Finite element analysis of time-dependent inelastic deformation in the presence of transient thermal stresses

A finite element formulation for the solution of time-dependent inelastic deformation problems for metallic structures, in the presence of transient thermal stresses, is presented in this paper. A rate formulation of the equations is used and any of a number of recently proposed combined creep-plasticity constitutive models with state variables can be adopted to describe material behaviour. The computer program developed can solve planar (plane strain and stress) and axisymmetric problems. Using one of the above-mentioned constitutive models, numerical results are presented for several illustrative problems, and comparisons of results, using either the quasi-steady or the unsteady diffusion equation for the determination of the temperature field, are carried out.     

An inverse approach to determine the constitutive model parameters from axial crushing of thin-walled square tubes

Knowledge of the behaviour of structural components is essential for their design under crash consideration. Constitutive models describe their material behaviour in finite element (FE) codes. These constitutive models are in relation to the material parameters which have to be determined. The strain rates commonly observed in crash events are in the range of 0–500 s^-1. Classic experimental devices such as Hopkinson’s bars do not easily cover this range of strain rates. An inverse numerical approach based on the experimental quasi-static and dynamic axial crushing of thin-walled square tubes has therefore been developed to determine the constitutive model’s parameters. The inverse method is applied in this paper in two stages to determine the power type elastic–plastic constitutive model’s parameters and the Cowper–Symonds constitutive model’s parameters. The identified power law is compared with the results obtained by quasi-static tensile tests and shows that the identified parameters are intrinsic to the material behaviour. The Cowper– Symond’s parameters identified by this method are then used in FE simulation to predict the dynamic response of the same square tube subjected to bending loading. The results obtained show a good correlation between the experimental and numerical results.     

Numerical implementation of a neural network based material model in finite element analysis

Neural network (NN) based constitutive models can capture non‐linear material behaviour. These models are versatile and have the capacity to continuously learn as additional material response data becomes available. NN constitutive models are increasingly used within the finite element (FE) method for the solution of boundary value problems. NN constitutive models, unlike commonly used plasticity models, do not require special integration procedures for implementation in FE analysis. NN constitutive model formulation does not use a material stiffness matrix concept in contrast to the elasto‐plastic matrix central to conventional plasticity based models. This paper addresses numerical implementation issues related to the use of NN constitutive models in FE analysis. A consistent material stiffness matrix is derived for the NN constitutive model that leads to efficient convergence of the FE Newton iterations. The proposed stiffness matrix is general and valid regardless of the material behaviour represented by the NN constitutive model. Two examples demonstrate the performance of the proposed NN constitutive model implementation. Copyright © 2004 John Wiley & Sons, Ltd.     

Numerical implementation of strain rate dependent thermo viscoelastic constitutive relation to simulate the mechanical behavior of PMMA

In this work, a nonlinear viscoelastic constitutive relation was implemented to describe the mechanical behavior of a transparent thermoplastic polymer polymethyl methacrylate (PMMA). The quasi-static and dynamic response of the polymer was studied under different temperatures and strain rates. The effect of temperature was incorporated in elastic and relaxation constants of the constitutive equation. The incremental form of constitutive model was developed by using Poila–Kirchhoff stress and Green strain tensors theory. The model was implemented numerically by establishing a user defined material subroutine in explicit finite element (FE) solver LS-DYNA. Finite element models for uniaxial quasi-static compressive test and high strain rate split Hopkinson pressure bar compression test were built to verify the accuracy of material subroutine. Numerical results were validated with experimental stress strain curves and the results showed that the model successfully predicted the mechanical behavior of PMMA at different temperatures for low and high strain rates. The material model was further engaged to ascertain the dynamic behavior of PMMA based aircraft windshield structure against bird impact. A good agreement between experimental and FE results showed that the suggested model can successfully be employed to assess the mechanical response of polymeric structures at different temperature and loading rates.     

Effect of process parameters on microstructural variables of a commercial TC6 titanium alloy disc

Abstract

The interaction between the deformation behaviour and the microstructure evolution is the main characteristic in the forging process of titanium alloy and this interaction is researched using finite element (FE) simulation. Coupled simulation of deformation behaviour with microstructure evolution has been carried out by means of a new constitutive equation presented by Li et al. (Mater. Sci. Technol., 2004, 20, 1256–1260). The effect of deformation temperature, hammer velocity,height reduction and shear factor on the microstructure variables, including grain size and volume fraction, has been studied in the forging process of the TC6 titanium alloy disc with deformation temperatures of 880–940°C, hammer velocities of 1·2–12 000 mm min^?1 and shear factor (m) of the friction of 0·1–0·4. The simulated results show that deformation temperature, hammer velocity and height reduction have a significant effect on themicrostructure evolution and this effect is more significant on the microstructure evolution in hot forging than that in isothermal forging. The simulated results are in good agreement with the experimental results.     

Application of optical field analysis of tensile tests for calibration of the Rusinek–Klepaczko constitutive relation of Ti6Al4V titanium alloy

In this paper, the application of the Rusinek–Klepaczko relation to describe the constitutive behaviour of Ti6Al4V titanium alloy with an HCP crystalline structure was proposed. The calibration of model coefficients was carried out on the basis of tensile tests. To obtain true stress–strain curves at quasi-static and dynamic loading conditions, the optical field measurement method was applied to determine the history of specimen cross-sections at the necking point. The outline of the specimen was tracked by virtual strain gauges implemented in TEMA Motion software. Adiabatic characteristics obtained at high strain rates using a pre-tension Hopkinson bar were corrected into quasi-isothermal using an analytical approach. Subsequently, a visco-plastic model calibrated using introduced methodology was validated using the finite element method. Engineering stress–strain curves, calculated using ABAQUS software incorporating the Rusinek–Klepaczko model, showed good agreement with experimental data at both quasi-static and dynamic deformation regimes. Moreover, numerical analysis of tensile tests shows that the strain, temperature and stress triaxiality distribution is non-homogenous in specimen cross-sections perpendicular to the loading direction. The value of the strain, temperature and stress triaxiality also depends on the strain rate.     

Finite element modelling of core thickness effects in aluminium foam/composite sandwich structures under flexural loading

This paper models the flexural behaviour of a composite sandwich structure with an aluminium foam core using the finite element (FE) code LS-DYNA. Two core thicknesses, 5 and 20 mm, were investigated. The FE results were compared with results from previous experimental work that measured full-field strain directly from the sample during testing. The deformation and failure behaviour predicted by the FE model compared well with the behaviour observed experimentally. The strain predicted by the FE model also agreed reasonably well with the distribution and magnitude of strain obtained experimentally. However, the FE model predicted lower peak load, which is most likely due to a size effect exhibited by aluminium foam. A simple modification of the FE model input parameters for the foam core subsequently produced good agreement between the model and experimental results.     

Finite Element Analysis and Experimental Measurement of Deformation Behavior for NiTi Plate With Stress Concentration Part Under Uniaxial Tensile Loading

Abstract: The aim of this study is to verify the effectiveness of ordinary phenomenological constitutive relation of NiTi shape memory alloy under mechanical loading at a constant temperature, sufficiently. First, finite element analysis is performed by using ordinary phenomenological constitutive relation for rectangular plate with double notch under tensile loading at a constant temperature. Next, uniaxial tensile loading is carried out for 50.5Ni49.5Ti rectangular plate with double notch. At the same time, macroscopic stress–strain curve and local strain distribution are measured by using in‐house measurement system on the basis of digital image correlation. As a result, it is found that the stress–strain curve obtained from finite element analysis is much different from those obtained experimental measurement, especially during stress‐induced martensite transformation. The result can be derived from the phenomena of local strain band behavior arising in NiTi under mechanical loading. The phenomenological constitutive model used in present finite element analysis is constructed under assumptions that the material has isotropic characteristics and shows homogeneous deformation. However, this experimental result suggests that the material itself has anisotropy microscopically. Furthermore, material shows unique inhomogeneous deformation. Also, there is possibility that these anisotropic characteristic and inhomogeneous deformation behaviour may derive from its microstructure. In future, to sufficiently describe the macroscopic stress–strain curve of NiTi we should take into consideration the material microstructure.     

Temperature dependent representation for Chaboche kinematic hardening model

Abstract

The assessment of high temperature components under cyclic deformation conditions increasingly relies on determinations of the stress–strain state at the critical location using non-linear finite element analysis. An important consideration in such finite element simulations is the used constitutive model. The Chaboche model has been widely accepted as an advanced model for such applications. This study evaluates the variation of Chaboche model parameters with temperature for low cycle fatigue conditions and introduces an approach to systematically calibrate the model for a range of temperatures, rather than for single temperatures. Furthermore, mathematical representations have been proposed to consider the effect of superimposed creep deformation on the Chaboche model parameters. Successful application of the proposed approach/formulation for representing the behaviour of a 10%Cr steel under low cycle fatigue and cyclic/hold deformation conditions for the temperature range of 20–625°C is presented.     

Optimum groove pressing die design to achieve desirable severely plastic deformed sheets

In this paper, considering the problems of common finite element (FE) codes that consider simple constitutive equations, a developed FE code that considers a new constitutive model is used to simulate the behavior of copper sheets under severe plastic deformation (SPD). The new proposed constitutive model, that considers dislocation densities in cell interiors and cell walls of material as true internal state variables, can investigate all stages of flow stress evolution of material during large plastic deformations and also can explain the effects of strain rate magnitude on the mechanical response of material, during room temperature SPD. The proposed FE analysis is used to investigate the effects of die design on the property of SPDed sheets by groove pressing (GP) processes. To do so, the GP processes through existent designations of dies are simulated and a good agreement between the modeling results and experimental data is obtained. In addition, a new die design is proposed that can eliminate the problems of the existent designations of dies and can produce the sheets with higher strength and more uniform hardness.     

Finite element analysis and experimental study of microstructure evolution of nitrogen alloyed ultralow carbon stainless steel during hot deformation

Abstract

Hot compression experiments of a nitrogen alloyed ultralow carbon stainless steel were performed in the temperature range of 1223–1423 K, at strain rates of 0.001–1 s^?1, and with deformation amounts of 30–70% on a Gleeble-3500 thermal-simulator. Based on the results from thermo-physical simulation experiments and metallographic analyses, a physically-based constitutive model and a dynamic recrystallisation (DRX) model of the studied steel were derived, and the developed models were further embedded into a finite element method (FEM) software. The microstructure evolution of the studied steel under various hot deformation conditions was simulated by FEM, and the effects of deformation amount, strain rate and temperature on the microstructure evolution were clarified. The results obtained from the finite element analysis were verified by the experiments. The finding confirms that the thermal-mechanical FEM coupled with the developed constitutive model and DRX model can be used to accurately predict the microstructure evolution of the studied steel during hot deformation.     

A simultaneous solution procedure for strong interactions of generalized Newtonian fluids and viscoelastic solids at large strains

The paper presents a methodology for numerical analyses of coupled systems exhibiting strong interactions of viscoelastic solids and generalized Newtonian fluids. In the monolithic approach, velocity variables are used for both solid and fluid, and the entire set of model equations is discretized with stabilized space–time finite elements. A viscoelastic material model for finite deformations, which is based on the concept of internal variables, describes the stress‐deformation behaviour of the solid. In the generalized Newtonian approach for the fluid, the viscosity depends on the shear strain rate, leading to common non‐Newtonian fluid models like the power‐law. The consideration of non‐linear constitutive equations for solid and fluid documents the capability of the monolithic space–time finite element formulation to deal with complex material models. The methodology is applied to fluid‐conveying cantilevered pipes in order to determine the influence of material non‐linearities on stability characteristics of coupled systems. Copyright © 2005 John Wiley & Sons, Ltd.     

A finite element simulator for spine orthopaedics with haptic interface

The human spine is a biomechanical structure that allows complex motions while providing stability and protection for the spinal cord during a variety of loading conditions. In this study, finite element models of spine are developed to investigate clinical problems as well as to predict its biomechanical behaviour. This research proposes a combination of an online real-time FE simulator and an offline nonlinear FEA solver. Haptic feedback is provided in the online FE simulator to enhance the human–computer interaction of the system. Primitive results of spinal deformation can be obtained from the haptic online FE simulator. The offline FEA solver provides detailed deformation and strain/stress information based on the primary simulation results from the online FE simulator.     

Establishment and comparison of four constitutive relationships of PC/ABS from low to high uniaxial strain rates

The objective of this paper is to accurately predict the rate/temperature-dependent deformation of a polycarbonate (PC) and acrylonitrile-butadiene-styrene (ABS) blend at low, moderate, and high strain rates for various temperatures. Four constitutive models have been employed to predict stress–strain responses of PC/ABS under these conditions, including the DSGZ model, the original Mulliken–Boyce (M–B) model, the modified M–B model, and an adiabatic model named the Wang model. To more accurately capture the large deformation of PC/ABS under the high strain rate loading, the original M–B model is modified by allowing for the evolution of the internal shear strength. All of the four constitutive models above have been implemented in the finite element software ABAQUS/Explicit. A comparison of prediction accuracies of the four constitutive models over a wide range of strain rates and temperatures has been presented. The modified M–B model is observed to be more accurate in predicting the deformation of PC/ABS at high strain rates for various temperatures than the original M–B model, and the Wang model is demonstrated to be the most accurate in simulating the deformation of PC/ABS at low, moderate, and high strain rates for various temperatures.     

Constitutive models for high-temperature flow behaviors of a Ni-based superalloy

The high-temperature deformation behaviors of a typical Ni-based superalloy are investigated by hot compression tests under the strain rate of 0.001–1 s⁻¹and temperature of 920–1040 °C. The experimental results show that the deformation behaviors of the studied superalloy are significantly affected by the deformation temperature, strain rate and strain. The flow stress increases with the increase of strain rate or the decrease of deformation temperature. The flow stress firstly increases with the strain to a peak value, showing the obvious work hardening behaviors. Then, the stress decreases with the further straining, indicating the dynamic flow softening behaviors. Considering the coupled effects of deformation temperature, strain rate and strain on the hot deformation behaviors of the studied Ni-based superalloy, the phenomenological constitutive models are established to describe the work hardening-dynamic recovery and dynamic softening behaviors. In the established models, the material constants are expressed as functions of the Zener–Hollomon parameter. The established constitutive models can give good correlations with the experimental results, which confirm an accurate and precise estimation of the flow stress for the studied Ni-based superalloy.     

Constitutive and damage modelling of H11 subjected to low‐cycle fatigue at high temperature

Hot‐work tool steel H11 is extensively applied in extrusion industries as extrusion tools. The understanding of its mechanical properties and damage evolution as well as failure is crucial for its implementation. In this paper, a finite element (FE) model employing Chaboche unified constitutive model and ductile damage rule is proposed to simulate the mechanical responses of H11 subjected to low‐cycle fatigue (LCF). Accumulated inelastic hysteresis energy is adopted to demonstrate the impact on damage initiation and evolution rules. A series of tension and LCF experiments were conducted to investigate H11's mechanical properties and its deterioration processes. In addition, to deeply understand the deformation and damage mechanism, scanning electron microscope (SEM) investigations were performed on the fracture section of gauge‐length part of the specimen after failure. Furthermore, the parameters in both constitutive model and damage rule are identified based on experimental data. The comparison of the hysteresis loop of the first cycle and stable cycle with different strain amplitudes demonstrates that the Chaboche constitutive model provides high precision to predict the evolution of mechanical properties. Based on the reliable achieved constitutive model, LCF behaviour prediction with damage rule was executed successfully using FE model and gains a good agreement with the experiments. It is believed that the proposed FE method lays the foundation of structure analysis and rapid design optimization in further applications.     

A locking‐free selective smoothed finite element method using tetrahedral and triangular elements with adaptive mesh rezoning for large deformation problems

A novel finite element (FE) formulation with adaptive mesh rezoning for large deformation problems is proposed. The proposed method takes the advantage of the selective smoothed FE method (S‐FEM), which has been recently developed as a locking‐free FE formulation with strain smoothing technique. We adopt the selective face‐based smoothed/node‐based smoothed FEM (FS/NS‐FEM‐T4) and edge‐based smoothed/node‐based smoothed FEM (ES/NS‐FEM‐T3) basically but modify them partly so that our method can handle any kind of material constitutive models other than elastic models. We also present an adaptive mesh rezoning method specialized for our S‐FEM formulation with material constitutive models in total form. Because of the modification of the selective S‐FEMs and specialization of adaptive mesh rezoning, our method is locking‐free for severely large deformation problems even with the use of tetrahedral and triangular meshes. The formulation details for static implicit analysis and several examples of analysis of the proposed method are presented in this paper to demonstrate its efficiency. Copyright © 2014 John Wiley & Sons, Ltd.