Role of surface chain mobility in crazing

Thin film experiments have shown that glassy thermoplastics exhibit enhanced molecular mobility across a 10 nm surface layer. This study examines its relevance to crazing. Surface mobility produces a steep yield stress gradient, which constrains the growth of plastic zones from surface flaws. During tensile tests, stresses in these zones increase until the bulk specimen either yields or fractures. Polycarbonate can sustain rising local stresses and strains without damage because its chains have relatively small cross-sectional areas, but high stresses in polystyrene produce chain scission, accelerated relaxation and cohesive failure. The partially degraded plastic zone breaks down to form craze fibrils, an internal necking process that is repeated during craze propagation and fibril drawing. In combination with the linear elastic fracture mechanics model for craze initiation, constraints on yielding around symmetrical surface flaws account for the strong dependence of critical tensile crazing stress σ_1cz on the second principal stress σ_2cz in biaxial tests.     

Microstructure and mechanics of crazes in oriented polystyrene

Crazes are produced in oriented polystyrene (PS) thin films, bonded to copper grids, by applying a tensile strain to the grids in directions parallel to, or perpendicular to the axis of molecular orientation. The crazes produced by straining parallel to the molecular orientation direction (parallel crazes) have a higher fibril volume fraction (v_f=0.45) than crazes in unoriented PS (v_f=0.25). The crazes produced by straining perpendicular to the molecular orientation direction (perpendicular crazes) have a much lower fibril volume fraction (v_f=0.05) than either parallel crazes or crazes in unoriented PS. These differences in fibril volume fraction are reflected in the micromechanics of the crazes. Perpendicular crazes show a higher stress concentration at the craze tip and a larger stress relief behind the craze tip than do the parallel crazes. The fibrils in long perpendicular crazes break down readily to form cracks whereas no parallel craze breakdown at similar strains is observed. These differences in craze microstructure and micromechanics are believed responsible for the marked anisotropy in the fracture properties of oriented glassy polymers.     

The micromechanics and microstructure of CO2 crazes in polystyrene

Although CO₂ at 1 atmosphere pressure is not a crazing and/or cracking agent for polystyrene (PS), we have established that it becomes one at higher pressure. Crazes grown from cracks in PS thin films in high pressure CO₂ are investigated using transmission electron microscopy (TEM). The fact that broken craze fibrils retract strongly upon exposure to high pressure CO₂ gas suggests that the primary effect of the CO₂ is plasticization, not surface energy reduction. Quantitative analyses of TEM micrographs of crazes grown at CO₂ pressures in the range 5 to 100 MPa at 34°C and 45°C have been carried out to find the craze fibril volume fractions v_f(x) and the surface displacements w(x) along each craze. From the fibril volume fraction profile along the craze, the dominant craze thickening mechanism of CO₂ crazes is shown to be the same as that for air crazes, i.e. the surface drawing mechanism, and not the fibril creep mechanism. The craze surface stress profile is computed from the craze surface displacements using a distributed dislocation analysis. These profiles all show a stress concentration at the craze tip which falls to a roughly constant value σ_b, over the rest of the craze. The fracture toughness G_Ic (and critical stress intensity factor K_Ic) for propagation of a crack in PS at these CO₂ pressures can also be computed. All these quantities (V_f, σ_b, G_Ic and K_Ic) show pronounced minima as a function of CO₂ pressure at 20 MPa, the same CO₂ pressure at which T_g of the polymer also reaches a minimum. These minima are more pronounced at 45°C than at 34°C. The G_Ic's and K_Ic's are depressed by orders of magnitude at the minimum, which corresponds to the qualitative observation that CO₂ becomes a severe cracking agent at these pressures. These observations provide additional confirmation that the major mechanism for the environmental crazing and cracking of PS by CO₂ is plasticization of the craze fibrils and surfaces.     

Craze behaviour in isotactic polystyrene: 1. Craze-spherulite interaction

The deformation of isotactic polystyrene (i-PS) in uniaxial tension at room temperature has been studied in detail by transmission electron microscopy. Quantitative analysis reveals that crazes in amorphous i-PS are similar to crazes formed in atactic polystyrene (a-PS) under the same conditions, except for a higher stress concentration at the craze tip. Fully spherulitic i-PS films contain crazes with very irregular paths which often nucleate at spherulite triple points. Craze-spherulite interactions have been observed in films which contain spherulites isolated in an amorphous matrix. Lamellae with their c-axis perpendicular to the tensile axis generally yield a higher craze fibril draw ratio than in the amorphous matrix. Lamellae with their c-axis parallel to the tensile axis cause a decrease in both λ and craze width. When the c-axis is in the plane of the film but oblique to the tensile axis, the craze deviates toward the centre of the spherulite. The entanglement network approach applied to crystalline i-PS predicts the correct anisotropic behaviour of λ when neutron scattering data on chain conformation in i-PS crystals are used.     

Identification of deformation behavior in high‐thermal‐resistant poly(acrylonitrile‐butadiene‐styrene) (ABS)

Deformation mechanisms in postfractured high‐thermal‐resistant poly(acrylonitrile‐butadiene‐styrene) (ABS) were investigated using transmission electron microscopy (TEM) and small‐angle X‐ray scattering (SAXS). Although crazes were clearly identified by TEM, they were not detectable by SAXS. This was possibly due to a short distance between sample and imaging plate in the SAXS set‐up and invisibility of craze fibril scattering from the postfractured samples. A rhomboid‐shaped SAXS pattern was obtained from ABS samples with high ductility but with no crazes shown in the TEM micrographs. It is believed that the rhomboid‐shaped SAXS pattern was generated from matrix shear yielding. The results show that a combination of TEM and SAXS enable us to distinguish crazing and shear yielding in the postfractured ABS. © 2001 John Wiley & Sons, Inc. J Appl Polym Sci 81: 1316–1321, 2001     

Ultra small-angle X-ray scattering studies on structural changes in micrometers upon uniaxial stretching of segmented polyurethaneureas

Ultra small-angle X-ray scattering (USAXS) experiments were conducted in order to examine structural changes in micrometers upon uniaxial stretching of elastomeric segmented polyurethaneureas at room temperature. It was possible to stretch the sample film up to α = 7.5 without break, where α designates the stretching ratio. Around α = 6.5 the sample became turbid, while it recovered transparency when the stress was removed. To understand this curious phenomenon, we conducted the USAXS experiments for the structural analyses in micrometers. Although a set of streaks appeared in the direction parallel to the stretching direction (SD) when the sample became turbid (around α = 7.2), more interesting result is that a set of streaks appeared in the direction perpendicular to SD much earlier around α = 5.0. Close examination of the scattering intensity profile revealed evolution of multiple interference peaks, which could be ascribed to the form factor of a lamellar particle. Since the streaks disappeared upon the removal of the stress, “lamellar particles” are considered to be crazes, which develop further into cracks in a subsequent stage. From the results of USAXS measurements, it is suggested that the lamellar-shaped crazes appeared around α = 5.0 being oriented parallel to SD, and further stretching created other lamellar-shaped crazes being oriented perpendicular to SD, which are co-existing with the preceding parallel crazes.     

The craze initiation response of a polystyrene and a styrene-acrylonitrile copolymer during physical aging

The influence of structural recovery or physical aging on the craze initiation of amorphous polystyrene and a styrene-acrylonitrile copolymer has been examined in two states of stress/deformation and at different temperatures. Studies of craze initiation in equibiaxial creep were performed using a “bubble” inflation test geometry while uniaxial elongation in stress relaxation conditions was studied by bending the specimen over a variable radius of a curvature test jig. All tests were performed by aging the specimen and testing it at the same temperature subsequent to a quench from above the glass transition to below it. The results are compared with expectations from three craze models: Sternstein and Ongchin (1), Argon (2), and Kambour (3). The results are most consistent with the model of Kambour, but discrepancies arise because, e.g., the impact of aging on the stress for crazing in the equibiaxial tests is different for the polystyrene than for the styrene-acrylonitrile copolymer. The results also suggest that there are two regimes of behavior for craze initiation under equibiaxial stresses, a behavior not manifested in the uniaxial stress relaxation experiments.     

Craze initiation and growth in high-impact polystyrene

Quantitative transmission electron microscopy and optical microscopy is used to study craze initiation and growth in thin films of high-impact polystyrene (HIPS). Dilution of the HIPS with unmodified polystyrene reduces the craze–craze interactions, permitting equilibrium growth and craze micromechanics to be studied. It is found that the equilibrium craze length depends on the size of the nucleating rubber particle, but not the internal structure; no short crazes less than a particle diameter are observed. The long crazes can be adequately modelled by the Dugdale model for crazes grown from crack tips. The effects of particle size and particle internal occlusion structure on craze nucleation have been separated. Craze nucleation is only slightly enhanced at highly occluded particles relative to craze nucleation at solid rubber particles of the same size. There is a strong size effect, however, which is independent of particle internal structure. Crazes are rarely nucleated from particles smaller than ～1 μm in diameter, even though these make up about half the total number. These craze nucleation and growth effects may be understood in terms of two hypotheses for craze nucleation: (1) the initial elastic stress enhancement at the rubber particle must exceed the stress concentration at a static craze tip and (2) the region of this enhanced stress must extend at least three fibril spacings from the particle into the glassy matrix. Since the spatial extent of the stress enhancement scales with the particle diameter, the second hypothesis accounts in a natural way for the inability of small rubber particles to nucleate crazes.     

Mechanical properties of sintered La9.33Si2Ge4O26 oxyapatite materials for SOFC electrolytes

Mechanical properties of La_9.33Si₂Ge₄O₂₆ prepared by mechanical alloying and subsequent sintering at 1300–1400 °C for 1 h were evaluated. Hardness and Young's modulus values in the range 7.3–9.6 GPa and 106–135 GPa, respectively, were obtained from nanohardness tests. The fracture toughness values derived from the Palmqvist method varied between 3.5 and 3.9 MPa m^1/2 from classical microindentation test with an indentation load of 9.8 N. Yield stress (σ_y) was determined by inverse analysis from microhardness tests. The maximum value of σ_y (1829 MPa) was obtained for the sample sintered at 1400 °C showing the highest density (5.42 g/cm³).     

Solvent stress crazing in PMMA: 1. Geometrical effects

Single crazes were propagated in poly(methyl methacrylate) (PMMA) by loading sheet specimens containing ‘starter’ cracks and immersed in various alcohols. Craze lengths and propagation velocities were measured (as functions of the applied load) using an ultrasonic scanning technique, for three types of behaviour. These were: (I) where craze arrest occurs after some growth; (II) where the craze grows at a constant velocity for an unlimited distance; and (III) where constant velocity growth continues after removal of the original ‘starter’ crack and re-application of the load. The results are analysed using the concept of an ‘equivalent crack’, whose length I turns out to be related to the length c₀ of the starter crack. At temperatures above a previously identified ‘characteristic temperature’, I is commensurate with c₀, but at lower temperatures, I?c₀. These results are discussed in terms of the strain hardening properties of the craze matter which fills the craze.     

Electrical conductivity relaxation in PVOH-LiClO4-Al2O3

We report on electrical conductivity relaxation measurements of solid polymer electrolytes (SPE) based on poly(vinyl alcohol) (PVOH) and LiClO₄ in which nanoporous Al₂O₃ particles with average pore diameter of 58 Å were dispersed. A power law frequency dependence of the real part of the electrical conductivity is observed as a function of temperature and composition. This behaviour is typical of systems in which correlated ionic motions in the SPE bulk material are responsible for ionic conductivity. This variation is well fitted to a Jonscher expression σ′(ω) = σ₀[1 + (ω/ω₀)^p] where σ₀ is the dc conductivity, ω₀ the characteristic angular frequency relaxation and p is the fractional exponent between 0 and 1. For a prototype membrane with composition 0.9PVOH − 0.1LiClO₄ + 7 wt.%Al₂O₃, it was found that the temperature dependence of σ₀ and ω₀, may be described by the VTF relationship, ? = ?₀ exp[−B/(T − T₀)], with approximately the same constant B and reference temperature T₀, indicating that ion mobility is coupled to the motions of the polymer chains. Moreover, p decreased with increasing temperature, from 0.68 at T = 319 K, to 0.4 at T = 437 K, indicating weaker correlation effects among mobile ions when the temperature is increased.     

Influence of oxidation on fatigue life of a carbon/silicon carbide composite in water vapor containing environments

The influence of oxidation on the fatigue life of two-dimensional carbon/silicon carbide composites in water vapor containing environments at 1300 °C was investigated. Tension–tension fatigue experiments were conducted at sinusoidal frequency of 3 Hz. Using a stress ratio (σ_min/σ_max) of 0.1, specimens were subjected to peak fatigue stresses of 90, 120 and 150 MPa. The mean residual strength of the specimens after survived 100,000 cycles with a peak stress of 90 MPa was 83.9% of that of the as-received composite. The mean fatigue lives of the specimens subjected to peak fatigue stresses of 120 and 150 MPa were 42,048 and 13,514 cycles, respectively. Oxidation was the dominant damage mechanism, which remarkably decreased the fatigue life. Oxidizing species diffusion within the composite defects was discussed. The higher the applied stresses, the larger the equivalent radius of the defect and the shorter the fatigue life.     

Craze fibril formation and breakdown

As crazes grow in areal extent they also increase in width. The areal growth involves craze tip advance which has been shown to occur by the Taylor meniscus instability. Craze widening, at least for air crazes, occurs by drawing more fibrillar material from the craze-bulk polymer interfaces at essentially constant extension ratio. Simple arguments will be given to predict the scale of the fibrillation in terms of the stress S at the craze tip and interfaces and an effective polymer surface energy (Γ) where: which assumes that all entangled chain crossing the surface are broken [γ represents the van-der-Waals (intermolecular) surface energy, d is the entanglement mesh size, v_E is the entanglement density, and U_b is the energy required to break a single backbone bond]. These arguments also give the rate of fibrillation as a function of S, a nominal plastic resistance σ_y and Γ and can explain the fact that the stress for crazing increases relative to that for shear deformation as the entanglement density of the polymer is increased. The geometrically necessary entanglement loss (either by scission as assumed above or by disentanglement- at temperatures just below T_g) that accompanies fibril formation has important consequences for fibril stability. The probability p that a given entangled chain is lost can be computed from simple geometrical considerations knowing the fibril diameter D, its extension ratio λ and the mesh size d; p increases rapidly as Dλ^½ becomes comparable to or less than d. These concepts can be tested in blends of high molecular weight polymer with chains of the same polymer that are too short to entangle.     

An investigation of intercalation-induced stresses generated during lithium transport through sol-gel derived LixMn2O4 film electrode using a laser beam deflection method

The stress changes Δσ generated during lithium transport through the sol-gel derived Li_xMn₂O₄ film electrodes annealed at 773 and 873 K were quantitatively determined as a function of the lithium stoichiometry x using a laser beam deflection method (LBDM). Δσ generated during a real potential step between an initial electrode potential and a final applied potential was uniquely specified by the Δσ versus x curve. The Li_xMn₂O₄ film annealed at 773 K for 24 h (low temperature (LT)-Li_xMn₂O₄) showed larger capacity than the Li_xMn₂O₄ film annealed at 873 K for 6 h (high temperature (HT)-Li_xMn₂O₄) and this result is ascribed to the fact that the smaller the grain size is, the more increases the electrochemically active area of the film electrode. From the analysis of the normalised Δσ transient measured simultaneously along with the cyclic voltammogram in the potential range of 2.5-3.4 VLi/Li⁺, it is found that normalised Δσ generated in the LT-Li_xMn₂O₄ was smaller than that in the HT-Li_xMn₂O₄ during the lithium intercalation/de-intercalation around 3.0 VLi/Li⁺ region. This result gives an experimental evidence for the fact that the Jahn-Teller distortion is suppressed by the increase in the average oxidation state of manganese with decreasing in annealing temperature.     

Molecular weight distribution effects on craze micromechanics

Quantitative transmission electron microscopy has been used to investigate the micromechanics of crazes in monodisperse and polydisperse polystyrene (PS). In the monodisperse PS, a large stress is observed at the craze tip, but this stress falls rapidly with distance behind the tip. In the polydisperse PS (or in blends in which a small percentage of monodisperse low molecular weight PS has been added to monodisperse high molecular weight PS) the stress at the craze tip is lower and falls much less rapidly with distance behind the craze tip. These changes are attributed to the effects of diluting the network of entangled high molecular weight chains with molecules that are too short to entangle. This dilution increases the molecular stress on the load bearing chains of the network, thus increasing the ease of craze fibrillation.     

The shape of the cohesive arch in hoppers and silos — Some theoretical considerations

Models of the cohesive arch have been developed in order to predict arch shape and test the circular arc hypothesis first proposed by Enstad [‘On the theory of arching in mass flow hoppers’, Chem. Eng. Sci., 1975, 30, 10, 1273-1283].A 2-dimensional arch was modelled. Vertical and horizontal force balances described the system, with 2 unknown: arch stress, σ_arc, and vertical arch co-ordinate y. A rotationally symmetrical system was also modelled and included the azimuthal stress σ_az. σ_az was related to σ_arc by a Mohr-Coulomb yield type of equation. These equations were solved numerically by an Euler method.A least squares fit was used to predict the equivalent circular arc radius R and circular arc co-ordinate y_circ. The square of deviation from the circle Σ(y − y_circ)² was used as a statistical measure of the goodness of fit to the circular arc.The arch shape was generally an excellent approximation to the circular arc. However, the arch diverged from the circular as arch span increased.A dimensionless group was defined: the Stress-Radius Number, N_SR, which incorporates the ratio of equivalent circular arc radius to the arch stress at the apex. N_SR was constant for a given set of conditions and was ideally equal to 1 for a 2-dimensional arch and 2 for a rotationally symmetrical arch with no overpressure.Arch thickness models had little effect upon arch shape but had a great influence upon stress. This affected the critical outlet dimension for flow.Rotationally symmetrical arches were very sensitive to the relation between azimuthal and arch stresses. This affected both arch shape and stresses.A critical outlet dimension was calculated and showed great variation dependent upon assumptions made. Jenike's approach of an arch of constant thickness with no overpressure yielded a conservative value.     

Electroformed iron and FeCo alloy

Iron and FeCo alloys were electroformed from additive-free acidic chloride baths. Film stress and magnetic properties were strongly influenced by deposition current density and operating temperature. In general, low film stress and low coercivity (H_C) was achieved with low current density and high operating temperature baths. SEM micrographs indicated that these conditions promote large grain growth. Coercivity of electroformed iron films linearly increased with increasing film stress, indicating that magnetoelastic energy is a dominant anisotropy. The addition of 0.25 M CaCl₂ improves current efficiency while maintaining low film stress. The lowest iron film stress of 5 MPa was achieved from 1.5 M FeCl₂ in the absence of CaCl₂ at 20 mA cm⁻² with a current efficiency of 91%. A “normal” codeposition of FeCo was observed in acidic chloride baths, where the deposition rate of Co²⁺ was faster than Fe²⁺. Film compositions also played an important role in magnetic properties of FeCo films in addition to film stress. Magnetic saturation (M_S) of FeCo films increased linearly with an increase in deposited Fe content. High magnetic saturation with low-stress (M_S of 2.3 T and σ=70 MPa) were achieved from 71Fe29Co films.     

An approach to yielding and toughness in rubber-modified thermoplastics

An interpretation of yielding and fracture of rubber-toughened polymers is attempted, considering the fracture mechanics behavior of the matrices, with the rubber particles as stress-intensification sites. The fit of effective tensile yield stresses of composites vs. particle radii defines a stress-intensity factor K_Yc for craze yielding much smaller than the classical fracture factor K_c, values are found for polystyrene and poly(styrene-co-acrylonitrile)-based polymers. These factors are considered characteristic for craze initiation and propagation in the matrices, while K_c, in turn, would include also the craze-crack transformation contribution. K_Yc appears independent of the rubbery-phase volume fraction and characteristics, but two different values are found and discussed for poly(styrene-co-acrylonitrile)-based materials in two different particle-size ranges. A similar treatment on notched specimens' yield stress indicates the presence of a maximum in different radius ranges for polystyrene and poly(styrene-co-acrylonitrile) matrices, with higher values than their breakdown stresses. This stress increment is in relation to the minimum particle size inducing and still stabilizing crazes and preventing crack formation. This maximum seems to control the reinforcing extent of the polymer matrix conditioning the Izod fracture initiation energy.     

More studies on the PVOH-LiH2PO4 polymer system

Polymer electrolytes based on poly(vinyl alcohol) (PVOH) and lithium dihydrogen-phosphate (LiH₂PO₄) with molar ratio of x = 0.07, 0.10 and 0.14 were prepared in order to investigate the mechanism of ionic motion. Admittance spectroscopy measurements were used to study electrical conductivity relaxation on both anhydrous and hydrated samples in the 5 Hz to 13 MHz frequency range and temperatures ranging from 25 to 150 °C. The conductance, G, shows dispersion above a crossover frequency, f_p. This behavior is typical of systems in which correlated ionic motions in the bulk material are responsible for ionic conductivity. For hydrated samples, results reveal that the temperature dependence of the dc-conductivity, σ₀ and the characteristic frequency, f_p, shows Arrhenius-type behavior with the same energy, E_σ. However, for anhydrous conductivity, a Vogel-Tamman-Fulcher (VTF) behavior is shown for both σ₀(T) and f_p(T), with the same pseudo activation energy, B and B_σ, respectively, thus indicating that they are correlated with chain mobility.     

Interactive software for calculating the principal stresses of compacted cohesive powders with the Warren-Spring equation

The Unconfined Yield Stress (σ_c) and Major Consolidation Stress (σ₁) of a cohesive powder′s compact are found by constructing two Mohr semicircles that are tangential to the Yield Loci Curve (YLC); the first passing through the origin (0,0) and the second at the consolidation conditions (σ₀,τ₀). When the YLC can be described by the Warren-Spring equation (τ/C)ⁿ = (σ + Τ)/Τ or an alternative algebraic expression, this translates into finding the solution of two pairs of simultaneous equations that set the conditions for the tangential YLC and corresponding Mohr semicircles to have the same value and slope at their respective contact points. Once the Mohr semicircle′s equation that corresponds to the consolidation conditions has been found, the Effective Angle of Internal Friction (δ) is calculated in a similar manner. The numerical calculation procedure has been automated in a freely downloadable program posted on the web as a Wolfram Project Demonstration. It allows the user to choose and adjust the values of C, T, n and σ₀, and the plot′s scales, by moving sliders on the computer screen. The program calculates and displays the corresponding values of σ_c, σ₁ and δ, and plots the YLC, two Mohr semicircles and the line that defines δ. Since a linear YLC is just a special case of the model where n = 1, the program can be used with input parameters originally obtained by linear regression. But although the program can render reasonable estimates of the principal stresses σ_c, σ₁ and δ in this case too, the physical meaning of C, and especially T, is unclear when calculated by extrapolation instead of being determined experimentally.