Numerical investigation of influence of the Martensite Volume Fraction on dp steels fracture behavior on the basis of digital material representation model

Development of the methodology for creating reliable digital material representation (DMR) models of dual-phase steels and investigation of influence of the martensite volume fraction on fracture behavior under tensile load are the main goals of the paper. First, an approach based on image processing algorithms for creating a DMR is described. Then, obtained digital microstructures are used as input for the numerical model of deformation, which takes into account mechanisms of ductile fracture. Ferrite and martensite material model parameters are evaluated on the basis of micropillar compression tests. Finally, the model is used to investigate the impact of the martensite volume fraction on the DP steel behavior under plastic deformation. Results of calculations are presented and discussed in the paper.

Multi-scale material modelling platform

The data includes material models suitable for modelling and simulation of multi-scale heterogeneous materials, as well as simulation results and experimental observations for verification and validation of simulated results.

Anisotropic hardening model based on non-associated flow rule and combined nonlinear kinematic hardening for sheet materials

 A material model for more effective analysis of plastic deformation of sheet materials is presented in this paper. The model is capable of considering the following aspects of plastic deformation behavior of sheet materials: the anisotropy in yielding stresses in different directions by using a quadratic yield function (based on Hill’s 1948 model and stress ratios), the anisotropy in work hardening by introducing non-constant flow stress hardening in different directions, the anisotropy in plastic strains in different directions by using a quadratic plastic potential function and non-associated flow rule (based on Hill’s 1948 model and plastic strain ratios, r-values), and finally some of the cyclic hardening phenomena such as Bauschinger’s effect and transient behavior for reverse loading by using a coupled nonlinear kinematic hardening (so-called Armstrong-Frederick-Chaboche model). Basic fundamentals of the plasticity of the model are presented in a general framework. Then, the model adjustment procedure is derived for the plasticity formulations. Also, a generic numerical stress integration procedure is developed based on backward-Euler method (so-called multistage return mapping algorithm). Different aspects of the model are verified for DP600 steel sheet. Results show that the new model is able to predict the sheet material behavior in both anisotropic hardening and cyclic hardening regimes more accurately. By featuring the above-mentioned facts in the presented constitutive model, it is expected that more accurate results can be obtained by implementing this model in computational simulations of sheet material forming processes. For instance, more precise results of springback prediction of the parts formed from highly anisotropic hardened materials or that of determining the forming limit diagrams is highly expected by using the developed material model.

A non-associated plasticity model with anisotropic and nonlinear kinematic hardening for simulation of sheet metal forming

A material model for more thorough analysis of plastic deformation of sheet materials is presented in this paper. This model considers the following aspects of plastic deformation behavior of sheet materials: (1) the anisotropy in yield stresses and in work hardening by using Hill's 1948 quadratic yield function and non-constant stress ratios which leads to different flow stress hardening in different directions, (2) the anisotropy in plastic strains by using a quadratic plastic potential function and non-associated flow rule, also based on Hill's 1948 model and r-values, and (3) the cyclic hardening phenomena such as the Bauschinger effect, permanent softening and transient behavior for reverse loading by using a coupled nonlinear kinematic hardening model. Plasticity fundamentals of the model were derived in a general framework and the model calibration procedure was presented for the plasticity formulations. Also, a generic numerical stress integration procedure was developed based on backward-Euler method, so-called multi-stage return mapping algorithm. The model was implemented in the framework of the finite element method to evaluate the simulation results of sheet metal forming processes. Different aspects of the model were verified for two sheet metals, namely DP600 steel and AA6022 aluminum alloy. Results show that the new model is able to accurately predict the sheet material behavior for both anisotropic hardening and cyclic hardening conditions. The drawing of channel sections and the subsequent springback were also simulated with this model for different drawbead configurations. Simulation results show that the current non-associated anisotropic hardening model is able to accurately predict the sidewall curl in the drawn channel sections.

A comparative study of guided wave propagation in timber poles with isotropic and transversely isotropic material models

Guided wave (GW) has been used for many years in non-destructive testing (NDT). There are various ways to generate the guided wave, including impact or impulse either manually or using devices. Although the method of impact or impulse is considered to be simple and practical in guided wave generation, it produces waves with broadband frequencies, which often make analysis much more difficult. The frequency bandwidth produced by manual impacts is usually at the low end, and is therefore justified when dealing with one dimensional wave propagation assumption in low strain integrity testing of cylindrical structures. Under such assumption if the velocity is known accurately, NDTs can produce reasonably good results for the condition assessment of the structure. However, for guided wave propagation in timber pole-like structures, it is rather complicated as timber is an orthotropic material and wave propagation in an orthotropic medium exhibits different characteristics from that in isotropic medium. It is possible to obtain solutions for guided wave propagation in orthotropic media for cylindrical structures, even though the orthotropic material greatly complicates GW propagation. In this paper, timber has been considered as a transversely isotropic (i.e. simplified orthotropic) material and a comparative study of GW propagation in a timber pole is conducted considering isotropic and transversely isotropic modelling. Phase velocity, group velocity and attenuation are the main parameters for this comparative study. Moreover, tractionfree situation and embedded geotechnical condition are also taken into consideration to evaluate the effect of boundary. Displacement profile, wave propagation pattern and power flow at particular frequency are utilized to determine different displacement components of longitudinal and flexural waves along and across the timber pole. Effect of temperature and moisture content (in terms of modulus of elasticity) in timber pole is also compared to show the variation in phase velocity.

Effect of elastic modulus and poisson's ratio on guided wave dispersion using transversely isotropic material modelling

Timber poles are commonly used for telecommunication and power distribution networks, wharves or jetties, piling or as a substructure of short span bridges. Most of the available techniques currently used for non-destructive testing (NDT) of timber structures are based on one-dimensional wave theory. If it is essential to detect small sized damage, it becomes necessary to consider guided wave (GW) propagation as the behaviour of different propagating modes cannot be represented by one-dimensional approximations. However, due to the orthotropic material properties of timber, the modelling of guided waves can be complex. No analytical solution can be found for plotting dispersion curves for orthotropic thick cylindrical waveguides even though very few literatures can be found on the theory of GW for anisotropic cylindrical waveguide. In addition, purely numerical approaches are available for solving these curves. In this paper, dispersion curves for orthotropic cylinders are computed using the scaled boundary finite element method (SBFEM) and compared with an isotropic material model to indicate the importance of considering timber as an anisotropic material. Moreover, some simplification is made on orthotropic behaviour of timber to make it transversely isotropic due to the fact that, analytical approaches for transversely isotropic cylinder are widely available in the literature. Also, the applicability of considering timber as a transversely isotropic material is discussed. As an orthotropic material, most material testing results of timber found in the literature include 9 elastic constants (three elastic moduli and six Poisson's ratios), hence it is essential to select the appropriate material properties for transversely isotropic material which includes only 5 elastic constants. Therefore, comparison between orthotropic and transversely isotropic material model is also presented in this article to reveal the effect of elastic moduli and Poisson's ratios on dispersion curves. Based on this study, some suggestions are proposed on selecting the parameters from an orthotropic model to transversely isotropic condition.

Simulation of the fastener manufacturing process

Cold forging of steel has been modelled using a physical simulation and the finite element method (FEM) to predict the conditions under which failure occurs. FEM was performed using FORGE2 software, which allows analysis of two-dimensional, axi-symmetric forging processes. Various cold forming processes were modelled. The material model has been validated through wire drawing and bulging experiments. The results will be applied to cold forging of industrial products such as fasteners.

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.

Simulation of three-point bending test of titanium foam for biomedical applications

Using Titanium (Ti) foam as an implant material is a new approach for biomedical applications and it is important to understand the mechanical behaviors of this new foam material. In the present study, the bending of the Ti foam has been simulated and compared against recently published data [1]. FE Analysis has been performed by Abaqus software. Stiffness and Yield strength of foams between 50% (cortical bone) to 80% (cancellous bone) porosity range were considered. This study showed that crushable foam material model in Abaqus, which has developed primarily for Aluminum (Al) foam alloys, is also valid for Ti Foam before any crack or damage occurs in the sample.

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.

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.

Springback investigation in roll forming of a V-section

To have fuel efficient vehicles with a lightweight structure, the use of High Strength Steels (HSS) and Advanced High Strength Steels (AHSS) in the body of automobiles is increasing. Roll forming is used widely to form AHSS materials. Roll forming is a continuous process in which a flat strip is shaped to the desired profile by passing through numerous sets of rolls. Formability and springback are two major concerns in the roll forming of AHSS materials. Previous studies have shown that the elastic modulus (Young's modulus) of AHSS materials can change when the material undergoes plastic deformation and the main goal of this study is to numerically investigate the effect of a change in elastic modulus during forming on springback in roll forming. Experimental loading-unloading tests have been performed to obtain the material properties of TRIP 700 steel and incorporate those in the material model used in the numerical simulation of the roll forming process. The finite element simulations were carried out using MSC-Marc and two different element types, a shell element and a solid-shell element, were investigated. The results show that the elastic modulus diminution due to plastic strain increases the springback angle by about 60% in the simple V-section roll forming analyzed in this study. © (2014) Trans Tech Publications, Switzerland.

Study on yield function and plastic potential under non-associated flow for accurate earing prediction in cup drawing

Prediction of more than four ears in a cup drawing process can be successfully achieved by considering r-value and stress directionalities. Yld2004-18p based on associated flow rule and Yld2000-2D based on non-associated flow rule are the examples. The former, however, is more costly in terms of computational efficiency than the latter. In this work, an anisotropic constitutive model based on non-associated flow rule which combines two different functions, Hill (1948) and Yld2000-2d, is implemented to a user defined material model. The accuracy of the anisotropic directionalities (yield stresses and plastic strain ratios) is evaluated. Simulation of a mini-die cup drawing with a body stock alloy predicted eight ears, in good agreement with the experimental results. The use of Hill (1948) model for the yield function and Yld2000-2d for plastic potential under the framework of non-associated flow rule led to accurate prediction of up to eight ears at the lower computational cost.

Wrinkling during cup drawing with NUMISHEET2014 benchmark test

Wrinkling occurs when a blank is subjected to compressive stresses during the forming process as in the flange of a cup during drawing. Although the failure limit due to plastic flow localization can be simply defined by the FLC at each point of a continuum, the wrinkling limit cannot be defined with simple variables such as strain, stress, and thickness. Wrinkling is strongly affected by the mechanical properties of the sheet material, the geometry of the tools and blank, and contact conditions. The analysis of wrinkling initiation and growth is, therefore, difficult to perform due to the complex synergistic effects of the controlling parameters. Because of these difficulties, the study of wrinkling has generally been conducted case by case. A unique wrinkling criterion, which could be used effectively for various sheet forming processes, has not yet been proposed. There were many investigations on the effect of process parameters (BHF and friction) and geometry on wrinkling. However, there are few reported results on the influence of the material model on wrinkling. This paper shows how strain hardening and r-values affect wrinkle formation in its magnitude, initiation, and direction through the NUMISHEET2014 benchmark test for wrinkling during cup drawing.

Constitutive modelling of high strength titanium alloy Ti-6Al-4 V for sheet forming applications at room temperature

To enable the design and optimisation of forming processes at room temperature the material behaviour of Ti-6Al-4 V needs to be accurately represented in numerical analysis and this requires an advanced material model. In particular, an accurate representation of the shape and size of the yield locus as well as its evolution during forming is important. In this study a rigorous set of experiments on the quasi-static deformation behaviour of a Ti-6Al-4 V alloy sheet sample at room temperature was conducted for various loading conditions and a constitutive material model developed. To quantify the anisotropy and asymmetry properties, tensile and compression tests were carried out for different specimen orientations. To examine the Bauschinger effect and the transient hardening behaviour in - plane tensile - compression and compression - tensile tests were performed. Balanced biaxial and plane strain tension tests were conducted to construct and validate the yield surface of the Ti-6Al-4 V alloy sheet sample at room temperature. A recently proposed anisotropic elastic-plastic constitutive material model, so-called HAH, was employed to describe the behaviour, in particular for load reversals. The HAH yield surface is composed of a stable component, which includes plastic anisotropy and is distorted by a fluctuating component. The key of the formulation is the use of a suitable yield function that reproduces the experimental observations well for the stable component. Meanwhile, the rapid evolution of the material structure must be captured at the macro - scale level by the fluctuating component embedded in the HAH model. Compared to conventional hardening equations, the proposed model leads to higher accuracy in predicting the Bauschinger effect and the transient hardening behaviour for the Ti-6Al-4 V sheet sample tested at room temperature.