On the size effect for micro-scale structures under the plane bulge test using the modified strain gradient theory

Lee, Hunkee; Jung, Bong-Bu; Kim, Dongseob; Park, Hyunchul

doi:10.1007/s12541-011-0115-7

Cited by 7 publications

(4 citation statements)

References 30 publications

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“…It is well known from forming of metals that deformation under compression is highly dependent on the tribology of the loading interface, with the amount of bulging or "barrelling" being proportional to the friction coefficient. [19] It has also been shown in other studies that frictional forces oppose the development of hoop strain near the ends of cylindrical specimens while reaching a maximum at half the height. [20,21] It follows then, that the stress state near the ends of the cylinder approximate one resulting from pure hydrostatic pressure.…”

Section: Strain Measurementsmentioning

confidence: 74%

Use of digital image correlation to measure strain recovery in particle toughened thermoset resins

Guzmán

Jackson

Jones

et al. 2018

Strain

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A methodology for finding the yield point of epoxy resins, both neat and particulate toughened, is described. Trends of the effect that particulate filling has on the time dependent response of these materials were constructed from observations made with stereo-based digital image correlation (3D-DIC), namely, creep and stress relaxation at constant load. The use of 3D-DIC also enabled the observation of differences in deformation mechanisms resulting from the particle addition. The focus is put on the technique’s potential to characterize materials and produce clear relationships between composition and mechanical strain response of any composition. The methodology proposed herein allows the observation and study of multiple deformation mechanisms from a single test, and thus can potentially minimize the number of specimens needed for a comprehensive test campaign

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Section: Strain Measurementsmentioning

confidence: 74%

Use of digital image correlation to measure strain recovery in particle toughened thermoset resins

Guzmán

Jackson

Jones

et al. 2018

Strain

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“…The constitutive model of classical mechanics fails to accurately capture the size effect in analyzing the mechanical behavior of smallscale structures due to its lack of microscopic characteristics such as grain boundaries, defects, and material heterogeneity. Therefore, to provide a comprehensive understanding of the significant size effect observed in small-scale systems, several non-classical continuum theories, including the nonlocal elasticity theory (NET) [18,19], the modified couple stress theory (MCST) [20,21], and the modified strain gradient theory (MSGT) [22,23], have been proposed to incorporate additional length scale parameters into the analysis and enhance our ability to accurately describe the mechanical behavior of materials at micro and nano scales.…”

Section: Introductionmentioning

confidence: 99%

Compliance-based topology optimization of multiple-phase materials related to the scale effect

Gan

2024

Preprint

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With the rapid advancement of technology, the device's size gradually tends to be miniaturized to the micro or nanoscale. However, the traditional framework based on classical mechanics is no longer sufficient to explain the impact of the scale effects on the mechanical behavior of these miniaturized structures. Furthermore, the increasing demand for multi-phase materials with excellent comprehensive performance also drives the growth of reverse design. Therefore, this study proposes a topological optimization design method for multi-phase materials that considers scale effects. The interpolation model of multi-phase materials utilizes elemental density to establish a mapping relationship with each phase material. The improved couple stress theory incorporates intrinsic characteristic length parameters to account for the scale effect in small-scale structures. Several numerical examples demonstrate that when the macroscopic size of the structure approaches the intrinsic characteristic length parameter, a significant scale effect occurs in the small-scale structure, leading to a redistribution of the topological configuration of the weak-phase material.

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“…Lee et al [40] found the strain gradient, which was the second derivative of displacement, played a very important role in the thin metal forming when the thickness was only several micrometres. Based on the non-homogeneity characteristics of the polycrystalline metallic materials, a modified model was proposed.…”

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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On the size effect for micro-scale structures under the plane bulge test using the modified strain gradient theory

Cited by 7 publications

References 30 publications

Use of digital image correlation to measure strain recovery in particle toughened thermoset resins

Use of digital image correlation to measure strain recovery in particle toughened thermoset resins

Compliance-based topology optimization of multiple-phase materials related to the scale effect

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

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