Effect of damage evolution on the fragmentation process of ductile metals
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摘要: 固体在冲击拉伸载荷作用下会断裂成多个碎片，基于线性内聚力断裂假设的Mott-Grady模型能较好地预测碎裂过程所产生的平均碎片尺度的下限。然而实际上，韧性金属的损伤演化是多元化的，为此通过数值模拟方法研究了不同损伤演化规律对韧性碎裂过程的影响。利用ABAQUS/Explicit动态有限元软件数值再现了韧性金属杆（45钢）在高应变率下拉伸碎裂的过程，分析了线性和非线性损伤演化对韧性碎裂过程的影响规律。结果表明：损伤演化规律对韧性金属的碎裂过程具有显著影响，非线性指标α越大，碎裂过程产生的碎片数越少；Grady-Kipp碎裂公式仍能在一定范围内预测韧性碎裂过程中产生的碎片尺寸；当非线性指标α远大于零时，在较低冲击拉伸载荷作用下，数值模拟结果和Grady-Kipp模型预测值偏差较大，随着应变率增大，数值模拟结果与Grady-Kipp模型预测值吻合较好。
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关键词:
- 韧性碎裂 /
- 损伤演化 /
- Grady-Kipp公式 /
- 碎片尺寸
Abstract: Solids will be broken into multiple fragments under dynamic tension loadings. The Mott-Grady model based on linear cohesive fracture can predict the lower limits of average fragment size during fragmentation process. However, the damage evolution of ductile materials is diversified. In this paper, the ductile fracture processes influenced by different damage evolutions were studied by numerical simulation. Using ABAQUS/Explicit dynamic finite element, we reproduced the tensile fracture process of ductile metal bar (45 steel) at high strain rates. The effects of linear/nonlinear damage evolutions on ductile fracture process were analyzed. The numerical results show that the damage evolution law has a significant influence on the fragmentation process of ductile metals. As the nonlinear parameter increases, the number of fragments decreases during fragmentation process. The Grady-Kipp formula can still reasonably predict the lower limits of the ductile fragment sizes in a certain range. When the non-linear index α was far greater than zero, there are conspicuous deviations between the numerical experiments and the Grady-Kipp model under the low impact loading. With increasing strain rate, the results by the numerical simulations are in agreement with the ones by the Grady-Kipp theoretical model.-
Key words:
- ductile fragmentation /
- damage evolution /
- Grady-Kipp formula /
- fragment size
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图 2 非线性损伤演化下内聚力断裂特性和损伤因子
Figure 2. The cohesive laws for separation and damage factor D under nonlinear damage evolutions
图 3 45钢杆的线性/非线性内聚力断裂曲线（初始应变率为2×104 s−1）
Figure 3. The cohesive laws for separation under linear/nonlinear damage evolutions at the strain rate of 2×104 s−1
图 4 不同损伤演化规律下一维杆碎裂后的形态
Figure 4. Fragmentized 1D stress bars under different damage evolution laws
图 7 损伤演化方式对碎裂过程的影响
Figure 7. The effect of different damage evolution laws on fragmentation process
图 8 不同损伤演化规律下的应力时程曲线
Figure 8. Stress-time curves under different damage evolution laws
图 9 无量纲应变率和无量纲碎片尺寸的关系
Figure 9. The relationship between normalized strain rate and normalized fragment size
图 10 α=10.0时，无量纲碎片尺寸与应变率的关系
Figure 10. Normalized fragment size vs normalized strain rate at cohesive parameter α=10.0
表 1 45钢材料的Johnson-Cook本构模型的物理参数
Table 1. Material parameters of the 45 steel
Material ρ/(kg·m−3) E/GPa ν c/(J·kg−1·K−1) $T_ {\rm{t} }$/K $T_ {\rm{m} }$/K Gc/(kN·m−1) 45 steel 7.8×103 203 0.29 447 298 1 765 25 Material m $\beta $ $\dot \varepsilon $/s−1 A/MPa B/MPa C n 45 steel 1.06 0.9 1 507 320 0.064 0.28 
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表 2 非线性损伤演化下内聚力断裂参数（断裂能Gc=25 kN/m）
Table 2. The cohesive parameters under nonlinear damage evolutions (Gc=25 kN/m)
$\alpha $ $u_{\rm{f}}^{{\rm{pl}}}$/μm $\alpha $ $u_{\rm{f}}^{{\rm{pl}}}$/μm $\alpha $ $u_{\rm{f}}^{{\rm{pl}}}$/μm $\alpha $ $u_{\rm{f}}^{{\rm{pl}}}$/μm −10.0 24.1 −5.0 26.9 −1.0 37.3 −0.1 42.7 0.1 44.2 1.0 52.0 5.0 112.0 10.0 217.0
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