Carbon fibre composites with rubber toughened matrices

In carbon fibre reinforced plastics (CFRP), the initial resistance to crack propagation parallel to fibres is determined largely by the matrix toughness. The fracture toughness (G _IC) of an epoxide resin can be increased considerably by the addition of butadieneacrylonitrile co-polymers (CTBN). These cause the precipitation of small spheres of a second phase and, for example, increaseG _IC from ～ 300 to ～ 3000 J m^?2 on the addition of 9 wt% CTBN. The large increases obtained in bulk resins are not obtained in CFRP, instead significant but modest increases are achieved. The suppression of toughness is related to the thickness of resin film through which the crack propagates.     

Apparent interfacial failure in mixed-mode adhesive fracture

Aluminium-epoxy adhesive specimens constructed with the bond at 45? to the direction of loading appear to fail very close to the interface. The actual locus of failure was investigated by¹⁴C labelling of the epoxy polymer and also by Auger spectroscopy profile analysis. Both techniques indicated a residual film of polymer a few hundred angstroms thick on the aluminium surface. The fracture energy of these specimens was determined and found to be affected by the surface roughness of the aluminium. The mixed-mode fracture energy (G _{I,II) C} ^45° of these specimens in the absence of any surface roughness effect (polished surfaces) was 140 J m^?2 compared to 136 J m^?2 for the same polymer in simple opening-modeG _{I C} adhesive fracture. The “interfacial” failure and the effect of surface finish on fracture are discussed in terms of the applied stress directing the failure toward the interface but the approach of the crack to the boundary being limited by the size of the crack tip deformation zone.     

Predicting stress corrosion crack growth rates when linear elastic fracture mechanics conditions are not operative

The growth rate of a stress corrosion crack in situations where linear elastic fracture mechanics (LEFM) conditions are not operative is predicted on the basis that the crack tip opening angle (CTOA) is related to the growth rate dc/dt, the functional relation between the CTOA and dc/dt being obtained by coupling theoretical results for crack growth under small-scale yielding conditions in an inert environment, with the experimentally determined power law relation between the crack tip stress intensity K and dc/dt for environmentally-assisted crack growth under LEFM conditions. Then, by assuming that the same CTOA-dc/dt relation applies to non-LEFM conditions, and by determining the CTOA under these conditions, it is in principle possible to predict the stress corrosion crack growth rate under non-LEFM conditions. A specific model: the plane strain deformation of a solid with two symmetrically situated deep cracks, and with tension of the small remaining ligament, is analyzed in detail, and the effects of the extent of plastic deformation and loading pattern (i.e., displacement or load control), on the predicted stress corrosion crack growth rate, are examined in detail. The results are compared with those obtained via application of the K versus dc/dt relation, its conversion to a J versus dc/dt correlation and then the determination of J, and also with those obtained on the assumption that a K approach is derectly applicable. The extent to which these latter approaches give conservative or non-conservative growth rate predictions when compared with the present paper's predictions, is discussed in relation to the extent of plastic deformation and loading pattern.     

Relationship between fracture parameters from two parameter fracture model and from size effect model

This paper studies the relationship between the two parameter fracture model and the size effect model. An equivalency between two models is first established based on infinitely large size specimens. Based on this equivalency, relationships between material fracture parameters (K _Ic ^s , CTOD_c) and (G _f, c_f) are derived. Using these relationships, values of (K _Ic ^s , CTOD_c) and (G _f, c_f) can be predicted from each other. It is found that the relationship betweenCTOD _c andc _f theoretically depends on both specimen geometry and initial crack length. However this dependency is numerically insignificant, except for tensile plate with a short center notch. The obtained results may explain why both the two parameter fracture model and the size effect model can reasonably predict fracture behavior of quasi-brittle materials.     

Fracture toughness and crack morphology in indentation fracture of brittle materials

The relationship between the indentation fracture toughness, K _c, and the fractal dimension of the crack, D, has been examined on the indentation-fractured specimens of SiC and AIN ceramics, a soda-lime glass and a WC-8%Co hard metal. A theoretical analysis of the crack morphology based on a fractal geometry model was then made to correlate the fractal dimension of the crack, D, with the fracture toughness, K _IC, in brittle materials. The fractal dimension of the indentation crack, D, was found to be in the range 1.024–1.145 in brittle materials in this study. The indentation fracture toughness, K _c, increased with increasing fractal dimension, D, of the crack in these materials. According to the present analysis, the fracture toughness, K _IC, can be expressed as the following function of the fractal dimension of the crack, D, such that $$In K_{IC} = {1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}\{ In[2\Gamma E/(1 - \nu ^2 )] - (D - 1)In r_L \}$$ Where Γ is the work done in creating a unit crack surface, E is Young's modulus, v is Poisson's ratio, and r _L is r _min/r _max, the ratio of the lower limit, r _min, to the upper limit, r _max, of the scale length, r, between which the crack exhibits a fractal nature (r _min ?r?r _max). The experimental data (except for WC-8%Co hard metal) obtained in this study and by other investigators have been fitted to the above equation. The factors which affect the prediction of the value of K _IC from the above equation have been discussed.     

The Transfer of Matrix Toughness to Composite Mode I Interlaminar Fracture Toughness in Glass-Fibre/vinyl Ester Composites

The transfer of matrix toughness to composite mode I interlaminar fracture toughness (G _Ic ) has been investigated in unidirectional glass-fibre reinforced composites with brittle and rubber-toughened vinyl ester matrices. Single-edge-notch bend (SENB) and double cantilever beam (DCB) specimens were used for matrix and composite G _Ic characteristion, respectively. The initial crack opening displacement rate was used as the parameter for comparison of G _Ic results. Matrix G _Ic was completely transferred to composite G _Ic for crack initiation (G _Ic-init) in the brittle-matrix composites, but in the toughened composites transfer was only partial due to the presence of fibres. The conclusion is that the maximum contribution to energy absorption by the matrix is more accurately reflected by G _Ic-init, and should be used for further assessment of the enhancing effect of fibre bridging during steady-state crack propagation, instead of matrix G _Ic . A plot of composite G _Ic for steady-state crack propagation, G _Ic-prop versus G _Ic-init indicates that the enhancing effect of fibre bridging is greater in the toughened composites. This enhancement is related to a larger deformation zone size in the toughened matrices.     

A failure criterion for brittle and quasi-brittle materials under any level of stress concentration

In this paper, we present a new criterion to predict the crack initiation under quasi-static loads from a geometrical weakness presenting an arbitrary stress concentration in brittle or quasi-brittle materials. Three material parameters were used in the establishment of the criterion, namely the ultimate stress σ_c, the critical energy release rate for crack growth G_c and the critical energy release rate for fracture under uniform uniaxial tension G_u. The use of these two critical energy release rates was justified by the observation of the fracture surfaces under different stress concentrations. The proposed three parameters’ concept enables to take the different stress concentration levels into account, thus provides a unified criterion to predict crack initiation for any stress concentration, whatever it is singular or regular. Numerous experimental studies were selected to verify the accuracy and efficiency of the criterion. It was shown that the proposed criterion is physically reasonable, highly accurate and easy to apply. It can be used in crack initiation prediction of engineering structures made of brittle or quasi-brittle materials.     

Orientation and loading condition dependence of fracture toughness in cortical bone

The fracture toughness at crack initiation were determined for bovine cortical bone under tension (mode I), shear (mode II), and tear (mode III). A total of 140 compact tension specimens, compact shear specimens and triple pantleg (TP) specimens were used to measure fracture toughness under tension, shear, and tear, respectively. Multiple-sample compliance method was utilized to measure the critical strain energy release rate (G_c) at the a/W=0.55 (crack length, a, to specimen width, W, ratio). The critical stress intensity factor (K_c) was also calculates from the critical loading (P_c) of the specimens at the a/W=0.55. The effect of the anisotropy of bone on its resistance to crack initiation under shear and tear loading was investigated as well. Fracture toughness of bone with precrack orientations parallel (designed as longitudinal fracture) and vertical (designed as transverse fracture) to the longitudinal axis of bone were compared. In longitudinal fracture, the critical strain energy release rate (G_c) of cortical bone under tension, shear, and tear was 644±102, 2430±836, and 1723±486 N/m, respectively. In transverse fracture, the critical strain energy release rate (G_c) of cortical bone under tension, shear, and tear was 1374±183, 4710±1284, and 4016±948 N/m, respectively. An unpaired t-test analysis demonstrated that the crack initiation fracture toughness of bone under shear and tear loading were significantly greater than that under tensile loading in both longitudinal and transverse fracture (P<0.0001 for all). Our results also suggest that cortical bone has been “designed” to prevent crack initiation in transverse fracture under tension, shear, and tear.     

Effects of SEBS-g-MA copolymer on non-isothermal crystallization kinetics of polypropylene

The non-isothermal crystallization kinetics of pure PP and PP/SEBS-g-MA blends up to volume fraction, Φ _d (0–0.50) was studied by differential scanning calorimetry at four different cooling rates. Crystallization parameters were analyzed by Ozawa and Liu models. The Ozawa model fits in the PP/SEBS-g-MA blends and indicates the effect of SEBS-g-MA copolymer on the crystallization process of polypropylene. Augis–Bennet model has been used to calculate activation energy, ?E, during non-isothermal crystallization process. The value of ?E decreased with SEBS-g-MA due to flexibility of SEBS-g-MA by which movements of chains of PP become easier.     

Generalized fracture mechanics of ductile steels

The generalized fracture mechanics approach is applied to two ductile steels, namely mild steel and 18/8 stainless steel in plane stress. The theory defines a fracture parameter \(\mathcal{T}\) , which is a truly plastic analogue of theJ contour integral and, for an edge crack specimen, is given by $$\mathcal{T} = k_1 ( \in _0 )cW_{0_c } $$ wherek ₁ is an explicit function,c is the crack length andε ₀, W_0c are respectively the strain and input energy density at fracture, remote from the crack. The functionk ₁(ε _o) is derived experimentally and the constancy of \(\mathcal{T}\) with respect to crack length and applied load is demonstrated. The variation of \(\mathcal{T}\) with crack extension during slow growth is investigated, as is the rate dependence of \(\mathcal{T}\) in mild steel.     

Static and energetic fracture parameters for rocks and concretes

The object of the paper is to determine the fracture toughness parameters K_1C,G _1C and J_1C for some aggregative materials. Values of the J-integral are calculated from load-displacement curves, following the procedure suggested by Begley and Landes for steel alloys. Some recurring experimental incoherences are explained applying Buckingham's Theorem for physical similitude and scale modeling to Fracture Mechanics. Thus a non-dimensional parameter can be defined (the test brittleness number), which governs the fracture-sensitivity phenomenon. The fracture parameters K_1C and J_1C are connected by a fictitious Young's modulus E^*, which is lower than the real modulus E and represents the stiffness of the damaged material near the crack tip before the extension. When the specimen sizes are so small that the material becomes fracture insensitive, then E^* appears higher than E.     

Fracture micromechanisms of bioabsorbable PLLA/PCL polymer blends

Poly(l-lactide) (PLLA) has actively been used as a biomaterial for resorbable bone fixation devices for use in orthopedic and oral surgeries. Recently, in order to improve the fracture properties of brittle PLLA, polymer blends of PLLA and a ductile bioabsorbable polymer, poly(ε-caprolactone) (PCL), have been developed. The aim of the present study is to elucidate details of the fracture behavior and toughening mechanisms of PLLA/PCL blends. PLLA/PCL blends with different PCL contents were developed, and the critical energy release rate at crack initiation, G_in, was then measured to assess the effect of PCL content. It was shown that G_in is dramatically improved by blending PCL with PLLA, and the maximum 51% of increase of G_in is acheived with 5 wt% of PCL. Polarizing optical microscopy (POM) and scanning electron microscopy (SEM) of crack growth behavior were also performed to characterize the fracture mechanism. PLLA/PCL showed multiple craze formation in the crack-tip region, and elongated fibrils and voids construct the crazes. SEM of fracture surface also indicated that stretched fibril structures are formed on the surface as a result of elongation of PCL spherulites under high tensile stress condition in the crack-tip region. Thus, these damage formations are considered to be the primary energy dissipation mechanisms that resulted in the improvement of fracture energy.     

On the relative fracture surface energies of the major and minor rhombohedra in low-quartz

The habits of both natural and synthetic crystals of low-quartz reveal that, under conditions of hydrothermal grówth, the major rhombohedronr {1 0 ¯1 1} is more developed than the minor rhombohedronz {01 ¯1 1}. The present work demonstrates that this preference ofr overz is reversed during fracture. It is also shown that neither the Hartman and Perdok [1] method nor that of Herring [2] can predict any difference in surface energy forr andz but that, by reducing the problem to the fracture or growth of a single SiO₄ tetrahedron, it is possible to account for both observations.     

Interlaminar and intralaminar fracture modes in 0/90 cross-ply glass/epoxy laminate

Delamination of a cross-ply 0/90 glass fibre-reinforced composite laminate with an epoxy-phenol matrix was studied using a double cantilever beam test. Fracture toughness was determined by measurement of bend angle of the cantilever beams. Results obtained with this method were in agreement with those from conventional compliance and area methods. Two different fracture modes were observed: interlaminar and intralaminar. In the interlaminar fracture mode, crack jumps in the space between two neighbouring 0° and 90° plies were observed. With the interlaminar fracture mode, during crack initiation G_Ic decreased with crack length. Intralaminar fracture mode consisted of the gradual growth of a crack through a 0° ply. Fibres bridging the opposite sides of the crack were observed in this case, and fracture toughness G_Ic did not change with crack length. G_Ic (420 J m⁻²) at intralaminar fracture mode was approximately twice that at interlaminar fracture mode (220 J m⁻²). The difference in fracture toughness was explained by the dissipation of energy by fibres bridging the opposite sides of the crack at intralaminar fracture mode.     

On the constancy of the specific enthalpy of fracture

The specific enthalpy of fracture due to ductile crack propagation in commercial polycarbonate sheet is calculated as ^* =A _1c/R _1c, whereA _1c is the critical energy release rate associated with the onset of unstable crack propagation andR _1c is the corresponding amount of damage (yielded material) formed per unit crack extension.A _1c andR _1c are determined from fatigue crack propagation experiments conducted at different maximum loads, load ratios and frequencies. The value of ^* obtained from all experiments is found to be 9.8±1.4 cal g^–1 (1cal = 4.184 J) which indicates that ^* is a material constant. This finding substantiates predictions of the crack layer theory.     

Polarization dependence of EXAFS and XANES spectra of superconducting films on the basis of Y-Ba-Cu-O

Superconducting films of Y-Ba-Cu-O have been studied by EXAFS and XANES spectroscopy. Films of thickness 1000 Å obtained by laser sputtering onto sapphire substrates hadT _c of about 90 K, ΔT _c of about 2 K and the \(\bar c\) axis orientation normal to the substrate surface. The EXAFS and XANES spectra were measured in the region of Y and CuK edges at different orientations of the sample with respect to the polarization vectorē. The spectra were measured in the surface-sensitive total electron yield detection mode. The observed differences between the spectra are discussed and compared with theoretical calculations.     

Fracture studies on polypropylene

Measurements of fracture surface energy have been made on polypropylene in the undrawn state and at different states of orientation over the temperature range ?60 to 60° C. Tear tests were employed and it was found that the fracture surface energy of unoriented material was of the order of 10⁴ to 10⁵ J m^?2. As orientation (represented by birefringence) increased, the fracture surface energy decreased by a factor of approximately 100 at room temperature but this factor was found to decrease with decreasing temperature. For all degrees of orientation, the fracture surface energy increased with increasing temperature in the range ?60 to 60°C, Scanning electron microscope studies showed a direct relation between the crack tip diameter and the fracture surface energy of unoriented specimens. From comparable studies on the tearing of rubber, Thomas has interpreted such a relationship as implying that the high values of fracture surface energy arise from the energy required to deform the material in the crack tip up to the breaking point. On this basis the reduction in fracture surface energy with increase in orientation may be regarded as being due to the associated diminution of the crack tip diameter. This interpretation is substantiated by direct measurements of crack tip diameter for specimens of intermediate and high orientation. Further microscopic studies of fracture surfaces indicate three modes of fracture which have been correlated with the appearance of the crack tip and tend to occur in certain ranges of birefringence.     

Sub-critical crack extension and crack resistance in polycrystalline alumina

Sub-critical crack extension can readily be observed in controlled fracture tests in fourpoint bending. A natural crack of any desired lengthc which exceeds the notch depthc ₀ by the amount c =c –c ₀ can be introduced into bend specimens by stable crack propagation. The stress intensity factor to achieve c increases considerably with increasing c. In pre-cracked specimens the stress intensity factorK _I0 to start the crack and the critical valueK _IC strongly depend on the natural crack length c whereasK _I0 andK _IC are independent ofc ₀ in solely notched specimens. From a quasi-continuous evaluation of the load-deflection curve recorded during controlled fracture, the differential work of fracture can be obtained as a function of the achieved crack length. It may be regarded as the crack extension resistanceR of the material because the balance between the energy release rateg ₁ andR is maintained throughout the experiment. By that, a formal analogy to theR-curve concept of fracture mechanics is given. The steady increase ofR is explained by multiple crack formation and by the interference of the fracture surfaces due to the angular development of the crack front.     

Thermal Conductivity of n-Aluminium Nitride-Added MgB2 Superconductor in Normal and Superconducting State

Thermal conductivity (k) of 0, 5, 10, and 15 wt.% aluminium nitride (n-AlN)-added polycrystalline MgB ₂ superconductors, synthesized by solid reaction is discussed both in the normal and superconducting states between 20 and 300 K. The prepared samples are characterized using X-ray diffraction (XRD) and field electron gun scanning electron microscope (FEG–SEM). Resistivity measurement confirms a decrease in superconducting transition temperature of MgB ₂ (T _c=38.5 K) with n-AlN addition and decreases to ～35 K in case of 15 wt.% n-AlN-added MgB ₂ sample. Thermal conductivity of both MgB ₂ and n-AlN-added MgB ₂ pellets does not show any hump around T _c, and the absolute values of k decrease with increasing n-AlN in MgB ₂. Temperature dependence of the thermal conductivity of MgB ₂ and n-AlN-added MgB ₂ has been analyzed, assuming the role of both electrons and phonons. The Wiedemann–Franz law does not work well for the present samples, which indicates inelastic scattering (L _eff < L ₀). Thermal conductivity of MgB ₂ and n-AlN-added MgB ₂ pellets is explained by assuming effective Lorentz number, L _eff= 0.1 L ₀. Electronic thermal conductivity in superconducting state ( \(k_{\text {el}}^{\mathrm {s}} )\) follows “two-gap model” and has been used to estimate the values of band gaps, relative contribution of each band in thermal transport, and intraband scattering relaxation time. The estimated values are fairly consistent with the previously reported results for MgB ₂. We further confirm that n-AlN addition in MgB ₂ introduces disorders in π bands, which reduce the π band gapsand intraband relaxation time ( \(\tau _{\pi }^{\text {im}})\) . The lattice contribution of thermal conductivity in both normal and superconducting states is analyzed in the terms of Callaway’s model, assuming various phonon scatterings. Our analysis indicates that the lattice thermal conductivity of MgB ₂ is dominated by phonon-sheet-like fault scattering. Addition of n-AlN in MgB ₂ enhances the phonon scattering from sheet-like faults, and dislocations induced strain field scattering by >7 times compared to that for pure MgB ₂ pellets.     

Compounds WAl<Subscript>4</Subscript>, WAl<Subscript>3</Subscript>, W<Subscript>3</Subscript>Al<Subscript>7</Subscript>, and WAl<Subscript>2</Subscript> and Al-W-N combustion products

X-ray diffraction data are presented for combustion products in the Al-W-N system. New, nonequilibrium intermetallic compounds have been identified, their diffraction patterns have been indexed, and their unit-cell parameters have been determined. The phases α-and β-WAl₄ are shown to exist in three isomorphous forms, differing in unit-cell centering. The phases α′-, α″-, and α?-WAl₄ are monoclinic, with a ₀ = 5.272 Å, b ₀ = 17.770 Å, c ₀ = 5.218 Å, β = 100.10°; point groups C12/c1, A12/n1, I12/a1, respectively. The phases β′-, β″-, and β?-WAl₄ are monoclinic, with a ₀ = 5.465 Å, b ₀ = 12.814 Å, c ₀ = 5.428 Å, β = 105.92°; point groups A112/m, B112/m, I112/m, respectively. The compounds WAl₂ and W₃Al₇, identified each in two isomorphous forms, differ in cell metrics (doubling) but possess the same point group: P222. WAl ₂ ^′ : orthorhombic, a ₀ = 5.793 Å, b ₀ = 3.740 Å, c ₀ = 6.852 Å. WAl ₂ ^″ : orthorhombic, a ₀ = 11.586 Å, b ₀ = 3.740 Å, c ₀ = 6.852 Å. W₃Al ₇ ^′ : orthorhombic, Pmm2, a ₀ = 6.225 Å, b ₀ = 4.806 Å, c ₀ = 4.437 Å. W₃Al ₇ ^″ : orthorhombic, Pmm2, a ₀ = 12.500 Å, b ₀ = 4.806 Å, c ₀ = 8.874 Å. The new phase WAl₃: triclinic, P1, a ₀ = 8.642 Å, b ₀ = 10.872 Å, c ₀ = 5.478 Å, α = 104.02°, β = 64.90°, γ = 107.15°.