Cross-scale approach for impact damage and fatigue based on the strain gradient theory
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摘要: 为兼顾考虑材料尺度效应和建模预测效率的冲击损伤和冲击疲劳研究方法，立足冲击损伤和疲劳过程中的金属塑性变形机理，研究了冲击损伤过程中尺度效应影响下的材料构效行为，建立了金属材料的去局域化、跨尺度冲击损伤本构理论，形成了面向先进制造多尺度金属材料的冲击损伤和疲劳的仿真方法。该方法利用低阶应变梯度理论实现尺度效应描述，在Johnson-Cook冲击动力学模型和Lemaitre冲击损伤模型的基础上，实现了跨尺度冲击动力学及损伤演化的描述，并可以在VUMAT子程序中便捷地实现该本构的有限元计算。有限元结果表明，材料的不均匀变形带来了较高的应变梯度，使得材料的应力水平在加工硬化及应变率硬化效应上进一步提升，同时也让材料更快地进入损伤阶段，导致承载力降低或提前失效，这与金属材料在强度与韧性间的拮抗关系保持了一致。Abstract: Impact damage and fatigue are emerging challenges in the defense industry and civil infrastructure. The more pronounced material size effect induced by advanced manufacturing processes makes mechanical analysis and life prediction in these contexts more complex. Currently, there is no convenient and effective method for predicting and designing the cross-scale impact damage and fatigue performance of metal materials. This research is based on the metallic plasticity mechanisms in the impact damage and fatigue processes, investigating the material performance under the influence of the material size effect during the impact damage process. A non-local, cross-scale impact and damage constitutive theory for metallic materials was developed, and an impact damage and fatigue simulation method for advanced manufactured metals was established. This method used the conventional theory of mechanism-based strain gradient (CMSG) to describe the size effect and was built on the Johnson-Cook impact dynamics model and Lemaitre impact damage model to describe cross-scale impact dynamics and damage evolution. This approach could be conveniently implemented in finite element analysis with the VUMAT and relevant subroutines. The present work established uniaxial and U-notch bending finite element models and verified the influence of work hardening, strain rate hardening, size effect, and damage effect on static and impact dynamic response of metals. Simulation results indicated the material behavior corresponds to the material characteristic and constitutive design. The distribution and evolution of the stress, strain, strain gradient, and damage before and after material failure are also discussed. The results show that the inhomogeneous deformation caused by advanced manufacturing processes leads to higher strain gradients, which further increase the flow stress through work hardening and strain rate hardening effects and strengthen the material. However, this also causes the material to enter the damage stage earlier, leading to reduced impact and fatigue-bearing capacity or premature failure. These findings are consistent with the inherent trade-off between strength and toughness of metallic materials.
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Key words:
- impact damage /
- impact fatigue /
- cross-scale mechanics /
- strain gradient plasticity
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图 1 本构有限元实现的程序流程框图
Figure 1. Diagram of the finite element implementation of the present constitutive relation
图 2 单轴拉伸和三点弯曲试样的有限元建模
Figure 2. Finite element modeling of uniaxial tension and U-notch bending specimens
图 3 单轴准静态和冲击载荷下的整体应力-应变关系
Figure 3. Comparison of stress-strain curves under uniaxial tension
图 4 在率效应和损伤效应作用下应力、应变、损伤和应变率的演化
Figure 4. Evolution of stress, strain, damage index, and strain rate under rate and damage effects
图 5 不同损伤参数对材料在冲击过程中的应力应变关系的影响
Figure 5. Inference of different damage parameters on the stress-strain relationship of material during impact
图 6 U缺口试样在冲击损伤破坏前后的整体应力分布
Figure 6. Stress distribution of the U-notch sample before and after impact damage and failure
图 7 损伤关键时刻的应力、应变、应变梯度及损伤度的演化过程
Figure 7. Evolution of stress, strain, strain gradient, and damage index at the moment of failure
图 8 单次大载荷冲击作用对尺度效应与应变率效应的影响
Figure 8. Stress, damage, and energy evolution under the impact of a large load with and without considering strain rate and strain gradient effects
图 9 多次较小载荷冲击作用下整体能量演化和局部应力应变等力学响应的演化过程
Figure 9. Evolution of energy and local mechanical response during multiple impacts
图 10 多次小载荷冲击作用对系统能量及损伤、应变演化及尺度效应、率效应的影响
Figure 10. Evolution of energy, damage, and strain during multiple impacts and influence of strain rate and strain gradient effects
表 1 有限元仿真采用的本构参数
Table 1. Constitutive parameters used in the finite element simulation
杨氏模量E/GPa 泊松比ν 屈服强度Y/MPa 幂硬化系数n 黏塑性参数m 材料特征长度l/μm 率硬化参数C 损伤参数S/MPa 损伤参数mD 210 0.3 1800 0.1 20 15 0.017 12 10.1 
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