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

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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Ultra-Thin Sheet Forming Analyses Considering Size Effects

Key Engineering Materials ◽

10.4028/www.scientific.net/kem.794.295 ◽

2019 ◽

Vol 794 ◽

pp. 295-304

Author(s):

Bon Young Ghoo ◽

Jun Ho Son ◽

Yasuyoshi Umezu ◽

Tei Hirashima ◽

Yuko Watanabe

Keyword(s):

Flow Stress ◽

Constitutive Equation ◽

Size Effect ◽

Size Effects ◽

Thin Sheet ◽

Scale Factor ◽

Fe Analysis ◽

Forming Process ◽

Deformation Modes ◽

Sheet Deformation

Based on robust numerical formulations and various material models, finite element (FE) analysis becomes a powerful tool in conventional sheet metal forming process. Unfortunately, the present constitutive equations irrelevant to thickness that describe well conventional sheet deformation modes have difficulties being applied directly to ultra-thin sheet deformation modes. In the present study, a constitutive equation considering size effect is established by introducing a scale factor that represents size effects through thickness and width directions. Uniaxial tensile tests were used to evaluate the scale factor of different thicknesses together with the parameter identification. The developed constitutive equation reveals that thickness is the most important factor effecting on the constitutive relation of ultra-thin sheet. 2D draw forming process of C7035 ultra-thin sheet is analyzed using JSTAMP/NV introducing the developed constitutive equation. The analysis results show that there are obvious differences in the punch forces and loading geometries according to the size effect through thickness direction. Specimen width has slight effect on the flow stress although specimen thickness has strong effect on the flow stress. It is expected that the proposed constitutive equation gives good applicability to FE analysis of micro-scale forming.

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Local material symmetry group for first- and second-order strain gradient fluids

Mathematics and Mechanics of Solids ◽

10.1177/10812865211021640 ◽

2021 ◽

pp. 108128652110216

Author(s):

Victor A. Eremeyev

Keyword(s):

Symmetry Group ◽

Strain Gradient ◽

Constitutive Equations ◽

Strain Energy ◽

Mass Density ◽

Material Model ◽

Second Order ◽

Material Symmetry ◽

Local Material ◽

Current Mass

Using an unified approach based on the local material symmetry group introduced for general first- and second-order strain gradient elastic media, we analyze the constitutive equations of strain gradient fluids. For the strain gradient medium there exists a strain energy density dependent on first- and higher-order gradients of placement vector, whereas for fluids a strain energy depends on a current mass density and its gradients. Both models found applications to modeling of materials with complex inner structure such as beam-lattice metamaterials and fluids at small scales. The local material symmetry group is formed through such transformations of a reference placement which cannot be experimentally detected within the considered material model. We show that considering maximal symmetry group, i.e. material with strain energy that is independent of the choice of a reference placement, one comes to the constitutive equations of gradient fluids introduced independently on general strain gradient continua.

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Computational second-order homogenization of materials with effective anisotropic strain-gradient behavior

International Journal of Solids and Structures ◽

10.1016/j.ijsolstr.2020.01.006 ◽

2020 ◽

Vol 191-192 ◽

pp. 434-448 ◽

Cited By ~ 8

Author(s):

J. Yvonnet ◽

N. Auffray ◽

V. Monchiet

Keyword(s):

Strain Gradient ◽

Second Order ◽

Anisotropic Strain

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Novel analysis for nanoindentation size effect using strain gradient plasticity

Scripta Materialia ◽

10.1016/j.scriptamat.2005.07.027 ◽

2005 ◽

Vol 53 (10) ◽

pp. 1135-1139 ◽

Cited By ~ 15

Author(s):

Hunkee Lee ◽

Seonghyun Ko ◽

Junsoo Han ◽

Hyunchul Park ◽

Woonbong Hwang

Keyword(s):

Size Effect ◽

Strain Gradient ◽

Strain Gradient Plasticity ◽

Gradient Plasticity

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Numerical Studies on Size Effect Behaviors of Glassy Polymers Based on Strain Gradient Elastoviscoplastic Model

Journal of Applied Mechanics ◽

10.1115/1.4041765 ◽

2018 ◽

Vol 86 (2) ◽

Author(s):

Yujun Deng ◽

Jin Wang ◽

Peiyun Yi ◽

Linfa Peng ◽

Xinmin Lai ◽

...

Keyword(s):

Finite Element ◽

Size Effect ◽

Strain Gradient ◽

Simulation Models ◽

Theoretical Models ◽

Deformation Energy ◽

Glassy Polymers ◽

Traditional Theory ◽

Fe Model ◽

Processing Load

The improvement of the accuracy and efficiency of microforming process of polymers is of great significance to meet the miniaturization of polymeric components. When the nonuniform deformation is reduced to the microscopic scale, however, the mechanics of polymers shows a strong reinforcement behavior. Traditional theoretical models of polymers which have not considered material feature lengths are difficult to describe the size effect in micron scale, and the process simulation models based on the traditional theory could not provide effective and precise guidance for polymer microfabrication techniques. The work reported here proposed strategies to simulate size effect behaviors of glassy polymers in microforming process. First, the strain gradient elastoviscoplastic model was derived to describe the size affected behaviors of glassy polymers. Based on the proposed constitutive model, an eight-node finite element with the consideration of nodes' rotation was developed. Then, the proposed finite element method was verified by comparisons between experiments and simulations for both uniaxial compression and microbending. Finally, based on the FE model, under the consideration of the effect of rotation gradient, the strain distribution, the deformation energy, and the processing load were discussed. These strategies are immediately applicable to other wide-ranging classes of microforming process of glassy polymers, thereby foreshadowing their use in process optimizations of microfabrication of polymer components.

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