Influence of temperature and strain rate on the mechanical behavior of three amorphous polymers: Characterization and modeling of the compressive yield stress

Uniaxial compression stress–strain tests were carried out on three commercial amorphous polymers: polycarbonate (PC), polymethylmethacrylate (PMMA), and polyamideimide (PAI). The experiments were conducted under a wide range of temperatures (−40 °C to 180 °C) and strain rates (0.0001 s⁻¹ up to 5000 s⁻¹). A modified split-Hopkinson pressure bar was used for high strain rate tests. Temperature and strain rate greatly influence the mechanical response of the three polymers. In particular, the yield stress is found to increase with decreasing temperature and with increasing strain rate. The experimental data for the compressive yield stress were modeled for a wide range of strain rates and temperatures according to a new formulation of the cooperative model based on a strain rate/temperature superposition principle. The modeling results of the cooperative model provide evidence on the secondary transition by linking the yield behavior to the energy associated to the β mechanical loss peak. The effect of hydrostatic pressure is also addressed from a modeling perspective.     

Mechanical behavior of Gamma-Met PX under uniaxial loading at elevated temperatures and high strain rates

Gamma titanium aluminides have received considerable attention over the last decade. These alloys are known to have low density, good high temperature strength retention and good oxidation and corrosion resistance. However, poor ductility and low fracture toughness have been the key limiting factors in the full utilization of these alloys. More recently, a new generation of gamma titanium aluminide alloys, commonly referred to as Gamma-Met PX, has been developed by GKSS, Germany. These alloys have been observed to have superior strength and better oxidation resistance at elevated temperatures when compared with conventional gamma titanium aluminides.The present paper discusses results of a study to understand the uniaxial mechanical behavior in both compression and tension of Gamma-Met PX at elevated temperatures and high strain rates. The compression and tensile tests are conducted using a modified Split-Hopkinson Bar apparatus at test temperatures ranging from room temperature to 900 °C and strain rates of up to 3500 s⁻¹. Under uniaxial compression, in the temperature range from room to 600 °C, the flow stress is observed to be nearly independent of test temperature. However, at temperatures higher than 600 °C thermal softening is observed at all strain rates with the rate of thermal softening increasing dramatically between 800 and 900 °C. The room temperature tensile tests show negligible strain-rate dependence on both yield stress and flow stress. With an increase in test temperature from room to 900 °C, the material shows a drop in both yield and flow stress at all levels of plastic strain. However, the measured flow stress is still higher when compared to nickel based super-alloys and other gamma titanium aluminides under similar test conditions. Also, no anomaly in yield stress is observed up to 900 °C.     

Thermo-mechanical response of nylon 101 under uniaxial and multi-axial loadings: Part I,Experimental results over wide ranges of temperatures and strain rates

A comprehensive study of the thermo-mechanical response of a thermoplastic polymer, nylon 101 is presented. Quasi-static and dynamic compression uniaxial and multi-axial experiments (stress states) were performed at a wide range of strain rates (10⁻⁵ to 5000 s⁻¹) and temperatures (−60 to 177 °C or −76 to 350 °F). The material is found to be non-linearly dependent on strain rate and temperature. The change in volume after plastic deformation is investigated and is found to be negligibly small. The relaxation and creep responses at room temperature are found to be dependent on strain rate and the stress–strain level at which these phenomena are initiated. Total deformation is decomposed into visco-elastic and visco-plastic components; these components have been determined at different levels of deformation. Results from non-proportional uniaxial to biaxial compression, and torsion experiments, are also reported for three different strain rates at room temperature. It is shown that nylon 101 has a response dependent on the hydrostatic pressure.     

TEMPERATURE EFFECT ON LOW-CYCLE FATIGUE BEHAVIOR OF NICKEL-BASED SINGLE CRYSTALLINE SUPERALLOY

The low-cycle fatigue （LCF） behavior of a nickel-based single crystal superalloy with [001] orientation was studied at an intermediate temperature of T0℃ and a higher temperature of To ＋ 250℃ under a constant low strain rate of 10^-3 s^-1 in ambient atmosphere. The superalloy exhibited cyclic tension-compression asymmetry which is dependent on the temperature and applied strain amplitude. Analysis on the fracture surfaces showed that the surface and subsurface casting micropores were the major crack initiation sites. Interior Ta-rich carbides were frequently observed in all specimens. Two distinct types of fracture were suggested by fractogaphy. One type was characterized by Mode-I cracking with a microscopically rough surface at To ＋ 250℃. Whereas the other type at lower temperature T0℃ favored either one or several of the octahedral {111} planes, in contrast to the normal Mode-I growth mode typically observed at low loading frequencies （several Hz）. The failure mechanisms for two cracking modes are shearing of γ＇ precipitates together with the matrix at T0℃ and cracking confined in the matrix and the γ/γ＇interface at To - 250℃.     

Synchronous Full-Field Strain and Temperature Measurement in Tensile Tests at Low,Intermediate and High Strain Rates

Tensile tests with simultaneous full-field strain and temperature measurements at the nominal strain rates of 0.01, 0.1, 1, 200 and 3000 s^?1 are presented. Three different testing methods with specimens of the same thin and flat gage-section geometry are utilized. The full-field deformation is measured on one side of the specimen, using the DIC technique with low and high speed visible cameras, and the full-field temperature is measured on the opposite side using an IR camera. Austenitic stainless steel is used as the test material. The results show that a similar deformation pattern evolves at all strain rates with an initial uniform deformation up to the strain of 0.25–0.35, followed by necking with localized deformation with a maximum strain of 0.7–0.95. The strain rate in the necking regions can exceed three times the nominal strain rate. The duration of the tests vary from 57 s at the lowest strain rate to 197 μs at the highest strain rate. The results show temperature rise at all strain rates. The temperature rise increases with strain rate as the test duration shortens and there is less time for the heat to dissipate. At a strain rate of 0.01 s^?1 the temperature rise is small (up to 48 °C) but noticeable. At a strain rate of 0.1 the temperature rises up to 140 °C and at a strain rate of 1 s^?1 up to 260 °C. The temperature increase in the tests at strain rates of 200 s^?1 and 3000 s^?1 is nearly the same with the maximum temperature reaching 375 °C.     

Analysis of a new hypoplastic equation

A new hypoplastic equation is proposed and its capacity of representing the mechanical behaviour of a silty soil is examined. In this constitutive equation a particular soil is characterised by four material constants having a clear physical meaning (three of them are standard in soil mechanics), which makes the calibration procedure and the interpretation of results easier. Its performance in the prediction of results of several laboratory tests (especially triaxial tests along different stress paths) and as compared to Cam–Clay predictions is, in general, good. The nonexistence of an elastic domain in hypoplasticity provides a more realistic response than that of Cam–Clay in stress paths in which the octahedral stress is reduced. The equation is able to reproduce important characteristics of soils as critical states, the normalised behaviour, the behaviour in proportional deformations, the behaviour in different stress paths. Besides, the equation is simple enough to permit a comprehensive analysis of its response. This is done with the help of the theory of systems of ordinary differential equations. Main results are analytical solutions in proportional deformations and the response diagram.     

Mechanics of the rate-dependent elastic–plastic deformation of glassy polymers from low to high strain rates

A combined experimental and analytical investigation has been performed to understand the mechanical behavior of two amorphous polymers—polycarbonate and poly(methyl methacrylate)—at strain rates ranging from 10⁻⁴ to 10⁴ s⁻¹. This range in strain rates was achieved in uniaxial tension and compression tests using a dynamic mechanical analyzer (DMA), a servo-hydraulic testing machine, and an aluminum split-Hopkinson pressure bar. DMA tension tests were used to characterize the viscoelastic behavior of these materials, with focus on the rate-dependent shift of material transition temperatures. Uniaxial compression tests on the servo-hydraulic machine (10⁻⁴ to 1 s⁻¹) and the split-Hopkinson pressure bar (10³ to 10⁴ s⁻¹) were used to characterize the rate-dependent yield and post-yield behavior. Both materials were observed to exhibit increased rate sensitivity of yield under the same strain rate/temperature conditions as the β-transition of the viscoelastic behavior. A physically based constitutive model for large strain deformation of thermoplastics was then extended to encompass high-rate conditions. The model accounts for the contributions of different molecular motions which become operational and important in different frequency regimes. The new features enable the model to not only capture the transition in the yield behavior, but also accurately predict the post-yield, large strain behavior over a wide range of temperatures and strain rates.     

Strength and deformation behaviors of veined marble specimens after vacuum heat treatment under conventional triaxial compression

The mechanical behaviors of rocks affected by high temperature and stress are generally believed to be significant for the stability of certain projects involving rocks, such as nuclear waste storage and geothermal resource exploitation. In this paper, veined marble specimens were treated to high temperature treatment and then used in conventional triaxial compression tests to investigate the effect of temperature, confining pressure, and vein angle on strength and deformation behaviors. The results show that the strength and deformation parameters of the veined marble specimens changed with the temperature, presenting a critical temperature of 600℃. The triaxial compression strength of a horizontal vein(β = 90°) is obviously larger than that of a vertical vein(β = 0°). The triaxial compression strength,elasticity modulus, and secant modulus have an approximately linear relation to the confining pressure. Finally,Mohr–Coulomb and Hoek–Brown criteria were respectively used to analyze the effect of confining pressure on triaxial compression strength.     

OPERATOR–SPLITTING COMPUTATION OF TURBULENT FLOW IN AN AXISYMMETRIC 180° NARROWING BEND USING SEVERAL k—ϵ MODELS AND WALL FUNCTIONS

This paper describes a finite element implementation of an operator-splitting algorithm for solving transient/steady turbulent flows and presents solutions for the turbulent flow in an axisymmetric 180° narrowing bend, a benchmark problem dealt with at the 1994 WUA-CFD annual meeting. Three k–ϵ based models are used: the standard linear k–ϵ model, a non-linear k–ϵ model and an RNG k–ϵ model. Flow separation after the bend, as observed in the experiment, is predicted by the RNG model and by both the linear and non-linear k–ϵε models with van Driest mixing length wall functions. Good agreement with experimental data of pressure distribution on bending walls is obtained by the present numerical simulation. Results show that there is very little difference between the linear and non-linear k–ϵε models in terms of predicted velocity fields and that the non-linearities mainly affect the distribution of turbulent normal stress and pressure, in analogy to the effect of second-order viscoelastic fluid models on laminar flow. Both the linear and non-linear k–ϵε models fail to predict any flow separation if logarithmic wall functions are used.     

Micro-mechanical modelling of strain induced porosity under generally compressive stress states

This paper is concerned with the nucleation and growth of voids in a titanium alloy undergoing high temperature deformations under generally compressive stress states typical of forging processes. A micro-mechanical model for void nucleation has been developed based on a debonding process between primary alpha particles and the beta matrix. The finite element model developed has been used to examine in detail the stress state sensitivity of void nucleation within the particle-matrix system. The results obtained are compared with other phenomenological approaches showing good agreement for most stress states, but giving different results for a range of compressive stress states. A continuum-level representation of the micro-mechanical results has been obtained and implemented into a finite element model. Cylindrical specimen compression tests have been carried out over the strain rate range 0.005-5.0s⁻¹ and temperature range 925–975°C under conditions of high specimen-die friction.Regions of stress triaxiality that are tensile in nature were therefore generated, and the specimens tested to an overall strain of 0.5 were sectioned, polished and etched. The resulting distributions of voids were quantified, and compared with those predicted using the finite element model discussed above. Good quantitative agreement was obtained both in terms of the magnitude of the area fractions of voids and their distributions. The model also captures reasonably well the strain rate and temperature dependence of the voiding. However, the model assumptions of uniform distributions of alpha particles which are all perfectly spherical and with identical interfacial bond strengths are overly simple, and need to be improved.     

Behaviors of three BCC metal over a wide range of strain rates and temperatures: experiments and modeling

The elastic–plastic behaviors of three body-centered cubic metals, tantalum, tantalum alloy with 2.5% tungsten, and AerMet 100 steel, are presented over a wide range of strains (15%), strain rates (10⁻⁶–10⁴ s⁻¹) and temperatures (77–600°F). Johnson-Cook and Zerilli-Armstrong models were found inadequate to describe the observations. A new viscoplastic model is proposed based on these experimental results. The proposed constitutive model gives good correlations with these experimental results and strain-rate jump experiments. In the next paper (Liang, R., Khan A.S., 2000. Behaviors of three BCC metals during non-proportional multi-axial loadings and predictions using a recently proposed model. International Journal of Plasticity, in press), multi-axial loading results on these materials and comparison with the proposed model will be presented.     

Experimental Technique to Characterize the Plastic Behaviour of Metallic Materials in a Wide Range of Temperatures and Strain Rates: Application to a High-Carbon Steel

This paper presents high temperature quasi-static and dynamic tensile testing. Samples are heated by an induction system controlled with a pyrometer. A high-speed camera (500 fps) is used to determine displacement fields with a digital image correlation software. For such tests a specific marking procedure of the sample is applied. This method is used to characterize the mechanical behaviour of a C68 high-carbon steel at temperatures up to 720 °C. Stress-strain curves are given from room temperature up to 720 °C at strain rates ranging from 400 /s to 4 × 10² /s.     

The mechanisms governing the activation of dislocation sources in aluminum at different strain rates

This article examines the time to activate Frank–Read sources in response to macroscopic strain rates ranging from 10¹ s⁻¹ to 10¹⁰ s⁻¹ in aluminium under athermal conditions. We develop analytical models of the bowing of a pinned dislocation segment as well as numerical simulations of three dimensional dislocation dynamics. We find that the strain rate has a direct influence on both the activation time and the source strength of Frank–Read sources at strain rates up to 10⁶ s⁻¹, and the source strength increases in almost direct proportion to the strain rate. This contributes to the increase in the yield stress of materials at these strain rates. Above 10⁶ s⁻¹, the speed of the bowing segments reaches values that exceed the domain of validity of the linear viscous drag law, and the drag law is modified to account for inertial effects on the motion of the dislocation. As a result the activation times of Frank–Read sources reach a finite limit at strain rates greater than 10⁸ s⁻¹, suggesting that Frank–Read sources are unable to operate before homogeneous nucleation relaxes elastic stresses at the higher strain rates of shock loading. Elastodynamic calculations are carried out to compare the contributions of Frank–Read sources and homogeneous nucleation of dislocations to plastic relaxation. We find that at strain rates of 5×10⁷ s⁻¹ homogeneous nucleation becomes the dominant generation mechanism.     

Multiaxial creep and cyclic plasticity in nickel-base superalloy C263

Physically-based constitutive equations for uniaxial creep deformation in nickel alloy C263 [Acta Mater. 50 (2002) 2917] have been generalised for multiaxial stress states using conventional von Mises type assumptions. A range of biaxial creep tests have been carried out on nickel alloy C263 in order to investigate the stress state sensitivity of creep damage evolution. The sensitivity has been quantified in C263 and embodied within the creep constitutive equations for this material. The equations have been implemented into finite element code. The resulting computed creep behaviour for a range of stress state compares well with experimental results. Creep tests have been carried out on double notched bar specimens over a range of nominal stress. The effect of the notches is to introduce multiaxial stress states local to the notches which influences creep damage evolution. Finite element models of the double notch bar specimens have been developed and used to test the ability of the model to predict correctly, or otherwise, the creep rupture lifetimes of components in which multiaxial stress states exist. Reasonable comparisons with experimental results are achieved. The γ^′ solvus temperature of C263 is about 925 °C, so that thermo-mechanical fatigue (TMF) loading in which the temperature exceeds the solvus leads to the dissolution of the γ^′ precipitate, and a resulting solution treated material. The cyclic plasticity and creep behaviour of the solution treated material is quite different to that of the material with standard heat treatment. A time-independent cyclic plasticity model with kinematic and isotropic hardening has been developed for solution treated and standard heat treated nickel-base superalloy C263. It has been combined with the physically-based creep model to provide constitutive equations for TMF in C263 over the temperature range 20–950 °C, capable of predicting deformation and life in creep cavitation-dominated TMF failure.     

Dehydration characteristics and mathematical modelling of lemon slices drying undergoing oven treatment

In this study, the effect of drying temperature on drying behaviour and mass transfer parameters of lemon slices was investigated. The drying experiments were conducted in a laboratory air ventilated oven dryer at temperatures of 50, 60 and 75 °C. It was observed that the drying temperature affected the drying time and drying rate significantly. Drying rate curves revealed that the process at the temperature levels taken place in the falling rate period entirely. The usefulness of eight thin layer models to simulate the drying kinetics was evaluated and the Midilli and Kucuk model showed the best fit to experimental drying curves. The effective moisture diffusivity was determined on the basis of Fick’s second law and obtained to be 1.62 × 10^?11, 3.25 × 10^?11 and 8.11 × 10^?11 m² s^?1 for the temperatures of 50, 60 and 75 °C, respectively. The activation energy and Arrhenius constant were calculated to be 60.08 kJ mol^?1 and 0.08511 m² s^?1, respectively. The average value of convective mass transfer coefficient for the drying temperatures of 50, 60 and 75 °C was calculated to be 5.71 × 10^?7, 1.62 × 10^?6 and 2.53 × 10^?6 m s^?1, respectively.     

Influence of Portevin-Le Chatelier Effect on Shear Strain Path Reversal in an Al-Mg Alloy at Room and High Temperatures

The main objective of this study is to characterize the mechanical behaviour of an Al-Mg alloy in conditions close to those encountered during sheet forming processes, i.e. with strain path changes and at strain rates and temperatures in the range 1.2×10^?3–1.2×10^?1 s^?1 and 25–200°C, respectively. The onset of jerky flow and the interaction of dynamic strain ageing with the work-hardening are investigated during reversed-loading in specific simple shear tests, which consist of loading up to various shear strain values followed by reloading in the opposite direction, combined with direct observations of the sample surface using a digital image correlation technique. Both strain path changes and temperature are clearly shown to influence the occurrence and onset of the Portevin-Le Chatelier (PLC) effect. Moreover, the Bauschinger effect observed in the material response shows that the PLC effect has a major influence on the kinematic contribution to work-hardening as well as its stagnation during the reloading stage, which could open up interesting lines of research to improve theoretical plasticity models for this family of aluminium alloys.     

An experimental investigation of a superplastic constitutive equation in Al–Mg–Si alloy composites reinforced with Si3N4 whiskers

Superplastic properties at 818 K were investigated by tensile tests for Al–Mg–Si alloy composites reinforced with Si₃N₄ whiskers whose volume fractions were 0–30%. The 20 and 30 vol.% composites exhibited large elongation of 615 and 285% at a high strain rate of 2×10⁻¹ s⁻¹, respectively. High strain rate superplasticity of the composites is attributed to the very small grain size of less than 3 μm. The stress–strain rate relation for the composites was almost the same as that of the alloy, taking into consideration the influences of threshold stress and grain size, and the relation was independent of the volume fraction of whisker. This is probably because grain boundary sliding was not hampered by the whiskers due to the presence of liquid phase for the composites.     

Plastic anisotropy and the role of non-basal slip in magnesium alloy AZ31B

Mechanistic explanations for the plastic behavior of a wrought magnesium alloy are developed using a combination of experimental and simulation techniques. Parameters affecting the practical sheet formability, such as strain hardening rate, strain rate sensitivity, the degree of anisotropy, and the stresses and strains at fracture, are examined systematically by conducting tensile tests of variously oriented samples at a range of temperatures (room temperature to 250 °C) and strain rates (10⁻⁵–0.1 s⁻¹). Polycrystal plasticity simulations are used to model the observed anisotropy and texture evolution. Strong in-plane anisotropy observed at low temperatures is attributed to the initial texture and the greater than anticipated non-basal cross-slip of dislocations with 〈a〉 type Burgers vectors. The agreement between the measured and simulated anisotropy and texture is further validated by direct observations of the dislocation microstructures using transmission electron microscopy. The increase in the ductility with temperature is accompanied by a decrease in the flow stress, an increase in the strain rate sensitivity, and a decrease in the normal anisotropy. Polycrystal simulations indicate that an increased activity of non-basal, 〈c + a〉, dislocations provides a self-consistent explanation for the observed changes in the anisotropy with increasing temperature.     

Investigation on rough rice drying kinetics at various thin layers of a deep bed

Moisture content gradients along the bed column are commonly neglected during simulation of deep-bed grain drying. In this study, rough rice drying kinetics at various thin layers of a deep bed was investigated. The experiments were conducted under different drying conditions and the data were compared with the values predicted by a previously developed non-equilibrium model for numerical simulation of grain drying. The moisture content gradients related to the rough rice column indicated that the higher the drying layer, the more was the moisture content at each drying time. The constant drying rate period was observed neither for any thin layers nor for the entire drying column. The drying rate of the lower layers continuously decreased with drying time, whereas that of the upper layers firstly increased and then decreased. The implemented model predicted drying process with a high accuracy at various layers. However, the values of maximum relative error (RE _max ) and mean relative error (MRE) increased as the air temperature increased, and reversely decreased with the air velocity. The higher values of MRE and RE _max were related to the layer 1 (0–5 cm bed height) at temperature of 60 °C and air velocity of 0.4 m s^?1, and the lower values belonged to the layer 4 (15–20 cm bed height) at temperature of 40 °C and air velocity of 0.9 m s^?1.     

A critical state sand model with elastic–plastic coupling

Soil elastic moduli are highly pressure-dependent. Experimental findings have indicated that the elastic shear modulus of sands depends on p^χ, where p is mean principal effective stress and χ is a non-dimensional parameter. χ practically remains unchanged for shear strains less than 10⁻⁵ where the mechanical behavior is purely elastic. However, experiments have revealed that the emergence of plasticity for shear strains larger than 10⁻⁵ provokes a gradual increase in χ. Technically, this observation is an elastic–plastic coupling effect in which plasticity causes to change the elastic characteristics. Here, this issue is considered in hyper-elasticity framework in conjunction with a critical state compatible bounding surface plasticity platform for granular soils. To this aim, constitutive equations linking χ to a proper kinematic hardening parameter are presented. Then, using the proposed approach, a hyper-elastic theory is modified to consider the mentioned elastic–plastic coupling effect in the whole domain of the elastoplastic behavior. Adopting the improved hyper-elasticity necessitates the modification of a number of basic plasticity platform elements. In this regard, dilatancy and plastic hardening modulus of the bounding surface platform are modified. Successful performance of the modified constitutive model is presented against experimental data of loading/unloading triaxial tests.