Effects of stress ratio on fatigue crack growth of thermoset epoxy resin

The influences of stress ratio (R) on fatigue crack growth (FCG) of thermoset epoxy resin with polyamine hardener were investigated. The FCG growth rates (da/dN) have been correlated by the linear-elastic fracture mechanics parameters (ΔK and K_max), and nonlinear-elastic fracture mechanics parameter (ΔJ). The effects of R on FCG were observed when the ΔK and ΔJ were used as fracture mechanics parameters for FCG. However, the K_max successfully characterized FCG under cyclic-dependent condition (FCGs at R = 0.1 and 0.4); but it failed to characterize the FCG under time-dependent condition (FCG at R = 0.7). As a time-dependent fracture mechanics parameter, C* was applied to correlate the time-dependent FCG rate (da/dt). A reasonable agreement was obtained between time-dependent FCG (R = 0.7) and creep crack growth (CCG) results.     

On the determination of the point of fracture initiation by the load separation criterion in J-testing of ductile polymers

The application of an experimental approach based on the load separation criterion for the determination of the point of fracture initiation in a fracture test on a ductile polymer was critically examined. To this aim, the fracture process outlined by the application of this method was related to that described by the visual analysis of the fracture surfaces obtained in fracture tests on nominally identical specimens, in which different levels of crack extension were produced. The material examined was an acrylonitrile-butadiene-styrene (ABS) resin, and the fracture tests were performed at low loading rate on single-edge notched in bending specimens.The results demonstrated that this load separation criterion based methodology is a promising approach for the determination of the point of fracture initiation, and for material fracture resistance, J_Ic, evaluation. The method also has experimental simplicity and a high degree of repeatability.     

Strain and damage sensing in additively manufactured CB/ABS polymer composites

In this study, an experimental investigation is performed to observe the electromechanical response of CB (carbon black)/Acrylonitrile butadiene styrene (ABS) additive manufactured composite under quasi-static (tensile, shear, and mode-I fracture) and dynamic (mode-I fracture) loading conditions for the potential damage sensing applications. Dog bone tensile, double v-notch shear, and single edge notch bending (SENB) specimen printed with three different configurations (0°/90°, +45°/-45°, and 0°) are considered for the quasi-static condition. A modified split Hopkinson pressure bar along with high-speed video camera is used for dynamic fracture experiments. Four-point probe technique coupled with a high-resolution data acquisition system is employed to obtain the real-time electrical response. In the case of tensile loading, +45°/-45° printed specimens show a nonlinear change of electrical resistance due to unique failure mode. Under the shear loading, electrical resistance remains unchanged during the elastic deformation. After the damage evolution, +45°/-45° printed specimens exhibit a higher rate of change in electrical resistance due to alignment of the filaments along the maximum principle shear stress direction. For both static and dynamic fracture loading, a minimal change of electrical resistance is observed before crack initiation. However, after the crack initiation, a sharp change of electrical resistance for 0°/90° printed specimens indicates a faster crack propagation as compared to the +45°/-45° printed specimens.     

Load separation principle in determination of J-R curve for ductile polymers: Suitability of different material deformation functions used in the normalization method

The load separation principle states that the load, P, can be represented as the multiplication of two independent functions: A crack geometry function, G(a), and a material deformation function, H(v). The principle constitutes the theoretical basis for the single-specimen J-integral experiment and the incremental calculation of J-integral crack growth resistance (J-R) curves. The normalization method is a new method, which assumes load separation and uses characteristic deformation properties of materials to relate load, displacement and crack length in a functional form. From the deformation material function or “material key curve”, J-R curve can be developed from a single precracking experiment. This investigation deals with the applicability of the load separation criterion to evaluation of ductile fracture mechanics parameters in rubber-modified polystyrene, polypropylene, rubber-modified PMMA, ABS resin and high-density polyethylene in the bending configuration. Different mathematical relationships for the deformation function (power law function, LMN function and combined power law straight line relationship) have been proposed and compared. The resulting J-R curves are in good agreement with those obtained by the traditional multiple-specimen technique. The results presented here imply that the use of a single load-displacement method for evaluation of J-integrals for ductile polymers is possible and hence also the normalization method can be used for evaluation of J-R curves from a single-test record.     

Epoxy/CNT@X nanocomposite: Improved quasi-static,dynamic fracture toughness,and conductive functionalities by non-ionic surfactant treatment

The present work investigated the effects of non-ionic surfactant treatment on the dispersibility, surface chemistry and structure of carbon nanotube (CNT) particles. Subsequently, the fracture experiments of as-prepared epoxy/CNT@X nanocomposites were carried out under quasi-static and dynamic loading conditions. By simply introducing the steric repulsive force between CNT@X filler and epoxy matrix, improved mode-I critical-stress-intensity factor (K_Ic) and dynamic crack initiation toughness (K_Ii^d) of the epoxy/CNT@X nanocomposite were simultaneously obtained without compromising other desired physical properties, such as electrical properties and electro-thermal behavior. In the case of SHPB impact loading, high-speed imaging along with digital-image-correlation (DIC) technology was utilized to determine dynamic fracture parameters. The results showed a notable reinforcement for the epoxy/CNT@X nanocomposite category, producing maximum increase of ~79% and ~153% in K_Ic and K_Ii^d values relative to epoxy/CNT nanocomposite at such maximum content of 1.0 wt%, respectively. The most delayed crack initiation time (59.9–68.4 μs) and slowest crack-tip velocity (229 ± 28 m/s) were also observed in the epoxy/CNT@X_1.0 case. These results may be explained by improved dispersibility and interfacial adhesion after surfactant treatment.     

Mechanical evaluation of polymeric filaments and their corresponding 3D printed samples

3D printing technologies permits to produce functional parts with complex geometries, optimized topologies or enhanced internal structures. The relationship between mechanical performance and manufacturing parameters should be exhaustively analyzed to warrant the long term success of printed products. In this work, the mechanical performance of filaments based on acrylonitrile butadiene styrene (ABS), polylactic acid (PLA) and polylactic acid/polyhydroxyalkanoate (PLA/PHA) was investigated and also compared with their corresponding 3D printed samples. In general, the specimen dimensional deviations were found to be within the tolerances defined by the standard testing protocols. Density values revealed a high level of filament fusion promoting a nearly solid internal structure. The filaments exhibited improved tensile performance with respect to their corresponding printed samples. Tensile and bending performance looked quite independent of the raster angle. Izod impact behavior was increased, for ABS systems printed with the ±45° raster orientation. Quasi-static fracture tests displayed improved crack initiation resistance with the 0°/90° raster angle. The crack propagation observed for the ±45° specimens, through the bonding of the inter-layers, suggests weak entanglements.     

Exponential gap relation and the rotational inelasticity of H2M systems

Previously published values of state-to-state integral inelastic cross sections for the H₂(J_i)—M (M  H, He, Li, Li⁺, H₂, CO₂) systems are fitted to the exponential gap relation for the rotational inelastic process to obtain the C value that reflects the magnitudes of relative cross sections. While the vibration of the rotor seems to have little influence, the C value is shown to decrease dramatically with increase in initial collision energy T_i, ΔC/ΔT_i being larger at lower T_i for all systems analysed, in accord with the prediction of the surprisal synthesis of Procaccia and Levine. For the only case of H₂(J_i)-Li⁺ for which results are available for several J_i, C decreases with increase in J_i or J_i(J_i + 1)). The C value predicted by Procaccia and Levine for H₂M systems falls within the range of C values calculated for the various collision partners. However, there is a noticeable change in C (albeit within a factor of two) with change in M, indicating that dynamical factors do play an important role in rotational inelastic processes.     

Mechanical properties of block copolymer vesicle and micelle modified epoxies

Block copolymers with and without reactive functionalities can improve fracture resistance in brittle epoxies even when added in relatively small amounts (<5 wt %). At certain compositions, amphiphilic block copolymers spontaneously self‐assemble into vesicles, spherical micelles, or wormlike micelles in thermoset resins, and these morphologies are retained with the full curing of the resins. The addition of such block copolymers leaves the glass‐transition temperature of these blends relatively unchanged, whereas the fracture resistance increases up to a factor of 3.5 for the vesicle‐modified blends. For epoxies modified with block copolymers self‐assembled into a spherical geometry (vesicles or spherical micelles), the fracture resistance scales with the ratio of the interparticle distance to the average vesicle (or spherical micelle) diameter (D_i/D_p) and increases as this quantity is reduced. Greater adhesion between the vesicle and epoxy resin improves the fracture resistance only at higher values of D_i/D_p, at which the materials are more brittle. Debonding and subsequent matrix plastic deformation are identified as the toughening mechanisms in these blends. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 2444–2456, 2003     

The use of load separation criterion and normalization method in ductile fracture characterization of thermoplastic polymers

Load separation is the theoretical basis for the single-specimen J-integral experiment and the incremental calculation of J-integral crack growth resistance (J-R) curves. This criterion has been experimentally studied in nongrowing crack records in several materials, and more recently a new method to extend the applicability to growing crack experiments has been proposed in testing steel. This article examines the applicability of the load separation criterion for evaluating ductile fracture mechanics parameters in rubber-modified polystyrenes and thermally treated polypropylene in the bending configuration. This criterion allows the load to be represented as the multiplication of two independent functions: a material deformation function and a crack geometry function. Its validity is evaluated with both stationary and growing crack experiments. η-factor calculation for smooth and side-grooved specimens was also tried using the simple method of Sharobeam and Landes, in order to identify material dependency. This article also investigates the applicability of the normalization method, based on the load separation criterion for evaluating J-R curves on PP and PS. A simple approach which combines a blunt notched and a precracked specimen experiment is proposed to determine the J-R curve of the materials studied. The resulting J-R curves are compared with multiple specimen results available in the literature for these materials. A good agreement between the J-R curves obtained from this simple method and from the multiple specimen technique was found. © 1996 John Wiley & Sons, Inc.     

Energy transfer as a function of collision energy. I Collision partners: Hydrogen halides + inert gases,hydrogen halides,H2S and propane

Infrared emission has been recorded from a heated seeded supersonic primary beam of HCl or HF (1) prior to collision with a target beam, and (2) subsequent to that collision. Mean collision energy and collision partner were varied systematically. After correction for elastic scattering, the net population change due to inelastic scattering in a translation—rotation (T ? R) energy-transfer encounter was obtained for specific J states ranging from J = 0–16 of vibrational level υ = 1 of the primary-beam molecule. The broad picture is that a net transfer into low-J states out of higher-J states takes place at low collision energies, and the converse at high collision energies. These observations are interpreted in terms of the “exponential model” for the relative cross sections of T ? R inelastic collisions, S^R (J_i → J_f), proposed earlier [J.C. Polanyi and K.B. Woodall, J. Chem. Phys. 56 (1972) 1563], modified here to satisfy microscopic reversibility. The constant C in the model, which governs the exponential decrease in S^R with increasing energy difference ΔE_J between J_f and J_i, can be derived, as a function of collision energy T, from the present experimental data; C decreases as T increases, i.e. larger ΔJ become more probable. In order to check the validity of the model, it was compared with 3D trajectory results; according to this criterion it was found to give a very good representation of S^R(J_i → J_f) with a single value for C, within a limited range of J_i. The collision partners HCl + HF exhibit anomalously efficient rotational deactivation; evidence is presented which indicates that at low collision energies this is due to resonant R → R transfer. Very efficient deactivation of HCl by HCl, at low collision energy, is likely to be due to V — V transfer.     

Highly discriminating distance-based topological index

A new topological indexJ (based on distance sumss_i as graph invariants) is proposed. For unsaturated or aromatic compounds, fractional bond orders are used in calculatings_i. The degeneracy ofJ is lowest among all single topological indices described so far. The asymptotic behaviour ofJ is discussed, e.g. whenn → ∞ in C_nH_{2n = 2},Jar π for linear alkanes, andJ → ∞ for highly branched ones.     

Collision rotational transfers in NaH A1Σ+ by He,Ar or H2 (and in KH A1Σ+ by H2)

The total and relative rotational transfer cross sections σ_total and σ_Ji-Jf, by collisions of NaH A¹Σ with He, Ar or H₂, are measured from υ′ = 4 and υ′ = 11, J₁′ = 6. The σ_total increase as υ′ increases. They are similar for He and H₂ but much greater for Ar especially at large υ′. In NaH A¹Σ⁺ the bond goes from covalent to ionic as υ′ increases: σ_total is very sensitive to an attractive potential due to the interaction of the permanent electric dipole moment of the molecule with the polarizability of the atom (α_Ar = 11 au, α_He = 1.37 au). The σ_Ji-Jf decrease monotonously as |J_f-J_i| increases and may be fitted by a scaling law. The variation with ΔJ depends on the colliding gas but does not change appreciably with υ′: most of the transfers could take place on the repulsive part of the interaction potential, the shape of which would not depend on υ′.     

Influence of block composition on crack toughness behaviour of styrene-b-(styrene-random-butadiene)-b-styrene triblock copolymers

The deformation and fracture behaviour of symmetric and asymmetric styrene-b-(styrene-random-butadiene)-b-styrene (S-SB-S) triblock copolymers with variations in their molecular architectures in terms of their outer PS block and the random SB middle block composition ratios have been investigated using essential work of fracture approach based on post yield fracture mechanics concept. The present investigations on crack resistance behaviour of these S-(S/B)-S triblock copolymers where effective interaction parameter (χ_eff) is systematically varied through the variation of block compositions and architecture is in continuation to our earlier communicated short article highlighting the phase behaviour-morphology and mechanical property interrelation. The crack initiation and propagation behaviours are correlated to morphology and dynamic mechanical properties as obtained from TEM, SAXS and DMA measurements. The influence of interaction parameter (χ-parameter) space which has been manipulated through the variation of block compositions has clearly manifested in their morphologies and in their mechanical properties. Further the kinetic aspects of fracture mechanical response have also been investigated where all the materials have clearly revealed block composition dependence. SEM analysis was carried out to understand the fracture modes prior to failure.     

Photoelectron spectra and angular distribution in reson three-photon ionization of atomic iron: J dependence

Kenetic energies and angular distributions of photoelectrons emitted by three-photon ionization fo atomic iron through two-photon resonant state e⁷D_J and e⁵ D_J, were measured, by using visible lasers. J-resolved photoelectron bands attributab to the a⁶D_J and a⁴F_j ionic states are reported.     

Interlaminar fracture toughness of unidirectional DCB specimens: A novel theoretical approach

A novel theoretical approach is presented to calculate the mode I interlaminar fracture toughness (G_Ic) of double cantilever beam (DCB) specimens with low ratio of initial crack length-to-thickness (a₀/2h). This method is based on a sixth-order beam theory, namely Reddy-Bickford beam (RB), on Winkler elastic foundation (WEF) to account for both transverse shear deformation of the beam and local effects at the delamination front (root rotation). RB with only two generalized displacements w and ?; and three boundary conditions at ends and loading points of a shear deformable beam gives more accurate results than the fourth-order Timoshenko beam theory. The accuracy of the proposed method in prediction of initiation G_Ic values is evaluated together with other available models considering the experimental fracture toughness for moderately thick unidirectional E-glass/epoxy DCB specimens with small initial delamination lengths.     

Influences of different dimensional carbon-based nanofillers on fracture and fatigue resistance of natural rubber composites

The dimensions of reinforcing filler is a key factor in influencing the fracture and fatigue of rubbers. Here, the fracture and fatigue resistance of natural rubber (NR) filled with different dimensional carbon-based fillers including zero-dimensional spherical carbon black (CB), one-dimensional fibrous carbon nanotubes (CNTs) and two-dimensional planar graphene oxide (GO) were explored. To obtain equal hardness, a control indicator in the rubber industry, the amounts of CB, CNTs, and GO were 10.7 vol%, 1.2 vol%, and 1.6 vol%, respectively. J-integral and dynamic fatigue tests revealed that NR filled with CB exhibited the best quasi-static fracture resistance and dynamic crack growth resistance. The much higher hysteresis loss of NR filled with CNTs weakened its fatigue resistance. The planar GO played a limited role in preventing crack growth. Furthermore, digital image correlation revealed that NR filled with CB had the highest strain amplification level and area at the crack tip, which dissipated the most local input energy and then improved the fracture and fatigue performance.     

Fracture characterization of ductile polymers through methods based on load separation

The applicability of load separation property based methods of determining J–R curves of ductile polymers is analysed in this work. Two methods are analysed: the load normalization method and the S_pb method. The load normalization method is based on the use of a plastic deformation dependent function which has an explicit functional form, H, whereas the S_pb method is based on the S_pb parameter, which was defined as the calculated load ratio between two specimens, one having a growing crack and the other with a non-propagated crack. The obtained J–R curves have been compared with those obtained experimentally in order to study the applicability and accuracy of both methods. Although both methods have been shown to be applicable, the load normalization method is the most accurate and the easiest to apply.     

Special fracture mechanics specimens for multilayer plastic pipes testing

Pipes consisting of layers of different materials (multilayer pipes) are considered. The fracture toughness value of the main pipe is taken into account as a parameter relevant to fracture assessment connected with the resistance of pipe material against slow crack growth. With the aim of simplifying estimation of main pipe material fracture toughness, non-homogeneous test specimens cut directly from multi-layer pipes are suggested and numerically analysed. The values of the corresponding stress intensity factor K_I and biaxiality factors B are calculated for the case of two and three layer test specimens. Based on the results obtained, the transferability of fracture toughness values measured on laboratory specimens to pipe systems is discussed. It is shown that in most cases of multi-layer commercial pipes and routine fracture toughness measurements the values of the stress intensity factor calculated on the basis of homogeneous specimens can be used.     

J and term dependences in the isotope shift of Eu I

High-resolution laser atomic beam spectroscopy has been applied to studyJ and term dependences in the isotope shift of the levels 4f ⁷5d6s a ¹⁰ D _J ,a ⁸ D _J of Eu I. A parametric analysis of the isotope shift has been performed. TheJ dependence is interpreted through two term-dependent parametersz _5d , and the term dependence through one parameterΔT:z _5d (a ¹⁰ D)=44.1 (2.6) MHz,z _5d (a ⁸ D)=55.9 (2.3) MHz,ΔT=408.5 (3.2) MHz. Ab initio Hartree-Fock and Dirac-Fock calculations have been made to interpret these parameters. Within the accuracy of the calculations the parameters can be attributed to field shift effects.     

Quasiclassical trajectory state-to-state cross sections for energy transfer in Ar+ OH(υ = 9,J = 0,4, and 8) collisions

State-to-state energy transfer cross sections have been computed for Ar + OH(υ₁ = 9; J_i = 0,4, and 8) at initial relative translational energy 0.2 eV using quasiclassical trajectories. The results show that a relatively small amount of initial rotational excitation has a significant effect on the energy transfer. The energy transfer for J_i = 8 is dominated by transitions for which the vibrational and rotational energy changes are such that the translational energy changes are minimized.