Isotropic Hardening Plasticity Research Articles

COMPARISON BETWEEN JOHNSON COOK’S PLASTICITY WITH DAMAGE MODEL AND ISOTROPIC HARDENING PLASTICITY WITH DUCTILE DAMAGE MODEL ON ALUMINIUM ALLOY SHEET 2024 T3 TENSILE TEST IN CORRELATING THE FINITE ELEMENT METHOD (FEM) TO THE EXPERIMENT TEST RESULT

Sometimes students and/or researchers are faced with a limited sample and data issue and need to choose carefully which approaches to be used, especially in performing analysis with numerical analysis. As there are a lot of numerical analysis approaches that are having similar purposes and the approaches can be used depending on the analysis cases and objectives. For example, Johnson Cook’s plasticity model and isotropic plasticity hardening model are the common approaches available and used in ABAQUS software to determine the metal and metal alloy plasticity or inelastic mechanical properties. Therefore, in this paper, two approaches – Johnson Cook’s plasticity with damage model and isotropic plasticity hardening with ductile damage model which is used to define the metal and metal alloy mechanical properties and performance are studied using ABAQUS Computer Aided Engineering (CAE) software and compared accordingly. In this study, the experimental result of the tensile test was used to determine the mechanical properties of the Aluminium alloy 2024 T3 sheet with 0.29mm thickness. Then the experiment test data are used to correlate the finite element method (FEM) model and the experimental test result by using Johnson Cook’s plasticity hardening with damage model approach and the isotropic hardening plasticity with ductile damage model approach. Based on the comparison with the experiment failure sample mode, both FEM model failure mode is closely identical to the experiment failure sample. From the mechanical properties comparison, Johnson Cook’s model shows a bigger deviation compared to the isotropic plasticity with ductile damage model in comparison to the experiment value. From this paper, it can be concluded that the ductile damage model is more appropriate to be used when the sample and data are limited.

Constitutive modelling of a self-healing composite matrix polymer material

In this work, a constitutive model of an intrinsically self-healing composite matrix material is presented. The developed model comprises a micro-damage initiation and evolution model, and a healing evolution model, which are combined with the von Mises linear isotropic hardening plasticity. It is implemented into the Abaqus/Standard user material subroutine UMAT and validated using experimental results of static tensile and two-cycle tensile tests performed on partially neutralised poly(ethylene-co-methacrylic acid) (EMAA) ionomer copolymer, Surlyn® 8940. In the development of the model, Continuum Damage Healing Mechanics (CDHM) concepts of nominal and healing configurations are used. In addition, these concepts are used along with the strain equivalence hypothesis to streamline the numerical implementation. The strain equivalence hypothesis relates strain and stress tensors in the nominal and the healing configuration. Finally, successful validation has shown that the developed model is able to accurately predict behaviour of Surlyn® 8940 coupons during tensile tests and it can precisely predict the accumulation of plastic strain.

Failure analysis of composite repaired pipes subjected to internal pressure

While around 60% of pipelines transmitting oil and gas worldwide experience corrosion and metal loss, the composite repair technique has become a popular option developed in recent decades. Employing a theoretical methodology, this study deals with corroded metallic pipes repaired by composite repair systems such that the focus is the impact of elastoplastic deformations on the failure pressure. In this methodology, the elastoplastic strains are taken into account by employing the bilinear isotropic hardening plastic flow theory with the von Mises yield criterion. Three modes are recognized based on the region where failure occurs, and the results are presented. The findings revealed that when the failure happens in the defect region, the proposed formula estimates the failure pressure more accurately than when it occurs either far from the defect or in the composite sleeve. Moreover, studying the bonding strength between the pipe, infill material, and composite patch shows that the interface bonding strength between the pipe and the polymer filler plays a more significant role than the interface bonding strength between the polymer filler and the composite repair. The results of this study can assist maintenance engineers in better evaluating the reliability of composite repaired pipelines.

Numerical and Experimental Studies on Hydro-Forming of a Thin Metallic Disc

This paper deals with the hydro-forming of a flat thin metallic disc to achieve a forward domed disc which will be subsequently adopted to manufacture a rupture disc. The plastic deformation induced by the hydraulic energy is numerically simulated through an isotropic hardening plasticity model using a non-linear explicit finite element analysis (FEA). The variation in disc’s central deformation, thickness, equivalent plastic stress and equivalent plastic strain with respect to the applied hydraulic pressure are determined from FEA simulations. The hydro-forming setup is then designed and manufactured, and the metallic disc is experimented under hydro-forming process. The reduction in thickness due to stretching of the thin disc is evaluated from experiment and simulation and a close agreement is found. This research attempt helped in finalizing the hydro-forming fluid pressure, the feasibility and the accuracy of practically achieving the desired geometry of the metallic disc. The near-fixidity effects on abrupt variation in sheet thickness and plastic strain are well captured through simulations which are very difficult to be studied through hydro-forming experiments.

Plastic work constrained elastoplastic topology optimization

AbstractAn elastoplastic topology optimization framework for limiting plastic work generation while maximizing stiffness is presented. The kinematics and constitutive model are based on finite strain linear isotropic hardening plasticity, and the balance laws are solved using a total Lagrangian finite element formulation. Aggregation of the specific plastic work combined with an adaptive normalization scheme efficiently constrains the maximum specific plastic work. The optimization problem is regularized using an augmented partial differential equation filter, and is solved by the method of moving asymptotes where path‐dependent sensitivities are derived using the adjoint method. The numerical examples show a clear dependence on the optimized maximum stiffness structures for different levels of constrained specific plastic work. It is also shown that due to the history dependency of the plasticity, the load path significantly influences the structural performance and optimized topology.

Finite Element Simulation Analysis on Residual Stress Relief of 7075 Aluminum Alloy Ring

Vibration stress relief (VSR) and thermal stress relief (TSR) are important method to eliminate the residual stress of structural parts. The thermal vibratory stress relief (TVSR) is a new method to decrease and homogenize the residual stress. Based on the stress relaxation tests and the equivalent vibration equation of modal analysis, the creep constitutive model and the bilinear isotropic hardening plasticity material model (BISO) are combined to establish the numerical simulation model of TVSR of 7075 aluminum alloy ring part. The simulation results show that four different initial blank residual stress levels are obtained after quenching process, and the residual stress elimination and homogenization effect of TSR and TVSR is better than that of VSR. TVSR has a better effect on both residual stress elimination and homogenization, and the residual stress relief rate can reach more than 20%.

Computational microstructural model of ordinary state-based Peridynamic theory for damage mechanisms, void nucleation, and propagation in DP600 steel

In this study, the evolution of microscopic damage mechanisms in DP600 was investigated by developing an ordinary state-based two-dimensional Peridynamic model. The real microstructure was extracted from scanning electron microscope (SEM) images and employed to predict the deformation and damage behavior of dual-phase (DP) steels under tension static loading. Isotropic hardening plasticity and nonlinear failure criterion were considered for both ferrite and martensite phases. The Peridynamic (PD) modeling procedure is improved to reduce simulation time and increase applied displacement steps. For improving the prediction of damage initiation, a new method was proposed for the properties of the martensite/ferrite interface. At four applied strains (no-damage, damage initiation, partly damage propagation, and coalescence of damages), deformation and damage patterns were investigated. The cumulative plastic stretch of interactions and the number of damaged interactions were obtained for every applied strain. These parameters were evaluated by the energy rate of acoustic emission signals. Void formation due to fracture of martensite particles and decohesion of the interface were predicted and validated by available experimental results and previous studies. Damage initiation was predicted in thin martensite grains, interfaces of martensite/ferrite, and sandwiched ferrite regions between martensite particles. In thin martensite phases, the crack was initiated at boundaries, and then it crossed through martensite phases. PD model successfully predicted crack propagation and branching that matched with the experimental data.

Finite Element Analysis of RC Beams by the Discrete Model and CBIS Model Using LS-DYNA

There are several techniques to simulate rebar reinforced concrete, such as smeared model, discrete model, embedded model, CLIS (constrained Lagrange in solid) model, and CBIS (constrained beam in solid) model. In this study, however, the interaction between the concrete elements and the reinforcement beam elements is only simulated by the discrete model and CBIS (constrained beam in solid) model. The efficiency and accuracy comparisons are investigated with reference to the analysis results by both models provided by LS-DYNA explicit finite element software. The geometric models are created using LS-PrePost, general purpose preprocessing software for meshing. The meshed models are imported to LS-DYNA where the input files are then analyzed. Winfrith and CSCM concrete material options are employed to describe the concrete damage behavior. The reinforcement material model is capable of isotropic and kinematic hardening plasticity. The load versus midspan deflection curves of the finite element models correlate with those of the experiment. Under the conditions of the same level of accuracy, the CBIS model is evaluated to have the following advantages over the discrete model. First, it has the advantage of reducing the time required for FE modeling; second, saving computer CPU time due to a reduction in total number of nodes; and third, securing a good aspect ratio of concrete elements.

Finite Element Analysis of Composite Matrix Material with Micro-damage Healing Ability

A novel constitutive model for modelling of polymer composite matrix material is proposed. Investigated material is an advanced ethylene/methacrylic acid (E/MAA) copolymer, DuPont™ Surlyn® 8940 thermoplastic resin, which exhibits intrinsic self-healing ability. The model incorporates damage evolution and healing model, and the von Mises linear isotropic hardening plasticity model and is validated with static tensile and two-cycle tensile tests on pure Surlyn® 8940 specimens. The concept of nominal and healing configurations is used in the development and numerical implementation of the model, which is additionally streamlined by the application of the strain equivalence hypothesis. Developed constitutive model enables accurate prediction of Surlyn® 8940 behaviour under tensile loading and precise prediction of accumulated plastic strain.

A new asymptotic crack tip model to predict failure processes

A two dimensional finite element asymptotic crack tip model (ABAQUS® code) to simulate crack tip opening displacement (CTOD) and damage in ductile materials has been developed. Pure Mode I is considered with asymptotic displacements applied on the outer boundary of the finite element mesh constructed using plane strain solid and cohesive elements. CTOD profiles and damage variation along cohesive element path are clearly observed. Evolution of CTOD for various ratios of solid/cohesive Young´s Modulus are also presented. The evolution of damage was based on a power law fracture criterion. In an effort to extend isotropic hardening plasticity theory to small scales, the research was focused on room-temperature crack growth in polycrystalline Aluminium alloys. In a future work, stress enhancement will be considered in a framework of cohesive zone modeling and strain gradient plasticity based on the micromechanics of dislocations. An asymptotic crack tip micro structured mesh will be also accounted into the finite element analysis.

Relationship between element-level and contact-level parameters of micromechanical and upscaled plasticity models for granular soils

The models for stress–strain behavior of granular soils can be generally categorized into two approaches: the conventional plasticity approach and the micromechanics-based approach. In this work, we upscale a micromechanical model to a commonly used isotropic hardening plasticity model by assuming the “same” constitutive laws at different scales. The mathematically derived relationships between element-level and contact-level parameters are presented based on the condition that the two models would predict the same mechanical response, and a parameter calibration procedure is proposed. A comparative study is then conducted to investigate the differences of the predicted element behaviors arisen from the two models.

Numerical modelling of blast-induced fractures in coal masses under high in-situ stresses

Borehole blasting is a technique widely applied to form fracture networks in coal masses. There are many original cracks in coal masses, such as bedding planes and cleat planes. Coal masses are also subjected to high in-situ stress deep underground. However, the effects of pre-existing cracks and in-situ stress on blast-induced fractures are not well understood. In this paper, the isotropic and kinematic hardening plasticity model considering compression and tensile failure is introduced to numerical models, and the contact interface is used to simulate the effect of jointed planes on coal-mass blasting. The effects of jointed plane, constant in-situ stress and lateral pressure coefficient on blast-induced cracks are explored, and the relative peak displacement (Δup) of jointed planes is considered as the basis for determining jointed plane failure. The results indicate that blast-induced cracks tend to expand along jointed planes in the coal mass; the in-situ stress enhances the compression effect and weakens the tension effect in the radial direction of the borehole; and the jointed plane failure zone in coal masses decreases with increasing in-situ stress. The lateral pressure coefficient also has a distinctive influence on blast-induced crack expansion.

Return-mapping algorithms for associative isotropic hardening plasticity using conic optimization

We present a mathematical programming approach for elastoplastic constitutive initial value problems. Consideration of the associative plasticity and a linear isotropic hardening model allowed us to formulate the local discrete constitutive equations as conic programs. Specifically, we demonstrate that implicit return-mapping schemes for well-known yield criteria, such as the Rankine, von Mises, Tresca, Drucker-Prager, and Mohr–Coulomb criteria, can be expressed as second-order and semidefinite conic programs. Additionally, we propose a novel scheme for the numerical evaluation of the consistent elastoplastic tangent operator based on a first-order parameter derivative of the optimal solutions.

Numerical simulation and absorbing boundary conditions for wave propagation in a semi-infinite media with a linear isotropic hardening plastic model

The theory of plastic wave propagation finds its applications in many geotechnical earthquake engineering problems. In this paper, a linear isotropic hardening plastic material is chosen to investigate the plastic wave propagation in a semi-infinite media. The dynamic response of a semi-infinite bar subjected to a triangular load is first derived. The numerical modelling scheme is then proposed and verified by the existing and derived analytical solutions. Novel artificial boundary conditions (ABCs), which are designed for transient dynamic analysis of plastic dilatational wave propagation problem in the media with a linear hardening plastic property, are developed and incorporated into the numerical scheme. Numerical examples illustrate the accuracy of the ABCs in reflecting the complex phenomenon of wave interaction, and reveal good absorption of outgoing stress waves. The study outcome provides reference for developing suitable ABCs for media with complicated nonlinear mechanical properties, and will facilitate the numerical technique in solving soil-structure seismic interaction problems.

Distributed plasticity model for analysis of steel structures subjected to fire using the direct stiffness method

This article develops a temperature-dependent distributed plasticity model in a direct stiffness method (DSM) based formulation for coupled nonlinear thermo-mechanical analysis of steel space frames. The developed framework considers geometric and material nonlinearities, and performs coupled thermo-mechanical analysis by a two-level spatial discretization strategy. An isotropic hardening plasticity in combination with the von Mises yield criterion is considered, where the temperature-dependent yield function is derived from the stress-strain relations of Eurocode 3. The effects permanent plastic strains, large deformations and temperature-dependent material properties are directly incorporated in to the force deformation relations derived in a DSM based setting. Such a DSM based framework in conjunction with the distributed plasticity model facilitates higher computational efficiency. To ensure full coupling between mechanical and thermal solvers, thermodynamically consistent plastic heating term is added to the energy balance of the system. Also, connection flexibility is accounted for by developing a zero-length spring element integrated with 1-D beam-column elements. Five numerical examples are presented to demonstrate the efficacy of the developed framework. Within the numerical investigation, the importance of plastic heating coupling in the context of macro modelling based structural fire analysis of steel structures is quantified and the results indicate that such a coupling can be ignored in such macro scale structural fire computations.

Investigation on forming–welding process chain for DC04 tube manufacturing using experiment and FEM simulation

A chained forming–welding process is to be investigated and analyzed using experimental verification and numerical simulation in which the material and mechanical properties are fully transferred between processes. The investigated part is in the form of a tube with dimension of 300 mm (l) × 20 mm (OD) × 1.5 mm (t) made of a low carbon steel material DC04 commonly used for automotive parts and support structure. At first, a series of experiment using industrial U-/O-bending machine and fully automated robotic gas metal arc welding (GMAW) process on longitudinal slot were sequentially conducted and analyzed towards final geometrical change, macrostructure, and residual stress. Further, numerical simulation method using specialized FEM software Simufact.Forming and Simufact.Welding is developed to predict the major properties following the actual process parameters during experimental forming and welding process. Throughout the simulation of forming and welding process, additive isotropic hardening plasticity model based on von Mises yield criterion is selected with a wide range of operating temperature and Goldak’s double-ellipsoid is defined as welding heat source model. Based on the analysis outcome, it can be concluded that coupled forming–welding process simulation can be suitably implemented to forecast major material and mechanical properties of tube manufacturing within accepted range of error under consideration of material history.

Elastoplastic CDM model based on Puck’s theory for the prediction of mechanical behavior of Fiber Reinforced Polymer (FRP) composites

In this paper, the plane stress version of the Puck’s failure theory is used as an indicator of the intra-laminar meso-damage initiation. The thermodynamically consistent damage evolution law is defined to accumulate the damage leading to the subsequent stiffness degradation coupled with the isotropic hardening plasticity. The model is formulated in incremental form keeping in view the implementation by following the plasticity theory which is later used in the Return Mapping Algorithm (RMA). In the implicit scheme based on the Newton-Raphson approach, the consistent tangent operator is derived for the current model. The developed model has been implemented in ABAQUS/Standard via UMAT subroutine in a strain-driven problem where strain tensor is provided as an independent argument into the solution scheme. The non-linear mechanical behavior and ultimate failure of Carbon Fiber Reinforced Polymers (CFRPs) laminates are predicted for the small strain time-independent boundary value problem. The results are compared with the experimental results collected from the previously published literature which exhibit better correspondence.

Numerical Study of the Plasticity-Induced Stabilization Effect on Martensitic Transformations in Shape Memory Alloys

It is well known that plastic deformations in shape memory alloys stabilize the martensitic phase. Furthermore, the knowledge concerning the plastic state is crucial for a reliable sustainability analysis of construction parts. Numerical simulations serve as a tool for the realistic investigation of the complex interactions between phase transformations and plastic deformations. To account also for irreversible deformations, we expand an energy-based material model by including a non-linear isotropic hardening plasticity model. An implementation of this material model into commercial finite element programs, e.g., Abaqus, offers the opportunity to analyze entire structural components at low costs and fast computation times. Along with the theoretical derivation and expansion of the model, several simulation results for various boundary value problems are presented and interpreted for improved construction designing.

An effective model for analysis of reinforced concrete members and structures under blast loading

The traditional fiber beam model has been widely used in the seismic analysis of reinforced concrete members and structures. However, the inability to capture shear failure restricts its application to blast loadings. In this article, a numerical model that considers both rate-dependent shear behavior and damage effect is proposed based on the traditional fiber beam element. This is achieved using the modified compression-field theory with a concrete damage model and bilinear steel model in the principal directions. Meanwhile, a condensed three-dimensional stress–strain relation from the isotropic hardening plasticity model is implemented to simulate longitudinal reinforcement bars, as large shear strain would be produced under severe blast loads. The proposed model is validated by comparing the numerical and test results. The high-fidelity physics-based finite element model, validated by the same experiment, is also used in the study to prove the efficiency of the proposed model. Case studies of a reinforced concrete beam and a six-story reinforced concrete frame structure subjected to blast loads are then carried out. The results indicate that the proposed model is reliable compared with the high-fidelity physics-based model. In addition to the accuracy, comparisons of the computational time show an excellent performance with respect to the efficiency of the proposed model.

Topology optimization based on finite strain plasticity

In this paper infinitesimal elasto-plastic based topology optimization is extended to finite strains. The employed model is based on rate-independent isotropic hardening plasticity and to separate the elastic deformation from the plastic deformation, use is made of the multiplicative split of the deformation gradient. The mechanical balance laws are solved using an implicit total Lagrangian formulation. The optimization problem is solved using the method of moving asymptotes and the sensitivity required to form convex separable approximations is derived using a path-dependent adjoint strategy. The optimization problem is regularized using a PDE-type filter. A simple boundary value problem where the plastic work is maximized is used to demonstrate the capability of the presented model. The numerical examples reveal that finite strain plasticity successfully can be combined with topology optimization.