Developed Material Model Research Articles

Crosspave: a multi-layer elastic analysis programme considering stress-dependent and cross-anisotropic behaviour of unbound aggregate pavement layers

ABSTRACT This manuscript describes the development of a new pavement analysis programme called CrossPave based on the Multi-Layered Elastic Theory (MLET) framework, but capable of accommodating stress-dependent and cross-anisotropic behaviour of unbound pavement layers. Generally, Finite Element (FE) based programmes such as ILLI-PAVE, MICH-PAVE, SENOL, GT-PAVE etc. or general-purpose FE programs with special user-defined material sub-routines have been used to model the stress-dependent nature of unbound materials. However, these FE programme are time consuming and need certain expertise, making them unfavourable for implementation into practice. Few MLET-based programmes such as KENLAYER and Everstress are capable of considering the stress-dependent nature of unbound materials, but fail to accommodate some of the recently developed material models. The newly developed pavement analysis programme, CrossPave, addresses these issues, and incorporates five different non-linear stress-dependent resilient modulus models for unbound materials. Details of the developmental effort are presented in this manuscript, along with results from validation efforts highlighting close agreement between KENLAYER, ILLI-PAVE and GT-PAVE. Critical pavement response parameters for two full-scale pavement sections were calculated using CrossPave, and have been compared against field-measured values. The CrossPave programme has been presented as an enhanced, ready-to-implement programme compared to other MLET-based alternatives.

Thinning prediction of hole-expansion test for DP980 sheet based on a non-associated flow rule

The hole expansion process is widely used in automotive engineering to produce various car parts (e.g., lower arm, trailing arm, control arm, and chassis parts). A numerical study of the hole expansion test for the 3rd generation of advanced high-strength steel sheets is an attractive research topic because of the sheets’ high strength and low formability. This study presents a numerical prediction of the thinning behaviors observed in the hole expansion test for a DP980 sheet using finite element analysis. The experimental data of the tested material obtained from several standard testing methods, including uniaxial tensile, biaxial tensile, and hole expansion tests, are freely supported in the NUMISHEET 2018 conference Benchmark 01. Accordingly, several material models have been developed based on non-associated flow rule (NAFR) by using Hill’s quadratic, Yld2000-2d, and Yoshida polynomial functions to describe the yield and potential surfaces of the tested material. In addition, the Kim-Tuan hardening model is adopted to correctly represent the stress-strain relationship until large strains. Hence, a user-defined material subroutine (UMAT) is developed in Abaqus/Standard package to simulate hole expansion tests using these developed material models. The simulation results reveal that adopting the NAFR theory in the finite element analysis is an efficient method of simulating the hole expansion test. Additionally, the accuracy of the potential surface plays a crucial role in the thinning behavior prediction in the hole expansion simulation. The experimental data obtained from the plane-strain tension tests are recommended for use in calibrating the yield function parameters.

Simulation of uniaxial stress\u2013strain response of 3D-printed polylactic acid by nonlinear finite element analysis

Accurate simulation of mechanical properties of 3D-printed objects can provide critical inputs to designers and manufacturers. Polylactic acid, a biodegradable polymer, is particularly important in this regard due to its excellent print quality and a wide range of applications. Herein, an accurate uniaxial stress–strain profile simulation of 3D-printed PLA is reported. Nonlinear Finite Element Analysis (FEA) was used to simulate the uniaxial tensile test and build a material model for the prediction of the stress–strain response. 3D model for this nonlinear FEA study was built in SolidWorks, and several measures were taken to simulate the nonlinear stress–strain response with high accuracy. Von Mises stress, resultant displacement, and strain plots were produced. Comparison with experimental data extracted from the literature was done to validate the FEA model. Fracture behavior was predicted by FEA stress distribution. Deviations between the stress–strain plot obtained by FEA from the experimentally obtained plot were minimal. The entire curve, except the failure zone, could be precisely simulated. Furthermore, the developed von Mises plasticity material model and the boundary conditions also captured the behavior of specimen under uniaxial tension load and the deviation between experimental results was minor. These results suggest that the developed material model could be useful in non-linear FEA studies on 3D printed PLA objects which are expected to withstand tensile stress.

A modified Johnson-Cook material model with strain gradient plasticity consideration for numerical simulation of cold spray process

Owing to the low processing temperatures and subsequent minimal thermal residual stresses, cold spray (CS) process has significant potential as a fabrication route for freeform components, thus making it a prospective additive manufacturing technology. Cold spray experiments have been accompanied by systematic computational modeling to optimize the coating deposition conditions and predict the coating properties and thereby their performance. One of the most widely used plasticity models for the prediction of material behavior at a high strain rate is the Johnson-Cook (JC) model. However, the model's shortcomings at the strain rates experienced during cold spray lead to inaccuracies in the predictions. Still, it is predominantly used owing to its simplicity and rich material parameters database. In this study, we have developed a modified form of the JC model to account for the viscous regimes experienced at high strain rates, which takes a simple mathematical form with less adjustable material parameters than previous modifications of the JC model. Subsequently, considering the inhomogeneous particle deformation in the presence of jetting, a strain gradient plasticity (SGP) consideration applicable to cold spray has been proposed. The predictions obtained from numerical simulations using the newly developed material model are found to be in good agreement with the cold spray experimental results. The new material model along with the SGP consideration developed in this study offers a critical new asset in numerical modeling of cold spray.

Nonlinear dynamic analysis of aniso-visco-hyperelastic dielectric elastomer actuators

Dielectric elastomers (DEs) are a class of highly deformable electro-active polymers (EAPs) employed for electromechanical transduction technology. Imparting anisotropy to the material behaviour of DEs by adding soft fibres has become promising for suppressing the electromechanical instability besides enhancing the actuation performance. Practically dielectric elastomer based devices undergoes transient motion, making dynamic analysis a crucial aspect for the design of such actuators. In this work, we analyse the electro-viscoelastic response of a transversely isotropic dielectric elastomer subjected to suddenly applied constant and harmonic electric loads. A material model of anisotropic viscoelastic dielectric elastomers is presented by additively decomposing the isotropic free energy density corresponding to DE matrix and anisotropic free energy density corresponding to fibre into equilibrium and viscous parts. Based on the developed material model, equations governing the dynamic motion of the actuator is derived using the Euler–Lagrange equation for non-conservative system. Evolution equations consistent with the laws of thermodynamics are presented to obtain the isotropic and anisotropic viscous stretches. Developed dynamic model is utilized for describing the dynamic response, instability analysis, periodicity, and resonance properties of a dielectric elastomer actuator for different values of viscoelasticity and anisotropy parameters. Phase portrait and Poincarè maps are presented to analyse the periodicity of the nonlinear oscillations of the actuator. The results reveal that viscoelasticity delays the onset of dynamic pull-in instability. Simultaneously, a quasi-periodic to periodic transition is also achieved. The results presented can help in efficient and robust designing of dielectric elastomer based actuators subjected to dynamic loading.

The effect of adipose tissue material properties on the lap belt-pelvis interaction: A global sensitivity analysis

The lap belt-pelvis interaction is one of the main factors influencing the risk for abdominal and lower extremity injuries during vehicular crashes. To numerically study the lap belt-pelvis interaction, biofidelic representation of subcutaneous adipose tissue appears essential, especially for obese occupants with a thick layer of adipose tissue. Therefore, in this study, a finite element model is constructed and a newly developed material model for adipose tissue from the previous work is implemented to study the mechanism of lap belt-pelvis interaction and how subcutaneous adipose tissue affects this. Global Sensitivity Analysis (GSA) is used to determine which aspects of the mechanical properties of adipose tissue play a major role in the lap belt-pelvis interaction. It is found that, firstly, the incompressibility condition of adipose tissue is the most influential parameter. Secondly, the nonlinear elastic and viscoelastic properties are influential because of experiencing large deformation. The findings of this study are meaningful for vehicular injury-oriented characterization of adipose tissue as well as improving the biofidelity of finite element human body models for human safety.

A physically based model of Ti6Al4V turning process to predict surface integrity improvements

In turning processes, surface improvements are strictly related to the physical phenomena induced by the involved thermo-mechanical loads. These phenomena are difficult to be analyzed while they occur, therefore the process simulation is a very important tool to deeply understand their evolution. Turning experiments were carried out on Ti6Al4V workpiece under different machining conditions. The microstructural modifications were analyzed in terms of metallurgical changes and micro-hardness. The physical mechanisms that occurred on the machined surface were investigated to construct a constitutive material flow model. The developed material model was implemented via sub-routine in a commercial FE software and validated through comparisons with experimental data (cutting forces, temperatures and microstructural modifications). The model was employed to predict the process variables of scientific interest (microstructural changes and surface improvement). The numerical results in main cutting forces, feed forces and temperatures prediction proved the accuracy and reliability of the proposed numerical model showing a good agreement with the experimental data.

Physics-based plasticity model incorporating microstructure changes for severe plastic deformation

During machining processes, materials undergo severe deformations that lead to different behavior than in the case of slow deformation. The microstructure changes, as a consequence, affect the materials properties and therefore influence the functionality of the component. Developing material models capable of capturing such changes is therefore critical to better understand the interaction process–materials. In this paper, we introduce a new physics model associating Mechanical Threshold Stress (MTS) with Dislocation Density (DD) models. The modeling and the experimental results of a series of large strain experiments on polycrystalline copper (OFHC) involving sequences of shear deformation and strain rate (varying from quasi-static to dynamic) are very similar to those observed in processes such as machining. The Kocks–Mecking model, using the mechanical threshold stress as an internal state variable, correlates well with experimental results and strain rate jump experiments. This model was compared to the well-known Johnson–Cook model that showed some shortcomings in capturing the stain jump. The results show a high effect of rate sensitivity of strain hardening at large strains. Coupling the mechanical threshold stress dislocation density (MTS–DD), material models were implemented in the Abaqus/Explicit FE code. The model shows potentialities in predicting an increase in dislocation density and a reduction in cell size. It could ideally be used in the modeling of machining processes.

Characterization of the isotropic-distortional hardening model and its application to commercially pure titanium sheets

Commercially pure titanium sheets have been widely used in various industrial applications owing to their lightweight nature, superior formability, and excellent corrosion resistance. Previous studies showed that accurate modelling of material characteristics, such as anisotropic yield function and hardening, is essential for the simulation of sheet metal forming with titanium sheets. For example, the non-quadratic anisotropic yield function Yld2000-2d and the modified Kim–Tuan hardening model were used to model initial anisotropy and reproduce flow stress curves at large strains. However, even with these advanced constitutive models for describing the anisotropic behavior of sheet metals, further improvement is necessary to simulate anisotropy evolution, or distortional hardening, in pure titanium sheets. In this study, distortional hardening was experimentally measured under both uniaxial and balanced biaxial loading conditions. Moreover, the evolution of the Yld2000-2d function was modelled as a function of equivalent plastic work. For validation, the developed material models were applied in finite element simulations to analyse deformation behavior in uniaxial tension, hydraulic bulge, and punch-stretching tests. It was confirmed that this approach accurately described material response during these three tests.

Material models for the thermoplastic material behaviour of a dual-phase steel on a microscopic and a macroscopic length scale

Material models for the thermoplastic material behaviour of a dual-phase steel on a microscopic and a macroscopic length scale are developed in a continuum mechanics framework. Since the microstructure of the material is composed of the two phases martensite and ferrite, appropriate model assumptions on the behaviour of the phases have to be made. In the present model, it is assumed that the martensitic phase behaves purely elastic and the temperature dependent yielding behaviour of the dual-phase steel is determined by the ferritic phase. In this phase, plastic deformation is the result of the movement of dislocations in the atomic lattice on preferred planes in preferred directions. As experiments have shown, the resistance to this movement is determined by an evolving dislocation arrangement as well as by the atomic lattice itself. Based on this experimental observation, dislocation densities are introduced as state variables to formulate a constitutive equation for the resistance to plastic deformation and to capture the dependence of the material behaviour on deformation and temperature history on a microscopic length scale. By analysing the elementary processes of multiplication and annihilation of dislocations and the dependence of these processes on temperature and deformation rate, evolution equations for the dislocation densities are formulated. Thermal activation is used to describe these dependences. Supplying constitutive equations for the Helmholtz free energy and the heat flux, the initial boundary value problem for the thermomechanically coupled problem on a microscopic length scale is formulated. To validate the developed material model, processes applied in experiments with single crystal specimens of pure iron are simulated and a comparison is made between experimental and numerical results. The material model on a macroscopic length scale is motivated by the model on a microscopic length scale. A state variable representing the total dislocation density is introduced to describe the influence of the deformation and temperature history on the material behaviour. For the validation of the material model, a comparison is made between experimental results obtained from forming of sheet metal specimens and the numerical model prediction.

Material and Damage Models of Randomly-Oriented Thermoplastic Composites for Crash Simulation

<div class="section abstract"><div class="htmlview paragraph">This study developed a material model with a damage function that supports finite element analyses in crash strength analyses of beams manufactured using randomly-oriented long fiber thermoplastics composites. These materials are composites with randomly-oriented carbon tow having a fiber length of approximately one inch, and are isotropic in-plane from a macro perspective, but exhibit different damage properties for tension and compression. In the out-of-plane direction, the influence of the resin matrix properties increases, and the materials properties are similar to those of laminate materials. This means they are anisotropic materials with physical properties that differ from those in the in-plane direction. In order to verify the influence of these characteristics, the damage process was observed by three-point bending of a flat plate, which is a mixed mode that includes tension, compression, and out-of-plane shear. Digital image correlation was used to analyze the strain distribution in the edgewise direction, and the results showed that damage progresses from the surface toward the inside of the plate. A damage model was created that takes this phenomenon into account. This damage model uses a format that organizes the difference between the in-plane tension and compression damage properties in terms of the triaxial stress level, and accumulates damage according to each stress level. This model also separately accumulates the out-of-plane shear damage, and associates it with the in-plane compression damage. The accuracy of the developed material model was verified by comparison with three-point bending tests of closed-hat-section beams. The verification results showed a close approximation in terms of the load- stroke profiles and fracture format. This indicates that a material model that takes into account in-plane and out-of-plane damage can accurately express macro bending behavior.</div></div>

Crystal plasticity modeling of 3rd generation multi-phase AHSS with martensitic transformation

A systematic constitutive modeling and calibration methodology were developed based on rate-independent crystal plasticity to predict the quasi static macroscopic behavior of 3rd generation multiphase advanced high strength steels (3GAHSS) prepared with a quenching and partitioning (Q&P) process. In the constitutive law, martensitic phase transformation induced by the elastic-plastic deformation of the retained austenite is represented by considering the Bain strain, the lattice invariant shear deformation, and the orientation relationship between parent austenite and transformed martensite. The amount that each martensite variant evolves is obtained through an optimization scheme that constrains the plastic deformation of the retained austenite to have minimum-energy during phase transformation. In-situ high energy X-ray diffraction (HEXRD) tensile test data was utilized for the characterization and calibration of the material model. Dislocation density based hardening parameters were separately obtained for each phase by iteratively performing crystal plasticity finite element (CPFE) simulations until the simulated stress-strain curves matched the experimentally measured curves from in-situ HEXRD. The 3D representative volume element (RVE) for the 3GAHSS was generated by utilizing Dream.3D and the MTEX Matlab toolbox software. The distributions of grain size and crystal orientation were analyzed based on the measured EBSD data and accounted for in the generation of the 3D RVE. For verification and validation of the constitutive model, crystal plasticity finite element simulations of a uniaxial tensile test were performed using the developed material model and the generated 3D RVE. Additional hypothetical RVEs were also generated by manipulating phase volume fractions, phase transformation speed, and phase properties to determine if these virtual 3GAHSS steels have improved mechanical properties. Also, forming limit curves (FLC) for the multiphase 3GAHSS were predicted from the CPFE simulation results.

Constitutive Equations Based on Non-associated Flow Rule for the Analysis of Forming of Anisotropic Sheet Metals

In this study, an anisotropic constitutive model based on the non-associated flow rule was developed for anisotropic sheet metals. This model was defined in the quadratic form of the Hill’s anisotropic function under a general three-dimensional stress condition. The anisotropic parameters for the yield function were identified using the directional planar yield stresses, bulge yield stress and shear yield stress, while those for the plastic potential function were identified using the directional r-values. A full expression related to the non-associated flow rule was applied and the model was implemented into the finite element code ABAQUS. A static-implicit analysis and the solid element were applied. Capability of the developed model for predicting the anisotropic behavior of sheet metal was investigated by considering two different sheet metal forming processes: cylindrical cup drawing of AA2090-T3, A6061P-T6 and SPCE; and hole expansion forming test of A6016-O. Cup heights and through-thickness strain distributions obtained from the simulations were compared with the experimental data. Results demonstrate that the developed material model considering 3D condition can improve accuracy of predicting the anisotropic behaviors. Furthermore, the simple formulations are efficient and user-friendly for computational analyses and solving the common industrial sheet metal forming problems.

Damage characterization of composites to support an orthotropic plasticity material model

The focus of this paper is the development of test procedures to characterize the damage-related behavior of a unidirectional composite at room temperature and quasi-static loading conditions and use the resulting data in the damage sub-model of a newly developed material model for orthotropic composites. This material model has three distinct sub-models to handle elastic and inelastic deformations, damage, and failure. A unidirectional composite—T800/F3900 that was the focus of our previous work, is used to illustrate how the deformation and damage-related experimental procedures are developed and used. The implementation of the damage sub-model into LS-DYNA is verified using single-element tests and validated using impact tests. Results show that the implementation yields reasonably accurate predictions of impact behavior involving deformation and damage in structural composites.

Low cycle fatigue analysis of ferrite-martensite dual-phase steel using advanced cyclic plasticity models

A computational model has been developed to predict the low cycle fatigue (LCF) characteristics of ferrite-martensite dual phase (DP) steel. LCF results of DP steel performed at strain amplitudes varying from 0.3% to 1.5% show initial cyclic hardening followed by cyclic softening behavior. Finite element simulation employing Chaboche model fails to capture the initial cyclic hardening behavior specifically at lower strain amplitudes. To predict the observed cyclic hardening and softening characteristics of DP steel with a progressive number of cycles, Ohno-Wang cyclic plasticity model has been modified by altering the yield function, which is formulated by incorporating a memory stress function. All the material parameters have been calibrated considering hysteresis loop of the first cycle of LCF result of ±1.5% uniaxial strain. The developed material model has been integrated with ABAQUS 6.14 finite element package to perform the LCF simulation. A comparison between simulation and experimental results for all strain amplitudes reveals that the proposed model has the better capability to predict the overall LCF characteristics of DP steel.

The effect of through thickness texture variation on the anisotropic mechanical response of an extruded Al-Mn-Fe-Si alloy

There is currently a significant scientific and industrial interest in developing material models for the simulation of plastic deformation of aluminum extrusions relevant to their forming and their response during in service events such as vehicle crash. The objective of this work is to evaluate the effect of through thickness crystallographic texture gradients on material mechanical behaviour. This has been studied using a combination of experiments (i.e. pilot scale extrusions and stress-strain curves with the R-value to characterize plastic anisotropy for different loading directions) and the visco-plastic self-consistent (VPSC) polycrystal plasticity simulations on a model alloy system. Two limiting conditions were examined, i.e. unrecrystallized and fully recrystallized conditions. The results of electron backscatter diffraction (EBSD) characterization show that there is a significant through thickness variation in texture for both cases. However, the implications of the texture gradient on the macroscopic plastic response were relatively minor for the unrecrystallized case but quite significant for the recrystallized case. This was manifested as a strong difference in the contraction of the surface layer compared to the centre of the extrudate, particularly in the case of tests at 45° and 90° to the extrusion direction. This was rationalized in terms of the differences in texture between the surface and the centre using VPSC simulations. Finally, it was proposed that this effect will be explored in future work as it may have important implications on the surface stress state which could affect damage initiation, growth and coalescence, particularly in bending situations.

A physically based constitutive model for predicting the surface integrity in machining of Waspaloy

During machining, surface modifications are directly related to the process dynamic affecting the thermo-mechanical properties of the materials. The physics phenomena (such as dynamic recrystallization, hardening and recovery effects) are difficult to be experimentally evaluated during the cutting operations, therefore the simulations are very important tools to understand their evolution. Orthogonal cutting experiments were conducted on Waspaloy under different cutting parameters and lubri-cooling conditions. The machined surfaces were evaluated via optical microscope and the surface integrity was analysed in terms of microstructural changes and microhardness. The deformation mechanisms that occurred in chip formation and on the machined surface were investigated in order to build-up a physically based constitutive model. Subsequently, the developed material model was implemented via sub-routine in a commercial Finite Element software. The numerical prediction strategy was validated through comparisons with experimental outcomes (cutting forces, temperature and metallurgical changes) and employed to predict the variables of scientific interest (microstructural modifications and microhardness). The overall absolute error in predicting the principal cutting force, feed force and temperature were approximately equal to 5%, 9% and 7% respectively. Furthermore, the developed model permits to explore the metallurgical changes and their evolution during the machining process varying cutting parameters and lubri-cooling conditions.

Material modeling of pure titanium sheet and its application to bulge test simulation

The hydraulic bulge test is widely used to obtain stress–strain data over large strain ranges. This study identifies plastic characteristics of pure titanium sheet by conducting several tensile tests and a hydraulic bulge test. Distortional hardening behavior of the tested material is examined experimentally by comparing the uniaxial tensile results of three specimens taken from different orientations. In addition, three stages of deformation were observed in biaxial stress–strain data obtained from the bulge test. Therefore, a constitutive model based on a non-associated flow rule is developed to describe the material characteristics. Evolution Hill’s quadratic functions are adapted to reproduce the yield surface and potential surface transients during plastic deformation. Additionally, a modified Voce hardening model is used to represent the effective stress–strain curve over large strain ranges to capture the three-stage hardening phenomenon of titanium sheet. The developed material model is then applied to simulate the bulge test to verify its accuracy. Based on simulation results, it is concluded that the distortional hardening behavior strongly affects the evaluation of apex height in the bulge test.

Modeling of creep and stress relaxation of the nickel‐base alloy NiCr20TiAl at isothermal and non‐isothermal loading conditions

AbstractThe design and dimensioning of new as well as the assessment of operating high‐temperature components in service require a precise prediction of creep and stress relaxation. The increasing share of renewable energies forces fossil‐fired power plants for increasing numbers of start‐ups and shut‐downs. Consequently, transient loading conditions need to be taken into account. In order to meet this demand, non‐isothermal creep equations are necessary, which enables a consistent prediction of creep strain and stress relaxation in a wide range of temperatures and stresses. In this paper, an approach for the visco‐plastic modeling of creep and stress relaxation for non‐isothermal loading conditions is presented. The strain portions creep, “negative creep” and initial plasticity, occurring at elevated temperatures are described by temperature‐dependent phenomenological equations. Within this paper, the adjustment of the parameters is based on a wide database of hot tensile tests, creep and annealing experiments. The nickel‐base alloy NiCr20TiAl has been examined in a temperature range from 450 °C to 650 °C. The developed material models have been successfully validated with isothermal and non‐isothermal relaxation experiments. Further, the recalculation of a staged relaxation test demonstrates the capability of the defined material laws in a wide stress range under isothermal and non‐isothermal loading conditions.

Experimental characterization of composites to support an orthotropic plasticity material model

Test procedures for characterizing the orthotropic behavior of a unidirectional composite at room temperature and quasi-static loading conditions are developed and discussed. The resulting data consisting of 12 stress–strain curves and associated material parameters are used in a newly developed material model—an orthotropic elasto-plastic constitutive model that is driven by tabulated stress–strain curves and other material properties that allow for the elastic and inelastic deformation model to be combined with damage and failure models. A unidirectional composite—T800/F3900, commonly used in the aerospace industry, is used to illustrate how the experimental procedures are developed and used. The generated data are then used to model a dynamic impact test. Results show that the developed framework implemented into a special version of LS-DYNA yields reasonably accurate predictions of the structural behavior.