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形態: カラー図版あり, Physical characteristics: Original contains color illustrations, Accepted: 2020-06-29, 資料番号: PA2120012000

The fracture toughness of the fine-grained nuclear graphite SNG742 has been investigated by observation of stable crack propagation in double cleavage drilled compression specimens. The three-dimensional displacement fields were obtained by digital volume correlation (DVC) of in situ laboratory X-ray computed tomographs. The crack tip location and crack opening displacements were determined using an image edge detection algorithm based on the wavelet modulus maxima. The Young modulus was estimated by fitting a finite element model to DVC displacement field data measured before crack initiation. Using the 3D crack geometry and the surrounding full-field 3D displacement fields as boundary conditions, the elastic strain energy release rate J and the three-dimensional stress intensity factors KI to KIII were then evaluated via the contour integral method. Constant mode I critical stress intensity factor was obtained along the curved crack fronts, with negligible shearing modes. This method allows evaluation of the fracture toughness without prior knowledge of elastic properties, and has potential applications to assess the effects of high temperature, oxidation and irradiation in small specimens of nuclear graphite.

This paper presents the thermo-elastic effect on materials having anisotropic behavior and stresses developed due to residual temperature on interlaminar delamination fracture characteristics of composite skin stiffener. For the preexisting interlaminar delaminations subjected to uniaxial loading and three-point bending of three-dimensional coupled field thermo-elastic finite element analyses have been accomplished. The individual mode of strain energy release rate along the delamination front has been evaluated by modified crack-closure integral method based on the concept of mechanics of linear elastic fracture. Qualitative comparison has been illustrated for the individual modes of energy release rate along the delamination front of skin stiffener for both the loadings. The influence of coupled field thermo-elastic material anisotropy of the constituting laminae has been reasoned for the asymmetric variation of total strain energy release rate along delamination front. This was found to be significantly higher for the case of residual thermal stresses compared to mechanical loading. Keywords: Thermo-elastic effect, Interlaminar delamination, Crack closure, Energy release rate, Residual thermal stress.

In this paper, the fatigue crack problems in piezoelectric materials under cyclic mechanical loading or alternating electric field were analyzed by a single-domain boundary element method. To determine the direction of the crack propagation, the fracture criteria of maximum of hoop mechanical strain energy release rate was used. Meanwhile, for evaluating the remaining life of the cracked piezoelectric specimens, the Paris-type laws based on different fracture parameters were employed and compared. All the involved fracture parameters were computed by the interaction integral method. Numerical examples were considered and analyzed for cyclic mechanical and electrical loadings, respectively. The comparisons showed the efficiency of the present BEM program in analyzing fatigue cracks and the choice of the effective fracture parameter in Paris’ law for life prediction.

International audience; In the framework of the adhesive bonding, the assessment of interfacial properties has an essential role in determining the adhesive joints' global responses. Various surface preparations are available for each type of metallic substrate. There are plenty of tests widely used for mechanical characterisation to determine the adhesive properties and few tests to assess interfacial properties. For such a case, a specific three-point bending test can be applied to examine the interactions between adhesive and substrate. On the other hand, a direct comparison of the critical force is not always possible because of geometrical incompatibility. A practical solution for the last issue is applying a coupled stress-energy criterion (CC) since the interface properties are independent of the substrate thickness. Hence, CC and the macro-element technique were applied to determine the interfacial properties using an aluminium alloy 2024-T3 as substrate and the adhesive DGEBA/DETA™ under many preparation conditions. As a result, the three-point bending test's overall behaviour was established in terms of interface strength (adherence), including incremental energy release rate and critical stress. Thus, this paper can be read as the first work towards the ability to predict the interface failure in the frame of three-point bending test using different geometries. In conclusion, the occurrence of an adhesive or cohesive failure and the unstable or a stable failure propagation of the bonded joints were sorted and classified as a function of interface properties.

This chapter deals with fracture mechanics of composites reinforced with short carbon and glass fibers. A short carbon fiber-reinforced polyamide 66 (SCFR-PA66) with 20 wt% fibers is introduced firstly. Then, dynamic fracture properties of the short glass fiber-reinforced polyamide 66 with 30 wt% of fibers (SGFR-PA66) are discussed. The influences of moisture on the fracture behavior of these materials are investigated through experimental studies. The impact properties of specimens are analyzed using a Charpy impact instrument. The fracture tests in the edgewise position of specimens are performed using Standard ISO 179. The results indicated that the moisture greatly affects the dynamic energy release rate of both materials. SGFR-PA66 has a higher dynamic energy release rate than SCFR-PA66. In addition, the dynamic energy release rate of both materials can be achieved at the same value when the moisture exceeds 2.4%. Finally, the fracture mechanism of SCFR-PA66 was investigated and analyzed. The energy release rate GIC of SCFR-PA66 was calculated to determine and predict the fracture properties of the material for the unidirectional short fiber composite.

The decrease of the apparent uniaxial tensile strength resulting from a single flawless spherical cavity in an infinite linear elastic continuum under uniaxial tension is investigated. To this end, a new generalized semianalytical expression for the stress intensity factor of an annular crack surrounding the spherical cavity under different loading conditions is proposed and validated. The apparent tensile strength is then estimated by four different approaches: two criteria implement a single condition, either on the stress field (Theory of Critical Distances) or on the energy release rate (equivalent Linear Elastic Fracture Mechanics), whereas the other two are stress-energy coupled criteria, namely the Finite Fracture Mechanics and the Cohesive Zone Model. Finally, theoretical predictions are discussed and compared with experimental data and atomistic simulations available in the literature, showing good correlation.

Effects of plastic constraint on the fracture of materials have been studied extensively. Often in such studies, the plastic constraint is divided into in-plane and out-of-plane directions and each treated separately. Such a separation adds considerable complexity to the engineering structural integrity assessment analyses. Despite previous suggestions for unifying the effects of constraint in a single parameter, the current engineering assessments have not been updated due to lack of direct experimental validation of such parameters. In this study, we directly measured the effects of in-plane and out-of-plane constraints, for the first time, in the form of plastic zone around the crack using advanced experimental techniques. The measurement of constraints in four specimens with different levels of in and out of plane constraints, allowed us to show and relate the interdependency of in and out of plane constraints. The tests were carried out using synchrotron X-ray tomography with in-situ loading. Attenuation contrast between the constituents of the metal matrix composite material used allowed the tomograms to be analysed using digital volume correlation which calculated the full-field displacement within the samples. The displacement fields were used via a finite element framework to calculate the energy release rate in the form of the J-integral along the crack fronts. The measured plastic zone sizes, dependant on the combined level of in plane and out of plane constraints, were used successfully to rank the J-Integral at fracture of the samples. It was therefore proved the level of plastic constraint can be quantified by using the size of the plastic zone as without separating it into two components thus simplifying the treatment of constraint in structural analyses significantly.

Made available in DSpace on 2019-10-04T18:54:24Z (GMT). No. of bitstreams: 0 Previous issue date: 2018-12-15 Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) Financiadora de Estudos e Projetos (FINEP), Brazil Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) This work focuses on Mode I fatigue induced delamination growth onset characterization of co-cured (CC), co-bonded (CB) and secondary bonded (SB) composite joints with an epoxy interleaf. The CC joints used in this work comprise only fibers and resin, while, CB and SB joints contain an adhesive film. Experimental tests were carried out at room temperature using double cantilever beam (DCB) specimens. The delamination behavior was evaluated in terms of the strain energy release rate (SERR) considering a no-growth criterion based on 10(6) cycles without crack propagation. For Mode I cyclic loading, the threshold values of the CB and SB joints were about 2.5 times higher than the one achieved by the CC joints, presenting a better performance in terms of fatigue delamination growth-onset. A fractographic study was conducted using scanning electron microscopy in order to relate the SERR results with the joint's failure mechanisms. It was observed that there is a good mechanical compatibility between the substrate and adhesive in the CB and SB joints studied herein. The results found in this paper indicated that the Mode I SERR threshold values were not significantly affected by the interleaf. (C) 2018 Elsevier Ltd. All rights reserved. Inst Tecnol Aeronaut, Div Engn Aeronaaut, BR-12228900 Sao Paulo, Brazil Fac Tecnol Sao Jose dos Campos, BR-12247014 Sao Paulo, Brazil Univ Estadual Paulista, Inst Ciencia & Tecnol, Dept Engn Ambiental, BR-12224300 Sao Paulo, Brazil Inst Pesquisas Tecnol, Lab Estruturas Leves, BR-12210131 Sao Paulo, Brazil Univ Estadual Paulista, Inst Ciencia & Tecnol, Dept Engn Ambiental, BR-12224300 Sao Paulo, Brazil CNPq: 301053/2016-2 Financiadora de Estudos e Projetos (FINEP), Brazil: 0114018300 FAPESP: 2015/16733-2 CAPES: 88887.126235/2016-00 CAPES: 88887.142318/2017-00

Mixed-mode bending (MMB) tests, together with double cantilever beam (DCB) and end-notched flexure (ENF) tests were conducted on Mongolian Scots pine to investigate the initial interlaminar fracture toughness of glued-laminated timber (glulam) under various mixed mode I/II conditions. By changing the loading lever location, a wide range of apparent ratios between mode I and mode II fracture were covered for MMB tests. Using the recorded critical load, interlaminar fracture toughness in terms of energy release rate was determined using compliance combination method (CCM), where the influence of growth ring orientations of adjacent laminae of glulam was highlighted. The results reveal the initial interlaminar fracture toughness was influenced by the growth ring orientation when mode II fracture component is larger. And an empirical power criterion was proven to be applicable to the mixed mode I/II interlaminar fracture toughness envelope of glulam. Keywords: Glulam, Interlaminar fracture, toughness, Growth ring orientation, Mixed-mode fracture

In macro-scaled plastic deformation, ductile fracture behaviors have been extensively investigated in terms of formation mechanism, deformation mechanics, influencing factors and fracture criteria. In micro-scaled plastic deformation, however, the fracture behaviors of materials are greatly different from those in macro-scale due to the existence of size effects. To explore the simultaneous interaction of size effect and stress condition on material fracture behavior in meso/micro-scaled plastic deformation, the tensile and compression tests of pure copper with various geometrical sizes and microstructures were conducted. The experiment results show that microvoids exist in compressed samples due to localization of shear band instead of macro fracture. Furthermore, the FE simulation is conducted by using the size dependent surface layer model, which aims to study the interaction of size effect and stress condition on material fracture behavior in multi-scaled plastic deformation. It is found that the stress triaxiality (T) generally increases with the ratio of surface grains η in compression statement. Fracture strain and fracture energy with positive T are much smaller than that with negative T regardless of geometrical and grain sizes. This research provides an in-depth understanding of the influences of size effect and stress condition on ductile fracture behavior in micro-scaled plastic deformation. Keywords: Size effect, Stress condition, Ductile fracture, Micro-scaled plastic deformation

Concepts to adjust the delamination behaviour of textile reinforced composites are investigated. The composite interfaces are modified by adjusting the interlaminar contact area using perforated PTFE-foils. According mode I and mode II energy release rates are determined and a progressive correlation between the interlaminar contact area and energy release rates is identified. The results are exploited within three point bending experiments to adapt the structural delamination and subsequent energy dissipation behaviour with the proposed interface modification concept. Two structural designs concepts are evaluated numerically: adjusting structural energy dissipation capacity and adjusting the peak levels as well as the characteristic trends of the structural reactive forces. It is demonstrated, that the mechanical response of composite structures can be tailored by controlling their delamination behaviour. Keywords: Delamination, Energy dissipation, Textile reinforcement, Composite, Energy release rate

1st Virtual European Conference on Fracture, In the design of adhesive structures, it is extremely important to accurately predict their strength and fracture properties (critical strain energy release rate in tension, GIC, and shear, GIIC). In most cases, the loads occur in mixed-mode (tension plus shear). Thus, it is of great importance the perception of fracture in these conditions, namely of the strain energy release rates in tension, GI, and shear, GII, relative to different crack propagation criteria or fracture envelopes. This comparison allows to determine the most suitable energetic propagation criterion to be used in cohesive zone models (CZM). The main objective of this work is to verify, by CZM, which is the power law parameter (α) that best suits the energetic crack propagation criterion for CZM modelling, using single-lap joints (SLJ) and double-lap joints (DLJ) with aluminium adherends and bonded with a ductile adhesive. With this purpose, numerical simulations of the SLJ and DLJ are carried out, and the maximum load (Pm) is compared with experiments. For the tested materials and geometries, the energetic criterion resulting from the experimental work provided matching numerical results and, thus, the fracture envelope was validated.

1st Virtual European Conference on Fracture, VECF1, online, 29 Jun 2020 - 1 Jul 2020; Procedia structural integrity 28, 1601-1620 (2020). doi:10.1016/j.prostr.2020.10.132 special issue: "1st Virtual European Conference on Fracture - VECF1 / Edited by Francesco Iacoviello, Aleksandar Sedmak, Liviu Marsavina, Bamber Blackman, Giuseppe Andrea Ferro, Valery Shlyannikov, Per St��hle, Zhiliang Zhang, Pedro M.G.P. Moreira, ��eljko Bo��ic, Leslie Banks-Sills", Published by Elsevier, Amsterdam

In this chapter, we provide three case studies for carrying out sensitivity analysis and uncertainty quantification (UQ) on mesoscale simulations. These three examples are focused on understanding the behavior of porous UO2, looking at grain growth and fracture simulations (using the phase field method) and effective thermal conductivity (using heat conduction simulations). UQ was also applied to mechanistic macroscale models that have been developed to predict the average grain size and the effective thermal conductivity. UQ and sensitivity analysis were carried out using the Dakota tool. The most sensitive parameters in the three areas were the grain boundary migration activation energy for the grain growth models, the thermal conductivity of bulk UO2 for the thermal conductivity models, and the UO2 energy release rate for the fracture model. In the future, the predicted simulation distributions need to be compared to experimental data for validation of the models.

A numerical and experimental study was performed to evaluate the critical strain energy release rate of wood under mode I loading (GIc), in the range of 30 C and 110 C. Pinus pinaster Ait. was employed as testing material, using the double cantilever beam (DCB) test, promoting fracture in the RL fracture sys- tem. The determination of Resistance-curves was accomplished using an equivalent crack length method, which does not require crack length measurement in the course of the experimental test. This aspect was found crucial since wood develops a non-negligible fracture process zone (FPZ) ahead of the crack tip, and the experiments required the use of a climate chamber with limited dimensions for visual access. It was observed that the critical energy release rate is affected by temperature within the referred range. Cohesive laws were also determined to replicate the experimental response as a function of the tested temperatures., The first author acknowledges FCT for the conceded financial support through the reference project UID/EEA/04436/2019. The second author acknowledges the ‘‘Laboratório Associado de Energia, Transportes e Aeronáutica” (LAETA) for the financial support by the project UID/EMS/50022/2013, and to the funding of Project NORTE-01-0145-FEDER-000022 – SciTech – Science and Technology for Competitive and Sustainable Industries, co-financed by Programa Operacional Regional do Norte (NORTE2020), through Fundo Europeu de Desenvolvimento Regional (FEDER).

Stress-induced self-separation is one of the most efficient process for preparing native GaN substrate. The control of GaN film thickness is the key point for GaN film separating from substrate completely. Considering the bowing of bilayer, we studied the radial stress in GaN film before separation. A shrunken circular delamination front model was proposed to derive the unrelaxed stress after separation, and the energy release rate for GaN/sapphire systems of different thicknesses was investigated during the whole separation process. A critical thickness about 500–700 μm was determined for separating 2-inch (5.08 cm) GaN film from a sapphire substrate. By precisely controlling the GaN film thickness around such critical thickness, the complete separation rate could be increased greatly to 74%, which is of great importance in realizing the industrialization of GaN substrate. Keywords: GaN, Stress-induced self-separation, Bilayer thick film, Residual stress, Fracture

Obreimoff reported his first instrumented measurements of the cleavage of muscovite mica in 1930 and that work helped to propel a greater understanding of fracture. This study builds upon that effort by investigating the role of compliance heterogeneities in brittle materials through mica splitting in a manner similar to Obreimoff. The natural layered structure of mica makes it ideal as a model system for studying fracture as crack propagation can be constrained along a single controlled cleavage plane. Cleavage through the insertion of a rounded wedge provides a straightforward mechanical setup that produces stable crack propagation, so long as the effects of friction and wedge geometry are properly considered. First, homogeneous mica sheets of uniform thickness are cleaved in ambient atmosphere to establish a baseline splitting force and critical strain energy release rate, similar Obreimoff’s original work. After establishing this baseline, mica sheets with prescribed thickness heterogeneities are investigated. It is found that the splitting force required to propagate a crack along a specimen with a sharp increase in layer thickness is significantly larger than the analogous homogeneous splitting forces, even though the crack is not deflected. This indicates that a sharp increase in stiffness can produce an increase in toughness in layered structures without the need for any actual toughness contrast between constituent components or any crack deflection. This toughening effect produced by compliance contrast may have implications in the context of layered ceramic composite design, where systems are often composed of a stiff outer shell and a more compliant and damage-tolerant functional layer.

In-situ fracture tests were carried out on the I12 beamline at the Diamond Light Source. Four Al-Ti metal-matrix composites (MMCs), with varying combinations of thickness and crack length, were studied to assess for the impact of in-plane and out-of-plane constraint. Synchrotron X-ray computed tomography and synchrotron X-ray diffraction were used to measure total strain and elastic strain respectively. The total strain was calculated via digital volume correlation, with Ti particles within the MMC providing sufficient texture to track the internal displacement vectors in 3D. The total, elastic-plastic strain energy release rate, J total was calculated from 2D slices extracted from the 3D displacement field, with J total reaching a maximum value at the sample surface. It is, however, still unclear whether calculating J total on a slice-by-slice basis provides an accurate representation of strain energy release rate across the crack front; techniques to evaluate the J-integral from the full 3D displacement field are being developed.

The effect of residual stress on the delamination behaviour of thin films is examined under four-point bending. Elastic film-substrate systems with and without the addition of a superlayer are analysed by constructing closed-form expressions for the energy release rate at steady-state delamination. The analytical results obtained with these expressions are compared to finite element results based on cohesive zone modelling, showing an excellentagreement. The closed-form expressions correctly reduce to simpler forms for film-substrate systems without residual stresses, and further include the special case of spontaneous delamination under the presence of a critical residual stress only. The closed-form expression for the elastic film-substrate system without a superlayer is used for indicating errors in alternative analytical expressions presented in the literature. Subsequently, the contribution of substrate plasticity to the delamination resistance is studied by means offinite element analyses for a range of (relative) film thicknesses and various values of the (relative) interfacial strength. For a compressive residual stress the delamination response typically is characterised by a transition from large scale yielding to small scale yielding under increasing film thickness, while for a tensile residual stress the limit of small scale yielding may not be reached at large film thickness when the interfacial strength is relatively high. Furthermore, stress relaxation induced by large scale yielding diminishes theinfluence of the residual stress on the delamination resistance under bending.

This paper investigates the energy release rate (ERR) in Mode II in-plane shear during delamination propagation under quasi-static and cyclic fatigue fracture loading with the 4-point end notched flexure (4-ENF) fracture test specimen. Wood joints bonded with three different adhesives, one rather brittle phenol resorcinol formaldehyde (PRF) and two different one component polyurethane (1C-PUR) adhesives with relatively low modulus of elasticity were tested in order to investigate the influence of the adhesive properties on the damage propagation under quasi-static and cyclic fatigue loading. A simple reduction method based on the specimens’ compliance was used to calculate the crack growth and the energy release rate during the test. Additionally, an automated analysis method was developed estimating the energy of crack initiation from quasi-static test results. This shall avoid introducing additional scatter due to operator-dependent, manual analysis. It was shown that the three tested adhesives are displaying similar ERR values under quasi-static loading. Under cyclic fatigue fracture loading, the more brittle PRF samples are showing a slower crack growth rate for similar energy release rate in comparison with the 1C-PUR adhesives. The proposed testing method, applied to adhesively bonded wood joints, has been shown to give satisfactory results. This can be used for the development of new adhesives with increased performance regarding fatigue delamination growth. The automated data analysis has potential for application on other materials under cyclic Mode II fatigue fracture loads.

Cohesive zone modelling (CZM) is widely used for predicting the strength of adhesive joints. The key variable for crack path modelling is the critical strain energy release rate (GC), which can be separated into the tensile (GIC) and shear (GIIC) components. In shear, the End Notched Flexure (ENF) test is widespread. However, other test methods exist and could be a viable replacement. This work aims to make a numerical evaluation between the ENF and Four-Point End Notched Flexure (4ENF) tests to determine GIIC of a ductile adhesive (SikaForce® 7752) and to provide shear CZM laws for further application in design. An inverse technique was used to obtain the shear CZM laws of the adhesive. It was concluded that the GIIC values obtained by the ENF and 4ENF tests are in good agreement. The numerical analysis led to unique shear CZM laws for both tests, with similar results.

An approximate solution is derived for the interfacial energy release rate of the inverted four-point bending test. The analysis builds on a previous model developed by one of the authors for an orthotropic edge-cracked layer subject to arbitrary generalized end forces. Contact forces exerted from the upper on the lower layer of the edge-cracked portion behind the delamination tip are introduced. Their value is chosen such that the two layers undergo the same deflection. The effects of both shear deformations along the layers and friction at the point of contact are taken into account within beam theories and approximate Coulomb model with a prescribed friction coefficient. The delamination energy release rate is derived for homogeneous and symmetric specimens. A parametric analysis is performed on varying the mechanical parameters of the model to analize the influence of shear deformations and friction. The results show that both shear deformations and friction affect the value of the energy release rate for short/intermediate interfacial cracks. For very long interfacial cracks the delamination energy release rate tends to a constant limit value which corresponds to that obtained within classical Euler-Bernoulli beam theory in absence of friction.

The dielectric breakdown strength of borosilicate glass was measured as a function of the length of a conducting filament in order to determine the critical energy release for the growth of a breakdown channel. The concept is similar to the experimental determination of the toughness in fracture mechanics and based on a Griffith type model for the electrical energy release rate in dielectric materials with space charge limited conductivity. By Focused-Ion-Beam-milling and Pt-deposition, up to 100 μm long conductive channels were fabricated in 163 μm thick borosilicate glass substrates. The dielectric breakdown strength of substrates with filaments longer than 30 μm could be very well described by a 1 f i l a m e n t l e n g t h -dependence predicted by the model Schneider, 2013. With these results for the first time a critical energy release rate for dielectric breakdown was determined being 6.30 ± 0.95 mJ/m.

In order to successfully model design-critical impact loading events on laminated composite structures, the rate-dependency of the composite material has to be correctly reflected. In this context, the rate-dependency of the strain-energy release rate for fibre tensile failure under high-rate loading conditions has not yet been satisfyingly explored. This study employed compact tension specimens consisting of IM7/8552 for dynamic testing on a split-Hopkinson tension bar system. Data reduction was based on the area method. The obtained strain-energy release rate for testing under high-rate conditions was determined to G I c , d y n f + = 82.0 ± 20.8 k J / m 2 , exhibiting a salient drop compared to its counterpart obtained under quasi-static loading ( G I c , Q S f + = 195.8 ± 18.0 k J / m 2 ). Analysis of the strain field surrounding the crack tip using digital image correlation (DIC) suggested a more extensive damage zone for testing under quasi-static than for high-rate loading. A fractographic analysis of the specimens did not indicate any pronounced difference in terms of fracture surface morphology across the two loading rate regimes.

This study presents two alternative methods to determine the cohesive law of bovine cortical bone under mode II loading, employing the End Notched Flexure (ENF) test. The direct method results from the combination of the progress of the mode II strain energy release rate with the crack tip shear displacement, obtained by digital image correlation. The resulting cohesive law is determined by differentiation of this relation relatively to the crack shear displacement. The inverse method employs finite element analyses with cohesive zone modelling, in association with an optimization procedure. The resulting strategy enables determining the cohesive law without establishing a pre-defined shape. The significant conclusion that comes out of this work is that both methods offer consistent results regarding the estimation of the cohesive law in bone. Given that the inverse method dispenses the use of sophisticated equipment to obtain the cohesive law in bone, it can be used as a more convenient procedure to accomplish efficient studies in the context of bone fracture characterization under mode II loading., The authors acknowledge the Portuguese Foundation for Science and Technology (FCT) for the conceded financial support through the research project PTDC/EME-PME/119093/2010 and through grant no. SFRH/BD/80046/2011. The second author acknowledges the "Laboratorio Associado de Energia, Transportes e Aeronautica" (LAETA) for the financial support by the project UID/EMS/50022/2013. The third author acknowledges FCT for the conceded financial support through the reference project UID/EEA/04436/2013, COMPETE 2020 with the code POCI-01-0145-FEDER-006941.All other authors acknowledges the European Investment Funds by FEDER/COMPETE/POCI- Operacional Competitiveness and Internacionalization Programme, under Project POCI-01-0145-FEDER-006958 and National Funds by FCT - Portuguese Foundation for Science and Technology, under the project UID/AGR/04033/2013.

Intralaminar cracking in layers of multidirectional laminates lead to reduced ability of these layers to carry load which is the reason for damaged laminate thermo-elastic properties reduction. The average stress reduction in the damaged layer is uniquely linked with displacements of the crack faces and, therefore, the crack opening displacements (CODs) and the crack face sliding displacements (CSDs) are alternative descriptors in damaged laminate stiffness predictions. In this chapter, exact closed form relationships are established linking thermo-elastic constants of the damaged laminate with crack density in layers and local parameters of the crack (average normalized COD and CSD). These robust local parameters depend on surrounding and damaged layer stiffness and thickness ratio-relationship, which is investigated numerically and described by simple fitting functions. It is also shown that the energy release rate (ERR) for propagation of the intralaminar crack in steady-state conditions has simple expression through the COD and CSD, leading to simple predictive tool for thin ply laminates where the cracking is propagation controlled.

Electrospun polyacrylonitrile (PAN) nanofibers were incorporated in an epoxy-based adhesive layer to improve the adhesive joint’s mechanical performance. The morphological study of the electrospun PAN nanofibers revealed that the fabricated nanofibers were smooth, continuous, and without beads. The average diameter of the nanofibers was determined to be 362 ± 87 nm. The Double Cantilever Beam (DCB) specimens were tested and the fracture energies were determined for the unreinforced and reinforced adhesives. The outstanding reinforcing capability of PAN nanofibers was demonstrated by significant improvements in fracture energy of the adhesive containing PAN nanofibers. A maximum improvement of 127% in the mode I fracture energy of adhesive was achieved by incorporating 2 g/m2 of PAN nanofibers into the adhesive layer. Moreover, the morphology of the fracture surfaces was examined using the Scanning Electron Microscopy (SEM) technique to evaluate the toughening mechanisms resulting from this improvement. This is a submitted manuscript of an article published by Elsevier Ltd in Theoretical and applied fracture mechanics, 26 July 2017.

The present chapter presents an analysis of the effects of cracks and delaminations on the strength of laminated fiber composites using the principles of fracture mechanics. Study of the various failure mechanisms (fiber breaks, matrix cracks, and interface debonds) during a progressively increasing load is not considered in this chapter. First, the strength of composites with through-thickness cracks is studied by fracture mechanics approach. Using effective modulus theory the heterogeneous, anisotropic fiber composite material is replaced by a homogeneous anisotropic elastic material. The equations for the stress components for an anisotropic elastic material are presented and the stain energy release rate is determined. Next, the problem of interlaminar cracking or delamination of laminated composites is studied. If the laminated structure carries bending loads delamination may cause severe loss of its bending strength and stiffness. The same happens in compression since the composite may buckle due to reduction of its bending stiffness. Delamination can occur under all three basic modes of crack growth, that is, under mode I, mode II and mode III or under combinations thereof. In this chapter delamination is studied under mode I, mode II, mode III and mixed-mode I and II loading.

Shaat, M., Aidi, B., Case, S. W., & Abdelkefi, A. (2017). Predictions of the frequencies of bending-torsion coupled laminated composite plates with discontinuities: Novel analytical modeling and experimental validation. Composite Structures, 180, 334-350., A novel analytical model that accurately represents the free vibration response of intact/damaged composite plates accounting for the bending-torsional coupling is developed. Unlike the existing models for the bending-torsion vibrations of composite plates, in the present model, the equations of motion are derived in an uncoupled form. It is then easier to derive analytical solutions for composite plates under coupled bending-torsion vibrations. In addition, for the first time, analytical solutions for the free bending and torsional vibrations of cantilever and clamped-clamped laminated composite plates with discontinuities including circular holes, rectangular holes, notches, and internal and edge cracks are easily obtained. Shifts in the natural frequencies due to discontinuities are modeled where the reductions in the plate stiffnesses are related to the amount of the energy release rate due to a defect formation. In order to verify the accuracy of the proposed model and the derived solutions, the proposed model is compared to the available conventional models. Moreover, experimental measurements of the free bending and torsional vibrations of carbon-fiber-laminated composite plates with circular holes is performed. A set of finite element analyses are carried out and compared to the experimental and the proposed model results. Then, a parametric study is presented in order to investigate the effects of the discontinuity size and location on the bending and torsional natural frequencies of laminated composite plates with various forms of discontinuities. The performed analyses demonstrate the accuracy of the proposed models to represent the free vibrations of laminated composite plates with discontinuities.

In the present work the interaction of a finite-length crack with a discrete climb dislocation is studied within the framework of the generalized continuum theory of couple-stress elasticity. The climb dislocation is placed on the crack plane resulting in an opening crack mode. For the solution of the crack problem the distributed dislocation technique is employed. Due to the nature of the boundary conditions that arise in couple-stress elasticity, the crack is modeled by a continuous distribution of translational and rotational defects. The distribution of these defects produces both stresses and couple stresses in the body. It is shown that the interaction problem is governed by a system of coupled singular integral equations with both Cauchy and logarithmic kernels which is solved numerically using an appropriate collocation technique. The results for the near-tip fields differ in several respects from the predictions of classical fracture mechanics. It is shown that a cracked couple-stress solid behaves in a more rigid way compared to one governed by classical elasticity. Moreover, the evaluation of the energy release rate in the crack-tips and the associated driving force exerted on the dislocation reveals an interesting ‘alternating’ behavior between strengthening and weakening of the crack, depending on the distance of the crack-tip to the dislocation core as well as on ratio of the material length, introduced by the couple-stress theory, to the length of the crack.

International audience; The aim of this work is to increase the study of the notch translaminar propagation of the woven structures, using the InfraRed Thermography (IRT). A test of notch propagation under quasi-static traction was developed and used to study the failure phenomena on two different draping sequences. For each study, a local estimation of dissipated energies, associated with different damages, is carried out using the measurement of the surface temperature field. The study of heat source fields combined with micrographic observations allowed to define the matrix micro-cracking as the predominant damage phenomenon in crack tip. The critical energy release rate, obtained using IRT, corresponds to critical energy release rate reported in the literature for translaminar rupture of laminates. Furthermore, when brittle cracking develops in a thermosetting matrix laminate, the majority of irreversible mechanical energy (>90%) is dissipated as heat. In the case of brittle cracking, the developed method proves to be an efficient alternative technique for the local measure of energy release rate, even in cases where the variations in stiffness due to cracking phenomena remain low.

This work addresses the determination of the cohesive law under mode I loading of bovine cortical bone tissue using the Double Cantilever Beam (DCB) test. Direct and inverse methods were proposed to assess the cohesive laws representative of bone fracture under mode I loading. The direct method combines the evolution of the strain energy release rate under mode I loading with the crack tip opening displacement that is monitored by digital image correlation technique. According to this method, the cohesive law is obtained by differentiation of such relation with respect to the crack opening. The inverse procedure is performed through a finite element analysis including cohesive zone modelling, conjointly with a devel- oped optimization algorithm. This identification strategy does not require a pre-established shape of the cohesive law as with the conventional inverse based procedures, which is viewed as a novelty of this work. It was concluded that both methods provide consistent results, being appellative tools concerning systematic and methodical studies dedicated to bone fracture characterization., The authors acknowledge the Portuguese Foundation for Science and Technology (FCT) for the conceded financial support through the research project PTDC/EME-PME/119093/2010 through grant no. SFRH/BD/80046/2011 and European investment funds by FEDER/COMPETE/POCI - Operacional Competitiveness and Internacionalization Programme, under Project POCI-01-0145-FEDER-006958 and National Funds by FCT - Portuguese Foundation for Science and Technology, under the project UID/AGR/04033/2013. This work is also supported by FCT with the reference project UID/EEA/04436/2013, COMPETE 2020 with the code POCI-01-0145-FEDER-006941., info:eu-repo/semantics/publishedVersion

The strength of materials containing flaws and cracks, such as cortical bone, cannot be completely described by strength-based criteria. A material's mechanical load-bearing capacity is a function of loading conditions, flaw size, and the material's fracture toughness. For a through-thickness crack in a large plate of isotropic, linear elastic material, the crack growth driving force is , where G is strain energy release rate per increment of crack growth (d U /d a ), is applied stress, a is crack length, and E is Young's modulus. A crack will grow when G exceeds the material's fracture toughness G c . Because cortical bone demonstrates non-negligible irreversible deformation before fracture, it violates linear elastic fracture mechanics (LEFM) assumptions. Consequently, fracture toughness is better described by the J -integral, which quantifies a strain energy release rate, like G , but it accounts for the energy absorbed by irreversible deformation at and around the crack tip. Therefore, this chapter explains how to perform fracture toughness tests on cortical bone, as well as how to analyze, present, and interpret results.

Concrete is a so called quasibrittle material which, despite predominantly elastic material response, exhibits in tension loading a stable non-linear fracture response, when tested under displacement control. The reason for the non-linearity is the development of a fracture process zone, in front of the crack, due to micro-cracking and crack bridging. The effect of the fracture process zone is to make the specimen sense the crack as being longer than a0 + Δa. The fracture process zone causes thus an effective increase in the crack driving force and apparent fracture resistance. Here, a novel LEFM based estimate of the effective stress intensity factor and the effective crack growth at maximum load in a fracture mechanics test is used to obtain a simple power law approximation of the effective K–R curve. It is shown that it is applicable to the description of not only different size specimens, but also specimens with varying geometry. The method is based on a new theoretical estimate of the effective crack growth corresponding to maximum load.

Moisture-induced buckle delamination of thin inorganic layers on a polymer substrate was studied. Moisture has been found to have a significant effect on the failure mode. Experimentally, an increase in the buckle width, height and the total buckle delamination length with time and humidity was observed. Moreover, a transition from straight to telephone-cord buckle pattern was taken place in a humid environment. Applying only a uniaxial compressive strain on the thin layers did not result in the transition from straight to telephone-cord. For a compliant substrate the transition from straight to telephone-cord buckle occurred at significantly higher ratio of residual strain over critical buckling strain than for a rigid substrate. A simple model for buckling was applied. Using the energy release rate, the interfacial toughness was investigated as a function of relative humidity.

International audience; In this paper, the main results obtained in the framework of a National French Agency project called DISFAT, standing for “Dissipation in Fatigue”, are presented. The project was dedicated to the microplastic mechanisms leading to crack initiation in the case of ductile metals loaded in very high cycle fatigue. Fatigue tests were carried out at 20 kHz using an ultrasonic facility. In order to investigate the microplastic mechanisms, slip markings at the surface of the specimens were observed and the self-heating of the specimen during the tests was measured by thermography to deduce the dissipated energy. Polycrystalline copper, α-brass and α-iron were investigated. A good correlation was found between persistent slip bands and dissipated energy. The dissipated energy for the three materials was of the same order of magnitude but while α-iron reached a stable dissipative state, the dissipated energy in the case of copper and α-brass was found to continue to increase gradually with increasing numbers of cycles. That change in dissipated energy during cycling was consistent with the development of persistent slip bands. Both were discussed with regard to the materials.

This article starts by reviewing elastic, elastoplastic, and plastic fracture in the light of the overall size of the crack-tip plastic zone relative to the dimensions of the crack. The morphologies of the surfaces and the relative magnitudes of the reversible elastic strain energy, irreversible work of fracture, and irreversible work of remote plastic flow are also discussed. Then, presentation focuses on sheet metal forming, where remote plastic flow predominates and imposes extensive irreversible deformation prior to cracking, in order to establish a correlation between fracture, critical damage, and crack opening modes. The final part covers the experimental procedures to determine fracture toughness and provides examples where crack propagation is necessary or catastrophic.

A comprehensive review of the most common or recently developed failure criteria for composites and adhesive is delineated in this chapter. The review provides a basis for the future discussion and application of these criteria to the evaluations of the static strength and damage tolerance of bonded repairs or bonded joints in composite airframe structures.

The propagation of fiber–matrix interfacial debonding under axial loading is analyzed, using the single-fiber fragmentation test as a reference, in order to determine fiber–matrix failure properties. A data reduction technique is presented in which the fiber–matrix Mode II interfacial fracture toughness is obtained from the measurements of the average debond crack growth. A set of boundary element models are employed to evaluate the energy release rate associated with interfacial crack propagation. The interfacial friction coefficient is parametrically varied until a constant value of the energy release rate (which is then equal to the fiber–matrix Mode II interfacial fracture toughness) is obtained. The applicability of the properties evaluated is demonstrated using a set of finite element models with cohesive elements.

Circular hollow sections have evolved to be a primary choice for the fixed type offshore structures (namely jackets) and the mobile type offshore platforms (jack-ups), due to its appealing characteristics in minimizing the wave forces and structural efficiency in resisting various loading conditions. This chapter highlights the recent developments in the failure analysis of welded tubular joints, covering the evaluation of the crack driving forces, the damage mechanics representation of the fracture process in tubular joints, failure assessment procedures, scaling of the material fracture resistance to the tubular joint level, and subsequently to the global structural level.

The continuous development observed in bonded joints, along with the improvements of the adhesives’ properties, are resulting in an increase of the bonded joint applications, as well as the variety of applications. Regarding the strength prediction of adhesive joints, two highly relevant methods are Fracture Mechanics and Cohesive Zone Models (CZM). By Fracture Mechanics, this is usually carried out by an energetic analysis. CZM enable the simulation of damage initiation and propagation. The tensile critical strain energy release rate ( G Ic ) of adhesives is one of the most important parameters for predicting the joint strength. Two of the most commonly used tests are the Double-Cantilever Beam (DCB) and the Tapered Double-Cantilever Beam (TDCB). This work aims to assess the capability of the DCB and TDCB test to estimate the value of G Ic of adhesive joints. Three types of adhesives with different levels of ductility are used, to study the accuracy of the typical data reduction methods under conditions that are not always consistent with Linear Elastic Fracture Mechanics (LEFM) principles. For both test protocols, methods that do not require measurement of the crack length ( a ) during the test are evaluated. In the DCB test, these are the Compliance Calibration Method (CCM), Corrected Beam Theory (CBT) and Compliance-Based Beam Method (CBBM). The methods used in the TDCB test are the Simple Beam Theory (SBT), CCM and CBT. With few exceptions, the results were consistent between the different methods considered for each test. The discrepancy of results is higher when comparing the two types of tests, except for the brittle adhesive. It was concluded that the data reduction methods for the TDCB test are too conservative to measure G Ic of ductile adhesives.

Fiber–matrix interface debonding initiated from random fiber breaks is known to be one of the key damage mechanisms in unidirectional (UD) composites subjected to quasi-static and cyclic (fatigue) loading. Growth of fiber–matrix interface debonds leads to stiffness reduction and eventually to the final failure of the UD composite through coalescence of multiple debond cracks. This chapter overviews the current state of the art in modeling fiber–matrix interface debonding in UD composites. The methods reviewed in this chapter are based on fracture mechanics principles of the energy release rate. Analytical models for steady-state debond growth are presented. Finite-element method (FEM) based models for analyzing the growth of short debonds and the effects of edges and neighboring fibers are also presented.

This chapter presents a damage tolerance analysis approach for ensuring scarf repairs can meet the required damage tolerance and fatigue durability requirements in the presence of disbond. Both the static strength and fatigue endurance of scarf joints are strongly influenced by the length of initial disband length. Facture mechanics approaches, the virtual crack closure, and the cohesive element method, are presented to capture the strain energy release rate of bond line flaws. The predictive model using the cohesive element model offers a robust technique to account for the effect of disbond on the ultimate strength of scarf joints and repairs. The fatigue life of adhesively bonded composite scarf joints with disbands is shown to be well predicted by a crack growth model. Together these analysis methods provide the necessary tools for meeting the no-growth or slow-growth design requirement.

A new interfacial fracture test method was developed for measuring the mixed-mode interfacial fracture toughness of thermal barrier coated material over a wide range of loading phase angles. The principle of this developed method is based on peeling the coating from the substrate due to compressive loading to the coating edge, as forming a shear loading to the interface, and slinging loading such as beam bending, as normal loading to the interface. The complete closed form of the energy release rate and associated complex stress intensity factor for our testing method is shown. An yttria stabilized zirconia (YSZ) coating, which was sprayed thermally on Ni-based superalloy, was tested using the testing device developed here. The results showed that the energy release rate for the coating-interfacial crack increased with loading phase angle, which is defined by tan−1 for a ratio of stress intensity factor K2 to K1. It was noticed that the interfacial energy release rate increasing with mode II loading could be mainly associated with the contact shielding effect due to crack surface roughness rubbing together.

In this paper, fatigue life estimation for delamination growth of laminated fibre reinforced polymer (FRP) composite structures in mode I and mode II based on fracture mechanics is presented. The proposed method was applied to delamination of glass/epoxy laminated composite. Both the threshold energy release rate (Gth) and the delamination propagation based on Paris’ law were studied. The double cantilever beam (DCB) specimen for mode I and 3 points End-Notched Flexure (3ENF) specimen for mode II were used for monotonic fracture tests and the resistance GIR and GIIR as a function of delamination length were determined. For DCB tests, the fatigue onset life test was conducted and the threshold energy release rate, GIth, was found for the subcritical region. Constant amplitude, displacement controlled cyclic fatigue test for both modes was conducted and the delamination crack growth rate (da/dN) as a function of maximum cyclic energy release rate GImax and GIImax for DCB and 3ENF specimens were determined, respectively. From curve fitting to the experimental data, the Paris’ law material constants C and m for mode I and mode II were obtained. Finally, the SEM fractography studies of delaminated surfaces of 3ENF static and fatigued specimens have been done and the different features observed on these surfaces were discussed.

The failure process of composite laminate under quasi-static or fatigue loading involves sequential accumulation of intra- and interlaminar cracking. Matrix cracking parallel to the fibres in the off-axis plies is the first damage mode observed. It triggers development of other harmful resin-dominated modes such as delaminations. In this chapter, analytical modelling of crack-induced delaminations in composite laminates subjected to general in-plane loading is presented and discussed. A two-dimensional shear lag analysis is used to determine ply stresses in a representative segment and the equivalent laminate concept is applied to derive expressions for mode I and mode II and the total strain energy release rate associated with uniform local delaminations. These expressions could be used with appropriate fracture criteria to estimate the onset of local delamination in an already cracked off-axis laminate. Dependence of strain energy release rate on crack density, delamination area and ply orientation angle in unbalanced symmetric laminates is examined and discussed, and the effect of crack-induced delamination on the laminate stiffness is predicted.

Intralaminar cracking in layers of laminates subjected to thermo-mechanical loading is analysed in this chapter. The prediction of the damage initiation and development is a very complex task, much more difficult than prediction of the damage effect on thermo-elastic properties. Simulation tools are still in the development stage and therefore the methodology and analysis methods suggested in this chapter (strength-based statistical approach to initiation of intralaminar cracks, experimental procedure for parameter determination in the model, crack propagation description using fracture mechanics) should be considered as one of the options that require experimental validation. If successful, this approach can be used for damage prediction in quasi-static as well as tension–tension fatigue loading.

The 3-D fracture model (GY) has been developed under the sponsorship of the Stimulation, Logging, and Formation Damage Research Program at the University of Texas at Austin. Recently, the mesh generation scheme in the code was modified to accommodate the growth of a hydraulic fracture in a complex distribution of in-situ stresses. The code was renamed the GYCO-1. The code was developed for internal use on hydraulic fracturing research and for the use of sponsoring industrial members. The propagation of a hydraulically induced fracture is approximated by the incremental process. Assume that the fracture is temporarily arrested by the fracture toughness (K IC ) or by the in-situ stress contrast. The front of the fracture is assumed to be stationary for a short time period. During this time period, the frac-fluid is pumped into the fracture causing the fluid pressure, fracture width, and stress intensity factor at the front to increase. The fracture front moves outward by a short distance when the stress intensity factor exceeds the fracture toughness. This distance is determined by the difference between the calculated stress intensity factor K I and the critical stress intensity factor of the rock medium.

From the mechanical design viewpoint, the inherent brittleness of thermosetting polymeric systems is a major disadvantage that limits their extensive applications. Micro- and nanoparticles incorporated into polymeric systems increase the toughness and enhance the fracture performance of such materials. This chapter first provides an overview of fracture toughness parameters based on the stress intensity factor and energy release rate. Then a review of the most common toughening techniques is presented, and the latest efforts to improve the toughness of brittle polymer matrices by means of different micro- and nanosized particles are introduced. Furthermore, research on the most important toughening mechanisms of nanoparticle-reinforced polymers, such as crack pinning, microcracks, crack deflection, crack bridging, plastic deformation, and plastic void growth is reviewed. The dependence of each mechanism on both the geometrical and mechanical properties of reinforcing particles is discussed. Finally, the key points in achieving optimum fracture toughness and mechanical properties of nanoparticle-reinforced polymeric resins are presented.