Simulation of fatigue performance of cross-ply composite laminates

The fatigue life of cross-ply composite laminates was evaluated using a statistical model. A modified shear-lag analysis was applied to describe the cycle-number-dependent stiffness reduction and consequent stress redistribution processes in the laminates resulted from both progressive transverse matrix cracking in transverse plies and local delamination at tips of transverse cracks. From the strength degradation behaviour and the static strength distribution of 0° plies as well as the fatigue behaviour of 90° plies, the fatigue life of cross-ply laminates with various types of lay-up can be simulated from the model. Predictions of fatigue performance are compared with experimental data for [0/90₂] _s , [02/90₂] _s and [0₂/90₄] _s graphite/epoxy cross-ply laminates: good agreements are obtained.     

Statistical model of the transverse ply cracking in cross-ply laminates by strength and fracture toughness based failure criteria

Cross-ply laminate subjected to tensile loading provides a relatively well understood and widely used model system for studying progressive cracking of the transverse ply. This test allows to identify material strength and/or toughness characteristics as well as to establish relation between damage level and the composite stiffness reduction. The transverse ply cracking is an inherently stochastic process due to the random variability of local material properties of the plies. The variability affects both crack initiation (governed by the local strength) and propagation (governed by the local fracture toughness). The primary aim of the present study is elucidation of the relative importance of these phenomena in the fragmentation process at different transverse and longitudinal ply thickness ratios. The effect of the random crack distribution on the mechanical properties reduction of the laminate is also considered. Transverse ply cracking in glass fiber/epoxy cross-ply laminates of the lay-ups [0₂/90₂]_s, [0/90₂]_s, and [0/90₄]_s is studied. Several specimens of each lay-up were subjected to uniaxial quasistatic tension to obtain crack density as a function of applied strain. Crack spacing distributions at the edge of the specimen also were determined at a predefined applied strain. Statistical model of the cracking process is derived, calibrated using crack density vs. strain data, and verified against the measured crack spacing distributions.     

Correlation between resin material variables and transverse cracking in composites

In this paper, the correlation between the resin material variables and the transverse cracking in composites is established. A theoretical model based on the fracture mechanics principle is built to describe thein situ failure process of transverse cracking. The central concept of the model is that the fracture is controlled by the plastic zone developed at the crack tip. Based on an approximate crack tip stress distribution, a quantitative representation is found to relate the laminate transverse cracking fracture toughness,G _c(comp), to certain resin properties: fracture toughness,G _c(resin), yield stress, _y, Young's modulus,E, and residual stress build-up, _R.G _c(comp) values of several fibre-glass/epoxy laminate systems were measured using the double torsion technique. The experimental results are found to be interpreted reasonably well by the theory. As a result, a clear picture of transverse cracking emerges. It seems that _y ²/E plays a more dominant role thanG _c(resin) in controllingG _c(comp). The residual stress _R can weaken the laminate significantly when its level is high. It is also shown that the failure model discussed here can be readily applied to laminate delamination failure as well as adhesive bond fracture.     

Full-field assessment of the damage process of laminated composite open-hole tensile specimens. Part II: Experimental results

The present paper deals with the investigation of the damage process of glass–epoxy quasi-isotropic laminated open-hole tensile test specimens. The effect of the scaling of ply thickness was also studied, comparing two lay-ups with the same global thickness, with ply-level scaling (PL) [−45₄/90₄/45₄/0₄]_s and sublaminate scaling (SL) [−45/90/45/0]_4s. The grid method was used to provide full-field displacements and strains at the surface of the specimen. It was shown that the cracks could easily be picked up by the method and that it was possible to follow the crack opening as a function of load as the tests proceeded. Moreover, processing the strain maps, it was possible to detect a non-linear behaviour of the material caused by the onset of subsurface cracks in the 90° plies. Finally, the difference between the two lay-ups was underlined. The PL specimens sustained much lower loads to first surface cracking than the SL specimens. It was clearly shown for both specimen types that before the onset of surface cracking, significant subsurface cracking occurred at the hole in the 90° plies. However, because of the higher loads sustained by the SL specimens, subsurface cracking in the 90° plies occurred not only at the hole but also away from the hole.     

Analysis of multiple matrix cracking in [±θm/90n]s composite laminates. Part 1: In-plane stiffness properties

In previous work Fan and Zhang¹ have proposed the equivalent constraint model (ECM) to predict the effect of matrix cracking on the in-plane stiffness properties of [±θ_m/90_n]_s composite laminates loaded in tension. The model is based on a two-dimensional shear-lag analysis where out-of-plane shear stresses in the constraining ±θ layers are assumed to vary linearly. In the present paper this shear-lag model is further developed to allow partial variation of shear stresses across the thickness of the constraining layers. The effect of non-uniform matrix cracking on the stiffness properties is also examined. Predictions of the new model compare favourably with experimental results for various multiply laminates and the discrepancy is less than that given by other theoretical models.     

Numerical Modeling of Combined Matrix Cracking and Delamination in Composite Laminates Using Cohesive Elements

Sub-laminate damage in the form of matrix cracking and delamination was simulated by using interface cohesive elements in the finite element (FE) software ABAQUS. Interface cohesive elements were inserted parallel to the fiber orientation in the transverse ply with equal spacing (matrix cracking) and between the interfaces (delamination). Matrix cracking initiation in the cohesive elements was based on stress traction separation laws and propagated under mixed-mode loading. We expanded the work of Shi et al. (Appl. Compos. Mater. 21, 57–70 2014) to include delamination and simulated additional [45/?45/0/90]_s and [0₂/90_n]_s {n?=?1,2,3} CFRP laminates and a [0/90₃]_s GFRP laminate. Delamination damage was quantified numerically in terms of damage dissipative energy. We observed that transverse matrix cracks can propagate to the ply interface and initiate delamination. We also observed for [0/90_n/0] laminates that as the number of 90° ply increases past n?=?2, the crack density decreases. The predicted crack density evolution compared well with experimental results and the equivalent constraint model (ECM) theory. Empirical relationships were established between crack density and applied stress by linear curve fitting. The reduction of laminate elastic modulus due to cracking was also computed numerically and it is in accordance with reported experimental measurements.     

Influence of intralaminar cracking on the apparent interlaminar mode I fracture toughness of cross‐ply laminates

One of the major difficulties in interlaminar fracture tests of multidirectional laminates is the high tendency for intralaminar cracking and the resulting wavy crack propagation. Experimental work showed that this occurred in double cantilever beam (DCB) tests of cross‐ply laminates having a starter crack on a 0°/90° interface. Moreover, under steady‐state propagation conditions, the apparent values of the critical strain energy release rate G_Ic were two times higher than those of 0°/0° specimens. In this paper, a finite‐element‐based progressive damage model was used to simulate crack propagation in cross‐ply specimens. The results showed that transverse cracking alone cannot be responsible for the above difference of G_Ic values. Therefore, the higher propagation G_Ic values for cross‐plies must be attributed to the more extensive fibre bridging observed and to plastic deformations of the 90° interfacial ply.     

Effects of T-stresses on fracture initiation for a closed crack in compression with frictional crack faces

This paper studies crack extension resulting from a closed crack in compression. The crack-tip field of such a crack contains a singular field relative to K _II and non-singular T-stresses T _x and T _y parallel and perpendicular to the crack plane, respectively. Using a modified maximum tensile stress criterion with the singular and non-singular terms, the kinking angle at the onset of crack growth is determined by a two parameter field involving the mode-II stress intensity factors and T-stresses, and at fracture initiation a wing crack may be created at an arbitrary angle from 0° to 90°. A compressive T _y increases the kinking angle and reinforces apparent mode-II fracture toughness, while a compressive T _x decreases the kinking angle and enhances apparent mode-II fracture toughness. The direction and resistance of fracture onset is strongly affected by T-stresses as well as frictional stress. The von Mises effective stress is determined for small-scale yielding near the crack tip. The effective stress contour shape exhibits a marked asymmetrical behavior unless 2T _x  = T _y  ≤ 0 for plane stress state. Coulomb friction between two crack faces generally increases the kinking angle, shrinks the size enclosed by the effective stress contour and enhances apparent fracture toughness. Field evidence and experimental observations of many phenomena involving the growth of closed cracks in compression agree well with theoretical predictions of the present model.     

Magnetic and electrical properties of Al3+-substituted MgFe2O4

The structural, magnetic and electrical properties of the Al³⁺-substituted disordered spinel system Mg(Fe_2–x Al _x )O₄ have been investigated by X-ray diffraction, magnetization, a.c. susceptibility and electrical resistivity measurements. The cation distribution derived from the X-ray diffractometry data was found to agree very well with the cation distribution obtained through Mössbauer spectroscopy. The variation of saturation magnetization per formula unit as a function of aluminium context, x, has been satisfactorily explained on the basis of Neel's collinear spin model and the slight discrepancy between the observed and calculated n _B values can be explained in terms of a random canting model. The Néel temperatures calculated theoretically by applying molecular field theory agreed well with the experimentally determined values from thermal variation of susceptibility and electrical resistivity. An unusual metal-like thermo-electric behaviour was found for the compositions with x 0.3 which was attributed to the decrease in the Fe-Fe separation distance arising from aluminium substitution.     

Characterisation of Transverse Cracking in a Quasi-Isotropic GFRP Laminate under Flexural Loading

Transverse cracking behaviour in a quasi-isotropic glass/epoxy (GFRP) laminate loaded in flexure is studied experimentally and theoretically. A theory developed for cross-ply laminates is applied to a [0°/90°/–45°/45°] _S quasi-isotropic laminate. An equivalent laminate is introduced to derive the Young's modulus of a cracked transverse ply on the basis of a shear lag analysis. The model predicts the flexural stiffness, the neutral axis position and the residual curvature as a function of the transverse crack density and the in-situ ply stress at first ply failure. Experimental results are obtained with the use of the applied moment – strain data in four-point flexural tests and compared with predictions. Time-dependent behaviour of the residual curvature is also investigated.The theoretical predictions are in reasonably good agreement with the experimental results. It is found that the decrease in the residual curvature after unloading is mainly ascribed to viscoelasticity of the material.     

A Study on the Mechanism of Crystal Cracking in GTA Welding of Copper Plates

Crystal cracking is one of the major defects when large copper structures are joined by gas tungsten arc welding (GTA welding). In order to research the mechanism of crystal cracking, the criterion for crystal cracking formation has been optimized based on Prokhorov's theory, which shows that the interior deformation rate (Δ?) is the main factor that leads to crystal cracking. A finite element model of thick copper plates in GTA welding based on the rigid constraint experiments has been established, and the Δ? variation of the welds is obtained. The physical model of the tendency of crystal cracking has been established, and then the mechanism of crystal cracking has been discussed systematically by comparing the variations between Δ? obtained from numerical simulations and the weld ductility (P_min) obtained from hot-tension experiments within the brittle temperature range (BTR). Results show that during GTA welding, the values of Δ? and P_min are varied, respectively, with the temperature descending, and the tendency of crystal cracking and expansion velocity can be controlled by the value of (Δ? ? P_min). Then experiments with the preheated temperatures of 300°C and 500°C, verified the validity of the optimized criterion of cracking.     

Damage Assessment of CFRP [90/±45/0] Composite Laminates over Fatigue Cycles

The present paper develops a stiffness-based model to characterize the progressive fatigue damage in quasi-isotropic carbon fiber reinforced polymer (CFRP) [90/±45/0] composite laminates with various stacking sequences. The damage model is constructed based on (i) cracking mechanism and damage progress in matrix (Region I), matrix-fiber interface (Region II) and fiber (Region III) and (ii) corresponding stiffness reduction of unidirectional plies of 90°, 0° and angle-ply laminates of ±45° as the number of cycles progresses. The proposed model accumulates damages of constituent plies constructing [90/±45/0] laminates by means of weighting factor η ₉₀, η ₀ and η ₄₅. These weighting factors were defined based on the damage progress over fatigue cycles within the plies 90°, 0° and ±45° of the composite laminates. Damage model has been verified using CFRP [90/±45/0] laminates samples made of graphite/epoxy 3501-6/AS4. Experimental fatigue damage data of [90/±45/0] composite laminates have fell between the predicted damage curves of 0°, 90° plies and ±45°, 0/±45° laminates over life cycles at various stress levels. Predicted damage results for CFRP [90/±45/0] laminates showed good agreement with experimental data. Effect of stacking sequence on the model of stiffness reduction has been assessed and it showed that proposed fatigue damage model successfully recognizes the changes in mechanism of fatigue damage development in quasi-isotropic composite laminates.     

Effect of Al3+-substitution on the electrical and magnetic properties of Ni1·05Sn0·05Fe1·9O4 ferrites

The effect of Al³⁺-substitution on d.c. resistivity, dielectric constant, initial permeability, saturation magnetization and Curie temperature has been studied for Ni_1·05Sn_0·05Al _x Fe_1·9−x O₄ ferrites, whereinx varies from 0 to 0·5 in steps of 0·1. The d.c. resistivity increases slowly forx⩽0·3 followed by a rapid increase forx>0·3. The variation is explained on the basis of Verwey hopping as well as polaron hopping mechanisms, and the dilution effect of Al³⁺ ions. The behaviour of dielectric constant is attributed to interfacial polarization and follows the Koops model. The saturation magnetization and the Curie temperature decrease continuously with increasing Al³⁺ content and are explained using the concepts of sublattice magnetization and exchange interactions. The decrease in initial permeability is attributed primarily to decrease in saturation magnetization. The dispersions in initial permeability and magnetic loss tangent are also discussed.     

Effect of particle size distribution on rheology of high concentration limestone–water slurry for economic pipeline transportation

The preparation of high concentration slurry requires careful selection of particle size distribution to achieve the required rheological properties for economic and efficient pipeline transportation. In the present study, the maximum static settled concentration (C_W-max) tests pertaining to limiting achievable concentration and rheological measurements were performed for limestone samples in the slurry concentration range of 60–78.5% by mass. The limestone samples with four distinct particle size ranges; i.e., <38, 38–90, 90–210, 210–300?µm were used to prepare five representative experimental samples by blending the fines (<38?µm) with other three coarse size ranges in definite mass proportions. The rheological behavior of the five limestone slurry samples with mono-modal, bimodal and multimodal packing characteristics indicated non-Newtonian flow behavior and fitted well to Bingham Plastic model in the concentration range of 60–78.5% by mass. The slurry samples with bimodal and multimodal packing characteristics indicated substantial reduction in slurry viscosity, yield stress and improved solids loading as compared to mono-modal one. The higher C_W-max values obtained for the specific blended (fines with coarse) limestone slurry samples were attributed to the packing effect and was correlated to the ratio of surface to surface separation for the coarse particles (β) to the average fine particle size (d_50-f) to achieve higher solids concentration. The reduction in slurry viscosity observed for the specific limestone samples was further substantiated by correlating the distribution modulus (ψ) derived from Farris theory. It may be inferred that these theoretical treatments correlating the experimental data can provide highly reliable guidance to the preparation of high concentration limestone slurry for economic pipeline transportation.     

On matrix crack saturation in composite laminates

This paper presents a comparative experimental investigation on matrix crack saturation in the constrained laminae of glass–fibre resin composite laminates. Fatigue tests under load and strain control were conducted on [±θ/90₃]_s and [0/±θ₄/0]_T laminates, respectively. The crack density was periodically measured by using digital image method and optical microscope examination during fatigue tests, to determine crack saturation. It is found that matrix crack saturation occurs in all laminates of different lay-ups under both stress and strain control cyclic loading. The crack density at saturation in the constrained plies is dependent on the cyclic loading type, the off-axis angle of the laminates, as well as the constraining ply. Based on the strain energy release rate, a crack saturation criterion is developed and the experimental findings are qualitatively analysed.     

Structural,magnetic properties,and induction heating behavior studies of cobalt ferrite nanopowders synthesized using modified co-precipitation method

Nanocrystalline cobalt ferrite CoFe₂O₄ powders have been successfully synthesized via modified co-precipitation at low temperature. Obviously, well crystalline CoFe₂O₄ phase was obtained from the precipitated precursors at pH 10 using 5?M NaOH as a base thermally treated at 80°C for 1?h in aqueous medium in the absence and the presence of 1000?ppm cetyl trimethyl ammonium bromide (CTAB) as well as sodium dodecyl sulfate (SDS) as cationic and anionic surfactants, respectively. Meanwhile, the spinel ferrite was observed with the similar conditions using ethylene glycol as an organic solvent. The microstructures of the formed powders exhibited nanospheres like structure with narrow size distribution from 6 to 10?nm. The magnetic properties of the formed cobalt ferrite powders strongly depend on the synthesis conditions. For instance, the highest saturation magnetization (M_s?=?36.2?emu/g) was achieved in the aqueous medium, whereas the lowest saturation magnetization (M_s?=?16.2?emu/g) was accomplished in the ethylene glycol medium. Indeed, heating properties of the CoFe₂O₄ samples in an alternating magnetic field (AMF) at 160?kHz were estimated. Of note, it is clear that the specific heat rate SAR values were in the range from 104.5 to 302.0?W/g at different synthesis conditions, making co-ferrite appropriate for hyperthermia treatment of cancer.     

Multiple film cracking in film/substrate systems with residual stresses and unidirectional loading

Multiple film cracking in film/substrate systems is analyzed in the present study. Specifically, the experimental measurements of multiple cracking of SiO _x films of various thicknesses on polyethylene terephthalate substrates are analyzed. The system is subjected to both residual stresses and unidirectional tensile loading. Considering a three- dimensional geometry, an analytical model is developed to derive the stress distribution in the system, and the film-cracking problem is analyzed using both the strength and the energy criteria. Compared to the strength criterion, the energy criterion shows better agreement with the measurements of the crack density versus applied strain relation.     

Multi-directional stiffness degradation induced by matrix cracking in composite laminates

A model was developed for predicting the stiffness degradation of fiber reinforced plastics (FRP), with ply configuration [0_m/±θ_n]_S, induced by matrix cracking under in-plane tension. The model assumes that the cracks in off-axis plies are uniformly distributed and a damage variable D is defined. Based on the theory of fracture mechanics, the elastic moduli of cracked matrix are obtained and indicated by the damage variable D, then the reduction of elastic moduli of laminates caused by the matrix cracks was studied. Comparison with experimental values for the glass/epoxy [90₃/0]_S, [0/90]_S and [0/±45]_S laminates shows good agreement with the theoretical prediction given by the presented model.     

On the Interplay of Jahn–Teller Physics and Mott Physics Leading to the Occurrence of Fermi Pockets Without Pseudogap Hypothesis and d-Wave High <Emphasis Type="Italic">T</Emphasis><Subscript>c</Subscript> Superconductivity in Underdoped Cuprate Superconductors

In this Festschrift paper celebrating Prof. Jacques Friedel 90 years’ birthday, we review the latest developments of the model proposed by Kamimura and Suwa, which bears important characteristics born from the interplay of Jahn–Teller physics and Mott physics. First it is shown that the feature of Fermi surfaces is the Fermi pockets constructed by doped holes under the coexistence of a metallic state and of local antiferromagnetic order. Then the phonon-involved mechanism based on the Kamimura–Suwa model is discussed; it leads to d-wave superconductivity. Further it is shown that T _c is higher in the cuprates with CuO₅ pyramid than those with CuO₆ octahedron. Finally a recent theoretical result on the energy distribution curves (EDCs) of angle-resolved photoemission spectroscopy (ARPES) below T _c is presented, and a remark is made on the phase diagram for underdoped cuprates.     

Numerical Analysis of Stress Concentration for Brittle Matrix Composites

A FEM numerical model is constructed of SiCf/LASIII glass-ceramic uni-direction plate under tension loading. The smeared crack method is used to deal with the failure point of fiber and matrix elements. The solution of the model gives the distribution of meso-stress of SiCf/LASIII glass-ceramic uni-direction plate. The stress concentration factor K and the size of stress concentration effect zone are also analyzed. The average saturation cracking space is obtained by a numerical method. The mesh length of the elements is also studied.