Probing the constitutive behavior of microcrystals by analyzing the dynamics of the micromechanical testing system
doi: 10.1007/s10409-021-09077-5
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摘要: 由于塑性失稳导致的应力-应变测量曲线中塑性变形信息的缺失, 使得微晶本构行为仍然很神秘. 此外, 应力-应变测量曲线在不同控制模式下的测量结果变化很大, 而本构行为不应受测量方法的影响. 此外, 由于微观力学测试系统的非线性动力学行为尚不清楚, 微晶真实本构行为的探究一直是一个挑战. 本文在位移控制和负载控制下对单晶铝微柱进行了详细的实验和分析. 为了解释实验结果, 文章基于微观力学测试原理开发了一个聚合参数物理模型, 该模型可直接将微观力学测试系统的非线性动力学与微晶的本构行为联系起来. 这表明应力-应变测量曲线的某些阶段由控制算法产生, 与本构行为无关. 通过求解微观力学测试系统的非线性动力学, 从平衡态开始的强塑性不稳定性(大应变爆发)归因于微晶的应变软化阶段. 文章还进行参数研究以减少塑性失稳对测量响应的影响. 本研究为开发各种本构模型和设计可靠的微观力学试验提供了重要的见解.Abstract: The constitutive behavior of microcrystals remains mysterious since very little, or no information regarding plastic deformation in the measured stress-strain curve is available due to plastic instability. Furthermore, the measured stress-strain curves vary greatly under different control modes, while constitutive behavior should remain unaffected by test methods. Beyond these reasons, probing the real constitutive behavior of microcrystals has long been a challenge because the nonlinear dynamical behaviors of micromechanical testing systems are unclear. Here, we perform and carefully analyze the experiments on single-crystal aluminum micropillars under displacement control and load control. To interpret these experimental results, a lumped-parameter physical model based on the principle of micromechanical testing is developed, which can directly relate nonlinear dynamics of the micromechanical testing system to the constitutive behavior of microcrystals. This reveals that some stages of the measured stress-strain curve attributed to the control algorithm are not related to constitutive behavior. By solving the nonlinear dynamics of the micromechanical testing system, intense plastic instability (large strain burst) starting from the equilibrium state is attributed to the strain-softening stage of microcrystals. Parametric studies are also performed to reduce the influence of plastic instability on the measured responses. This study provides critical insights for developing various constitutive models and designing a reliable micromechanical testing system.
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1. Scanning electron microscopy (SEM) images of the micron-sized sample used for compression tests under a displacement control and b load control.
2. Some stages of the measured mechanical response under displacement control are not related to constitutive behavior. a The experimental stress-strain curve was obtained under displacement control. Red markers are the data points sampled by the displacement and force sensor. b Representative stress-strain curve under displacement control. A few or no data points are sampled during the forward surge stage. c Analysis of the evolution of displacement and load in the time domain. Load drop is mainly attributed to the control algorithm.
3. The experimental stress-strain curve was obtained under displacement control. Red cross markers are the data points sampled by the displacement and force sensor, and no data point is sampled during the forward surge stage (Movie S1).
4. The experimental stress-strain curve was obtained under displacement control. Multiple strain bursts with varying degrees of instability occur during deformation. Red cross markers are the data points sampled by the displacement and force sensor, and a few or no data points are sampled during the forward surge stage. The measured stress drops to a specific value (Movie S2).
5. The experimental stress-strain curve was obtained under displacement control. Red cross markers are the data points sampled by the displacement and force sensor, and a few data points are sampled during the forward surge stage. The measured stress drops to zero (Movie S3).
6. Connection and difference of the measured mechanical responses between displacement control and load control. a The experimental stress-strain curve was obtained under load control. b Representative stress-strain curve under load control. c Analysis of the evolution of displacement and load in the time domain. The controller does not respond to the displacement jump since it controls the load.
7. A lumped-parameter physical model based on the principle of the micromechanical testing system. a Schematic diagram of the principle of the micromechanical testing system. b A simplified lumped-parameter mechanical model with the loading system and micropillar connected in series. c Force equilibrium analysis of the loading system and micropillar.
8. Nonlinear dynamical behaviors of the micromechanical testing system. The dimensionless displacement, velocity, and force equilibrium of the micropillar vary as a function of time. The dimensionless displacement and velocity of the loading system also change with time.
9. Dynamical characteristic of the experimental setup. a Dimensionless displacement of the indenter and micropillar as a function of time when m=1.5. b Dimensionless velocity of indenter and micropillar. c Dimensionless displacement of the indenter and micropillar as a function of time when m=150. d Dimensionless velocity of indenter and micropillar.
10. The stress-strain curves are described by the constitutive function equation. The influence of the parameter m on the degree of strain softening is illustrated. E and ε0 is set as
61.9 GPa and 0.1, respectively. During the strain-softening stage, the absolute value of the slope under the condition m=150 is much larger than that under the condition m=1.5.
11. Numerical solutions of the governing equations of the experimental setup: dimensionless velocity of indenter and micropillar as a function of time when a Ml/Mp=50; b Ml/Mp=100; c Ml/Mp=200; d Ml/Mp=400.
12. The dimensionless velocity of the micropillar changes with time, and the burst velocity increases as the mass ratio of the loading system to micropillar (Ml/Mp) increases.
13. Numerical solutions of the governing equations of the experimental setup: dimensionless velocity of indenter and micropillar as a function of time when a Kp/Kl=0.2; b Kp/Kl=0.4; c Kp/Kl=0.6; d Kp/Kl=0.8.
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