Skip to main content
SpringerLink
Log in

Effect of Tensile Pre-strain and Specimen Orientation on Tearing Resistance Parameters of DP 780 Steel Sheet Determined Using Essential Work of Fracture Method

  • Technical Article
  • Published:
Journal of Materials Engineering and Performance Aims and scope Submit manuscript

Abstract

Essential work of fracture (EWF) concept has been used to characterize the tearing resistance of a 1-mm-thick automotive grade dual-phase 780 steel sheet. The present study has been done to observe the effect of tensile pre-strain, specimen orientation and notch root radius on tearing resistance parameters obtained from EWF testing of double-edge notched tensile (DENT) specimens. Additionally, the estimated crack tip opening angle (CTOA, \({\psi }^{e}\)) obtained through EWF testing has been compared with its fracture mechanics counterpart, i.e., stable crack tip opening angle value (\({\varphi }_{c}\)) obtained via an experimental route using DENT specimens, adopting the essence of the standard CTOA testing procedure prescribed in ASTM 2472.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11

Similar content being viewed by others

Data Availability

The raw/processed data required to reproduce these findings cannot be shared at this time as the data also form part of an ongoing study.

Abbreviations

\(a, \Delta a\) :

Notch/crack length, crack extension

\({J}_{\mathrm{c}}\) :

Critical value of \(J-\) integral for crack initiation

\(l,\rho\) :

Specimen ligament length, notch root radius

\({l}_{\mathrm{max}},{l}_{\mathrm{min}}\) :

Maximum, minimum \(l\) for applying EWF method

\(L\) :

Parameters used in optical measurement of \(\varphi\)

\(n,{R}^{2}\) :

Strain hardening exponent, linear correlation coefficient

\(P,{P}_{\mathrm{max}}\) :

Load, maximum load

\(t,W\) :

Sheet thickness, specimen width

\({v}_{\mathrm{f}}\) :

Final gauge/extensometer displacement (data at 90% load drop)

\({W}_{\mathrm{e}},{W}_{\mathrm{p}}\) :

Total energy spent in FPZ, in PDZ enclosing FPZ

\({W}_{\mathrm{f}},{w}_{\mathrm{e}}\) :

Total work of fracture, specific essential work of fracture

\({\beta w}_{\mathrm{p}},\beta\) :

Volumetric plastic work density in the PDZ, plastic zone shape factor

\(\delta ,{\delta }_{\mathrm{c}}\) :

Crack tip opening displacement, critical value of \(\delta\) for crack initiation

\({\delta }_{\mathrm{c}}^{\mathrm{e}},{\psi }^{\mathrm{e}}\) :

Opening across the FPZ, angle of opening of FPZ for a fully growing crack

\({\sigma }_{\mathrm{max}},{\tilde{\sigma }}_{\mathrm{max}}\) :

Maximum net section ligament stress, mean of the \({\sigma }_{\mathrm{max}}\) values

\({\sigma }_{\mathrm{ut}},{\sigma }_{\mathrm{y}}\) :

Ultimate tensile strength, yield stress

\({\upsigma }_{\mathrm{flow}}\) :

Flow stress

\(\varphi ,{\varphi }_{\mathrm{c}}\) :

CTOA (optically measured), critical CTOA (optically measured)

CTOA:

Crack tip opening angle

CTOD:

Crack tip opening displacement

DENT:

Double-edge notched tension

EWF:

Essential work of fracture

FPZ:

Fracture process zone

PDZ:

Plastic deformation zone

References

  1. T.L. Anderson, Fracture Mechanics: Fundamentals and Applications, CRC Press, 2017.

    Book  Google Scholar 

  2. X.-K. Zhu and J.A. Joyce, Review of Fracture Toughness (G, K, J, CTOD, CTOA) Testing and Standardization, Eng. Fract. Mech., 2012, 85, p 1–46.

    Article  Google Scholar 

  3. V. Naumenko and I. Limanskii, Fracture Resistance of Sheet Metals and Thin-Wall Structures. Part 1. Critical Review, Strength Mater., 2014, 46(1), p 18–37.

    Article  Google Scholar 

  4. T. Pardoen, F. Hachez, B. Marchioni, P. Blyth, and A. Atkins, Mode I Fracture of Sheet Metal, J. Mech. Phys. Solids, 2004, 52(2), p 423–452.

    Article  CAS  Google Scholar 

  5. K.-H. Schwalbe, J.C. Newman Jr., and J.L. Shannon Jr., Fracture Mechanics Testing on Specimens with Low Constraint––Standardisation Activities within ISO and ASTM, Eng. Fract. Mech., 2005, 72(4), p 557–576.

    Article  Google Scholar 

  6. T. Pardoen, Y. Marchal, and F. Delannay, Essential Work of Fracture Compared to Fracture Mechanics—Towards a Thickness Independent Plane Stress Toughness, Eng. Fract. Mech., 2002, 69(5), p 617–631.

    Article  Google Scholar 

  7. ASTM, E., 2472–06: Standard Test Method for Determination of Resistance to Stable Crack Extension Under low Constraint Conditions. Annual Book of ASTM Standards, ASTM International, West Conshohocken, 2007. 3.

  8. J. Heerens and M. Schödel, On the Determination of Crack Tip Opening Angle, CTOA, Using Light Microscopy and δ5 Measurement Technique, Eng. Fract. Mech., 2003, 70(3–4), p 417–426.

    Article  Google Scholar 

  9. P.P. Darcis, C.N. McCowan, H. Windhoff, J.D. McColskey, and T.A. Siewert, Crack Tip Opening Angle Optical Measurement Methods in Five Pipeline Steels, Eng. Fract. Mech., 2008, 75(8), p 2453–2468.

    Article  Google Scholar 

  10. D.J. Horsley, Background to the use of CTOA for Prediction of Dynamic Ductile Fracture Arrest in Pipelines, Eng. Fract. Mech., 2003, 70(3–4), p 547–552.

    Article  Google Scholar 

  11. M. James and J. Newman, The Effect of Crack Tunneling on Crack Growth: Experiments and CTOA Analyses, Eng. Fract. Mech., 2003, 70(3), p 457–468.

    Article  Google Scholar 

  12. S. Mahmoud and K. Lease, The Effect of Specimen Thickness on the Experimental Characterization of Critical Crack-Tip-Opening Angle in 2024–T351 Aluminum Alloy, Eng. Fract. Mech., 2003, 70(3), p 443–456.

    Article  Google Scholar 

  13. J. Newman, M. James, and U. Zerbst, A Review of the CTOA/CTOD Fracture Criterion, Eng. Fract. Mech., 2003, 70(3), p 371–385.

    Article  Google Scholar 

  14. Sutton, M., D. Dawicke, and J. Newman, Orientation Effects on the Measurement and Analysis of Critical CTOA in an Aluminum Alloy Sheet. Fracture Mechanics: 26th Volume1995, ASTM International.

  15. J. Wang and J. Shuai, Measurement and Analysis of Crack Tip Opening Angle in Pipeline Steels, Eng. Fract. Mech., 2012, 79, p 36–49.

    Article  Google Scholar 

  16. R. Sarkar, S.K. Chandra, P.S. De, P. Chakraborti, and S.K. Ray, Evaluation of Ductile Tearing Resistance of Dual-Phase DP 780 Grade Automotive Steel Sheet from Essential Work of Fracture (EWF) tests, Theoret. Appl. Fract. Mech., 2019, 103, p 102278.

    Article  CAS  Google Scholar 

  17. S.K. Chandra, R. Sarkar, A. Bhowmick, P. De, P. Chakraborti, and S.K. Ray, Fracture Toughness Evaluation of Interstitial Free Steel Sheet using Essential Work of Fracture (EWF) Method, Eng. Fract. Mech., 2018, 204, p 29–45.

    Article  Google Scholar 

  18. B. Cotterell and J. Reddel, The Essential Work of Plane Stress Ductile Fracture, Int. J. Fract., 1977, 13(3), p 267–277.

    Article  CAS  Google Scholar 

  19. M. Faccoli, G. Cornacchia, M. Gelfi, A. Panvini, and R. Roberti, Notch Ductility of Steels for Automotive Components, Eng. Fract. Mech., 2014, 127, p 181–193.

    Article  Google Scholar 

  20. S. Sahoo, N. Padmapriya, P.S. De, P.C. Chakraborti, and S.K. Ray, Ductile Tearing Resistance Indexing of Automotive Grade DP 590 Steel Sheets: EWF Testing Using DENT Specimens, J. Mater. Eng. Perform., 2018, 27(4), p 2018–2023. https://doi.org/10.1007/s11665-018-3293-y

    Article  CAS  Google Scholar 

  21. T. Pardoen, Y. Marchal, and F. Delannay, Thickness Dependence of Cracking Resistance in Thin Aluminium Plates, J. Mech. Phys. Solids, 1999, 47(10), p 2093–2123.

    Article  CAS  Google Scholar 

  22. Y. Mai and B. Cotterell, Effects of Pre-strain on Plane Stress Ductile Fracture in α-Brass, J. Mater. Sci., 1980, 15(9), p 2296–2306.

    Article  CAS  Google Scholar 

  23. Y. Marchal and F. Delannay, Influence of Test Parameters on the Measurement of the Essential Work of Fracture of Zinc Sheets, Int. J. Fract., 1996, 80(4), p 295–310.

    Article  CAS  Google Scholar 

  24. S. Hashemi, Determination of the Fracture Toughness of Polybutylene Terephthalate (PBT) Film by the Essential Work Method: EFFECT of Specimen Size and Geometry, Polym. Eng. Sci., 2000, 40(3), p 798–808.

    Article  CAS  Google Scholar 

  25. Y.W. Mai and P. Powell, Essential Work of Fracture and j-integral Measurements for Ductile Polymers, J. Polym. Sci., Part B Polym. Phys., 1991, 29(7), p 785–793.

    Article  CAS  Google Scholar 

  26. Y.-W. Mai and B. Cotterell, On the Essential Work of Ductile Fracture in Polymers, Int. J. Fract., 1986, 32(2), p 105–125.

    Article  CAS  Google Scholar 

  27. B. Cotterell, T. Pardoen, and A. Atkins, Measuring Toughness and the Cohesive Stress–Displacement Relationship by the Essential Work of Fracture Concept, Eng. Fract. Mech., 2005, 72(6), p 827–848.

    Article  Google Scholar 

  28. S.K. Chandra, R. Sarkar, A. Bhowmick, P. De, P. Chakraborti, and S.K. Ray, Evaluation of Ductile Tearing Resistance of an Interstitial Free Steel Sheet Using SENT Specimens, Eng. Fract. Mech., 2020, 238, p 107257.

    Article  Google Scholar 

  29. M. James, Intergranular Crack Paths During Fatigue in Interstitial-free Steels, Eng. Fract. Mech., 2010, 77(11), p 1998–2007.

    Article  Google Scholar 

  30. S. Sivaprasad, S. Tarafder, V.R. Ranganath, and K.K. Ray, Effect of Prestrain on Fracture Toughness of HSLA Steels, Mater. Sci. Eng. A, 2000, 284(1–2), p 195–201.

    Article  Google Scholar 

  31. P. Liaw and J. Landes, Influence of Prestrain History on Fracture Toughness Properties of Steels, Metall. Trans. A, 1986, 17(3), p 473.

    Article  Google Scholar 

  32. Taktak, W. and R. Elleuch. in The Pre-strain Impact on Tensile Properties and Fracture Toughness of AA5754-H111 Aluminum Alloy. International Conference on advances in Materials, Mechanics and Manufacturing. 2021. Springer

  33. Y. Mai and K. Pilko, The Essential Work of Plane Stress Ductile Fracture of a Strain-Aged Steel, J. Mater. Sci., 1979, 14(2), p 386–394.

    Article  CAS  Google Scholar 

  34. R. Hill, On Discontinuous Plastic States, with Special Reference to Localized Necking in Thin Sheets, J. Mech. Phys. Solids, 1952, 1(1), p 19–30.

    Article  Google Scholar 

  35. J. Wu and Y.-W. Mai, The Essential Fracture Work Concept for Toughness Measurement of Ductile Polymers, Polym. Eng. Sci., 1996, 36(18), p 2275–2288.

    Article  CAS  Google Scholar 

  36. E.Q. Clutton, ESIS TC4 Experience with the Essential Work of Fracture Method, European Structural Integrity Society. Elsevier, 2000, p 187–199

    Google Scholar 

  37. E.Q. Clutton, Essential Work of Fracture, European Structural Integrity Society. Elsevier, 2001, p 177–195

    Google Scholar 

Download references

Acknowledgments

Authors deeply acknowledge the valuable discussion with Dr. Saradindukumar Ray, former Ministry of Steel Chair Professor, Metallurgical and Material Engineering Department, Jadavpur University, Kolkata 700032, India, during the course of present work.

Author information

Authors and Affiliations

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

    A. D. Bhowmick, R. Sarkar, S. K. Chandra, P. S. De & P. C. Chakraborti

  2. Institute of Frontier Materials, Deakin University Geelong Waurn Ponds Campus, Geelong, VIC, 3216, Australia

    R. Sarkar

  3. Department of Engineering Design, Indian Institute of Technology, Madras, 600036, India

    P. S. De

Authors
  1. A. D. Bhowmick
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. R. Sarkar
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. S. K. Chandra
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. P. S. De
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. P. C. Chakraborti
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to P. C. Chakraborti.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Bhowmick, A.D., Sarkar, R., Chandra, S.K. et al. Effect of Tensile Pre-strain and Specimen Orientation on Tearing Resistance Parameters of DP 780 Steel Sheet Determined Using Essential Work of Fracture Method. J. of Materi Eng and Perform 32, 6866–6875 (2023). https://doi.org/10.1007/s11665-022-07583-w

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11665-022-07583-w

Keywords

Search

Navigation