An improved technique for the solution of edge crack problem for finite plate

This paper provides a detailed examination for the edge crack problem of finite plate. The Williams expansion for the crack problem is used first. Secondly, the complex potentials for the central crack problem are used in the present study, which is called the improved technique hereafter. In both techniques, the eigenfunction expansion variational method (EEVM) is used for evaluating the undetermined coefficients in the expansion form. The ratio of height versus width of plate (h/w) is varying from 1.5, 1.0, 0.75, 0.5, 0.4, 0.3 to 0.25. The ratio of edge crack length versus width of plate (a/w) takes two sets: (1) a/w = 0.1, 0.2, … to 0.9, (2) a/w = 0.01, 0.02, … to 0.09. The detailed computation proves that for moderate cases of the a/w ratio, for example, 0.2 < a/w < 08, the deviations for SIFs and T-stress from two techniques are minor. However, for the case of short edge crack length, for example, a/w < 0.05, the deviations for SIFs and T-stress from two techniques are significant. It is found that the Williams expansion may not be suitable for the short edge crack, for example, a/w < 0.05.     

Modeling and experimental analysis in lifespan of a precision epoxy resin mold

Micro‐hot embossing is a highly effective process for fabricating micro‐devices with microfeatures in polymeric materials. One of the most troublesome problems in precision machinery industry is the time and expense needed to produce a mold for microreplication. Epoxy resin mold has been successfully employed for microreplication using micro‐hot embossing. However, the junction of the groove and sprue of the backing plate has serious local stress concentration, leading to the reduction of lifespan of a precision epoxy resin mold during the micro‐hot embossing molding. This work presents an effective method for enhancing the lifespan of a precision epoxy resin mold using reduction of local stress concentration. The numerical models were developed for predicting the maximum stress using ANSYS software. The ANSYS simulations have been carried out and the predicted results show good agreement with experimental tests. The junction of the groove and sprue of the backing plate was machined with chamfer to revaluate lifespan of the epoxy resin mold using micro‐hot embossing molding. Micro‐hot embossing verification test showed that the lifespan of epoxy resin mold with chamfer is about 2.2 times that of the conventional epoxy resin mold.     

Stress intensity factors in finite orthotropic plates with a crack under mixed mode deformation

Mixed mode fracture problem is analyzed for the finite orthotropic plate where an inclined crack parallel to the fibre direction is centrally placed. Modified mapping collocation method with both uniform stress and uniform displacement boundary conditions is utilized to calculate stress intensity correction factors for glass/ epoxy and graphite/epoxy composites. Computed results are presented for selected combinations of crack length to width ratio L/W and plate aspect ratio H/W with various fibre orientations.     

Dynamic characterization of the thickness-tapered laminated plant fiber-reinforced polymer composite plates

Evolution of the laminated woven natural fiber fabric-reinforced polymer composite structures makes a way to the development of the non-uniform laminated composite structures in order to achieve the stiffness variation throughout the structure. An attempt is made in this work to carry out the experimental and numerical investigations on the dynamic characteristics of the thickness-tapered laminated woven jute/epoxy and woven aloe/epoxy composite plates. The governing differential equations of motion for the thickness-tapered laminated composite plate are developed using the h-p version FEM based on higher order shear deformation theory. The validation of the present finite element formulation is carried out by comparing the natural frequencies obtained using the finite element formulation with those natural frequencies determined experimentally. The developed model is further validated with the available literature works on tapered composite plate to confirm the efficiency of h-p version FEM. This work also explores the study of the vibrational characteristics of composite plates under the influence of plant fiber’s transverse isotropic material characteristics and porosity associated with plant fiber composites through the elastic constants evaluated in the author’s previous work. Also the influences of aspect ratios, ply orientations, and taper angles under various end conditions on the natural frequencies of the woven jute/epoxy composite plate are studied using the present finite element formulation. The forced vibration response of the thickness-tapered laminated woven jute/epoxy composite plate under the harmonic force excitation is carried out considering CFCF and CFFF end conditions.     

Fractographic study of transverse cracks in a fibre composite

Transverse fracture of unidirectional fibre composites was studied in a model glass/epoxy composite in which 1 mm-diameter rods had been used in place of fibres. The fracture surface resulting from transverse cracking in this model system was studied by scanning electron microscopy (SEM). The interaction of the crack with the epoxy matrix resin and the glass rods was the following: Cracks in the resin appeared to have effected a debonding at the glassmatrix interface before reaching the glass. The debonding then propagated along the interface and induced secondary cracks ahead of the primary debonding crack. The confluence of the secondary and primary cracks resulted in sharp ridges being formed on the matrix resin surface, produced by plastic deformation of the rigid epoxy resin. These appeared as a field of parabolic marks. Considering the brittleness of the resin, the amount of plastic deformation indicated by the ridges was astonishing. As the debonding continued around the glass rod, a transverse corrugated texture developed on the resin surface, again produced by plastic deformation. Finally, the cracks reentered the matrix from small patches of polymer adhering especially strongly to the glass surface. The overall fracture energy of transverse cracking of unidirectional fibre composites is suggested to consist, therefore, of the following elements in addition to crack propagation in the matrix resin: (a) the glass-resin debonding before the incoming cracks reach the glass, (b) the initiation of secondary cracks or debonds at the interface, (c) the plastic deformation in generating the ridges on the rigid resin surface, appearing both as the paraboloids and the transverse corrugation, and (d) cracking of the matrix reinitiated at the opposite side of the glass. The use of an enlarged glass reinforcement in this study provided a more direct observation of the properties of transverse crack propagation in composite materials than would have been possible with the small, roughly 10m fibres.     

Progressive edge cracked aluminium plate repaired with adhesively bonded composite patch under full width disbond

In this study, the crack growth behaviour of an aluminium plate cracked at the tip and repaired with a bonded boron/epoxy composite patch in the case of full-width disbond was investigated. This effect is the imperfection which could result during the bonded patch of the repaired structure. Disbonds of various sizes and situated at different positions with respect to the crack tip as well as the effect of adhesive and patch thickness on repair performance were examined. An analysis procedure involving the efficient finite element modelling applied to cracked plate, adhesive and composite patch was used to compute the stress intensity factors. The crack growth rate is dominated by the stress intensity factor near the location and size of the pre-existing disbonds. The cracked plate and disbond propagation result in an increase in the patch deformation. The patch does not have an influence on the crack growth when the ratio 2a/d_R exceeds 0.8.     

Effect of fiber orientation on fracture toughness of laminated composite plates [0°/θ°]s

Fracture toughness of single edge notched fiber reinforced composite plates is investigated experimentally. Load–displacement curves for unidirectional carbon fiber/epoxy resin reinforced composite plates are obtained experimentally under tensile load. Fracture toughness is obtained by determining failure loads. For numerical study, ANSYS is used. Material properties of laminates are calculated with classical laminated plate theory and applied to the finite element model by using plane element. Stiffness matrix of laminates is determined and shell element is chosen for numerical solution. Critical stress intensity factors are calculated with Displacement Correlation Method under experimental failure load conditions.     

Fracture analysis of Kevlar-49/epoxy and e-glass/epoxy doublers for reinforcement of cracked aluminum plates

Adhesively bonded composite patch repair is efficient means to regain load carrying capacity, alleviate the crack growth, and improve the service life of the damaged structure. In this paper, three dimensional finite element models are developed to examine the fracture behavior of a single edge V-notched Aluminum plate repaired with Kevlar-49/epoxy or e-glass/epoxy pre-preg patches on both sides. Contour integral method was used for evaluating the stress intensity factor (SIF), an indicator of the crack stability. The load transfer mechanisms, stress distribution, damage variable (D), and crack mouth opening displacement (CMOD), were also presented to estimate the effectiveness of composite patch repair. The influence of the patch material, crack length and the adhesive thickness has been investigated. Results have shown that the crack induced damage increased nonlinearly with a larger crack size. With the composite patch repairs, SIF is reduced to 1/7–1/10 of that of the bare plate and CMOD decreased by 79%. The damage variable is reduced significantly and the load capacity is increased. A thinner adhesive layer results in a higher percentage of load shared by the composite patch.     

On the influence of a bimaterial interface on dynamic stress intensity factors

Summary The method of dynamic Green's function and the integral transforms are applied to investigate the elasto-dynamic stress intensity factor of a crack straddling an interface of a bimaterial composite. The crack which extends to infinity on one side is assumed to extend an arbitrary distancea on the other side of the interface. Anti-plane line loads are suddenly applied at timet=0 on either side of the crack surface at arbitrary distancesl ₁ andl ₂ from the interface. The effect of the interface on the dynamic stress field near the crack tip is studied. It is found that the transmitted wave through the interface and reflected wave from the interface serve to increase or decrease the stress field in the vicinity of the crack tip depending on the elastic properties of the two materials.     

Toughening boron/epoxy bonded joints using the resin film infusion technique

Bonded boron/epoxy repairs to aircraft can be susceptible to fatigue damage and crack propagation at high levels of in-service loading. In an effort to improve the fatigue tolerance of these repairs, an attempt has been made to improve the mode I fracture toughness. Two techniques for toughening boron/epoxy plies for use in bonded composite repairs were investigated. Firstly, the resin film infusion technique was used with dry boron fibres and the rubber-toughened film adhesive FM73 to produce a toughened boron/epoxy ply. The second technique involved co-curing a boron/epoxy laminate with FM73 adhesive. Bonded joints, comprising various toughened and un-toughened boron/epoxy adherends and FM73 adhesive, were made into fracture toughness specimens and tested. The fracture toughness for crack initiation increased from 328 J/m² for the un-toughened specimens to 1600 and 3100 J/m², respectively, for the two toughened specimens. The second technique, however, produced unstable fractures. Fractography revealed that the boron fibre-to-resin interface was the preferred failure path in all cases.     

Failure of brittle polymers by slow crack growth

The variation of crack velocity (V) with stress intensity factor (K _I) at the tip of a crack has been measured for an epoxy resin containing 42% by volume of irregularly-shaped silica particles. It has been found that at crack velocities above 10^–5 m sec^–1 the crack propagates primarily through the silica particles, whereas at velocities below this value, failure occurs primarily by particle pull-out. This variation in fracture mode is accompanied by a corresponding change in slope of the V(K) curve. Using data obtained from creep rupture experiments and the derived V(K) relationship, it has been possible to estimate the size of the inherent flaw in the composite. This was found to be approximately twice the average particle diameter which is also equal to the size of the largest particles (140 m). Fracture of the unfilled epoxy resin and the effect of environment upon slow crack growth in the composite have also been investigated.     

On elastic–plastic fracture behavior of a bi-layered composite plate with a sub-interface crack under mixed mode loading

A generalized Irwin model is proposed to investigate elastic–plastic fracture behavior of a bi-layered composite plate with a sub-interface crack under combined tension and shear loading. The dependence of the stress intensity factors, the plastic zone size, the effective stress intensity factor and the crack tip opening displacement on the crack depth h, the Dundurs’ parameters and the phase angle θ is discussed in detail. Numerical results show that in most cases, if the crack is embedded in a stiffer material, when the crack is close to the interface, the plastic zone size and the crack tip opening displacement will increase. On the contrary, if the crack is embedded in a softer material, when the crack is close to the interface, the plastic zone size and the crack tip opening displacement will decrease.     

Accelerated ageing behaviors of aluminum plate with composite patches under salt fog effect

The present study investigated the salt fog effect on the quasi-static tensile and fatigue properties of the center-cracked aluminum plates which were single-sidedly repaired with C_f/epoxy composite patches. The results show that the salt fog has minimal impact on the quasi-static tensile properties of the epoxy resin and C_f/epoxy composites; while the quasi-static tensile and fatigue properties of the repaired and unrepaired specimens all decrease with the exposure time of the salt fog increasing. Compared to the unrepaired specimens, the repaired specimens have high resistance to salt fog degradation. Within the 0–900 h range of exposure time, the repaired specimens completely fail when the fatigue crack length is equal to the width of the aluminum plate. However, as the exposure time is larger than 900 h, the repaired specimens can still bear fatigue loading when the fatigue crack propagates through the aluminum plate.     

Fatigue crack growth behavior of silica particulate reinforced epoxy resin composite

In the present work, fatigue crack growth tests of epoxy resin composite reinforced with silica particle under various R-ratios were carried out to investigate the effect of R-ratio on crack growth behavior and to discuss fatigue crack growth mechanism. Crack growth curves arranged by ΔK showed clear R-ratio dependence even under no crack closure, where the values of ΔK_th were 0.82 and 0.33 MPa √m for R = 0.1 and 0.7 respectively. However, crack growth curves arranged by K_max merged into almost one curve regardless of R-ratio, which indicated that crack growth behavior of the present composite was time-dependent. The value of K_max,th were in the range from 0.78 to 1.12 MPa √m. In situ crack growth observation revealed the crack growth mechanism: micro-cracking near the interface between silica particle and resin matrix occurs ahead of a main crack and then micro-cracks coalesce with a main crack to grow. The crack path was in the epoxy matrix, which was consistent with the time-dependent crack growth.     

Crack propagation in a glass particle-filled epoxy resin

Crack propagation in an epoxy resin reinforced with spherical glass particles has been followed using a double-torsion test. In particular the effect of strain rate, volume fraction and particle size upon the stability of propagation, the Young's modulus, the critical stress intensity factor,K _Ic and the fracture energy,G _Ic has been studied. It has been shown that the crack propagation behaviour can be explained principally in terms of crack pinning, although it has been found that propagation is also affected by blunting the breakdown of the particle—matrix interface. It has been demonstrated that crack-front pinning is consistent with a critical crack opening displacement criterion.     

Fracture criterion for kinking cracks in a tri-material adhesively bonded joint under mixed mode loading

The fracture behavior of a composite/adhesive/steel bonded joint was investigated by using double cantilever beam specimens. A starter crack is embedded at the steel/adhesive interface by inserting Teflon tape. The composite adherend is a random carbon fiber reinforced vinyl ester resin composite while the other adherend is cold rolled steel. The adhesive is a one-part epoxy that is heat cured. The Fernlund-Spelt mixed mode loading fixture was employed to generate five different mode mixities. Due to the dissimilar adherends, crack turning into the adhesive (or crack kinking) associated with joint failure, was observed. The bulk fracture toughness of the adhesive was measured separately by using standard compact tension specimens. The strain energy release rates for kinking cracks at the critical loads were calculated by a commercial finite element analysis software ABAQUS in conjunction with the virtual crack closure technique. Two fracture criteria related to strain energy release rates were examined. These are (1) maximum energy release rate criterion (G_max) and, (2) mode I facture criterion (G_II = 0). They are shown to be equivalent in this study. That is, crack kinking takes place at the angle close to maximum G or G_I (also minimum G_II, with a value that is approximately zero). The average value of G_IC obtained from bulk adhesive tests using compact tension specimens is shown to be an accurate indicator of the mode I fracture toughness of the kinking cracks within the adhesive layer. It is concluded that the crack in tri-material adhesively bonded joint tends to initiate into the adhesive along a path that promotes failure in pure mode I, locally.     

Interfacial fatigue crack propagation in microscopic model composite using bifiber shear specimens

Interfacial fatigue crack growth behavior in GF/epoxy model composites was investigated using bifiber shear (BFS) specimens in a scanning electron microscope. The specimen is composed of two E-glass filaments with diameters of 23 and 40 μm, and bisphenol A type epoxy is impregnated between the filaments. The crack growth behavior under different stress ratios was investigated to clarify the fatigue crack growth mechanism. The change in the crack growth rate, da/dN, was not monotonic with crack length, suggesting a variation in the resistance to fatigue crack growth along a single filament. The resistance to fatigue crack growth of the interface is much smaller than that of composite laminates. The fatigue crack growth mechanism of the glass fiber/epoxy interface under different stress ratios is controlled by the maximum energy release rate, G_max, which is completely different from that of composite laminates.     

Crack growth induced delamination on steel members reinforced by prestressed composite patch

ABSTRACT Prestressed composite patch bonded on cracked steel section is a promising technique to reinforce cracked details or to prevent fatigue cracking on steel structural elements. It introduces compressive stresses that produce a crack closure effect. Moreover, it modifies the crack geometry by bridging the crack faces and so reduces the stress intensity range at the crack tip. Fatigue tests were performed on notched steel plate reinforced by CFRP strips as a step toward the validation of crack patching for fatigue life extension of riveted steel bridges. A crack growth induced debonded region in the adhesive‐plate interface was observed using an optical technique. Moreover, the size of the debonded region significantly influences the efficiency of the crack repair. Debond crack total strain energy release rate is computed by the modified virtual crack closure technique (MVCCT). A parametric analysis is performed to investigate the influence of some design parameters such as the composite patch Young's modulus, the adhesive thickness and the pretension level on the adhesive‐plate interface debond.     

Interlaminar Fracture Testing Method for CFRP Using Tensile Loading with Acoustic Emission Analysis

A method is described to characterize the uniformity of interlaminar fracture toughness of laminated carbon-fiber-reinforced polymer (CFRP) composites fabricated by the modified vacuum assisted resin transfer molding process. To prepare specimens for Mode I fracture toughness tests, pieces were sectioned from the inlet and vent regions of a CFRP plate ([+30/-30]₆), with a starter crack inserted. The specimens were packed between two rectangular epoxy plates to apply a load using a universal testing machine. Acoustic energy signals were monitored using two sensors attached to the epoxy plates during tensile loading. The difference between the material properties of specimens from the inlet and vent regions of the CFRP plate were statistically compared using one-way analysis of variance (ANOVA); we show that the specimens showed no statistically significant differences in the interlaminar fracture characteristics depending on the part of the mold from which they were taken.     

Crack tip stress fields for thin,cracked plates in bending,shear and twisting: A comparison of plate theory and three-dimensional elasticity theory solutions

A three-dimensional finite element study of crack tip fields in thin plates under bending, shearing, and twisting loads is carried out to study the relation of the plate theory crack tip fields to the actual, three dimensional crack tip fields. In the region r>0.5h the Kirchhoff theory is a good approximation of the three dimensional stress fields for symmetric plate bending. The Reissner theory gives a good approximation in the region r<0.1h. Similar results are found for the shear and twisting problems, although for pure shear loading, the Kirchhoff theory is a good approximation somewhat farther r>h from the crack tip than in the bending problem. In the case of shear loading the near tip out-of-plane shear stresses do not vary quadratically through the thickness as in plate theory, but are nearly constant, except in the neighborhood of the free surface. Quadratic variation, as predicted by plate theory, is observed for r>h. Energy release rates based on the Kirchhoff and Reissner theories agree well with those computed by means of three dimensional finite element analyses.