The Mathematical Study of an Edge Crack in Two Different Specified Models under Time-Harmonic Wave Disturbance

Trivedi, N.; Das, Subir; Craciun, Eduard‐Marius

doi:10.1007/s11029-022-10007-4

Cited by 25 publications

(6 citation statements)

References 32 publications

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“…Diankui and Hong [17] found a solution to an interfacial linear fracture that interacts with a circular cavity. Investigation of how time-harmonic shear wave disturbance affected the edge crack problem has been addressed in [18]. Semi-infinite crack growth has been exhibited in [19] to show that edge wave phase speed exhibits dual dependency on current and frequency, which results in distinct asymptotic behaviors.…”

Section: Introductionmentioning

confidence: 99%

Wiener–Hopf method to solve the anti-plane problem of moving semi-infinite crack in orthotropic composite materials

Das,

Tanwar,

Das

et al. 2024

Mathematics and Mechanics of Solids

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This paper contains the solution to the problem of a semi-infinite moving crack situated in an orthotropic strip bonded between two identical strips. The crack moves with a constant velocity, and the surface is under shear wave disturbance. We first examine the equations of elasticity, which include equilibrium equations and stress and displacement constitutive relations with the model-specific continuity and boundary conditions. Using the Fourier integral transform, the standard form for the Wiener–Hopf (W-H) equation is obtained, which is solved using the W-H method. The analytical expressions for the considered crack problem have been obtained for stress intensity factor (SIF), normalized stress intensity factor (NSIF), and stress magnification factor (SMF). The behavior of NSIF has been graphically presented for particular cases of composite materials for different crack propagation velocities and various depth ratios of the strips. The novelty of this paper lies in the analytic solutions using the W-H method for the semi-infinite moving crack problem under the influence of anti-plane shear waves. The pictorial presentations of normalized SIF clearly show their dependency on strip depths, crack propagation velocities and elastic constants.

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Section: Introductionmentioning

confidence: 99%

Wiener–Hopf method to solve the anti-plane problem of moving semi-infinite crack in orthotropic composite materials

Das,

Tanwar,

Das

et al. 2024

Mathematics and Mechanics of Solids

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“…The fatigue testing using the resonance method is not yet standardized [ 3 ], although it is currently applied in many scientific works [ 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 , 20 ] and there are some companies that produce specialized stands for specific application of resonance fatigue testing.…”

Section: Introductionmentioning

confidence: 99%

Numerical and Experimental Study of the Fatigue Behavior for a Medical Rehabilitation Exoskeleton Device Using the Resonance Method

et al. 2023

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“…Their study highlighted the significance of adjusting various parameters to control and comprehend SIF and COD values, provided valuable insights into the behavior of cracks in orthotropic materials. Trivedi et al [26] investigated the SIFs at the tip of an edge crack in two distinct orthotropic models. The first model involved an orthotropic strip with finite thickness bonded to an orthotropic half-plane, while the second model featured an orthotropic vertical semi-infinite strip of the same thickness.…”

Section: Introductionmentioning

confidence: 99%

“…Trivedi et al. [26] investigated the SIFs at the tip of an edge crack in two distinct orthotropic models. The first model involved an orthotropic strip with finite thickness bonded to an orthotropic half‐plane, while the second model featured an orthotropic vertical semi‐infinite strip of the same thickness.…”

Section: Introductionmentioning

confidence: 99%

Analytical calculation of stress intensity factors for orthotropic plates containing cracks emanating from a circular hole using Schwarz integration

Moussavian,

Jafari,

Hajimohammadi

2023

Z Angew Math Mech

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In this paper, a new analytical method is presented to determine the stress intensity factors (SIFs) of a generally orthotropic plate with cracks emanating from a circular hole. Therefore, using the Schwartz integration method, for the first time, the analytical solution is provided based on the complex variable method. In order to use the Schwartz's theorem in solving complex integrals, a new presentation of the mapping function has been presented, which leads to providing a simpler solution. After calculating the potential functions, the SIFs are determined for the circular hole with one and two cracks. Then, the effect of parameters such as fiber angle, different and unequal crack lengths, and different loadings are studied. To validate the results of the present analytical solution, some results have been compared with the results from other references. Comparing the results showed that the current solution has good accuracy and is reliable and the fiber angle has a significant effect on the mode II SIF. In the case that the fibers are along the crack length and the loading is perpendicular to the crack direction, the mode II SIF is zero, but if the fibers are not along the crack length, the value of the mode II SIF will not be zero. It is also shown that increasing the length of one crack increases the SIF of another crack as well.

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The Mathematical Study of an Edge Crack in Two Different Specified Models under Time-Harmonic Wave Disturbance

Cited by 25 publications

References 32 publications

Wiener–Hopf method to solve the anti-plane problem of moving semi-infinite crack in orthotropic composite materials

Wiener–Hopf method to solve the anti-plane problem of moving semi-infinite crack in orthotropic composite materials

Numerical and Experimental Study of the Fatigue Behavior for a Medical Rehabilitation Exoskeleton Device Using the Resonance Method

Analytical calculation of stress intensity factors for orthotropic plates containing cracks emanating from a circular hole using Schwarz integration

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