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Journal articles on the topic 'Macrocrack'

Author: Grafiati

Published: 3 June 2025

Last updated: 31 July 2025

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1

Eterashvili, Tamaz, G. Abuladze, L. Kotiashvili, T. Dzigrashvili, and M. Vardosanidze. "SEM Study of Fatigue Crack Propagation in Chromium Martensitic Steel after LCF." Key Engineering Materials 754 (September 2017): 15–18. http://dx.doi.org/10.4028/www.scientific.net/kem.754.15.

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Crack propagation after low-cycle fatigue (LCF) deformation has been studied in the chromium martensitic structural steel. Although the study of a fundamental mechanism of fatigue crack growth has received much attention over the last decade, it still remains a sufficiently complex problem and needs full understanding. Moreover, the recent studies show that the cracks propagate discontinuously even on the millisecond timescale, and their growth rate significantly depends on a microstructure of the material. In the present work the boundaries of the former austenitic grains were revealed on the

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2

Winkler, Andreas, Pia Bunger, Paula Morales Lang, Christine Schumann, Martin Brüggenwirth, and Moritz Knoche. "Mode of Action of Calcium in Reducing Macrocracking of Sweet Cherry Fruit." J. Amer. Soc. Hort. Sci. 149, no. 2 (2024): 61–74. http://dx.doi.org/10.21273/jashs05354-23.

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Rain cracking (hereinafter referred to as macrocracking) severely impacts the production of sweet cherry (Prunus avium). Calcium (Ca) sprays can reduce macrocracking, but the reported responses to Ca sprays are variable and inconsistent. The objective of this study was to establish the physiological mechanism through which Ca reduces macrocracking in sweet cherry fruit. Six spray applications of 50 mM CaCl2 had no effect on macrocracking (assessed using a standardized immersion assay) despite a 28% increase in the Ca-to-dry mass ratio. Similarly, during another experiment, there was no effect

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3

Li, Xu, Xiaotao Li, Hongda Yang, and Xiaoyu Jiang. "Interaction between a Macrocrack and a Cluster of Microcracks by Muskhelishvili’s Complex Potential Method." Mathematical Problems in Engineering 2018 (October 9, 2018): 1–12. http://dx.doi.org/10.1155/2018/8049318.

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The interaction between a macrocrack and a cluster of microcracks has been investigated based on Muskhelishvili’s complex potential method. A step-by-step subproblem procedure is used to satisfy the stress boundary conditions on each crack surface. The interactions between a cluster of microcracks and a macrocrack and the interaction among microcracks are analyzed. Three damage configurations as chained, reverse-chained, and randomly distributed microcracks have been designed to simulate the damage around the macrocrack tip. The solution of an infinite elastic plane containing a macrocrack and

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4

Popov, А. V., V. Yu Voloshina, E. M. Evdokimov, and D. S. Krivoshein. "A MODEL FOR ASSESSING THE DEGREE OF DANGER OF DEFECTS IN ACOUSTIC EMISSION DIAGNOSTICS OF PIPELINES OF HYDRAULIC SYSTEMS OF AIRCRAFT." Kontrol'. Diagnostika, no. 320 (February 2025): 14–21. https://doi.org/10.14489/td.2025.02.pp.014-021.

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A model for assessing the degree of hazard of defects has been developed, based on identifying the moment of formation of macrocracks (predestruction state) in the material of steel pipelines of aircraft hydraulic systems during their loading, where the deviation of the parameters of the recorded amplitude distributions of acoustic emission from the Poisson type is used as a criterion for the formation of a macrocrack. The results of experimental studies of controlled steel pipelines of the 12X18N10T brand under the pressure of the working fluid on a hydraulic test bench are presented.

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5

Rubinstein, A. A. "Macrocrack-Microdefect Interaction." Journal of Applied Mechanics 53, no. 3 (1986): 505–10. http://dx.doi.org/10.1115/1.3171803.

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Elastic interactions (in terms of the stress intensity factor variation) of the macrocrack (represented as semi-infinite crack) with microdefects such as finite size, arbitrarily positioned crack, circular hole or inclusion are considered. A solution for the problem of the interaction with dilational inclusion is also given. The influence of the crack tip geometry on the surrounding stress field is studied by analyzing the case of crack-hole coalescence. Problems are considered in terms of complex stress potentials for linear elasticity and formulated as a singular integral equation on the sem

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6

Taufiqullah, Taufiqullah, Setyo Nugroho Adhi, Dadan Ramdan Raden, Sasmita Firmansyah, Rodotun Siti, and Ramelan Aditianto. "Fabrication of macrocrack-free thick chromium duplex plating for remanufacturing applications." Eastern-European Journal of Enterprise Technologies 3, no. 12 (117) (2022): 42–51. https://doi.org/10.15587/1729-4061.2022.258728.

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The remanufacturing process of a hydraulic cylinder rod becomes a challenging prospect in the industrial sector producing heavy equipment. That is because remanufactured components can have the same product quality as new components with a more economical price. Hard chromium electrodeposition is a well-known technique to provide a protective coating for the cylinder rod so that it has favorable wear and corrosion resistance properties. Associated with remanufacturing applications, the used chromium plating covering the cylinder rod should be removed first before applying the new chromium one.

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7

Sahnoun, Mohamed, Djamel Ouinas, B. Bachir Bouiadjra, J. Vina Olay, and J. Vina Olay. "Numerical Modelling of the Interaction Macro–Multimicrocracks in a Pipe under Tensile Stress." Advanced Materials Research 1105 (May 2015): 245–50. http://dx.doi.org/10.4028/www.scientific.net/amr.1105.245.

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In this paper, the evaluation of the SIFof a macrocrack in interaction with one or several microcracks in a material containing a geometrical defect was investigated. Several configurations were considered in order to apprehend the mechanisms induced by the interaction effect and in particular the effects of reduction and/or amplification of the stress field between macro and single or multiple microcracks. The obtained results show that, macro–microcrack spacing is an important parameter if the microscopic crack is relatively close to the macrocrack-tip. The macrocrack has the tendency to acc

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8

Du, Jianhuan, Jingang Wang, and Zhu Fu. "Influence of Interaction between Microcracks and Macrocracks on Crack Propagation of Asphalt Concrete." Materials 17, no. 12 (2024): 2877. http://dx.doi.org/10.3390/ma17122877.

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This paper aims to reveal the interaction relationship between microcracks and macrocracks and the influence of the interaction on the crack propagation behavior. A theoretical model of asphalt concrete was established for the interaction between microcracks with different crack densities and a macrocrack. And a meso-structure model of AC-13 dense-graded asphalt concrete was established by combining the Talyor medium method and the DEM (discrete element method). Macro and micro parameters, such as the stress–strain characteristics, crack evolution parameters, and crack tip stress field, were o

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9

Chen, L. H., K. C. Huang, and Y. C. Chen. "Acoustic Emission at Wedge Indentation Fracture in Quasi-Brittle Materials." Journal of Mechanics 25, no. 2 (2009): 213–23. http://dx.doi.org/10.1017/s1727719100002677.

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AbstractTo improve the safety and automation of mechanical excavation methods used in tunnels, this present report studied the behavior of rock materials indented by a single cutter, based on the theory of indentation fracture mechanics. The development of microcracks during the indentation process and the correlation between microcracks and macrocracks was investigated using the nondestructive technique of acoustic emission. Microseismic activity of the microcracks received by the acoustic emission (AE) technique was used to interpret and represent the initiation and propagation of macrocrack

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10

Eterashvili, Tamaz, T. Dzigrashvili, and M. Vardosanidze. "Initial Aspects of Low-Cycle Fatigue Fracture of Martensitic Steels." Key Engineering Materials 348-349 (September 2007): 385–88. http://dx.doi.org/10.4028/www.scientific.net/kem.348-349.385.

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This study deals with the SEM and optical microscopic characterization of fatigue plastic deformation process during fatigue crack initiation to understand where, why and how cracks initiate under conditions of low cycle fatigue. Samples were prepared from the 13Х11Н2В2МФ high-chromium stainless steel used for fusion power applications. The low-cycle tests were conducted at room temperature with the standard V-notched samples prepared from conventional stainless steel. The following characteristics were studied during fatigue tests: 1 macrocrack propagation, 2. interaction between macrocrack a

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11

Rossi, Pierre. "Basis of A New Numerical Model of the Concrete/Steel Bond in Reinforced Concrete Structures." April 2023 4, no. 2 (2023): 1–5. http://dx.doi.org/10.36937/cebacom.2023.5839.

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This paper presents the basis of a new modeling approach of the concrete/steel bond. This approach has for objective to consider the macrocrack propagation through the steel rebar and the sliding along this rebar due to concrete microcracking. Concerning the macrocracks propagation a probabilistic semi-explicit cracking model is presented. This model integrates damage and linear fracture mechanics theories. Concerning the non-linear behaviour along the rebar, a very simple deterministic damage model is presented. A simple layer of volume elements is used to model the bond zone. Numerically spe

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12

Chiang, C. R. "Stress Field Around a Rounded Crack Tip." Journal of Applied Mechanics 58, no. 3 (1991): 834–36. http://dx.doi.org/10.1115/1.2897270.

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A method based on the eigenfunction (Williams stress functions) expansion is developed to examine the stress distribution around the tip region of a macrocrack which has some specific micro configuration. In particular, a macrocrack running into a micro hole under mode I condition is analyzed in detail. The coefficients associated with each eigenfunction are determined by a collocation procedure and the convergence of the numerical results is shown to be quite satisfactory.

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13

Lin, I. H. "Macrocrack-dislocation pile-up interactions." Materials Science and Engineering 81 (August 1986): 325–35. http://dx.doi.org/10.1016/0025-5416(86)90272-7.

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14

Молоков, К. А., and В. В. Новиков. "Assessment of the residual reliability of ship hull structures made of ferrite-pearlite steels with macrocracks based on structural and mechanical characteristics." MORSKIE INTELLEKTUAL`NYE TEHNOLOGII)</msg> 2, no. 3(65) (2024): 102–9. http://dx.doi.org/10.37220/mit.2024.65.3.013.

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Надежность конструкций судового корпуса напрямую связана с критической плотностью повреждений и их величиной. В условиях волнения и вибраций корпус испытывает циклические нагружения с разными частотами и амплитудами, поэтому его эксплуатация в жизненном цикле судна практически маловероятна без повреждений в виде возникающих микро и макротрещин трещин. Актуальной задачей остается определение плотности повреждений или их величины, необходимых для оценки момента начала катастрофического разрушения. На основе некоторых допущений и упрощений получена аналитическая зависимость существенно влияющих н

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15

Rita, Mariane Rodrigues, Pierre Rossi, Eduardo de Moraes Rego Fairbairn, and Fernando Luiz Bastos Ribeiro. "Determination of the Probabilistic Properties of the Critical Fracture Energy of Concrete Integrating Scale Effect Aspects." Applied Sciences 14, no. 1 (2024): 462. http://dx.doi.org/10.3390/app14010462.

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This paper presents an extension of the validation domain of a previously validated three-dimensional probabilistic semi-explicit cracking numerical model, which was initially validated for a specific concrete mix design. This model is implemented in a finite element code. The primary objective of this study is to propose a function that enables the estimation of the critical fracture energy parameter utilized in the model and validate its effectiveness for various concrete mix designs. The model focuses on macrocrack propagation and introduces significant aspects such as employing volume elem

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16

Eterashvili, Tamaz, Temur Dzigrashvili, and M. Vardosanidze. "SEM Study of the Influence of Microstructure on Low Cycle Fatigue Crack Growth in Martensitic Steel I." Key Engineering Materials 774 (August 2018): 96–100. http://dx.doi.org/10.4028/www.scientific.net/kem.774.96.

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Distribution of fatigue cracks in chromium martensitic steel after low cycle fatigue (LCF) tests at room temperature has been studied using SEM, and the experimental evidences of localized plastic flow (LPF) are presented. The influence of the location of LPF and the microstructure elements on the trajectory and growth of microcracks is also considered. The dimensions of plastic zones ahead of macrocrack tip as well as at its edges were measured in the process of crack propagation inside of the sample. The processes occurring in plastic zone, particularly ahead of macrocrack tip, were analyzed

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17

Zhao, LiGuo, and YiHeng Chen. "Effect of the T-Stress in Microcrack Shielding Problems." Journal of Applied Mechanics 65, no. 1 (1998): 71–75. http://dx.doi.org/10.1115/1.2789048.

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The effect of the T-stress in microcrack shielding problems is studied by solving the interaction problem of a macrocrack with near tip microcracks applying a discrete model. The T-stress has no effect on the results for the parallel microcrack cases; however, it plays an important role for the oriented microcrack cases, especially for large values of the T-stress and large distances of the microcrack center from the macrocrack tip. In determining the shielding or amplification effect of the oriented microcracks, it is necessary to consider the effect of the T-stress. The effect of the T-stres

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18

Liu, Dejun, Hai Pu, Hongyang Ni, and Guohui Zhang. "Experimental Study on the Physical and Mechanical Properties of Cemented Gangue Backfill under Acid Mine Water Erosion." Applied Sciences 14, no. 1 (2023): 107. http://dx.doi.org/10.3390/app14010107.

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Ensuring the structural safety of cemented gangue backfill (CGB) is crucial for safe mining operations. However, the complex mine water environment makes it susceptible to erosion by chemical ions, which have a significant time dependency. In this study, we evaluated the appearance, mass change, and unconfined compressive strength (UCS) of CGB during different chemical erosion times. We also determined the effect of chemical ion erosion time on the stress threshold for crack initiation and development in the specimens using acoustic emission (AE). Additionally, we examined the chemical erosion

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19

Chen, Y. H., and J. J. Han. "Macrocrack-Microcrack Interaction in Piezoelectric Materials, Part II: Numerical Results and Discussions." Journal of Applied Mechanics 66, no. 2 (1999): 522–27. http://dx.doi.org/10.1115/1.2791078.

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Numerical results are shown in figures and tables. The major features for the traditional stress intensity factors and the electric displacement intensity factor against the microcrack location angle and the distance of the microcrack center from the macrocrack tip are discussed. It is shown that, unlike single-crack problems, the mechanical loading and the electric loading are coupled together since the microcrack not only releases the near-tip stresses, but also disturbs the near-tip electric field. Furthermore, the influence of the electric loading on the mechanical strain energy release ra

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20

Yun, Hyun Do, Sun Woo Kim, and Esther Cheon. "Tensile Response and Fracture Process of High-Performance Hybrid Fiber-Reinforced Cement Composites." Key Engineering Materials 324-325 (November 2006): 715–18. http://dx.doi.org/10.4028/www.scientific.net/kem.324-325.715.

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Five twisted steel fibers (steel cord, SC) are used to improve the post-cracking behavior of cement composites. In addition to these steel cord macrofibers, microfibers are used to enhance the pre- and post-cracking strength and behavior. The three specific hybrid fiber blends pursued in this investigation are SC and polyethylene (PE), SC and polypropylene (PP) as well as SC and polyvinyl alcohol (PVA) fibers. The research results show that SC macrofibers with high ultimate strain, strength and bond stress can bridge the macrocracks in the matrix. Therefore, cement-based composites reinforced

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21

Saksala, Timo. "Effect of Grain Level Anisotropy on Numerical Rock Fracture Behaviour under Dynamic Loading." EPJ Web of Conferences 250 (2021): 02024. http://dx.doi.org/10.1051/epjconf/202125002024.

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The effect of rock crystal anisotropy is tested in numerical simulation of rock fracture at the laboratory sample level of scale. For this end, a numerical model based on the embedded discontinuity finite element method is applied here in simulations of uniaxial tension test on granitic rock. The rock material, consisting of Quartz (trigonal), Feldspar (triclinic) and Biotite (taken hexagonal here), is described as a linear elastic (up to fracture) heterogeneous and anisotropic material, which fails upon reaching the tensile strength of the individual constituent minerals. In the simulations o

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22

Son, Minjae, Gyuyong Kim, Hongseop Kim, et al. "Effect of Fiber Blending Ratio on the Tensile Properties of Steel Fiber Hybrid Reinforced Cementitious Composites under Different Strain Rates." Materials 14, no. 16 (2021): 4504. http://dx.doi.org/10.3390/ma14164504.

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In this study, a high-performance hybrid fiber-reinforced cementitious composite (HP-HFRCC) was prepared, by mixing hooked steel fiber (HSF) and smooth steel fiber (SSF) at different blending ratios, to evaluate the synergistic effect of the blending ratio between HSF and SSF and the strain rate on the tensile properties of HP-HFRCC. The experimental results showed that the micro- and macrocrack control capacities of HP-HFRCC varied depending on the blending ratio and strain rate, and the requirement for deriving the appropriate blending ratio was confirmed. Among the HP-HFRCC specimens, the s

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23

Hurtado, Grecia, and Moritz Knoche. "Necked strawberries are especially susceptible to cracking." PeerJ 11 (May 11, 2023): e15402. http://dx.doi.org/10.7717/peerj.15402.

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Fruit cracking is a commercially important disorder that reduces both quantity and quality of strawberries (Fragaria × ananassa Duch.). The objective was to identify the physiological mechanism of cracking and the factors affecting cracking. Cracking is more common in necked than in normal-shaped fruit. Most macroscopic cracks (‘macrocracks’) occur in the seedless neck. Large fruit is more cracking susceptible than medium size or small fruit. Macrocrack orientation is predominantly latitudinal in the proximal region of the neck and longitudinal in the mid and distal regions of the neck. The ne

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24

Rubinstein, Asher A. "Crack-Path Effect on Material Toughness." Journal of Applied Mechanics 57, no. 1 (1990): 97–103. http://dx.doi.org/10.1115/1.2888331.

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The material-toughening mechanism based on the crack-path deflection is studied. This investigation is based on a model which consists of a macrocrack (semi-infinite crack), with a curvilinear segment at the crack tip, situated in a brittle solid. The effect of material toughening is evaluated by comparison of the remote stress field parameters, such as the stress intensity factors (controlled by a loading on a macroscale), to effective values of these parameters acting in the vicinity of a crack tip (microscale). The effects of the curvilinear crack path are separated into three groups: crack

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25

Fukunaga, Y., M. Enoki, T. Kishi, and J. Kihara. "Dynamic Green’s Function of Finite Media by Finite Difference Method." Journal of Vibration and Acoustics 112, no. 1 (1990): 45–52. http://dx.doi.org/10.1115/1.2930097.

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A three-dimensional finite difference method (FDM) has been developed for the computation of elastic wave propagation in finite media containing a macrocrack, with a new treatment of boundary conditions of surfaces. The method can be used for the simulation of dynamic Green’s functions of an arbitrary rectangular parallelepiped medium with a macrocrack such as a compact tension (CT) specimen. The validity of the method has been confirmed by comparison with theoretical solutions of the plate problem for a monopole source and a double source. The method was then applied to the computation of Gre

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26

Rubinstein, Asher A. "Macrocrack interaction with semi-infinite microcrack array." International Journal of Fracture 27, no. 2 (1985): 113–19. http://dx.doi.org/10.1007/bf00040390.

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Rubinstein, A. A., and H. C. Choi. "Macrocrack interaction with transverse array of microcracks." International Journal of Fracture 36, no. 1 (1988): 15–26. http://dx.doi.org/10.1007/bf00034814.

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28

Tian, Wen-ye, and U. Gabbert. "Macrocrack–microcrack interaction problem in magnetoelectroelastic solids." Mechanics of Materials 37, no. 5 (2005): 565–92. http://dx.doi.org/10.1016/j.mechmat.2004.04.008.

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29

Karihaloo, B. L., and X. Huang. "Asymptotics of three-dimensional macrocrack-microcrack interaction." International Journal of Solids and Structures 32, no. 11 (1995): 1495–500. http://dx.doi.org/10.1016/0020-7683(94)00240-w.

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30

Gao, S., X. M. Wang, and Y. P. Shen. "Macrocrack interacting with microcrack on the interface." International Journal of Fracture 73, no. 4 (1995): R71—R77. http://dx.doi.org/10.1007/bf00027281.

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31

Ostash, O. P., and V. V. Panasyuk. "A unified model of initiation and growth of fatigue macrocracks. part 3. stage of growth of a macrocrack." Materials Science 35, no. 3 (1999): 299–309. http://dx.doi.org/10.1007/bf02355474.

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32

Rita, Mariane Rodrigues, Pierre Rossi, Eduardo de Moraes Rego Fairbairn, et al. "Three-Dimensional Probabilistic Semi-Explicit Cracking Model for Concrete Structures." Applied Sciences 14, no. 6 (2024): 2298. http://dx.doi.org/10.3390/app14062298.

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This paper introduces a three-dimensional (3D) semi-explicit probabilistic numerical model for simulating crack propagation within the framework of the finite element method. The model specifically addresses macrocrack propagation using linear volume elements. The criteria governing the macrocrack propagation is based on the softening behavior observed in concrete under uniaxial tension. This softening behavior corresponds to a dissipated cracking energy that is equal to the mode I critical fracture energy (GIC) used in the Linear Elastic Fracture Mechanics theory (LEFM). The probabilistic nat

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Sakane, M., M. Ohnami, and M. Sawada. "Fracture Modes and Low Cycle Biaxial Fatigue Life at Elevated Temperature." Journal of Engineering Materials and Technology 109, no. 3 (1987): 236–43. http://dx.doi.org/10.1115/1.3225970.

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This paper describes the crack growth direction in biaxial low cycle fatigue under combined axial and torsional stresses in hollow cylindrical specimens of type 304 stainless steel at 923 K in air. Three types of crack are identified, namely macrocrack greater than 1 mm in length, subcracks between 0.1 mm and 1.0 mm in length, and microcracks less than 0.1 mm in length. The macrocrack direction as well as that of the subcrack depends on the principal strain ratio but the microcrack is mode I for all the principal strain ranges tested. The connection of the three types of crack is discussed in

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Cai, H., and K. T. Faber. "On the Use of Approximation Methods for Microcrack Shielding Problems." Journal of Applied Mechanics 59, no. 3 (1992): 497–501. http://dx.doi.org/10.1115/1.2893751.

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There is experimental evidence that stress-induced microcracking near a macrocrack tip enhances the fracture toughness of brittle materials. In considering the interaction of the macrocrack with multiple microcracks using a discrete model, it is essential to use approximation methods in order to keep the amount of the computation to a tractable level. However, when crack distances are small, the results of the approximation methods can be significantly different from the numerical solution based upon the exact formulation. The results obtained by these approximation methods will be compared wi

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35

Bidos, Volodymyr, Taras Markiv, and Serhiy Solodkyy. "MECHANICAL PROPERTIES OF CEMENT CONCRETES INCORPORATING GROUND TIRE RUBBER." Theory and Building Practice 2021, no. 1 (2021): 106–12. http://dx.doi.org/10.23939/jtbp2021.01.106.

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This article proves the possibility of replacing aggregates in concrete mixtures with rubber, which is obtained by grinding used car tires. It was found that the replacement of crushed coarse aggregate in the amount of 10 vol.% with ground rubber from used car tires increases the bending strength by 23% The compressive strength does not change significantly. When working in the subcritical stage of deformation (until the macrocrack shifts), concrete with the replacement of the coarse aggregate is preferred, as the energy consumption of which for elastic deformation (We) exceeds the base concre

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Tamuzs, V., N. Romalis, and V. Petrova. "Influence of microcracks on thermal fracture of macrocrack." Theoretical and Applied Fracture Mechanics 19, no. 3 (1993): 207–25. http://dx.doi.org/10.1016/0167-8442(93)90022-4.

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Han, Jian-Jun, and Yi-Heng Chen. "J-integral analysis for microhole interacting with macrocrack." International Journal of Fracture 82, no. 2 (1996): R21—R24. http://dx.doi.org/10.1007/bf00034664.

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Eterashvili, Tamaz, Elguja Kutelia, T. Dzigrashvili, and M. Vardosanidze. "SEM Study of High-Chromium Martensitic Steel LCF Fracture." Key Engineering Materials 465 (January 2011): 298–301. http://dx.doi.org/10.4028/www.scientific.net/kem.465.298.

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Low cycle fatigue of high-chromium 13Х11Н2В2МФ stainless steel has been studied after cyclic tests at room temperature with the frequency of loading, 0.45Hz and amplitude, ± 1mm. The samples were v-notched with the dimensions x2x50, where =3mm. The peculiarities of fatigue crack propagation and influence of heat treatment, sizes of grains and laths, and disposition of microcrack and microstructure elements of the steel were studied. Next, the main effect on propagation direction is caused by the shape of grains and laths. It turned apparent that main microcrack is composed of individual mic

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Chen, Y. H., and J. J. Han. "Macrocrack-Microcrack Interaction in Piezoelectric Materials, Part I: Basic Formulations and J-Analysis." Journal of Applied Mechanics 66, no. 2 (1999): 514–21. http://dx.doi.org/10.1115/1.2791077.

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The macrocrack-microcrack interaction problem in transversely isotropic piezoelectric materials is studied. The microcracks near a macrocrack tip in the process zone are assumed to be parallel to the latter, while the poling direction of the piezoelectric materials is assumed to be perpendicular to the cracks. Three kinds of elementary solutions with different crack configurations and under different loading conditions are given, from which the interaction problem is reduced to a system of Fredholm integral equations by using the pseudo-traction electric displacement method (abbreviated PTED).

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Ostash, O. "A unified approach to fatigue macrocrack initiation and propagation." International Journal of Fatigue 25, no. 8 (2003): 703–8. http://dx.doi.org/10.1016/s0142-1123(03)00054-9.

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Lovisa, A. C., D. J. Henderson, J. D. Ginger, and G. Walker. "Characterising fatigue macrocrack initiation in profiled steel roof cladding." Engineering Structures 125 (October 2016): 364–73. http://dx.doi.org/10.1016/j.engstruct.2016.07.020.

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Da Yu Tzou and Chen Er-Ping. "Mesocrack damage induced by a macrocrack in heterogeneous materials." Engineering Fracture Mechanics 39, no. 2 (1991): 347–58. http://dx.doi.org/10.1016/0013-7944(91)90049-7.

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Wang, X. M., S. Gao, and Y. P. Shen. "Discussion on the neutral angle of macrocrack-microcrack interaction." Engineering Fracture Mechanics 54, no. 4 (1996): 597–99. http://dx.doi.org/10.1016/0013-7944(95)00186-7.

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Sato, Hiroshi, Hideyuki Aoki, Takatoshi Miura, and John W. Patrick. "Numerical analysis of macrocrack formation behaviour in lump coke." Fuel 76, no. 9 (1997): 879–85. http://dx.doi.org/10.1016/s0016-2361(97)00047-1.

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Pauchard, Ludovic, Bérengère Abou, and Ken Sekimoto. "Influence of Mechanical Properties of Nanoparticles on Macrocrack Formation." Langmuir 25, no. 12 (2009): 6672–77. http://dx.doi.org/10.1021/la9001384.

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Shiue, Sham‐Tsong, Tong‐Yi Zhang, and Sanboh Lee. "An edge dislocation near a macrocrack with a microcrack." Journal of Applied Physics 74, no. 10 (1993): 6079–87. http://dx.doi.org/10.1063/1.355192.

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Russell, S. G. "Diffusional growth of grain boundary voids near a macrocrack." Theoretical and Applied Fracture Mechanics 11, no. 3 (1989): 169–86. http://dx.doi.org/10.1016/0167-8442(89)90003-7.

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Skal’skii, V. R., V. B. Mikhal’chuk, Yu S. Okrepkii, and R. M. Plakhtii. "Determination of macrocrack start moment by acoustic-emission signals." Strength of Materials 38, no. 5 (2006): 559–64. http://dx.doi.org/10.1007/s11223-006-0077-7.

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Maji, A. K., and J. Wang. "Fracture mechanics of a tension-shear macrocrack in rocks." Experimental Mechanics 32, no. 2 (1992): 190–96. http://dx.doi.org/10.1007/bf02324732.

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Kaminsky, Anatoly A., and Mikhail F. Selivanov. "Mode II Macrocrack Initiation in Orthotropic Composite Viscoelastic Plate." International Journal of Fracture 139, no. 1 (2006): 153–60. http://dx.doi.org/10.1007/s10704-006-8373-6.

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