Two-phase Constitutive Model Research Articles

A multi-scale framework for life reduction assessment of turbine blade caused by microstructural degradation

The prolonged thermal exposure with centrifugal load results in microstructural degradation, which ultimately leads to a reduction in the fatigue and creep resistance of the turbine blades. The present work proposes a multi-scale framework to estimate the life reduction of turbine blades, which combines a microstructural degradation model, a two-phase constitutive model, and a microstructure-dependent fatigue and creep life reduction model. The framework with multi-scale models is validated by a Single Crystal (SC) Ni-based superalloy at the microstructural length-scale and is then applied to calculate the microstructural degradation and the fatigue and creep life reduction of turbine blades under two specific service conditions. The simulation results and quantitative analysis show that the microstructural degradation and fatigue and creep life reduction of the turbine blade are heavily influenced by the variations in the proportion of the intermediate state, namely, the maximum rotor speed status, in the two specific service conditions. The intermediate state accelerates the microstructural degradation and leads to a reduction of the life, especially the effective fatigue life reserve due to the higher temperature and rotational speed than that of the 93% maximum rotor speed status marked as the reference state. The proposed multi-scale framework provides a capable approach to analyze the reduction of the fatigue and creep life for turbine blade induced by microstructural degradation, which can assist to determine a reasonable Time Between Overhaul (TBO) of the engine.

Experiments and modelling for characterisation and validation of a two-phase constitutive model for describing sands under explosive loading

Specification of constitutive equations and validation of advanced material models is a developing area which is yet to be adequate for the complexity of granular geological materials such as sands and soils. In consideration of these materials as an air-solid mixture, the present work suggests a consistent procedure for specifying the constitutive equations to close a two-phase model for these materials. The following data are used: (i) Hugoniot data for the solid constituent specifying the equation of state; (ii) rate sensitive strength data of the solid constituent for the plasticity constitutive equations; (iii) data from Split Hopkinson Pressure Bar (SHPB) tests for the compaction kinetic; and (iv) post-test analysis of encapsulated samples loaded by High Explosive for the consolidation response. The model specified with this procedure and implemented in the CTH hydrocode is validated with independent tests in an axisymmetric setup. The suggested experimental setup observes deformation in time of a circular plate loaded by sand ejecta from a detonating buried HE charge, using flash X-ray radiography. These experiments characterise both temporal and spatial distribution of the impulse and also enable an integral assessment. The experimental investigation of a calcite sand, several silica sand variants, a glass powder and a soil mixture was conducted in the present paper, employing the methodology developed for the material characterisation and model validation. Comparison of the test results for these materials with the calculations demonstrated a good agreement.

Analysis of Film Blowing with Flow-enhanced Crystallization

Abstract An analysis of the steady-state film blowing process based on a two-phase constitutive model that accounts for flow-enhanced crystallization is presented. The amorphous melt phase is represented by a multi-mode Giesekus constitutive equation with a transformation-dependent relaxation time and the semi-crystalline phase is represented by a rigid rod model. The relaxation times in the two constitutive equations are linked by an Avrami, temperature-dependent rate expression which contains a term in the Helmholtz free energy to account for flow-enhancement. Comparisons are made to experimental data for film blowing of linear low density (LLDPE) and low density (LDPE) polyethylenes. Excellent fits for the bubble radius, temperature, and crystallinity are shown. It is also shown that the ratio of amorphous stress to total stress at the “lock-in” point provides an excellent correlating variable for the elongation to break and yield strength properties of the as-blown film. Inclusion of multiple relaxation times in the Giesekus model offers insights on the controlling role of the maximum relaxation time in the stress profiles and locking-in behavior due to crystallization.

A Two-phase Constitutive Model with Damage for Tungsten Heavy Alloy

Tungsten heavy alloy is a kind of two-phase alloy composed of high-strength tungsten phase and binder phase with good-plasticity. Its mechanical properties and damage evolution are affected by both phases. The static and dynamic mechanical tests of 92.5W-4.9Ni-2.1Fe-0.5Co are carried out. According to the characteristics of stress-strain curves, KHL model is selected as the constitutive model of the material. Then, combined with Eshelby equivalent inclusion theory and Mori Tanaka mean field theory, the stress-strain relationship of each phase in tungsten heavy alloy is studied by introducing representative volume element (RVE). The damage evolution model considering the strain rate effect is proposed, and according to the different loading states, a two-phase constitutive model with damage is established. By compiling the UMAT subroutine, the test conditions of different strain rates are calculated in ABAQUS software. The simulation results are in good agreement with the test results, and the validity of the proposed model is verified.

An Improved Discontinuous Deformation Analysis to Solve Both Shear and Tensile Failure Problems

This paper is mainly aimed to present an improved DDA (discontinuous deformation analysis) that can deal well with both shear and tensile failure problems. Firstly, the shear mechanism of DDA is detailed investigated. The results show that when handling the frictional interface, the critical shear resistance can be accurately determined only if the penalty value is carefully selected, however, when handling the cohesive interface, the critical shear resistance is significantly underestimated. The inaccurate prediction is due to the inconsistent distribution of normal force and shear force between the two vertex-to-edge contacts in one edge-to-edge contact. Here an edge-to-edge treatment is introduced into DDA. Secondly, to moderately reflect the tensile failure process of rock masses, a two-phase constitutive model is introduced into the DDA with edge-to-edge treatment, and the improved DDA is obtained. Finally, the improved DDA is used to simulate the failure process of gypsum centrifuge model. The results show the improved DDA can deal well with rock failure problems by shear or tension failure.

TWO-PHASE MODEL IN VISCOELASTICITY AND VISCOPLASTICITY OF SEMICRYSTALLINE POLYMERS

Observations are reported on isotactic polypropylene in tensile relaxation tests and in loading–unloading tests followed by relaxation after retraction at temperatures ranging from room temperatures up to 100°C. A two-phase constitutive model is developed for the mechanical response of semicrystalline polymers where crystalline and amorphous phases are treated as viscoelastoplastic continua with different laws of plastic flow. Adjustable parameters in the stress–strain relations are found by fitting the observations. Ability of the model to describe characteristic features of the viscoelastic and viscoplastic behavior of polypropylene at various temperatures is confirmed by numerical simulation and comparison of its results with experimental data in additional tests.

A phenomenological two-phase constitutive model for porous shape memory alloys

We present a two-phase constitutive model for pseudoelastoplastic behavior of porous shape memory alloys (SMAs). The model consists of a dense SMA phase and a porous plasticity phase. The overall response of the porous SMA is obtained by a weighted average of responses of individual phases. Based on the chosen constitutive model parameters, the model incorporates the pseudoelastic and pseudoplastic behavior simultaneously (commonly reported for porous SMAs) as well as sequentially (i.e. dense SMAs; pseudoelastic deformation followed by the pseudoplastic deformation until failure). The presented model also incorporates failure due to the deviatoric (shear band formation) and volumetric (void growth and coalescence) plastic deformation. The model is calibrated by representative volume elements (RVEs) with different sizes of spherical voids that are solved by unit cell finite element calculations. The overall response of the model is tested against experimental results from literature. Finally, application of the presented constitutive model has been presented by performing finite element simulations of the deformation and failure in unaixial dog-bone shaped specimen and compact tension (CT) test specimen. Results show a good agreement with the experimental data reported in the literature.

Conventional Plasticity Constitutive Model for Shape Memory Alloys

A two-phase constitutive model for shape memory alloys (SMAs) is proposed based on the fact that SMAs is dynamically composed of austenite and martensite. The behavior of SMAs is regarded as the dynamic combination of the individual behavior of each phase. This model can describe the main characteristics of SMAs, such as pseudoelasticity and shape memory effect. The corresponding numerical algorithm was also developed to describe the main features of shape memory alloy Au-47.5at.%Cd.

Constitutive modeling of strain rate effects in nanocrystalline and ultrafine grained polycrystals

We present a variational two-phase constitutive model capable of capturing the enhanced rate sensitivity in nanocrystalline (nc) and ultrafine-grained (ufg) fcc metals. The nc/ufg-material consists of a grain interior phase and a grain boundary affected zone (GBAZ). The behavior of the GBAZ is described by a rate-dependent isotropic porous plasticity model, whereas a rate-independent crystal-plasticity model which accounts for the transition from partial dislocation to full dislocation mediated plasticity is employed for the grain interior. The scale bridging from a single grain to a polycrystal is done by a Taylor-type homogenization. It is shown that the enhanced rate sensitivity caused by the grain size refinement is successfully captured by the proposed model.

Time-dependent response of polypropylene after strain reversal

Observations are reported in tensile relaxation tests on specimens subjected to stretching up to various maximum strains ϵ max followed by retraction to various minimum strains ϵ. Experimental data show that shapes of relaxation curves on pre-loaded samples are strongly affected by strain increment Δ ϵ = ϵ max − ϵ: (i) when Δ ϵ is small, stress monotonically decays with time, (ii) with an increase in Δ ϵ, the relaxation process becomes non-monotonic, and (iii) at relatively large increments Δ ϵ, stress grows with time. A two-phase constitutive model is derived for the viscoelastic and viscoplastic responses of semicrystalline polymers under arbitrary deformations with small strains. Adjustable parameters in the stress–strain relations are found by fitting the observations. Numerical simulation demonstrates that the model correctly describes the time-dependent behavior of polypropylene subjected to cyclic pre-loading in creep and relaxation tests.

Analysis of Film Blowing with Flow-enhanced Crystallization

Abstract An analysis of the steady-state film blowing process based on a two-phase constitutive model that accounts for flow-enhanced crystallization is presented. The amorphous melt phase is represented by a multi-mode Giesekus constitutive equation with a transformation-dependent relaxation time and the semi-crystalline phase is represented by a rigid rod model. The relaxation times in the two constitutive equations are linked by an Avrami, temperature-dependent rate expression which contains a term in the Helmholtz free energy to account for flow-enhancement. Comparisons are made to experimental data for film blowing of linear low density (LLDPE) and low density (LDPE) polyethylenes. Excellent fits for the bubble radius, temperature, and crystallinity are shown. It is also shown that the ratio of amorphous stress to total stress at the “lock-in” point provides an excellent correlating variable for the elongation to break and yield strength properties of the as-blown film. Inclusion of multiple relaxati...

Analysis of Film Blowing with Flow-enhanced Crystallization

Abstract An analysis of the steady-state film blowing process based on a two-phase constitutive model that accounts for flow-enhanced crystallization is presented. The amorphous melt phase is represented by a multi-mode Giesekus constitutive equation with a transformation-dependent relaxation time and the semi-crystalline phase is represented by a rigid rod model. The relaxation times in the two constitutive equations are linked by an Avrami, temperature-dependent rate expression which contains a term in the Helmholtz free energy to account for flow-enhancement. Comparisons are made to experimental data for film blowing of linear low density (LLDPE) and low density (LDPE) polyethylenes. Excellent fits for the bubble radius, temperature, and crystallinity are shown. It is also shown that the ratio of amorphous stress to total stress at the “lock-in” point provides an excellent correlating variable for the elongation to break and yield strength properties of the as-blown film. Inclusion of multiple relaxati...

Sensitivity analysis of low-speed melt spinning of isotactic polypropylene

Linearized sensitivity analysis of fiber spinning has been studied using a two-phase constitutive model that includes the effects of crystallization. The analysis focuses on sensitivity predictions for the low-speed melt spinning of isotactic polypropylene and comparison to the experimental results of Young and Denn [1989, Disturbance propagation in melt spinning. Chemical Engineering Science 44, 1807–1818]. Modifications in an earlier-developed two-phase model enable comparisons of two different constitutive equations for the melt phase, namely the Giesekus and extended pom-pom models. Comparisons with sensitivity data for low-speed spinning conditions demonstrate that the incorporation of crystallization effects leads to improved predictions of the magnitude and trends of the perturbation frequency dependence for both constitutive equations. At low spin speeds where flow-enhanced crystallization effects are negligible, the sensitivity is predicted to decrease with increasing cooling and this trend is also shown to be consistent with increased crystallinity.

A comprehensive description for shape memory alloys with a two-phase constitutive model

A comprehensive description for the constitutive behavior of polycrystalline shape memory alloys (SMAs) is proposed based on the concept that a SMA is dynamically composed of austenite and martensite, the constitutive behavior of which is a dynamic combination of the individual behavior of each of the two phases. In the interested ranges of stress and temperature the behavior of austenite is assumed to be linearly elastic while that of martensite elastoplastic. The main features of SMAs such as ferroelasticity at lower temperature, shape memory effect (SME), pseudoelasticity at higher temperature and other typical features can be successfully replicated with the proposed constitutive model. The ferroelasticity, pseudoelasticity and SME of SMA Au–47.5 at.%Cd subjected to uniaxial forward and reverse loading and the pseudoelasticity of Cu–Al–Zn–Mn SMA polycrystal subjected to proportional and nonproportional complex stress or strain histories are analyzed and compared with the experimental results.

Two-phase Simulation of Tubular Film Blowing of Crystalline Polymers

Abstract Traditionally, modeling of the film blowing process consisted mainly of balances of the forces on a single layer of thin film and a mathematically defined freeze-line. In this publication we develop an alternative approach for the theoretical analysis for film blowing of crystalline polymer melts by treating the film as two layers, crystallized and amorphous. Therefore, a two-phase constitutive model is presented for the process simulation of the tubular film blowing of crystalline polymer melts. An upper convected Maxwell equation of state with a single relaxation time and the Oldroyd derivative is applied to the amorphous or liquid-like phase while a perfect plastic-elastic model with yield is used to describe the deformations of the crystallized phase. The model interpretations and predictions are obtained and found to be in qualitative agreement with published results. For polyethylene the model appears to help explain the interactions of the processing conditions and fluid-mechanics in the film blowing process of crystalline polymers.