The effect of strain rate on craze yielding,shear yielding,and brittle fracture of polymers at 77°K

The tensile strength of poly(methyl methacrylate) (PMMA), polycarbonate (PC), polychlorotrifluoroethylene, and polysulfone was measured in liquid nitrogen over the strain rate range of 2 × 10^?4 to 660 min^?1. These polymers deformed by crazing which was induced by the liquid nitrogen. The stress versus log strain rate curve was sigmoidal in that its slope increased and then decreased with strain rate. Above a critical strain rate of about 200 min^?1, which varied somewhat with the polymer, crazing was not observed with the optical microscope; the behavior became brittle, and the tensile strength became constant. The nonlinear behavior of stress versus log strain rate at low strain rates was associated with a decrease in activation volume with increasing strain rate whereas the nonlinear behavior at high strain rates was associated with an increase in density and decrease in length of the crazes with strain rate. The strain rate effect was the basis for calculating the diffusion coefficient of nitrogen into the polymers at 77°K. The shear deformation mode of PC was measured under compression and under tension. The compressive strength versus log strain rate was linear throughout the entire range giving a compression shear activation volume of 360 ų. The shear tensile strength of PC varied only slightly with strain rate when compared to the compressive strength. The brittle fracture stress of PMMA, in the absence of crazing, in compression and in tension, did not vary with strain rate.     

Characterization of the compressive deformation behavior with strain rate effect of low-density polymeric foams

This study investigates the compressive deformation behavior of a low-density polymeric foam at different strain rates. The material tested has micron-sized pores with a closed cell structure. The porosity is about 94%. During a uni-axial compressive test, the macroscopic stress–strain curve indicates a plateau region during plastic deformation. Finite Element Method (FEM) simulation was carried out, in which the yield criterion considered both components of Mises stress and hydrostatic stress. By using the present FEM and experimental data, we established a computational model for the plastic deformation behavior of porous material. To verify our model, several indentation experiments with different indenters (spherical indentation and wedge indentation) were carried out to generate various tri-axial stress states. From the series of experiments and computations, we observed good agreement between the experimental data and that generated by the computational model. In addition, the strain rate effect is examined for a more reliable prediction of plastic deformation. Therefore, the present computational model can predict the plastic deformation behavior (including time-dependent properties) of porous material subjected to uni-axial compression and indentation loadings.     

Mechanical response of three semi crystalline polymers under different stress states: Experimental investigation and modelling

The mechanical responses of high‐density polyethylene (HDPE), polypropylene (PP) and polyamide 6 (PA 6) were experimentally investigated for a wide range of stress states and strain rates. This was accomplished by testing numerous specimens with different geometries. The uniaxial compression of cylindrical unnotched specimens and the uniaxial tensile behaviour of dumbbell specimens at different strain rates, was determined. A series of biaxial loading tests (combined shear and tension/compression, pure shear, pure tension/compression) using a designed Arcan testing apparatus were also performed. Flat and cylindrical notched specimens with different curvature radii were additionally tested in order to explore a wider range of stress states. The Drucker‐Prager yield criterion was calibrated with a set of experimental data, for which analytical formulae for stresses are available, and then applied to predict the deformation behaviour under different stress states, prior to strain localization. The results of the numerical simulations show that the Drucker‐Prager model can capture the initial elastic range and the post‐elastic response very satisfactorily. For triaxial and biaxial stress states there is a good agreement, however some load‐displacement responses are only satisfactorily described. Deviations observed in the predicted and experimental results are very likely attributed to the third invariant stress tensor, which was not explored in the model calibration. The evolution of stress triaxiality and Lode angle parameters with equivalent plastic strain were extracted and analysed for several specimens. The results show a plastic yielding behaviour sensitive to the stress state, which can be attributed to different combinations of stress triaxialities and Lode angle parameters.     

Crazing in polyethylene

The tensile stress—strain curves of various types of polyethylene were compared from 77 to 298 K in nitrogen, isopentane, and the inert environment of helium at various strain rates. It was found that in general polyethylene crazes in a gas such as nitrogen at a temperature below 1.6 times its boiling point and in isopentane. Although the behavior of polyethylenes is similar to that of other polymers with regard to crazing in gases at low temperatures, they are in general less sensitive to the gas. The decrease in tensile strength of polyethylene in an environmental gas increases with crystallinity. The differences in the intrinsic low-temperature brittle fracture stress are attributed to differences in the density of tie molecules. The intrinsic yield point at room temperature showed the usual increase with increasing crystallinity, but all the polyethylenes have the same yield point below the γ transition temperature.     

Cyclic stress–strain behavior of the dry polycarbonate craze

Equipment and methods have been developed which allow photomicrographic determination of the stress–strain properties of the individual craze. Serial cyclic tensile tests on polycarbonate crazes are described. Under stress the typical dry polycarbonate craze thickens solely by straining; no adjacent polymer of normal density is converted to craze material. The craze exhibits a yield stress followed by a recoverable flow to roughly 40–50% strain at 6000–8000 psi. On return to zero stress the craze exhibits creep recovery at a decelerating rate. The yield stress and loss factor of each cycle decrease with increasing initial strain and cycles initiating at 50% strain or more show completely Hookean behavior. Creep recovery results in recovery of yield stress and loss factor also. Craze tensile behavior is suggested to be essentially an extension of the craze formation process. Decrease in elastic modulus and yield stress with increasing strain are rationalized in terms of strain-produced decrease in density and resultant increase in stress concentration factor on the microscopic polymer elements of the craze. Polymer surface tension and the large internal specific surface area of the craze are suggested to be important factors in the large creep recovery rates of the craze.     

Aspects of fatigue failure mechanisms in polymer fuel cell membranes

The swelling‐driven fatigue behavior of polymer fuel cell membranes during relative humidity (RH) cycling is investigated. In particular, swelling‐induced membrane stresses are obtained from a numerical model simulating fuel cell RH cycle tests, and compared to the lifetimes obtained experimentally from tests conducted in the absence of electrochemical effects. A strong correlation between the lifetimes of the membranes in the actual tests and model results is obtained. In general, higher RH (or swelling) amplitude results in larger stress amplitudes and shorter lifetime, that is, fewer cycles to failure. Tensile stresses are needed for forming local cavities in the membrane, which may eventually lead to craze formation. Cavitation is less likely to occur in compressed membrane at high humidities. The stress–lifetime plots for polymer fuel cell membranes exhibit similar features to those observed for other polymers. The crazing criterion for polymers suggests that craze initiation during RH cycling is more likely to occur in the low compression regions, such as under the channels, which is in agreement with experimental observations. © 2011 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 49: 1506–1517, 2011     

Constitutive model calibration of the time and temperature-dependent behavior of high density polyethylene

HDPE is commonly used in pipelines and piping for industrial and societal infrastructure. Like most polymers, HDPE's mechanical properties are sensitive to temperature and show time dependent properties. The temperature effect on both the short and long term compressive and tensile behavior of HDPE, in a combined manner, have not been investigated thoroughly in the past. Especially the constitutive behavior of HDPE, incorporating temperature effects on its long and short term behavior, could be essential when designing such infrastructural components. Hence, the temperature effect on the short and long term response in tension and compression of HDPE is investigated in this study. The short term tensile and compressive stress-strain behavior at 23, 40, 60, and 80 °C were obtained through experiments at constant displacement rate and temperature. Tensile and compressive stress relaxation (e.g. long term) behavior at 23, 40, 50, 60, 70, and 80 °C were investigated through stress relaxation tests. The experimental results from the short term tests showed that both the tensile and compression moduli and yield strength of HDPE decrease linearly with the increase in temperature. It is also shown from the long term test that relaxation modulus in tension and compression are highly dependent on temperature. Based on the experimental results, the constitutive three network model (TNM) was calibrated and implemented in a FEA model, which was then validated through a three point bending (3 PB) relaxation test with a prescribed temperature profile. The FEA model and the calibrated model results agree markedly well with the experimental results, which indicates that the model can be used reliably to predict the temperature dependent short and long term behavior of HDPE in design and analysis of HDPE components.     

Deformation and fracture behavior of poly(vinylidene fluoride‐trifluorethylene) ferroelectric copolymer films under uniaxial tension

The deformation and fracture behavior under uniaxial tension was characterized for P(VDF‐TrFE) 68/32 mol % copolymer films prepared under two different processing conditions. It was found that the copolymer films prepared by solution casting and then annealing show a typical polymeric brittle fracture feature. For the copolymer films prepared by stretching the solution‐cast films and then annealing process, a typical linearly strengthening stage occurs in the stress–strain curve after yielding, and the polymer film samples fracture at a much larger maximum strain and a higher tensile strength than those prepared by the former process. SEM observation and XRD analysis were carried out to examine the morphology and microstructure change during uniaxial tension. The results show that for the stretched film samples, the polymer chains undergo slipping or further reorientation during uniaxial tension, causing the increase of the peak intensity in the X‐ray diffraction pattern. For the directly annealed ones, no yielding phenomenon is observed and there is no apparent X‐ray diffraction intensity change. It was suggested that the highly‐oriented fibril structure of the stretched film samples contributes to the linearly strengthening stage after yielding in the stress–strain curve. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 3255–3260, 2005     

Comparison of interfacial properties of electrodeposited single carbon fiber/epoxy composites using tensile and compressive fragmentation tests and acoustic emission

Interfacial and microfailure properties of carbon fiber/epoxy composites were evaluated using both tensile fragmentation and compressive Broutman tests with an aid of acoustic emission (AE). A monomeric and two polymeric coupling agents were applied via the electrodeposition (ED) and the dipping applications. A monomeric and a polymeric coupling agent showed significant and comparable improvements in interfacial shear strength (IFSS) compared to the untreated case under both tensile and compressive tests. Typical microfailure modes including cone-shaped fiber break, matrix cracking, and partial interlayer failure were observed under tension, whereas the diagonal slipped failure at both ends of the fractured fiber exhibited under compression. Adsorption and shear displacement mechanisms at the interface were described in terms of electrical attraction and primary and secondary bonding forces. For both the untreated and the treated cases AE distributions were separated well in tension, whereas AE distributions were rather closely overlapped in compression. It might be because of the difference in molecular failure energies and failure mechanisms between tension and compression. The maximum AE voltage for the waveform of either carbon or large-diameter basalt fiber breakages in tension exhibited much larger than that in compression. AE could provide more likely the quantitative information on the interfacial adhesion and microfailure.     

Craze initiation of glassy polymers under the action of crazing agent

This paper deals with the formation of crazes that may be caused by an external load on glassy polymers wetted with kerosene. First, the orientation of crazes has been determined when applying a uniaxial tension to a specimen of cold-rolled polyvinyl chloride sheet at various angles to the rolling direction. The critical stress for craze initiation in poly(methyl methacrylate) and polyvinyl chloride rods has been investigated under combined tension–torsion loading. It is shown that: (1) in an anisotropic, as well as an isotropic polymer, the direction of crazes is perpendicular to that of the maximum strain calculated by taking into account the internal stress due to rolling; and (2) under the action of a crazing agent, crazing may occur even under the pure torsional load, i.e., in the absence of dilatational stress.     

石墨烯/聚乙烯复合材料及其拉伸性能的分子动力学模拟

利用分子动力学方法,模拟石墨烯/聚乙烯复合材料的微观结构和性能,并采用单轴拉伸模拟方法研究石墨烯/聚乙烯复合材料的拉伸性能.结果表明,在石墨烯/聚乙烯复合材料平衡构型中,聚乙烯基体分子在石墨烯表面处形成多层吸附层,吸附层处于动态稳定状态,层内分子可以发生扩散迁移.吸附层内聚乙烯分子发生"吸附固化"现象,分子弯曲程度减弱,发生有序排列,且在垂直于石墨烯方向的运动性能受到抑制.拉伸模拟结果表明,石墨烯能够提高聚乙烯材料的拉伸性能.在弹性区和屈服区,石墨烯阻碍了复合材料在垂直于拉伸方向的压缩变形,聚乙烯分子"吸附固化"结构保持稳定,引起体系整体应力的迅速升高.在软化区,由于石墨烯发生剧烈弯曲,"吸附固化"结构发生破坏,最终引起体系应力迅速减小.在弹性区和屈服区,体系应变主要引起了非键相互作用的改变.在软化区之后,应变主要导致了体系内分子成键相互作用的改变.应变速率能够提高复合材料的屈服应力,而不改变复合材料应力应变的整体趋势.     

Irreversible deformation of isotactic polypropylene in the pre-yield regime

In the modeling of the mechanical response of a polymer over a large strain range, the nonlinear viscoelastic and viscoplastic behavior must be considered. For many polymers, nonlinear behavior is observed at low loads, e.g. by a stress-dependence of the creep compliance for stresses above 2 MPa in case of the polypropylene used in this study. Additionally, plastic deformation has been observed at strains below the yield point for several polymers. In this study, the irreversible deformation by cavitation and shear yielding of polypropylene are characterized in the pre-yield regime in uniaxial tensile tests using digital image correlation. The recovery of strain after unloading at a prescribed strain level is measured and used to identify the evolution of the plastic strain during uniaxial tension. An experimental technique for simultaneous determination of the true stress–true strain curve and the degree of stress whitening, which relates to the amount of cavitation, is introduced and the initiation of cavitation is compared to the plastic deformation detected in strain recovery at various temperatures.     

A test method for the determination of the stress cracking effects of liquid environments on thermoplastics by measurement of critical strain

The stress cracking effect of liquids on thermoplastic materials can be quantified by measuring the critical strain to cause cracking or crazing. The critical strain is ideally defined as the value of applied strain, for a given material and liquid combination, below which no cracking or crazing occurs. A method is described for the determination of critical strain using a simple straining jig. A strain gauge extensometer attached directly to the specimen is used to accurately monitor the applied strain while visual observation of the sample is used to record the time to crack or craze.Critical strain values measured by this technique are quoted for various alcohols and ketones in contact with polycarbonate and compared with literature values.     

Prediction of yield and long‐term failure of oriented polypropylene: Kinetics and anisotropy

The time‐dependent yield and failure behavior of off‐axis loaded uniaxially oriented polypropylene tape is investigated. The yield and failure behavior is described with an anisotropic viscoplastic model. A viscoplastic flow rule is used with an equivalent stress, based on Hill's anisotropic yield criterion, and the Eyring flow theory combined with a critical equivalent strain definition. This model is based on factorization of the rate and draw ratio dependence and is capable of quantitatively predicting the rate, angle and draw ratio dependence of the yield stress as well as time‐to‐failure in various off‐axis tensile loading conditions characterized solely from the transverse direction. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 2026–2035, 2009     

Effects of stereo-defect distribution on the crystalline morphology and tensile behavior of isotactic polypropylene prepared by compression molding process

In this study, the aggregation morphology, tensile behavior, and morphology evolution during the tensile test of two isotactic polypropylene (iPP) samples with similar molecular weight and average isotacticity but different uniformities of stereo-defect distribution are investigated by differential scanning calorimetry (DSC), two-dimensional wide angle X-ray diffraction (2D-WAXD), and scanning electronic microscopy (SEM). The results revealed that the uniformity of stereo-defect distribution of iPP determines the crystalline structure and aggregation morphology, and further influences the tensile behavior and morphology evolution during the tensile test. For PP-A with less uniform stereo-defect distribution, its ability of crystallization is stronger compared with PP-B, resulting in smaller spherulite sizes, higher melting point and degree of crystallinity, and narrower distribution of lamellar thickness of the compression molding specimens. During the tensile test, mainly the inter-spherulite deformation takes place at the early stage for deformation, which further results in drastic deformation of lamellar and high degree of reorientation at the strain increases, exhibiting higher yield strength and elastic modulus, and lower elongation at break compared with PP-B; for PP-B with more uniform stereo-defect distribution, larger spherulite sizes, lower melting point and degree of crystallinity in its compression molding sample are observed. During the tensile test, intra-spherulite deformation mainly takes place, which can disperse the tensile stress more uniformly. As the strain increases, lower degree of crystalline destruction and reorientation of the crystallites take place. The yield strength and elastic modulus of PP-B is lower than PP-A, and its elongation at break is higher.     

Effect of stress on the fire reaction properties of polymer composite laminates

A small-scale loading frame was used to apply tensile and compressive stresses to glass vinyl ester and glass polyester laminates in a cone calorimeter under a heat flux of 75 kW m⁻². It was found, for the first time, that stress has a small but significant effect on the fire reaction properties. Increasing tensile stress increased heat release rate and smoke production while shortening the time-to-ignition. Compressive stress had the reverse effect. This was attributed to the fact that tensile stress promotes the formation of matrix microcracks, facilitating the evolution of flammable volatiles. This hypothesis is further supported by the observation that stress has the greatest effect on the early heat and smoke release peaks, with a lower effect on the final ‘run-out’ values.Stress rupture (time-to-failure) curves were produced for tension and compression. In tension, the behaviour was fibre dominated, with times-to-failure being roughly 10 times those in compression. Compressive failure involved resin dominated local fibre kinking, initiated near to the rear face of the specimen. The failure time was determined by a significant proportion of the specimen reaching its glass transition temperature.     

Investigation of different influences on the fatigue behaviour of industrial rubbers

Load conditions used typically for fatigue life investigations can differ strongly from the conditions for real rubber products. For example, the frequency of the laboratory measurements is increased and the product load curve is simplified to a sine. In this paper, industrial rubber blends (SBR/BR/NR blends) under tension–compression load are used. First, the influence of a higher frequency (5 Hz) compared to the product relevant frequency (1 Hz) is investigated. A higher frequency does not influence the fatigue life but certainly the sample temperature and material behaviour. This is further investigated by varying the ambient temperature for 1 Hz measurements and the strain rate. Second, a non-sinusoidal wave form depicting the product loading case is selected. The load oscillates between tension and compression with dwell periods in every cycle. The results are comparable to those of a sine wave with the same frequency.     

The effect of strain rate on solvent crazing of poly(ethylene terephthalate) in solutions of poly(ethylene oxide) of various molecular masses

The effect of strain rate on the behavior of PET during its tensile drawing in highly viscous liquids, such as liquid PEG (M 400) and semidilute solutions of PEO (M = (4 × 10⁴)−(1 × 10⁶)), is studied. With an increase in strain rate, the mechanism of tensile drawing of PET in PEG changes from solvent crazing to shearing; at the same time, over the selected interval of strain rates, tensile drawing of PET in semidilute solutions of PEO proceeds via the mechanism of solvent crazing. During tensile drawing of PET in PEO solutions, the behavior of PET is almost the same as the mechanism of tensile drawing in a pure solvent. This result indicates that, in the course of flow of the polymer solution through the formed porous structure, PEO is filtered off in the local tip region of the growing craze.     

Rejuvenation of PLLA: Effect of plastic deformation and orientation on physical ageing in poly(l‐lactic acid) films

Poly(l ‐lactic acid) (PLLA) is a bio‐degradable polyester which exhibits brittle behaviour due to relatively fast physical ageing of the amorphous phase. This work describes the effects of thermal rejuvenation and molecular orientation of the amorphous phase on this physical ageing process. Uniaxial compression testing showed that physical ageing of the amorphous phase increases the yield stress and the associated strain softening response, both contributing to the observed embrittlement of PLLA in tension. Molecular orientation at constant crystallinity was applied by uniaxial and biaxial plastic deformation just above the glass transition temperature, up to plastic strains of 200% to avoid strain‐induced crystallisation. Using stress‐relaxation experiments combined with tensile testing, both as a function of ageing time, it is shown that both uniaxial and biaxial plastic deformation in excess of 150% plastic strain, decelerates and possibly prohibits the physical ageing process. The oriented monofilaments and films have improved mechanical properties such as stiffness, strength and strain‐to‐break, which were not affected by physical ageing during the whole testing period (40 days). In addition, plastic deformation to higher draw ratios and/or higher temperatures strongly enhanced crystallinity and resulted in PLLA monofilaments and films that also exhibited tough behaviour, not affected by physical ageing. © 2016 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2016 , 54, 2233–2244     

A theory for environmental craze yielding of polymers at low temperatures

It has been recently discovered that polymers craze at low temperatures in the presence of nitrogen or argon. A quantitative theory has been developed which explains (1) the critical temperature above which the phenomenon disappears, (2) the critical stress for nucleating a craze, (3) the effect of strain rate on the yield point and size of crazes, (4) the drop in the load during craze yielding, and (5) the increase in strength of the polymer in N₂ or Ar at high strain rates so that the ultimate strength may exceed that in He or vacuum. The crazing action of the gases is described qualitatively at the molecular level.