Viscoplastic–plastic modelling of IN792

At high temperatures metallic materials behave in a viscous manner exemplified by strain rate dependence, stress relaxation and creep deformation. At low temperatures however, these effects are extremely small, and the behaviour is strain rate independent and shows no or very small relaxation effects. Finally there exists an intermediate region, in which the material behaviour is close to strain rate independent for high strain rates but at the same time shows time dependent inelastic effects, such as stress relaxation and creep. For IN792 this occurs at temperatures around 650 °C. The article describes the extension of a power-law viscoplastic model describing the behaviour of IN792 at 850 °C, also to describe the behaviour at 650 °C, by bounding the elastic–viscoplastic stress-space by a plastic yield surface. The model parameters have been estimated using data from creep test and tailored step relaxation tests, and the model fits well to both the step relaxation data aimed at resembling relevant component conditions and long term creep data.     

Constitutive equations for the nonlinear viscoelastic and viscoplastic behavior of thermoplastic elastomers

Observations are reported in uniaxial tensile tests with constant strain rates at moderate finite deformations, as well as in creep and relaxation tests on a thermoplastic elastomer (ethylene–octene copolymer) at room temperature. A constitutive model is developed for the viscoelastic and viscoplastic responses of a polymer at arbitrary three-dimensional deformations with finite strains. A thermoplastic elastomer is treated as an incompressible heterogeneous transient network of strands. Its viscoelastic behavior is associated with separation of active strands from their junctions and merging of dangling strands with the network. The viscoplastic response reflects sliding of junctions between strands with respect to their reference positions. Stress–strain relations are derived by using the laws of thermodynamics. They involve six adjustable parameters that are found by fitting the experimental data. To examine the accuracy of the model predictions, plane-strain compressive tests with constant strain rates and relaxation tests at compression are performed. Good agreement is demonstrated between the observations and the results of numerical simulation.     

Modeling of viscoplastic rate-dependent hardening-softening behavior of hot mix asphalt in compression

The objective of this paper is to model viscoplastic rate-dependent hardening-softening behavior that is experimentally observed from hot mix asphalt (HMA) under repetitive creep and recovery loading in compression. A differential equation is utilized to incorporate the effects of the stress history into yield stress, and an internal variable representing rate dependence in the equation is set as a function of the viscoplastic strain rate to address the change in rate dependence of the material due to gradual hardening. Also, a separate rate-dependent function concept is adopted to describe the difference in rate dependence of the yield stress during unloading and loading. The developed viscoplastic model is applied using the time–temperature superposition principle and shows good agreement with the measured viscoplastic responses of HMA under repetitive creep and recovery loading with various load levels and rest periods.     

Applicability of Anisotropic Viscoelasticity of Paper at Small Deformations

In this paper the applicability of two-dimensional phenomenlogical linear viscoelastic modelling aimed at printing applications is presented. An iterative algorithm is used to find model parameters evaluated from dynamic mechanical testing at stationary conditions. Experiments are performed in the time domain with different load stimuli in either displacement or force control. The experiments are compared to model predictions.The results show that only small deviations were found on model parameters from the algorithm used on either the loss or the storage properties of paper. This was illustrated by converting line spectra from storage compliances to loss compliances within the frequency domain. The harmonic properties were obtained at conditions with nonlinear material behaviour. Despite this, the two-dimensional linear viscoelastic model described well the behaviour of paper at different states of stress and strain at levels adequate for web-fed printing. The usefulness of the relation between retardances and relaxances was examined by comparing model predictions with different driving stimuli resulting in either creep or relaxation. The time-dependent transverse strain of machine-made paper due to either longitudinal stress relaxation or creep was demonstrated. Finally, extensions of the present model including inelastic material behaviour were discussed.     

High temperature mechanical spectroscopy and creep of calcium hexaluminate

Samples of calcium hexaluminate (CA₆) were studied by four-point bending creep tests and mechanical spectroscopy at temperatures between 1300 and 1600 K. By using the temperature-compensated time concept, proposed by Dorn (1954, 1956), activation enthalpies of the order of 620 kJ/mol were deduced from both the isothermal creep and the internal friction measurements. A generic curve, “ master curve”, is obtained by a superposition of the isothermal mechanical loss spectrum along the temperature-compensated frequency axis. The master curve is composed of two components: a high-frequency part (peak) and a low-frequency part (exponential background). Both the peak and the background decrease after performing torsional creep. Additionally, the peak shifts towards higher frequency after annealing. The high temperature mechanical loss behavior of CA₆ is discussed in terms of a dislocation model invoking anelastic and viscoplastic relaxation phenomena.     

Creep failure model of a tempered martensitic stainless steel integrating multiple deformation and damage mechanisms

A new model considering both deformation and damage evolution under multiple viscoplastic mechanisms is used to represent high temperature creep deformation and damage of a martensitic stainless steel in a wide range of load levels. First, an experimental database is built to characterise both creep flow and damage behaviour using tests on various kinds of specimens. The parameters of the model are fitted to the results and to literature data for long term creep exposure. An attempt is made to use the model to predict creep time to failure up to 10⁵ h.     

Uniaxial nonlinear viscoelastic viscoplastic modeling of polypropylene

This paper presents the application of the Schapery viscoelastic and the Perzyna viscoplastic models to strain recovery data of polypropylene. In a previous study, the recovery of strain after monotonic uniaxial tensile loading was measured to gather information on the viscoelasticity and viscoplasticity. The viscoplastic strains from several load histories were determined and are used to calibrate the viscoplastic model. The parameters of the one-dimensional Schapery model are then found by nonlinear optimization using the strain recovery history. The prediction of stress relaxation and creep behavior is investigated.     

New achievements in visco-elastoplastic constitutive model and temperature sensitivity of glasphalt

This paper focuses on the experimental investigation on temperature sensitivity and visco-elastoplastic behaviour of glasphalt. Classic Burgers creep model could only describe the viscoelastic behaviour of materials before the third creep-phase, so a viscoplastic string is added in series with classic Burgers model in order to predict the visco-elastoplastic behaviour of glasphalt. In this research, the effects of loading stress and temperature on creep behaviour of glasphalt under dynamic loading are investigated. In addition, some methods were used to solve model parameters and then predictions from proposed model were compared with experimental results. It was shown that creep testing curves coincided well with theoretic curves, validating that modified Burgers model can completely characterise creep behaviour of glasphalt. Besides, temperature sensitivity of glasphalt was evaluated by using indirect tensile stiffness modulus test, and stiffness modulus behaviour model of glasphalt was presented based on the experimental results and numerical analysis.     

A computational comparison of the inelastic constitutive models of hart and miller

Summary The uniaxial response behavior of Hart's and Miller's nonelastic constitutive equations is compared. These models have been selected because they are fully developed and have been applied on the uniaxial nonelastic response behavior of different materials. Among these for stainless steel AISI 316 the complete set of material parameters for both models has been published. Based on these parameter sets a comparison of both models is performed including monotonic strain controlled tensile tests, creep tests, load relaxation tests and cyclic tests. The predictions of both models are compared with available experimental data.Both models can not describe the whole range of experimental data. For Hart's model one essential flow parameter had to be adjusted to obtain a reasonable simulation of creep experiments. Further it gives unrealistic predictions for strain cycling. The incorporation of a so-called negative strain rate sensitivity severly restricts the practical applicability of Miller's model. Additionally in the high temperature regime the response curves for load relaxation tests deviate considerably from the experimentally observed ones at low strain rates. Both models have to be improved for practical applications.With 11 Figures     

Creep life assessment method for online monitoring of steam turbine rotors

The principal objective of work was to develop fast and accurate method for online creep life monitoring of steam turbine rotors. For this purpose, a characteristic strain model of creep was investigated and validated using test data of 2%CrMoV rotor steel. The model was then used to determine creep damage functions which are introduced to compute creep damage at a constant temperature based on the Robinson time fraction rule. Finite element (FE) creep calculations of a turbine rotor were performed using the same creep model to obtain reference damage results for validating the proposed method. Comparisons of the results obtained using both methods showed a very good accuracy of the online creep damage predictions.     

A nonlinear viscoelastic–viscoplastic model for adhesives

We consider the nonlinear viscoelastic–viscoplastic behavior of adhesives. We develop a one-dimensional nonlinear model by combining Schapery’s nonlinear single integral model and Perzyna’s viscoplastic model. The viscoplastic strain was solved iteratively using the von Mises yield criterion and nonlinear kinematic hardening. The combined viscoelastic–viscoplastic model was solved using Newton’s iteration and implemented into a finite element model. The model was calibrated using creep-recovery data from bulk adhesives and verified from the cyclic behavior of the bulk adhesives. The finite element model results agreed with experimental creep and cyclic responses, including recoverable and permanent strain after load removal. Although the contribution of the viscoplastic strain was small, both viscoplastic and viscoelastic components of strain response were required to describe the adhesive creep and cyclic response.

     

Modelling the Non-Linear Viscoelastic and Viscoplastic Behaviour of Aramid Fibre Yarns

A non-linear viscoelastic viscoplastic model is proposed for the tensilebehaviour of aramid fibres, based on an analysis of the deformationmechanisms of these materials. This model uses the macroscopicformulation developed by Schapery together with the plasticity conceptof Perzyna. A simple identification procedure for the model parametershas been developed using creep/recovery cycles at different load levels.The identification reveals that two of the four parameters of theviscoelastic model (g ₁ and a _σ) are independent of stresslevel. This may be due to the simple and regular nature of the fibrestructure. The model enables the parameters which characterise thenon-linear reversible viscoelasticity to be identified independentlyfrom those which characterise the viscoplasticity. The model predictionsare compared to experimental data for a more complex load sequence andreasonable correlation is obtained.     

A temperature dependent creep damage model for polycrystalline ice

We present a continuum damage model for the temperature dependent creep response of polycrystalline ice under a multiaxial state of stress, suited for ice in polar regions. The proposed model is based on a thermo-viscoelastic constitutive law for ice creep and a local orthotropic damage accumulation law for tension, compression and shear loadings. Orthotropic damage is represented by a symmetric second-order damage tensor and its effect on creep is incorporated through the effective stress concept. The unknown model parameters are first calibrated using published experimental data from constant uniaxial stress tests and then predictions are made for constant strain rate and multiaxial loadings. The predicted results are in good agreement with both experimental and numerical results in the literature illustrating the viability of the proposed model. The model is mainly intended for studying the failure mechanisms of polar ice at low deformation rates with depth varying temperature profiles.     

Viscoplastic response and creep failure time prediction of polymers based on the transient network model

The nonlinear viscoelastic/viscoplastic response of polymeric materials is described by a new model based on previous works in terms of monotonic loading, stress–relaxation, and creep. In the proposed analysis, following a constitutive equation of viscoelasticity, based on the transient network theory, essential modifications are introduced, which account for the nonlinearity and viscoplasticity at small elastic and finite plastic strain regime. In addition, viscoplastic response is successfully analyzed by a proper kinematic formulation, which is combined with a functional form of the rate of plastic deformation. A three-dimensional constitutive equation is then derived for an isotropic incompressible medium. This analysis is capable of capturing the main aspects of inelastic response and the instability stage taking place at the tertiary creep, related to the creep failure. Model simulations described successfully the experimental data of polypropylene, which were performed elsewhere.     

Creep-recovery behaviour of cork

Creep tests were performed in cork samples under compression, at different temperatures between 0 and 50 °C. Master curves for the creep behaviour along the radial and axial directions could be constructed from short-time creep experiments, that could be described by a simple empirical model. The temperature shift factors were used to build a relaxation plot, where, assuming an Arrhenius model, an activation energy of 172 kJ mol^− 1 was obtained from the data in the two principal directions. Comparison with previous dynamic mechanical analysis (DMA) and dielectric results suggests that the relaxation behaviour observed around room temperature could play an active role in the molecular mechanisms underlying the creep process in cork. From preliminary recovery studies it was seen that a fraction of the strain resulting from creep is preserved permanently, especially if the load is applied along the axial direction. This irreversible strain exhibited a linear relationship with the logarithm of the creep time, thus not being related to the irreversible viscous flow intrinsic to the material. Scanning electronic microscopy observations showed that creep could, in fact, lead to the bucking of the cellular structure of cork, this process being an active and time-dependent contributor for the permanent deformation of cork upon creep.     

Creep rupture and viscoelastoplasticity of polypropylene

Observations are reported on isotactic polypropylene in tensile tests with various strain rates, relaxation tests at various strains, and creep tests with various stresses at room temperature. Constitutive equations are derived for the viscoelastic and viscoplastic responses of semicrystalline polymers at three-dimensional deformations with small strains. The stress-strain relations involve eight material constants that are found by fitting the experimental data. The model is applied to the numerical analysis of creep failure of polypropylene under various deformation modes (uniaxial tension, equi-biaxial tension, shear, multiple-step creep tests).     

Damage mechanics based predictions of creep crack growth in 316 stainless steel

This paper describes a novel modelling process for creep crack growth prediction of a 316 stainless steel using continuum damage mechanics, in conjunction with finite element (FE) analysis. A damage material behaviour model, proposed by Liu and Murakami [1], was used which is believed to have advantages in modelling components with cracks. The methods used to obtain the material properties in the multiaxial form of the creep damage and creep strain equations are described, based on uniaxial creep and creep crack growth test data obtained at 600 °C. Most of the material constants were obtained from uniaxial creep test data. However, a novel procedure was developed to determine the tri-axial stress state parameter in the damage model by use of creep crack growth data obtained from testing of compact tension (CT) specimens. The full set of material properties derived were then used to model the creep crack growth for a set of thumbnail crack specimen creep tests which were also tested at 600 °C. Excellent predictions have been achieved when comparing the predicted surface profiles to those obtained from experiments. The results obtained clearly show the validity and capability of the continuum damage modelling approach, which has been established, in modelling the creep crack growth for components with complex initial crack shapes.