THE EXPERIMENTAL AND NUMERICAL STUDY OF THE FORCES DURING THE INCREMENTAL FORMING OF TITANIUM SHEETS

Incremental forming is a rapid prototyping process that allows sheets to be formed without using forming tools, using a numerically controlled machine tool. A wide variety of shapes can be generated with this process. The objective of this work is to study through experimental tests and numerical simulations the behavior of ASTM grade 2 titanium during incremental point forming (SPIF). A Spinner MFG850 machining center from ISET in JENDOUBA coupled to a multi-component force sensor FN7325 was used for the forming of thin sheets by this process. As the diameter of the punch and its incremental movement are parameters having a direct effect on the forming force, tests with diameters of the punches dp varying between 10 and 15 mm and various paths made up of circular movements in the horizontal plane have been carried out experimentally. Numerical simulation is carried out in large elastoplastic deformations with ABAQUS/explicit. Comparisons of the evolution of the forming force for different values of the diameter of the punch dp and of the displacement step ∆zare carried out.

Noncompressed cylindrical layer shock loading in anisothermic conditions

На примере нескольких задач о нагружении упруговязкопластического и термоупругого цилиндрических слоёв с предварительными деформациями показаны основные моменты, на которые следует обратить внимание при комплексном моделировании отклика на существенно нестационарное воздействие термоупругой несжимаемой среды с вязкопластическими свойствами. Отмечены нюансы, касающиеся употребления соотношений теории больших упругопластических деформаций, применения метода лучевых рядов и использования специальных схем численных расчётов. Представлены зависимости скачков температуры и добавочного давления на плоскополяризованных поверхностях сильного разрыва, определены скорости волн нагрузки и круговой поляризации. The main points witch should be paid attention of modeling the response of thermoelastic incompressible medium with viscoplastic properties to the essentially unsteady effect are shown by the example of several problems on loading elastoviscoplastic and thermoelastic cylindrical layers with preliminary deformations. Some remarks were noted regarding to the use of the relations of the theory of finite elastoplastic deformations, the ray series method application and special numerical calculation schemes. The dependencies of temperature and additional pressure breaks on plane-polarized strong discontinuities surfaces, loading and circular polarized waves velocities are determined.

Choice of materials properties and of shell molds structure by investment models

The paper presents a mathematical model optimizing the choice of material and morphological structure of the shell mold (SM), which has the highest resistance to cracking when pouring liquid metal into it. To solve this problem, the theory of small elastoplastic deformations and the heat equation, as well as proven numerical methods, were used. The objective function min – max was constructed from control variables characterizing the properties of the molding material of the shell. The process of heating an axisymmetric shell mold was considered when pouring liquid metal into it. The resistance of the shell form was estimated by the stresses arising in it. An algorithm for solving this problem was compiled. Using numerical schemes and program complexes developed in previous studies, an algorithm for solving the optimization problem was constructed and the values of control variables were found in which the shell mold does not break even in the presence of a rigid process – pouring steel into a cold shell mold. Analysis of the influence of weight of each of the found parameters on the value of the constructed objective function is given. Using a mathematical experiment, the morphological structure of the shell mold was studied. The shell mold of five layers is considered. The corrected system of equations makes it possible to take into account the properties of the layers made of different materials. Calculations were performed when the layer of the shell mold from material found by optimization occupies different positions in its cross section. In this case, the remaining layers of the mold are made of traditional ceramics. The optimal location of this layer was found. It is shown that the presence of several layers with the found properties does not affect the increase in crack resistance of the shell mold.

A.A. ILYUSHIN'S FINAL RELATION, ALTERNATIVE EQUIVALENT RELATIONS AND VERSIONS OF ITS APPROXIMATION IN PROBLEMS OF ELASTIC DEFORMATION OF PLATES AND SHELLS. PART 2: ALTERNATIVE EQUIVALENT RELATIONS OF A.A. ILYUSHIN

The finiterelationship between the forces and moments of plates and shells in the parametric form of the theory of small elastoplastic deformations is investigated of A.A. Ilyushin, to determine the load-bearing capacity of structures from a material without hardening. A geometric image of the exact yield surface in the space of generalized stresses is obtained. In the firstpart of the article the conclusion of the finalrelation is given. In the second and third parts, by introducing other parameters, alternative equivalent dependences of the finalrelationship have been developed and variants of its approximation for application in computational practice are considered. In the fourth part, additional properties of the finalrelationship are considered, the possibility and necessity of its use in problems of plastic deformation of plates and shells is shown.

On instability of constitutive models for isotropic elastic-perfectly plastic material behaviour at finite deformations

The main goal of this work is to test the possibility of a newly introduced constitutive law to model the behaviour of the isotropic elastic-perfectly plastic material which is exposed to large elastoplastic deformations. The proposed constitutive relation is based on the hypo-elastic relation and the inelastic INTERATOM model. The verification of the model is done by its implementation into the commercial software ABAQUS/Standard via the user subroutine UMAT. For that purpose, the large simple shear problem is studied where selected objective corotational rates, i.e. the logarithmic rate, the Jaumann rate and the Green-Naghdi rate, are individually implemented in the aforementioned constitutive relations. The obtained results are compared mutually and with the relevant literature. The proposed constitutive model is also used to test the behaviour of the part of a real engineering structure, i.e. a seismic isolator, in order to obtain the correct input data for further analysis of superstructure behaviour due to seismic excitation.

INTEGRATED STATE VARIABLE OF PERSISTENT CONTACT JOINTS OF PARTS OF CUTTERS WITH BLOCK-MODULAR STRUCTURE

The increase in the health of block cutters when achieving the operational characteristics of persistent contact joints of their elements is considered. The results of changes in the regulated parameters of the surface profile of the block housing using the saturation phenomenon are presented. The operational characteristics of block cutters change their values during operation, due to wear of frequently replaced parts (for example, 100 changes of cutting blocks correspond to the operating mode of contacting surfaces when normal pressure is applied at Pn = 10 MPa and relative speed of 10 m/min per 1 minute), as well as elastoplastic deformations of their elements. By these characteristics we mean the performance (rigidity of the structure, the flexibility of its parts, etc.) tools. Their change causes deviations of the specified properties of the surfaces of the parts of the cutters from the set values. Preset properties include the state of contact when irregularities in the profile of the deformable surface fill the depressions of the contacted surface. In order to minimize such deviations, it is necessary to achieve a state of the surface layer of contact pairs of elements so that these parameters stabilize (reach equilibrium values) during operation. For this, it is proposed to use the complex state variable of the surface layer for contact compounds with saturation.

A.A. ILYUSHIN S FINAL RELATION, ALTERNATIVE EQUIVALENT RELATIONS AND VERSIONS OF ITS APPROXIMATION IN PROBLEMS OF PLASTIC DEFORMATION OF PLATES AND SHELLS PART 1: A.A. ILYUSHIN S FINAL RELATION

The finite relationship between the forces and moments of plates and shells in the parametric form of the theory of small elastoplastic deformations is investigated of A.A. Ilyushin, to determine the load-bearing ca­pacity of structures from a material without hardening. A geometric image of the exact yield surface in the space of generalized stresses is obtained. In the first part of the article the conclusion of the final relation is given. In the second and third parts, by introducing other parameters, alternative equivalent dependences of the final rela­tionship have been developed and variants of its approximation for application in computational practice are considered. In the fourth part, additional properties of the final relationship are considered, the possibility and necessity of its use in problems of plastic deformation of plates and shells is shown.

Influence of the Elastoplastic Strain on Fatigue Durability Determined with the Use of the Spectral Method

The paper presents experimental static and fatigue tests results under random loading conditions for the bending of 0H18N9 steel. The experimental results were used in performing calculations, according to the theoretical assumptions of the spectral method of fatigue life assessment, including elastoplastic deformations. The presented solution extends the use of the spectral method for material fatigue life assessment, in terms of loading conditions, above Hooke’s law theorem. The work includes computational verification of the proposal to extend the applicability of the spectral method of determining fatigue life for the range of elastoplastic deformations. One of the aims of the proposed modification was to supplement the stress amplitudes used to calculate the probability density function of the power spectral density of the signal with correction, due to the plastic deformation and its use for notched elements. The authors have tested the method using four of the most popular probability density functions used in commercial software. The obtained results of comparisons between the experimental and calculation results show that the proposed algorithm, tested using the Dirlik, Benasciutti–Tovo, Lalanne, and Zhao–Baker models, does not overestimate fatigue life, which means that the calculations are on the safe side. The obtained results prove that the elastoplastic deformations can be applied within the frequency domain for fatigue life calculations.