiF12 models by simulation
表 1 模拟中采用的模型信息
Table 1. Model information in simulations
Sample No. Flyer material Window material v/(m·s–1) Sample’s thickness/mm Ref. LiF01 Al Quartz 340.0 1.35 [6] LiF02 Al Quartz 340.0 1.98 [6] LiF03 LiF LiF 423.8 3.0 [17] LiF04 LiF LiF 1 321.6 3.0 [17] LiF05 LiF LiF 1 641.5 3.0 [17] LiF06 Fused sillica Fused sillica 340.9 1.143 [18] LiF11, LiF12, LiF13 LiF LiF 340.0 3.0 Note: LiF01–LiF06 models were built based on the parameters of specimens and experiments in references, while LiF11–
LiF13 models were designed for comparison of profile characteristic differences with successively increased specimen
doping concentration.
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表 2 <100> LiF的超弹性本构参数
Table 2. Hyperelastic constitutive parameters of <100> LiF
Subscript Cij/GPa $\dfrac{{{\rm{d}}{{C}_{ij}}}}{{{\rm{d}}{p}}}$ $\dfrac{{{\rm{d}}{{C}_{ij}}}}{{{\rm{d}}{T}}}/(\rm MPa \cdot K^{-1})$ K0/GPa $ K_0^{\prime}$ ρ0/(g·cm–3) cV/(J·kg–1·K–1) Γm 11 113.97 9.97 –75.56 69.97 4.43 2.64 1 612.02 1.68 12 47.67 2.73 –28.39 44 63.64 1.38 –13.94
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表 3 <100> LiF的晶体塑性本构参数
Table 3. Crystal plasticity constitutive parameters of <100> LiF
Sample No. τ0/MPa B n ${\dot \gamma _{{\rm{off}}}}$/μs–1 ${\dot \gamma _{\rm{0}}}$/μs–1 m λ $\dfrac{{{\tau _{\rm T}}}}{\theta}/{\rm μs}^{-1}$ LiF01, LiF02, LiF11 121.0 4.0 0.08 3.5×10–9 0.12 0.09 4.7×10–2 0.15 LiF03, LiF04, LiF05, LiF12 113.9 0.30 LiF06, LiF13 86.4 0.40
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