Time-dependent behavior of nylon-6 under uniaxial and biaxial loadings at constant rate

The large deformation behavior of nylon-6 when subjected to constant loading rate tests has been investigated experimentally. Three types of loadings—tension, torsion, and combined tension-torsion—have been used and the strain histories for each type analyzed. It is shown that a piecewise power law in time can adequately describe the strain histories up to equivalent strains as high as 30 percent for all cases. This piecewise power law shows well-defined transitions from one mode to the other while each mode is characterized by a power law exponent valid for all types of loading. On the basis of experimental results, it is also possible to establish the functional form of various kernels involved in the Green-Rivlin representation of the non-linear viscoelastic behavior of nylon-6. This method of finding kernels is much simpler than the conventional method of carrying out a large number of multi-step creep tests. A comparison is also made between the results of the present work and the well-known Findley equation, particularly with respect to the instantaneous strain response of materials.     

A viscoelastic–plastic constitutive model for uniaxial ratcheting behaviors of polycarbonate

In this paper, a modified viscoelastic–plastic constitutive model has been proposed on the framework of Anand's work to describe the uniaxial ratcheting behavior of polycarbonate (PC) under tension–tension cyclic loading. The experimental observation illustrates that the previously accumulated deformation has an assignable influence on the subsequent material response during the ratcheting process of PC. Thus, the deformation resistance in the viscoelastic micromechanism is assumed to be evolving with the local accumulated inelastic strain rather than keeping unchanged in the original Anand's model. The proposed model is validated firstly by the monotonic tension and creep experiment results of PC. Then, its capability to describe the uniaxial ratcheting behaviors is compared with Anand model. Finally, the modified model is adopted to study the effect of mean stress, stress amplitude, loading rate, and peak holding time on the ratcheting behaviors of PC. It is shown that the proposed model can predict reasonably the uniaxial tension–tension ratcheting behavior of polymer. POLYM. ENG. SCI., 55:2559–2565, 2015. © 2015 Society of Plastics Engineers     

Some aspects of the mechanical response of BMI 5250‐4 neat resin at 191°C: Experiment and modeling

The inelastic deformation behavior of BMI‐5250‐4 neat resin, a high‐temperature polymer, was investigated at 191°C. The effects of loading rate on monotonic stress–strain behavior as well as the effect of prior stress rate on creep behavior were explored. Positive nonlinear rate sensitivity was observed in monotonic loading. Creep response was found to be significantly influenced by prior stress rate. Effect of loading history on creep was studied in stepwise creep tests, where specimens were subjected to a constant stress rate loading followed by unloading to zero stress with intermittent creep periods during both loading and unloading. The strain‐time behavior was strongly influenced by prior deformation history. Negative creep was observed on the unloading path. In addition, the behavior of the material was characterized in terms of a nonlinear viscoelastic model by means of creep and recovery tests at 191°C. The model was employed to predict the response of the material under monotonic loading/unloading and multi‐step load histories. © 2007 Wiley Periodicals, Inc. J Appl Polym Sci, 2008     

Multi-parameter models of the viscoelastic/plastic mechanical properties of coatings via combined nanoindentation and non-linear finite element modeling

Coatings deteriorate from a variety of failure mechanisms. To improve coating durability and/or enable structure-performance correlations, it is necessary to develop more advanced methods of mechanical characterization. For complex multifunctional coatings, multi-parametric constitutive models that simultaneously account for elastic, viscoelastic, and plastic mechanical properties should be used, especially when mechanical properties in the (macro-scale) bulk state differ from properties that occur as a result of thin-film application, post-treatment processes, or aging effects. The nanoindentation creep experiment combined with non-linear finite element modeling of nanoindentation is an effective tool for characterizing the properties of such coatings. Three- and four-parameter viscoelastic/plastic finite element models, implemented using the ABAQUS™ commercial finite element software, have been developed to simulate the isotropic indentation response of coatings. Unified constitutive models where both plastic and viscoelastic deformation are considered simultaneously have not been published previously within the indentation modeling literature. The parameters are determined by an optimization program that automatically matches the load vs. indentation deformation plot from the nanoindentation experiment, with the load vs. indentation deformation plot obtained by the finite element simulation. The computed parameters become a unique “thumbprint” for a particular coating. These parameters may then be used as input data for more complex simulations, for example, capable of computing stress and strain fields, strain energy dissipation, residual stress, and residual strain during particulate scratching; or various other forms of mechanical loading.     

On the nonlinear characterization of the long term behavior of polymeric materials

In the linear viscoelastic range the long term behavior of viscoelastic materials—such as polymers—can be described by using exponential series with a limited number of terms for the approximation of the relaxation modulus or of the creep compliance. This procedure can be extended to the nonlinear viscoelastic range by multiplying the linear parameters of the material by certain nonlinearity factors, which depend upon the level of the applied loading. Application of this method to stress relaxation data of several polymers has shown that nonlinearity factors can be approximated as linear functions of the applied constant strain. From creep tests, on the other hand, one can observe that the immediate strain response to the suddenly applied stress is linear elastic even in the nonlinear viscoelastic range of the investigated polymer. The computation of the linear viscoelastic material parameters as well as of the nonlinearity factors is conducted numerically by using least squares techniques. Good agreement between computed results and experimental data can be observed in the presented examples.     

Uniaxial compressive creep of polytetrafluoroethylene

A machine to measure the creep deformation of plastics under uniaxial compressive loads is described. The problems associated with accurate creep testing in compression, primarily the application of a uniform stress to the specimen and the measurement of the resultant strain, receive particular attention. For the specimen geometries used, the effect on the measured strain of frictional restraints at the specimen ends is negligible provided the strain measurement is made with an extensometer attached to the specimen. The effect of fabrication techniques on the deformation behavior of polytetrafluoroethylene (PTFE) has been examined. Sintering time and temperature are found to be the most significant variables in the processing of PTFE. A comparison of uniaxial tensile and compressive creep data has shown that the non-linear viscoelastic behavior of the material extends into the low strain region.     

A comparison between simple shear,elongation, and equal biaxial extension deformations

The rheology of a high molecular weight polyisobutylene “Vistanex” L-80 is measured at 20°C under constant stress creep loading in simple shear and simple elongation and compared with published data for biaxial extension. These data can be reduced to a single curve by the application of simple geometric parameters and instability during extensional flows may be interpreted on the basis of the Considère construction. The results are further extended by dynamic measurements to estimate the viscoelastic response of this material over a time scale of nine orders of magnitude. The rheological response shows an approximately linear relationship with stress up to elongation strains of 1.0, and, because of this, the results do not illuminate the present controversy over the selection of different equations of state to represent non-linear polymer melt flow. However, this body of data, which the authors believe to be the most comprehensive presently available in terms of strain level and deformation geometry, does demonstrate that a viscoelastic polymer can respond to different deformation geometries in a simple manner.     

Creep-based characterization of nonlinear relaxation behavior of plastics

It is a matter of fact that creep experiments can be conducted more easily and accurately than stress relaxation experiments, since it is easier to maintain a stress constant (for instance by a “dead weight”) than a strain constant. Nevertheless, in practice, structural parts made of plastics (which are nonlinear viscoelastic materials) are very often loaded under stress-relaxation conditions. The present paper presents an approach to predict the behavior of a nonlinear viscoelastic material under stress-relaxation-type loading, based on data obtained from creep-type experiments. The nonlinear creep compliance is described mathematically by an exponential series with a limited number of terms and a single nonlinearity function depicting the transient behavior. The nonlinear behavior of the material under constant strain (i.e., stress relaxation) is then obtained by dividing the considered time range into very short time intervals in which constant stresses are acting, while the different values of the applied stresses are chosen in a manner that guarantees the same stain at the end of each interval. In this way, one performs a numerical nonlinear superposition of the effects of the loadings in the various intervals, leading to the desired results under stress relaxation. A comparison of theoretical results with experiments conducted on some thermoplastic materials shows good agreement.     

Micromechanical model of time-dependent damage and deformation behavior for an orthogonal 3D-woven SiC/SiC composite at elevated temperature in vacuum

This paper presents a micromechanical model to predict the time-dependent damage and deformation behavior of an orthogonal 3-D woven SiC fiber/BN interface/SiC matrix composite under constant tensile loading at elevated temperature in vacuum. In-situ observation under monotonic tensile loading at room temperature, load–unload tensile testing at 1200 °C in argon, and constant load tensile testing at 1200 °C in vacuum were conducted to investigate the effects of microscopic damage on deformation behavior. The experimentally obtained results led to production of a time-dependent nonlinear stress–strain response model for the orthogonal 3-D woven SiC/SiC. It was established using the linear viscoelastic model, micro-damage propagation model, and a shear-lag model. The predicted creep deformation was found to agree well with the experimentally obtained results.     

Deformation behavior of an epoxy resin subject to multiaxial loadings. Part I: Experimental investigations

The mechanical behavior of an epoxy resin (Epon 826) was studied by performing a series of tests on thin‐walled tubular specimens. These tests deal with different aspects of the mechanical behavior of this epoxy resin. The deformation behavior, such as viscoelastic behavior, hydrostatic stress effect, multiaxial behavior and loading path effect, was investigated. It was found that the Epon 826 epoxy resin is a highly nonlinear viscoelastic material. The effect of hydrostatic pressure on the deformation behavior of this epoxy is not significant. However, it shows different tensile and compressive deformation behavior. The loading path was found to have an observable effect on the deformation response of this epoxy, especially in the high stress/strain range.     

On the effects of modifiers on the viscoelastic behavior of composites

Some of the details concerning the reasons for the difference in behavior between untoughened and toughened composites are presented. This work demonstrates the influence of localized plastic deformation on the viscoelastic behavior of polymer composites. As an example, the presence of a thermoplastic modifier and its potential influence on the microscale deformation is presented by using two micromechanical models to determine the conditions under which the observed behavior may occur. Results suggest that the effect of thermoplastic tougheners is to increase the amount of time-dependent plastic deformation in loadings that produce sufficiently large local stress concentrations. The tougheners, however, do not seem to change the functional form of the time-dependent response, rather they change the magnitude of this response. The two models discussed are used to qualitatively characterize these phenomena by relating model parameters to constituent properties. Differences in observed behavior with respect to plastic deformation in creep tests vs. tests such as dynamic mechanical analysis are attributed to the small deformations in the latter test types, which do create insufficient localized zones of plastic deformation.     

Microstructure transformation and stress-strain behavior of isotactic polypropylene under large plastic deformation

The macroscopic stress-strain behavior of monoclinic polypropylene samples was investigated at 70°C under uniaxial tension and simple shear by means of a special videometric testing system that gives access to the constitutive equation of plastic behavior at constant strain rate up to large deformation. At several levels of plastic strain, the microstructural evolution of the material was characterized by means of X-ray scattering, densitometry and viscoelastic analysis. It appears that the strain hardening is high in tension, whereas it is nearly zero in shear. This behavior is associated with the development of a fiber texture in tension, which differs drastically from the planar crystalline texture developed in shear. Furthermore, it is shown that structural damage takes place as the plastic deformation proceeds in tension, while only little damage is recorded in shear. A viscoplastic model has been developed that specifically tales into account the various slip systems activated in the polypropylene crystallites and the elastic interactions of the lamellae through a self-consistent scheme. Simulations based on this model reproduce correctly the contrasting strain-hardening in tension and in shear and the different crystalline textures induced for these two loading paths.     

Mechanical behaviour of isotactic polypropylene subjected to various strain histories in uniaxial extension

The mechanical behaviour of a slowly quenched isotactic polypropylene has been studied for various strain histories in extension. Creep, constant rate of strain, and constant rate of loading experiments were carried out at deformations up to and beyond the point where necking occurs. A creep diagram, which includes the failure envelope, is presented. From the available data we have also obtained an extrapolated surface of the single step stress-relaxation behaviour. From this surface we can calculate, using the Bernstein and Zapas theory on the instability of viscoelastic bars, the deformation at which necking occurs for various strain histories.     

Empirical nonlinear viscoelastic model for injection molded thermoplastic composite

Injection molded components made from fiber reinforced thermoplastics exhibit strong viscoelastic behavior. In the present study, the bending creep tests show that the 43-wt% glass fiber reinforced polyamide 66 is highly stress-dependent and requires a nonlinear viscoelastic representation. However, such representation is complex for isotropic materials and is even more arduous for composite materials. In order to overcome this complexity, an empirical approach is used herein to develop a viscoelastic model based on a simple power law with stress-dependent parameters. The proposed model demonstrates high stress sensitivity and agrees with experimental data over a wide range of applied stress.     

Master curves of viscoelastic behavior in the plastic region of a solid polymer

Stress relaxation and creep tests following strain ramps were made on Mylar, both above and below the yield stress. The ramp velocity was varied over a 40-fold range. All data exhibit nonlinear viscoelastic behavior. However, those obtained above the yield point, i.e., in the plastic region, could be reduced to single master curves for both the creep and the relaxation tests by means of a simple time shift factor. This factor is inversely proportional to the strain rate existing just prior to the test.     

Effect of Relative Humidity on the Viscoelastic and Mechanical Properties of Spray-Dried Powder Compacts

Spray-dried powder compacts exhibit viscoelastic properties such as stress relaxation, creep, and delayed elastic strain. This behavior is attributed to the organic binder, which forms bridges between the particles in spray-dried granules, thereby affecting their deformation characteristics. The viscosity and distribution of the binder within the powder compact can affect its mechanical and viscoelastic properties. In this study, the powder was conditioned at different ambient relative humidity (RH) levels, to vary the binder viscosity. Load deformation, stress relaxation, fracture strength, and fracture toughness behavior of ferrite powder compacts were studied as a function of ambient RH both before and after compaction. The loading rate was found to significantly affect the time-dependent response, and the relaxation times decreased at high humidity levels during compaction. It is proposed that increasing the humidity level during compaction increases the number of particle–particle contacts. This simple mechanism of binder redistribution led to slower relaxation times, increases in fracture strength, and elastic modulus of the green bodies, without significantly altering the fracture toughness when powders were compacted at high humidity to a given density.     

Nonlinear viscoelastic modeling of soft polymers

A one‐dimensional phenomenological constitutive model, representing the nonlinear viscoelastic behavior of polymers is developed in this study. The proposed model is based on a modification of the well‐known three element standard solid model. The linear dashpot is replaced by an Eyring type one, while the nonlinearity is enhanced by a nonlinear, strain dependent spring constant. The new constitutive model was proved to be capable of capturing the main aspects of nonlinear viscoelastic response, namely, monotonic and cyclic loading, creep and stress relaxation, with the same parameter values. Model validation was tested on the experimental results at various modes of deformation for two elastomeric type materials, performed elsewhere. A very good agreement between model simulations and experimental data was obtained in all cases. © 2015 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2015 , 132, 42141.