Lagrangian inverse analysis method for studying dynamic constitutive relation of brittle materials based on all-fiber laser interference velocity measurement technique

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Journal of Vibration and Shock ›› 2019, Vol. 38 ›› Issue (11) : 116-120.

DING Yuanyuan, ZHANG Zhen, LAI Huawei, WANG Yonggang

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Abstract

Based on the multi-probe all-fiber laser interference velocity measurement technique, on a split Hopkinson pressure bar system, a Lagrangian inverse analysis test device for long rod specimens was built to study the dynamic constitutive relation of brittle materials. In order to monitor the axial mass point velocity of a long rod specimen, a new method of laser oblique incidence was proposed, and the feasibility and correctness of this new method were verified. Based on the 1-D stress wave propagation theory, the conversion relation between Euler mass point velocity and Lagrange one was established. It was shown that fracture strains are very small for brittle materials, so the difference between Euler mass point velocity and Lagrange one can be neglected. Using multi-mass point velocity time history curves, path lines were constructed to connect the whole velocity field, and then zero initial conditions were combined to realize numerical solving with Lagrangian inverse analysis method, and obtain the dynamic stress-strain relation curve of the brittle material PMMA. This constitutive relation curve was compared with those of Hopkinson pressure bar test and quasi-static state compression test.

Key words

Laser interferometry / Lagrangian inverse analysis / Particle velocity / Dynamic constitutive relation.

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DING Yuanyuan, ZHANG Zhen, LAI Huawei, WANG Yonggang. Lagrangian inverse analysis method for studying dynamic constitutive relation of brittle materials based on all-fiber laser interference velocity measurement technique[J]. Journal of Vibration and Shock, 2019, 38(11): 116-120

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