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Application of digital image correlation and Williams series approximation to characterize mode I stress intensity factor

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Abstract

Existing methods of stress intensity factor (SIF) estimation are commonly based on the contact measurements of crack length with subsequent computation at taking into account the specimen geometry and loading process. The paper aims at the enhancement and verification of the non-contact and easily implemented technique for the assessment of mode I SIF during mechanical tests. Displacement fields constructed by digital image correlation (DIC) were approximated using Williams series in order to determine precise crack tip coordinates and proceed to the computation of stress intensity factor (SIF). The approximation algorithm was tested on linear-elastic and elastic–plastic ABAQUS models under various stress levels and the different Williams series term number. Besides numerical modeling of SIF, the algorithm was tested through assessment of crack propagation parameters under fatigue crack growth with the use of coarse- and fine-grained titanium samples. For the crack length range a/W ≤ 0.3, the approximation algorithm using the Williams series may be employed for estimating crack tip coordinates (crack length) and mode I stress intensity factor with satisfactory level of accuracy. The results of the study appeared to hold the promise of automated non-contact measurements of the crack length as well as stress intensity factor under fatigue crack propagation by employing DIC and appropriate high-performance real-time computing.

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Abbreviations

\({a}_{n}\) , \({b}_{n}\) :

Constants in Williams series

a/W :

Crack length divided on the specimen overall width

Dx :

Error of the crack tip coordinate estimation along the x-axis

G :

Shear modulus

H :

Hessian matrix

K I , K II :

Mode I and II stress intensity factors

m :

Number of terms in Williams series

N :

The number of displacement vectors, provided by digital image correlation computation

R y :

Radius of the plastic zone

Tx, Ty, R :

Terms in Williams series responsible for offset due to rigid body motion along x, y-axis, and rotation

u :

Displacement components along x-axis

v :

Displacement components along y-axis

(\({x}_{0}\) , \({y}_{0}\)):

Crack tip coordinates along x- and y-axis

\(\lambda\) :

The coefficient for the algorithm step in Newton–Raphson method

ν :

Poisson's ratio

σ y :

Yield stress

AE:

Approximation error [pixels]

CTE:

Crack tip coordinate estimation error [pixels]

CTOD:

Crack tip opening displacement

DIC:

Digital image correlation

FEM:

Finite element modeling

SIF:

Stress intensity factor

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Acknowledgements

The research was funded by Government research assignment for ISPMS SB RAS, project FWRW-2021-0010.

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Authors and Affiliations

  1. Institute of Strength Physics and Materials Science, 2/4, Akademichesky pr., Tomsk, Russian Federation, 634055

    Alexander Eremin, Pavel Lyubutin & Sergey Panin

  2. Tomsk Polytechnic University, 30, Lenina pr., Tomsk, Russian Federation, 634050

    Alexander Eremin, Sergey Panin & Ramasubbu Sunder

  3. BISS Division, ITW-India (P) Ltd, 497E, 14th Cross Road, Bangalore, 560058, India

    Ramasubbu Sunder

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Eremin, A., Lyubutin, P., Panin, S. et al. Application of digital image correlation and Williams series approximation to characterize mode I stress intensity factor. Acta Mech 233, 5089–5104 (2022). https://doi.org/10.1007/s00707-022-03374-5

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