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Determination of \(\varvec{\eta }_{{\varvec{p}}}\) factor for clamped SENT thin sheet specimens of an Interstitial Free steel

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Abstract

The present study addresses determination of the plastic “eta factor” \(\eta _{p}\) for single edge notched tensile (SENT) specimens of an interstitial-free (IF) steel sheet (thickness \(=\) 1 mm) for crack depth ratios in the range of 0.2 to 0.9. Two well-established \(\eta _{p}\) determination methods for thick fracture mechanics specimens proved adequate for the present purpose. Analyses using load-displacement data from mechanical tests and also from 3-D finite element simulations were used to verify the applicability of one of these adopted methods up to extensive crack tip necking even beyond crack initiation. Further analyses indicate that \(\eta _{p}\) thus determined (i) can be used for fatigue pre-cracked sheet specimens, and (ii) is consistent with the contour integral definition of J integral. Use of \(\eta _{p}\) thus determined for measuring initiation fracture toughness in notched specimens is also illustrated.

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Abbreviations

\(A_{P}\) :

Plastic component of work done

a :

Notch/crack length

\(C_{M}, \,C_{S}\) :

Machine elastic compliance, specimen elastic compliance

\(E,E^{'}\) :

Youngs modulus, effective elastic modulus

H :

Free length of specimen between the two jaw grips

\(J_{c}J_{p}^{c}\) :

Critical value of the Jintegral, \(J_{p}\) at crack initiation

\({J;J}_{e}, J_{p}\) :

J integral parameter; elastic, plastic component of J

\(J_{p}^{max}\) :

Maximum value of path independent contour J integral for fixed z computed with the adopted FE meshing

K :

Stress intensity factor

l :

Specimen ligament length

\(\rho \) :

Notch root radius

z :

Distance from specimen surface in the thickness direction

n :

Hollomon strain hardening parameter

P :

Load

\(S_{k}\) :

Load separation factor (Eq. 7)

\(t, \, t_{n}\) :

Sheet specimen thickness, ligament width at neck

\(v_{p}\) :

Specimen plastic displacement

\(v_{a}, \, v_{s}\) :

Actuator displacement, specimen free length (H) extension

W :

Specimen width

\(\delta \) :

Crack tip opening displacement (CTOD)

\(\delta _{c}\) :

Critical value of \(\delta \) for crack initiation

\(\eta _{p}\) :

Plastic “eta factor”

CTOD:

Crack tip opening displacement

DENT:

Double-edge notched tension

FE:

Finite element

IF:

Interstitial free

SENT:

Single-edge notched tension

\(A_{M}, G\left( \frac{l}{W} \right) H\left( \frac{v_{p}}{W} \right) \) :

constant, functions in Eq. (4)

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Acknowledgements

Authors acknowledge that the experimental research has been done in the DST-FIST sponsored equipment (Grant Sanction No. SR/FST/ETI-404/2015(c)). Authors also acknowledge TATA Steel Ltd., Jamshedpur, India for providing the required steel that has been used in the present research.

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Author notes

  1. R. Sarkar

    Present address: Institute of Frontier Materials, Deakin University Geelong Waurn Ponds Campus, Waurn Ponds VIC, 3216, Australia

  2. P. S. De

    Present address: Department of Engineering Design, Indian Institute of Technology Madras, Chennai, 600036, India

Authors and Affiliations

  1. Metallurgical and Material Engineering Department, Jadavpur University, Kolkata, 700032, India

    S. K. Chandra, R. Sarkar, P. S. De, P. C. Chakraborti & S. K. Ray

  2. Department of Mechanical Engineering, Jadavpur University, Kolkata, 700032, India

    Sukalpa Choudhury & Mrinmoy Jana

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  1. S. K. Chandra
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Correspondence to P. C. Chakraborti.

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Chandra, S.K., Sarkar, R., Choudhury, S. et al. Determination of \(\varvec{\eta }_{{\varvec{p}}}\) factor for clamped SENT thin sheet specimens of an Interstitial Free steel. Int J Fract 227, 137–152 (2021). https://doi.org/10.1007/s10704-020-00493-9

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