Viscoelasticity, viscoplasticity, and creep failure of polypropylene/clay nanocomposites

Observations are reported on polypropylene/clay nanocomposites in tensile tests with various strain rates, relaxation tests at various strains, and creep tests with various stresses at room temperature. New constitutive equations are derived in viscoelasticity and viscoplasticity of nanocomposites. Adjustable parameters are found by fitting the experimental data. The stress–strain relations are applied to the analysis of creep rupture. It is demonstrated that reinforcement of polypropylene with 1 wt.% of nanoclay induces an increase in time to failure by an order of magnitude.     

Creep failure of polypropylene: experiments and constitutive modeling

Observations are reported on isotactic polypropylene in uniaxial tensile tests with various strain rates, relaxation tests with various strains, and creep tests with various stresses at ambient temperature. Constitutive equations are derived for the viscoelastic–viscoplastic responses and damage of a semicrystalline polymer at three-dimensional deformations. Adjustable parameters in the stress–strain relations are found by fitting the experimental data. The model is applied to predict creep-failure diagrams in the entire interval of stresses. A phenomenological approach is proposed to determine a knee stress, at which transition occurs from ductile to brittle rupture. Accuracy of this method is evaluated by numerical simulation.     

Creep Crack Growth in Polypropylene Film with Various Crack Lengths at Diverse Stresses and Temperatures

Creep crack growth rates were measured using centrally cracked tension specimens of thin polypropylene film with different crack lengths at various stresses and temperatures. The creep crack growth rates were correlated with the stress intensity factor. There was the region of the minimum constant crack growth rate which occupied more than 70% of the total creep failure life. This constant creep crack growth rate characteristics were analyzed on the basis of the stress-dependent Arrhenius type thermally activated process.     

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.     

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.     

Prediction of the long-term creep behaviour of hydroxyapatite-filled polyethylmethacrylate bone cements

The creep behaviour of bone cements based on polyethylmethacrylate, with and without addition of hydroxyapatite filler has been investigated, in order to determine the effect of hydroxyapatite filling and to investigate methods of predicting the long-term creep behaviour from short-term tests. The materials were produced under laboratory conditions and tested in tension in Ringer’s solution, as the study was intended to investigate the inherent materials behaviour rather than to simulate realistic conditions. The effects of adding hydroxyapatite were to increase the short-term stiffness and more significantly to decrease the creep rate. Short-term creep tests of up to 10⁶ s were conducted at various temperatures, stresses and ageing states. These were then used to investigate various methods of extrapolation to long-term behaviour. The use of time-temperature superposition was found to be useful, though it takes no account of ongoing physical ageing and so gives a significant overestimate of long-term creep strains. Stress-time superposition was less useful and also excludes ageing effects. The use of ‘effective time’ theory was more successful, but requires a large number of short-term tests. The most effective method was that of the ‘integrated time’ approach, which required fewer tests yet still gave good correlations with longer-term data.     

Thermo-viscoelastic responses of multilayered polymer composites: Experimental and numerical studies

This study presents experimental works and finite element (FE) analyses of nonlinear thermo-viscoelastic behaviors of multilayered (pultruded) composites under tension. Creep tests are conducted on E-glass/polyester composites having 0°, 45° and 90° off-axis fiber orientations at various temperatures and stresses. Isochronous creep curves show that the nonlinear stress–strain responses increase with time and temperature for composites tested at higher temperatures (75–125 °F) while there is no particular trend seen at lower temperatures (0–50 °F). A convolution integral model is used for the time–stress–temperature dependent responses. The nonlinear viscoelastic model is implemented in FE framework for analyzing responses of viscoelastic pultruded structures. Sensitivity analysis is conducted to examine error in measuring strains during experiments by simulating the creep tests using FE.     

The construction and stability of a surface mounted vibratingwire strain guage

The construction of a surface–mounted vibratingwire strain gauge for use in creep tests is described and some results on the stability of the gauge are presented. Novel features of the gauge construction include a pressed one–piece clamp for holding the wire and provision for a secondary strain measuring system. Relaxation of the vibrating wire caused relaxation of the gauge. There was no significant relaxation due to the clamping method. Cyclic straining of the gauge before use virtually eliminated zero displacement. The use of an unloaded control specimen, which is gauged at the same time and with the same wire tension as the creep specimen, is recommended. Alternatively, relaxation measurements on the wire can be used to correct measured strains. Either of these procedures will reduce the effect of gauge relaxation on creep strains to less than 3 μstrain.     

Microstructure and modelling of the deformation behaviour of CoCr22Ni22W14 in hot-tensile- and creep tests

The present study describes the application of hot tension experiments in order to predict the creep and tensile behaviour of the highly loaded superalloy CoCr₂2Ni₂₂W₁₄. The results of mechanical tests and transmission electron microscopy (TEM) investigations have been used as input data in a model which describes the high temperature plastic deformation. A common log - log σ plot of tensile and creep data shows a systematic shift of about 10% towards higher stresses in the case of tensile loading. In creep tests the dislocation densities reach their steady-state values at the points of minimal strain rates, whereas in tensile tests the dislocation densities increase at any given time until the tensile strength is reached at significantly higher strains. Under the condition of equal true stresses subgrain formation is more pronounced after tensile than after creep deformation. By including the experimentally determined dislocation densities, the constitutive model yields qualitatively correct predictions of the creep and tensile behaviour.     

Application of fractional derivative models in linear viscoelastic problems

Appropriate knowledge of viscoelastic properties of polymers and elastomers is of fundamental importance for a correct modelization and analysis of structures where such materials are present, especially when dealing with dynamic and vibration problems. In this paper experimental results of a series of compression and tension tests on specimens of styrene-butadiene rubber and polypropylene plastic are presented; tests consist of creep and relaxation tests, as well as cyclic loading at different frequencies. Experimental data are then used to calibrate some linear viscoelastic models; besides the classical approach based on a combination in series or parallel of standard mechanical elements as springs and dashpots, particular emphasis is given to the application of models whose constitutive equations are based on differential equations of fractional order (Fractional Derivative Model). The two approaches are compared analyzing their capability to reproduce all the experimental data for given materials; also, the main computational issues related with these models are addressed, and the advantage of using a limited number of parameters is demonstrated.     

Effect of temperature on the viscoelastic and viscoplastic behavior of polypropylene

Observations are reported on isotactic polypropylene in tensile tests with various cross-head speeds and relaxation tests in a wide interval of temperatures ranging from room temperature to 120°C. A constitutive model is derived for the viscoelastic and viscoplastic responses of a semicrystalline polymer at arbitrary deformations with small strains. The stress–strain relations involve 6 adjustable parameters that are found by fitting the experimental data. The presence of a critical temperature is demonstrated at which some parameters of the model reach their maxima. This temperature is associated with the α-relaxation temperature of polypropylene.     

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.     

The effect of annealing on the elastoplastic and viscoelastic responses of isotactic polypropylene

Observations are reported on isotactic polypropylene (i) in a series of tensile tests with a constant strain rate on specimens annealed for 24 h at various temperatures in the range from 110 to 150 °C, (ii) in two series of creep tests in the subyield region of deformations on samples not subjected to thermal treatment and on specimens annealed at 140 °C, and (iii) in a series of tensile relaxation tests on non-annealed specimens. Constitutive equations are derived for the elastoplastic and non-linear viscoelastic responses of semicrystalline polymers. A polymer is treated as an equivalent transient network of macro-molecules bridged by junctions (physical cross-links, entanglements and lamellar blocks). The network is assumed to be highly heterogeneous, and it is thought of as an ensemble of meso-regions with different activation energies for separation of strands from temporary nodes. The elastoplastic behavior is modelled as sliding of junctions in meso-domains with respect to their reference positions driven by macro-deformation. The viscoelastic response is attributed to detachment of active strands from temporary junctions and attachment of dangling chains to the network. Constitutive equations for isothermal deformations with small strains are derived by using the laws of thermodynamics. Adjustable parameters in the stress–strain relations are found by fitting the experimental data.     

Cyclic viscoelastoplasticity of polypropylene: effects of crystalline structure

Observations are reported on two grades of polypropylene in tensile tests with various strain rates, relaxation tests with various strains, and cyclic tests with a stress-controlled program (ratcheting). Experiments are performed on isotactic polypropylene (iPP) manufactured by the Ziegler?CNatta catalysis and metallocene-catalyzed polypropylene (mPP). The time- and rate-dependent behaviors of iPP and mPP in tensile tests and relaxation tests are quite similar, whereas their responses in cyclic tests differ pronouncedly: The number of cycles necessary for mPP to reach a required ratcheting strain exceeds that for iPP by an order of magnitude. To rationalize these observations, a constitutive model is developed in cyclic viscoelastoplasticity of semicrystalline polymers, and its adjustable parameters are found by fitting the experimental data. Slowing down of growth of ratcheting strain in mPP is attributed to the presence of small crystalline domains in amorphous regions that act as physical cross-links. The effect of the strain rate on the number of cycles to failure is studied numerically.     

Zeitstandverhalten warmfester Stähle bei zyklischer und bei intermittierender Beanspruchung

Creep and Creep Rupture Behaviour of Heat Resistant Steels under Cyclic and Intermittent Loading Conditions On typical heat resistant steels creep and creep rupture tests under rectangular cyclical conditions of tension stress or/and temperature were continued. Comparable creep and creep rupture tests with tension and compression phases and with intermittent loading conditions were started. Besides this single-stage loading conditions, double-stage loading conditions were investigated. The test results are analysed with the modified life fraction rule. Concepts of relative life are improved and partly new established.     

应力水平和纤维角度对CGF/PP复合材料蠕变行为的影响及其Burgers模型参数的数值预测

采用DMA的Creep模式分别测试了短时间内（15 min）聚丙烯（PP）在不同应力水平和温度下的单向拉伸蠕变行为,长时间内（10 h）连续玻璃纤维增强聚丙烯（CGF/PP）复合材料单层板在不同应力水平和不同纤维角度上的拉伸蠕变行为。利用Burgers黏弹性模型拟合了蠕变测试数据,构建了相关参数与应力水平和纤维角度的依赖性。结果表明:PP和CGF/PP单层板的蠕变柔量均随应力增大而显著增加,稳态蠕变速率也随之增加,蠕变模量保留率明显下降,PP基体的黏弹性主要决定了CGF/PP单层板在低应力水平下的蠕变行为; 30%应力水平下,偏轴拉伸的纤维角度在0°~90°范围内存在拉-剪耦合效应,在45°时最为显著,此时稳态蠕变速率和蠕变变形量最大;利用四元件Burgers黏弹性模型拟合各条件下蠕变曲线得到的数值模型与实验数据具有较好的相关性,相关系数达到0.99,从得到的数值模型可知相关模型参数存在明显的应力和角度依赖关系;利用模型参数的数值拟合公式分别预测10 MPa应力下0°纤维方向的蠕变曲线及45°纤维方向上30%应力水平的偏轴蠕变曲线均与实验曲线一致,表明本文得到的数值模型的可靠性。      

Stress/strain/time relations for ice under uniaxial compression

Results of mechanical tests involving uniaxial compression of isotropic ice at ?5°C were analysed and interpreted. Constant load (CL) creep tests were made for applied stresses in the range 0.8 to 3.8 MPa, and “strength” tests under constant displacement rate (CD) were made for applied strain rates in the range 10^?7 to 10^?3 s^?1. Results from CL tests and CD tests corresponded closely, giving much the same information about failure strains, strength, creep rates, time to failure, stress/strain-rate relations, and suchlike. Empirical stress/strain-rate relations were developed for three distinct states of strain: (1) for the initial yield point, where axial strains are typically of the order of 0.1%, (2) for the ductile yield point, where axial strains are typically of the order of 1%, (3) for an axial strain of 10%. Stress/strain-rate relations and stress/strain relations for constant duration of CL loading were examined for load durations up to half an hour. The elapsed time up to the ductile yield point (～1% strain) was related to stress and to strain rate for CL tests and CD tests, and correspondence of the results was demonstrated both for interrelationship between CL and CD tests and for compatibility with the appropriate stress/strain-rate relations. The elapsed time up to the initial yield point was also considered. It was shown that CD stress/strain curves can be constructed from a suitable family of CL creep curves, and vice versa.The characteristics of CL creep curves and CD stress/strain curves were examined in some detail, considering relations between strain rates for certain identifiable points on creep curves, and relations between stresses for certain identifiable parts of stress/strain curves. Effective values for quasi-elastic moduli were considered. The strains for various critical points were compared with each other and with the strains at which rates of acoustic emissions reach maximum values.     

CRACK GROWTH RATES DURING CREEP, FATIGUE AND CREEP-FATIGUE IN AN AUSTENITIC FEATURE WELD SPECIMEN

Abstract— Static creep crack growth tests and displacement controlled fatigue and creep-fatigue crack growth tests have been performed on austenitic feature weld specimens at 650°C. The creep-fatigue tests incorporated hold times of up to 96 h. During these tests, crack growth appeared to comprise cyclic and dwell components. Cyclic crack growth components were characterised by the fracture mechanics parameter K whilst creep crack growth contributions were correlated with C *. In order to determine K and C * for the non-standard feature weld specimen, elastic and elastic-plastic creep finite element analyses were conducted. Good correspondence is shown between the feature weld data and comparable data from compact tension specimen tests on similar materials. Equations obtained from the compact tension specimen results, which describe total crack growth rates as the sum of the cyclic and dwell contributions, are shown to adequately describe the features test results also. Furthermore, it is demonstrated that a reference stress approach can be used to estimate C * for the features specimens.     

Cyclic viscoelastoplasticity of polypropylene/nanoclay composites

Observations are reported on isotactic polypropylene/organically modified nanoclay hybrids with concentrations of filler ranging from 0 to 5 wt.% in cyclic tensile tests with a stress?Ccontrolled program (oscillations between various maximum stresses and the zero minimum stress). A pronounced effect of nanofiller is demonstrated: reinforcement with 2?wt.% of clay results in strong reduction of maximum and minimum strains per cycle and growth of number of cycles to failure compared with neat polypropylene. To rationalize these findings, a constitutive model is developed in cyclic viscoelasticity and viscoplasticity of polymer nanocomposites. Adjustable parameters in the stress?Cstrain relations are found by fitting experimental data. The model correctly describes the growth of the ratcheting strain and shows that fatigue failure is driven by a pronounced increase in plastic strain in the crystalline phase. To assess the influence of loading conditions on the changes in the material parameters, experimental data on polypropylene are studied in cyclic tests with a strain?Ccontrolled program (oscillations between fixed maximum and minimum strains) and a mixed program (oscillations between various maximum strains and the zero minimum stress). Numerical simulation confirms the ability of the model to predict the evolution of stress?Cstrain diagrams with the number of cycles.