Strain rate dependence of failure processes in polycarbonate and nylon

A study has been made of two types of failure, namely, monotonic fractures using Charpy-type specimens and fatigue crack propagation using rectangular plates containing an initial central notch. The work was conducted on an amorphous polymer (polycarbonate) and a semicrystalline polymer (nylon N 6.6). Monotonic tests were performed in an Instron testing machine between 0.002 and 20 in./min, and in a Charpy testing machine between 2000 and 11800 in./min. The cyclic tests (under constant K conditions) were carried out at frequencies that ranged from 0.1 to 20 Hz. A model for the relationship between the cyclic rate of crack growth and appropriate LEFM parameters, previously described, has now been converted into cyclic strain energy transformations. In computing the strain energy, the value of the time-dependent modulus of the material was used; and under cyclic loading conditions the glassy (short time) value was employed. The authors have proposed that the modulus measurements obtained at very low temperatures, where the viscous response of the material is highly restricted, will approximate the glassy value, E_g, found by conducting relaxation measurement tests at different temperatures down to ?197°C. Within the range of tests conducted, the fracture toughness values of both PC and N 6.6 apparently decrease with increase in loading rate. Fatigue crack growth in both materials is influenced by loading frequency and cyclic waveform. These variations may be related to the magnitude of the viscous energy loss and hence to the available energy for crack extension per cycle.     

Dynamic mechanical response of model epoxy networks in the glassy state

The dynamic mechanical properties of model epoxy-amine networks are investigated in the glassy state over a wide range of frequencies, at temperatures between 123 K and 350 K. The effects of crosslink density and network chain flexibility on the β relaxation are examined. Motions responsible for the β process begin to develop at the same temperature, whatever the crosslink density. However, an increase in crosslink density is accompanied by an increase in amplitude and a broadening towards high temperatures of both damping tan δ and loss modulus E″. This effect is responsible for the decrease of elastic modulus E′ at room temperature with increasing crosslink density.     

Critical regimes of oscillatory deformation of polymeric systems above glass transition and melting temperatures

High molecular weight linear polymers and their concentrated solutions were investigated over a wide range of frequencies and amplitudes of oscillatory deformation. At definite critical deformation and stress amplitudes, the resistance to deformation drops abruptly as a result of the rupture of continuity of polymer specimens in the region of action of the highest shear stresses. The lowest critical values of deformation rate amplitudes are inversely proportional to the initial viscosity and correspond quantitatively to the critical shear rates at which the spurt occurs during the flow of polymeric systems in ducts. The spurt effect is due to the transition of the polymer systems to the forced high-elastic state, in which they behave like quasi-cured polymers whose deformability is always limited. Up to the critical values of the stress amplitudes, narrow-distribution high molecular weight linear flexible-chain polymers behave like Hookean bodies, whereas the broad-distribution polymers show a sharply defined nonlinear behavior which asymptotically passes to a spurt. The amplitude dependence of the dynamic characteristics of the high molecular weight linear polymers, as well as their non-Newtonian behavior, is due to polymolecularity. An increase in deformation amplitudes reduces the frequency at which the spurt, and hence the transition of the polymer systems to the high-elastic state, is observed. Therefore, under conditions of oscillatory deformation the physical state (fluid or high-elastic) is determined not only by the frequency but also by the value of deformation. In the high-elastic state region (estimated at low amplitude deformation), the critical deformation amplitude is frequency independent and has an unambiguous relationship with the molecular mass of the chain (M_e) between the entanglements. For the bulk polymers studied, the spurt in the high-elastic state occurs at stress amplitudes of the order of 10⁵ N/m² irrespective of frequency, molecular mass, or polymolecularity. In concentrated polymer solutions, in the high-elastic state the critical stress amplitudes decrease with reducing polymer content, whereas the critical deformation amplitudes increase.     

Mechanical behavior and structure of single beads of homogeneous and macroporous styrene–divinylbenzene copolymers

The stress–stain and ultimate behavior in compression of homogeneous and macroporous beads of styrene–divinylbenzene copolymers has been investigated in the dry state or in equilibrium with toluene, acetone, methanol, and water. The penetration modulus A indicates sensitively the transition from the glassy into the rubbery state induced by an increase in temperature or swelling. For macroporous copolymers, A of the glassy polymers is mainly determined by the porosity P, while in the rubbery region it primarily depends on the matrix structure (degree of crosslinking and concentration and composition of the diluent). The high value of the slope s of the A vs. P dependence (s ～ ?3) for macroporous copolymers is evidence of the complex deformation mechanism (bucking of pore walls). The relative compression at break, ε_b=0.3–0.4, is independent of the composition, and the compressive strength is roughly proportional to the penetration modulus.     

Fatigue behavior and life prediction of PI/SiO2 nanocomposite films

In this report, the fatigue behavior and lifetime of Polyimide/silica (PI/SiO₂) hybrid films are investigated. To evaluate the fatigue property of this class of hybrid films, the stress‐life cyclic experiments under tension–tension fatigue loading with 10 Hz of the frequency are performed, and the stress ratio is 0.1. Dynamic creep and cyclic softening/hardening are analyzed based on the change of hysteresis loops during the fatigue process. The structure‐property relations are discussed to further understand their phenomenon and deformation mechanisms. To predict the fatigue life of this class of hybrid films, a semiempirical model is proposed based on fatigue modulus concept. The simulated results are well agreeable with the testing values. © 2009 Wiley Periodicals, Inc. J Appl Polym Sci, 2009     

Fatigue response and constitutive behavior modeling of poly(ethylene terephthalate) unreinforced and nanocomposite fibers using genetic neural networks

The constitutive behavior of poly(ethylene terephthalate) (PET) unreinforced (control) and PET fibers reinforced with 5 wt% vapor‐grown carbon nanofibers (VGCNFs) under uniaxial tension and subsequent to fatigue loading has been evaluated utilizing various analytical models. Two types of fatigue tests were performed: (1) Long cycle fatigue at 50 Hz (glassy fatigue) to evaluate fatigue resistance and (2) fatigue at 5 Hz (rubbery fatigue) to evaluate residual strength performance. The long cycle fatigue results at 50 Hz indicated that the PET‐VGCNF sample exhibited an increased fatigue resistance of almost two orders of magnitude when compared to the PET unreinforced filament. The results of the fatigue tests at 5 Hz indicated that the constitutive response of both the PET control and PET‐VGCNF samples changed subsequent to fatigue loading. The large deformation uniaxial constitutive response of the PET and PET‐VGCNF fibers was modeled utilizing genetic‐algorithm (GA) based training neural networks. The results showed that the large deformation uniaxial tension constitutive behavior of both PET unreinforced and PET‐VGCNF samples with and without prior fatigue can be represented with good accuracy utilizing neural networks trained via genetic‐based backpropagation algorithms, once the appropriate post‐fatigue constitutive behavior is utilized. Experimental data of uniaxial tensile tests and experimental postfatigue constitutive data have been implemented into the networks for adequate training. The fatigue tests were conducted under tension‐tension fatigue conditions with variations in the stress ratio (R), maximum stress (σ_max), number of cycles (N), and the residual creep strain (ε_R). POLYM. COMPOS., 2012. © 2012 Society of Plastics Engineers     

Elevated temperature aging of HIPS

The effects of aging at 85°C on a rubber-modified polystyrene (HIPS) have been studied as a function of aging time in both air and nitrogen. Four different types of physical measurements were carried out on the aged samples. These included mechanical relaxation measurements, tensile stress–strain measurements, creep measurements at several stresses, and measurements of fatigue lifetime under applied tension–compression stress. Aging in nitrogen is largely a physical aging process and results in higher modulus, higher tensile strength, and longer delay times to the onset of accelerating creep deformation. But tensile ductility and fatigue lifetime tend to reduce, and there is no change in location of T_g of the rubber phase. Aging in air involves both chemical and physical aging, and the changes that occur depend on which process dominates. For long-time aging of 150 h or more, the rubber-phase T_g is shifted to higher temperatures and the associated loss peak is broadened due to crosslinking. Also, the tensile strength, tensile ductility, creep delay time, and fatigue life all reduce. These effects are attributed to oxidative attack and embrittlement. SEM micrographs reveal variations in fracture surface morphology due to the mode of testing and to the aging medium.     

Frequency sensitivity of fatigue processes in polymeric solids

One is faced with an interesting challenge when trying to explain the effect of test frequency on polymer fatigue performance. While hysteretic heating arguments appear sufficient to explain a diminution of fatigue resistance with increasing cyclic frequency in unnotched test samples, the enhancement of fatigue resistance in many polymers with increasing cyclic frequency in notched samples is still not clearly understood. In large measure, this is due to contradictory trends in fre-quency-sensitive material properties which affect the fatigue process. In this paper, a number of proposed fatigue models dealing with the time and strain rate dependence of elastic modulus, yield strength, creep and localized crack tip heating are examined and confronted with available data from the literature. Additional fatigue crack propagation data for poly(methyl methacrylate), poly (vinyl chloride), polystyrene, poly-carbonate, nylon 66, poly(vinylidene fluoride) and poly(2,6-dimethylphenylene oxide) were obtained and are reported herein. These data were obtained over a maximum frequency range of 0.1 to 100 Hz and, for selected polymers, with various waveforms. Frequency sensitivity is shown to be greatest in those polymers that show a high tendency for crazing. Relative fatigue behavior is found to reflect a competition between strain rate and creep effects. Where creep effects dominate, the total crack growth rate may be viewed as consisting of the summation of pure fatigue and creep components, respectively. Finally, the β transition appears to have a role, with frequency sensitivity being at a maximum for polymers where the β transition at room temperature occurs in the range of the experimental test frequency.     

Cyclic deformation and relaxation characteristics in polypropylene

Cyclic deformation and stress relaxation after cyclic preloading in polypropylene were investigated by using an electrohydraulic, servocontrolled testing machine. The cyclic deformation tests were performed under various sets of strain rate, number of cycles, and strain amplitude in the as-received sample and a quenched sample. The stress relaxation tests were made after a cyclic preloading in both samples. The distinctive shape of the hysteresis loop, termed a propeller-like shape, is characteristic of the as-received polypropylene with large spherulites, in marked contrast to the behavior of metals. The curves at strain amplitudes from ± 1.5% to ± 5% indicate a propeller-like shape; these loops change into the steady state response as the number of cycles (N) is increased up to N = 30 to 50. The drop of stress in relaxation tests for the quenched samples is smaller than that for the as-received samples at the same strain levels. This stress drop behavior reflects the difference of spherulite structure. The stress relaxation behavior depends on the morphology, the predetermined strain amplitude, and the process of the tests.     

Influence of nano‐organomontmorillonite on the viscoelasticity of the poly(trimethylene terephthalate)/glass fiber/organomontmorillonite hybrid nanocomposites materials

The influences of organically modified montmorillonite (OMMT) on the viscoelasticity of poly(trimethylene terephthalate)/glass fiber/OMMT (PTT/GF/OMMT) hybrid nanocomposite materials at liquid, elastic and glassy states, respectively, were investigated by using the rotational rheometer and dynamic mechanical analyzer (DMA). The viscoelasticity results suggest that OMMT has many important influences on the structure, modulus and toughness of the hybrid nanocomposite materials. At melton state, the shear‐thinning phenomena of the hybrid composite melts become remarkable with increasing OMMT content. At low frequency, the shear storage modulus (G′) and shear loss modulus (G″) of the melts increase with increasing OMMT content. The melt's elastic response increases by OMMT, and OMMT improves the creep resistance of the melts; in addition, the stress relaxation of the hybrid composite melts become slow with increasing OMMT content, and the stress leavings becomes much higher with increasing OMMT content. At glassy state, the storage modulus of the hybrid nanocomposites increases with increasing OMMT content, while the materials' loss modulus increases first and then decreases with increasing OMMT content; therefore, OMMT nanosheets have reinforcement effect on the composites, and it also has definite toughening effect on the hybrid composite when the OMMT content is no >2 wt%. At rubbery state, the hybrid composites show lower decreasing storage modulus but have lower cold‐crystallization ability than that of pure PTT and PTT/GF composite. POLYM. COMPOS., 35:795–805, 2014. © 2013 Society of Plastics Engineers     

Effective volume changes during fatigue and fracture of polyacetal

Conventional tensile dilatometry techniques are extended to cyclic fatigue applications to study volume changes that occur during controlled-load cyclic fatigue of polyacetal. During fatigue, in-situ measures of the irreversible and elastic volume change are monitored together with dynamic viscoelastic parameters (E′, E″, and Tan δ), and changes in the energy densities (strain energy, potential energy, and irreversible work). The results show that the effective irreversible volume of the polyacetal gradually increases over a wide range of applied cyclic stress. However, at high stress levels and/or frequencies (i.e., low-cycle, thermally dominated regime), the effective Poisson's ratio of the polyacetal increases as it softens (evidenced by the dynamic viscoelastic data). Conversely, at lower stress levels, the Poisson's ratio continually decreases coincident with decreases in the loss modulus (E″) and the irreversible work density. These results are indicative of entirely different mechanisms governing the low-cycle (high stress level) and high-cycle (low stress) regimes. Also, comparisons between tensile and fatigue dilatometry studies show that the dilational-strain response of samples fatigued at high stress levels are similar to data obtained from monotonic tensile dilatometry. However, the dilationstrain response of samples fatigued at lower stress levels are distinctly different from low-cycle fatigue and tensile dilatometry.     

Kinetics of fatigue and creep crack propagation in PVC pipe

The kinetics of creep and fatigue crack growth in PVC pipe were studied in order to develop a methodology for predicting long‐term creep fracture from short‐term fatigue tests. Fatigue and creep crack propagation followed the conventional Paris law formulations with the same power 2.7: da/dt = A_fΔK^2.7_I and da/dt = BK^2.7_I, respectively. The activation energy for creep crack propagation, obtained from the temperature dependence of the Paris law prefactor, allowed extrapolation of high temperature creep fracture to low temperature creep crack growth rates. The activation energy for fatigue crack propagation was much lower than that for creep. Therefore, fatigue and creep could not be directly correlated by using the prefactor in the covenentional Paris law formulations. Furthermore, a unique value of the Paris law prefactor did not describe frequency and R‐ratio (amplitude) effects in fatigue crack propagation. Nevertheless, conformity of crack growth rates measured under all conditions to the same Paris law power suggested that correlation should be sought in alternative formulations of the crack growth rate.     

Enhanced fatigue life of carbon nanotube‐reinforced epoxy composites

The effects of carbon nanotube (CNT) inclusion on cyclic fatigue behavior and the residual mechanical properties of epoxy composites after different degrees of fatigue have been studied. Tension–tension cyclic fatigue tests were conducted at various load levels (25–50 MPa) to establish the relationship between stress and the number of cycles to failure (S–N curves). The residual strength and modulus were measured after loading at 30 MPa for 5000, 15,000, and 25,000 cycles. The incorporation of a small amount of CNTs increased the fatigue life of epoxy in the high‐cycle, low‐stress‐amplitude regime by 1550%. Micrographs indicate the key mechanisms for enhancement in fatigue life such as CNT crack‐bridging and pullout. POLYM. ENG. SCI., 52:1882–1887, 2012. © 2012 Society of Plastics Engineers     

Evaluation of fatigue lifetime and elucidation of fatigue mechanism in plasticized poly(vinyl chloride) in terms of dynamic viscoelasticity

The fatigue behavior of plasticized poly(vinyl chloride) was investigated by means of a tension–compression-type fatigue apparatus. Complex elastic modulus and mechanical loss tangent were obtained continuously with time under the conditions of constant ambient temperature as a function of imposed strain amplitude. Brittle failure was observed under the conditions of low ambient temperatures and small strain amplitudes, or forced convection of air, whereas thermal failure was observed under the conditions of high ambient temperatures, or large strain amplitudes and natural convection of air. In the case of brittle failure, the dynamic storage modulus E′ exhibited a maximum and the loss tangent tanδ exhibited a minimum on approaching the point of failure. In the case of thermal failure, E′ decreased and tanδ increased monotonously until the onset of thermal failure. It was found that failure occurs when the effective energy loss reaches a certain magnitude depending on an ambient temperature. The fatigue criterion was represented schematically from a standpoint of self-heating. When the heat generation rate of the specimen under cyclic staining is larger than that of the heat transfer to the surroundings, thermal failure takes place. In this case, the specimen temperature increases up to a limiting constant temperature corresponding to the α-absorption temperature. When the heat generation rate is nearly equal to that of the heat transfer to the surroundings, the specimen temperature does not change appreciably and brittle failure takes place.     

Modeling deformation of a melt-infiltrated SiC/SiC composite under fatigue loading

Results from fatigue experiments done on a SiC/SiC composite are presented. A micromechanics-based model is used to study the observed behavior under cyclic loading. The model includes consideration of progressive damage, creep and oxidation of the fiber and matrix. Comparison of model predictions with test data showed that the deformation during fatigue in this material is explained primarily by damage in the form of matrix microcracking and interface debonding, in combination with creep under the cyclic load. Stiffness of the material was observed to not change significantly during fatigue indicating that the contribution of fiber fracture to deformation is limited. Fiber fracture however was found to determine final failure of the composite. Failure under cyclic fatigue loading was found to be affected by load transfer from the matrix to the fiber due to damage and creep, and by progressive degradation of the load-carrying fibers due to the combined effect of oxidation and load cycling.     

Damage assessment of alumina fibre-reinforced mullite ceramic matrix composites subjected to cyclic fatigue at ambient and elevated temperatures

The damage evaluation behaviour of alumina fibre-reinforced mullite ceramic matrix composites subjected to cyclic fatigue was investigated by means of acoustic emission (AE) monitoring and forced resonance techniques. AE technique provided sufficient information about the damage initiation and progression in real time whilst the forced resonance (FR) technique allowed the detection of changes in elastic modulus (E) and internal friction (Q⁻¹) that occurred with increasing number of cyclic fatigue at room temperature. From the two non-destructive detection techniques results combined with microstructural observations, it is concluded that the composite cyclic fatigue damage evolution begins with multiple crack formation within the matrix and is followed by delamination (interfacial failure). Final failure of the composite is caused by fibre fracture and extensive cyclic sliding along the fibre/matrix interface. The strong bonding between mullite matrix and alumina fibre caused by the glassy phase within the mullite matrix determined the fatigue performance of the composite at 1350°C. Regions with glassy phase failed catastrophically as a result of early fibre fracture.     

Mechanical properties of polymer‐ceramic nanocomposite coatings by depth‐sensing indentation

The mechanical properties of antimony‐doped tin oxide (ATO) nanoparticle/poly (vinyl acetate‐co‐acrylic) (PVAc‐co‐acrylic) coatings with various ATO contents were investigated using depth‐sensing indentation. These coatings were prepared from aqueous dispersions of ATO and PVAc‐co‐acrylic latex. Three types of methods, including a prolonged load holding time, analysis of the pull‐off portion of the unloading curve, and dynamic indentation, were used to characterize the mechanical properties of these composite coatings. As compared to dynamic indentation, quasistatic conventional indentation even with a prolonged load holding time and analysis of the pull‐off portion of unloading curves generate more scattered coating modulus data. This is due to the effect of creep deformation and inconsistency of the pull‐off portion dimension, respectively. The results obtained using dynamic indentation are more reliable because the technique minimizes the effect of creep deformation using a combination load including static and dynamic components. The dynamic indentation results indicate that the addition of the ATO nanoparticles made the composite coatings stiffer and more elastic solid–like. For example, the storage indentation modulus of the PVAc‐co‐acrylic coating is ～1 GPa and tan δ is ～1.6; the addition of 0.50 volume fraction of ATO increased the modulus to ～5 GPa and reduced the tan δ to ～0.01. POLYM. ENG. Sci. 45:207–216, 2005. © 2005 Society of Plastics Engineers.     

Analysis of fatigue behavior of high-density polyethylene based on dynamic viscoelastic measurements during the fatigue process

The fatigue behavior of high-density polyethylene was studied by measuring the variation in the dynamic viscoelasticity during the fatigue process. Brittle failure was observed under the conditions of small imposed strain amplitude, low ambient temperature, and large heat transfer coefficient to the surroundings. Ductile failure was observed under the conditions of large imposed strain amplitude, high ambient temperature, and small heat transfer coefficient to the surroundings. In the case of brittle failure, absolute value of dynamic complex modulus, ∣E^*∣, showed maximum and phase difference, δ, did minimum on approaching the point of failure. In the case of ductile failure, ∣E^*∣ decreased and δ increased monotonously from the start of the fatigue testing. The effect of environmental conditions on fatigue behavior was elucidated in terms of the heat transfer coefficient to the surroundings. As both forced convection of air and water enlarge the heat transfer coefficient, temperature rise of the specimen hardly occured and brittle failure took place preferentially. The coefficient, ?, was introduced to express the ratio of the actual generated heat to the hysteresis loss. With increase of the magnitude of the strain amplitude, the nonlinear viscoelastic behavior appeared and ? became smaller. A positive correlation between ? and lifetime was found. As the heat generation rate does not strongly affect lifetime, it was concluded that the hysteresis loss with low efficiency of heat generation would contribute to the fatigue failure. The relationship between average hysteresis loss and lifetime was proposed. The total hysteresis loss up to fatigue failure is constant, being independent of ambient temperature and imposed strain amplitude. The cumulative damage theory of fatigue failure was proposed based on hysteresis loss.     

Fatigue and environmental resistance of polyester and nylon fibers

The fatigue resistance of individual synthetic fibers can govern the performance of complex fiber assemblies such as tire cord and marine rope under certain loading conditions. This paper explores the relative performance of polyester and nylon 6,6 fibers and yarns, both dry and in aqueous solutions, primarily synthetic seawater. Fiber failure over a range of loading conditions and frequencies was found to occur at a critical cumulative strain, governed by a creep rupture process; the cyclic lifetime for both fibers is predictable using a simple creep rupture based theory. Polyester is more resistant to creep rupture, and consequently outperforms nylon 6,6 in cyclic fatigue. The advantage of polyester is considerably greater in aqueous solutions, where the performance of the nylon is diminished. Other comparisons indicate that the particular polyester fibers studied have higher stiffness and strength, lower strain to failure, and much lower hysteresis energy absorption compared with the nylon. The actual fatigue performance of complex fiber assemblies such as ropes is also limited under many conditions by factors not present in single fiber or yarn fatigue, including hysteric heating and internal and external abrasion.