Elastic stress analysis of blunt V-notches under mixed mode loading by considering higher order terms

Mirzaei, A.M.; Ayatollahi, M.R.; Bahrami, Bahador; Berto, Filippo

doi:10.1016/j.apm.2019.09.049

Cited by 29 publications

(4 citation statements)

References 34 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…[4][5][6][7] Up to now, researchers have proposed various analytical, 8-10 experimental, [11][12][13] and numerical [14][15][16][17] methods to calculate the unknown coefficients of the series expansions. As one of the numerical methods, Ayatollahi and his colleagues [18][19][20][21][22][23] proposed and utilized the finite element over-deterministic (FEOD) method to evaluate the coefficients of stress series for various notch geometries under mixed-mode in-plane loading. They demonstrated that at least the first two nonsingular terms of stress field should be considered beside the singular term to obtain accurate analytical stress field around sharp notches.…”

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

View full text Add to dashboard Cite

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.

show abstract

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

View full text Add to dashboard Cite

show abstract

“…And, following Carpenter's efforts, by combining the Kolosov-Muskhelishvili approach with Neuber's conformal mapping [2,13], a substantial attempt to provide a unified approach to the analysis of cracks, sharp and blunt V-notches was proposed by Lazzarin and Tovo [18]. In order to improve the accuracy of the approach and its application, much further work has been done (see, e.g., [19][20][21]). In these studies notch problems are treated by a stress function series expansion, or by employing a series terms to find asymptotic or approximate solutions.…”

Section: * Corresponding Authorsmentioning

confidence: 99%

A Parabolic Notch Interacting With a Generalized Antiplane Singularity

Ma¹,

Chen

Hills

2022

Journal of Applied Mechanics

View full text Add to dashboard Cite

In this study, the interaction of a parabolic notch with a generalized anti-plane singularity is studied and its analytical solution is derived. The singularity may be either an anti-plane concentrated force or a screw dislocation, and separate solutions for each of these are found. The driving force present on the screw dislocation due to the notch free boundary is obtained. It is found that a dislocation-free zone may exist beneath the notch root surface when the screw dislocation is placed on the notch geometric symmetry axis, as the driving force will pull dislocations to the free boundary where they will be annihilated. The solutions developed in this study may be used as building blocks to model the damage of material near a parabolic notch under anti-plane load conditions, and therefore serve as a step in quantifying crack nucleation conditions.

show abstract

“…Thus, three additional terms of

w_{0}

C_{φ} r \sin θ

, and

C_{ψ} r \cos θ

were added to the displacement series to form Equation 14 to consider the out‐of‐plane rigid body translation and rotations of notch tip around

x

and

y

axes, respectively. FEOD method has been discussed elaborately in Ayatollahi and Nejati 30 and Mirzaei et al 31 …”

Section: Analytical Frameworkmentioning

confidence: 99%

On the effects of higher order stress terms in pure mode III loading of bi‐material notches

Bahrami

Ayatollahi

Mehraban

et al. 2022

Fatigue Fract Eng Mat Struct

Self Cite

View full text Add to dashboard Cite

The effects of higher order terms (HOTs) on the stress distribution at the vicinity of the sharp corner of two bonded dissimilar materials were investigated under pure out‐of‐plane (mode III) loading. To achieve this aim, finite element (FE) analysis in conjunction with the over‐deterministic technique were performed for two specimens, each containing four different notch opening angles. The coefficients of singular and non‐singular stress terms were then computed from the displacement field determined from the FE analysis. The elastic stresses obtained directly from the FE analysis were compared with those reconstructed from the truncated series expansions, in order to validate the accuracy of the calculated coefficients. The numerical results show that although the contribution of HOTs in the out‐of‐plane stress field is less than that of the in‐plane notch problems, ignoring their effects can lead to considerable errors in the stress field estimation. The magnitude of numerical error depends on the geometry and loading conditions of the bi‐material notch.

show abstract

Elastic stress analysis of blunt V-notches under mixed mode loading by considering higher order terms

Cited by 29 publications

References 34 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

A Parabolic Notch Interacting With a Generalized Antiplane Singularity

On the effects of higher order stress terms in pure mode III loading of bi‐material notches

Contact Info

Product

Resources

About