Journal articles: 'Quasi-static crack evolution'

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NEGRI, MATTEO, and CHRISTOPH ORTNER. "QUASI-STATIC CRACK PROPAGATION BY GRIFFITH'S CRITERION." Mathematical Models and Methods in Applied Sciences 18, no. 11 (November 2008): 1895–925. http://dx.doi.org/10.1142/s0218202508003236.

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We consider the propagation of a crack in a brittle material along a prescribed crack path and define a quasi-static evolution by means of stationary points of the free energy. We show that this evolution satisfies Griffith's criterion in a suitable form which takes into account both stable and unstable propagations, as well as an energy balance formula which accounts for dissipation in the unstable regime. If the load is monotonically increasing, this solution is explicit and almost everywhere unique. For more general loads we construct a solution via time discretization. Finally, we consider a finite element discretization of the problem and prove convergence of the discrete solutions.

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Hentati, Hamdi, Radhi Abdelmoula, Aref Maalej, and Khalil Maalej. "Quasi Static Analysis of Anti-Plane Shear Crack." Applied Mechanics and Materials 232 (November 2012): 92–96. http://dx.doi.org/10.4028/www.scientific.net/amm.232.92.

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Fracture mechanics has been revisited by proposing different models of quasi static brittle fracture. In this work, the problem of the quasi static crack propagation is based on variational approach. It requires no prior knowledge of the crack path or of its topology. Moreover, it is capable of modeling crack initiation. In the numerical experiments, we use a standard linear (P1) Lagrange finite element method for discretization. We perform numerical simulations of a piece of brittle material without initial crack. An alternate minimizations algorithm is used. Based on these numerical results, we determine the influence of numerical parameters on the evolution of energies and crack propagation. We show also the necessity of considering the kinetic term and the crack propagation becomes dynamic.

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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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Negri, Matteo, and Rodica Toader. "Scaling in fracture mechanics by Bažant law: From finite to linearized elasticity." Mathematical Models and Methods in Applied Sciences 25, no. 07 (April 14, 2015): 1389–420. http://dx.doi.org/10.1142/s0218202515500360.

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We consider crack propagation in brittle nonlinear elastic materials in the context of quasi-static evolutions of energetic type. Given a sequence of self-similar domains nΩ on which the imposed boundary conditions scale according to Bažant's law, we show, in agreement with several experimental data, that the corresponding sequence of evolutions converges (for n → ∞) to the evolution of a crack in a brittle linear-elastic material.

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Maso, Gianni Dal, and Chiara Zanini. "Quasi-static crack growth for a cohesive zone model with prescribed crack path." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 137, no. 2 (2007): 253–79. http://dx.doi.org/10.1017/s030821050500079x.

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In this paper we study the quasi-static crack growth for a cohesive zone model. We assume that the crack path is prescribed and we study the time evolution of the crack in the framework of the variational theory of rate-independent processes.

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Yasin Said, Mohamed, and Jianjun Chen. "Study on Defect Evolution of Steel Strip under High-speed Cold Rolling." Journal of Physics: Conference Series 2430, no. 1 (February 1, 2023): 012023. http://dx.doi.org/10.1088/1742-6596/2430/1/012023.

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Abstract In this paper the strain rate effect of the material was quantitatively tested by INSTRON tensile testing machine and Zwick/Roell HTM5020 high-speed tensile testing machine. The dimple size of the fracture surface of the tensile specimen was determined and analyzed by using the scanning electron microscope. Based on the Cowper-Symonds constitutive model, the parameters in the dynamic constitutive model and the true stress-strain curve under quasi-static condition were obtained by combining the results of quasi-static and dynamic tensile tests and the finite element numerical analyses. Considering the strain rate effect of the material the effects of cold rolling speed on the evolution of different types of defects were analyzed by the ANSYS/LS-DYNA dynamics code. The results show that with the increasing of crack length and decreasing of crack width, the critical rolling speed decreases. But if the crack length is less than 5 mm and the aspect ratio of crack length to crack width is larger than 5, the critical rolling speed of crack growth can be much large.

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J. Larsen, Christopher. "Local minimality and crack prediction in quasi-static Griffith fracture evolution." Discrete & Continuous Dynamical Systems - S 6, no. 1 (2013): 121–29. http://dx.doi.org/10.3934/dcdss.2013.6.121.

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Nifagin, V. A., and M. A. Gundina. "QUASISTATIC STATIONARY GROWTH OF ELASTOPLASTICAL CRACK." Vestnik of Samara University. Natural Science Series 20, no. 7 (May 30, 2017): 85–95. http://dx.doi.org/10.18287/2541-7525-2014-20-7-85-95.

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The boundary value problem with relations to the theory of ﬂow with non- linear hardening in derivatives stress and strain tensors in the parameter loading is formulated to estimate local mechanical properties in the vicinity of crack tip of mode of loading for plane strain of elastic-plastic material at the stage of quasi-static growth. Complete solutions are obtained by the method of asymp- totic decompositions. The redistribution of stress and strain ﬁelds in the plastic region at quasi-static growing crack for the intermediate structure is investigat- ed. The form of plastic zones was found in the evolution of fracture process of material. We also obtained direct estimates of errors and diameters of con- vergence when dropping residues of series.

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Li, Ling, EA Flores-Johnson, Luming Shen, and Gwénaëlle Proust. "Effects of heat treatment and strain rate on the microstructure and mechanical properties of 6061 Al alloy." International Journal of Damage Mechanics 25, no. 1 (January 23, 2015): 26–41. http://dx.doi.org/10.1177/1056789515569088.

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In the present work, the effects of heat treatment and strain rate on mechanical behaviour and microstructure evolution of aluminium alloy 6061 have been investigated. The micro-crack initiation and crystallographic texture evolution are obtained from scanning electron microscope and electron back-scatter diffraction experiments. Quasi-static and high strain rate compression tests are conducted on AA6061 specimens that underwent two different heat treatments: the as-received material with the original T6 heat treatment and the heat treated and artificially aged specimens. For the high strain rate compression (∼2000 and ∼4000 s−1) tests, the split Hopkinson pressure bar apparatus is used. It is observed that the additional heat treatment has significantly reduced the yield strength of the material. Furthermore, electron back-scatter diffraction results show that the higher the applied strain rate is, the less significant change will happen to the texture. Scanning electron microscope images show that, for both T6 and HT specimens, the number and size of micro-cracks in the dynamic compressed specimens are smaller than in the quasi-static deformed specimen. Therefore, the strain rate is considered to be the dominant factor in forming micro-cracks.

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Nozères, Frédéric, Hervé Couque, Rémi Boulanger, Yann Quirion, Patrice Bailly, and Jérôme Limido. "Numerical modelling strategies using implicit and explicit methods to simulate quasi-static and dynamic three-points bend fracture tests of a ductile steel." EPJ Web of Conferences 250 (2021): 02033. http://dx.doi.org/10.1051/epjconf/202125002033.

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Three-point bend fracture tests have been conducted at different loading rates with a quadratic martensitic steel. The failure energy has been found to increase with loading rate. To get insights in this increase a numerical investigation has been undertaken with different strategies using ABAQUS and IMPETUS softwares in order to address quasi-static and dynamic loading conditions. Simulations were conducted with the ABAQUS software in order to carry out a comparative analysis of both implicit and explicit approaches. In addition to standard Finite Element Method (FEM) applied to quasi-static and dynamic conditions, the eXtended-Finite Element Method (X-FEM) was applied to quasistatic conditions. In both approaches, implicit and explicit, crack initiation and propagation were governed by a critical plastic strain threshold combined with a displacement-based damage evolution criterion. Simulations conducted with the IMPETUS software use an explicit approach and second order elements for both quasi-static and dynamic loading conditions. A node-splitting method using an energy-based damage criterion was employed to simulate the crack initiation and propagation. Experimental data and numerical results have been compared, allowing to determine the ability of these two softwares to simulate accurately three-point bend fracture tests.

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Sornette, D., and C. Vanneste. "Faults self-organized by repeated earthquakes in a quasi-static antiplane crack model." Nonlinear Processes in Geophysics 3, no. 1 (March 31, 1996): 1–12. http://dx.doi.org/10.5194/npg-3-1-1996.

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Abstract. We study a 2D quasi-static discrete crack anti-plane model of a tectonic plate with long range elastic forces and quenched disorder. The plate is driven at its border and the load is transferred to all elements through elastic forces. This model can be considered as belonging to the class of self-organized models which may exhibit spontaneous criticality, with four additional ingredients compared to sandpile models, namely quenched disorder, boundary driving, long range forces and fast time crack rules. In this "crack" model, as in the "dislocation" version previously studied, we find that the occurrence of repeated earthquakes organizes the activity on well-defined fault-like structures. In contrast with the "dislocation" model, after a transient, the time evolution becomes periodic with run-aways ending each cycle. This stems from the "crack" stress transfer rule preventing criticality to organize in favour of cyclic behaviour. For sufficiently large disorder and weak stress drop, these large events are preceded by a complex spacetime history of foreshock activity, characterized by a Gutenberg-Richter power law distribution with universal exponent B = 1±0.05. This is similar to a power law distribution of small nucleating droplets before the nucleation of the macroscopic phase in a first-order phase transition. For large disorder and large stress drop, and for certain specific initial disorder configurations, the stress field becomes frustrated in fast time: out-of-plane deformations (thrust and normal faulting) and/or a genuine dynamics must be introduced to resolve this frustration.

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Purnomo and Putu Hadi Setyarini. "Fracture Propagation Pathways Pattern on UV-Irradiated Double-Edge Cracked of Mordenite Zeolite-HDPE Composites." Key Engineering Materials 851 (July 2020): 128–34. http://dx.doi.org/10.4028/www.scientific.net/kem.851.128.

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Mechanical failure of zeolite-high density polyethylene (HDPE) material applied to skull bone implants is a material fracture that cannot be controlled. An important step to minimize failure due to fracture is to understand the fracture characteristics indicated by the propagation path pattern. This study aimed to investigate the fracture propagation pathways of zeolite-HDPE composites in quasi-static conditions. UV-irradiated Double-edge cracked zeolite-HDPE composite was tested in mode I (a stress perpendicular to the plane of the crack) in a universal testing machine (UTM) with a crosshead speed of 2 mm/min at a constant room temperature of approximately 25°C. The stress and elongation were registered by the UTM. During loading, the evolution of cracks in the ligament length region was recorded with the camera so that the crack propagation pathway until the total fracture occurs can be clearly observed. The results show that the crack propagation pathway patterns were not all straight and parallel to the ligament length. They are also found in a deviant state of the ligament length line by forming an angle α. created between the ligament length line and the fracture propagation deviation direction. This deviation occurs after the crack propagates straight away from the initial-cracks.

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Du, Wen Wen, Qian Wang, Deng Hui Zhao, and Lin Wang. "Study on the Evolution of Adiabatic Shear Band of a High Strength Steel." Applied Mechanics and Materials 782 (August 2015): 143–50. http://dx.doi.org/10.4028/www.scientific.net/amm.782.143.

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The evolution process of a high strength steel which subjected with three different heat treatment proceedings and gets different quasi-static tensile properties was investigated in this paper. To precisely control the plastic deformation of the cylinder and capture the development process of adiabatic shear bands, stopper ring was used in Split Hopkinson Pressure Bar (SHPB). Combining the stress-strain curves and microstructures after SHPB tests, the microstructure evolution from the nucleation of adiabatic shear bands to fracture of the cylindrical steel were observed. The experimental results have demonstrated that there are similar fracture procedures of the steel treated through different heat treatments. Shear bands form firstly, then micro-cracks develop from shear bands, and lead to macro-crack finally. However, the critical strains for nucleation of ASBs and the time spending on the fracture procedure of the steel treated at different heat treatments are different. Samples treated at 900°C/AC exhibit the best resistance to adiabatic shear sensitivity when compressed under high strain rates.

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Neumeister, Peter, Hannes Kessler, and Herbert Balke. "Effect of switching stresses on domain evolution during quasi-static crack growth in a ferroelastic single crystal." Acta Materialia 58, no. 7 (April 2010): 2577–84. http://dx.doi.org/10.1016/j.actamat.2009.12.044.

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Hao, Qijun, Xiaohui Liu, Ankui Hu, Yu Zheng, and Xiaoping Zhao. "Research on Stress Threshold of Deep Buried Coal Rock under Quasi-Static Strain Rate Based on Acoustic Emission." Advances in Civil Engineering 2020 (September 21, 2020): 1–13. http://dx.doi.org/10.1155/2020/8893971.

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The deformation and failure process of coal rock under different strain rates is a significant challenge which must be solved in dynamic excavation. It is important to study the influence of strain rate on the evolution of coal rock crack. The triaxial compression tests and acoustic emission tests under the strain rate of 10−5 s−1 to 10−3 s−1 were conducted on coal rock using MTS 815 hydraulic servo-control testing machine. During the loading process, acoustic emission energy and spatial distribution have obvious stage characteristics. The damage variable is defined by acoustic emission energy, and the rate of damage evolution is obviously affected by the strain rate. Based on stage characteristics of acoustic emission energy, spatial distribution, and damage evolution, the use of damage evolution curve to determine stress threshold is proposed. In order to verify the rationality of the damage evolution method, the stress threshold values determined by damage evolution method and existing method are compared and analyzed. In order to study the effect of strain rate and confining pressure on the stress threshold, the stress thresholds under uniaxial and triaxial stress states at different strain rates were analyzed.

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Yun, Kumchol, Songhun Kwak, Zhenqing Wang, Mengzhou Chang, Jonggun Kim, Jingbiao Liu, and Cholsu Ri. "A Damage Model Reflecting the Interaction between Delamination and Intralaminar Crack for Failure Analysis of FRP Laminates." Applied Sciences 9, no. 2 (January 16, 2019): 314. http://dx.doi.org/10.3390/app9020314.

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In this paper, a progressive damage model reflecting the interaction between delamination and intralaminar crack is developed to predict fracture behaviors and the ultimate load-bearing ability of the fiber-reinforced polymer laminates subject to quasi-static load. Initiation and evolution of intralaminar crack in composites are modeled using a continuum damage mechanics model, which has the capability to reliably predict the discrete crack direction by introducing the crack direction parameter while analyzing the multi-failure of FRP composites. Delamination is modeled using a cohesive zone method with the mixed bilinear law. When the continuum damage model and cohesive zone model are used together, the interactive behavior between multiple failure mechanisms such as delamination induced by matrix cracking often seen in the failure of composite laminates is not generally captured. Interaction between delamination and intralaminar crack in FRP composite structures is investigated in detail and reflected in a finite element analysis in order to eliminate the drawbacks of using both models together. Good agreements between numerical results and experimental data are obtained.

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Zeng, Qing Na, Sheng Li Lv, Lei Jiang Yao, and Xiao Yan Tong. "Damage Mechanism of Plain Weave C/SiC Composites Subjected to Quasi-Static Indentation Loading." Advanced Materials Research 211-212 (February 2011): 217–21. http://dx.doi.org/10.4028/www.scientific.net/amr.211-212.217.

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Quasi-static indentation (QSI) tests on plain weave carbon fiber reinforced silicon carbide (C/SiC) ceramic matrix composites (CMC) have been performed to study the damage evolution law and damage modes. Acoustic emission (AE) and Ultrasonic C-scan techniques are creatively used to monitor the damage process and detect the indented damage, respectively. The damage development process could be described by three evidently different stages: initial crack tips spreading along within the matrix, matrix cracking and delamination as well as fiber bundles breakage of different layers. The AE activity indicated that the main damage modes are matrix cracking and delamination in the first two stages, once the pressing force exceeds the peak load the damage mode will change into fiber bundles breakage. Moreover, the damage procured in the QSI test is slightly lower than that produced in the low velocity impact (LVI) test under the equivalent energy, the correspondence between the two test methods is reasonably good.

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Li, Hui, Cheng Chen, Tongguang Wang, and Long Wang. "Experimental Study of Stepped-Lap Scarf Joint Repair for Spar Cap Damage of Wind Turbine Blade in Service." Applied Sciences 10, no. 3 (January 31, 2020): 922. http://dx.doi.org/10.3390/app10030922.

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The objective of this paper was to design configuration parameters for a stepped-lap scarf joint repair, which can be used for spar cap damage of a wind turbine blade in service and to realize the post-repair monitoring. Two experimental studies were included. First, tensile test for the unidirectional tape specimens with a large aspect ratio repaired using a multiple stepped-lap scarf joint method was carried out. The results showed that the reinforcement layer could effectively improve the load-carrying capacity of the repaired zone. The stepped-lap joint surface was identified as the weak part of the spar cap repair, which should be monitored. Second, by embedding carbon nanotube buckypaper sensors on the stepped-lap joint surface of the repaired specimens, quasi-static tensile tests and fatigue tests were carried out. According to the resistance response of the sensors, the quasi-static tensile test confirmed the failure processes, namely the stiffness turning point, damage evolution, crack propagation, and fracture. The fatigue test could accurately identify the progressive failure, namely the initial damage, damage accumulation, initial cracking, and crack propagation to structural failure. The above tests provided an important configuration parameter basis for evaluating the spar cap repair scheme and presented a promising method for the health monitoring of a spar cap after repair.

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Vodička, R. "Applications of a phase-field fracture model to materials with inclusions." IOP Conference Series: Materials Science and Engineering 1252, no. 1 (September 1, 2022): 012024. http://dx.doi.org/10.1088/1757-899x/1252/1/012024.

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Abstract Fracture in materials with inclusions is considered in the computational model of this contribution which allows prediction of crack propagation. The inclusions cause that cracks may appear inside the materials or along matrix-inclusion interfaces. The presented model can treat them both using two internal variables in a fashion of damage mechanics so that fracture is a consequence of the damage. The first variable is defined at the interface represented by a thin degradable adhesive layer so that an appropriate stress-strain relationship can be obtained as in cohesive zone models. The second variable is defined in the structural domains as a phase-field fracture variable which causes elastic properties degradation in a narrow material strip that forms a smeared crack. Both these damaging schemes are expressed in a unique quasi-static energy evolution process. The numerical solution approach is thus rendered from a variational form with a staggered time stepping procedure related to a separation of deformation variables from the damage ones and using non-linear programming algorithms implemented together within an own MATLAB finite element code. The numerical simulations with the model include simplified structural and material elements.

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Almi, Stefano. "Energy release rate and quasi-static evolution via vanishing viscosity in a fracture model depending on the crack opening." ESAIM: Control, Optimisation and Calculus of Variations 23, no. 3 (March 20, 2017): 791–826. http://dx.doi.org/10.1051/cocv/2016014.

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Schreiber, Christoph, Charlotte Kuhn, Ralf Müller, and Tarek Zohdi. "A phase field modeling approach of cyclic fatigue crack growth." International Journal of Fracture 225, no. 1 (July 17, 2020): 89–100. http://dx.doi.org/10.1007/s10704-020-00468-w.

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AbstractPhase field modeling of fracture has been in the focus of research for over a decade now. The field has gained attention properly due to its benefiting features for the numerical simulations even for complex crack problems. The framework was so far applied to quasi static and dynamic fracture for brittle as well as for ductile materials with isotropic and also with anisotropic fracture resistance. However, fracture due to cyclic mechanical fatigue, which is a very important phenomenon regarding a safe, durable and also economical design of structures, is considered only recently in terms of phase field modeling. While in first phase field models the material’s fracture toughness becomes degraded to simulate fatigue crack growth, we present an alternative method within this work, where the driving force for the fatigue mechanism increases due to cyclic loading. This new contribution is governed by the evolution of fatigue damage, which can be approximated by a linear law, namely the Miner’s rule, for damage accumulation. The proposed model is able to predict nucleation as well as growth of a fatigue crack. Furthermore, by an assessment of crack growth rates obtained from several numerical simulations by a conventional approach for the description of fatigue crack growth, it is shown that the presented model is able to predict realistic behavior.

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Pham, Kim, Hanen Amor, Jean-Jacques Marigo, and Corrado Maurini. "Gradient Damage Models and Their Use to Approximate Brittle Fracture." International Journal of Damage Mechanics 20, no. 4 (November 25, 2010): 618–52. http://dx.doi.org/10.1177/1056789510386852.

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In its numerical implementation, the variational approach to brittle fracture approximates the crack evolution in an elastic solid through the use of gradient damage models. In this article, we first formulate the quasi-static evolution problem for a general class of such damage models. Then, we introduce a stability criterion in terms of the positivity of the second derivative of the total energy under the unilateral constraint induced by the irreversibility of damage. These concepts are applied in the particular setting of a one-dimensional traction test. We construct homogeneous as well as localized damage solutions in a closed form and illustrate the concepts of loss of stability, of scale effects, of damage localization, and of structural failure. Considering several specific constitutive models, stress—displacement curves, stability diagrams, and energy dissipation provide identification criteria for the relevant material parameters, such as limit stress and internal length. Finally, the 1D analytical results are compared with the numerical solution of the evolution problem in a 2D setting.

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Zhang, Yan-nan, Wei Zhou, and Peng-fei Zhang. "Quasi-static indentation damage and residual compressive failure analysis of carbon fiber composites using acoustic emission and micro-computed tomography." Journal of Composite Materials 54, no. 2 (July 4, 2019): 229–42. http://dx.doi.org/10.1177/0021998319861140.

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In present research, the internal damage evolution and failure characteristics of carbon fiber woven composites under indentation and residual compressive loads were studied by using acoustic emission technology and X-ray micro-computed tomography. Real-time acoustic emission signals originating from internal damage of composites under applied loads were obtained and analyzed by the k-means clustering algorithm. Moreover, the internal damage characteristics were observed by the reconstructed three-dimensional model and the slice images of composite specimens. The results showed that the higher the indentation force reading, the more acoustic emission signals with high amplitude and frequency (over 300 kHz) are generated. Furthermore, the early acoustic emission signals with high-frequency were observed under residual compressive loads. It can be attributed to serious failures of fibers with the increase of static indentation loads. In addition, the internal damages such as delamination, debonding, crack and fiber breakage can be clearly characterized by micro-computed tomography and scanning electron microscopy observation. The complementary technology combing acoustic emission with micro-computed tomography can provide a better understanding of internal damages and evolution behaviors of the composites.

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Han, Jike, Bo Yin, Michael Kaliske, and Kenjiro Tarada. "Incorporation of gradient-enhanced microplane damage model into isogeometric analysis." Engineering Computations 38, no. 8 (June 4, 2021): 3388–415. http://dx.doi.org/10.1108/ec-08-2020-0455.

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Purpose This study aims to develop a new analysis approach devised by incorporating a gradient-enhanced microplane damage model (GeMpDM) into isogeometric analysis (IGA), which shows computational stability and capability in accurately predicting crack propagations in structures with complex geometries. Design/methodology/approach For the non-local microplane damage modeling, the maximum modified von-Mises equivalent strain among all microplanes is regularized as a representative quantity. This characterization implies that only one additional governing equation is considered, which improves computational efficiency dramatically. By combined use of GeMpDM and IGA, quasi-static and dynamic numerical analyses are conducted to demonstrate the capability in predicting crack paths of complex geometries in comparison to FEM and experimental results. Findings The implicit scheme with the adopted damage model shows favorable numerical stability and the numerical results exhibit appropriate convergence characteristics concerning the mesh size. The damage evolution is successfully controlled by a tension-compression damage factor. Thanks to the advanced geometric design capability of IGA, the details of crack patterns can be predicted reliably, which are somewhat difficult to be acquired by FEM. Additionally, the damage distribution obtained in the dynamic analysis is in close agreement with experimental results. Originality/value The paper originally incorporates GeMpDM into IGA. Especially, only one non-local variable is considered besides the displacement field, which improves the computational efficiency and favorable convergence characteristics within the IGA framework. Also, enjoying the geometric design ability of IGA, the proposed analysis method is capable of accurately predicting crack paths reflecting the complex geometries of target structures.

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Jen, Yi-Ming, and Yu-Ching Huang. "Improvement in Tensile Quasi-Static and Fatigue Properties of Carbon Fiber-Reinforced Epoxy Laminates with Matrices Modified by Carbon Nanotubes and Graphene Nanoplatelets Hybrid Nanofillers." Nanomaterials 11, no. 12 (December 20, 2021): 3459. http://dx.doi.org/10.3390/nano11123459.

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The monotonic and cyclic properties of carbon fiber-reinforced epoxy (CFEP) laminate specimens with matrices modified by multiwalled carbon nanotubes (MWCNTs) and graphene nanoplatelets (GNPs) were experimentally studied. The laminate specimens were fabricated by the hand lay-up procedure and six MWCNT:GNP weight ratios, i.e., 0:0, 10:0, 0:10, 5:5, 9:1, and 1:9, were considered to prepare the nanoparticle-modified epoxy resin by using an ultrasonic homogenizer and a planetary centrifugal mixer. Then, these laminate specimens with their matrices modified under various nanofiller ratios were employed to investigate the influence of the number of nanofiller types and hybrid nanofiller ratios on the quasi-static strength, fatigue strength, and mode I fracture toughness. The experimental results show that adding individual types of nanoparticles has a slight influence on the quasi-static and fatigue strengths of the CFEP laminates. However, the remarkable synergistic effect of MWCNTs and GNPs on the studied mechanical properties of the CFEP laminates with matrices reinforced by hybrid nanoparticles has been observed. Examining the evolution of stiffness-based degradation indicates that adding hybrid nanoparticles to the matrix can reduce the degradation effectively. The high experimental data of the mode I fracture toughness of hybrid nano-CFEP laminates demonstrate that embedding hybrid nanoparticles in the matrix is beneficial to the interlaminar properties, further improving the fatigue strength. The pushout mechanism of the MWCNTs and the crack deflection effect of the GNPs suppress the growth and linkage of microcracks in the matrix. Furthermore, the bridging effect of the nanoparticles at the fiber/matrix interface retards the interfacial debonding, further improving the resistance to delamination propagation.

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Madivala, Manjunatha, Alexander Schwedt, Ulrich Prahl, and Wolfgang Bleck. "Strain Hardening, Damage and Fracture Behavior of Al-Added High Mn TWIP Steels." Metals 9, no. 3 (March 21, 2019): 367. http://dx.doi.org/10.3390/met9030367.

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The strain hardening and damage behavior of Al-added twinning induced plasticity (TWIP) steels were investigated. The study was focused on comparing two different alloying concepts by varying C and Mn contents with stacking fault energy (SFE) values of 24 mJ/m 2 and 29 mJ/m 2 . The evolution of microstructure, deformation mechanisms and micro-cracks development with increasing deformation was analyzed. Al-addition has led to the decrease of C diffusivity and reduction in tendency for Mn-C short-range ordering resulting in the suppression of serrated flow caused due to dynamic strain aging (DSA) in an alloy with 0.3 wt.% C at room temperature and quasi-static testing, while DSA was delayed in an alloy with 0.6 wt.% C. However, an alloy with 0.6 wt.% C showing DSA effect exhibited enhanced strain hardening and ductility compared to an alloy with 0.3 wt.% C without DSA effect. Twinning was identified as the most predominant deformation mode in both the alloys, which occurred along with dislocation glide. Al-addition has increased SFE thereby delaying the nucleation of deformation twins and prolonged saturation of twinning, which resulted in micro-cracks initiation only just prior to necking or failure. The increased stress concentration caused by the interception of deformation twins or slip bands at grain boundaries (GB) has led to the development of micro-cracks mainly at GB and triple junctions. Deformation twins and slip bands played a vital role in assisting inter-granular crack initiation and propagation. Micro-cracks that developed at manganese sulfide and aluminum nitride inclusions showed no tendency for growth even after large deformation indicating the minimal detrimental effect on the tensile properties.

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Xie, Yi, Jianxi Ren, Tailang Caoxi, Xu Chen, and Mengchen Yun. "Triaxial Compression Fracture Characteristics and Constitutive Model of Frozen–Thawed Fissured Quasi-Sandstone." Applied Sciences 12, no. 13 (June 25, 2022): 6454. http://dx.doi.org/10.3390/app12136454.

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The artificial frozen wall crossing the water-rich sand layer is prone to failure during thawing. To study the loading fracture characteristics and damage evolution of single-fissured sandstone after thawing, quasi-sandstones with prefabricated single fissure at different angles were prepared using the sandstone of the Luohe Formation as the original rock to conduct freeze–thaw tests with various temperature differences, and triaxial compression tests were performed on the samples. Based on the distribution theory of rock micro-element strength and static elastic modulus, a damage constitutive model of single-fissured quasi-sandstone under freezing–thawing and confining pressure was established. The results show that with the decrease in freezing temperature, the amount of flake spalling on the sample surface increases, and the frost-heaving cracks of quasi-sandstone become more numerous and longer, which makes the single-fissured quasi-sandstone tend to have a more complex tensile–shear hybrid failure than a shear failure. Moreover, with the increase in fissure angle, the absolute value of the freezing temperature required to produce frost-heaving cracks increases. An S-shaped damage evolution curve corresponds to each stage of triaxial compression of single-fissured quasi-sandstone. With the decrease in freezing temperature, the strength of rock after thawing decreases, and the brittleness characteristics strengthen.

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Bruno, Caterina L. E., Paola Antonaci, Pietro G. Bocca, Antonio S. Gliozzi, and Marco Scalerandi. "Linking Elastic Nonlinearity and Cracks Growth in Mortar Samples." Key Engineering Materials 417-418 (October 2009): 293–96. http://dx.doi.org/10.4028/www.scientific.net/kem.417-418.293.

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One of the signatures of the presence of cracks in a sample is the nonlinearity in its elastic response to an impingent ultrasonic wave. The Fourier analysis is often inadequate to monitor the evolution of nonlinearity, since the signal-to-noise ratio of higher order harmonics is very low. In order to overcome this drawback, we suggest an alternative procedure to extract nonlinearity indicators from a recorded ultrasonic signal, based on the amplitude dependence of the response of the system. The procedure is first described and then used to analyse the evolution of the nonlinearity due to cracks induced by a quasi-static loading in mortar samples. Our approach allows to distinguish the compaction phase from the micro-damage progression and the pre-rupture phases.

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Negri, M. "From phase field to sharp cracks: Convergence of quasi-static evolutions in a special setting." Applied Mathematics Letters 26, no. 2 (February 2013): 219–24. http://dx.doi.org/10.1016/j.aml.2012.08.016.

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Li, Tian Yi, Jean Jacques Marigo, Daniel Guilbaud, and Serguei Potapov. "Variational Approach to Dynamic Brittle Fracture via Gradient Damage Models." Applied Mechanics and Materials 784 (August 2015): 334–41. http://dx.doi.org/10.4028/www.scientific.net/amm.784.334.

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In this paper we present a family of gradient-enhanced continuum damage models which can be viewed as a regularization of the variational approach to fracture capable of predicting in a unified framework the onset and space-time dynamic propagation (growth, kinking, branching, arrest) of complex cracks in quasi-brittle materials under severe dynamic loading. The dynamic evolution problem for a general class of such damage models is formulated as a variational inequality involving the action integral of a generalized Lagrangian and its physical interpretation is given. Finite-element based implementation is then detailed and mathematical optimization methods are directly used at the structural scale exploiting fully the variational nature of the formulation. Finally, the link with the classical dynamic Griffith theory and with the original quasi-static model as well as various dynamic fracture phenomena are illustrated by representative numerical examples in quantitative accordance with theoretical or experimental results.

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Meola, Carosena, Simone Boccardi, and Giovanni Maria Carlomagno. "The Contribution of Infrared Thermography in the Characterization of Glass/Epoxy Laminates through Remote Sensing of Thermal-Stress Coupled Effects." Proceedings 15, no. 1 (July 12, 2019): 21. http://dx.doi.org/10.3390/proceedings2019015021.

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Mechanical stresses of materials are generally coupled with temperature variations and then, monitoring such variations can help gaining information about the material behavior under the applied loads. This can be accomplished with an infrared imaging device, which can be advantageously exploited to sense the thermal radiation associated with mechanical stresses and to obtain a legible explicative temperature map. In the present paper, glass/epoxy is used as material case study to show that thermal signatures visualized during the load application can be decoded into knowledge, which can contribute to the material characterization. In particular, glass/epoxy specimens are subjected to three types of tests: cantilever beam alternate bending, quasi-static bending and low velocity impact. Thermal images are acquired in time sequence during each test and after post-processed and analyzed. It is possible to get data about the damage initiation and its evolution under either quasi-static bending, or impact. In particular, a cute analysis of thermal images supplies information about damage types (matrix cracks, or fibers breakage) and extension of delamination, as well of the impact duration and the time to reach peak contact force. It is also possible to well depict the harmonic cantilever beam oscillations through the associated small temperature variations.

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Gomez, Q., and I. R. Ionescu. "Micro-mechanical fracture dynamics and damage modelling in brittle materials." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 379, no. 2196 (March 15, 2021): 20200125. http://dx.doi.org/10.1098/rsta.2020.0125.

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This study explores the interplay between wave propagation and damage in brittle materials. The damage models, based on micro-mechanical fracture dynamics, capture any possible unstable growth of micro-cracks, introducing a macroscopic loss of stability. After stating the non-dimensional mathematical problem describing the wave propagation with damage, we introduce a non-dimensional number, called the microscopic evolution index, which links the micro and macro scales and discriminates the microscopic scale behaviour. For large values of microscopic evolution index, corresponding to a microscopic quasi-static process coupled with a macroscopic dynamic one, the macroscopic dynamic system could lose its hyperbolicity or become very stiff and generate shock waves. A semi-analytical solution to the one-dimensional wave propagation problem with damage, which could be very useful in the accuracy evaluation of the numerical schemes, was constructed. Concerning the asymptotic behaviour of the dynamic exact solution on the microscopic evolution index (or on the strain rate), an important strain rate sensitivity was found: the pulse loses its amplitude for decreasing strain rate and, starting with a critical value, the micro-scale model is rate independent. A possible regularization technique to smooth the shock waves at low and moderate strain rates is discussed. Finally, some numerical results analyse the role played by the the friction on the micro-cracks in the damage modelling of blast wave propagation. This article is part of the theme issue ‘Fracture dynamics of solid materials: from particles to the globe’.

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Zhang, Xiaolong, and Zheng Zhong. "Thermo-Chemo-Elasticity Considering Solid State Reaction and the Displacement Potential Approach to Quasi-Static Chemo-Mechanical Problems." International Journal of Applied Mechanics 10, no. 10 (December 2018): 1850112. http://dx.doi.org/10.1142/s1758825118501120.

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Engineering materials and structures represent complex behaviors when reacting to superposed influences of mechanical forces, high temperature, diffusion and reaction of chemicals, which could cause large internal stresses and further induce cracks or failure. To determine the material reliability and integrity, the multi-field interactions and stresses/strains evolutions need to be identified at first. We proposed a theory of thermo-chemo-elasticity considering solid state reactions between the solid phase and absorbed chemicals in a stressed-solid. Both diffusion–reaction induced chemical strains and thermal dilations are taken into account as functions of species concentration, reaction extent and temperature. The fully coupled conservation laws, constitutive equations and chemical kinetics are formulated for the initial-boundary problem. For isotropic solids, we developed a displacement potential approach for steady-state 3D problems of thermo-chemo-elasticity. Solutions can be found from particular solutions of displacement potential and homogeneous solution of thermo-chemo Lamé equation. This approach is also available for transient chemo-mechanical problems in thermal equilibrium providing that quasi-static conditions are introduced. We exemplified the model with a reaction-dominated problem of a core–shell structure subjected to chemo-mechanical loading and the results demonstrate the capability of the model in dealing with comprehensive influences of solid state reaction and species diffusion on solids.

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Bahmani, Bahador, Reza Abedi, and Philip Clarke. "A Stochastic Bulk Damage Model Based on Mohr-Coulomb Failure Criterion for Dynamic Rock Fracture." Applied Sciences 9, no. 5 (February 26, 2019): 830. http://dx.doi.org/10.3390/app9050830.

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We present a stochastic bulk damage model for rock fracture. The decomposition of strain or stress tensor to its negative and positive parts is often used to drive damage and evaluate the effective stress tensor. However, they typically fail to correctly model rock fracture in compression. We propose a damage force model based on the Mohr-Coulomb failure criterion and an effective stress relation that remedy this problem. An evolution equation specifies the rate at which damage tends to its quasi-static limit. The relaxation time of the model introduces an intrinsic length scale for dynamic fracture and addresses the mesh sensitivity problem of earlier damage models. The ordinary differential form of the damage equation makes this remedy quite simple and enables capturing the loading rate sensitivity of strain-stress response. The asynchronous Spacetime Discontinuous Galerkin (aSDG) method is used for macroscopic simulations. To study the effect of rock inhomogeneity, the Karhunen-Loeve method is used to realize random fields for rock cohesion. It is shown that inhomogeneity greatly differentiates fracture patterns from those of a homogeneous rock, including the location of zones with maximum damage. Moreover, as the correlation length of the random field decreases, fracture patterns resemble angled-cracks observed in compressive rock fracture.

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Badal, Rufat, Manuel Friedrich, and Joscha Seutter. "Existence of quasi-static crack evolution for atomistic systems." Forces in Mechanics, November 2022, 100138. http://dx.doi.org/10.1016/j.finmec.2022.100138.

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Xu, Hao, Marta Kuczynska, Natalja Schafet, Fabian Welschinger, and Jörg Hohe. "FE-based damage modeling approach for short fiber reinforced thermoplastics under quasi-static load coupling anisotropic viscoplasticity and matrix degradation." Journal of Composite Materials, June 19, 2022, 002199832211093. http://dx.doi.org/10.1177/00219983221109327.

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It is challenging to predict the material degradation and crack initiation of short fiber reinforced thermoplastics (SFRT) components with high computation efficiency and low parameter identification effort. To achieve that, this work utilizes a hybrid method combining micro- and macro-mechanical approaches to describe the damage-coupled material behavior of SFRT. The Mori-Tanaka mean-field homogenization method is used to determine the effective linear elastic properties of SFRT, whereas the consideration of plasticity is based on a macro-mechanical anisotropic viscoplastic model. The effect of micro-damage in the matrix material on the macroscopic behaviors of SFRT is considered within the Continuum Damage Mechanics (CDM) framework. A nonlinear damage evolution law is implemented to account for the nonlinearity in the damage evolution. Targeting industrial applications, the proposed damage-coupled material model is implemented into the commercial FE software ANSYS with a novel stepwise damage updating process, requiring no user-defined subroutine. The model is calibrated with experimental data on flat specimens under monotonic and cyclic tensile loading. The FE simulation with the calibrated material model accurately describes the anisotropic deformation and crack initiation of the investigated SFRT material observed in experiments.

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Bhat, Harsha S., Ares J. Rosakis, and Charles G. Sammis. "A Micromechanics Based Constitutive Model for Brittle Failure at High Strain Rates." Journal of Applied Mechanics 79, no. 3 (April 5, 2012). http://dx.doi.org/10.1115/1.4005897.

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The micromechanical damage mechanics formulated by Ashby and Sammis, 1990, “The Damage Mechanics of Brittle Solids in Compression,” Pure Appl. Geophys., 133(3), pp. 489–521, and generalized by Deshpande and Evans 2008, “Inelastic Deformation and Energy Dissipation in Ceramics: A Mechanism-Based Constitutive Model,” J. Mech. Phys. Solids, 56(10), pp. 3077–3100. has been extended to allow for a more generalized stress state and to incorporate an experimentally motivated new crack growth (damage evolution) law that is valid over a wide range of loading rates. This law is sensitive to both the crack tip stress field and its time derivative. Incorporating this feature produces additional strain-rate sensitivity in the constitutive response. The model is also experimentally verified by predicting the failure strength of Dionysus-Pentelicon marble over strain rates ranging from ∼10− 6to 103s− 1. Model parameters determined from quasi-static experiments were used to predict the failure strength at higher loading rates. Agreement with experimental results was excellent.

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Zanuy Sánchez, Carlos, and Gonzalo S. D. Ulzurrun. "Time-variation of shear forces affecting the impact resistance of reinforced concrete beams." Hormigón y Acero, November 18, 2022. http://dx.doi.org/10.33586/hya.2022.3088.

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One of the most hazardous scenarios for reinforced concrete (RC) members is due to the actuation of impact loads. Such impacts may be either accidental or induced events. Experimental research has demonstrated that the failure mode of RC beams is strongly governed by shear, due either to the formation of a shear plug close to the impact point or to the full development of inclined shear-bending cracks along the shear span. In order to analyze the shear strength under impact conditions, it is essential to understand how the development of inertia forces leads to a time-dependent distribution of shear forces and bending moments which differs significantly to those produced by quasi-static loads. In the paper, an experimentally-based determination of shear forces and follow-up of crack pattern is presented for RC beams tested under impact loads. A Digital Image Correlation technique supported by a high-speed camera is used to understand the evolution of shear forces at critical sections and to discuss the ultimate shear strength provided by M-V interaction diagrams.

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Gao, Yushan, Wei Jiang, and Shihui Huo. "Fracture mechanism and failure criterion of S-07 steel for liquid rocket engine." Multidiscipline Modeling in Materials and Structures, March 1, 2023. http://dx.doi.org/10.1108/mmms-11-2022-0257.

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PurposeThe fracture mechanism of S-07 steel was investigated by observing the fracture surface of the specimens with scanning electron microscope (SEM). Furthermore, the overall elastic–plastic behaviors and the stress state evolution during the loading procedure of all specimens were simulated by FE analysis to obtain the local strain at crack nucleated location and the average triaxiality of each type of specimen.Design/methodology/approachThree types of tests under various stress states were performed to study the ductile fracture characteristics of S-07 high strength steel in quasi-static condition.FindingsUnder tensile and torsion loading conditions, S-07 steel exhibits two distinctive rupture mechanisms: the growth and internal necking of voids governs the rupture mechanism in tension dominated loading mode, while the change of void shape and internal shearing in the ligaments between voids dominants for shear conditions.Originality/valueThe failure criterion for S-07 steel considering the influence of the triaxial stress state was established.

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Journal articles on the topic 'Quasi-static crack evolution'

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