A strain gage technique for mode I notch stress intensity factor of sharp V-notched configurations

Paul, Pranjol; Murthy, K.S.R.K.; Chakraborty, Debabrata

doi:10.1016/j.tafmec.2018.01.001

Cited by 23 publications

(5 citation statements)

References 47 publications

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“…Substituting the dimensions of the CBD samples, the fracture load, and the dimensionless parameter K * I into Equation (2), the fracture toughness is K Ic = 0.977 MPa √ m. Finally, K SV If and K SV IIf are the critical notch stress intensity factors (NSIFs) for mode I and mode II loading conditions, extensively utilized in the literature to describe the fracture resistance of SV-notched specimens against brittle fracture. The values of NSIFs for SVNBD samples, as well as for other V-notched (rounded or sharp tip) samples, can be obtained from the stress, strain or displacements fields determined for some specific points around the notch border, which can be derived numerically (e.g., finite element method [15,16]) or experimentally (e.g., digital image correlation [13], use of strain gauge [14], photoelasticity [12], etc.). After that, a set of linear equations in which the NSIFs are unknown are obtained according to the formulations proposed for the aforementioned fields (for example, the relations derived by Williams [17] for stress components around the SV-notch tip).…”

Section: Displays Examplesmentioning

confidence: 99%

“…Using the digital image correlation method, Bahrami et al [13] obtained the values of NSIFs for diagonally loaded square plates having SV-notch under pure mode I, mixed mode I/II and pure mode II loading. The NSIF parameters have been determined for SV-notched sample by Paul et al [14] utilizing robust and simple single strain gages. In addition to experimental methods, there are a number of studies that deal with the calculation of NSIFs.…”

Section: Introductionmentioning

confidence: 99%

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Mixed Mode Fracture Investigation of Rock Specimens Containing Sharp V-Notches

et al. 2022

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This work aims to assess both experimentally and analytically the fracture behavior of rock specimens containing sharp V-notches (SV-notches) subjected to mixed mode I/II loading. To this end, firstly, several mixed mode fracture tests were conducted on Brazilian disk specimens weakened by an SV-notch (SVNBD sample), performed in their corresponding center and with various notch opening angles. Secondly, the fracture resistance of the tested samples was predicted using a criterion named MTS-FEM. This approach is based on the maximum tangential stress (MTS) criterion, in which the tangential stress is determined from the finite element method (FEM). Additionally, in the present research, the required critical distance is calculated directly from finite element analyses performed on cracked samples. Comparing the experimental results and the analytical predictions, it is shown that the fracture curves obtained from the MTS-FEM criterion are in agreement with the experimental results. These results are achieved without the need for the calculation of stress series expansion coefficients, as an additional advantage of the proposed approach.

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Section: Displays Examplesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Mixed Mode Fracture Investigation of Rock Specimens Containing Sharp V-Notches

et al. 2022

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“…Similarly, the strain field can be obtained as (Paul et al)

\begin{matrix} lefttrue \\ \{\begin{matrix} center \\ ε_{x} \\ ε_{y} \\ γ_{italicxy} \end{matrix}\} = \sum_{n = 1}^{\infty} Re \{\frac{λ_{n}^{1} A_{n}}{2 {italicGr}^{1 - λ_{n}^{1}}} \{\begin{matrix} center \\ (2 κ^{'} + λ_{n}^{I} cos 2 α + cos 2 {italicαλ}_{n}^{I}) cos (λ_{n}^{I} - 1) θ - (λ_{n}^{I} - 1) cos (λ_{n}^{I} - 3) θ \\ (2 κ^{'} - λ_{n}^{I} cos 2 α - cos 2 {italicαλ}_{n}^{I}) cos (λ_{n}^{I} - 1) θ + (λ_{n}^{I} - 1) cos (λ_{n}^{I} - 3) θ \\ - 2 (λ_{n}^{I} cos 2 α + cos 2 {italicαλ}_{n}^{I}) sin (λ_{n}^{I} - 1) θ + 2 (λ_{n}^{I} - 1) sin (λ_{n}^{I} - 3) θ \end{matrix}\}\} \\ + \sum_{n = 1}^{\infty} Re \{\frac{λ_{n}^{italicII} B_{n}}{2 {italicGr}^{1 - λ_{n}^{italicII}}} \{\begin{matrix} center \\ - (2 κ^{'} + λ_{n}^{italicII} cos 2 α - cos 2 {italicαλ}_{n}^{italicII}) sin (λ_{n}^{italicII} - 1) θ + () \end{matrix}\}\} \end{matrix}

…”

Section: Stress and Displacement Fields Due To A Sharp Notchmentioning

confidence: 99%

“…Similarly, the strain field can be obtained as (Paul et al 55 ) where (r, θ) denote the in-plane polar coordinates as shown in Figure 1, n is the number of terms in the infinite series, Re() denotes real part of variables, A n and B n (n ≠ 2 for B n , as n = 2 produces only rigid body rotation) are Williams coefficients for mode I and mode II, respectively corresponding to n-th term, κ ′ = (1 − ν)/(1 + ν) for plane stress and 1 − 2ν for plane strain conditions, G = E/ 2(1 + ν) is the shear modulus, and E and ν are the Young's modulus and Poisson's ratio, respectively. λ I n and λ II n are the mode I and mode II eigenvalues which can be obtained, respectively, from the following characteristic equations:…”

Section: Stress and Displacement Fields Due To A Sharp Notchmentioning

confidence: 99%

Calculation of mixed mode (I/II) stress intensities at sharp V‐notches using finite element notch opening and sliding displacements

Hussain

Murthy

2019

Fatigue Fract Eng Mat Struct

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In this paper, a simple, robust, and an efficient technique has been proposed for accurate estimation of mixed mode (I/II) notch stress intensity factors (NSIFs) of sharp V‐notched configurations using finite element notch opening and sliding displacements at the selected number of nodes along the notch flanks. Unlike the crack problems, displacement field is rarely employed in the notch problems due to complexities introduced by the presence of rigid body displacements. One of the main emphasis of the present work is to neatly bypass these rigid body displacements and develop a simple approach for accurate computation of the NSIFs so that it can be easily incorporated in the existing code. Several benchmark problems have been analyzed. The results obtained using the present method show excellent agreement with the solutions available in the literature. Some new results have also been reported in the present work.

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“…The stress intensity factor (SIF) K, which characterises the stress field strength near the crack tip, can be used to estimate whether the crack will become unstable [1]. There are many ways to measure the SIF experimentally, such as strain-based techniques [2,3] and photoelastic methods [4]. However, the photoelastic method is usually applicable only to transparent materials.…”

Section: Introductionmentioning

confidence: 99%

Optimisation Method for Determination of Crack Tip Position Based on Gauss-Newton Iterative Technique

Yang

Wei

Liang

et al. 2021

Chin. J. Mech. Eng.

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In the digital image correlation research of fatigue crack growth rate, the accuracy of the crack tip position determines the accuracy of the calculation of the stress intensity factor, thereby affecting the life prediction. This paper proposes a Gauss-Newton iteration method for solving the crack tip position. The conventional linear fitting method provides an iterative initial solution for this method, and the preconditioned conjugate gradient method is used to solve the ill-conditioned matrix. A noise-added artificial displacement field is used to verify the feasibility of the method, which shows that all parameters can be solved with satisfactory results. The actual stress intensity factor solution case shows that the stress intensity factor value obtained by the method in this paper is very close to the finite element result, and the relative error between the two is only − 0.621%; The Williams coefficient obtained by this method can also better define the contour of the plastic zone at the crack tip, and the maximum relative error with the test plastic zone area is − 11.29%. The relative error between the contour of the plastic zone defined by the conventional method and the area of the experimental plastic zone reached a maximum of 26.05%. The crack tip coordinates, stress intensity factors, and plastic zone contour changes in the loading and unloading phases are explored. The results show that the crack tip change during the loading process is faster than the change during the unloading process; the stress intensity factor during the unloading process under the same load condition is larger than that during the loading process; under the same load, the theoretical plastic zone during the unloading process is higher than that during the loading process.

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A strain gage technique for mode I notch stress intensity factor of sharp V-notched configurations

Cited by 23 publications

References 47 publications

Mixed Mode Fracture Investigation of Rock Specimens Containing Sharp V-Notches

Mixed Mode Fracture Investigation of Rock Specimens Containing Sharp V-Notches

Calculation of mixed mode (I/II) stress intensities at sharp V‐notches using finite element notch opening and sliding displacements

Optimisation Method for Determination of Crack Tip Position Based on Gauss-Newton Iterative Technique

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