Analysis of the Failure Process of Elements Subjected to Monotonic and Cyclic Loading Using the Wierzbicki–Bai Model

This article presents the results of a simulation in which smooth cylindrical and ring-notched samples were subjected to monotonic and fatigue loads in an ultra-short-life range, made of Inconel 718 super alloy. The samples displayed different behaviors as a result of different geometries that introduced varying levels of stress triaxiality and loading methods. The simulations used the Wierzbicki–Bai model, which took into account the influence of stress tensors and stress-deviator invariants on the behavior of the material. The difference in the behaviors of the smoothed and notched specimens subjected to tensile and fatigue loads were identified and described. The numerical results were qualitatively supported by the results of the experiments presented in the literature.

VOID EVOLUTION BEHAVIOR AND CLOSURE CRITERION INSIDE LARGE SHAFT FORGINGS DURING A FORGING PROCESS

In this study, the effects of different void positions, void shapes and sizes on the evolution of voids were discussed in detail using experiments and simulations. The results show that the influence of the void size on the void closure can be ignored, while the void position and void shape have a great influence on the closure of a void. Considering the complexity of the void-shape change in a forging process, we proposed a quantitative expression of the void-shape coefficient, which is affected by the effective stress and effective strain. Meanwhile, the void-shape evaluation parameter, defined as a function of the stress deviator, effective strain and effective stress, was proposed to describe the changes in the void aspect ratio. Finally, WHF (wide die heavy blow) forging experiments were conducted using a 5MN hydraulic press to verify the numerical-simulation results. Based on the experimental and simulation results, a new mathematical model for void-closure determination was established during a forging process of large shaft forgings. The experimental results were consistent with the simulation results, showing that the void-closure model can accurately determine whether a void is closed or not.

Thick-walled spherical shell problem

Introduction. Cylindrical and spherical shells are extensively used in engineering. They face internal and/or external pressure and heat. Stresses and strains distribution in elastoplastic shells has been studied by many scientists. Numerous works involve the use of the von Mises yield conditions, maximum shear stress, maximum reduced stress. These condi- tions do not include the dependence on the first invariant of the stress tensor and the sign of the third invariant of the stress deviator. In some cases, it is possible to obtain numerical-analytical solutions for stresses, displacements and de- formations for bodies with spherical and cylindrical symmetry under axisymmetric thermal and force action.Materials and Methods. The problem on the state of a thick-walled elastoplastic shell is solved within the framework of the theory of small deformations. A plasticity condition is proposed, which takes into account the dependence of the stress tensor on three independent invariants, and also considers the sign of the third invariant of the stress deviator and translational hardening of the material. A disconnected thermoelastoplastic problem is being solved. To estimate the stresses in the region of the elastic state of a spherical shell, an equivalent stress is introduced, which is similar to the selected plasticity function. The construction of the stress vector hodograph is used as a method for verification of the stress state.Results. The problem has an analytical solution for linear plasticity functions. A solution is obtained when the strength- ening of the material is taken into account. Analytical and graphical relationships between the parameters of external action for the elastic or elastoplastic states of the sphere are determined. For a combined load, variants are possible when the plastic region is generated at the inner and outer boundaries of the sphere or between these boundaries.Discussion and Conclusions. The calculation results have shown that taking into account the plastic compressibility and the dependence of the plastic limit on temperature can have a significant impact on the stress and strain state of a hollow sphere. In this case, taking into account the first invariant of the stress tensor under the plasticity condition leads to the fact that not only the pressure drop between the outer and inner boundaries of the spherical shell, but the pressure values at these boundaries, can vary within a limited range. In this formulation of the problem, when there is only thermal action, the hollow sphere does not completely pass into the plastic state. The research results provide predicting the behavior of an object (a hollow sphere) that experiences centrally symmetric distributed power and thermal external influences.

Strength Characteristics of Clay–Rubber Waste Mixtures in Low-Frequency Cyclic Triaxial Tests

This paper presents the results of consolidated and undrained (CU) triaxial cyclic tests related to the influence of tire waste addition on the strength characteristics of two different soils from Southern Poland: unswelling kaolin and swelling red clay. The test procedure included the normally consolidated remolded specimens prepared from pure red clay (RC) and kaolin (K) and their mixtures with two different fractions of shredded rubber powder (P) and granulate (G) in 5%, 10%, and 25% mass proportions. All samples were subjected to low-frequency cyclic loading carried out with a constant stress amplitude. Analysis of the results includes consideration of the effect of rubber additive and number of load cycles on the development of excess pore pressure and axial strain during the cyclic load operation and on the maximum stress deviator value. A general decrease in the shear strength due to the cyclic load operation was observed, and various effects of shear strength depended on the mixture content and size of the rubber waste particles. In general, the use of soil–rubber mixtures, especially for expansive soils and powder, should be treated with caution for cyclic loading.

Effect of the third invariant on the formation of necking instabilities in ductile plates subjected to plane strain tension

In this paper, we have investigated the effect of the third invariant of the stress deviator on the formation of necking instabilities in isotropic metallic plates subjected to plane strain tension. For that purpose, we have performed finite element calculations and linear stability analysis for initial equivalent strain rates ranging from 10^−4 s−1 to 8 · 10^4 s−1. The plastic behavior of the material has been escribed with the isotropic Drucker yield criterion [11], which depends on both the second and third invariant of the stress deviator, and a parameter c which determines the ratio between the yield stresses in uniaxial tension and in pure shear \sigma_T /\tau_Y . For c = 0, Drucker yield criterion [11] reduces to the von Mises yield criterion [32] while for c = 81/66, the Hershey-Hosford (m = 6) yield criterion [19, 22] is recovered. The results obtained with both finite element calculations and linear stability analysis show the same overall trends and there is also quantitative agreement for most of the loading rates considered. In the quasi-static regime, while the specimen elongation when necking occurs is virtually insensitive to the value of the parameter c, both finite element results and analytical calculations using Considère criterion [10] show that the necking strain increases as the parameter c decreases, bringing out the effect of the third invariant of the stress deviator on the formation of quasi-static necks. In contrast, at high initial equivalent strain rates, when the influence of inertia on the necking process becomes important, both finite element simulations and linear stability analysis show that the effect of the third invariant is reversed, notably for long necking wavelengths, with the specimen elongation when necking occurs increasing as the parameter c increases, and the necking strain decreasing as the parameter c decreases.

EVALUATION OF THE RESOURCE CHARACTERISTICS OF POLYCRYSTALLINE STRUCTURAL ALLOYS UNDER CYCLIC THERMOMECHANICAL LOADING

The main physical regularities of complex thermoviscoplastic deformation and accumulation of damage in structural materials (metals and their alloys) under various modes of cyclic combined thermomechanical loading and mathematical models of these processes are considered. A mathematical model of the mechanics of a damaged medium has been developed, which makes it possible to simulate the cyclic viscoelastoplastic behavior and determine the resource characteristics of polycrystalline structural alloys under the combined action of degradation mechanisms that combine material fatigue and creep. The model is based on the joint integration of equations describing the kinetics of the stress-strain state and damage accumulation processes. The final relation to the model is the strength criterion, the fulfillment of which corresponds to the formation of a macrocrack. The plasticity equations are based on the basic principles of the flow theory. To describe the creep process in the stress space, a family of equipotential creep surfaces of the corresponding radius and having a common center is introduced. The relationship between the creep equations and the thermoplasticity equations describing “instantaneous” plastic deformations is carried out at the loading stage through the stress deviator and the corresponding algorithm for determining and at the loading stage by means of certain relationships between “temporary” and “instantaneous” scalar and tensor quantities. At the stage of development of damage scattered throughout the volume, the effect of damage on the physical and mechanical characteristics of the material is observed. This influence can be taken into account by introducing effective stresses. In the general case, stresses, plastic strains, and creep strains are determined by integrating the thermal creep equations by the four-point Runge-Kutta method with correction of the stress deviator and subsequent determination of stresses according to the thermoplasticity equations, taking into account the average creep strain rate at a new time. The relationships that simulate the accumulation of damage are based on the energy approach to determining the resource characteristics. The kinetics of fatigue damage accumulation is based on the introduction of a scalar parameter of damage to a structural material and a unified model form for representing the degradation mechanism under fatigue and creep conditions. The influence of scattered damage on the physical and mechanical characteristics of the material is taken into account by introducing effective stresses. The results of numerical simulation of cyclic thermoplastic deformation and accumulation of fatigue damage in heat-resistant alloys (Haynes188) under combined thermomechanical loading are presented. Particular attention is paid to the issues of modeling the processes of cyclic thermoplastic deformation and the accumulation of fatigue damage for complex deformation processes accompanied by the rotation of the main areas of stress and strain tensors.

Metal structure prediction in cross-wedge rolling processes

A method of computer prediction of the size of metal grains, their disorientation, grain boundaries and dislocation density, depending on the modes of cross-wedge rolling, is considered. The regularities of the formation of the parameters of the metal structure depending on the stress state are revealed by methods of computer simulation. The stress state is described by two parameters: the average stress and the parameter of the third invariant of the stress deviator. The effect of the stress state in the deformation zone on the metal structure parameters was determined for the first time. The new method allows improvement of the quality of products by computer optimization of rolling modes. The results of determining the metal structure and parameters of the stress-strain state in the deformation zone during hot rolling of the water pump shaft of steel 45 are presented. The verification and analysis of the data of virtual experiments on the formation of the structure of structural steels in the processes of cross-wedge rolling are carried out. To analyze the output data of the simulation, the parameters for predicting the calculation of grain boundaries and grain size were used. The created computer model for predicting the characteristics of metal structures, depending on the modes of plastic deformation, provides, at minimal cost and without carrying out field experiments, finding the optimal thermodynamic and stress-strain modes of plastic flow of metal, which guarantee the highest operational properties of the products obtained.

Influence of different loading paths on the multiaxial fatigue behavior of 2024 aluminum alloy under the same amplitude values of the second invariant of the stress deviator tensor

2024 aluminum alloy is a common aeronautic material. During operations, construction elements made of aluminum alloys undertake complex cyclic loadings. Therefore, it is important to estimate the influence of these loadings on the durability of the material. Hereby, multiaxial fatigue tests with the same amplitude values of the second invariant of the stress deviator tensor are conducted, and test data are analyzed. The modified Sines method is utilized to predict fatigue experimental data. Results show that the model is accurate enough to fatigue behavior prediction of 2024 aluminum alloy.