Mechanics of Time-Dependent Materials

The ductile failure behavior of materials is of great relevance for the modeling of forming and cutting processes, as the stable process parameter range is strongly influenced by the maximum deformation up to failure. Many publications show that the failure behavior not only depends on the material but also on the loading conditions which differ from process to process. For the characterization of the ductile failure behavior of normalized AISI 1045 experiments and finite element simulations were performed to identify the influence of stress triaxiality, plastic strain rate and temperature on failure strain. For the validation of the analytically based failure model the results for a dynamically loaded shear specimen were compared for finite element simulation and experiment. The failure model developed shows a good description of the experimentally observed material response.

In the present work, the effect of viscoelasticity on the yield behaviour of a polycarbonate, PC, was studied and the identification of a yield criterion which takes into account the effects of the mechanical history on the onset of plastic strain, was attempted. The attention was focused on the shear yielding plastic deformation process and different loading histories were performed under uniaxial compression: constant strain rate at different rates, stress relaxation at different applied strain levels, creep under different stress levels. Some tests were also carried out under shear loading, in which the hydrostatic stress component is equal to zero and its effect on the yield onset can be considered. For the definition of a yield criterion, different quantities, some already proposed in an analogous work on a styrene-acrylonitrile copolymer (SAN), were considered and determined at yield onset for each of the applied loading histories. The results obtained in this work show that the relative ratios of the viscoelastic strain over the overall strain and of viscoelastic energy over the deformation work are fairly constant irrespective of both loading history and stress state. The re-elaboration of the data previously obtained on SAN is consistent with these results. Discussing the experimental data, differences between the mechanical behaviour of the two glassy polymers were pointed out and a more difficult activation of the plastic deformation process of PC than SAN was generally observed.

The creep–fatigue crack-growth tests of HASTELLOY® X alloy were carried out at the temperatures of 649°C, 816°C, and 927°C in laboratory air. The experiments were conducted under a constant stress-intensity-factor-range (ΔK) control mode with a R-ratio of 0.05. In the constant ΔK tests, a ΔK of 27.5MPa Ö{m}\sqrt{\mathrm{m}} and a triangular waveform with a frequency of 0.333 Hz were used. Various tensile hold times at the maximum load were imposed to study fatigue and creep–fatigue interactions. Crack lengths were measured by a direct current potential drop method. In this paper, effects of hold time and temperature on the crack-growth rates are discussed. Furthermore, the crack-growth rates of the HASTELLOY® X alloy are compared to those of the HAYNES® 188 and HAYNES® 230® superalloys.

Plastics and fiber-reinforced plastics (FRP) are used in the aerospace industry because of their mechanical properties. However, despite their excellent high-temperature mechanical properties, plastics and FRP eventually deform visco-elastically at high temperatures. Most of the research has focused on the creep behavior of FRPs, but few studies have investigated the linear visco-elastic behavior. Linear visco-elastic behavior and non-linear visco-elastic behavior occur with physical aging in these plastics. In this study, the non-linear visco-elastic behavior of plastics and FRP was investigated based on the bending creep deformation of polycarbonate (PC) and polyoxymethylene (POM). Moreover, the effects of the fiber volume fraction on the creep characteristics were investigated using glass fiber-reinforced polycarbonate (GFRPC). The creep deformation was calculated using the linear visco-elastic theory based on these effects, and comparison between experimental and estimated data showed that the creep analysis sufficiently predicted the creep behavior. KeywordsCreep–Time–Temperature–Physical aging–Crystallization–Crystallinity–Polycarbonate–Polyoxymethylene–Creep analysis–Time–temperature superposition principle

Creep-fatigue tests of Type 304 stainless steel were carriedout using smooth round bar specimens. Cavities and small cracksinitiated inside the specimen were observed on the cross-section bymeans of a scanning laser microscope. The results obtained aresummarized as follows. (1) From the beginning of the creep-fatigue test,spherical cavities appear at random locations on grain boundaries, oneafter another. (2) The cavities on the grain boundaries perpendicular tothe stress axis preferentially grow, and change shape from spherical toflat oblate (or crack-like). (3) When the ligament area on a grainboundary plane reduces to a half, the cavities coalesce and bring abouta complete break of the grain boundary, which is defined as theinitiation of a small crack. (4) Mean growth rate of cavities and crackslocates in the vicinity of the crack propagation law which can bederived from the relationship between the propagation rate of largecrack and creep J-integral range fortime-dependent fatigue of Type 304 stainless steel.

This paper presents a 3D moisture-stress numerical analysis for timber structures under variable humidity and load conditions. An orthotropic viscoelastic-mechanosorptive material model is specialized on the basis of previous models. Both the constitutive model and the equations needed to describe the moisture flow across the structure are implemented into user subroutines of the Abaqus finite element code and a coupled moisture-stress analysis is performed for several types of mechanical loads and moisture changes. The presented computational approach is validated by analyzing some wood tests described in the literature and comparing the computational results with the reported experimental data.

The uniaxial compressive mechanical response of an epoxy, Epon 828/T-403, was experimentally, measured over a strain-rate range of 1.1 10-4 to 5.2 103 s-1. A modified split Hopkinson pressure bar was employed to apply dynamic compressive loading over a very short time of 0.2 millisecond, whereas an MTS was used to conduct quasi-static experiments at a duration of 0.2 to 2,000 seconds to determine strain-rate sensitivity. The experimental results show that the compressive strength of the epoxy increases with increasing strain rate until adiabatic heating offsets the strain-rate hardening. A constitutive model based on the Johnson–Cook model was constructed to describe the stress-strain behavior of the epoxy at the strain rates tested. A Ludwig equation was modified to model the stress-strain behavior at a reference strain rate, which included elastic deformation, a yield-like peak, and a strain-softening region. A hyperbolic tangent function provided a good description of the strain-rate effect. The material constants in this proposed model were determined using the experimental results.

Experimental results on the uniaxial compressive stress-strainbehavior of Epon 828/T-403 over a strain rate range from 1.1 10–4 to 5.2 103 s–1were simulated using a viscoelastic viscoplastic constitutive modeldeveloped by Hasan and Boyce (1995). An optimal combination of materialparameters for the constitutive model was determined by curve-fittingthe experimental results. A comparison between the modeling andexperimental results shows that this model, with proper parameters, iscapable of capturing the strain-rate effects, as well as the typicalpolymeric compressive stress-strain behavior, of Epon 828/T-403, whichincludes the stages of linearly elastic, nonlinearly elastic, yield-like(peak) behavior, strain softening, and nearly perfect flow. For all thestress-strain behavior modeled over seven decades of strain rate span,the maximum error between modeling and experimental results is less than25%. The temperature increase induced by the dissipated plasticwork is also computed and found to be between 3 and8C at these strain rates.

This article concerns certain aspects of the time-dependent response ofcross-ply polymeric composites consisting of stitched graphite fiberstrands embedded in urethane resin. Experimental data were collected atseveral levels of stress and temperature, as well as at various loadorientations. The time-dependent strains were shown to consist of thesum of a fully recoverable viscoelastic component and a permanentportion, which could be expressed empirically. The utility andshortcomings of the power-law creep form are being examined, suggestingthat its validity for making long term predictions may require that`short time' data must be collected over durations that exceed a certaintime-span. The article presents several results that demonstrate thepredictive capabilities of some of the formulations employed therein.

In this paper some experimental results and analyses regarding the behavior of AISI 420 martensitic stainless steel under different environmental conditions are presented. That way, mechanical properties like ultimate tensile strength and 0.2 percent offset yield strength at lowered and elevated temperatures as well as short-time creep behavior for selected stress levels at selected elevated temperatures of mentioned material are shown. The temperature effect on mentioned mechanical properties is also presented. Fracture toughness was calculated on the basis of Charpy impact energy. Experimentally obtained results can be of importance for structure designers. KeywordsAISI 420 steel–Mechanical properties–Lowered and elevated temperatures–Creep behavior–Fracture toughness assessment

When a proton exchange membrane (PEM) based fuel cell is placed in service, hygrothermal stresses develop within the membrane and vary widely with internal operating environment. These hygrothermal stresses associated with hygral contraction and expansion at the operating conditions are believed to be critical in membrane mechanical integrity and durability. Understanding and accurately modeling the viscoelastic constitutive properties of a PEM is important for making hygrothermal stress predictions in the cyclic temperature and humidity environment of operating fuel cells. The tensile stress relaxation moduli of a commercially available PEM, Gore-Select® 57, were obtained over a range of humidities and temperatures. These tests were performed using TA Instruments 2980 and Q800 dynamic mechanical analyzers (DMA), which are capable of applying specified tensile loading conditions on small membrane samples at a given temperature. A special humidity chamber was built in the form of a cup that encloses tension clamps of the DMA. The chamber was inserted in the heating furnace of the DMA and connected to a gas humidification unit by means of plastic tubing through a slot in the chamber. Stress relaxation data over a temperature range of 40–90°C and relative humidity range of 30–90% were obtained. Thermal and hygral master curves were constructed using thermal and hygral shift factors and were used to form a hygrothermal master curve using the time temperature moisture superposition principle. The master curve was also constructed independently using just one shift factor. The hygrothermal master curve was fitted with a 10-term Prony series for use in finite element software. The hygrothermal master curve was then validated using longer term tests. The relaxation modulus from longer term data matches well with the hygrothermal master curve. The long term test showed a plateau at longer times, suggesting an equilibrium modulus.

Polymers are becoming increasingly used in aerospace structural applications, where they experience complex, non-static loads. Correspondingly, the mechanical properties at high strain rates are of increasing importance in these applications. This paper investigates the compressive properties of Epon 826 epoxy resin cured with diethynolamine (DEA) across strain rates from 10−3 to 104s−1. Specimens were tested using an Instron mechanical testing machine for static loading, traditional split Hopkinson pressure bars (SHPBs) for high strain rates, and a miniaturized SHPB for ultra-high strain rates. Additionally, the material was tested using dynamic mechanical analysis to determine the effects of time and temperature equivalences on the strain rate behavior of the samples. The experimental data is used to fit the Mulliken-Boyce model, modified for one-dimension, which is able to capture the compressive mechanical properties over a range of strain rates.

In this paper, we study the transient flow of branched polymer melts with contrasting shear and elongational properties in planar 4:1 abrupt and rounded-corner contractions. This includes Single and Double Extended forms of the Pom–Pom model (SXPP and DXPP), comparing the transient behaviour for these two different models. With the DXPP version, the evolution of the molecular-chain backbone stretch (λ) is described by a dynamic equation, whilst in the SXPP form, stretch is an instantaneous algebraic function of the stress tensor (τ). Simulations are performed with a hybrid finite volume/element algorithm. The momentum and continuity equations are solved by a Taylor–Galerkin/pressure-correction finite element method, whilst the constitutive equation is dealt with by a cell-vertex finite volume algorithm. We demonstrate some novel features due to the influence and imposition of realistic transient boundary conditions on evolutionary flow-structure. The different effects of various model parameter choices are also exposed through transient field response in principle stress difference fringe patterns, rates of deformation, first and second normal stress difference, stress and stretch. KeywordsPom–pom model–Transient shear and extensional viscosity–Branched molecular structure–Sharp and rounded-corner contraction

The creep of paper is accelerated by moisture cycling, an effect known as mechano-sorptive creep. In this paper, the effect of different amplitudes of the moisture content is investigated experimentally and numerically. Tensile creep tests were made in a climate chamber. Low basis weight isotropic sheets were used in the tests. The moisture content history was measured during each creep test using a balance placed in the climate chamber. The experimental results are compared to predictions using a theoretical network model. A brief description of the model is given. In the model it is assumed that the anisotropic hygroexpansion of the fibres produces large stresses at the fibre–fibre bonds when moisture changes. The resulting stress state will accelerate creep if the material obeys creep laws that are nonlinear in stress. A quite good fit between the theoretical model and the experimental creep curves is obtained.

The relaxation phenomena defined by De Groot and Mazur (1962)describe the internal reorganizations linked to the return toequilibrium of media subjected to external perturbations of lowamplitude (near the equilibrium state). Far from equilibrium, anytheoretical approach to these phenomena has to include the followinginformation: the internal reorganizations are multiple and theirkinetics are nonlinear. Indeed, much experimental evidence has lead tothis conclusion. A classical example for the analysis of relaxationsnear the glass transition is the experimental study of the volumerecovery of PVAc (Polyvinylacetate) done by Kovacs (1963).Over many years, we have developed an approach in the framework ofirreversible thermodynamics, called the Distribution of Non-LinearRelaxations (DNLR) to establish constitutive laws for various materialsunder coupled physical solicitations. It is based on a generalization ofthe fundamental Gibbs equation (1902) for systems outside equilibrium.This relation combines the two laws of thermodynamics into a singleexpression; for example, the internal energy e =e(s, v, n i , )depends on the whole of the state variables, including theentropy s. The salient points of the DNLR approach are (i)to naturally take account of the couplings found in physics, (ii) themultiplicity of the mechanisms of internal reorganization and (iii) thenonlinearity of the kinetics for the return to equilibrium.The aim of this paper is then (i) to present in this first part thebases, the formalism, and the framework of the DNLR approach and (ii) ina second part to check the pertinence of this general DNLR strategy tosimulate the experimental data of Kovacs concerning PVAc. This developedmodeling will be compared to other works already done in the literature.

This is the second paper in the series addressing the constitutive modeling of dynamically loaded elastomeric products such as power transmission belts. During the normal operation of such belts certain segments of the belt structure are loaded via tooth-like cyclical loading. When the time-dependent properties of the elastomeric material “match” the time-scale of the dynamic loading a strain accumulation (incrementation) process occurs. It was shown that the location of a critical rotation speed strongly depends on the distribution (shape) of the retardation spectrum, whereas the magnitude of the accumulated strain is governed by the strength of the corresponding spectrum lines. These interrelations are extremely non-linear. The strain accumulation process is most intensive at the beginning of the drive belt operation, and is less intensive for longer belts. The strain accumulation process is governed by the spectrum lines that are positioned within a certain region, which we call the Strain Accumulation Window (SAW). An SAW is always located to the right of the spectrum line, L i , at log (ω λ i )=0, where ω is the operational angular velocity. The width of the SAW depends on the width of the material spectrum. Based on the following analysis a new designing criterion is proposed for use in engineering applications for selecting a proper material for general drive-belt operations.

Measurements are described and analyzed for the determination of thedynamic bulk compliance for Poly(vinyl acetate) [PVAc] as a function offrequency and temperature at atmospheric pressure to generate a mastercompliance curve over a total frequency range of about 12 decades.Measurements are based on the compressibility of a specimen confined to anoil-filled cavity resulting from pressurization by a piezoelectricdriver and response of a like receiver. Experimental problems addressinglimitations in resolution capability are discussed. The results arecompared with the classical measurements obtained by McKinney andBelcher over thirty years ago. Further comparison of the bulk with shearcompliance data shows that the extent of the transition ranges for thetwo material functions are comparable, but the two transitions belong todifferent time scales, that of the bulk response falling mostly into theglassy domain of the shear behavior. One concludes thus that forlinearly viscoelastic response the molecular mechanisms contributing toshear and bulk deformations have different conformational sources.

Because of the strong environmental sensitivity of poly(vinyl acetate), PVAc, especially with respect to moisture, and the fact that shear deformation is essentially equivoluminal up to moderate strain levels, little has been reported in the literature on the nonlinear mechanical creep behavior of this polymeric material loaded in shear. This paper presents the results of torsional tests which establish the shear response through the linear zone and well into the nonlinear region. Test specimens were thin-walled cylinders giving an approximately uniform deformation field. Because of carefully chosen wall thickness to length ratio, it is considered that these measurements represent some of the most accurate nonlinear shear results to date in the strain range above 1%. Measurements of stress, strain and creep compliance were made at temperatures near the glass transition temperature and somewhat below it. Isochronal shear stress-strain dependence into the nonlinear range was used to establish limits of viscoelastic linearity during creep. As temperature is increased toward the glass transition, the limit shows a greater dependence on stress than on strain. The stored distortional strain energy at the limit of linearity was not a constant but varied with temperature and load. Thus, these results appear not to support the concept of stored energy as a material property defining the threshold for nonlinear viscoelastic behavior. Strain during the short-time load-up period gives evidence that PVAc is also subject to nonlinear elasticity in the glassy response region.

Craze growth in a styrene-acrylonitrile copolymer (SAN) wasstudied as a function of time after a quench (physical aging) at fourdifferent temperatures between 22 and 60C. Thecraze growth experiments were performed in stress relaxation conditions.The craze length was found to grow linearly on a logarithmic loadingtime scale. A transition in the logarithmic growth rate was found tooccur on the logarithmic aging time scale. The transition was observedas a change in rate from high to approximately five times slower andoccurred over a relatively narrow range of aging times. The growth ratein the slow growth regime was relatively insensitive to temperature forall four temperatures studied. The transition was found to move toshorter aging times as temperature increases. Although the craze lengthbetween crazes in a sample could differ to a large extent, the growthrates themselves, were found to vary only within a20% band.

Measurements on the creep behavior of injection moldedstyrene-acrylonitrile copolymer (SAN) samples are described andanalyzed. It is shown that the processing conditions have a distincteffect on the tendency to creep and that the differences in creepbehavior are mainly due to differences in frozen-in free volume, whereasthe different state of molecular orientation and internal stress haveonly a neglegible effect on the creep behavior. In addition, the timebetween processing and testing of the material plays an important rolefor the deformation behavior of the amorphous polymer; this phenomenonis known as physical aging. A slower cooling rate during thesolidification of the injection molded part, as well as a longer agingtime, lead to a reduced free volume and therefore to a reduced tendencyto creep.

Residual stress states within certain classes of polymeric adhesives andcoatings subjected to cyclic temperature conditions can becomeincreasingly tensile with exposure to cyclic temperature conditions.Under some conditions, these tensile stresses are believed to beresponsible for initiating debonds which may eventually propagatethroughout the bond. In certain potting-type applications in which thepolymer is constrained in a particular fashion, these debonded layerscan shrink extensively. In an industrial application, this shrinkage hasreached as much as 15%, nearly two orders of magnitude larger thanexpected based on simple thermal contraction. This paper provides athermal racheting explanation for this dramatic shrinkage. Numericalstudies have confirmed the explanation, and provide additional insightsinto the effects of temperature range, coefficient of friction betweenthe adhesive and substrates, and the viscoelastic nature of theadhesive. Based on the hysteretic nature of the normal forces whichaffect the frictional forces, the proposed mechanism usesfriction hysteresis under cyclic thermal conditions to explain observedshrinkage.

Techniques to characterize the mechanical properties ofadhesives in a bonded geometry are important because thebehavior can differ from that of bulk adhesive samples.Although there are a number of such tests, the simplicity ofthe sandwich beam specimen makes itattractive. This test involves three-point bending of a beam madeby bonding together two metal strips with the adhesive. Forlinear elastic materials, the shear modulus of the adhesive canbe calculated from the bending stiffness of the beam with anumber of published analyses. This paper conducts experimentsto examine the sandwich test and the potential to extend it toviscoelastic adhesives since standard viscoelastic testequipment can easily measure three-point bending. The results showthat the stiffness of the sandwich beam is sensitive to thepresence of the adhesive throughout most of the interestingrange for adhesive properties. Second, when tested as afunction temperature and time (or frequency), the stiffness ofthe beam behaves like a classic viscoelastic property. Finally,in the rubbery, elastic range, the shear moduli calculated frombeam tests with thick bonds agreed with those obtained fromtests on bulk samples for adhesives. In the temperature rangewhere the adhesive is hard (glassy behavior), however, problemswere observed for the geometries tested here. Some of theseproblems may be attributable to assumptions made in theanalyses used, and this suggests the need for a new analysisthat addresses these limiting assumptions and extends the testto viscoelastic materials.

This paper describes the development of a nonlinear viscoelastic modelthat can account for rate dependence at large strains. The model wasbased on tensile and shear experiments on a urethane structuraladhesive. The most striking observation was that the stress-strainbehavior at large strains was rate dependent. As a result, a rate-dependent rubbery shear modulus was added to Popelars shear modifiedfree volume model. This was very effective in predicting ramp shearbehavior over a range of strain rates and temperatures. Thecorrespondence of model results and tensile data was reasonable below20% strain. At higher strains, the model over predicted the stresslevels for a given strain. This may have been due to the accumulation ofdamage, which has yet to be included in the model. The model was unableto capture the effect of salt water on the tensile behavior of theurethane.

Aerogels are low-density, highly nano-porous materials. Their engineering applications are limited due to their brittleness and hydrophilicity. Recently, a strong lightweight crosslinked silica aerogel has been developed by encapsulating the skeletal framework of amine-modified silica aerogels with polyureas derived by isocyanate. The mesoporous structure of the underlying silica framework is preserved through conformal polymer coating, and the thermal conductivity remains low. Characterization has been conducted on the thermal, physical properties and the mechanical properties under quasi-static loading conditions. In this paper, we present results on the dynamic compressive behavior of the crosslinked silica aerogel (CSA) using a split Hopkinson pressure bar (SHPB). A new tubing pulse shaper was employed to help reach the dynamic stress equilibrium and constant strain rate. The stress-strain relationship was determined at high strain rates within 114–4386 s−1. The effects of strain rate, density, specimen thickness and water absorption on the dynamic behavior of the CSA were investigated through a series of dynamic experiments. The Young’s moduli (or 0.2% offset compressive yield strengths) at a strain rate ∼350 s−1 were determined as 10.96/2.08, 159.5/6.75, 192.2/7.68, 304.6/11.46, 407.0/20.91 and 640.5/30.47 MPa for CSA with densities 0.205, 0.454, 0.492, 0.551, 0.628 and 0.731 g cm−3, respectively. The deformation and failure behaviors of a native silica aerogel with density (0.472 g cm−3), approximately the same as a typical CSA sample were observed with a high speed digital camera. Digital image correlation technique was used to determine the surface strains through a series of images acquired using high speed photography. The relative uniform axial deformation indicated that localized compaction did not occur at a compressive strain level of ∼17%, suggesting most likely failure mechanism at high strain rate to be different from that under quasi-static loading condition. The Poisson’s ratio was determined to be 0.162 in nonlinear regime under high strain rates. CSA samples failed generally by splitting, but were much more ductile than native silica aerogels.