ON FINITE ELEMENT FORMULATIONS FOR LARGE ELASTIC–PLASTIC DEFORMATIONS

Author(s):  
A. NEEDLEMAN
Symmetry ◽  
2020 ◽  
Vol 13 (1) ◽  
pp. 39
Author(s):  
Łukasz Warguła ◽  
Dominik Wojtkowiak ◽  
Mateusz Kukla ◽  
Krzysztof Talaśka

This article presents the results of experimental research on the mechanical properties of pine wood (Pinus L. Sp. Pl. 1000. 1753). In the course of the research process, stress-strain curves were determined for cases of tensile, compression and shear of standardized shapes samples. The collected data set was used to determine several material constants such as: modulus of elasticity, shear modulus or yield point. The aim of the research was to determine the material properties necessary to develop the model used in the finite element analysis (FEM), which demonstrates the symmetrical nature of the stress distribution in the sample. This model will be used to analyze the process of grinding wood base materials in terms of the peak cutting force estimation and the tool geometry influence determination. The main purpose of the developed model will be to determine the maximum stress value necessary to estimate the destructive force for the tested wood sample. The tests were carried out for timber of around 8.74% and 19.9% moisture content (MC). Significant differences were found between the mechanical properties of wood depending on moisture content and the direction of the applied force depending on the arrangement of wood fibers. Unlike other studies in the literature, this one relates to all three stress states (tensile, compression and shear) in all significant directions (anatomical). To verify the usability of the determined mechanical parameters of wood, all three strength tests (tensile, compression and shear) were mapped in the FEM analysis. The accuracy of the model in determining the maximum destructive force of the material is equal to the average 8% (for tensile testing 14%, compression 2.5%, shear 6.5%), while the average coverage of the FEM characteristic with the results of the strength test in the field of elastic-plastic deformations with the adopted ±15% error overlap on average by about 77%. The analyses were performed in the ABAQUS/Standard 2020 program in the field of elastic-plastic deformations. Research with the use of numerical models after extension with a damage model will enable the design of energy-saving and durable grinding machines.


Vestnik MGSU ◽  
2021 ◽  
pp. 294-305
Author(s):  
Evgeny A. Moiseichik ◽  
Yuri V. Vasilevich ◽  
Aliaksandr E. Moiseichik ◽  
Aliaksei M. Yaznevich ◽  
Aliaksandr A. Yakauleu

Introduction. In the transverse and longitudinal sections of the rods with a periodic profile, there are layers with different structural and phase states, physical and mechanical characteristics, stress state and resistance to external influences. The appearance of plastic deformations in the bases of the depressions and other defects of a periodic profile during stre­tching of the rods leads to a decrease in the resistance to corrosion damage due to the occurrence of galvanic pairs between inhomogeneous sections of the rod. This makes the computational and experimental studies of the deformed state of such rods under tension urgent. Materials and methods. The finite element modeling of the deformation process during the elastic-plastic work of steel was carried out using the ANSYS software complex and solid models of the rods under study. Experimental tests of the samples were carried out using an R-50 tensile testing machine with the recording of a load-elongation diagram in accordance with the requirements of GOST 1497. The process of deformation of the samples was displayed by photographic recording. After the destruction of the samples, the geometric dimensions (lengths, changes in cross-sections) were measured, the typical types of samples and their fragments, and fractures were photographed. Results. On experimental and finite-element models, it was found that during elastic-plastic deformation of steel rods in dangerous sections, a change in the angle of inclination of the banks of periodic protrusions (undercuts) affects the volume of plastically deformable material at the base of the undercuts. Such an analysis of the models in the limiting state has shown that the volume of the plastically deformed material is significantly reduced at the angles of the protrusions at their bases with the axis of the rod close to 900. The calculation established that the plastically deformed area at the base of sharp undercuts is more than a hundred times smaller than the corresponding volume at the base of the gently sloping undercuts. In samples with a group of protrusions, constraint of plastic deformations at the base occurs only for protrusions, the width of which is comparable to the diameter of the rod in weakened sections. The greatest development of equivalent plastic deformations is observed at the base between narrow projections. Damage to the outer layers of quasi-composite rods with a periodic profile causes significant changes in the stress-strain state of the rods under tension. Conclusions. The finite element modeling of the tensile work of steel rods with a periodic profile with a quasi-composite structure is a complex multifactorial problem. Plastic deformations develop in the depressions of the periodic profile. At the same time, undeformed areas remain in the metal of the protrusions. These zones have different potentials and between them the occurrence of internal galvanic currents is possible, leading to the acceleration of corrosion processes.


2020 ◽  
Vol 17 ◽  
pp. 00199
Author(s):  
Arsen Dzhabrailov ◽  
Anatoly Nikolaev ◽  
Natalya Gureeva

The article describes an algorithm for calculating an axisymmetrically loaded shell structure with a branching meridian, taking into account elastic-plastic deformations when loading based on the deformation theory of plasticity without assuming that the material is incompressible during plastic deformations. The correct relations which determine the static conjugation conditions of several revolution shells in the joint assembly are used. A comparative analysis of finite element solutions is presented for various options plasticity matrix development at the loading stage.


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