Skip to main content
SpringerLink
Log in

On the evaluation of energy release rate and mode mixity for ductile asymmetric four point bend specimens

  • Original Paper
  • Published:
International Journal of Fracture Aims and scope Submit manuscript

Abstract

A method for evaluating the contributions from mode I and II components of loading to the energy release rate J in ductile asymmetric four-point bend (4-PB) specimens is proposed. The validity of the method is established by conducting elastic-plastic finite element analysis of several asymmetric 4-PB specimens exhibiting a range of mode mixities from pure mode I to II and having different crack length to width (a / W) ratios. Further, a definition of plastic mode mixity is introduced based on the near-tip opening and sliding displacements. This definition and the proposed method to evaluate J are easy to apply since the required crack opening and sliding displacements can be determined from in-situ optical imaging coupled with Digital Image Correlation (DIC) technique. The application of the proposed methodology is demonstrated by analyzing mixed-mode fracture experiments being conducted with a magnesium alloy. It is found that the critical value of J at crack initiation reduces as loading changes from mode I to II.

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
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16

Similar content being viewed by others

References

  • Aoki S, Kishimoto K, Yoshida T, Sakata M (1987) A finite element study of the near crack tip deformation of a ductile material under mixed-mode loading. J Mech Phys Solids 35(4):431–455

    Article  Google Scholar 

  • Aoki S, Kishimoto K, Yoshida T, Sakata M, Richard HA (1990) Elastic–plastic fracture behavior of an aluminum alloy under mixed-mode loading. J Mech Phys Solids 38(2):195–213

    Article  Google Scholar 

  • Arun Roy Y, Narasimhan R (1999) Constraint effects on ductile fracture processes near a notch tip under mixed-mode loading. Eng Fract Mech 62(6):511–534

    Article  Google Scholar 

  • Arun Roy Y, Narasimhan R, Arora PR (1999) Experimental investigation of constraint effects on mixed-mode fracture initiation in a ductile aluminum alloy. Acta Mater 47(5):1587–1596

    Article  Google Scholar 

  • ASTM E1820-13e1 (2013) Standard test method for measurement of fracture toughness, West Conshohocken, PA: ASTM International

  • Ayatollahi MR, Aliha MRM (2011) On the use of an antisymmetric fourpoint bend specimen for mode II fracture experiments. Fatigue Fract Eng M 11:898–907

    Article  Google Scholar 

  • Banks-Sills L, Sherman D (1991) \(J_{II}\) fracture testing of a plastically deforming material. Int J Fract 50:15–26

    Google Scholar 

  • Banks-Sills L, Arcan M, Bortman Y (1984) A mixed-mode fracture specimen for mode II dominant deformation. Eng Fract Mech 20(1):145–157

    Article  Google Scholar 

  • Bhattacharjee D, Knott JF (1994) Ductile fracture in HY100 steel under mixed-mode I/Mode II loading. Acta Metall Mater 42:1747–1754

    Article  CAS  Google Scholar 

  • Chowdhury SR, Narasimhan R (2000) A cohesive finite element formulation for modelling fracture and delamination in solids. Sadhana Acad Proc Eng Sci 25(6):561–587

    Google Scholar 

  • Ghosal AK, Narasimhan R (1994) A finite element analysis of mixed-mode fracture initiation by ductile failure. J Mech Phys Solids 42(6):953–978

    Article  Google Scholar 

  • Ghosal AK, Narasimhan R (1996) Numerical simulations of hole growth and ductile fracture initiation under mixed-mode loading. Int J Fract 77(4):281–304

    Article  CAS  Google Scholar 

  • Ghosal AK, Narasimhan R (1997) A finite element study of the effect of void initiation and growth on mixed-mode ductile fracture. Mech Mater 25(2):113–127

    Article  Google Scholar 

  • Green A, Hundy B (1956) Initial plastic yielding in notch bend tests. J Mech Phys Solids 4(2):128–144

    Article  Google Scholar 

  • Kamat SV, Hirth JP (1996) Mixed mode I/II fracture toughness of 2034 aluminum alloys. Acta Mater 44:201–208

    Article  CAS  Google Scholar 

  • Maccagno TM, Knott JF (1989) The fracture behaviour of PMMA in mixed-modes I and II. Eng Frac Mech 34:65–86

    Article  Google Scholar 

  • Maccagno TM, Knott JF (1992) The mixed-mode I/II fracture behaviour of lightly tempered HY130 steel at room temperature. Eng Fract Mech 41(6):805–820

    Article  Google Scholar 

  • Merkle JG, Corten HT (1974) \(J\) integral analysis for the compact specimen, considering axial force as well as bending effects. J Press Vessel Technol Trans ASME 96(4):286–292

    Article  Google Scholar 

  • Moran B, Ortiz M, Shih CF (1990) Formulation of implicit finite element methods for multiplicative finite deformation plasticity. Int J Numer Methods Eng 29:483–514

    Article  Google Scholar 

  • Nakamura T, Shih CF, Freund LB (1986) Analysis of a dynamically loaded three-point-bend ductile fracture specimen. Eng Fract Mech 25(3):323–339

    Article  Google Scholar 

  • Needleman A (1982) Finite elements for finite strain plasticity problems. In: Lee EH, Mallett RL (eds) Plasticity of metals at finite strain: theory, experiment and computation. RPI Troy, NY, pp 387–436

  • Oskui H, Abuzar ES, Soltani N (2018) Characterization of elastic–plastic fracture toughness of AM60 Mg alloy under mixed-mode loading conditions. Eng Fract Mech 204:388–403

    Article  Google Scholar 

  • Prasad NS, Narasimhan R, Suwas S (2015) Fracture behavior of magnesium alloys role of tensile twinning. Acta Mater 94:281–293

    Article  CAS  Google Scholar 

  • Prasad NS, Narasimhan R, Suwas S (2018) Effect of notch acuity on the fracture behavior of AZ31 Mg alloy. Eng Fract Mech 187:241–261

    Article  Google Scholar 

  • Rice JR, Paris PC, Merkle JG (1973) Some further results of j-integral analysis and estimates. ASTM STP 536:231–245

    Google Scholar 

  • Richard H, Benitz K (1983) A loading device for the creation of mixed-mode in fracture mechanics. Int J Fract 22(2):R55–R58

    Article  Google Scholar 

  • Sakata M, Aoki S, Kishimoto K, Tokizawa M, Chikugo H (1985) Mixed-mode elastic–plastic fracture of 2024–t351 aluminum alloy. Trans Jpn Soc Mech Eng A 51(469):2129–2136

    Article  Google Scholar 

  • Shih CF (1974) Small scale yielding analysis of mixed-mode plane strain crack problems. ASTM STP 560:187–210

    Google Scholar 

  • Shih CF, Asaro RJ (1988) Elastic-plastic analysis of cracks on bimaterial interfaces: part I—small scale yielding. J Appl Mech 55(2):299–316

    Article  Google Scholar 

  • Sreeramulu K, Sharma P, Narasimhan R, Mishra RK (2010) Numerical simulations of crack tip fields in polycrystalline plastic solids. Eng Fract Mech 77(8):1253–1274

    Article  Google Scholar 

  • Symington M, Shih C, Ortiz M (1988) Tables of plane strain mixed-mode plastic crack tip fields. Brown University Division of Engineering, Providence

    Google Scholar 

  • Tandaiya P, Ramamurty U, Narasimhan R (2009) Mixed mode (I and II) crack tip fields in bulk metallic glasses. J Mech Phys Solids 57(11):1880–1897

    Article  CAS  Google Scholar 

  • Tandaiya P, Narasimhan R, Ramamurty U (2013) On the mechanism and the length scales involved in the ductile fracture of a bulk metallic glass. Acta Mater 61(5):1558–1570

    Article  CAS  Google Scholar 

  • Tohgo K, Ishii H (1992) Elastic–plastic fracture toughness test under mixed mode I-II loading. Eng Fract Mech 41(4):529–540

    Article  Google Scholar 

  • Tohgo K, Otsuka A, Gao HW (1988) The behavior of ductile crack initiation from a notch under mixed mode loading. In: Sakata M (ed) Proceedings of the Far East Fracture Group workshop, vol 37. Tokyo Institute of Technology, Japan, p 101

  • Vaishakh KV (2019) Numerical and experimental studies on the deformation and fracture behavior of magnesium alloys. Ph.D. thesis in progress, Indian Institute of Science, Bangalore, India

  • Wang KJ, Hsu CL, Kao H (1977) Calculation of stress intensity factors for combined mode bend specimens. Fract 4:123–133

    Google Scholar 

Download references

Acknowledgements

R. Narasimhan would like to gratefully acknowledge the Science and Engineering Research Board (SERB) for financial support under the J. C. Bose Fellowship scheme.

Author information

Authors and Affiliations

  1. Department of Mechanical Engineering, Indian Institute of Science, Bangalore, 560012, India

    K. V. Vaishakh & R. Narasimhan

Authors
  1. K. V. Vaishakh
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. R. Narasimhan
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to R. Narasimhan.

Additional information

Publisher's Note

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

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Vaishakh, K.V., Narasimhan, R. On the evaluation of energy release rate and mode mixity for ductile asymmetric four point bend specimens. Int J Fract 217, 65–82 (2019). https://doi.org/10.1007/s10704-019-00369-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10704-019-00369-7

Keywords

Search

Navigation