Optimization of Embedded Optical Sensor Location in Composite Repairs

Optical fibers were embedded in a bonded composite patch in order to detect the strain field variations of a load bearing structure. The study concentrated on a classical cracked metallic structure repaired with this smart patch and using finite element analysis. Six different laminates constituted the model of the composite patch, a layered structure with three-dimensional elements. Each laminate is assumed to have different mechanical properties, according to the case under any specific study, in order to simulate different stacking sequence or material used. A resin rich eye pocket has also been modeled in order to simulate the exact form of the resin area produced during the manufacturing process. The patch is bonded over a cracked aluminum sheet through a small adhesive layer placed in between. External loads were applied only on the metal structure, as in a real repair case. The primary loading axis of the metal was assumed to be parallel to the direction of the optical fibers. The different nature of the materials that form the composite patch generated complex mechanical interactions between the fibers and the surrounding material, resulting in a complicated stress field along the optical fiber sensor, which affects the structural integrity of both the patch and the repair. Different optical fiber positions were considered, moving towards the horizontal and vertical dimensions of the patch, as well as different patch architectures (single and double patch configurations), with the hope of studying their effect on the structural integrity of the patch.     

Computational Analysis and Optimization for Smart Patching Repairs

A classical cracked metallic structure, repaired with a smart bonded composite patch with embedded optical fibers (to detect the strain field variations of the loaded structure), has been studied here-in. Finite element analysis was used, where-in the composite patch was modeled as a layered structure with three-dimensional elements constituting six different laminae. Each lamina is assumed to have different mechanical properties, according to the studied case, in order to simulate different stacking sequence. A resin rich eye pocket has also been modeled in order to simulate the exact form of resin area produced during the manufacturing process. The patch is bonded over a cracked aluminum sheet through a small adhesive layer placed in between. External loads were applied only on the metal structure, as in a real repair case. The primary loading axis of the metal was assumed to be parallel to the direction of the optical fibers. Due to the different nature of the materials that form the composite patch, complex mechanical interactions between the fibers and the surrounding material occur, resulting in a complicated strain field along the optical fiber sensor. This affects the structural integrity of both the patch and the repair. Different optical fiber layer positions were considered, to study their effect on the resulting strain field and the structural integrity of the patch. Analysis concluded that the best available embedding position of an optical fiber in a laminated patch coincides to the one predicted as neutral surface, according to Rose's analytical equations.     

Modeling of crack bridging in a unidirectional metal matrix composite

The effective fatigue crack driving force and crack opening profiles were determined analytically for fatigue tested unidirectional composite specimens exhibiting fiber bridging. The crack closure pressure due to bridging was modeled using two approaches; the fiber pressure model and the shear lag model. For both closure models, the Bueckner weight function method and the finite element method were used to calculate crack opening displacements and the crack driving force. The predicted near crack tip opening profile agreed well with the experimentally measured profiles for single edge notch SCS-6/Ti-15-3 metal matrix composite specimens. The numerically determined effective crack driving force, K _eff, was calculated using both models to correlate the measured crack growth rate in the composite. The calculated K _eff from both models accounted for the crack bridging by showing a good agreement between the measured fatigue crack growth rates of the bridged composite and that of unreinforced, unbridged titanium matrix alloy specimens.     

Simulating Crack Trajectories from a radially loaded hole

A procedure for determining the trajectory of growth of a crack in the neighbourhood of a stress-raising feature is described, The method relies on first determining the underlying stress field, and then formulating an integral equation along the (generally) curvilinear contour of the crack, which ensures that its surfaces remain traction free. The crack tip stress intensities are calculated, from which an increment of growth is found using the ^max criterion. The technique is then applied to the determination of the growth trajectory for a crack growing from a circular hole loaded by pressing a pin against its boundary.     

Asymptotic tensile crack-tip stress fields in elastic-perfectly plastic crystals

For a crack in an elastic-perfectly plastic crystal, there exist more than one asymptotic stress field around the crack tip. The condition governing which field occurs cannot be determined by the asymptotic fields, but depends on external loading conditions. For a plane-strain tensile crack in the (0 1 0) plane and growing in the [1 0 1] direction in a face-centered-cubic (fcc) crystal, there exist three asymptotic stress fields around the crack tip, including a previously established four-sector field and two new families of three-sector fields. The four-sector field gives a large mean stress ahead of the crack, 6.12, where is the critical resolved shear stress for slip systems {1 1 1}1 1 0. The first family of three-sector fields is parameterized by a single parameter p ranging from 0 to 1. In the limit p=0, the field degenerates to uniform tension in the direction parallel to the crack surface. In the other limit p=1, the corresponding field gives the maximum mean stress, 4.90 , in the family. The other family of three-sector fields also has two limits: one corresponds to uniform compression parallel to the crack, and the other provides the maximum mean stress in the family, 2.45 much less than the four-sector field. The stress distributions obtained by the finite element method confirm not only the four-sector field, but also two families of fields.     

Effect of mixed mode I and II loading on the fracture surface of polymethyl methacrylate (PMMA)

In this paper studies conducted on Polymethyl methacrylate (PMMA) under combined bending and shear loading are described. A strong dependency of fracture surface features on the mixed mode stress state is observed. Close to pure mode I, the fracture surface is mirror-like in appearance. With increasing mode II component the fracture surface becomes misty and parabolic markings appear on the fracture surface. These observations indicate that the level of stress ahead of the crack tip increases with increasing mode II component. The mixed mode specimens are also observed to fracture at much higher stresses than the pure mode I specimen, contrary to the predictions of the fracture criteria based on linear elastic fracture mechanics (LEFM). The fracture surface features and the higher stresses at fracture in the mixed mode specimens are explained in terms of the increase in stiffness (which has been related to an increase in the effective stress intensity factor per unit opening displacement) with the introduction of a mode II component and the geometry of the 3-dimensional crack tip.     

The value of the J-integral at the onset of crack extension from a weld defect: Weld material is softer than parent material

The paper addresses the problem of crack extension in a weld in an engineering structure for the case where the weld crack is parallel to the plane of the weld, a situation for which the J-integral is path independent with regard to any contour surrounding a crack tip. Assuming that crack extension is associated with the attainment of a critical crack tip opening displacement _w, a theoretical analysis based on the strip yield representation of plastic deformation shows, for the case where the weld material is softer than the parent material, how the relation between the value of J at the onset of crack extension and _w depends on the flow properties of the weld and parent materials, the crack size and the weld thickness.     

Cohesive crack models for semi-brittle materials derived from localization of damage coupled to plasticity

Based on discontinuous displacement approximation of the continuum and shear band kinematics, two cohesive crack models are derived within the constitutive framework of coupled damage and plasticity. The models employ the Rankine fracture criterion, and the model parameters are determined from a uniaxial tension test (mode I cracking). Bifurcation analysis is used in order to diagnose critical directions along which the crack will gradually develop and propagate. These directions depend on the actual stress state and are kept fixed after fracture has initiated, whereby a fixed crack model is obtained. A discrete crack strategy is employed at the finite element implementation in the sense that interfaces (that represent the cohesive crack) are introduced along inter-element boundaries. This implementation strategy calls for gradual realignment of the mesh as a key feature of the algorithm. Numerical results from the analysis of mixed mode fracture in a notched concrete plate are presented.     

Predicting fatigue crack growth under irregular loading

We describe a model for predicting fatigue crack growth (FCG) with the presence in the loading spectrum of peak and block tensile overloads. The model is based on account for the following factors influencing crack growth retardation: change of the quantity K_op as a consequence of the induction of a system of residual compressive stresses at the crack tip and increase of the degree of crack closure that is due to plastic deformation of the material in the wake of the tip of the growing crack; plastic blunting of the crack tip. We propose a technique for quantitative prediction of the residual crack tip opening (radius of the blunted tip) after a peak tensile overload. Experimental verification of the proposed FCG model with differing applied load irregularity showed that the model may serve as the basis of a method for predicting the service life of cracked structural members operating in irregular loading regimes.Translated from Problemy Prochnosti, No. 8, pp. 3–16, August, 1994.     

The edge interface crack

An analysis of a crack lying along an interface between two elastically dissimilar quarter-planes, and breaking the free surface is given. The method of distributed dislocations is employed and the nominal stress field is taken to be uniform along the length of the line of the crack. Models for crack tip behaviour are discussed and it is shown that a simplified quadrature can be used to extract the crack extension force for cases where small-scale contact obtains. Values of the crack extension force are given, displayed on the , diagram.     

Critical assessment of the application of the J-integral and CTOD concepts to circumferentially cracked copper bars

The aim of this work is to explore experimentally the validity of the concepts of J-integral and crack tip opening displacement for characterizing the stress and strain state at the tip of an axisymmetrical crack in a bar undergoing large plastic strain before crack extension. The tests are made on extruded copper round bars presenting a very high ductility. Three different analytical formulations of the J-integral proposed in the literature for circumferentially cracked bars are compared at initiation of cracking. The limit between shallow crack and deep crack geometries is experimentally demonstrated. It is found that, in neither of these geometries, J and _CTOD are dominant. However, the ratio J_c/_c is constant for deep cracks, which suggests an alternative fracture criterion consisting in postulating the dissipation of an average critical energy per unit volume until crack extension.     

Three-dimensional interactions of a crack front with arrays of penny-shaped microcracks

Three-dimensional interactions of a crack front with arrays of penny-shaped microcracks are considered. The work extends the earlier analysis of 2-D crack-microcrack interactions to the 3-D configurations.After analysing simple elementary interaction events (involving only one microcrack) we solve the interaction problem for a number of sample arrays (containing up to 50 microcracks)-realizations of certain microcrack statistics.Statistical aspects of the problem are examined. The interaction effects are found to fluctuate, even qualitatively (from shielding to amplification) along the crack front: the intervals of reduced stress intensity factors (SIFs) alternate with local peaks of SIFs that enhance local front advances. Thus, no statistically stable effect of stress shielding is found (at least, for the microcrack statistics considered): the toughening by microcracking, if it exists, may be due to a statistics of the microcrack centers which is biased towards shielding configurations or to expenditure of energy on nucleation of new microcracks, rather than elastic interactions with them. Similarly to the 2-D case, stochastic asymmetries in the microcrack field produce noticeable secondary modes on the main crack (i.e., modes II and III under mode I loading); this may be partially responsible for crack kinking and an irregular crack path.The short range interactions (several microcracks closest to the main crack tip) play a dominant role. Their impact on the main crack is quite sensitive to the individual microcrack locations and cannot be adequately reproduced by modelling the short range microcracking zone by an effective elastic material of reduced stiffness.The interaction effects in 3-D are found to be weaker than in 2-D.     

Hardness of bi-layer films on a leadframe substrate

The indentation hardness and elastic modulus of leadframe materials that consist of Cu alloy substrate and Ni/Pd bi-layer films of differing thicknesses are characterised using the micro-hardness and nano-indentation tests. The true hardness of the individual substrate and film layers is evaluated based on the empirical relationship between the measured composite hardness and the volume of plastically deformed material of film layers. It is found that the composite hardness determined from the nano-indentation test increases rapidly toward a peak at extremely low indentation depth of less than about 20–30 m for all materials studied, due mainly to the finite value of the indenter tip radius and the rough surface of the specimen on the nano-scale. The composite hardness for the coated specimens decreases with further increasing indentation depth toward the hardness value of the substrate, because of the strong influence of the film/substrate interaction and the indentation size effect. The nano-indentation test in general gives higher true hardness values than those obtained from the micro-hardness test. Nevertheless, the relative hardness values of the substrate and films determined from the two tests are consistent. The hardness of Ni film is about 20 to 50% greater than that of Cu alloy, whereas the hardness of Pd film is 7 to 11 times the Ni film in the nano-indentation test.     

The stress dependence of the crack growth rate during creep

An equation is derived for the crack growth rate under creep conditions. In the model, the propagation of a grain boundary crack is controlled by the plastic growth of cavities located in the grain boundaries ahead of the crack. It is assumed that the cavities grow by power law creep in the elastic crack tip stress field. Hence, the stress dependence of the crack velocity is provided through the elastic stress intensity factor, i.e., dC/dt=BK _I ^p .The cavity spacing, , appears as an important factor in the coefficient,B ^–(p–2)/2. At large values of , corresponding to less severe creep damage in the grain boundaries, the above equation would predict very low values for the crack velocity. Under such conditions, we suggest that another mechanism, whose stress dependence is provided through the net section stress, becomes active, i.e., dC/dt=B _net ^p . Since increases with decreasing applied stress, one should observe the _net correlation at low stresses. The results of recent creep crack growth experiments which tend to support this hypothesis are presented.

---

Résumé On dérive une équation décrivant la vitesse de propagation d'une fissure dans les conditions de fluage. Dans ce modèle, la propagation d'une fissure aux frontières de grains est contrôlée par la croissance dans le domaine plastique de cavités situées aux frontières de grains en avant de la fissure.On suppose que les cavités s'étendent dans le champ de contraintes élastiques situées à l'extrémité de la fissure en suivant une loi de fluage parabolique. Dès lors, la dépendance de la vitesse de la fissuration en fonction de la contrainte est fournie par un facteur d'intensité de contrainte élastique, c'est-à-dire dC/dt=BK _I ^p .L'espace entre les cavités, , apparaît être un facteur important dans les coefficientsB. Pour de grandes valeurs de , qui correspondent à un dommage moins sévère par fluage aux frontières des grains, l'équation ci-dessus permettrait de prédire des valeurs très faibles de la vitesse de fissuration.Sous ces conditions, il est suggèré qu'un autre mécanisme, dont la dépendance de la contrainte est fournie par la contrainte agissant sur la section droite, devient plus actif; on a alors dC/dt=B _nette ^p .Comme augmente lorsque la contrainte appliquée diminue, on devrait observer une corrélation de nette à basses contraintes.Les résultats d'essais de croissance de fissure sous des conditions de fluage effectués récemment tendent à supporter cette hypothèse et sont présentés.

     

Experimental and numerical studies in model composites Part I: Experimental results

Results on strength, apparent toughness, fatigue crack growth and fiber debonding on specially made composite materials are reported. The compact tension composite specimen used consisted of an epoxy matrix and layers of long aligned glass or kevlar fibers that were equally spaced. The experimental data on crack initiation strength showed that for a range of fiber spacing , the composite's strength _A , scaled with the fiber spacing in the form of % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGak0dh9WrFfpC0xh9vqqj-hEeeu0xXdbba9frFj0-OqFf% ea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs0dXdbPYxe9vr0-vr% 0-vqpWqaaeaabaGaciaacaqabeaadaqaaqaaaOqaaiabeo8aZnaaBa% aaleaaieGacaWFbbaabeaakmaakaaabaGaeq4UdWgaleqaaOGaeyyp% a0JaeqOUdSgaaa!3EB5!\[\sigma _A \sqrt \lambda = \kappa \]. The apparent toughness of the composite specimens increased with a decrease in fiber spacing. Two sets of fatigue crack propagation experiments were performed. The first one was on specimens with the same fiber spacing and under different applied loads. The second set was on specimens with different fiber diameter and the same loading conditions. While crack arrest was observed in the first set, crack arrest was seen in the second set for the relatively large diameter fibers and specimen fracture for the relatively thin fibers. A method, based on fracture mechanics principles and crack opening displacements, for evaluating bridging tractions is outlined. Using this method, simulations for the bridging tractions and stress intensity factor were carried out using a linear crack opening profile. The total stress intensity factor was found to decrease with crack length. The debonding in the bridging zone, on specimens with different fiber spacing, was evaluated using a one dimensional debonding analysis. The model was calibrated with the debonding on the first fiber and consequently used to describe debonding on the bridging zone of specimens with different fiber spacing. In spite of the assumptions adopted in the present studies, the model seems to describe debonding well.     

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.     

On approach of crack tip energy release rate for a semi-permeable crack when electromechanical loads become very large

This paper presents an investigation on the approach of the crack tip energy release rate (ERR) for a semi-permeable crack full with air/vacuum or Silicon oil when the electromechanical loads become very large. Numerical results for a central semi-permeable crack, respectively, in seven kinds of piezoelectric ceramics are compared with those for a central impermeable crack when the mechanical loads vary from 50 to 100 MPa and the electric loads are fixed to be 1 MV/m, 0, and –1 MV/m, respectively, within the range of practical interest. It is verified that McMeekings statement (2004): as the electromechanical loads become very large, the crack tip ERR approaches the values associated with an impermeable crack is actually valid under very large mechanical and positive electric loads. However, under very large mechanical and negative electric loads, the approach is quite different showing large discrepancies between the calculated values for the semi-permeable crack and those for an impermeable crack in all seven kinds of piezoelectric ceramics. This means that his statement is not valid when the electric loads are negative even though the mechanical loads still remain very large although, mathematically, McMeekings statement is correct if McMeekings statement: very large is replaced by infinitely large. Moreover, under purely mechanical loads his statement is uncertain, depending on which kind of piezoelectric ceramic is used. It is concluded that, generally speaking, the crack tip ERR for a semi-permeable crack does not approach the values associated with an impermeable crack, depending on the direction of the electric loads with respect to the poling axis. Physically, this is because of the inherent piezoelectric effect that yields the surface charges distributed on the crack surfaces for a semi-permeable crack under the mechanical loads, whereas on the surfaces of an impermeable crack the unphysical charge-free condition leads to incorrect estimations: the applied mechanical loads do not yield any surface charges on the crack surfaces. The influence of the permittivity of medium inside the semi-permeable crack gap on McMeekings statement is discussed too. It is found that Silicon oil yields larger discrepancies than air from those for an impermeable crack.     

Fatigue crack growth behaviour of tungsten carbide-cobalt hardmetals

Fatigue crack propagation studies have been carried out on a range of WC-Co hardmetals of varying cobalt content and grain size using a constant-stress intensity factor double torsion test specimen geometry. Results have confirmed the marked influence of mean stress (throughK _max), which is interpreted in terms of static modes of fracture occurring in conjunction with a true fatigue process, the existence of which can be rationalized through the absence of any frequency effect. Dramatic increases in fatigue crack growth rate are found asK _max approaches that value of stress intensity factor ( 0.9K_IC) for which static crack growth under monotonic load (or static fatigue) occurs in these materials. Lower crack growth rates, however, produce fractographic features indistinguishable from those resulting from fast fracture. These observations, and the important effect of increasing mean free path of the cobalt binder in reducing fatigue crack growth rate, can reasonably be explained through a consideration of the mechanism of fatigue crack advance through ligament rupture of the cobalt binder at the tip of a propagating crack.     

Experimental and numerical studies in model composites Part II: Numerical results

A numerical approach using the boundary element method for strength and toughness of a composite with long aligned fibers is reported. The three-dimensional problem is reduced to a two-dimensional one by substituting the rows of fibers with layers of appropriate width and elastic constants. The configuration examined in this work is a compact tension specimen similar to that used in the experimental studies (Part I, [1]). The experimental results on strength and apparent fracture toughness are compared with the numerical results. For the particular geometry and fiber spacing, the numerical simulations are in good agreement with the experimental findings, i.e. the composite's strength _A , scales with the fiber spacing , in the form of _A . Using the numerical formalism a number of different geometries was examined. The simulations suggested that if the external specimen characteristics remain the same and the fiber spacing in the direction of crack advance is changed, then the strength of the composite specimen can be expressed _A . If the fiber spacing varies in both directions simultaneously, for a certain range of , it can be considered that the composite's strength _A , is proportional to _A .