An optimal-order error estimate for the mass-conservative characteristic finite element scheme

Wang, Hongmei; Rui, Hongxing; Zhang, Shuai

doi:10.1016/j.amc.2012.04.004

Cited by 2 publications

(1 citation statement)

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“…Thin metal sheet micro-forming process, well-known for their process simplicity, high production rate, minimized material waste, near-net-shapes, excellent mechanical properties [1,2], and close tolerances [3], are claimed to be the most suitable process to fabricate micro-parts in the fields of electronics [4], medical devices, Micro Electro Mechanical Systems (MEMS) [5], and Micro System Technology (MST) [6 -10]. However, there are challenges in the thin metal sheet forming process when the sheet thickness is decreased to the level of micrometres, because of the unknown deformation mechanics and material behaviour which called the "second order size effect" [11 -15].…”

Section: Introduction mentioning

confidence: 99%

Constitutive Model of Thin Metal Sheet in Bulging Test Considering Strain Gradient Hardening

Wan¹,

Wei²,

Yang³

2020

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The study of the size effect was one of the most important subjects in the field of micro-forming. To investigate the stress of the thin sheet in the bulging test with the second order size effect, a constitutive equation considering the strain gradient hardening was proposed. Based on the equation, the stress of the thin sheet during the bulging test was calculated by the finite element method. The bulging tests with various thicknesses of brass sheets and radiuses of punching balls were performed to verify the proposed equation. The results showed that the constitutive equation could capture the stress variations, while the simulation using the constitutive equation from the conventional theory of plasticity showed the results with large deviation from those of the experiment. It was found that the stress was sensitive to the thickness of the sheet and the radius of the punching ball in bulging test of thin brass sheet. The bulging of the thin brass sheet with a thickness below ten times of its material intrinsic length would cause the generation of the geometrically necessary dislocations, which induced the strain gradient hardening. Besides that, the decrement of the punching ball radius would also increase the inhomogeneous deformation and enhance the strain gradient hardening during the thin sheet bulging process. The strain gradient hardening during the thin sheet bulging test was related to the strain of the sheet. The hardening effect of the strain gradient was obvious when the strain was small. The strain gradient hardening should be considered in the thin sheet bulging test with the second order size effect.

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