Non-linear viscoelasticity and viscoplasticity of isotactic polypropylene

Observations are reported in tensile tests with constant cross-head speeds (ranging from 5 to 200 mm/min), relaxation tests (at strains from 0.02 to 0.08), creep tests (at stresses from 15.0 to 25.0 MPa) and recovery tests (after straining up to the maximal strains ranging from 0.04 to 0.12 and subsequent retraction) on isotactic polypropylene at room temperature. A constitutive model is derived for the time- and rate-dependent responses of a semicrystalline polymer at isothermal deformation with small strains. A polymer is treated as an equivalent heterogeneous network of chains bridged by temporary junctions (entanglements, physical cross-links and lamellar blocks). The network is thought of as an ensemble of meso-regions linked with each other. The viscoelastic behavior of the ensemble reflects thermally-induced rearrangement of strands (separation of active strands from temporary junctions and merging of dangling strands with the network). To describe the viscoplastic response, the entire plastic deformation is split into the sum of two components: one of them is associated with sliding of junctions in the non-affine network of chains, while the other accounts for coarse slip and fragmentation of lamellar blocks. Stress–strain relations and kinetic equations for the plastic strains are developed by using the laws of thermodynamics. The constitutive equations involve five material constants that are found by fitting the observations. Fair agreement is demonstrated between the experimental data and the results of numerical simulation.     

Three-dimensional, finite deformation, viscoplastic constitutive models for polymeric materials

A general methodology for developing three-dimensional. finite deformation, viscoplastic constitutive models for polymeric materials is presented. The development begins with the presentation of a one-dimensional spring and dashpot construction which exhibits behavior typical of polymeric materials, namely strain-rate dependence, stress relaxation, and creep. The one-dimensional construction serves as a starting point for the development of a three-dimensional, finite deformation, viscoplastic constitutive model which also exhibits typical polymeric behavior. Furthermore, the three-dimensional constitutive model may be easily generalized to incorporate an arbitrary number of inelastic processes, representing (inelastic) microstructural deformation mechanisms operating on different time scales. Strain-rate dependence, stress relaxation, and creep phenomena are discussed in detail for a simple version of the constitutive model. Test data for a particular polymer is used to validate the simple model. It is concluded that the methodology provides a flexible approach to modeling polymeric materials over a wide range of loading conditions.     

Creep and Fatigue Failure in Single- and Double Hot Arm MEMS Thermal Actuators

Determination of the failure mechanisms of mechanical devices is the key to the design of reliable products. This paper reports an investigation on creep and fatigue failure of microelectromechanical (MEMS) thermal actuators. Finite element modeling is used to predict thermomechanical behavior of actuators under low to moderate voltage differences. The modeling results are compared with experimental results to evaluate the models. Two probable failure modes associated with thermal actuators, that is, fatigue and creep, are investigated, and it is found that creep is the dominant failure mechanism. The creep behaviors of several U-shape and double hot arm thermal MEMS actuators are examined, and their deformation-time curves are obtained numerically and experimentally. The curves follow a typical three-stage creep curve usually observed in metals. The creep life cycles of the devices are compared on the basis of their stress and temperature distributions. This study shows that actuators with the maximum temperature occurring at the location where the high stress is induced have shorter life spans than those experiencing the high stress away from the maximum temperature location. It is concluded that the double hot arm actuators with equal length have longer creep life than the U-shape (single hot arm) actuators.     

Creep characterization of a type 316 austenitic steel

Creep data on a type 316 austeni tic steel are presented covering the temperature range 550-675°C and in volving test times up to 30 000 h. The data have been used to inv estigate the efficiency of traditional and recent methods of presenting creep data , the formulation of creep constit utive equations, and the valid ity of certain parametric relationships designed to aid extrapolation. Th e article introduces a form of the steel which will subsequently appear in a study of multi-axial stress/creep relationships and the development of a design method for creep conditions.     

Creep behavior and manufacturing parameters of wood flour filled polypropylene composites

The influence of wood flour content, coupling agent and stress loading level on the creep behavior of wood flour–polypropylene composites was investigated. Maleated polypropylene (MAPP; Epolene G-3003™) was used as the coupling agent to treat the wood flour used as reinforcing filler for polypropylene composite. The tensile strength and modulus of various wood flour–polypropylene composites (WPCs), manufactured using the melt blending, extrusion, and palletizing methods, were measured before performing the creep test. The residual tensile strength, creep strain, and fractional deflection of the resultant wood flour–polypropylene composites were measured by means of the creep test. It was shown that the tensile strength decreased with increasing wood flour level in the composites. The creep strain also decreased as the wood flour level increased. The presence of the coupling agent increased the tensile strength of the wood flour–polypropylene composites, compared with the specimens made of pure polypropylene. For those composites containing the coupling agent, the creep deflection was significantly lower than those made without any coupling agent. The creep strains of the WPC specimens observed during the creep test fitted perfectly with the four-element burger creep model. Further investigation is required of the effects of combined mechanical and environmental loading in varying proportions.     

Cracking and Creep Role in Displacements at Constant Load: Concrete Solids in Compression

The main assumption on the basis of the identifying model of the effective law, developed by the Author, is the impossibility of considering the specimen as a continuum, when an identifying procedure from load-displacement to stress-strain in uniaxial compression is attempted. Actually, a failure mechanism with propagation of a macro-crack was found to activate from the very beginning of the uniaxial compression test forth. This leads to considering the acquired displacements as composed by two quotes: one constitutive, due to the material strain, and one of crack opening. Since the ratio between these two quotes is not constant during the compression test, the properties of the displacement field (which attains to structural properties) cannot be transposed to the strain field (which attains to material properties) through a mere scale factor. In this context, also creep takes on a different meaning, in the sense that time-dependence is an effect observed in the displacement field that does not necessarily correspond to a property of the strain field, i.e., the creep. In other words, it is not possible to exclude a-priori that the time-dependence of displacements is induced by crack propagation alone. A time-dependent motion of crack opening could activate and affect the displacements acquisition. The aim of the present work is to investigate the role played in displacement time-dependence both by creep and crack propagation. Results of an experimental program are presented here, stating the strict relationship existing between the increasing of displacement and the propagation of cracks at constant load.     

Creep rupture behaviour of low alloy ferritic steel weldments

To establish differences in rupture lives and ductilities between parent metal, weld metal and weldjoint, a commercial heat of lCrMoV cast steel welded with 21/4Cr1M0 steel electrodes was creep tested over a range of stresses at 550°C using constant load creep testing units. The results indicate that, while there is no significant variation in rupture lives, ductility in the weldjoint showed a decreasing trend over longer periods of testing. In weldjoint specimens that comprised parent metal, heat affected zone (HAZ) and weld metal, fracture occurred in the weld metal quite near to the fusion boundary over the entire range of stresses. The rupture ductility in the weldjoint was found to be lower than in parent or weld metal.

Scanning electron microscopy (SEM) revealed the fracture surfaces of parent and weld metal to be heavily dimpled, the dimples originating mostly around carbide precipitates, whereas the fracture surfaces of the weldjoint were found to be somewhat faceted.

The results of the present work suggest that weldments made with 2114CrlMo steel deposits possess comparable creep lives to the parent metal of 1CrMoV steel, and the weld metal in the weldjoint near the fusion boundary exhibits a tendency to embrittle over longer periods of testing.     

Viscoelasticity and viscoplasticity of semicrystalline polymers: Structure–property relations for high-density polyethylene

Observations are reported on two commercial grades of high-density polyethylene (HDPE) in uniaxial tensile tests, relaxation tests, creep tests and cyclic tests with a strain-controlled deformation program. Constitutive equations are derived for the viscoelastic and viscoplastic responses of semicrystalline polymers at three-dimensional deformation with small strains. A polymer is modeled as a two-phase continuum consisting of a crystalline skeleton and an amorphous phase treated as a transient network of chains. Its viscoelastic response is associated with thermally activated rearrangement of strands in the temporary network. The viscoplastic behavior reflects fine and coarse slip of lamellar stacks and sliding of junctions between chains in the network. Adjustable parameters in the stress–strain relations are found by fitting the experimental data. The study focuses on the effect of molecular weight of HDPE on its mechanical properties.     

Creep crack growth characteristics of polypropylene film at various temperatures

Creep crack growth rates were measured using centrally cracked tension specimens of thin polypropylene film at various temperatures and stress levels. The creep crack growth rates were correlated with the stress intensity factor. The experimental results showed that there is the region of the minimum constant crack growth rate which occupies more than 75% of the total creep failure life. This steady or constant creep crack growth rate depends on the test temperature and the initial stress intensity factor. The constant creep crack growth rate characteristics were analyzed on the basis of the Arrhenius type thermally activated process. It is found that creep crack growth behavior is closely related to the crack tip opening displacement and the creep zone size.     

Mechanisms for tertiary creep of single crystal superalloy

During the thermal-mechanical loading of high temperature single crystal turbine components, all three creep—stages: primary, secondary and tertiary, manifest themselves and, hence, none of them can be neglected. The development of a creep law that includes all three stages is especially important in the case of non-homogeneous thermal loading of the component where significant stress redistribution and relaxation will result. Thus, local creep analysis is crucial for proper design of damage tolerant airfoils. We have developed a crystallographic-based constitutive model and fully coupled it with damage kinetics. The model extends existing approaches for cyclic and thermal-cyclic loading of anisotropic elasto-viscoplastic deformation behavior and damage kinetics of single-crystal materials, allowing prediction of tertiary creep and failure initiation of high temperature components. Our damage model bridges the gap between dislocation dynamics and the continuum mechanics scales and can be used to represent tertiary as well as primary and secondary creep.     

Creep of granular materials

This paper examines the creep of brittle granular materials subjected to one-dimensional compression. One-dimensional creep tests were performed on aggregates of brittle pasta and compared with the behaviour of sand at much higher stress levels. It was found that for both materials, creep strain is proportional to the logarithm of time. One possible mechanism for creep is particle crushing. However, it is usually difficult to measure changes in the particle size distribution during creep because the fines produced are so small, and the mass of fines is too small to measure accurately unless creep is permitted for a very long time. However, for pasta, the particle fragments produced are large, and it is found that particle crushing does occur during creep for 24 hours. This is consistent with the proposition that the behaviour of all brittle granular materials is essentially the same. A micro mechanical argument is then summarised which predicts that creep strain should be proportional to log time.     

Creep and drying shrinkage of concrete containing GGBFS

Experiments were conducted on 150 × 600 mm cylindrical specimens to investigate creep and drying shrinkage of concrete containing ground granulated blast furnace slag (GGBFS). The creep strain was measured for 150 days under a constant sustained load. The creep strain recovery was measured for one subsequent month after the removal of the sustained load. The shrinkage strain was also measured for 180 days. The amount of cement replacement by GGBFS was 20%, 40% and 60% by weight of cement. The test results indicate that higher GGBFS percentage exhibits higher creep and shrinkage strains. At 150 days of sustained loading, the average creep coefficients of 20%, 40% and 60% GGBFS concrete are 16.3%, 33.3% and 55.2% higher than plain concrete. In the absence of a creep and shrinkage prediction model for GGBFS concrete, a modification factor is suggested for incorporating the effect of GGBFS proportion in the existing models. The available models for predicting creep and shrinkage strain of plain concrete are compared.     

Creep of the eye sclera

 Irreversible stretching (creep) of the eye sclera, considered as a cause of the high myopia, has been studied experimentally. Both dramatic acceleration and significant deceleration of the sclera creep have been observed in the presence of some enzymes. Creep of various connective tissues caused by static and cyclic mechanical stresses (gravity, blood pressure, etc.) can manifest in many age and pathological changes in human body. Authors express the hope that investigations in this area and finding appropriate inhibitors may replace surgery (eye, cosmetic) by prophylactic therapy. Received: 21 July 1998 / Accepted: 28 August 1998     

Viscoplastic response and modeling of asphalt-aggregate mixes

The strain response of asphalt-aggregate mixes to applied stresses is decomposed additively into a viscoelastic part and a viscoplastic part. The paper focuses on the response and modeling of the viscoplastic component; it includes the development of a multiaxial constitutive formulation that is capable of generating: (i) strain hardening when the loading is applied in one direction; (ii) strain softening immediately after stress reversals; (iii) volumetric changes under uniaxial conditions or isotropic conditions, or both; and (iv) directional non-symmetry. In order to investigate the model’s capabilities, four tests were performed sequentially on one asphalt sample. The tests were limited to pre-peak conditions and one temperature and consisted of creep and recovery sequences in uniaxial tension, uniaxial compression, isotropic compression and uniaxial tension-compression. Analysis of the results showed that the new theory, once calibrated, was able to adequately reproduce the viscoplastic strain component; its forecastability, however, was found limited.     

Creep of an electroslag refined aluminium alloy

The creep resistance ofelectroslag refined aluminium alloyRR 58 has been studied in the temperature range 450-485°C and compared with that ofpermanent-mould cast, unrefined alloy. The electroslag refined RR 58 had a greater creep resistance than the unrefined alloy; this improvement has been attributed to the reduction in hydrogen content, macroporosity and microporosity, the removal ofoxide inclusions and the fine an uniform dispersion ofsecond phase precipitates in refined alloy. From the estimated activation energy for high temperature creep deformation (155 ^kJ mol_-1), a self-diffusion mechanism has been identified as rate controlling for both refined and unrefinedRR 58. The rate equation ?= A¹[sinh (ασ)]_nexp(–Q/RT] has been found to be applicable for RR 58 deformed under creep conditions in the range oftemperatures and strain rates studied     

Creep failures of overheated boiler, superheater and reformer tubes

Internally pressurised tubes are critical components in heat-exchanger applications, such as boiler water tubes, steam superheater elements and chemical plant reformer tubes. Tubes in such applications are vulnerable to temperature excursions: as a consequence the material may enter the creep regime, and creep deformation (bulging) and even fracture (longitudinal rupture) may subsequently occur, with serious consequences. It is estimated that 10% of all power-plant breakdowns are caused by creep fractures of boiler tubes. In general, 30% of all tube failures in boilers and reformers are caused by creep. This paper gives details of four case studies in which internally pressurised tubes failed by creep bulging and rupture (two boilers, one superheater and one reformer). The conditions of temperature and time under which the failures occurred are deduced from the morphology of fracture and the changes in microstructure, and are correlated with the deformation-mechanism and fracture-mechanism maps for the tube materials.     

Creep behaviour of polyethylene and polypropylene

Tensile creep tests and stress reduction studies during creep have been carried out for polyethylene and polypropylene. The results obtained suggest that a consistent approach for the presentation of creep data for these polymeric materials can be obtained since the creep curves at 293K for polyethylene and polypropylene over a wide stress range can be superimposed by describing the variation of creep strain,, with time,t, as= ₀ + _p [1 – exp (–K t)] + t, where ₀ is the initial strain on loading, _p is the primary creep strain, is the secondary creep rate, andK is a constant.     

Comparative study on stress–strain hysteresis response of SAC solder joints under thermal cycles

The present study attempts to evaluate the stress-strain hysteresis responses of SAC solder joints in Resistor and FleXBGA144 packages subjected to thermal cyclic loading using several constitutive models. The total deformation of the solder material consists of elastic, rate-independent plastic and rate-dependent creep components. The constitutive models discussed in this study each weighted elastic, plastic and creep deformations differently. At low stresses SAC solder alloys were found to be creep resistant, where at higher stresses, the influence of different microstructures disappears as matrix-creep dominates in this region. Thus, the proper constitutive model requires all the three ingredients of the elastic, the creep, and the time-independent plastic data for different stress levels to effectively predict the hysteresis behavior of the SAC solder alloys. The hysteresis loops predicted by constitutive models were also found in close agreement with the loops generated by FEM for the SAC solder joint subjected to thermal cycling.