Impact of the electromagnetic field pressure on the bending of high convex-side

A large number of aircraft parts made of sheet materials are used as flanges, common to such parts is the presence of walls, sides, and various elements that increase rigidity and reduce mass. These sheet parts are complex, mostly closed forms, which by plastic deformation methods require a rather complex stamping tools. Technological methods of manufacturing have certain disadvantages associated with the need to refine the shaping. In addition, the frequent updating of product designs and their constant improvement with a significant amount of experimental and small-scale production required the creation of technological methods that provide a significant reduction in terms of preparation. When punching sheet metal parts, in particular, by the pressure of magnetic-pulse field, the accuracy of shaping is mainly influenced by the shape of the flange in the process of deformation. At the final stage of shaping, an impact contact occurs between the flange of the part with the die or form-block. On impact, elastic unloading of the flange occurs due to the removal of inertial tensile stresses along the generatrix. After the impact contact, dynamic springing or rebound of the flange occurs.

Calculation of residual stresses in the state of elastic unloading of a preheated inhomogeneous thermoelastoplastic material under conditions of toroidal symmetry

Статья посвящена численному моделированию остаточных напряжений в неоднородном торе. Материал тора полагается термоупругопластическим. Расчет температурных напряжений происходит в рамках квазистатического приближения. Рассчитываются поля остаточных напряжений и деформаций. Приводятся численные результаты решения краевой задачи в тороидальных координатах. Рассматриваются случаи длинного тора и возможность аналитического приближения исходной краевой задачи. The article is devoted to the numerical simulation of residual stresses in an inhomogeneous torus. The torus material is assumed to be thermoelastoplastic. The calculation of temperature stresses is carried out within the framework of the quasi-static approximation. Residual stress and strain fields are calculated. Numerical results of solving the boundary value problem in toroidal coordinates are presented. The cases of a long torus and the possibility of an analytical approximation of the original boundary value problem are considered

Finite Plane Strain Bending under Tension of Isotropic and Kinematic Hardening Sheets

The present paper provides a semianalytic solution for finite plane strain bending under tension of an incompressible elastic/plastic sheet using a material model that combines isotropic and kinematic hardening. A numerical treatment is only necessary to solve transcendental equations and evaluate ordinary integrals. An arbitrary function of the equivalent plastic strain controls isotropic hardening, and Prager’s law describes kinematic hardening. In general, the sheet consists of one elastic and two plastic regions. The solution is valid if the size of each plastic region increases. Parameters involved in the constitutive equations determine which of the plastic regions reaches its maximum size. The thickness of the elastic region is quite narrow when the present solution breaks down. Elastic unloading is also considered. A numerical example illustrates the general solution assuming that the tensile force is given, including pure bending as a particular case. This numerical solution demonstrates a significant effect of the parameter involved in Prager’s law on the bending moment and the distribution of stresses at loading, but a small effect on the distribution of residual stresses after unloading. This parameter also affects the range of validity of the solution that predicts purely elastic unloading.

Finite Pure Plane Strain Bending of Inhomogeneous Anisotropic Sheets

The present paper concerns the general solution for finite plane strain pure bending of incompressible, orthotropic sheets. In contrast to available solutions, the new solution is valid for inhomogeneous distributions of plastic properties. The solution is semi-analytic. A numerical treatment is only necessary for solving transcendent equations and evaluating ordinary integrals. The solution’s starting point is a transformation between Eulerian and Lagrangian coordinates that is valid for a wide class of constitutive equations. The symmetric distribution relative to the center line of the sheet is separately treated where it is advantageous. It is shown that this type of symmetry simplifies the solution. Hill’s quadratic yield criterion is adopted. Both elastic/plastic and rigid/plastic solutions are derived. Elastic unloading is also considered, and it is shown that reverse plastic yielding occurs at a relatively large inside radius. An illustrative example uses real experimental data. The distribution of plastic properties is symmetric in this example. It is shown that the difference between the elastic/plastic and rigid/plastic solutions is negligible, except at the very beginning of the process. However, the rigid/plastic solution is much simpler and, therefore, can be recommended for practical use at large strains, including calculating the residual stresses.

Thermoelastic plastic deformation of a functional gradient material under conditions of central symmetry

В работе рассматривается ряд краевых задач теории термоупругопластического деформирования материала в условиях тороидальной симметрии. Рассмотрен процесс упругой разгрузки предварительно нагретого объекта. Рассчитаны поля остаточных напряжений и перемещений. Получены точные формулы для аналитического решения поставленной краевой задачи A number of boundary value problems of the theory of thermoelastoplastic deformation of a material under conditions of toroidal symmetry are presented. The process of elastic unloading of a heated object is considered. The fields of residual stresses and displacements are calculated. Exact formulas are obtained for the analytical solution of the stated boundary value problem.

A comparative study of the dynamic fragmentation of non-linear elastic and elasto-plastic rings: the roles of stored elastic energy and plastic dissipation

We develop a comparative analysis of the processes of dynamic necking and fragmentation in elasto-plastic and hyperelastic ductile rings subjected to rapid radial expansion. For that purpose, ?nite element simulationshave been carried out using the commercial code ABAQUS/Explicit. Expanding velocities which range between25 m=s and 600 m=s have been investigated. The elasto-plastic material and the hyperelastic material are modelled with constitutive equations which provide nearly the same stress-strain response during monotonic uniaxial tensile loading, and fracture is assumed to occur at the same level of deformation energy. The computations have revealed that, while the number of necks nucleated in the elasto-plastic and hyperelastic rings is similar, the mechanisms which control their development are significantly different. In the elasto-plastic rings several necks are arrested due to the stress waves which travel the specimen after the localization process has started, and thus the number of fractures in the ring is significantly lower than the number of incepted necks. On the contrary, these stress waves do not stop the development of any neck in the hyperelastic rings. The elastic energy released from the sections of the ring which are unloading during the localization processfuels the development of the necks. Hence, for the whole range of investigated velocities, the proportion of necks that develop into fracture sites is much greater for the hyperelastic rings than for the elasto-plastic ones. The comparison between the numerical results obtained for both materials brings to light the roles of elastic unloading and plastic dissipation in multiple necking and fragmentation processes.

Influence of the Replacement of the Actual Plastic Orthotropy with Various Approximations of Normal Anisotropy on Residual Stresses and Strains in a Thin Disk Subjected to External Pressure

Plastic anisotropy is very common to metallic materials. This property may significantly affect the performance of structures. However, the actual orthotropic yield criterion is often replaced with a criterion based on the assumption of normal anisotropy. The present paper aims to reveal the influence of this replacement on the distribution of strains and residual strains in a thin hollow disk under plane stress conditions. The boundary-value problem is intentionally formulated such that it is possible to obtain an exact semi-analytical solution without relaxing the boundary conditions. It is assumed that the disk is loaded by external pressure, followed by elastic unloading. The comparative analysis of the distributions of residual strains shows a significant deviation of the distribution resulting from the solutions based on the assumption of normal anisotropy from the distribution found using the actual orthotropic yield criterion. This finding shows that replacing the actual orthotropic yield criterion with the assumption of normal anisotropy may result in very inaccurate predictions. The type of anisotropy accepted is of practical importance because it usually results from such processes as drawing end extrusion with an axis of symmetry.

Design of a disk-mandrel assembly for achieving rotational autofrettage in the disk

Rotational autofrettage is a recently proposed method to induce beneficial residual stresses in axisymmetric hollow cylindrical bodies. The feasibility of the process has been studied for both disks and cylinders used in many engineering applications. The earlier analyses of rotational autofrettage of disks are based on certain assumptions. One of the crucial assumptions is the free rotation of the disk. However, the free rotation of the disk is practically difficult. In practice, it is feasible to rotate the disk by shrink-fitting it over a solid cylindrical mandrel. In view of this, a design of a disk-mandrel assembly for achieving rotational autofrettage in disks is proposed in this article. The main aim of the design is to obtain appropriate values of the disk-mandrel interference and the rotational speed of the assembly to prevent the loss of contact of the disk with the mandrel during rotation. The critical speeds corresponding to the yield onset, contact separation and the full plastic deformation of the disk are obtained as a function of shrink interference. The safe operating design parameters can be decided by plotting the critical speeds with varying interference values. A detailed stress analysis during elastic-plastic loading of the assembly followed by the analysis of residual stresses in the assembly after unloading is presented. The analysis is based on the plane stress assumption, Tresca yield criterion and elastic unloading. The analysis is validated with a finite element method model in ABAQUS. The proposed design is illustrated through the numerical example of an ASTM A723 disk-mandrel assembly to achieve rotational autofrettage in the disk. With a small overstrain level of 17.5% in the disk, a large magnitude of compressive residual stress, viz., 0.52 times the yield stress, is induced.

The Influence of Thermomechanical Coupling on the Behaviour of Athick-Walled Metallic Tube Subjected to Internal Pressure

In this study, the influence of thermomechanical coupling effect - the effect of thermal expansion due to dissipation of the energy of plastic deformation, with and without taking into account the stored energy of plastic deformation (SEPD) for the distribution of stresses, strains, temperature, the applied pressure and the residual stresses is examined. The residual stresses remain in a thick-walled tube (a cylindrical thick-walled tank) after removing the internal pressure in the process of purely elastic unloading. The analysis is made on the example of an analitycal solution for a thick-walled tube subjected to a quasistatically increasing internal pressure for the case of adiabatic processes (without heat flow). Since the loading with internal pressure is quasi-static (monotonic), then neglecting the process of heat flow can lead to some different results in calculated stresses, deformations, temperature, internal pressure and residual stresses. The calculations for isothermal type of processes of deformations (without heat or ideal cooling) are also performed for the estimation of these differences. The results calculated for the process with heat flow should be intermediate between the values obtained for isothermal and adiabatic processes.