Review and extension of compliance information for common crack growth specimens

Elastic compliance expressions for compact type (CT) and WOL specimens have been formulated for a wide range of crack lengths (0.2 a/W 0.975) using results from Newman's modified boundary collection techniques and Wilson's deep crack analysis. The location of the axis of rotation of the specimen arms at various crack lengths has been calculated and subsequently used in a proposed extrapolation technique to predict compliance at any location of the specimen convenient for measuring deflection during a crack growth test. The predicted compliances were found to be in excellent agreement with expreimental values for the two specimen types considered. Compliance expressions are also included for the center crack tension specimen.

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Résumé Des expressions de compliance élastique pour des éprouvettes du type compacte (CT) et WOL ont été formulées pour une gamme large de longueurs de fissuration (a/W compris entre 0.2 et 0.975) en utilisant les résultats tirés de l'application des techniques modifiées de collationnement aux frontières selon Newman ainsi que de l'analyse d'une fissure profonde d'après Wilson. La localisation de l'axe de rotation des bras de l'éprouvette pour différents longueurs de fissure a été calculée et utilisée en conséquence dans une technique d'extrapolation proposée pour prédire la compliance à toutes localisations de l'éprouvette convenant pour la mesure de la déflection durant un essai de croissance de fissure. Les compliances prédites ont été trouvées en excellent accord avec les valeurs expérimentales pour les deux types d'éprouvette considérés. Les expressions de compliance ont également été formulées pour un éprouvette de traction à fissure centrale.

     

Integrable K-solutions for common fatigue crack growth specimens

Alternative stress intensity factor solutions are developed for several common fatigue crack propagation specimens. Unlike the K-solutions presently employed, the K-solutions developed herein allow direct integration of the Paris fatigue crack growth rate power law while retaining the same degree of accuracy.     

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.     

Finite element analysis of crack mouth opening displacement compliance in crack length evaluation for clamped single edge tension specimens

In the unloading compliance method developed for clamped single edge tension (SE(T)) specimens, six crack mouth opening displacement (CMOD)‐based compliance equations (i.e. a/W = f(BCE′)) were proposed for the crack length evaluation without clearly clarifying the corresponding predictive accuracies. In addition, the effective elastic modulus (E_e) that reflects the actual state of stress should also be introduced in the crack length evaluation for SE(T) specimens, because the actual state of stress in the remaining ligament of the test specimen is neither plane stress (E) nor plane strain (E′). In this study, two‐dimensional (2D) plane strain and three‐dimensional (3D) finite element analyses (FEAs) are carried out to investigate predictive accuracies of the six compliance equations. In both 2D and 3D FEA, specimens with a wide range of crack lengths and geometric configurations are included. For a given specimen, the value of E_e that presents the equivalent stress state in the remaining ligament is calculated on the basis of 3D FEA data. A set of formulae for the clamped SE(T) specimen is proposed that allows to evaluate E_e from the corresponding CMOD compliance. This approach is verified using numerical data. The observations of the numerical verification suggest that the use of E_e instead of E or E′ in CMOD‐based compliance equations markedly improves the accuracy of the predicted crack length for clamped SE(T) specimens.     

Quasistatic thermal crack growth in unidirectionally fiber reinforced composite materials

Micromechanical investigations concerning the quasistatic thermal crack propagation in self-stressed unidirectionally reinforced composite structures with a low-fiber volume fraction have been performed. Thus, in order to gain certain microstructural informations about the thermal shock resistance of those reinforced composites different cracked unit cells of several two-phase composites as well as ensembles of such composite microcomponents are considered which are subjected to thermal loading. Therein the principal facets of composite material failure theories, emphazising matrix cracking, fiber breaking and interfacial debonding, respectively, have been studied. The resulting mixed boundary-value problems of the stationary plane thermoelasticity are solved numerically by using standard finite element programs. Further, the influences of the fiber diameters, different shapes of the fiber-matrix interfaces as well as of the external boundaries of the microcomponents on the crack opening displacement $\text{u}{}_{\mathrm{y}}{}^{\mathrm{c}}$ and the opening mode stress intensity factor $\text{K}{}_{\mathrm{I}}$, respectively, have been investigated. Numerical results are given for an Al₂O₃ matrix/Molybdenum fiber composite by consideration of different crack configurations.     

Fatigue crack growth behavior of cracked aluminum plate repaired with composite patch

In this study, we investigated the fatigue crack growth behavior of cracked aluminum plate repaired with bonded composite patch especially in thick plate. Adhesively bonded composite patch repair technique has been successfully applied to military aircraft repair and expanded its application to commercial aircraft industry recently. Also this technique has been expanded its application to the repair of load bearing primary structure from secondary structure repair. Therefore, a through understanding of crack growth behavior of thick panel repaired with bonded composite patch is needed. We investigated the fatigue crack growth behavior of thick panel repaired with bonded composite patch using the stress intensity factor range (ΔK) and fatigue crack growth rate (da/dN). The stress intensity factor of patched crack was determined from experimental result by comparing the crack growth behavior of specimens with and without repair. Also, by considering the three-dimensional (3D) stress state of patch crack, 3D finite element analyses were performed to obtain the stress intensity factor of crack repaired by bonded composite patch. Two types of crack front modeling, i.e. uniform crack front model and skew crack front model, were used. The stress intensity factor calculated using FEM was compared with the experimentally determined values.     

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.     

Analysis of cracked steel members reinforced by pre-stress composite patch

Pre‐stress bonded composite patch is a promising technique to reinforce steel member damaged by fatigue. The effectiveness of this technique was verified by fatigue tests on notched steel plates. Results showed that the application of carbon fibre reinforced plastic (CFRP) strips and, eventually, the introduction of a compressive stress by pretension of the CFRP strips prior to bonding produced a significant increment of the remaining fatigue life. In this paper, the stress intensity factor in the notched plates is computed by a two‐dimensional finite element model in connection with the three‐layer technique in order to reduce the computational effort. Due to high stress concentration at the plate crack tip, debond is assumed at the adhesive–plate interface. The goal is to illustrate the influence of some reinforcement parameters such as the composite strip stiffness, the pre‐stress level, the adhesive layer thickness and the size of the debonded region on the effectiveness of the composite patch reinforcement.     

Creep crack growth in a short glass fibres reinforced polypropylene composite

In this paper the creep crack propagation in a short glass fibre reinforced polypropylene composite has been investigated at various temperatures in the range from 32 to 60°C. Creep crack speed (da/dt) resulted initially decreasing till a minimum value, and then gradually increasing up to instability and fracture. Both initial and minimum crack speed values were found to strongly increase as test temperature increased. Moreover, isothermal curves of the applied stress intensity factor K _appl as a function of the crack speed (da/dt) were obtained at various temperatures. Portions of these curves in the stable crack acceleration region were hence shifted along the da/dt, axis according to a time-temperature reduction scheme, thus allowing the construction of a creep crack propagation master curve. The shift factor values, a _T for the creep crack propagation master curve appeared to be higher than those obtained, in the same temperature range, from dynamic mechanical measurements in a linear viscoelastic regime.     

Fatigue crack growth in SiC particulates reinforced Al matrix graded composite

The SiC/Al graded composite was fabricated by powder metallurgy processing and its fatigue crack growth behavior was studied. The volume percentage of SiC particulates was distributed from 5 to 30% layer by layer on the cross section. Since the aluminium was dissolved together, there was no evident interface between the two layers with different volume fraction of SiC particulates. Fatigue crack growth was in direction of from 5 to 30% SiC layers under sinusoidal wave-form. The retardation of fatigue crack growth was found when crack propagated from low volume fraction of SiC to high volume fraction of SiC. The crack deflection and branching between two layers were observed, which decreased crack growth rates. In view of crack tip driving force, the plasticity mismatch between the layers shielded crack tip driving force, i.e. decreased the effective J-integral at the tip of the crack as the plastic zone of the crack tip spread from the weaker material into the stronger material.     

Fatigue crack growth analysis of stiffened cracked panel repaired with bonded composite patch

Fatigue crack growth behavior in a stiffened thin 2024-T3 aluminum panel repaired with one-sided adhesively bonded composite patch was investigated through experiments and analyses. The patch had three plies of unidirectional boron/epoxy composite. 2024-T3 aluminum stiffeners were riveted as well as bonded on the panel. Stiffeners were oriented in the loading direction and were spaced at either 102 mm or 152 mm with a crack centered between them. Also, un-repaired cracked panel with and without stiffeners were studied. Experiment involved tension-tension fatigue at constant amplitude with maximum stress of 120 MPa and stress ratio of 0.05. Bonded composite patch repair increased fatigue life about five-fold in the case of stiffened panels while it increased about ten fold in the case of un-stiffened panels. Fatigue life also increased with decrease of the distance between the stiffeners for both repaired and un-repaired panels. A three-dimensional finite element method was used to analyze the experiments. Residual thermal stresses, developed during patch bonding, requires the knowledge of temperature at which adhesive becomes effective in creating a bond between the structure and patch in the analysis. A simple method to estimate the effective curing temperature range is suggested in this study. The computed stress intensity factor versus measured crack growth relationships for all panel configurations were consistent and in agreement with the counterpart from the test material. Thus, the present approach provides a means to analyze the fatigue crack growth behavior of stiffened structures repaired with adhesively bonded composite patch.     

Characterization of fatigue crack growth in aluminium panels with a bonded composite patch

This study introduces an analytical procedure to characterize the fatigue crack growth behavior in an aluminium panel repaired with a bonded composite patch. This procedure involves the computation of the stress intensity factor from a two-dimensional finite element method consisting of three layers to model cracked plate, adhesive and composite patch. In this three layer finite element analysis, as recently introduced by the authors, two-dimensional Mindlin plate elements with transverse shear deformation capability are used. The computed stress intensity factor is then compared with the experimental counterpart. The latter was obtained from the measured fatigue crack growth rate of an aluminium panel with a bonded patch by using the power law relationship (Paris Law) of an unpatched aluminum panel. Both a completely bonded patch (with no debond) and a partially bonded patch (with debond) are investigated in this study. This procedure, thus, provides an effective and reliable technique to predict the fatigue life of a repaired structure with a bonded patch, or alternatively, it can be used to design the bonded composite patch configuration to enhance the fatigue life of cracked structure.     

An analysis of the energy release rate for non-coplanar crack growth in fiber reinforced composite materials

In view of the fact that non-coplaner crack growth is a common characteristic of crack propagation in fiber reinforced composite materials, an attempt is made to derive the equation of the energy release rateG for non-coplaner crack extension in orthotropic linear elastic solids. Combining the idea developed in our previous paper and the analysis by Sihet al., the equation ofG is obtained for the cases of plane symmetric loading, plane skew-symmetric loading, antiplane shear loading, and a combination of these. The result will serve as a basic tool for developing a fracture mechanics approach to composites.     

Crack/fiber interaction and crack growth resistance behavior in microfiber reinforced mortar specimens

Performance enhancement due to microfibers is well known. However, fracture processes that lead to strain hardening behavior in microfiber reinforced composites are not well understood. Crack growth resistance behavior of mortar reinforced with steel microfibers and polypropylene microfibers was investigated in-situ during load application. The polypropylene fibers were inter-ground in the cement mill to enhance the fiber/matrix interfacial frictional stress. A more homogeneous fiber distribution was observed in the inter-ground polypropylene composites compared to the steel microfiber reinforced composites. In steel microfiber reinforced composites the dominant toughening mechanisms were multiple microcracking and successive debonding along the fiber/matrix interface. Fiber pullout, the dominant mechanism in conventional macrofiber reinforced composites was rarely observed. In-situ observation of crack/fiber interaction in the inter-ground polymer fibers also revealed multiple microcracking along the length of the fibers followed by fiber pullout.     

Back-face strain compliance relation for compact specimens for wide range in crack lengths

A back-face strain (BFS) compliance relation has been developed for the standard compact C(T) specimen for a very wide range in crack-length-to-width (a/W) ratios. Both finite-element and boundary-element methods were used to develop the BFS relation for a/W ratios from 0.2 to 0.95. In addition, experimentally determined compliance values on four metallic materials compared well with the new relation over nearly the complete a/W range. The new relation can be used to monitor crack-length-against-cycles using computerized crack-monitoring systems that are currently used with the crack-mouth-opening-displacement (CMOD) gage method, and the relation has been cast in a standard form compatible with existing compliance crack length monitoring systems.     

On the unloading compliance method for crack length measurement

Unloading compliance tests have been performed on blunt notched Charpy specimens in order to quantify the extraneous displacements arising during unloading in a three point bend fracture toughness testing fixture. An expression is derived which quantifies the extraneous displacements and enables the unloading compliance to be accurately evaluated. Results are presented from tests on pre-cracked Charpy specimens which demonstrate close agreement between measured crack lengths and those predicted using the corrected unloading compliance.     

An inclusion model for crack arrest in a composite reinforced by sliding fibers

The inclusion model of Mori and Mura for crack arrest in fiber reinforced materials is extended. The analysis is restricted to short fibers. The sliding of fibers is allowed along fiber-matrix interfaces. Analytical expressions for energy release rate and extra energy dissipation during crack extension are obtained. Sliding fibers result in a larger energy release rate than non-sliding and perfectly bridging fibers. However, the energy dissipation accompanied by sliding offers additional resistance to the extension of a crack. Fibers of smaller radius decrease the energy release rate and raise the energy dissipation more efficiently.     

Strain-gauge compliance measurements near the crack tip for crack closure evaluation: Applicability and accuracy

The “plasticity-induced crack closure” phenomenon is the leading mechanism which controls the main effects on fatigue crack growth (e.g. stress ratio and load interaction effects) in metallic materials. Experimental tests, consisting mainly in global and/or local compliance measurements of the considered specimen, are usually carried out to quantify the physical phenomenon, but some aspects concerning the elaboration of acquired local compliance signals are not yet clear. From the analytical point of view, the so-called “Strip-Yield” model has proven to be the most versatile and powerful tool for estimating crack closure levels, but its application to structural steels is not yet straightforward due to the delicate calibration process.The present work tries to add some new ideas on the elaboration of local compliance experimental data, obtained from a M(T) specimen, simulating the measurements by means of an optimised Strip-Yield model implementation enriched by a novel module based on the Westergaard’s elastic complex potentials. The application of the method to the calibration of the Strip-Yield model has been already successfully faced elsewhere, so here the analytical results gave the possibility, together with dedicated FEM analyses, to investigate some of the different parameters and to state some conclusions about the reliability and applicability of local compliance measurements.