Bilinear Plastic Research Articles

Comparison of wheel wear models for the simulation of railway wheels subjected to plastic deformation

In this paper, using bi-linear, multi-linear, and non-linear plastic strain models, the applicability of four typical wear models is studied to assess rail wheel wear, which include the Archard, Pearce, Usfd, and Braghin models. Firstly, the instantaneous wear of four models is calculated within a contact area, and an equivalent wear coefficient is used to express the proportional relationship between wear models quantitatively. A uniform expression of the wear models has been derived analytically, and the instantaneous wear rate based on the different wear models is evaluated under harmonic excitation. The rapid wear rate fluctuation for different wear models is then calculated under harmonic excitation, and the influence of speed on the wear fluctuation is studied. The results show that the four wear models have a similar result in calculating the instantaneous wear. In addition, the frequency characteristics of excitation can be accurately reflected in a general sense, and the degree of fluctuation is similar. However, the wear model does not fit the bi-linear plastic model well. It is observed that speed significantly affects the frequency and amplitude of wear fluctuation, the wear model can adapt well to the plastic model at high speed, and the wear depth increases with an increase in speed. This work has demonstrated that the wear model has poor adaptability with the bi-linear plastic model but can be successfully combined with multi-linear and non-linear plastic models to predict rail wheel wear during plastic deformation.

The Effect of Surface Defects Interaction on the Strength of a Pressurised Spherical Shell

Spherical pressure vessels are widely used in various industrial processes, for storage and transportation of compressed gases, liquids and other substances. Since most pressure vessels are made of metals, they are often prone to pitting corrosion. To assess and ensure long-term reliability and strength of the structure, it is necessary to analyse stresses concentrated in the vicinity of defects. The present paper focuses on the effect of interaction of neighbouring defects on the stress state of the pressure vessel. А spherical shell with multiple surface defects, under internal pressure is considered. The defects are assumed to have a shape of nearly hemispherical notches of equal sizes with the depth equal to half of its curvature radius. Different numbers of notches with their random arrangement along the equator of the shell are considered. The stress state of the shell is analysed by finite element method using the ANSYS Workbench package. Calculations are made within the frame-work of bilinear plasticity hardening model and linearly elastic model. The effect of the distance between neighbouring defects on the growth of stresses in the vessel for various numbers of random and periodical defects is investigated. The maximum values of stresses were observed in the zones of sharp edges formed between the notches, which slightly overlap or almost touch one another. It is shown that the distance between neighbouring defects is an important but not the only factor affecting the growth of maximum stresses in the pressure vessel weakened by defects.

Thermal in-plane stability of concrete-filled steel tubular arches

This paper analytically and numerically investigates the pre-buckling response and in-plane stability boundaries of circular concrete-filled steel tubular (CFST) arches subjected to combined thermal and mechanical loading. The governing non-linear equations of equilibrium are obtained using energy methods and both elastic and inelastic material behaviour is considered. A novel mechanically derived non-discretisation numerical method is proposed for the pre-buckling analysis. The stress-strain relation of the confining steel tube is described using a bi-linear plasticity model, and an inelastic material model is adopted for the concrete core which considers the effects of confinement and transient thermal strain. The result is a system of first-order differential equations which can be numerically solved with known boundary conditions including fixed ends, pinned ends or crowned-pinned cases. Closed-form solutions are presented for the elastic anti-symmetric bifurcation loads, whilst the inelastic anti-symmetric buckling strength was studied using finite element (FE) analysis. The FE model is verified by comparison to the derived analytical and numerical models which show a high level of agreement. Additionally, a sensitivity analysis is conducted which explores the influence of the constitutive material law for the concrete core and contact model for the steel-concrete interface on critical buckling loads.

FE Modeling of Circular, Elliptic, and Triangular Isolated Slabs With a Continuous Damage Model

The nonlinear behaviour of reinforced concrete circular, elliptic and triangular isolated slabs was studied using computational mechanics. Concrete was modelled with a damage model which includes softening, while the behaviour of the reinforcing steel was modelled with a 1D bilinear plasticity model. The constitutive models and the finite element method were validated by comparing the computed numerical results with the experimental results of a rectangular slab reported in the scientific literature. The coefficient method is proposed for its simplicity to calculate design bending moments in slabs with circular, elliptic and triangular geometries. These coefficients were computed from the FE analysis. The layout of steel reinforcement is proposed, particularly lengths of zones for positive and negative moments, respectively. The crack paths are showed, which are depending on the boundary conditions, acting loads and geometry of the slabs.

Constant‐ductility inelastic displacement ratios for displacement‐based seismic design of self‐centering structures

SummaryThis paper focuses on constant‐ductility inelastic displacement ratios of self‐centering single‐degree‐of‐freedom (SDF) systems with two different levels of energy dissipation capacity, in the presence of 5% viscous damping ratio. A statistical analysis is developed considering an earthquake database composed of 228 ground motions recorded in California with magnitudes greater than six and organized for NEHRP soil class, ground motion duration, and peak ground acceleration. The response of self‐centering SDF systems with large variability of initial periods, ductility levels, and postyield stiffness ratios is investigated and compared with the responses of SDF systems with bilinear plastic, Clough, and Takeda hysteresis. The inelastic demand variation with soil class, initial period, postyield stiffness ratio, unloading stiffness degradation, ductility level, and hysteretic behavior is highlighted. Simple and conservative analytical estimates of constant‐ductility inelastic displacement ratios for mean and 90th percentile values in terms of initial period, ductility level, and postyield stiffness ratio are proposed to allow the extension of the Displacement‐Based Design via Inelastic Displacement Ratio (CμDBD) to self‐centering structural systems.

Numerical Modelling of Seismic Behavior of Retrofitted RC Beam-Column Joints

In the event of an earthquake, the beam-column joints in the reinforced concrete moment-resisting frame structures are affected by a high level of deformations and stresses. Due to these deformations and stresses, the joint can be damaged and even fractured in some cases. The failure of the beam-column joint can cause the building to collapse. In recent years, particular attention has been paid to strengthening joints in the substandard RC buildings. In this paper, the beam-column joint is investigated considering the nonlinear behavior for concrete and steel. For concrete, the damage plasticity model and for reinforcing steels bilinear plasticity model is used. Several examples of tested joints in the technical literature have been modeled before and after strengthening, then numerical and experimental results are compared. Seismic performance of joints has also been studied. The results of this research show good agreement between the results of finite element model and experimental results. Moreover, the retrofitting method have shown could improves the seismic performance of the joint.

A Computational Study of the Effects of Strain Hardening in Micro-asperity Friction Models

In this paper, we study the effects of plastic strain hardening and damage on the friction response of a surface at the microscopic and macroscopic scales. At the microscale, the role played by hardening and damage in the response of a single asperity is determined using three-dimensional finite element analysis. The sample materials for the asperity are Al 2024-T3 and Ti6Al4V, which are modeled as isotropic bilinear plastic and include Johnson–Cook damage. The friction responses for two different damage models (Johnson–Cook and Bao–Wierzbicki) are also compared for the perfectly plastic case. In the simulations the asperity is initially compressed in order to induce a normal preload and then sheared to study the friction response. Then a statistical homogenization approach is used to propagate these effects to the macroscale. Toward this end, the surface is modeled as an isotropic Gaussian random process. The computed microscale responses are parameterized, and the overall macroscopic response of the surface is determined. Results of this study show that, at the microscale, strain hardening increases the coefficient of friction, particularly at low interference values. Similarly, material response plays a significant role at the macroscale over a wide range of normal force values.

Cyclic plasticity using Prager’s translation rule and both nonlinear kinematic and isotropic hardening: Theory, validation and algorithmic implementation

Finite element analysis of structures under elasto-plastic nonproportional cyclic loadings is useful in seismic engineering, fatigue analysis and ductile fracture. Usual models with nonlinear stress–strain curves in cyclic behavior are based on Mróz multisurface plasticity, bounding surface models or models derived from the Armstrong–Frederick rule. These models depart from the associative Prager’s rule with the main purpose of modeling aspects of cyclic nonlinear hardening. In this paper we develop a model for cyclic plasticity within the framework of the associative classical plasticity theory using Prager’s rule accounting for anisotropic nonlinear kinematic hardening coupled with nonlinear isotropic hardening. We include the validation of the theory against several uniaxial and multiaxial cyclic experiments and an efficient fully implicit radial return algorithm. The parameters of the model are obtained directly by a discretization of the uniaxial stress–strain behavior. Remarkably, both the presented theory and the computational algorithm automatically recover classical bi-linear plasticity and the Krieg and Key algorithm if the user-prescribed stress–strain curve is bilinear.

Numerical simulations of Taylor anvil-on-rod impact tests using classical and new approaches

Plastic deformation of samples undergoing Taylor anvil-on-rod impact test is simulated utilising finite element method (FEM). Classical (bilinear plasticity using von Mises stress, Johnson-Cook plasticity model) plasticity models and a new plasticity model based on notion of incubation time of plastic flow initiation are employed to model dynamic deformation of tested samples. In order to verify the obtained solutions, the received predictions are compared to available experimental measurements of deformed sample shapes for two different materials (copper, aluminium) and various initial sample velocities. It is shown that bilinear von Mises plasticity model is not able to provide satisfactory coincidence between the shape of the sample boundary received in numerical simulations and in real experimental conditions. At the same time, models accounting for rate dependency of deformation are providing much more accurate results. Substitution of the concept of "dynamic" yielding stress of a material, depending on the rate of deformation by characteristic time of plastic stress relaxation provides a powerful tool for robust prediction of plastic deformation for a wide range of strain rates. The parameter of the characteristic relaxation time has a clear physical interpretation and theoretically can be evaluated from microstructural studies.

In-situ high temperature stress analysis of Ti(C,N) coatings on functionally graded cemented carbides by energy dispersive synchrotron X-ray diffraction

We report on in-situ high temperature X-ray thermal stress analysis of chemically graded Ti(C,N) coatings deposited on functionally graded cemented carbide substrates by chemical vapor deposition. The in-situ analyses were performed by energy dispersive X-ray diffraction using synchrotron radiation. The samples were subjected to one individual thermal cycle from room temperature to 800°C and cooled down to room temperature again. The stresses were determined using the sin2ψ method in the Ψ geometry combined with scattering vector measurements in order to unravel the compositional influences on the lattice strain distributions. It was found that the Ti(C,N) thin film presents a cycling residual stress behavior (tensile–compressive–tensile) connected to the temperature cycle. If top-blasting is applied on the thin film layer after the coating process, compressive stresses are generated. These compressive stresses induced by top-blasting are partially released after the high temperature thermal cycle. The functionalization of the cemented carbide substrate influences the level of stresses developed in the coating. The stress behavior as a function of temperature is discussed with the support of finite element modeling by introducing a bi-linear plasticity model to calculate strain relationships which is in agreement with the synchrotron measurements.

Coeficientes de diseño y trayectorias de agrietamiento de losas aisladas circulares, elípticas y triangulares

Design coefficients and cracking paths for circular, elliptical and triangular labsare obtained by damage mechanics were determined. The nonlinear behavior of the reinforced concrete was simulated with a damage model which considers softening, whereas the behavior of the reinforcing steel was modeling with a bilinear plasticity model which has a Von Mises yield surface. The constitutive models and the finite element method were validated by comparing the computed numerical results with the experimental results of a rectangular slab reported in the scientific literature. The distribution of the reinforcing steel was proposed based on linear elastic analysis with plate elements. The coefficients were computed with elastic and nonlinear analyses, noticing that the last has a variation because of the stress redistribution. The crack paths are shown, which are dependent on the boundary conditions. The coefficients and the distribution of the reinforcing steel are a base on the regulation for the analysis and design of slabs with this kind of geometry.

Elastic and elastic-plastic finite element analysis of hollow tubes with axisymmetric internal projections under combined axial and pressure loading

This paper discusses the behaviour of hollow tubes with axisymmetric internal projections subjected to combined axial and internal pressure loading. Predictions from an extensive elastic and elastic-plastic finite element analysis are presented for a typical geometry and a range of loading combinations, using a simplified bilinear elastic-perfectly plastic material model. The axial loading case, previously analysed, is extended to cover the additional effect of internal pressure. All the predicted stress and strain data are found to depend on the applied loading conditions. The results are normalized with respect to material properties and can therefore be applied to geometrically similar components made from other materials, which can be represented by the same material models.

Determination of Young's modulus by spherical indentation

In this paper we consider elastic plastic materials that are tested by spherical indentation. Finite element calculations, which take into account nonlinear geometry properties, are carried out in order to determine the influence of the plastic history on the unloading response of the material. Two different iterative methods are proposed for determining Young's modulus under the assumption of a bilinear plasticity law. The first method deals with loading and unloading parts of the indentation test, whereas the second one deals only with unloading parts of the indentation test.

Analysis of welding-induced residual stresses with the ADINA system

The welding-induced residual stresses analysis procedure (WIRSAP), based on the ADINA system of nonlinear finite element software, is described and the results of several WIRSAP analyses are discussed. Several two-dimensional (2D) axisymmetric WIRSAP analyses have been performed for pipe girth welds and for several multi-pass girth-like welds attaching small nozzles to large, thick-walled pressure vessels. The analytical methodology follows closely the basic techniques outlined by Rybicki et al., enhanced by the use of several specialized modeling techniques available in the ADINA system. For example, the element birth option is used to simulate the addition of weld metal, and the mixed pressure/ displacement element formulation is used, in conjunction with the temperature-dependent bi-linear plasticity material model. Some of the welds analyzed involve backing rings, which were subsequently ‘machined off’ via use of the element death option. The auto-time-stepping algorithm and the matrix update iteration scheme are used in the structural solutions. WIRSAP involves, in general, a pass-by-pass analysis of the uncoupled thermal and structural problems, but some analyses have been performed with an ‘enveloping’ technique for grouping several weld passes together to study the feasibility of modeling multi-pass welds on a layer-by-layer basis. The analyses discussed here are all 2D, but most are large problems ( > 5000 nodes and > 5000 four-noded elements, with a large number of solution steps). As such, they pose significant challenges to both software and hardware resources. Pre- and post-processing operations are performed on a network of Silicon Graphics workstations, and ADINA and ADINA-T are executed on a 64 MW, eight-processor CRAY Y/MP. Nominally 50 solution steps are utilized for each weld pass, and weld joints involving as many as 31 individual weld passes have been analyzed on a pass-by-pass basis. Results from several of these WIRSAP analyses are discussed, and the potential use of WIRSAP in a hypothetic attachment weld design optimization study is illustrated.