Two-layer Viscoplasticity Model Research Articles

Investigation of in-plane visco-deformation in PMMA indentation via TLV model calibrated with tensile specimens

Time-dependent in-plane deformation in PMMA indentation is investigated via two-layer visco-plasticity model (TLV). The parameters of TLV model for PMMA were calibrated for tensile specimens using finite element analysis (FEA) and an optimization approach. The TLV model with the calibrated parameters was then employed to simulate nano- and micro-indentation behaviors including creep, relaxation, and other responses under various test conditions. Comparisons of experimental and FEA indentation load-depth curves showed agreement except the last unloading segment. This discrepancy was attributed to the inability of TLV model in replicating the delayed elastic recovery. In addition, deformation recovery with in-plane displacement (ui) was observed over a few days after indentation load removal. The characteristics of ui recovery and the factors influencing its magnitude are discussed. The proportionality of relative ui recovery rate prominently featured in the viscoelastic properties of PMMA, regardless of indentation history.

Numerical Simulation of Mold Filling of Polymeric Materials with Friction Effect during Hot Embossing Process at Micro Scale.

The filling efficiency during the hot embossing process at micro scale is essential for micro-component replication. The presence of the unfilled area is often due to the inadequate behavior law applied to the embossed materials. This research consists of the identification of viscoplastic law (two-layer viscoplastic model) of polymers and the optimization of processing parameters. Mechanical tests have been performed for two polymers at 20 °C and 30 °C above their glass transition temperature. The viscoplastic parameters are characterized based on stress-strain curves from the compression tests. The influences of imposed displacement, temperature, and friction on mold filling are investigated. The processing parameters are optimized to achieving the complete filling of micro cavities. The replication of a micro-structured cavity has been effectuated using this process and the experimental observations validate the results in the simulation, which confirms the efficiency of the proposed numerical approach.

Application of two‐layer viscoplasticity model to predict a semicrystalline polymer response under compression and microindentation

AbstractPolymeric materials are widely used in structural components and systems, and the accurate prediction of their complex time‐dependent behavior is critical. Several constitutive models are available for different types of mechanical behaviors and loading conditions. However, selecting the model and the correct calibration of its parameters is often a challenge. This paper evaluates the applicability of the two‐layer viscoplasticity (TLV) model to predict the viscoplastic behavior of polyvinylidene fluoride (PVDF) in a large range of strain rates and complex states of strain. The setting of parameters and model validation was made by performing experimentally and numerically uniaxial compression tests and relaxation tests. The model parameters were also analyzed in performing microindentation tests. The TLV model using the same set of parameters selected well predicted the PVDF behavior in a wide variety of compressive loading conditions.

Powerful calibration strategy for the two-layer viscoplastic model

An efficient numerical integration scheme is proposed for the uniaxial loading of the two-layer viscoplastic (TLVP) model, which is a built-in material model in the commercial finite element software Abaqus. The particular version of the TLVP model under investigation is governed by linear isotropic plastic hardening rule with time-hardening nonlinear creep law. The new integration scheme can be easily implemented in any programming environment leading to a fast and robust tool to obtain the stress response in uniaxial loading for a given input strain history. The accuracy of the proposed algorithm is demonstrated and validated by comparing the results obtained with it to those calculated by Abaqus. A new calibration software with a graphical user interface is developed, which can fit the material parameters to the experimental data with arbitrary strain history in a uniaxial loading case. The new software is freely available to download from the webpage of the authors, and it is free to use for research purposes. The excellent performance of the new program is demonstrated by fitting the material parameters to three distinct experimental data sets.

Influence of elastic-viscoplastic behaviour on the filling efficiency of amorphous thermoplastic polymer during the micro hot embossing process

Abstract An unsolved issue in simulating the hot embossing of polymers is modelling the unfilled structured mould. This is because the constitutive law of such polymers has not been adequately determined, especially at the microscale or smaller. The present study investigated the influence of the elastic-viscoplastic behaviour on the filling efficiency of an amorphous polymer during the micro hot embossing process. Constitutive equations based on the two-layer viscoplastic model were used to simulate the hot embossing process. The micro-cavity of the mould was completely filled by the polymer, and the elastic, viscous, and plastic behaviours were considered simultaneously in the simulation. Compression tests were performed to identify the model parameter values for poly-methyl methacrylate. A numerical simulation was performed to analyse the contributions of the polymer’s elastic, viscous, and plastic behaviours. The unfilled area in the micro-cavity was evaluated after a displacement of 0.2 mm was applied to the mould. This was used as an indicator to compare the mould filling efficiency with those of the elastoplastic and elastic-viscoplastic constitutive models. The analysis led to the selection of an optimal elastic-viscoplastic model to completely fill the micro-cavity, which was consistent with the experimental results.

To study the effects of nano-additives and nano-indentation variables on viscoplastic behaviour of a polymeric orthopaedic bone cement

PMMA-based orthopaedic cement is an essential medical grade material in the modern healthcare system which has been widely used for the fixation of prostheses in total joint replacement surgeries. A PMMA bone cement is an intrinsically viscoplastic biomaterial, and a review of its constitutive material models seems to be of great importance to design, functionalize and improve the properties of these biomaterials. In this article, using the simultaneous analyses of experimental nano-indentation results and finite element simulation of a well-known two-layer viscoplasticity model, the effect of adding three types of nano-additives including hydroxyapatite (HA), Alumina (Al2O3), and single-walled carbon nanotubes (SWCNTs) on the viscoplastic behaviour of the cement was examined. Additionally, the effect of the experimental conditions such as loading rate, holding time and unloading rate on the viscoplastic behaviour of the cement was investigated. Making an analogy between the numerical and experimental results, the optimal constitutive material model for each case study was obtained. Moreover, by comparing the results with the condition where no nano-additives were added into the cement matrix, the effectiveness of the nano-supplements on the constitutive model was evaluated.

Nanoscale serration and creep characteristics of Al0.5CoCrCuFeNi high-entropy alloys

Nanoindentation tests were performed to investigate the nano-scale plastic deformation in the Al0.5CoCrCuFeNi high entropy alloys at room temperature (RT) and 200 °C, respectively. Serrated plastic flow, manifested as discrete bursts of plasticity on the load-displacement curves, was observed for both temperatures during the loading period, and its behavior and dependence on the temperature was analyzed from the experimental perspective. Creep occurred during the nanoindentation holding period and exhibited very large stress exponent, implying that the dislocation glide-climb is the dominant mechanism. The creep simulations with a two-layer viscoplastic model further revealed that the deformation at a higher temperature (e.g., 200 °C) featured a greater and faster-growing plastic zone underneath the indenter, implying more pronounced dislocation activities.

Numerical and experimental investigation of the applicability of pellet impacts for impulse excitation

This work presents dynamic finite element simulations of various pellet impacts in order to investigate their applicability during impulse excitation in modal analysis. Compared to the classical impulse excitation with modal hammer, the approach of pellet shots provides shorter impact time and reduces the multi-hitting effect leading a wider relevant frequency range of the frequency response function (FRF). However, the estimation of the contact characteristics requires the complete understanding of the material behaviour of the investigated commercial airsoft pellets and steel bearing balls. The behaviour of the airsoft pellet shows elastic, yielding and viscous properties during the impact, whereas the deformation of the bearing ball is mostly elastic. The commercial FE software ABAQUS offers the two-layer viscoplastic model to capture the complex material behaviour of the airsoft pellet. Based on the FE simulations of both pellets an estimation is provided for the relevant frequency range, where the force spectrum is considered to be mostly constant and the FRF is proportional with the FFT of the output signal. In order to highlight the benefits and the applicability of the excitation with pellet shots experimental work has been carried out. The comparison of the measured FRFs shows that using this novel approach wide relevant frequency domain can be reached with excellent accuracy and repeatability, which could benefit in the modal analysis of structures with high natural frequencies.

A constitutive material model for a commercial PMMA bone cement using a combination of nano-indentation test and finite element analysis

To obtain accurate mechanical properties of an orthopedic Polymethylmethacrylate (PMMA-based) bone cement, nanomechanical testing was performed. Due to visoelastic characteristics of this polymer-like bone cement, the mechanical properties cannot be identified using conventional indentation methods. A well-known two-layer viscoplasticity model was selected and simulated in a finite element solver. A complete analogical study between the results of the finite element simulation and the experimental data was made to reach the best optimized parameters for the selected model. It is shown that the proposed model can be used to obtain the constitutive material relationship for polymeric materials.

Characterization of a thermoplastic foam material with the two-layer viscoplastic model

This article presents the mechanical characterization of a particular thermoplastic foam material applied in thermoforming processes. During the thermoforming process such materials undergo large deformations, which shows elastic, viscous and yielding properties as well. Additionally, the material behavior is strongly temperature-dependent. The only available material model implemented in the commercial finite element software ABAQUS, which can describe such material behavior properly, is the so-called “two-layer viscoplastic model”. This model is comprised of an elastic-plastic network in parallel with a Maxwell-type viscoelastic branch characterized by a nonlinear dashpot. In our investigations mechanical tests have been performed on several temperatures and based on the experimental results, the material parameters have been fitted using the external optimization software ISIGHT, since the analytical stress-solution for the two-layer viscoplastic model is not available.

Temperature-dependent mechanical behaviour of PMMA: Experimental analysis and modelling

An experimental study of temperature-dependent mechanical behaviour of Poly-methyl methacrylate (PMMA) was performed at a range of temperatures (20 °C, 40 °C, 60 °C and 80 °C) below its glass transition point (108 °C) under uniaxial tension and three-point bending loading conditions. This study was accompanied by simulations aimed at identification of material parameters for two different constitutive material models. Experimental flow curves obtained for PMMA were used in elasto-plastic analysis, while a sim-flow optimization tool was employed for a two-layer viscoplasticity model. The temperature increase significantly affected mechanical behaviour of PMMA, with quasi-brittle fracture at room temperature and super-plastic behaviour (ε>110%) at 80 °C. The two-layer viscoplasticity material model was found to agree better with the experimental data obtained for uniaxial tension than the elasto-plastic description.

Analysis of fatigue cracks of cylinder heads in diesel engines

Loading conditions and complex geometry have led cylinder heads to become the most challenging parts of diesel engines. One of the most important durability problems in diesel engines is due to cracks in the valves bridge area. The purpose of this study is thermo-mechanical analysis of cylinder heads of diesel engines using a two-layer viscoplasticity model. The results of the thermo-mechanical analysis indicate that the maximum temperature and stress occurr in the valves bridge. The results of the finite element analysis correspond with the experimental tests carried out by researchers, and illustrate cracks in cylinder heads in this region. The results of the thermo-mechanical analysis show that when the engine is running, the stress in the region is compressive, caused by thermal loading and combustion pressure.When the engine is shut off, the compressive stress turns into tensile stress because of assembly loads. The valves bridge is under cyclic tensile and compressive stress state and thus is subject to low cycle fatigue. After several cycles fatigue cracks will appear in this region. The lifetime of this part can be determined through finite element analysis instead of experimental tests. The viscous strain is greater than the plastic strain which is not negligible.

Effect of Constitutive Model on Thermomechanical Fatigue Life Prediction

In this paper, thermomechanical fatigue life (TMF) prediction is performed on an automotive exhaust manifold using in-house postprocessor code (Hotlife) with four different constitutive models: elastoplastic model with kinematic hardening, two-layer viscoplastic model, and two unified elasto-viscoplastic models based on the equations proposed by Sehitoglu and Chaboche, respectively. Commercial FEA software Abaqus has been used for the analysis. The first two models are already available in Abaqus; the Chaboche and Sehitoglu models were implemented using a user material subroutine (UMAT, available in Abaqus). The stress and strain histories calculated by these four models are output to Hotlife for post-processing. The results from the prediction are then compared to the experimental TMF life obtained from a component thermal fatigue bench test. Result show the Hotlife calculations based on the two implemented elasto-viscoplastic models yield better correlation with test results.

Stress analysis of thermal barrier coating system subjected to out-of-phase thermo-mechanical loadings considering roughness and porosity effect

This paper presents the out-of-phase thermo-mechanical stress analysis of thermal barrier coating (TBC) system in real working conditions used as thermal barrier in diesel engine cylinder heads. The coating system in this research comprises 350μm zirconium oxide top coat (TC) and 150μm metallic bond coat (BC). These layers were deposited on the substrate, aluminum A356 alloy, by the aid of air plasma spray (APS) method. Afterwards, the specimen was subjected to thermo-mechanical fatigue (TMF) loadings. Based on the experimental conditions, FE simulations were performed by both time-independent and time-dependent substrate material properties in ABAQUS software. Simulation results related to heat transfer analysis demonstrate only about 10.5% comparative error compared to experimental results. Moreover, defining time-dependent properties, which were obtained from two-layer visco-plastic model, yields results with 15% less comparative error in comparison to the results based on time-independent material properties. In addition, the effects of roughness and porosity in coating layers and substrate were studied on three different models by the aid of a scanning electron microscopy image. Obtained results based on real geometry illustrate that consideration of porosity in TC layer has an effective role in the stress distribution of this layer. However, BC layer stress distribution is much more dependent on interface morphology.

An effective inverse procedure for identifying viscoplastic material properties of polymer Nafion

An effective inverse procedure is suggested to identify the viscoplastic material properties of polymer Nafion, by minimizing differences in the force–displacement responses of uniaxial tension test between experimental and simulation results. In this procedure, a two-layer viscoplastic constitutive model is adopted to describe the viscoplastic behavior of Nafion. A response surface method is used as a forward solver to calculate the force–displacement response for given material property varying continuously in a certain range. An intergeneration projection genetic algorithm (IP-GA) is then employed as the inverse operator on the response surface to determine the unknown key constants. The selected viscoplastic constants, A, n and f, are varied iteratively using the proposed inverse procedure until the stopping criterion is satisfied. The identification results for two cases demonstrate the effectiveness of the present inverse procedure, as well as its robustness to the noises effects. It is found that this procedure is a potentially useful tool to effectively help determine the viscoplastic material properties of polymer Nafion.

Experimental and numerical evaluations of stress relaxation in A356 aluminium alloy subjected to out-of-phase thermomechanical cyclic loadings

In this study, the stress relaxation has been measured experimentally and has been also calculated numerically by the finite element method in the A356·0 aluminium–silicon–magnesium alloy, under out-of-phase thermomechanical cyclic loadings. To get this objective, strain based thermomechanical fatigue tests were performed on cylindrical specimens, at an out-of-phase condition. In this loading condition, when the temperature was maximum, the mechanical strain was compressive and vice versa. These fatigue experiments were repeated at various dwell times, in which the temperature was held at the maximum temperature. This hold time was considered as 5, 30, 60 and 180 s and then the stress relaxation was measured during the mid-life cycle of each test. Besides, the finite element analysis was also conducted on the material to simulate the stress relaxation numerically. A two-layer visco-plastic model was applied to simulate the high temperature cyclic behavior of the material. Finite element results showed a good agreement with experimental results, which were obtained from thermomechanical fatigue tests on the A356·0 aluminium alloy. The two-layer visco-plastic model could properly predict the stress relaxation at elevated temperatures, during various dwell times.

Stress–strain time-dependent behavior of A356.0 aluminum alloy subjected to cyclic thermal and mechanical loadings

This article presents the cyclic behavior of the A356.0 aluminum alloy under low-cycle fatigue (or isothermal) and thermo-mechanical fatigue loadings. Since the thermo-mechanical fatigue (TMF) test is time consuming and has high costs in comparison to low-cycle fatigue (LCF) tests, the purpose of this research is to use LCF test results to predict the TMF behavior of the material. A time-independent model, considering the combined nonlinear isotropic/kinematic hardening law, was used to predict the TMF behavior of the material. Material constants of this model were calibrated based on room-temperature and high-temperature low-cycle fatigue tests. The nonlinear isotropic/kinematic hardening law could accurately estimate the stress–strain hysteresis loop for the LCF condition; however, for the out-of-phase TMF, the condition could not predict properly the stress value due to the strain rate effect. Therefore, a two-layer visco-plastic model and also the Johnson–Cook law were applied to improve the estimation of the stress–strain hysteresis loop. Related finite element results based on the two-layer visco-plastic model demonstrated a good agreement with experimental TMF data of the A356.0 alloy.

Determination of elastic and viscoplastic material properties obtained from indentation tests using a combined finite element analysis and optimization approach

Conventional indentation tests do not provide an accurate estimation of viscoplastic material properties. In this work, a combined finite element analysis and optimization approach is developed for the determination of elastic–plastic and creep material properties using only a single indentation loading–unloading curve based on a two-layer viscoplasticity model. Utilizing the indentation loading–unloading curve obtained from a finite element-simulated experiment with a spherical and a conical indenter, a set of six key material properties (Young’s modulus, yield stress, work hardening exponent and three creep parameters) can be determined. Non-linear optimization algorithms are used with different sets of initial material properties, leading to good agreements with the numerically simulated target loading–unloading curves.

Experimental and Numerical Characterization of the Cyclic Thermomechanical Behavior of a High Temperature Forming Tool Alloy

This paper describes high temperature cyclic and creep relaxation testing and modeling of a high nickel-chromium material (XN40F) for application to the life prediction of superplastic forming (SPF) tools. An experimental test program to characterize the high temperature cyclic elastic-plastic-creep behavior of the material over a range of temperatures between 20°C and 900°C is described. The objective of the material testing is the development of a high temperature material model for cyclic analyses and life prediction of SPF dies for SPF of titanium aerospace components. A two-layer viscoplasticity model, which combines both creep and combined isotropic-kinematic plasticity, is chosen to represent the material behavior. The process of material constant identification for this model is presented, and the predicted results are compared with the rate-dependent (isothermal) experimental results. The temperature-dependent material model is furthermore applied to simulative thermomechanical fatigue tests, designed to represent the temperature and stress-strain cycling associated with the most damaging phase of the die cycle. The model is shown to give good correlation with the test data, thus vindicating future application of the material model in thermomechanical analyses of SPF dies for distortion and life prediction.

Thermo-Mechanical Analysis and Lifing of Ni-Cr SPF Tool

The paper describes the aniso-thermo-mechanical analysis of a representative large industrial SPF (XN40F, high nickel-chromium) tool. Sequentially coupled thermo-mechanical analyses under realistic loading conditions are developed within a general purpose non-linear FE code, ABAQUS to predict and analyse the complex temperature-stress-strain cycles of the SPF tool. A temperature-dependent, two-layer visco-plasticity model which combines both creep and combined isotropic-kinematic plasticity is chosen to represent the material behaviour. The material constants are identified from multiple strain-range isothermal cyclic tests and stress relaxation tests, over a range of temperatures between 20°C and 900°C. The FE predicted stress-strain data is used in stress-strain-life equations obtained from isothermal fatigue lifing tests at 900°C and the identified constants are validated against the TMF tests and simulative SPF tool test, designed to represent the temperature and stress-strain cycling associated with the most damaging phase of the tool cycle. The predicted SPF tool life is consistent with the simulative SPF tool test life and industrial observations.