Academic literature on the topic 'Quasi static crack growth'

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Journal articles on the topic "Quasi static crack growth"

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Pavelko, Vitalijs. "On the Crack Quasi-Static Growth." Key Engineering Materials 827 (December 2019): 312–17. http://dx.doi.org/10.4028/www.scientific.net/kem.827.312.

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The theoretical model of quasi-static crack growth in the elastic-plastic material under load variation in a wide range. Small-scale yielding is principal assumption and main restriction of proposed theory. The model of crack growth provides for continues and interrelated both the crack propagation and plastic deformation development. The nonlinear first-order differential equation describes the quasi-static process of crack growth. In dimensionless form this equation invariant in respect to geometrical configuration and material. The critical size of the plastic zone is proposed as the characteristics of material resistance which is directly connected with the fracture toughness, but more convenient in practical applications of invariant equation. The demonstration of solution is performed for the double cantilever beam that widely used as the standard (DCB) sample for measurement of the mode-I interlaminar fracture toughness. he short analysis of some properties of solution of the invariant equation and its application is done.
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Csomós, Zilia, and János Lukács. "Fatigue Crack Growth Tests on Glass Fibre Reinforced Polymer Matrix Composite." Materials Science Forum 473-474 (January 2005): 189–94. http://dx.doi.org/10.4028/www.scientific.net/msf.473-474.189.

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E-glass fibre reinforced polyester matrix composite was investigated, which was made by pullwinding process. Round three point bending (RTPB) specimens were tested under quasi-static and mode I cyclic loading conditions. Load vs. displacement (F-f), load vs. crack opening displacement (F-v) and crack opening displacement range vs. number of cycles (ΔCOD-N) curves were registered and analysed. Interfacial cracks were caused the final longitudinal fracture of the specimens under quasi-static and cyclic loading conditions.
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Almi, Stefano, Gianni Dal Maso, and Rodica Toader. "Quasi-static crack growth in hydraulic fracture." Nonlinear Analysis: Theory, Methods & Applications 109 (November 2014): 301–18. http://dx.doi.org/10.1016/j.na.2014.07.009.

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Goleniewski, G. "Quasi-static crack growth in viscoelastic materials." Journal of the Mechanics and Physics of Solids 38, no. 3 (January 1990): 361–78. http://dx.doi.org/10.1016/0022-5096(90)90004-n.

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Alshoaibi, Abdulnaser M., and Yahya Ali Fageehi. "Simulation of Quasi-Static Crack Propagation by Adaptive Finite Element Method." Metals 11, no. 1 (January 6, 2021): 98. http://dx.doi.org/10.3390/met11010098.

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The finite element method (FEM) is a widely used technique in research, including but not restricted to the growth of cracks in engineering applications. However, failure to use fine meshes poses problems in modeling the singular stress field around the crack tip in the singular element region. This work aims at using the original source code program by Visual FORTRAN language to predict the crack propagation and fatigue lifetime using the adaptive dens mesh finite element method. This developed program involves the adaptive mesh generator according to the advancing front method as well as both the pre-processing and post-processing for the crack growth simulation under linear elastic fracture mechanics theory. The stress state at a crack tip is characterized by the stress intensity factor associated with the rate of crack growth. The quarter-point singular elements are constructed around the crack tip to accurately represent the singularity of this region. Under linear elastic fracture mechanics (LEFM) with an assumption in various configurations, the Paris law model was employed to evaluate mixed-mode fatigue life for two specimens under constant amplitude loading. The framework includes a progressive analysis of the stress intensity factors (SIFs), the direction of crack growth, and the estimation of fatigue life. The results of the analysis are consistent with other experimental and numerical studies in the literature for the prediction of the fatigue crack growth trajectories as well as the calculation of stress intensity factors.
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Schneider, Jens, and Jonas Hilcken. "Cyclical fatigue of annealed and of thermally tempered soda-lime-silica glass." MATEC Web of Conferences 165 (2018): 18003. http://dx.doi.org/10.1051/matecconf/201816518003.

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We present experimental and theoretical investigations on the cyclic fatigue of annealed and of thermally tempered soda-lime-silica glass. Static fatigue due to subcritical crack growth at micro cracks significantly decreases the macroscopic strength of soda-lime-silica glass and causes a time-dependent strength reduction. A subsequent thermal tempering process is typically used to induce residual surface compression stresses, which inhibit the crack growth of surface cracks, and corresponding bulk tension stresses. From the experimental results we show that the existing models for static fatigue used in linear elastic fracture mechanics can be used for the lifetime prediction of cyclically loaded annealed glass and thermally tempered glass, although the (static) crack growth exponent slightly decreases in cyclic loading. The equivalent duration of tensile stress at the crack tip of a micro crack governs the crack growths and not the number of cycles. The threshold for subcritical crack growth determined from the cyclic experiments was found to be in good agreement with data from literature. But unlike in strength tests with singular and quasi-static re-loading, it could be found that periodic loading with load free intervals does not lead to a strength increase by crack healing effects. Based on the results, an engineering design concept for cyclically loaded glass is presented.
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Judt, P., and Andreas Ricoeur. "Quasi-Static Simulation of Crack Growth in Elastic Materials Considering Internal Boundaries and Interfaces." Key Engineering Materials 525-526 (November 2012): 181–84. http://dx.doi.org/10.4028/www.scientific.net/kem.525-526.181.

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This work presents numerical methods used for predicting crack paths in technicalstructures based on the theory of linear elastic fracture mechanics. The FE-method is usedin combination with an efficient remeshing algorithm to simulate crack growth. A post pro-cessor providing loading parameters such as the J-integral and stress intensity factors (SIF) ispresented. Path-independent contour integrals are used to avoid special requirements concern-ing crack tip meshing and to enable efficient calculations for domains including interfaces andinternal boundaries. In particular, the interaction of cracks and internal boundaries and inter-faces is investigated. The simulation combines crack propagation within elastic bodies and atbi-material interfaces. The latter is based on a cohesive zone model. The presented numericalresults of crack paths are verified by experiments.
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Almi, Stefano. "Quasi-static hydraulic crack growth driven by Darcy’s law." Advances in Calculus of Variations 11, no. 2 (April 1, 2018): 161–91. http://dx.doi.org/10.1515/acv-2016-0029.

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AbstractIn the framework of rate independent processes, we present a variational model of quasi-static crack growth in hydraulic fracture. We first introduce the energy functional and study the equilibrium conditions of an unbounded linearly elastic body subject to a remote strain {\epsilon\in\mathbb{R}} and with a sufficiently regular crack Γ filled by a volume V of incompressible fluid. In particular, we are able to find the pressure p of the fluid inside the crack as a function of Γ, V, and ϵ. Then we study the problem of quasi-static evolution for our model, imposing that the fluid volume V and the fluid pressure p are related by Darcy’s law. We show the existence of such an evolution, and we prove that it satisfies a weak notion of the so-called Griffith’s criterion.
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Kwon, Young W., and Joshua H. Gordis. "Frequency Domain Structural Synthesis Applied to Quasi-Static Crack Growth Modeling." Shock and Vibration 16, no. 6 (2009): 637–46. http://dx.doi.org/10.1155/2009/978437.

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Quasi-static crack growth in a composite beam was modeled using the structural synthesis technique along with a finite element model. The considered crack was an interface crack in the shear mode (i.e. mode II), which occurs frequently in the scarf joint of composite structures. The analysis model was a composite beam with an edge crack at the midplane of the beam subjected to a three-point bending load. In the finite element model, beam finite elements with translational degrees of freedom only were used to model the crack conveniently. Then, frequency domain structural synthesis (substructure coupling) was applied to reduce the computational time associated with a repeated finite element calculation with crack growth. The quasi-static interface crack growth in a composite beam was predicted using the developed computational technique, and its result was compared to experimental data. The computational and experimental results agree well. In addition, the substructure-based synthesis technique showed the significantly improved computational efficiency when compared to the conventional full analysis.
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Watanabe, Masaaki. "Criteria of Dynamic Crack Initiation." Journal of Applied Mechanics 61, no. 1 (March 1, 1994): 221–23. http://dx.doi.org/10.1115/1.2901410.

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A criteria of dynamic crack initiation is proposed as Klcdyn=Klcσcdyn.σctq.s.tαS/2 for t≤tq.s., where Klcdyn. is the dynamic critical stress intensity factor for initiation and Klc, the static fracture toughness. σc and σcdyn. are critical stresses for a growth of microcracks generated at the tip of a crack, in quasi-static and dynamic loading conditions, respectively. tq.s. is the characteristic time of quasi-static growth of a crack and t is a loading time. αs is a positive number. This criteria is compared with various different experiments and found to be in qualitative agreement with them.
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Dissertations / Theses on the topic "Quasi static crack growth"

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Prasanna, Kumar Siddharth. "Parametric Sensitivities of XFEM Based Prognosis for Quasi-static Tensile Crack Growth." Thesis, Virginia Tech, 2017. http://hdl.handle.net/10919/78724.

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Understanding failure mechanics of mechanical equipment is one of the most important aspects of structural and aerospace engineering. Crack growth being one of the major forms of failure in structural components has been studied for several decades to achieve greater reliability and guarantee higher safety standards. Conventional approaches using the finite element framework provides accurate solutions, yet they require extremely complicated numerical approaches or highly fine mesh densities which is computationally expensive and yet suffers from several numerical instabilities such as element entanglement or overly soften element behavior. The eXtended Finite Element Method (XFEM) is a relatively recent concept developed for modeling geometric discontinuities and singularities by introducing the addition of new terms to the classical shape functions in order to allow the finite element formulation to remain the same. XFEM does not require the necessity of computationally expensive numerical schemes such as active remeshing and allows for easier crack representation. In this work, verifies the validity of this new concept for quasi-static crack growth in tension with Abaqus' XFEM is employed. In the course of the work, the effect of various parameters that are involved in the modelling of the crack are parametrically analyzed. The load-displacement data and crack growth were used as the comparison criterion. It was found that XFEM is unable to accurately represent crack growth in the models in the elastic region without direct manipulation of the material properties. The crack growth in the plastic region is found to be affected by certain parameters allowing us to tailor the model to a small degree. This thesis attempts to provide a greater understanding into the parametric dependencies of XFEM crack growth.
Master of Science
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Zavatta, Nicola <1991&gt. "Crack growth in adhesively bonded joints under quasi-static and fatigue loading." Doctoral thesis, Alma Mater Studiorum - Università di Bologna, 2020. http://amsdottorato.unibo.it/9464/1/Zavatta_Nicola_tesi.pdf.

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Adhesively bonded joints are attracting increasing interest in the aerospace industry. However, incomplete knowledge of fatigue crack growth in adhesive bonds is a major concern to their application. This thesis investigates several aspects of crack growth in adhesively bonded joints. The influence of adhesive thickness on fatigue crack growth under mode I loading was addressed by a combination of experimental tests and numerical simulations. Increased crack growth was found in thicker specimens. This was explained as a result of increased energy available for crack growth in thicker adhesives, while the crack growth resistance was found not to be affected by the thickness. Formation of micro-cracks promoted by increased plasticity is thought to be the source of increased crack growth. Cohesive zone models were applied to the study of mode I and mode II quasi-static crack growth. A strong dependence on the input parameters was observed. In particular, the effect of viscous regularization on the solution was investigated. A proof of consistency of the viscous solution was proposed. It was shown that a low value of viscosity is needed to obtain consistent results. Finally, disbond arrest in bonded GLARE was studied by means of fatigue tests on bolted cracked lap shear specimens. The experiments evidenced a moderate decrease of the crack growth rate near the bolt. This was further investigated by numerical computations, which showed a significant change of the strain energy release rate around the bolt from mixed mode I/II to almost pure mode II. Outside this region, good predictions of the fatigue crack growth rate could be obtained by a combination of existing models from the literature. Extensive adherent cracking was observed, which led to the conclusion that crack arrest in GLARE comes from a balance of adhesive crack growth retardation and adherent cracking.
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Bybordiani, Milad. "Efficient Simulation of Quasi-static and Dynamic Crack Propagation using Enhanced Finite Elements." Thesis, The University of Sydney, 2022. https://hdl.handle.net/2123/27703.

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Failure analysis is a crucial step in design and assessment of many concrete structures such as dams, bridges and buildings which entails treatment of cracks and fractures. Given the complexities associated with the mechanics of the problem, this was historically tackled based on crude simplifications. However, the introduction of computers in the mid last century, paved the way towards the use and further development of finite elements methods. In the broad sense, these approaches can be categorised into smeared and discrete crack models. While in the former a crack was represented as a continuum material property, the latter treats the crack more realistically as a discontinuity in the displacement field. In this regard, many state-of-the-art approaches for predicting discrete fracture within the finite element framework were designed by enhancing the continuous displacement field with a discontinuous counterpart. These methods provided unprecedented versatility in simulation of crack propagation with a path independent of the background mesh. However, they come with a range of challenges concerning accuracy and efficiency. Examples are but not limited to inaccurate local stress solutions around the crack, increase in the system dimensions upon crack evolution, and ill-conditioned system of equations. In addition, these methods tend to nullify the critical time step in dynamic cases when an explicit time integration is employed. Aiming at overcoming these issues, this thesis introduces a range of finite element based methods for quasi-static and dynamic crack propagation. The performance of the methods are verified using a wide range of well-known analytical, experimental and numerical data. In terms of efficiency, different criteria such as analysis time in statics and critical time step size in dynamics were considered.
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Alang, Nasrul Azuan. "Prediction of long-term static and cyclic creep rupture and crack growth of grade 92 steels under different stress states." Thesis, Imperial College London, 2017. http://hdl.handle.net/10044/1/60640.

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During long-term exposure in creep or creep-fatigue environment, the creep strength of 9-12%Cr steel drops significantly due to the damage developed from metallurgical and microstructural changes occurring in complex subgrain structures. As creep time increases, failure strain of the material is reduced and the reduction is further enhanced under multiaxial condition, where a localised damage zone formed thus leading to crack initiation and growth under increased constraint. The present work focuses on high-temperature creep and fatigue behaviour, and life prediction of Grade 92 steel. Long-term data from literature is utilised to establish creep constitutive properties and to develop the predictive model. The expected scatter in the data is accounted for and it is shown that the important upper and lower bound trend under short and long-term tests can be identified irrespective of the variability of the data. Modelling approach is first applied to the stress-based Continuum Damage Mechanics (CDM) model coupled with a concept of representative stress to predict notched bar failures. Exponential-type predictive model which consists of two material constants, compared to standard CDM model with six is proposed as an alternative to the prediction. Furthermore, a semi-empirical constraint-based approach to predict creep rupture and crack growth under simple and complex stress state condition is presented. The model relates the Monkman-Grant failure strain to the constraint which arises from the geometry and time-dependent creep damage process in microscopic level. The model is consistent with the NSW (Nikbin-Smith-Webster) crack growth model which predicts the crack initiation and growth under the range of plane stress and strain. Finally, finite element (FE) analysis is performed on plain and notched bar to examine the influence of stress state on creep rupture and damage behaviour, and to validate the proposed predictive approach. The model is sufficiently simple yet reliable in predicting long-term failures.
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Liu, Hongquan. "Ply clustering effect on composite laminates under low-velocity impact using FEA." Thesis, Cranfield University, 2012. http://dspace.lib.cranfield.ac.uk/handle/1826/7310.

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With the development of the design and manufacture technology, composite materials are widely used in the aeronautical industry. But, one of the main concerns which affects the application of composites is foreign object impact. The damages induced by the Low Velocity Impact (LVI), which can significantly reduce the strength of the structures, can’t be easily inspected routinely. The so-called Barely Visible Impact Damages (BVID) due to LVI typically includes interlaminar delamination, matrix cracks and fibre fracture at the back face. Previous researches have shown that the results of LVI test are similar to that of the Quasi-Static Load (QSL) test. The initiation and propagation of delamination can be detected more easily in the QSL test and the displacement and reaction force of the impactor can be controlled and measured much more accurately. Moreover, it is easier to model QSL tests than dynamic impacts. To investigate the impact damage induced by LVI, a Finite Element (FE) model employing cohesive elements was used. At the same time, the ply clustering effect, when several plies of the same orientation were stack together, was modelled in the FE model in terms of damage resistance and damage size. A bilinear traction-separation law was introduced in the cohesive elements employed to simulate the initiation and propagation of the impact damage and delamination. Firstly, a 2D FE model of the Double Cantilever Beam (DCB) and End Notched Flexure (ENF) specimens were built using the commercial FEM software ABAQUS. The results have shown that the cohesive elements can be used to simulate mode I and mode II delamination sufficiently and correctly. Secondly, an FE model of a composite plate under QSL but without simulating damage was built using the continuum shell elements. Agreement between the FEA results with published test results is good enough to validate the capability of continuum shell elements and cohesive elements in modelling the composite laminate under the transverse load condition (QSL). Thirdly, an FE model containing discrete interface delamination and matrix cracks at the back face of the composite plate was built by pre-setting the cohesive failure elements at potential damage locations according to the experimental observation. A cross-ply laminate was modelled first where fewer interfaces could be delaminated. Good agreement was found in terms of the delamination area and impactor’s displacement-force curve. Finally, the effect of ply clustering on impact damage resistance was studied using Quasi-Isotropic (QI) layup laminates. Because of the limited time available for calculation, the simulation was only partly completed for the quasi-isotropic laminates (L2 configuration) which have more delaminated interfaces. The results showed that cohesive elements obeying the bilinear traction-separation law were capable of predicting the reaction force in quasi-isotropic laminates. However, discrepancies with the test results in terms of delamination area were observed for quasi-isotropic laminates. These discrepancies are mainly attributed to the simplification of matrix cracks simulation and compressive load at the interface in the thickness direction which is not taken into account.
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Phan, Ngoc Anh. "Simulation of time-dependent crack propagation in a quasi-brittle material under relative humidity variations based on cohesive zone approach : application to wood." Thesis, Bordeaux, 2016. http://www.theses.fr/2016BORD0008/document.

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Cette thèse est consacrée à la simulation du comportement à la rupture de bois sous des chargements à long terme et sous des conditions d'Humidité Relatives (HR) de l'air variables. Il est connu que le bois est un matériau fortement hygroscopique, ses propriétés mécaniques et de rupture sont en effet très dépendantes de sa teneur en eau. En outre, la stabilité d'une fissure existante dans un élément structural peut être fortement influencée parles variations, en particulier brusques, d'humidité relative qui peut conduire à la rupture inattendue de l'élément.L'approche thermodynamique proposée intègre l'effet de mécanosorption dans l'expression analytique de la déformation, en découplant les déformations mécaniques et celles dues au comportement mécanosorptif du matériau. En outre, la rupture quasi-fragile du matériau boisest traduite par un modèle de zone cohésive dont les paramètres de cohésion sont fonctions de la teneur en eau afin de simuler l’effet de l'humidité sur les propriétés de rupture. Sur cette base, une formulation incrémentale permet l'intégration de l'effet des variations soudaines d’humidité relative (autrement dit, le choc hydrique) sur la zone d’élaboration(zone cohésive) en introduisant un champ de contraintes supplémentaires le long de cette zone. Fonction de la variation de HR, ce champ de contraintes supplémentaires dépend de l'état de contrainte et de l'ouverture de la fissure le long de la zone cohésive, mais également de l'humidité en pointe de fissure (matériau non endommagé). Dans l'analyse par éléments finis, un opérateur tangent algorithmique est utilisé pour résoudre le problème non linéaire en combinant le modèle de mécanosorption et le modèle de zone cohésive et en intégrant l'effet du choc hydrique.La simulation du comportement d'une éprouvette entaillée soumise à un chargement constant et à des variations cycliques de HR montre un fort couplage entre le comportement mécanosorptif et l'effet du choc hydrique HR sur la zone d’élaboration. Ce couplage entraîne une augmentation de la propagation des fissures et conduit à une fissuration plus précoce par rapport à celle obtenue à partir du modèle de mécanosorption seul ou à partir du modèle de zone cohésive en intégrant l'effet des variations soudaines de HR. En outre, le couplage entre le modèle mécanosorptif et le modèle de zone cohésive en intégrant l'effet du chochydrique montre l'intérêt d'une telle approche numérique pour décrire le comportement complexe des éléments de charpente en bois soumis à des conditions climatiques variables,comportement qui ne peut être prédit par une simple superposition des deux modélisations
This thesis is dedicated to the simulation of the fracture behavior of wood under long-termloading and variable relative humidity conditions. Indeed, wood is well-known to be a highlyhygroscopic material in so far as its mechanical and fracture properties are very dependenton moisture. Moreover, the stability of an existent crack in a structural element can bestrongly affected by the sudden variations of relative humidity (RH) and can lead tounexpected failure of the element.The thermodynamic approach proposed in this thesis includes the mechano-sorptive effect inthe analytical expression of the deformation, by operating a decoupling of the strain in amechanical part and a mechano-sorptive part in material. Moreover, the quasi-brittle fractureof wood is here simulated from a cohesive zone model whose cohesive parameters arefunctions of the moisture in order to mimic the moisture-dependent character of the fractureproperties. On this basis, an increment formulation allows the integration of the effect ofsudden RH variations on the fracture process zone (cohesive zone) by introducing anadditional stress field along this zone. As a function of the RH variation, this additional stressfield depends on not only the stress state and the crack opening along the cohesive zone butalso the material moisture ahead of the zone (undamaged material). In the finite elementanalysis, an algorithmic tangent operator is used to solve the non-linear problem combiningmechano-sorptive model and cohesive zone model including the effect of sudden RHvariations.The simulation of a notched structural element submitted to a constant load and cyclic RHvariations exhibits a strong coupling between the mechano-sorptive behavior and the effectof the RH variations on the fracture process zone (FPZ). This coupling results in an increaseof the crack propagation kinetic and leads to a precocious failure compared to those obtainedfrom the mechano-sorptive model or from the effect of sudden RH variations on the FPZ.Moreover, the coupling between the mechano-sorptive model and the effect of sudden RHvariations on the FPZ which cannot be predicted by a simple superposition of both effects,showing the interest of such a numerical approach in order to describe the complex behaviorof wood structural elements submitted to variable climatic conditions
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Laforet, Adrien. "Rupture différée en fatigue statique aux très hautes températures (800° - 1300°) des fils Hi-Nicalon, des composites Hi-Nicalon/Type PyC/SiC et des composites Hi-Nicalon/Type PyC/B4C." Thesis, Bordeaux 1, 2009. http://www.theses.fr/2009BOR13783/document.

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La rupture différée des fibres SiC de type Hi-Nicalon à l’échelle multifilamentaire, des minicomposites de type Hi-Nicalon/PyC/SiC et Hi-Nicalon/type PyC/B4C a été étudiée à l’aide de moyens d’essais spécifiques et innovants. Des essais de fatigue statique sous air aux très hautes températures (900°C-1300°C) avec mesure des déformations ont ainsi pu être réalisés sur ces différents matériaux. Les résultats expérimentaux obtenus (durée de vie, déformation, lois de comportement en traction) ont permis de comprendre et de modéliser les mécanismes responsables de la rupture différée aux différentes échelles : - Les fils Hi-Nicalon rompent par mécanisme de fissuration lente activé par l’oxydation du carbone libre des fibres. Le mécanisme de fissuration est perturbé par la formation rapide d’oxyde SiO2 à partir de 1000°C : pour les faibles contraintes, la cinétique de fissuration lente est ralentie par formation d’oxyde protecteur empêchant l’accès de l’oxygène aux fissures ; pour les fortes contraintes, la rupture des fils est prématurée à cause de collages inter-fibres (fibre-oxyde-fibre). A 1200°C, le mécanisme de fluage semble être à l’origine de la rupture quasi-instantanée du matériau pour des contraintes supérieures à 200 MPa. - Les minicomposites Hi-Nicalon/type PyC/SiC rompent par mécanisme de fissuration lente ralenti par la présence de matrice SiC et par la formation d’oxyde SiO2 limitant l’accès de l’oxygène aux fibres. le mécanisme de fluage est observé à partir de 1200°C mais il n’a jamais été responsable de la rupture du matériau. - Les minicomposites Hi-Nicalon/type PyC/B4C rompent par mécanisme de fissuration lente ralenti par formation d’oxyde B2O3 à 900°C pour les fortes contraintes. Pour les autres températures et pour les faibles contraintes à 900°C le mécanisme de rupture est la diminution rapide du diamètre des fibres à cause de l’augmentation de la cinétique d’oxydation des fibres par l’oxyde B2O3. Des modèles analytiques basés sur ces différents mécanismes permettent de prévoir la durée de vie du matériau en prenant en compte les incertitudes de mesure et la variabilité des résultats de durée de vie
Delayed failure of SiC Hi-Nicalon multifilament tows (500 fibers), minicomposites Hi-Nicalon/type PyC/SiC and Hi-Nicalon/type PyC/B4C was investigated in static fatigue, in air, at high temperatures (900°C – 1300°C) using specific and innovative devices. Static fatigue tests with measure of strain were performed on these materials. The experimental results (lifetime, strain, tensile behavior) have helped to understand and model the mechanisms responsible for the delayed failure at the different scales: - Hi-Nicalon tows rupture is caused by subcritical crack growth mechanism activated by oxidation of free carbon in the fibres. This phenomenon is disrupted by fast oxide SiO2 formation over 900°C: subcritical crack growth kinetic slows down for low stresses because of protective oxide formation which prevents the cracks from oxygen; For high stresses, the lifetime of Hi-Nicalon tows is weaker because of fibers interactions (fiber-oxide-fiber). At last, creep seems to cause the rupture of the tows for stresses over 200 MPa at 1200°C. - Hi-Nicalon/type PyC/SiC minicomposites break by subcritical crack growth slowed down by the SiC matrix and by the SiO2 formation which limit the access of the oxygen to the fibers. Creep occurs at 1200°C but it isn’t responsible of the rupture. - Hi-Nicalon/type PyC/B4C minicomposites break by subcritical crack growth slowed down by the formation of B2O3 oxide at 900°C for high stresses. The rupture is caused by the fast decrease of the diameter of the fibers at the other temperatures and for low stresses at 900°C. The oxidation kinetic of the fibers increases because of the dissolution of silica coating by B2O3 oxide. Analytical modeling was performed to schedule the lifetime of these materials and the variability of the experimental results is studied
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De, Melo Loseille Olivier. "Prévision de la durée de vie des composites à matrice céramique auto cicatrisante, en fatigue statique, à haute température (= 800°C)." Thesis, Bordeaux 1, 2010. http://www.theses.fr/2010BOR12010/document.

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La rupture différée d’un composite SiC/SiC a été étudiée en fatigue statique, sous air, aux températures intermédiaires (500°C-800°C). Les résultats expérimentaux (durée de vie, loi de comportement en traction, déformation) et les fractographies ont permis d’identifier les modes de rupture de fibre qui interviennent dans la rupture différée. Un modèle mécanique probabiliste multiéchelle a été développé pour simuler le comportement en fatigue et prévoir la durée de vie. La microstructure est décrite par des distributions statistiques identifiées à partir des résultats de l’étude fractographique. Des diagrammes d’endurance du composite en fatigue ont été calculés pour prévoir la durée de vie. Ces derniers confirment que la tenue du composite est dictée par les fils. La modélisation montre que la microstructure joue un rôle déterminant sur la durée de vie et sa variabilité. Des relations microstructures-propriétés sont établies. Le lien entre contrainte résiduelle et durée de vie est également examiné. Une approche fiabiliste sur les échantillons à information faible est menée à l’aide de l’inférence bayésienne. Les résultats concordent avec l’approche mécanique
Delayed failure of SiC/SiC woven composite is studied under static fatigue, in air, for intermediate temperatures (500°C – 800°C). Experimental results and fractographic examination are used to identify damage mechanisms. A multi-scale probabilistic facture based model is proposed to simulate damage kinetics in longitudinal tows. Microstructure is described with appropriate statistical distributions identified on fractographic investigations. Simulations demonstrate a significant effect of the microstructure on the lifetime of the tows. Microstructure – properties relations are established
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Beckstein, Pascal. "Methodenentwicklung zur Simulation von Strömungen mit freier Oberfläche unter dem Einfluss elektromagnetischer Wechselfelder." Doctoral thesis, Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2018. http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-232474.

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Im Bereich der industriellen Metallurgie und Kristallzüchtung treten bei zahlreichen Anwendungen, wo magnetische Wechselfelder zur induktiven Beeinflussung von leitfähigen Werkstoffen eingesetzt werden, auch Strömungen mit freier Oberfläche auf. Das Anwendungsspektrum reicht dabei vom einfachen Aufschmelzen eines Metalls in einem offenen Tiegel bis hin zur vollständigen Levitation. Auch der sogenannte RGS-Prozess, ein substratbasiertes Kristallisationsverfahren zur Herstellung siliziumbasierter Dünnschichtmaterialien, ist dafür ein Beispiel. Um bei solchen Prozessen die Interaktion von Magnetfeld und Strömung zu untersuchen, ist die numerische Simulationen ein wertvolles Hilfsmittel. Für beliebige dreidimensionale Probleme werden entsprechende Berechnungen bisher durch eine externe Kopplung kommerzieller Programme realisiert, die für Magnetfeld und Strömung jeweils unterschiedliche numerische Techniken nutzen. Diese Vorgehensweise ist jedoch im Allgemeinen mit unnötigem Rechenaufwand verbunden. In dieser Arbeit wird ein neu entwickelter Methodenapparat auf Basis der FVM vorgestellt, mit welchem sich diese Art von Berechnungen effizient durchführen lassen. Mit der Implementierung dieser Methoden in foam-extend, einer erweiterten Version der quelloffenen Software OpenFOAM, ist daraus ein leistungsfähiges Werkzeug in Form einer freien Simulationsplattform entstanden, welches sich durch einen modularen Aufbau leicht erweitern lässt. Mit dieser Plattform wurden in foam-extend auch erstmalig dreidimensionale Induktionsprozesse im Frequenzraum gelöst.
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Jhin, Minseok. "Crack Growth Rate and Crack Path in Adhesively Bonded Joints: Comparison of Creep, Fatigue and Fracture." Thesis, 2012. http://hdl.handle.net/1807/33256.

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The relationship between crack path and test method was examined by comparing the performance of adhesive-adherend combinations (six) in quasi-static fracture, mixed-mode fatigue, and creep crack growth. Crack paths in creep and quasi-static fracture were similar due to similar crack-tip plastic zone sizes in the epoxy adhesive even though the crack growth rates in creep were much smaller. Under condensed moisture and mixed-mode, creep and threshold fatigue tests produced interfacial failure. Under room-temperature dry environment, near threshold mixed-mode fatigue was interfacial, but was not in creep or quasi-static fracture. Smaller plastic zone size and crack path proximity to the interface that followed increased the sensitivity of near threshold, mixed-mode fatigue to surface properties. Therefore, the interfacial or cohesive failure of an adhesive system, which may judge the quality of the bond, can be a function of the test being conducted and may not be an absolute indicator of joint quality.
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Books on the topic "Quasi static crack growth"

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United States. National Aeronautics and Space Administration. Scientific and Technical Information Division., ed. Fracture toughness and crack growth of Zerodur. [Washington, DC]: National Aeronautics and Space Administration, Office of Management, Scientific and Technical Information Division, 1990.

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Book chapters on the topic "Quasi static crack growth"

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Babadjian, Jean-François. "Stability of Quasi-Static Crack Evolution through Dimensional Reduction." In IUTAM Symposium on Variational Concepts with Applications to the Mechanics of Materials, 1–13. Dordrecht: Springer Netherlands, 2010. http://dx.doi.org/10.1007/978-90-481-9195-6_1.

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Procaccia, Itamar. "Dynamical Instabilities of Quasi-Static Crack Propagation under Thermal Stress." In Continuum Models and Discrete Systems, 251. Dordrecht: Springer Netherlands, 2004. http://dx.doi.org/10.1007/978-1-4020-2316-3_40.

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Negi, Alok, and Sachin Kumar. "Crack Growth Simulation in Quasi-brittle Materials Using a Localizing Gradient Damage Model." In Lecture Notes in Mechanical Engineering, 223–31. Singapore: Springer Singapore, 2020. http://dx.doi.org/10.1007/978-981-15-0772-4_20.

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Ogawa, Takeshi, Motohisa Hirose, and Keiro Tokaji. "Evaluation of Elevated-Temperature Crack Growth in Ceramics under Static and Cyclic Loads." In Plastic Deformation of Ceramics, 643–52. Boston, MA: Springer US, 1995. http://dx.doi.org/10.1007/978-1-4899-1441-5_56.

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Negri, Matteo. "Quasi-Static Evolutions in Brittle Fracture Generated by Gradient Flows: Sharp Crack and Phase-Field Approaches." In Innovative Numerical Approaches for Multi-Field and Multi-Scale Problems, 197–216. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-39022-2_9.

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Fukuyama, Eiichi, Chihiro Hashimoto, and Mitsuhiro Matsu’ura. "Simulation of the Transition of Earthquake Rupture from Quasi-static Growth to Dynamic Propagation." In Earthquake Processes: Physical Modelling, Numerical Simulation and Data Analysis Part I, 2057–66. Basel: Birkhäuser Basel, 2002. http://dx.doi.org/10.1007/978-3-0348-8203-3_10.

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Liang, Wen Yan, Yong Jun Wang, Zhen Qing Wang, and Hong Qing Lv. "The Perfect Elastic-Viscoplastic Field at Mode I Quasi-Static Propagating Crack-Tip in Rate-Sensitive Material." In Fracture and Damage Mechanics V, 17–20. Stafa: Trans Tech Publications Ltd., 2006. http://dx.doi.org/10.4028/0-87849-413-8.17.

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Karihaloo, B. L., and Q. Z. Xiao. "Accurate Simulation of Frictionless and Frictional Cohesive Crack Growth in Quasi-Brittle Materials Using XFEM." In IUTAM Symposium on Discretization Methods for Evolving Discontinuities, 233–54. Dordrecht: Springer Netherlands, 2007. http://dx.doi.org/10.1007/978-1-4020-6530-9_14.

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Liang, Wen Yan, Zhen Qing Wang, Hong Quing Lu, and Yong Jun Wang. "The Elastic-Viscoplastic Field at the Tip of Mode II Quasi-Static Propagating Crack in Rate-Sensitive Material." In Advances in Composite Materials and Structures, 109–12. Stafa: Trans Tech Publications Ltd., 2007. http://dx.doi.org/10.4028/0-87849-427-8.109.

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Miyahara, Nobuyuki, Yoshiharu Mutoh, Kouhei Yamaishi, Keizo Uematsu, and Makoto Inoue. "The Effects of Grain Size on Strength, Fracture Toughness, and Static Fatigue Crack Growth in Alumina." In Grain Boundary Controlled Properties of Fine Ceramics, 125–36. Dordrecht: Springer Netherlands, 1992. http://dx.doi.org/10.1007/978-94-011-1878-1_14.

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Conference papers on the topic "Quasi static crack growth"

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Pavelko, Vitalijs. "The model of quasi-static growth of a crack and its some application." In FRACTURE AND DAMAGE MECHANICS: Theory, Simulation and Experiment. AIP Publishing, 2020. http://dx.doi.org/10.1063/5.0034981.

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Kapania, Rakesh K., Dhaval P. Makhecha, Eric R. Johnson, Josh Simon, and David A. Dillard. "Modeling Stable and Unstable Crack Growth Observed in Quasi-Static Adhesively Bonded Beam Tests." In ASME 2004 International Mechanical Engineering Congress and Exposition. ASMEDC, 2004. http://dx.doi.org/10.1115/imece2004-59765.

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An experimental and computational study of an adhesively bonded, double cantilevered beam (DCB) under quasi-static loading is presented. The polymeric adhesives are either an acrylic or an epoxy, and the adherends are 6061 aluminum alloy. DCB tests bonded with the acrylic exhibited stable crack growth, while the DCB tests bonded with the epoxy exhibited unstable crack growth. The responses of the DCB test speciments were modeled in the ABAQUS/Standard® software package. Interface finite elements were located between bulk elements to model crack initiation and crack growth in the adhesive. These interface elements are implemented as user-defined elements in ABAQUS®, and the material law relating the interfacial tractions to the separation displacements is based on a cohesive zone model (CZM). Using interface elements only to model the acrylic adhesive, the simulation correlates very well to the test. Good correlation between the simulation and the test for the epoxy adhesive is achieved if both bulk modeling of the adhesive and inertia of the specimen are included.
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Baxevanis, Theocharis, Dimitris Lagoudas, and Chad Landis. "Mode I Steady Crack-Growth in Superelastic Shape Memory Alloys." In ASME 2012 Conference on Smart Materials, Adaptive Structures and Intelligent Systems. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/smasis2012-7934.

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A numerical analysis of quasi-static, steady state crack growth in superelastic Shape Memory Alloys (SMAs) under small-scale transformation conditions is carried out for plane strain, mode I loading. Crack growth is assumed to proceed at a critical level of the crack-tip energy release rate. Finite-element results concerning the mechanical fields near the advancing crack tip are presented and the ratio of the far-field applied energy release rate to the crack-tip energy release rate is obtained for a range of thermomechanical parameters. A substantial fracture toughening is observed associated with closure stresses placed on the crack tip by the transformed material left behind in the wake of the advancing crack tip.
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Wang, Xin, George Roy, Su Xu, and William R. Tyson. "Numerical Simulation of Ductile Crack Growth in Pipeline Steels." In ASME 2007 Pressure Vessels and Piping Conference. ASMEDC, 2007. http://dx.doi.org/10.1115/pvp2007-26812.

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This paper presents numerical studies on stable crack extension of high toughness gas pipeline steels (X80) using the 2D and 3D computational cell approach. The Gurson-Tvergaard dilatant plasticity model for voided materials is used to describe the degradation of material stress capacity. Fixed-size, computational cell elements defined over a thin layer at the crack plane provide an explicit length scale for the continuum damage process. Outside this layer, the material is modeled as undamaged by void growth. The key micro-mechanics parameters are D, the thickness of the computational cell layer, and ƒ0, the initial cell porosity. Calibration of these parameters is conducted using analysis of ductile tearing from testing of Charpy-sized bending specimens. The resulting computational model enables the study of effects on crack growth of specimen size, geometry and loading mode. Computational and experimental studies are described for shallow and deep DWTT (drop weight tear test) specimens under quasi-static loading conditions.
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Shahani, Amir Reza, and Mohammad Reza Amini Fasakhodi. "Analytical Modeling of Dynamic Crack Propagation in DCB Specimens." In ASME 2009 Pressure Vessels and Piping Conference. ASMEDC, 2009. http://dx.doi.org/10.1115/pvp2009-78055.

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An analytical solution via the beam theory considering shear deformation effects is developed to solve the static and dynamic fracture problem in a bounded medium such as DCB (Double Cantilever Beam) specimen. In the static case, the stress intensity factor (SIF) is derived at the crack tip through the compliance approach for fixed displacement conditions. In the dynamic case, the energy balance criterion is employed to obtain the equation of motion for a running crack and the problem is solved supposing quasi-static crack propagation. Finally, a closed form relation for the crack propagation velocity versus specimen parameters and crack growth resistance of the material is found. Therefore, the effects of various parameters are investigated on the crack growth velocity. It is shown that the reacceleration of crack growth appears when the crack tip approaches the end of specimen under fixed displacement loading. The predicted results are compared with those cited in the literature and a good agreement is observed. It is seen that shear deformation effects are more significant when the small values of a0/h is considered in the analysis.
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Margolin, B. Z., V. N. Fomenko, and A. A. Sorokin. "Analysis of Crack Growth Conditions in WWER Internals Undergone High Neutron Irradiation." In ASME 2009 Pressure Vessels and Piping Conference. ASMEDC, 2009. http://dx.doi.org/10.1115/pvp2009-77097.

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Conditions of stable and unstable crack growth by the mechanism of ductile fracture under quasi-static loading are analyzed. Simulation of crack growth by the finite element method (FEM) based on the strain fracture criterion was carried out. The effect of ratio of an elementary crack extension size to a plastic zone size on the kind of JR-curves is investigated. Based on these investigations conditions are determined under which unstable crack growth is possible for small scale and large scale yielding. The criterion is formulated for the absence of unstable crack growth in highly irradiated austenitic materials including the situation when the Feγ→Feα transition happens.
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LI, GANG, and GUILLAUME RENAUD. "EVALUATION OF COMPOSITE DCB DELAMINATION GROWTH BY COMBINING EXPERIMENTAL DATA AND NUMERICAL ANALYSIS." In Proceedings for the American Society for Composites-Thirty Seventh Technical Conference. Destech Publications, Inc., 2022. http://dx.doi.org/10.12783/asc37/36369.

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A study of quasi-static mode I delamination in a laminated unidirectional composite double cantilever beam (DCB) configuration was conducted experimentally and numerically. A two-dimensional (2D) finite element (FE) correction method that consisted of a series of analyses of the DCB compliances at different delamination lengths was conducted to establish an analytical correlation between the delamination length and the DCB opening compliance. This analytical correlation was then used to determine the delamination length provided the experimentally measured compliance. Consequently, the problematic delamination lengths generated from in-situ optical measurement were evaluated and corrected. Also, the fracture resistance curve was updated using the corrected delamination lengths. Good agreement in the loaddisplacement variation was then obtained between the experimental results and the subsequent 2D DCB FE modelling results using cohesive elements. Commentaries on the DCB quasi-static failure analysis and modelling using the cohesive zone modelling technique and the virtual crack closure technique were also provided.
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Koch, Brendan M. L., Calvin Lo, Tomoko Sano, and James David Hogan. "Bulking as a Mechanism in the Failure of Advanced Ceramics." In 2019 15th Hypervelocity Impact Symposium. American Society of Mechanical Engineers, 2019. http://dx.doi.org/10.1115/hvis2019-022.

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Abstract Failure in brittle materials is characterized by crack growth and fracture, processes which involve an increase in the volume of a sample to accommodate these cracks. This process is called bulking and it is known to be an important factor in the failure of materials such as ceramics, stone, and concrete. While volumetric strains are obtainable under quasi-static conditions, under dynamic conditions technical challenges have stood in the way of obtaining multi-dimensional strain data that would allow for assessment of bulking under the sort loading conditions that would simulate a high velocity impact. Advances in digital-image-correlation and ultra-high-speed-photography have however opened up the capacity to obtain this higher dimensional data. This data in turn has prompted an assessment of prior theory to produce a framework through which stress-strain behavior can be expressed in terms of changes to multiple elastic constants simultaneously. This presentation offers initial results in quasi-static and dynamic experiments and discusses the implications for brittle material behavior and crack evolution phenomenon under a variety of conditions.
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Makhecha, Dhaval P., Rakesh K. Kapania, Eric R. Johnson, David A. Dillard, George C. Jacob, and J. Michael Starbuck. "Rate-Dependent Cohesive Zone Modeling of Unstable Crack Growth in an Epoxy Adhesive." In ASME 2005 International Mechanical Engineering Congress and Exposition. ASMEDC, 2005. http://dx.doi.org/10.1115/imece2005-81317.

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This paper presents the development and numerical implementation of a rate dependent fracture model of an epoxy adhesive. Previous mode I fracture tests conducted under quasistatic, displacement controlled loading of an aluminum double cantilever beam (DCB) bonded with the epoxy exhibited unstable crack growth in the adhesive. Results from mode I fracture tests of compact tension specimens made from bulk adhesive at increasing cross head opening speeds are reported in this paper. The compact tension tests results showed a decreasing critical strain energy release rate with increasing cross head speed, with the critical energy release rate at 1 m/s cross head speed equal to about 20% of its quasi-static value. Two rate dependent cohesive zone models are formulated based on the compact tension test data. A cohesive de-cohesive relationship was postulated between the tractions acting across the crack faces and the opening displacement and opening velocity. These rate dependent cohesive zone models are implemented in a interface finite element to model discrete crack growth in the adhesive. The reaction force history from simulation of the DCB test is in good agreement with the test data using only the rate dependent interface element to model the adhesive.
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Zheng, W., D. Bibby, J. Li, J. T. Bowker, J. A. Gianetto, R. W. Revie, and G. Williams. "Near-Neutral pH SCC of Two Line Pipe Steels Under Quasi-Static Stressing Conditions." In 2006 International Pipeline Conference. ASMEDC, 2006. http://dx.doi.org/10.1115/ipc2006-10084.

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Most published SCC results for the near-neutral pH condition were produced under cyclic loading. However, the presence of stress corrosion cracks in pipeline systems involving very small pressure fluctuations suggests the cracking should initiate and grow without large dynamic loads. This study was designed to investigate this issue. A Grade 448 (X-65) line pipe steel and a prototype Grade 550 (X-80) steel were evaluated in near-neutral pH solutions. The maximum stress applied was at 95% of the respective yield strengths and the R values applied were between 0.98 and 1.0. Two solutions were used for each steel: NS4 and NS4/clay mixture. The solutions were purged with a gas mixture of 95%N2 and 5%CO2. Recognizing that the crack propagation rate can be very slow under such near-static conditions, relatively long-term tests were carried out. The durations of the three tests using the prototype Grade 550 (X-80) steel were 110 days, 54 days and 26 days, and the duration for the X-65 steel was 110 days. After 110 days, the majority of the cracks in the Grade 550 (X-80) steel were in the range of 5 to 30 micrometers (μm) deep, giving an average crack propagation rate of 2*10−9 mm/s. Tests at short durations revealed that only a few cracks were detectable after 26 days and that several more cracks were produced after 54 days. So majority of the cracks in the 110-day were likely produced after 54 days of testing. The NS4/clay mixture was found to be less aggressive than the NS4 solution for both steels studied. The cracks in the prototype Grade 550 (X-80) steel were deeper and more numerous in comparison with the X-65 steel. Possible reasons for this observation are also explored in terms of the presence of martensite-austenite (MA) phase in the Grade 550 (X-80) steel.
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Reports on the topic "Quasi static crack growth"

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Schovanec, L., and J. R. Walton. The Energy Release Rate for a Quasi-Static Mode I Crack in a Nonhomogeneous Linearly Viscoelastic Body. Fort Belvoir, VA: Defense Technical Information Center, September 1986. http://dx.doi.org/10.21236/ada175184.

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Tylczak, Joseph. Measurement of Fatigue and Static Crack Growth Rate of X65 Line Pipe Steel in 3.5% NaCl containing CO2 under Cathodic Polarization. Office of Scientific and Technical Information (OSTI), May 2020. http://dx.doi.org/10.2172/1634188.

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Snyder, Victor A., Dani Or, Amos Hadas, and S. Assouline. Characterization of Post-Tillage Soil Fragmentation and Rejoining Affecting Soil Pore Space Evolution and Transport Properties. United States Department of Agriculture, April 2002. http://dx.doi.org/10.32747/2002.7580670.bard.

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Tillage modifies soil structure, altering conditions for plant growth and transport processes through the soil. However, the resulting loose structure is unstable and susceptible to collapse due to aggregate fragmentation during wetting and drying cycles, and coalescense of moist aggregates by internal capillary forces and external compactive stresses. Presently, limited understanding of these complex processes often leads to consideration of the soil plow layer as a static porous medium. With the purpose of filling some of this knowledge gap, the objectives of this Project were to: 1) Identify and quantify the major factors causing breakdown of primary soil fragments produced by tillage into smaller secondary fragments; 2) Identify and quantify the. physical processes involved in the coalescence of primary and secondary fragments and surfaces of weakness; 3) Measure temporal changes in pore-size distributions and hydraulic properties of reconstructed aggregate beds as a function of specified initial conditions and wetting/drying events; and 4) Construct a process-based model of post-tillage changes in soil structural and hydraulic properties of the plow layer and validate it against field experiments. A dynamic theory of capillary-driven plastic deformation of adjoining aggregates was developed, where instantaneous rate of change in geometry of aggregates and inter-aggregate pores was related to current geometry of the solid-gas-liquid system and measured soil rheological functions. The theory and supporting data showed that consolidation of aggregate beds is largely an event-driven process, restricted to a fairly narrow range of soil water contents where capillary suction is great enough to generate coalescence but where soil mechanical strength is still low enough to allow plastic deforn1ation of aggregates. The theory was also used to explain effects of transient external loading on compaction of aggregate beds. A stochastic forInalism was developed for modeling soil pore space evolution, based on the Fokker Planck equation (FPE). Analytical solutions for the FPE were developed, with parameters which can be measured empirically or related to the mechanistic aggregate deformation model. Pre-existing results from field experiments were used to illustrate how the FPE formalism can be applied to field data. Fragmentation of soil clods after tillage was observed to be an event-driven (as opposed to continuous) process that occurred only during wetting, and only as clods approached the saturation point. The major mechanism of fragmentation of large aggregates seemed to be differential soil swelling behind the wetting front. Aggregate "explosion" due to air entrapment seemed limited to small aggregates wetted simultaneously over their entire surface. Breakdown of large aggregates from 11 clay soils during successive wetting and drying cycles produced fragment size distributions which differed primarily by a scale factor l (essentially equivalent to the Van Bavel mean weight diameter), so that evolution of fragment size distributions could be modeled in terms of changes in l. For a given number of wetting and drying cycles, l decreased systematically with increasing plasticity index. When air-dry soil clods were slightly weakened by a single wetting event, and then allowed to "age" for six weeks at constant high water content, drop-shatter resistance in aged relative to non-aged clods was found to increase in proportion to plasticity index. This seemed consistent with the rheological model, which predicts faster plastic coalescence around small voids and sharp cracks (with resulting soil strengthening) in soils with low resistance to plastic yield and flow. A new theory of crack growth in "idealized" elastoplastic materials was formulated, with potential application to soil fracture phenomena. The theory was preliminarily (and successfully) tested using carbon steel, a ductile material which closely approximates ideal elastoplastic behavior, and for which the necessary fracture data existed in the literature.
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