Development of the sheared edge in the trimming of steel and light metal sheet, part 2 - mechanisms and modelling

The shearing behavior of a drawing-steel and aluminum alloy were investigated using hardness contours of partially deformed samples and a finite element model of the trimming process. Results showed that the stress and strain distributions within the work-piece were more strongly dependent on the punch penetration than the material properties of the work-piece. Differences in the final fracture surface profile and burr formation of the drawing-steel and aluminum alloy were a consequence of the shape of the stress and strain distribution when the crack in the sample became unstable, not when it was initiated. Results and existing literature suggest that a correlation may exist between the strain-rate sensitivity of the work-piece material and the burr mechanism and fracture surface profile of the trimmed part.

Comparison of the strain distribution obtained from multi scale and conventional approaches to modelling extrusion

An investigation of the application of a multi scale CAFE model to prediction of the strain localization phenomena in industrial processes, such as extrusion, is presented in this work. Extrusion involves the formation of a strong strain localization zone, which influences the final product microstructure and may lead to a coarse grain layer close to the surface. Modelling of the shape of this zone and prediction of the strain magnitude will allow computer aided design of the extrusion process and optimisation of the technological parameters with respect to the microstructure and properties of the products. Thus, the particular objective of this work is comparison of the FE and CAFE predictions of strain localization in the shear zone area in extrusion. Advantages and disadvantages of the developed CAFE model are also discussed on the basis of the simulation results.

Modelling factors of square tubes in high speed bending situations

Accurate finite element crash simulations of side impact depend upon a thorough understanding of dynamic tube bending. There is a need to understand the dynamic bending mode of square sections (equivalent of automotive structural parts) to obtain a greater confidence in CAE. This work varied strain rate and material definitions, such as Cowper-Symonds vs Zerilli-Armstrong, as well as initial velocity and yield strength. The results show that most of the plastic work is done between strains rates of 30 ¿ 300/s and strains up to 0.3. Peak strain rates were marginally above 1000/s with maximum strain greater than 1. When the strain rate definition and material model were modified, it was shown that a higher yield stress produced a higher reaction force. These results would suggest that the strain rate sensitivity needs to be carefully identified for accurate crash simulations.

Application of radial return mapping algorithm for finite strain elastoplasticity in a hybrid finite element and particle-in-cell model

The radial return mapping algorithm within the computational context of a hybrid Finite Element and Particle-In-Cell (FE/PIC) method is constructed to allow a fluid flow FE/PIC code to be applied solid mechanic problems with large displacements and large deformations. The FE/PIC method retains the robustness of an Eulerian mesh and enables tracking of material deformation by a set of Lagrangian particles or material points. In the FE/PIC approach the particle velocities are interpolated from nodal velocities and then the particle position is updated using a suitable integration scheme, such as the 4th order Runge-Kutta scheme[1]. The strain increments are obtained from gradients of the nodal velocities at the material point positions, which are then used to evaluate the stress increment and update history variables. To obtain the stress increment from the strain increment, the nonlinear constitutive equations are solved in an incremental iterative integration scheme based on a radial return mapping algorithm[2]. A plane stress extension of a rectangular shape J2 elastoplastic material with isotropic, kinematic and combined hardening is performed as an example and for validation of the enhanced FE/PIC method. It is shown that the method is suitable for analysis of problems in crystal plasticity and metal forming. The method is specifically suitable for simulation of neighbouring microstructural phases with different constitutive equations in a multiscale material modelling framework.

Multiscale particle-in-cell modelling for advanced high strength steels

Advanced High Strength Steels (AHSS) offer outstanding characteristics for efficient and economic use of steel. The unique features of AHSS are direct result of careful heat treatment that creates martensite in the steel microstructure. Martensite and carbon content in the microstructure greatly affects the mechanical properties of AHSS, underlining more importance on microstructural discontinuities and their multiphase characteristics. In this paper, we present the Multiscale Particle-In-Cell (MPIC) method for microstructural modelling of AHSS. A specific particle method [1] usually used in fluid mechanics is adapted and implemented in a parallel multiscale framework. This multiscale method is based on homogenisation theories; with Particle-In-Cell (PIC) method in both micro and macroscale, and offers several advantages in comparison to finite element (FE) based formulation. Application of this method to a benchmark uniaxial tension test is presented and compared with conventional FE solutions.

Advanced modelling of forming high strength steels

The thesis presents a novel approach in the multiscale modelling of Advanced High Strength Steels for prediction of the microstructural effects in forming processes. The results are compared with that of experiments and finite element method. The method is proved to be suitable for complexities in the multiphase AHSS.

Modelling the side impact of carbon fiber tubes

Metallic tubes have been extensively studied for their crashworthiness as they closely resemble automotive crash rails. Recently, the demand to improve fuel economy and reduce vehicle emissions has led automobile manufacturers to explore the crash properties of light weight materials such as fibre reinforced polymer composites, metallic foams and sandwich structures in order to use them as crash barriers. This paper discusses the response of carbon fibre reinforced polymer (CFRP) tubes and their failure mechanisms during side impact. The energy absorption of CFRP tubes is compared to similar Aluminium tubes. The response of the CFRP tubes during impact was modelled using Abaqus finite element software with a composite fabric material model. The material inputs were given based on standard tension and compression test results and the in-plane damage was defined based on cyclic shear tests. The failure modes and energy absorption observed during the tests were well represented by the finite element model.

Post processing of the hot torsion test results using a multi-dimensional modelling approach

A model selection scheme was extended to a multi-dimensional representation of the hot torsion test torque, twist and twist rate data to calculate partial derivatives of the torque data with respect to twist and twist rate. These enabled calculation of the instantaneous strain and strain rate hardening indices in the Fields and Backofen method. The concept of an iso-parametric shape function has been borrowed from the finite element method for adding twist rate as a dependant variable to the torque-twist models identified by the model selection scheme. Expressions to calculate the hardening indices, when employing a rational model of torsion data, were derived and presented. Subsequently, the models were used for post processing the data and determining hot strength behaviour, taking into account variations of strain and strain rate hardening indices during the deformation. To substantiate the technique, the hot flow behaviour of API-X70 micro-alloyed steel was determined using a range of hot torsion test data for the material. The flow stress obtained using the instantaneous hardening indices were compared with that obtained by the orthodox technique. For the investigated cases, the onset of dynamic recrystallization (DRX) predicted by the presented technique deviated considerably from those obtained when the average indices were used.

The indentation behaviour of carbon fibre composite tubes-experiments & modelling

Metallic tubes have been extensively studied for their crashworthiness as they closely resemble automotive crash rails. Recently, the demand to produce lighter weight, yet safer vehicles has led to the need to understand the crash behaviour of novel materials, such as fibre reinforced polymer composites, metallic foams and sandwich structures. This paper discusses the static indentation response of Carbon Fibre Reinforced Polymer (CFRP) tubes. The side impact on a CFRP tube involves various failure mechanisms. This paper highlights these mechanisms and compares the energy absorption of CFRP tubes with similar Aluminium tubes. The response of the CFRP tubes during bending was modelled using ABAQUS finite element software with a composite fabric material model. The material inputs were given based on standard tension and compression test results and the in-plane damage was defined based on cyclic shear tests. The failure modes and energy absorption observed during the tests were well represented by the finite element model.

Spectral element modelling of wave propagation with boundary and structural discontinuity reflections

Spectral element method is very efficient in modelling high-frequency stress wave propagation because it works in the frequency domain. It does not need to use very fine meshes in order to capture high frequency wave energy as the time domain methods do, such as finite element method. However, the conventional spectral element method requires a throw-off element to be added to the structural boundaries to act as a conduit for energy to transmit out of the system. This makes the method difficult to model wave reflection at boundaries. To overcome this limitation, imaginary spectral elements are proposed in this study, which are combined with the real structural elements to model wave reflections at structural boundaries. The efficiency and accuracy of this proposed approach is verified by comparing the numerical simulation results with measured results of one dimensional stress wave propagation in a steel bar. The method is also applied to model wave propagation in a steel bar with not only boundary reflection, but also reflections from single and multiple cracks. The reflection and transmission coefficients, which are obtained from the discrete spring model, are adopted to quantify the discontinuities. Experimental tests of wave propagation in a steel bar with one crack of different depths are also carried out. Numerical simulations and experimental results show that the proposed method is effective and reliable in modelling wave propagation in one-dimensional waveguides with reflections from boundary and structural discontinuities. The proposed method can be applied to effectively model stress wave propagation for structural damage detection.

Modelling of bending-dominated forming processes of metal sheets

Theoretical solutions, finite element models, and experimental techniques are developed for three major sheet metal forming operations: bending (pure bending and cyclic bending), die bending, and deep drawing. These have been applied to two different commercial quality cold-rolled steels, one stainless steel, and one magnesium alloy.

Current distribution and Lorentz field modelling using cathode designs : a parametric approach

A mathematical model of magnetohydrodynamic (MHD) effects in an aluminium cell using numerical approximation of a finite element method is presented. The model predicts the current distribution in the cell and calculates the Lorentz force from the external magnetic field in molten metal for cathode blocks with different surface inclinations.

The findings indicated that the cathode surface inclinations have significant influence on cathode current density and Lorentz field distribution in the molten metal. The results establish a trend for the current density and associated MHD force distributions with increase in cathode inclination angle, φ. It has been found that cathode with φ = 5^o inclination could decrease 16 to 20 % of Lorentz force in the molten metal.

Finite element model updating using estimation of distribution algorithm

Finite Element (FE) model updating has been attracting research attentions in structural engineering fields for over 20 years. Its immense importance to the design, construction and maintenance of civil and mechanical structures has been highly recognised. However, many sources of uncertainties may affect the updating results. These uncertainties may be caused by FE modelling errors, measurement noises, signal processing techniques, and so on. Therefore, research efforts on model updating have been focusing on tackling with uncertainties for a long time. Recently, a new type of evolutionary algorithms has been developed to address uncertainty problems, known as Estimation of Distribution Algorithms (EDAs). EDAs are evolutionary algorithms based on estimation and sampling from probabilistic models and able to overcome some of the drawbacks exhibited by traditional genetic algorithms (GAs). In this paper, a numerical steel simple beam is constructed in commercial software ANSYS. The various damage scenarios are simulated and EDAs are employed to identify damages via FE model updating process. The results show that the performances of EDAs for model updating are efficient and reliable.

Fracture modelling of DP780 sheets using a hybrid experimental-numerical method and two-dimensional digital image correlation

This paper is concerned with the construction of fracture envelopes of DP780 sheets using two methods: a hybrid experimental-numerical method; two-dimensional digital image correlation (2D-DIC). For the hybrid method, four types of ductile fracture tests were carried out covering a wide range of stress states on specimens: with a central hole; two symmetric circular notches; flat grooved; and diagonally double-notched. Based on the fracture strain and loading paths identified with finite element simulation, a fracture envelope was obtained by employing the three-parameter modified Mohr-Coulomb fracture model. In addition, the fracture surface strain was directly measured using 2D-DIC. Loading histories of each test were extracted from a surface element of a three dimensional finite element model. The comparison of fracture envelopes constructed by the two methods reveals that there is little difference. Thus, it can be concluded that 2D-DIC is applicable to fracture modelling of DP780 sheets despite the assumption of the plane stress condition even after necking

Modelling of the stiffness evolution of truss core structures damaged by plastic buckling

A finite element study based on 1D beam element model is performed in order to investigate the mechanical behavior of an elasto-plastic beam loaded in axial compression over its buckling limit. The mode of loading is related to the damage of truss-cored beams in truss-cored laminates. The analysis takes into account the effects of geometry and material properties. The results of the FEM analysis are used for developing a simple mechanical model based on the basic Euler-Bernoulli beam theory and accounts for the beam compressibility. The model uses phenomenological functions containing parameters related to the basic material and geometrical properties. The presented model is developed in the form of closed solution which does not require complex numerical methods or extensive parametric studies. Predictions of the compressive stiffness degradation of truss-cored composites are made with the proposed model and compared with the results of FEM simulations. The error of the stiffness prediction with respect to the FEM results is within 10% over a 5 fold range of stiffness.