High-Temperature Deformation of SiC-Whisker-Reinforced MgO-PSZ/Mullite Composites

The effect of 33.5 vol% SiC whisker loading on high-temperature deformation of 1 wt% MgO-38.5 wt% zirconia-mullite composites was studied between 1300° and 1400°C. At strain rates of 10⁻⁶ to 5 × 10⁻⁴/s the creep resistance of zirconia-mullite composites without SiC reinforcement was inferior to monolithic mullite of similar grain size. Analysis of the results suggested that the decreased creep resistance of mullite-zirconia composites compared to pure mullite could be at least partially explained by mechanical effects of the weaker zirconia phase, increased effective diffusivity of mullite by zirconia addition, and to the differences in mullite grain morphology. With SiC whisker reinforcement, the deformation rate at high stress was nearly the same as that of the unrein-forced material, but at low stress the creep rates of the SiC-reinforced material were significantly lowered. The stress dependence of the creep rate of unreinforced material suggested that diffusional creep was the operative mechanism, while the reinforced material behaved as if a threshold stress for creep existed. The threshold stress could be rationalized based on a whisker network model. This was supported by data on other whisker-containing materials; however, the threshold stress had a temperature dependence that was orders of magnitude higher than the elastic constants, leaving the physical model incomplete. The effects of residual stresses and amorphous phases at whisker/matrix interfaces are invoked to help complete the physical model for creep threshold stress.     

Semi-analytical solution for electro-thermo-mechanical non-stationary creep behaviour of rotating disk made of nonlinear piezoelectric polymer

Electro-thermo-mechanical non-stationary creep response of a rotating disk made of nonlinear polymeric piezoelectric material has been investigated. The viscoelastic properties of the material are time, stress and temperature dependent which vary along radius. The long-term creep constitutive equation is the Burgers viscoelastic model. A non-homogeneous differential equation with variable coefficients is derived using stress-displacement relations, equilibrium equation, charge equation of electrostatics and the Maxwell equation. Time-dependent creep strains are involved in the non-homogeneous term of the differential equation. A semi-analytical solution has been developed to obtain displacement, stresses, strains and electric potential in terms of creep strains. Then, Prandtl–Reuss relations and the creep constitutive model are employed in a novel numerical procedure based on the Mendelson method to obtain history of displacement, stresses, electric potential and strains. It has been concluded that the displacement is increasing with time while effective stresses are decreasing. The results are validated by finite element methods modelling using ABAQUS software. A very good agreements between the results can be observed.     

Mechanical spectroscopy of creep appearance in fine-grained yttria-stabilized zirconia

Mechanical spectroscopy or internal friction measurements were performed at high temperature in 3 mol% yttria-stabilized tetragonal zirconia. The mechanical loss spectrum is composed of a relaxation peak and a high temperature exponential background. It is shown that the transition from the peak to the exponential background accounts for creep appearance in the material. Mechanical loss is interpreted as due to grain boundary sliding. The associated activation enthalpy was found to be of 540 kJ/mol. In the low stress creep regime involved here a stress exponent of 2 and a grain size parameter of 1 are reported. A threshold stress behavior was observed, which can be associated with the obstacles limiting grain boundary sliding in this low stress regime.     

Effect of Creep Damage on the Tensile Creep Behavior of a Siliconized Silicon Carbide

The tensile creep behavior of a siliconized silicon carbide was investigated in air, under applied stresses of 103 to 172 MPa for the temperature range of 1100° to 1200°C. At 1100°C, the steady-state stress exponent for creep was approximately 4 under applied stresses less than the threshold for creep damage (132 MPa). At applied stresses greater than the threshold stress for creep damage, the stress exponent increased to approximately 10. The activation energy for steady-state creep at 103 MPa was approximately 175 kJ/mol for the temperature range of 1100° to 1200°C. Under applied stresses of 137 and 172 MPa, the activation energy for creep increased to 210 and 350 kJ/mol, respectively, for the same temperature range. Creep deformation in the siliconized silicon carbide below the threshold stress for creep damage was determined to be controlled by dislocation processes in the silicon phase. At applied stresses above the threshold stress for creep damage, creep damage enhanced the rate of deformation, resulting in an increased stress exponent and activation energy for creep. The contribution of creep damage to the deformation process was shown to increase the stress exponent from 4 to 10.     

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     

Approximate Theory of Thermal Stress Resistance of Brittle Ceramics Involving Creep

The effect of stress relaxation by creep on the thermal stress fracture of brittle ceramics at high temperature under conditions of quasi-static heat flow is discussed. It is shown that, to a good approximation, thermal stress relaxation rates can be calculated on the basis of creep rates which correspond to the minimum temperature of the ceramic workpiece. For materials exhibiting linear stress-creep rate dependence, expressions for the relaxation time and maximum temperature difference or heat flux to which ceramic bodies can be subjected are derived in terms of the material variables affecting thermal stress fracture and stress relaxation by creep. A numerical example shows that high-temperature creep can materially affect the thermal stress behavior of brittle ceramics. Appropriate thermal stress parameters are proposed to form the basis of proper material selection for high-temperature environments involving thermal stress and stress relaxation by creep. Conditions for which thermal stress calculations should be based on an elastic or viscoelastic analysis are outlined.     

Evaluation of the characteristics of a viscoelastic material from creep analysis using the universal viscoelastic model. I. Isolation of the elastic component designated as the “Projected Elastic Limit”

In a preceding publication this author introduced a new universal viscoelastic model to describe a definitive relationship between constant strain rate, creep, and stress relaxation analysis for viscoelastic polymeric compounds. One extremely important characteristic of this new model is that it also characterizes secondary creep very well. Because secondary creep is the linear portion of creep after the completion of primary creep, then a straight line with a slope and an intercept can describe secondary creep. To effectively define a straight line in the secondary creep region it was found necessary to obtain averages of the instantaneous slope and the instantaneous intercept strain by averaging over a series of equally spaced data points in the secondary slope region. Most importantly, this average intercept strain was found to be independent of creep stress and creep time. This means that all the secondary creep straight lines must pass through the same intercept creep strain for all creep stresses. The results presented in this study strongly indicate that this secondary creep intercept strain is independent of creep stress and creep time, and appears to increase as the value of the efficiency of yield energy dissipation decreases. Because a decrease in the efficiency of yield energy dissipation, n, appears to correlate with an increase in the elastic solid like character of a material, then it appears that this secondary creep intercept strain should be a direct measure of the strain that the material can survive to retain its full elastic character. Therefore, this secondary creep intercept strain has been designated as the “Projected Elastic Limit” of a given viscoelastic material. © 2003 Wiley Periodicals, Inc. J Appl Polym Sci 89: 2923–2936, 2003     

Application of time‐temperature superposition to energy limit of linear viscoelastic behavior

The energy approach for evaluation of the limits of linear viscoelastic (LVE) behavior is considered. The approach of Foux and Bruller based on the Reiner‐Weissenberg dynamic theory of strength is developed for the temperature effect. Value of the stored energy at the limit of LVE is considered as the material characteristic independent on loading conditions and temperature. Time–temperature superposition principle is extended for the energy calculations. Curves of the stored energy calculated for different temperatures are shifted to each other in the logarithmic time axes similarly as creep compliance and relaxation modulus curves in creep and tension tests, respectively. Temperature is considered as a factor that accelerates transition form linear to non‐LVE at the same stored energy threshold. This is proved by example of polyvinylchloride by comparing temperature dependences of the stress limits of LVE determined in two independent test series: tensile creep and constant strain rate tests. © 2009 Wiley Periodicals, Inc. J Appl Polym Sci, 2009     

Non-linear creep of polymers under superimposed static and dynamic stress

The non-linear creep of polymeric materials under super-imposed static and dynamic stress is considered theoretically. The equation of state due to Green, Rivlin, and Spencer to-gether with the power law of time dependence for the kernel functions as suggested by Nakada is assumed to characterize the non-linear materials. Expressions for creep strain under constant static, oscillatory dynamic and superimposed static and dynamic stress are obtained in terms of the material constants and time dependent functions, called dynamic creep functions. It is shown that the creep strain due to dynamic stressing is damped as the number of stress cycles is increased. Damping is faster if the power law of time dependence is high. Expressions for the cumulative creep strain after multiple stress cycles are also obtained in terms of cumulative strain functions. All these functions are evaluated numerically at one thousand stress cycles. Finally, a special case of stress history is considered where the stress periodically reaches zero. It is shown that the ratio of the strains due to dynamic and static stressing can be characterized by the power law parameter when the mean stress is either very high or very low. Due to the slow damping when the power law parameter is small, the decrease of the strain ratio with number of cycles is slow compared to higher power law parameters.     

Separating stress and time dependent effects in the temperature dependent creep of polyethylene nanocomposites

The nonlinear time dependent creep of linear‐low density polyethylene (LLDPE) reinforced with montmorillonite layered silicate was investigated. A previous study related the time/stress dependence of creep compliance of the material at room temperature using the Burger and Kohlrausch‐Williams‐Watts models. Using both the creep and recovery compliance curves, we employ the Schapery formulation to study the relationship between deformation, time, stress, and temperature of LLDPE nanocomposites. Smooth mastercurves are constructed using time–temperature–stress superposition principles. The stress and temperature‐related creep constants and shift factors were determined for the material using the Schapery nonlinear viscoelastic equation. The prediction results confirm the enhanced creep resistance of nanofillers even at extended time scales and low temperatures. POLYM. ENG. SCI., 50:1646–1657, 2010. © 2010 Society of Plastics Engineers     

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.     

Application of time–stress superposition to viscoelastic behavior of polyamide 6,6 fiber and its “true” elastic modulus

The viscoelastic behavior of semi‐crystalline polyamide 6,6 fiber is exploited in viscoelastically prestressed polymeric matrix composites. To understand better the underlying prestress mechanisms, strain–time performance of the fiber material is investigated in this work, under high creep stress values (330–665 MPa). A latch‐based Weibull model enables prediction of the “true” elastic modulus through instantaneous deformation from the creep‐recovery data, giving 4.6 ± 0.4 GPa. The fiber shows approximate linear viscoelastic characteristics, so that the time–stress superposition principle (TSSP) can be implemented, with a linear relationship between the stress shift factor and applied stress. The resulting master creep curve enables creep behavior at 330 MPa to be predicted over a large timescale, thus creep at 590 MPa for 24 h would be equivalent to a 330 MPa creep stress for ～5200 years. Similarly, the TSSP is applied to the resulting recovery data, to obtain a master recovery curve. This is equivalent to load removal in the master creep curve, in which the yarns would have been subjected to 330 MPa creep stress for ～4.56 × 10⁷ h. Since our work involves high stress values, the findings may be of interest to those involved with long‐term load‐bearing applications using polyamide materials. © 2017 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2017 , 134, 44971.     

A method for determination of time‐ and temperature‐dependences of stress threshold of linear–nonlinear viscoelastic transition: Energy‐Based Approach

A methodology for determination of time‐ and temperature‐dependences of stress threshold of linear–nonlinear viscoelastic transition is proposed and validated by example of uniaxial creep of epoxy resin. Energy approach is applied for characterization of the region of linear viscoelasticity (LVE) and the threshold of LVE is given in the stress–strain representation as the master curve independent of time and temperature. Time‐ and temperature‐dependences of the stress threshold are calculated by extending LVE theory and time–temperature superposition principles (TTSP) to the energy relations. Reasonable agreement between experimental data and calculations is obtained. It is shown that number of tests required for characterization of LVE region in a wide range of test time and temperatures can be considerably reduced by applying the proposed methodology. © 2011 Wiley Periodicals, Inc. J Appl Polym Sci, 2011     

PE100燃气管材的非线性蠕变行为及其本构模型研究

对PE100燃气管材开展不同应力水平（2.4~9.6 MPa）下的常温蠕变测试,结果显示应力不超过5.4 MPa时,材料的蠕变柔量与应力水平无关,呈现出线性黏弹性行为,当应力高于5.4 MPa时,材料发生非线性黏弹性蠕变。基于单积分型非线性黏弹性本构理论,采用Findley模型对蠕变行为进行分析,并与Struik经验模型进行比较。结果表明,Findley模型和Struik模型均能较好地描述PE100管材的蠕变行为,但对高应力下的非线性蠕变行为,Findley模型比Struik模型描述得更准确。     

Dimensional stability of polystyrene/polymeric liquid crystal blends

Recovery experiments above T_g have been performed on polymeric liquid crystal (PLC) - polystyrene (PS) blend sheets obtained from extrusion and subsequent hot drawing. The data reported show that a significant improvement of the dimensional stability of a drawn thermoplastic material can be obtained by adding a low percentage of non-compatible polymeric liquid crystals that are oriented during the hot drawing process. The fibrils formed act as a constraint for a certain amount of polymer surrounding them and consequently these highly oriented sheets, once exposed to high temperature, will mainly stress relax and do not creep. This effect disappears when the melting temperature of the oriented crystalline phase is reached. Compatible PLC-PS blends do not show any improvement on the dimensional stability compared to the unfilled matrix.     

Effects of prior aging at 288°C in air and in argon environments on creep response of PMR‐15 neat resin

The creep behavior of PMR‐15 neat resin, a polyimide thermoset polymer, aged in air and in argon environments at 288°C for up to 1000 h was evaluated. Creep tests were performed at 288°C at creep stress levels of 10 and 20 MPa. Creep periods of at least 25‐h in duration were followed by 50‐h periods of recovery at zero stress. Prior isothermal aging increased the elastic modulus and significantly decreased the polymer's capacity to accumulate creep strain. The aging environment had little influence on creep and recovery behaviors. However, aging in air dramatically degraded the tensile strength of the material. Dynamic mechanical analysis revealed an increase in the glass transition temperature from ∼330°C to ∼336°C after 1000 h in argon or in air at 288°C. The rise in the glass transition temperature with aging time is attributed to an increase in the crosslink density of the PMR‐15 polyimide. Increase in the crosslink density due to aging in both air and argon environments is likely behind the changes in the elastic modulus and the decreased capacity for inelastic straining. A visibly damaged surface layer of ∼0.16 mm thickness was observed in specimens aged in air for 1000 h. Results indicate that the unoxidized core material governs the overall mechanical response, whereas the oxidized surface layer causes a decrease in tensile strength by acting as a crack initiation site and promoting early failures. © 2008 Wiley Periodicals, Inc. J Appl Polym Sci, 2009     

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.     

An interpretation of the critical strain measure for polymers

During creep deformation many polymeric materials exhibit small cracklike zones, crazes. In the literature it is reported that crazing will not occur if the strain is kept under a critical value, specific for each material. This fact has importance in avoiding rupture. In this work a uniaxial theory is put forward that is based on a creep law describing the buildup of internal stress and on the Kachanov damage law. Crazing is here regarded to be a stage in the damage accumulation process, the final stage of which is rupture. Relations among the critical strain, the corresponding critical stress, and the minimum stress leading to creep rupture are derived. Some conditions that are necessary for the critical strain concept to work are formulated.     

Accelerated characterization of a chopped fiber composite using a strain energy failure criterion

The creep and creep rupture response of a chopped fiber composite material (SMC-R50) were investigated experimentally and analytically. The goal of this research was to use the short time laboratory data to predict long time creep and creep rupture behavior. The creep response data up to 200 min duration were obtained at various constant temperature and stress levels. The short time creep data were then modeled using a modified power law equation. The modified power law equation contains the parameters of the so-called accelerated characterization procedure. Using this power law equation, the short time creep response at the elevated temperatures were able to successfully predict the long time creep response at a lower temperature and stress level. To predict the creep rupture behavior, the modified power law equation was then coupled with a strain energy based failure criterion. It was found that the same parameters that were used in the prediction of the long-time creep response can also be used to predict the creep rupture. At a given temperature level, the strain energy density related to creep rupture was found to be a constant. Furthermore, this strain energy density was found to increase with an increase in temperature. With a limited amount of data, it was found that the strain energy based failure criterion coupled with the modified power law equation can be used to predict long time creep rupture behavior.