Analytical study on the mode III stress fields due to blunt notches with cracks

Zappalorto, Michele; Salviato, Marco; Maragoni, L.

doi:10.1111/ffe.12936

Cited by 7 publications

(3 citation statements)

References 33 publications

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“…Seweryn and Molski 24 presented the stress and displacement fields' solution around the notch tip under antiplane shear loading and different boundary conditions. Zappalorto and his coworkers [25][26][27][28][29] utilized complex variable approach for determination of elastic stress distribution around different notch shapes in a round shaft under torsion. Their solution exactly matches the Seweryn's solution for sharp notches, when the notch angle tends to zero.…”

Section: Introductionmentioning

confidence: 99%

Higher order stress terms in sharp notch problems under pure‐out‐of‐plane loading

Mehraban

Ayatollahi

Bahrami

et al. 2021

Fatigue Fract Eng Mat Struct

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Current paper studies the effects of higher order terms (HOTs) on the stress and displacement fields around sharp V-notched components under pure antiplane shear (mode III) loading. For this aim, two V-notched test samples each containing four different notch angles are simulated in a finite element (FE) commercial software. Subsequently, the over-deterministic technique is used as an approach to calculate the coefficients of singular and nonsingular terms out of the nodal displacement values. To verify the accuracy of the values calculated as the coefficients, the stress field reconstructed from the truncated series expansions is compared with the direct nodal outputs of FE analysis. The results demonstrate that the use of nonsingular terms of the asymptotic series expansion is necessary only in the case that the distribution of stress at far distances from the notch tip is sought and the notch angle is small. To check the stability of the results, some of the parameters which affect accurate determination of unknown coefficients and convergence of the numerical results are studied.

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Section: Introductionmentioning

confidence: 99%

Higher order stress terms in sharp notch problems under pure‐out‐of‐plane loading

Mehraban

Ayatollahi

Bahrami

et al. 2021

Fatigue Fract Eng Mat Struct

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“…Leveraging the relation between the electric field, the electric potential, and the current density along with the C-R conditions on the curvilinear coordinates, one can write the Cartesian components of the current density as J x = c∂v=∂x and J y = c∂u=∂x. It is worth noting that, since j 0 = d j= d z = ∂u=∂x + i∂v=∂x, the Cartesian components of the current density represent the real and imaginary parts of the first derivative of the conformal map used to describe the domain, j = j z ð Þ [28,29,33]. Accordingly, the current density can be written as…”

Section: General Solutionmentioning

confidence: 99%

Enhancing the electrical and thermal conductivities of polymer composites via curvilinear fibers: An analytical study

Salviato

Phenisee

2019

Mathematics and Mechanics of Solids

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The new generation of manufacturing technologies such as additive manufacturing and automated fiber placement has enabled the development of material systems with desired functional and mechanical properties via particular designs of inhomogeneities and their mesostructural arrangement. Among these systems, particularly interesting are materials exhibiting curvilinear transverse isotropy (CTI), in which the inhomogeneities take the form of continuous fibers following curvilinear paths designed to, for example, optimize the electric and thermal conductivity, and the mechanical performance of the system. In this context, the present work proposes a general framework for the exact, closed-form solution of electrostatic problems in materials featuring CTI. First, the general equations for the fiber paths that optimize the electric conductivity are derived, leveraging a proper conformal coordinate system. Then, the continuity equation for the curvilinear transversely isotropic system is derived in terms of electrostatic potential. A general exact, closed-form expression for the electrostatic potential and electric field is derived and validated by finite element analysis. Finally, potential avenues for the development of materials with superior electric conductivity and damage sensing capabilities are discussed.

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“…A series of studies are initiated to seek the analytical solutions of notches and cracks [11][12][13] . Based on the analytical framework, the notch stress intensity factor (NSIF) is applied to the weld roots of welded joints with inclusion of the T-stress component [14] .…”

Section: Introductionmentioning

confidence: 99%

Analytical solution for the stress field of hierarchical defects: multiscale framework and applications

Sheng

2020

Appl. Math. Mech.-Engl. Ed.

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Hierarchical defects are defined as adjacent defects at different length scales. Involved are the two scales where the stress field distribution is interrelated. Based on the complex variable method and conformal mapping, a multiscale framework for solving the problems of hierarchical defects is formulated. The separated representations of mapping function, the governing equations of potentials, and the stress field are subsequently obtained. The proposed multiscale framework can be used to solve a variety of simplified engineering problems. The case in point is the analytical solution of a macroscopic elliptic hole with a microscopic circular edge defect. The results indicate that the microscopic defect aggregates the stress concentration on the macroscopic defect and likely leads to global propagation and rupture. Multiple micro-defects have interactive effects on the distribution of the stress field. The level of stress concentration may be reduced by the coalescence of micro-defects. This work provides a unified method to analytically investigate the influence of edge micro-defects within the scope of multiscale hierarchy. The formulated multiscale approach can also be potentially applied to materials with hierarchical defects, such as additive manufacturing and bio-inspired materials.

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Analytical study on the mode III stress fields due to blunt notches with cracks

Cited by 7 publications

References 33 publications

Higher order stress terms in sharp notch problems under pure‐out‐of‐plane loading

Higher order stress terms in sharp notch problems under pure‐out‐of‐plane loading

Enhancing the electrical and thermal conductivities of polymer composites via curvilinear fibers: An analytical study

Analytical solution for the stress field of hierarchical defects: multiscale framework and applications

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