Identification of the cap model of elastoplasticity of non-compact media under compressive mean stress

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Resumo

A program of basic tests and a method for identifying a three-dimensional model of the elastoplastic behavior of an isotropic porous or powdery consolidated medium experiencing arbitrary quasi-static loading under compressive medium stress at room temperature are proposed. The medium under consideration under compressive medium stresses is compacted with increasing effective stress, which leads to a nonlinear change in elastic modules, hardening and dilatancy (coupling of shear and volumetric components of deformations) in the yield region. To describe this behavior, the cap model of DiMaggio and Sandler, which is present in application software packages, is considered. As basic tests, the free and constrained compression of a cylindrical sample is considered according to a special program containing the stages of loading and unloading with a sequential increase in the amplitude voltage. Samples with a given porosity for free compression tests are manufactured using a tight compression test rig. According to the initial slope of the discharge curves, the values of the elastic modulus for free and constrained compression are determined in a certain range of porosity changes, according to which the Poisson’s ratio is determined. The five constants of the cap model are correctly and explicitly determined by the deformation curve of the material under constrained compression over a wide range of changes in axial deformation (and density), the flow stress under free compression of the sample at some density, and the assumption that the coefficient of transverse deformation in the yield region is equal to the Poisson’s ratio. The elastic and plastic constants were determined according to the test data of powdered paraffin grade T1 with a fraction of 0.63 mm. The corresponding model is applicable for numerical simulation of extrusion processes and mold filling for casting by melting models, processes for manufacturing blanks of non-melting polymer composites by powder technology, stamping sealing elements from flexible graphite and other pressure treatment processes of non-compact media.

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Sobre autores

A. Adamov

Institute of Continuous Media Mechanics of the Ural Branch of Russian Academy of Science

Autor responsável pela correspondência
Email: adamov@icmm.ru
Rússia, Perm

I. Keller

Institute of Continuous Media Mechanics of the Ural Branch of Russian Academy of Science

Email: kie@icmm.ru
Rússia, Perm

S. Zhilin

Institute of Mechanical Engineering and Metallurgy of the Far Eastern Branch of the Russian Academy of Sciences

Email: zhilin@imim.ru
Rússia, Komsomolsk-on-Amur

N. Bogdanova

Institute of Mechanical Engineering and Metallurgy of the Far Eastern Branch of the Russian Academy of Sciences

Email: joyful289@inbox.ru
Rússia, Komsomolsk-on-Amur

Bibliografia

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2. Fig. 1. Yield curve in the DiMaggio-Sandler model on the Buzhinsky diagram with the coefficient of adhesion equal to zero for two states of hardening and the direction of normals at the yield points under proportional loading

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3. Fig. 2a. Dependences of θ on R at v = 0.22

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4. Fig. 3. Test equipment for free (a) and constrained (b) compression

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5. Fig. 4a. Strain curves of samples under free compression. Stresses in MPa, density in g/cm3

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6. Fig. 5. Elastic moduli under free (red) and constrained (blue) compression depending on density. MPa is plotted along the vertical axis, g/cm3 along the horizontal axis.

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7. Fig. 6a. Strain curves under constrained compression: monotonic loading (blue - experiment, red - approximation). MPa are plotted along the vertical axis.

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8. Fig. 7. Curves of hardening under free (red) and constrained (blue) compression described by the model. MPa are plotted along the vertical axis.

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9. Fig. 8. Tangent of the angle of inclination of the direction of the deformation vector in the Buzhinsky plane depending on the ratio of compressive stresses under triaxial compression for two sets of constants (Table 2): the first is the red curve, the second is the blue curve

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10. Fig. 2b. Dependences of /f on R at v = 0.22

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11. Fig. 4b. Curves of unloading of samples under free compression. Stresses in MPa, density in g/cm3

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12. Fig. 6b. Strain curves under constrained compression: loading with unloading (blue - experiment, red - approximation). MPa are plotted along the vertical axis

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