Homogenization based macroscopic model of phase transformations and cyclic plasticity in pearlitic steel

In this contribution macroscopic modeling of phase transformations and mechanical behavior of low alloy steels are developed and investigated. Such modeling is of importance in simulations of transient thermo-mechanical processes which can cause phase transformations, examples from the railway industry include train braking induced frictional heating as well as rail grinding and welding operations. We adopt a modeling approach which includes phase transformation kinetics and individual constitutive models for the phases in combination with different homogenization methods. Algorithmic implementations of the isostrain, isostress and self-consistent homogenization methods are presented and demonstrated in finite element simulations of a laser heating experiment. Stress field results from the different homogenization methods are compared against each other and also against experimental data. The importance of including transformation induced plasticity in the modeling is highlighted, as well as the multi-phase stages of the heating and cooling

Modelling of temperature and strain rate dependent behaviour of pearlitic steel in block braked railway wheels

Block braked railway wheels are subjected to thermal and rolling contact loading. The thermal loading results in high temperatures and thermal stresses which cause slow time dependent processes such as creep, relaxation and static recovery of the wheel material. At the same time, the rolling contact loading implies a very fast mechanical load application. This paper is focused on material modeling of pearlitic steel for a wide range of loading rates at elevated temperatures. The starting point is a viscoplasticity model including nonlinear isotropic and kinematic hardening. The Delobelle overstress function is employed to capture strain rate dependent response of the material. The model also includes static recovery of the hardening to capture slower viscous (diffusion dominated) behaviour of the material. Experiments for the pearlitic wheel steel ER7 in terms of cyclic strain-controlled uniaxial tests with hold-time, uniaxial ratchetting tests including rapid cycles and biaxial cyclic tests with tension/compression and torsion are used to calibrate the material model. These experiments were performed under isothermal conditions at different temperatures. In the ratchetting tests, higher loading rates are obtained and these have been used to calibrate the high strain rate response of the viscoplasticity model. The paper is concluded with a numerical example of a block braked wheel where the importance of accounting for the viscoplasticity in modelling is highlighted

Multi-fastener single-lap joints in composite structures

This thesis deals with composite joints. Designing such joints is more difficult than metallic joints due to the mechanical properties of composite materials. Composites are anisotropic and have a limited ability of yielding. The low degree of yielding means that stress concentrations are not relieved by plastic deformation, which is important in multi-fastener single-lap joints. The distribution of load between the fasteners may be more uneven than in metallic joints due to that the stress concentrations around the holes are not relieved. Single-lap joints have an eccentric load path which generates a nonuniform bolt-hole contact pressure through the plate thickness. This generates out-of-plane deflection of the joint, termed secondary bending. Such nonuniform contact stress severely limits the strength of the joint. The nonuniform contact stress distribution is affected by several factors, e.g. bolthole clearance and secondary bending. The first part of the work is devoted to investigating secondary bending, and its effect on stresses in the joint. A novel technique to study secondary bending has been developed and used in a parametric study. It is based on the calculation of specimen curvature from out-of-plane deflections measured with an optical technique. It is shown that the specimen curvature is correlated to the conventional definition of secondary bending, which involves strain measurements on both sides of the plate. The two most important parameters affecting specimen curvature was found to be the overlap length and the thickness of the plates. The finite element method was used to study the influence of secondary bending on joint strength. Secondary bending was changed in magnitude by altering the length of the overlap region in a two-fastener specimen. It was found that secondary bending affects the local stress field around the fasteners and that it may change the strength and the mode of failure. The second part is concerned with the load distribution and prediction of joint strength. A detailed finite element model was developed to calculate the load distribution while accounting for bolt-hole clearances, bolt clamp-up, secondary bending and friction. An experimental programme was conducted in order to validate the finite element model by means of instrumented fasteners. Good agreement between simulations and experiments was achieved and it was found that bolt-hole clearance is the most important factor in terms of load distribution between the fasteners. Sensitivity to this parameter was found to be large, implying that temperature changes could affect the load distribution if member plates with different thermal expansion properties are used. Calculating the load distribution in structures with a large number of fasteners is in general not feasible with detailed finite element models based on continuum elements. A simplified, computationally effective model of a multi-fastener, singlelap joint has been developed by means of structural finite elements. The model accounts for bolt-hole clearances, bolt clamp-up, secondary bending and friction. Comparisons with the detailed finite element model and experiments validated the accuracy of the simplified model. A parametric study was conducted where it was found that an increased stiffness mismatch between the plates generates a more uneven load distribution, while reducing the length of the overlap region has the opposite effect. Increasing the stiffness of a fastener shifts some of the load from the nearest fasteners to that particular fastener. An idealized optimization study was conducted in order to minimize bearing stresses in the joint with restrictions on the increase of joint weight and net-section stresses. Maximum bearing stress was reduced from 220 MPa to 120 MPa while both weight and net-section stresses decreased. A procedure to predict bearing strength based on the results from the simplified model was developed. It was established by an experimental programme that fiber micro-buckling is the initial failure mode. The stress state in the laminate was determined through force and moment equilibrium, based on output from the finite element model. An existing criterion was used to predict the fiber microbuckling, and thus the initial failure. Predictions were compared with experiments which validated the method. The small computational cost required by the procedure suggests that the method is applicable on large scale structures and suitable to use in conjunction with iterative schemes such as optimization and statistical investigations.QC 2011012

Simple and efficient prediction of bearing failure in single shear, composite lap joints

A straightforward procedure to predict bearing strength in bolted composite structures has been developed. The method is based on a finite element analysis, using structural elements, followed by a post-processing procedure. Bolt-hole clearance, friction between member plates, fastener clamp-up and fastener deformation is accounted for. Forces calculated in the FE-analysis are converted into a local stress field which is used in an existing criterion to predict fiber microbuckling in the most critically loaded lamina. Predictions were compared with experiments which validated the method. The small computational cost required by the procedure suggests that the method is applicable on large scale structures and suitable to use in conjunction with iterative schemes such as optimization and statistical investigations.QC 20130819</p

Modelling of cyclic plasticity and phase transformations during repeated local heating events in rail and wheel steels

Short term local friction heating in railway operation might occur when a railway wheelset skids along the rail. The consequent temperature elevation is significant and in the pearlitic rail and wheel steels results in phase transformations. The temperature dependent differences in thermal expansion, density and mechanical properties of the phases result in residual stresses which can cause thermal damage in rail and wheel steels.This study is an improvement of Finite Element (FE) modelling incorporating phase transformation kinetics law describing transformation and evolution of volume fraction of phases. The FE modelling has included coupled thermal and mechanical analysis to compute residual stresses near the wheel-rail contact

Simple and efficient prediction of bearing failure in single shear, composite lap joints

A straightforward procedure to predict bearing strength in bolted composite structures has been developed. The method is based on a finite element analysis, using structural elements, followed by a post-processing procedure. Bolt-hole clearance, friction between member plates, fastener clamp-up and fastener deformation is accounted for. Forces calculated in the FE-analysis are converted into a local stress field which is used in an existing criterion to predict fiber microbuckling in the most critically loaded lamina. Predictions were compared with experiments which validated the method. The small computational cost required by the procedure suggests that the method is applicable on large scale structures and suitable to use in conjunction with iterative schemes such as optimization and statistical investigations.QC 20130819</p

Modeling of kinematic hardening at large biaxial deformations in pearlitic rail steel

Using an Axial-Torsion testing machine, pearlitic R260 steel specimens are twisted until fracture under different axial loads. A well established framework for finite elastoplasticity with kinematic hardening is used to model the deformation of the specimens. In particular, we evaluate the ability of different kinematic hardening laws to predict the observed biaxial load versus displacement response. It is found that the combination of Armstrong-Frederick dynamic recovery and Burlet-Cailletaud radial evanescence saturation is efficient even for the large strains achieved in this study. The results are less conclusive on the appropriateness of replacing the Armstrong-Frederick with an Ohno-Wang type of kinematic hardening law