Delayed yielding of epoxy resin. II. Behavior under constant stress

Creep tests were carried out on epoxy resin specimens at room temperature and at different high stress levels under tension, compression, and flexure. Compared with the behavior at constant strain rate (CSR) reported in Part I of this work, creep strain–time curves revealed a distinct delayed yielding region of constant minimum rate (secondary creep) followed by a post-yielding region of increasing slope (tertiary creep). In all cases, results indicate linearity between creep stress and log secondary creep rate, which is almost coincident with the corresponding relationship between yield stress and strain rate obtained in subsequent CSR loading cycles with the same specimens. The similarity in behavior under both the creep and CSR modes conforms to Eyring's theory of non-Newtonian viscous flow at high stress levels and low temperature. Theoretical analysis yields reasonable values of the activation volume, which is unaffected by the loading and test modes or by loading history, and could thus be regarded as an intrinsic parameter of the microstructure, inherently related to the viscoplastic process involved. The above considerations indicate a deviatoric stress-biased diffusional mechanism as the predominant factor in the yielding of an amorphous glassy epoxy system.     

Relaxation phenomenon in epoxy glass aged under post‐yield strain

Relaxation phenomenon in epoxy glass aged under shear strain larger than an upper yield point was studied. After aged under post‐yield strain for various aging periods, cylindrical specimens of epoxy glass were twisted clockwise (in the same direction as the prestrain) or counterclockwise (the opposite direction to the direction of the prestrain). The evolution of yield points was significantly different from that of the specimens aged under preyield strain. There exist two knee‐like yield points on stress–strain curves of specimens twisted counterclockwise: one evolved toward to an upper yield point and merged the other knee‐like yield point whose stress value was almost independent of aging time. On the basis of the experimental results, we proposed a combined relaxation model of two relaxation mechanisms: one is relaxation results in an isotropic structure whose center in stress space is the stress value in the terminal zone and the other is kinetic relaxation of the isotropic center. The combined relaxation indicated the possibility of phase transition caused by postyield strain, and therefore the higher yield stress than that of an annealed specimen was not resulted from strain‐accelerated aging, but presumably resulted from a structural change under postyield strain. POLYM. ENG. SCI. 46:630–634, 2006. © 2006 Society of Plastics Engineers     

Structural relaxation and evolution of yield stress in epoxy glass aged under shear strain

Hollow cylindrical specimens of annealed epoxy glass were twisted and then aged for various periods of time under shear strain. At the end of the aging process, we twisted the specimens again to determine the stress–strain relations. For specimens aged under a shear strain of 0.005 or 0.01, the stress relaxation behavior was almost independent of the amount of strain imposed, and the value of stress at the upper yield point, regardless of aging time, was almost the same as that of the annealed specimen. On the other hand, for specimens aged under a strain of 0.02 or 0.04, the stress relaxation behavior depended on the value of the strain applied, and the value of stress at the upper yield point first decreased and subsequently increased with increasing aging time. These results led us to the following conclusions: If epoxy glass is strained largely, the originally stable structure becomes unstable. Also, when epoxy glass is aged under strain, the stability of the structure continues to decrease for a short period of time after deformation ceases, and then increases with increasing aging time. POLYM. ENG. SCI. 45:20–24, 2005. © 2004 Society of Plastics Engineers.     

The effect of time and temperature on the mechanical behavior of a “plasticized” epoxy resin under different loading modes

Epoxy–Versamid specimens were loaded in tension, compression, and flexure at different strain rates and temperatures to determine mode of failure, yield stress and strain, and tangent and relaxation moduli. Stress-strain curves were used to define brittle, ductile, ductile-rubbery, and rubbery modes of behavior which prevailed in different temperature-strain rate regions. The time-temperature superposition principle was applied to yield stress, initial tangent moduli, and relaxation moduli data for all three types of loading. The transition regions, tangent and relaxation moduli, and shift factors were the same in tension, compression, and flexure. Thus the most convenient mode of loading can be used to determine the general time-temperature dependence. The ratio of compressive-to-tensile yield stress was almost constant over the entire ductile region. Flexural yielding data were used to predict yield stress in tension and compression, and stress relaxation master curves were shown to be related to elastic modulus vs. strain rate curves. The yielding phenomenon was interpreted using Eyring's theory of non-Newtonian viscoplastic flow. The apparent activation energy and activation volume were larger for tension than compression. A theory is offered to explain why yielding can occur in a cross-linked system.     

Mechanical modeling of initiation of localized yielding under plane stress conditions in rigid-rigid polymer alloys

Two-dimensional Finite Element Method simulations, which involve consideration of the nonlinearity of a material, have been conducted to gain understanding about the rigid-rigid polymer toughening concept we proposed. The simulation results for the plane stress condition indicate that as long as the inclusion phase possesses (i) a 60% difference in the tangent modulus from that of the matrix at any given strain level prior to failure or (ii) smaller yield or craze stain than the yield strain of the matrix, then, localized shear yielding will occur around the inclusion. A toughened rigid-rigid polymer alloy system can then be obtained. The plain strain case is also discussed with an implementation of the rigid-rigid polymer toughening concept.     

The effect of temperature on the delayed yield and failure of “plasticized” epoxy resin

Epoxy-Versamid specimens were loaded in tension up to failure at different constant strain-rates and temperatures. Results revealed three modes of behavior prevailing at different temperature-strain-rate regions and associated with brittle, ductile and rubbery failure modes. The ductile region was found to be confined within a narrow band on the temperature-strain-rate plane, and is characterized by a yield plateau in the stress-strain curve and by linear dependence of yield stress on log strain rate and temperature. Yield strain seems to be almost unaffected by strain-rate, but decreases slightly with temperature rise. Analysis indicated that experimental data within the ductile region are consistent with Eyring's formulation for non-Newtonian viscoplastic flows. It leads to the evaluation of the “apparent activation energy” and activation volume for the two epoxy systems tested. Comparison with previous work indicates that the above parameters as well as yield stress and elastic modulus tend to increase with the decrease of the Versamid content in the resin.     

Crack-tip fields for porous solids with pressure-sensitive matrices and for rubber-modified epoxies

Based on a set of constitutive relations developed for porous solids with rate-dependent pressure-sensitive matrices, the stress, strain and void volume fraction distributions are investigated near the crack tip with a finite root radius under mode I, plane strain, and small-scale yielding conditions. A rubber-modified epoxy is taken as our model. The rubber particles are taken as the void volume fraction from the view of stress-carrying capacity when the epoxy is subject to extensive plastic deformation. The set of constitutive relations for porous solids is based on a generalized Gurson yield criterion for porous solids with pressure-sensitive matrices. The set of constitutive relations has been implemented into finite element code ABAQUS to investigate the near-tip field of a crack in porous solids. Our numerical results indicate that the plastic zones, the intense straining zones, and large void volume fraction contours are long and narrow ahead of a crack tip in porous solids with moderately large initial void volume fractions. The strain softening and subsequent hardening of the matrices also make these zones more concentrated ahead of the tip. As the initial void volume fraction or the pressure sensitivity of the matrices increases with a decrease of plastic dilatancy, these zones become more elongated ahead of the tip. The cavitation of the rubber particles in the rubber-modified epoxy is also considered via a stress-controlled void nucleation model. The numerical results for the rubber-modified epoxy based on the nucleation criterion show that the shape and size of the intense straining and cavitation zones agree well with the corresponding experimental results.     

玻璃钢层合板的超低温双切口层间剪切强度研究

本文采用三维有限元法对双切口剪切试验测定玻璃钢层合析牟超低温层间剪切强度进行了理论分析和研究，解析用的层合板有效弹性系数由组分材料的弹性系数和织物结构的代表体积单元求得。数值解析发现，。当切口间隔与厚度之比较小时，双切口剪切试验片可产生较均匀的剪切应力分布。通过与二限元求得。数值解析发现，当切口间隔与厚度之比较小时，双切口剪切试验片可产生较均匀的剪切应力分布。通过与二维有限元解析结果的对比分析。阐     

Specimen design,manufacturing and testing procedures for flat carbon fiber reinforced plastic laminates under biaxial loading

The optimization of a specimen design allowing the investigation of the biaxial strength of composite laminates over the full range of failure strain was the primary objective of this work. Multiaxial strength criteria are often found unreliable mainly as a result of the inherent complexity of biaxial tests and, in many cases, as a result of inefficient specimen designs. As a result of a development program combining numerical simulations and experimental measurements, a flat cruciform-shaped specimen has been developed for carbon fiber reinforced plastic (CFRP) laminates. The design fulfills the basic criteria for such a specimen, namely allowing for a uniform biaxial stress/strain state to exist in the gauge area and for testing the virgin material up to failure in both the tension-tension and tension-compression quadrants of the strain/stress space. The fabrication of the specimen is described and a three-step testing procedure for generating biaxial strength data is proposed. Typical results obtained from specimens of the proposed configuration tested in accordance with this procedure are presented. Results compare well with those obtained from tubular specimens, thus confirming the effectiveness of the proposed design. Experimental data obtained for the AS4/3501-6 carbon/epoxy composite system are finally compared against strength predictions of recognized failure theories.     

Deformation and fracture behaviour of a rubber-toughened epoxy: 2. Failure criteria

In part 1 the microstructure and fracture characteristics of a rubber-modified epoxy, and for comparison that of the unmodified epoxy, were examined in detail. Based on this analysis a qualitative mechanism involving cavitation, shear yielding and plastic flow was proposed. As an extension of this work, the present paper considers the yield behaviour of the epoxy material and uses the data determined, together with the previously reported fracture results, to calculate values of the crack opening displacement. The rate/temperature dependence of the crack opening displacement and the correlations established between stress intensity factor, K_Ic, yield stress and type of crack growth suggest that the extent of crack tip blunting largely governs the relative toughness of the epoxy materials and induces transitions in the types of crack growth observed. A quantitative expression is then presented which successfully describes the fracture toughness values over a wide range of temperatures and rates. The two parameters in this expression are shown to be material constants and therefore provide a unique failure criterion. They can be viewed simply as curve-fitting parameters but they may also have some significance in terms of a critical stress that must act over a critical distance ahead of the crack tip to produce crack growth.     

Changes in the thermomechanical behavior of epoxy glasses under the state of strain aging

Changes in thermomechanical behavior with structural relaxation taking place in epoxy glasses were studied. Differential scanning calorimetry measurements and thermostimulated strain recovery tests were performed for specimens deformed and then aged under fixed strain. In the course of heating, the specimens started to absorb thermal energy, whereas plastic strain was still stable. At higher temperatures, plastic strain started recovery, which was accompanied by exothermic behavior of the specimen. With an increase in the aging duration, the endothermic peak signified and moved to a higher temperature. These results indicated that the longer the aging duration was, the harder the plastic strain and strain energy were frozen in the glassy structure. This freeze‐strain phenomenon was observed for crosslinked epoxy glass, as well as polymeric glasses with linear molecular structures, aged under strain. © 2007 Wiley Periodicals, Inc. J Appl Polym Sci, 2008     

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.     

Physical characteristics of plasticized epoxy system in the post-yield stage

Thermo-rheological analysis was conducted on epoxy–Versamid specimens drawn from different portions of beams subjected to a yield test. M_c values, characterizing the crosslink density and determined by a special method, show insignificant variation for unstressed (virgin), pre-yield, and post-yield zones of the material. It was concluded that the yielding process in the plasticized epoxy system consists mainly in disruption of physical bonds.     

Strength of cylindrical butt joints bonded with epoxy adhesives under combined static or high-rate loading

The influence of loading rates and the combined stress states of tension and shearing on the strength, strain, and absorbed energy of an adhesively bonded joint was experimentally investigated. Cylindrical butt joint specimens were prepared and strength tests were performed on the specimens with a servo-controlled hydraulic testing machine that combined tension and torsion loading. Two types of epoxy adhesives, ductile and brittle, were applied to the specimens. The tests were performed under a quasi-static condition of 6.67×10⁻² MPa/s and a high-rate loading condition of 1.00×10³ MPa/s. The results of the combined loading tests showed that the states of the fractured surfaces were not affected by the loading rates. As for the ratio of tensile and shear loading, adhesive failure tended to partially occur when the ratio of shear loading was very high. The strength points for the specimens bonded with each adhesive were distributed in a stress plane of tension and shearing and could be fitted with a curve that was described by an equation with exponential parameters that were not influenced by the strain rate; however, other parameters that described the intercepts were influenced. The failure strains and absorbed energies for the brittle adhesive were slightly dependent on the strain rate, but this dependency was unclear for the ductile adhesive.     

Dynamical Flow Properties of Single Crystals of Sapphire, I

The tensile deformation of sapphire was studied as a function of the temperature and of the strain rate. The ranges of the two variables were approximately 1200° to 1700°C and 10⁻³ to 10⁻¹in. per in. per minute. The work showed the existence of a relatively sharp temperature transition between completely brittle fracture and massive plastic flow, the specific transition temperature being sensitively related to the strain rate. For the limits of the rate range used, the transition temperature increased from approximately 1270° to 1520°c. In going through a range of only a few degrees of temperature near the transition, it was possible to obtain either no plastic flow on the low-temperature side or a relatively large amount of the order of a 100% extension on the high-temperature side. The stress-strain relation for plastic flow was found to be characterized by a pronounced yield-point drop; i.e., the stress required to initiate macroscopic flow was approximately double that required for subsequent flow. The magnitudes of both the upper and lower yield stresses were temperature sensitive and both decreased approximately exponentially with increasing temperature for a given strain rate. An inverse dependency of a similar kind was found for the effect of strain rate under conditions of isothermal testing. On the other hand, the fracture stress before yielding was found to be essentially independent of both temperature and strain rate, lying in a scatter band of approximately 16,000 to 20,000 psi. As the testing temperature at a given strain rate was lowered, the plastic yield stress therefore rose sharply. The transition temperature between ductile and brittle behavior was interpreted to correspond to the temperature at which the upper yield stress equaled the fracture stress. Since the lower yield stress was only half the upper yield stress, extensive flow then became possible whenever the transition temperature for yielding was exceeded.     

The effect of time and temperature on the mechanical behavior of epoxy composites

A crosslinked epoxy resin consisting of a 60/40 weight ratio of Epon 815 and Versamid 140 and composites of this material with glass beads, unidirectional glass fibers and air (foams) were tested in tension, compression and flexure to determine the effect of time and temperature on the elastic properties, yield properties and modes of failure. Unidirectional continuous fiber-filled samples were tested at different fiber orientation angles with respect to the stress axis. Strain rates ranged from 10^?4 to 10 in./in.-min and the temperature from ?1 to 107°C. Isotherms of tangent modulus versus strain rate were shifted to form master modulus curves. The moduli of the filled composites and the foams were predictable over the entire strain rate range. It was concluded that the time-temperature shift factors for tangent moduli and the time-temperature shift factors for stress relaxation were identical and were independent of the type and concentration of filler as well as the mode of loading. The material was found to change from a brittle-to-ductile-to-rubbery failure mode with the transition temperatures being a function of strain rate, filler content, filler type and fiber orientation angle, indicating that the transition is perhaps dependent on the state of stress. In the ductile region, an approximately linear relationship between yield stress and log strain is evident in all cases. The isotherms of yield stress versus log strain rate were shifted to form a practically linear master plot that can be used to predict the yield stress of the composites at any temperature and strain rate in the ductile region. The time-temperature shift factors for yielding were found to be independent of the type, concentration and orientation of filler and the mode of loading. Thus, the composite shift factors seem to be a property of the matrix and not dependent on the state of stress. The compressive-to-tensile yield stress ratio was practically invariant with strain rate for the unfilled matrix, while fillers and voids raised this ratio and caused it to increase with a decrease in strain rate. The yield strain of the composites is less than the unfilled matrix and is a function of fiber orientation and strain rate.     

Yield and internal stresses in aluminum filled epoxy resin. A compression test and positron annihilation analysis

The influence of the filler content on the mechanical properties of an epoxy resin composite filled with aluminum powder was investigated. Compressive tests were performed at room temperature and at different strain rates. The response of the composites was also studied by positron annihilation lifetime spectroscopy. The dependence of the yield stress on the filler content is shown. The results are discussed in terms of a proposed model that takes into account the contribution of the filler powder. To this purpose information from positron spectroscopy is important since it allows to correctly evaluate the internal stresses introduced in the composite epoxy lattice by the metal filler.     

多壁碳纳米管/玻璃纤维/环氧树脂界面粘结特性研究

本文对一种多壁碳纳米管进行表面酸化和胺化改性处理,通过超声波分散制备碳纳米管/玻璃纤维/环氧树脂单丝复合试样,采用单丝断裂法研究碳纳米管对玻璃纤维/环氧树脂界面粘结特性的影响。实验结果表明,加入碳纳米管后环氧树脂弯曲性能提高,单丝复合体系的拉伸应力-应变曲线在屈服点之后产生波动。通过比较纤维断点数-应变曲线、偏光下纤维断点形貌以及断口形貌SEM图像发现,对于玻璃纤维体系,加入硅烷偶联剂KH560后,碳纳米管可明显提高玻璃纤维/环氧界面粘结强度,并以胺化碳管改性体系影响最为显著。     

Measurement of the residual mechanical properties of crazed polycarbonate. II: Design of experiments analysis

The Design of Experiments (DOE) approach was used to build quantitative empirical models of the residual mechanical properties of crazed polycarbonate as functions of relative craze density, crazing stress, and strain rate. Crazing did not affect the yielding behavior of polycarbonate, but increasing the strain rate increased the yield stress according to the Eyring theory. The Eyring activation volume for yielding of crazed polycarbonate was measured to fall between reported values for conformational changes of a dilute solution of polycarbonate chains and yielding of uncrazed polycarbonate. Also, with as little as 1% relative craze density, the failure stress was approximately 10% lower and the ductility was, on the average, 50% lower than for uncrazed polycarbonate properties. It was also found that increasing the crazing stress from 40 to 45 MPa increased the failure stress and ductility for a given magnitude of relative craze density.     

Mechanical and open hole tensile properties of self‐reinforced PET composites with recycled PET fiber reinforcement

The tensile strength of notched composites is an important factor for composite structural design. However, no literature is available on the notch sensitivity of self‐reinforced polymer composites. In this study, self‐reinforced recycled poly (ethylene terephthalate) (srrPET) composites were produced by film stacking from fabrics composed of double covered uncommingled yarns (DCUY). Composite specimens were subjected to uniaxial tensile, flexural, and Izod impact tests and the related results compared with earlier ones achieved on srPET composites reinforced with nonrecycled technical PET fibers. Effects of open circular holes on the tensile strength of srrPETs were studied at various width‐to‐hole diameter (W/D) ratios of the specimens. In the open hole tensile (OHT) measurements bilinear (yielding followed by post‐yield hardening) stress–strain curves were recorded. The srrPET composites had extremely high yield strength retention (up to 142%) and high breaking strength retention (up to 81%) due to the superior ductile nature of the srrPETs, which induces plastic yielding near the hole thereby reducing the stress concentration effect. The results proved that srrPET composites are tough, ductile notch‐insensitive materials. © 2016 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2016 , 133, 43682.