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Jean-françois Molinari - One of the best experts on this subject based on the ideXlab platform.
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Dynamic Crack propagation with a variational phase-field model: limiting speed, Crack Branching and velocity-toughening mechanisms
International Journal of Fracture, 2017Co-Authors: Jeremy Bleyer, Clément Roux-langlois, Jean-françois MolinariAbstract:We address the simulation of dynamic Crack propagation in brittle materials using a regularized phase-field description, which can also be interpreted as a damage-gradient model. Benefiting from a variational framework, the dynamic evolution of the mechanical fields are obtained as a succession of energy minimizations. We investigate the capacity of such a simple model to reproduce specific experimental features of dynamic in-plane fracture. These include the Crack Branching phenomenon as well as the existence of a limiting Crack velocity below the Rayleigh wave speed for mode I propagation. Numerical results show that, when a Crack accelerates, the damaged band tends to widen in a direction perpendicular to the propagation direction, before forming two distinct macroscopic branches. This transition from a single Crack propagation to a branched configuration is described by a well-defined master-curve of the apparent fracture energy $$\varGamma $$Γ as an increasing function of the Crack velocity. This $$\varGamma (v)$$Γ(v) relationship can be associated, from a macroscopic point of view, with the well-known velocity-toughening mechanism. These results also support the existence of a critical value of the energy release rate associated with Branching: a critical value of approximately 2$$G_c$$Gc is observed i.e. the fracture energy contribution of two Crack tips. Finally, our work demonstrates the efficiency of the phase-field approach to simulate Crack propagation dynamics interacting with heterogeneities, revealing the complex interplay between heterogeneity patterns and Branching mechanisms.
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Variational phase field model for brittle fracture : insights on dynamic Crack Branching and propagation in heterogeneous media
2016Co-Authors: Jeremy Bleyer, Clément Roux-langlois, Jean-françois MolinariAbstract:Simulating Crack nucleation and propagation remains a challenging problematic because of the complexity of Crack patterns observed in fracture mechanics experiments. Whereas some numerical methods aim at explicitly tracking the Crack front evolution, an interesting alternative is offered by continuous approaches of brittle fracture which consist in representing the Crack topology using a continuous field varying from 0 (sound material) to 1 (fully Cracked material) accross an internal length scale. This « phase field » approach benefits from a variational framework, strongly related to gradient damage models, and can be seen as a regularization of the variational approach to fracture developed by Francfort and Marigo in 1998. Moreover, it does not require any a priori knowledge of the Crack path or topology, its evolution being driven only by energy minimization. Using such an approach combined to a finite-element discretization, the present work aims at providing some insights on Crack propagation in a dynamic context. More specifically, Crack Branching (splitting of a single Crack in two or more Cracks) is a characteristic phenomenon of dynamic brittle fracture which still lacks a sound theoretical explanation. Numerical simulations will help us better understand some aspects of the Branching phenomenon, especially the role played by material heterogeneities in the onset or delay of Crack Branching.
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a non local continuum damage approach to model dynamic Crack Branching
International Journal for Numerical Methods in Engineering, 2015Co-Authors: Cyprien Wolff, Nicolas Richart, Jean-françois MolinariAbstract:Dynamic Crack Branching instabilities in a brittle material are studied numerically by using a non-local damage model. PMMA is taken as our model brittle material. The simulated Crack patterns, Crack velocities and dissipated energies, compare favorably to experimental data gathered from the literature, as long as the critical strain for damage initiation as well as the parameters for a rate-dependent damage law are carefully selected. Nonetheless, the transition from a straight Crack propagation to the emergence of Crack branches is very sensitive to the damage initiation threshold. The transition regime is thus a particularly interesting challenge for numerical approaches. We advocate using the present numerical study as a benchmark to test the robustness of alternative non-local numerical approaches.
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dynamic Crack propagation with cohesive elements a methodology to address mesh dependency
International Journal for Numerical Methods in Engineering, 2004Co-Authors: F Zhou, Jean-françois MolinariAbstract:In this paper, two brittle fracture problems are numerically simulated: the failure of a ceramic ring under centrifugal loading and Crack Branching in a PMMA strip. A three-dimensional finite element package in which cohesive elements are dynamically inserted has been developed. The cohesive elements' strength is chosen to follow a modified weakest link Weibull distribution. The probability of introducing a weak cohesive element is set to increase with the cohesive element size. This reflects the physically based effect according to which larger elements are more likely to contain defects. The calculations illustrate how the area dependence of the Weibull model can be used to effectively address mesh dependency. On the other hand, regular Weibull distributions have failed to reduce mesh dependency for the examples shown in this paper. The ceramic ring calculations revealed that two distinct phenomena appear depending on the magnitude of the Weibull modulus. For low Weibull modulus, the fragmentation of the ring is dominated by heterogeneities. Whereas many Cracks were generated, few of them could propagate to the outer surface. Monte Carlo simulations revealed that for highly heterogeneous rings, the number of small fragments was large and that few large fragments were generated. For high Weibull modulus, signifying that the ring is close to being homogeneous, the fragmentation process was very different. Monte Carlo simulations highlighted that a larger number of large fragments are generated due to Crack Branching. Copyright (C) 2003 John Wiley Sons, Ltd.
Binjun Fei - One of the best experts on this subject based on the ideXlab platform.
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a link up resulted fatigue Crack Branching in al cu mg alloy
International Journal of Fatigue, 2016Co-Authors: Rui Bao, Ting Zhang, Binjun FeiAbstract:Abstract Fatigue Crack Branching phenomena in Al–Cu–Mg alloy 2324-T39 are studied. Both spectrum and constant amplitude loading cases are examined. A novel type of Crack Branching process and mechanism is present, which results from the link-up of the secondary Crack with the main Crack. The grain shapes in 2324-T39 are different from those in the 2024 and 2524 alloys, and their interaction with the plastic zone size contributes to the appearance of this type of Crack Branching. FE analysis shows that the surface secondary Crack is located near the plastic zone boundaries of the main Crack.
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load effects on macroscopic scale fatigue Crack growth path in 2324 t39 aluminium alloy thin plates
International Journal of Fatigue, 2014Co-Authors: Ting Zhang, Rui Bao, Binjun FeiAbstract:Abstract In the present paper, an experimental study is accomplished to characterise the load effects, including K -level, stress ratio, overloads and underloads, on fatigue Crack growth path in aluminium alloy 2324-T39 thin plates under constant amplitude (CA) and simple variable amplitude (VA) loading conditions. Crack growth in L–T and T–L oriented specimens is also examined. The test results indicate that the Crack path in the L–T oriented specimens under CA loading is remarkably meandering, but no significant Crack Branching is observed, compared with T–L oriented specimens; tension overloads produce macroscopic Crack Branching, and the K -level seems to be the principal factor on Crack path deviation.
Josko Ožbolt - One of the best experts on this subject based on the ideXlab platform.
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dynamic fracture of concrete l specimen experimental and numerical study
Engineering Fracture Mechanics, 2015Co-Authors: Josko Ožbolt, Akanshu Sharma, Natalija Bede, Uwe MayerAbstract:To confirm the findings of previously performed numerical studies, experimental and numerical studies on L-specimen loaded under different loading rates are performed. For strain rates lower than 10/s the response is controlled primarily by the rate dependent constitutive law. For higher strain rates a change in Crack direction, Crack Branching and progressive increase of resistance are observed. This is attributed to inertia and not to rate dependent strength. The comparison between numerical and experimental results shows that modeling approach based on continuum mechanics, rate dependent microplane model and standard finite elements predicts complex phenomena related to dynamic fracture of concrete realistically.
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dynamic fracture of concrete compact tension specimen experimental and numerical study
International Journal of Solids and Structures, 2013Co-Authors: Josko Ožbolt, Josipa Bosnjak, E SolaAbstract:Abstract Compared to quasi-static loading concrete loaded by higher loading rates acts in a different way. There is an influence of strain-rate and inertia on resistance, failure mode and Crack pattern. With increase of loading rate failure mode changes from mode-I to mixed mode. Moreover, theoretical and numerical investigations indicate that after the Crack reaches critical velocity there is progressive increase of resistance and Crack Branching. These phenomena have recently been demonstrated and discussed by Ožbolt et al. (2011) on numerical study of compact tension specimen (CTS) loaded by different loading rates. The aim of the present paper is to experimentally verify the results obtained numerically. Therefore, the tests and additional numerical studies on CTS are carried out. The experiments fully confirm the results of numerical prediction discussed in Ožbolt et al. (2011) . The same as in the numerical study it is shown that for strain rates lower than approximately 50/s the structural response is controlled by the rate dependent constitutive law, however, for higher strain rates Crack Branching and progressive increase of resistance is observed. This is attributed to structural inertia and not the rate dependent strength of concrete. Maximum Crack velocity of approximately 800 m/s is measured before initiation of Crack Branching. The comparison between numerical and experimental results shows that relatively simple modeling approach based on continuum mechanics, rate dependent microplane model and standard finite elements is capable to realistically predict complex phenomena related to dynamic fracture of concrete.
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numerical simulation of dynamic fracture of concrete through uniaxial tension and l specimen
Engineering Fracture Mechanics, 2012Co-Authors: Josko Ožbolt, Akanshu SharmaAbstract:Abstract Dynamic fracture of concrete is numerically evaluated using uniaxial tension and L-specimen. Previous work by authors demonstrated interesting aspects such as Crack Branching beyond threshold Crack speed. Uniaxial tensile behaviour of concrete under dynamic loads is difficult to study even numerically due to local problems near loading points. A specimen is designed to numerically assess the dynamic tensile behaviour that seems to be practical enough for carrying out experimental studies as well. The results demonstrate various phenomena such as Crack Branching, intercepting and re-Branching. Dynamic behaviour of L-specimen shows that the direction of Crack propagation strongly depends on displacement rate.
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dynamic fracture of concrete compact tension specimen
International Journal of Solids and Structures, 2011Co-Authors: Josko Ožbolt, Akanshu Sharma, Hanswolf ReinhardtAbstract:The behavior of concrete structures is strongly influenced by the loading rate. Compared to quasi-static loading concrete loaded by impact loading acts in a different way. First, there is a strain-rate influence on strength, stiffness, and ductility, and, second, there are inertia forces activated. Both influences are clearly demonstrated in experiments. Moreover, for concrete structures, which exhibit damage and fracture phenomena, the failure mode and Cracking pattern depend on loading rate. In general, there is a tendency that with the increase of loading rate the failure mode changes from mode-I to mixed mode. Furthermore, theoretical and experimental investigations indicate that after the Crack reaches critical speed of propagation there is Crack Branching. The present paper focuses on 3D finite-element study of the Crack propagation of the concrete compact tension specimen. The rate sensitive microplane model is used as a constitutive law for concrete. The strain-rate influence is captured by the activation energy theory. Inertia forces are implicitly accounted for through dynamic finite element analysis. The results of the study show that the fracture of the specimen strongly depends on the loading rate. For relatively low loading rates there is a single Crack due to the mode-I fracture. However, with the increase of loading rate Crack Branching is observed. Up to certain threshold (critical) loading rate the maximal Crack velocity increases with increase of loading rate, however, for higher loading rates maximal velocity of the Crack propagation becomes independent of the loading rate. The critical Crack velocity at the onset of Crack Branching is found to be approximately 500 m/s.
Ting Zhang - One of the best experts on this subject based on the ideXlab platform.
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fatigue Crack Branching in laser melting deposited ti 55511 alloy
International Journal of Fatigue, 2019Co-Authors: Kai Wang, Rui Bao, Ting Zhang, Binchao Liu, Zhongwei Yang, Bao JiangAbstract:Abstract Significant Crack Branching was observed in constant amplitude fatigue Crack growth test of laser melting deposited Ti–55511 alloy. Fracture microscopic observations indicate that the orderly distributed αp laths is the most important factor as it contributes a lot to the initiation of secondary Cracks and coalescence of microCracks. Propagation of subsurface secondary Cracks led to remarkable Crack Branching observed on the specimen surface. The Crack tip strain fields were measured by digital image correlation method, which gave a good monitoring of the Crack Branching process and helps a lot to understand the mechanism of Crack Branching behavior.
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a link up resulted fatigue Crack Branching in al cu mg alloy
International Journal of Fatigue, 2016Co-Authors: Rui Bao, Ting Zhang, Binjun FeiAbstract:Abstract Fatigue Crack Branching phenomena in Al–Cu–Mg alloy 2324-T39 are studied. Both spectrum and constant amplitude loading cases are examined. A novel type of Crack Branching process and mechanism is present, which results from the link-up of the secondary Crack with the main Crack. The grain shapes in 2324-T39 are different from those in the 2024 and 2524 alloys, and their interaction with the plastic zone size contributes to the appearance of this type of Crack Branching. FE analysis shows that the surface secondary Crack is located near the plastic zone boundaries of the main Crack.
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load effects on macroscopic scale fatigue Crack growth path in 2324 t39 aluminium alloy thin plates
International Journal of Fatigue, 2014Co-Authors: Ting Zhang, Rui Bao, Binjun FeiAbstract:Abstract In the present paper, an experimental study is accomplished to characterise the load effects, including K -level, stress ratio, overloads and underloads, on fatigue Crack growth path in aluminium alloy 2324-T39 thin plates under constant amplitude (CA) and simple variable amplitude (VA) loading conditions. Crack growth in L–T and T–L oriented specimens is also examined. The test results indicate that the Crack path in the L–T oriented specimens under CA loading is remarkably meandering, but no significant Crack Branching is observed, compared with T–L oriented specimens; tension overloads produce macroscopic Crack Branching, and the K -level seems to be the principal factor on Crack path deviation.
Rui Bao - One of the best experts on this subject based on the ideXlab platform.
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fatigue Crack Branching in laser melting deposited ti 55511 alloy
International Journal of Fatigue, 2019Co-Authors: Kai Wang, Rui Bao, Ting Zhang, Binchao Liu, Zhongwei Yang, Bao JiangAbstract:Abstract Significant Crack Branching was observed in constant amplitude fatigue Crack growth test of laser melting deposited Ti–55511 alloy. Fracture microscopic observations indicate that the orderly distributed αp laths is the most important factor as it contributes a lot to the initiation of secondary Cracks and coalescence of microCracks. Propagation of subsurface secondary Cracks led to remarkable Crack Branching observed on the specimen surface. The Crack tip strain fields were measured by digital image correlation method, which gave a good monitoring of the Crack Branching process and helps a lot to understand the mechanism of Crack Branching behavior.
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a link up resulted fatigue Crack Branching in al cu mg alloy
International Journal of Fatigue, 2016Co-Authors: Rui Bao, Ting Zhang, Binjun FeiAbstract:Abstract Fatigue Crack Branching phenomena in Al–Cu–Mg alloy 2324-T39 are studied. Both spectrum and constant amplitude loading cases are examined. A novel type of Crack Branching process and mechanism is present, which results from the link-up of the secondary Crack with the main Crack. The grain shapes in 2324-T39 are different from those in the 2024 and 2524 alloys, and their interaction with the plastic zone size contributes to the appearance of this type of Crack Branching. FE analysis shows that the surface secondary Crack is located near the plastic zone boundaries of the main Crack.
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load effects on macroscopic scale fatigue Crack growth path in 2324 t39 aluminium alloy thin plates
International Journal of Fatigue, 2014Co-Authors: Ting Zhang, Rui Bao, Binjun FeiAbstract:Abstract In the present paper, an experimental study is accomplished to characterise the load effects, including K -level, stress ratio, overloads and underloads, on fatigue Crack growth path in aluminium alloy 2324-T39 thin plates under constant amplitude (CA) and simple variable amplitude (VA) loading conditions. Crack growth in L–T and T–L oriented specimens is also examined. The test results indicate that the Crack path in the L–T oriented specimens under CA loading is remarkably meandering, but no significant Crack Branching is observed, compared with T–L oriented specimens; tension overloads produce macroscopic Crack Branching, and the K -level seems to be the principal factor on Crack path deviation.
