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Development of a Specimen for In-Situ Diffraction Planar Biaxial Experiments

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Part of the Conference Proceedings of the Society for Experimental Mechanics Series book series (CPSEMS)

Abstract

In this paper, the design of cruciform shaped, planar biaxial loading specimens using finite element analysis, mechanical testing, and digital image correlation is discussed. The specimens were designed to be capable of arbitrary combinations of tension and compression loading. Digital image correlation results from uniaxial tension tests of first-generation specimen infer key design attributes of second-generation specimen. Finite element results are compared with a plane stress analytical formulation and differences between the two are attributed to stress concentration fields originating at the intersection of specimen arms. These results motivate a parametric finite element geometry optimization of second-generation specimen.

Keywords

  • SEM
  • DIC
  • FEA
  • Planar biaxial
  • Compression

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Abbreviations

E :

Young’s modulus

ε 11 :

Strain in the 11 direction

ε 22 :

Strain in the 22 direction

λ a :

Ratio of 11–22 direction applied surface tractions

λ ga :

Analytical formulation ratio of 11–22 direction gage stresses

λ gs :

FEA simulation ratio of 11–22 direction gage stresses

ν :

Poisson’s ratio

σ 11 :

Stress in the 11 direction

σ 11a :

Applied surface traction in the 11 direction

σ 11ga :

Analytical formulation gage stress in the 11 direction

σ 11gs :

FEA simulation gage stress in the 11 direction

σ 22 :

Stress in the 22 direction

σ 22a :

Applied surface traction in the 22 direction

σ 22ga :

Analytical formulation gage stress in the 22 direction

σ 22gs :

FEA simulation gage stress in the 22 direction

References

  1. Metallic materials—sheet and strip—biaxial tensile testing method using a cruciform test piece, ISO 16842:2014

    Google Scholar 

  2. Abu-Farha, F., Hector Jr., L.G., Khraisheh, M.: Cruciform-shaped specimens for elevated temperature biaxial testing of lightweight materials. JOM 61(8), 48–56 (2009)

    CrossRef  Google Scholar 

  3. Demmerle, S., Boehler, J.P.: Optimal design of biaxial tensile cruciform specimens. J. Mech. Phys. Solids 41(1), 143–181 (1993)

    CrossRef  Google Scholar 

  4. Hanabusa, Y., Takizawa, H., Kuwabara, T.: Numerical verification of a biaxial tensile test method using a cruciform specimen. J. Mater. Process. Technol. 213(6), 961–970 (2013)

    CrossRef  Google Scholar 

  5. Hu, J.-J., Chen, G.-W., Liu, Y.-C., Hsu, S.-S.: Influence of specimen geometry on the estimation of the planar biaxial mechanical properties of cruciform specimens. Exp. Mech. 54(4), 615–631 (2014)

    CrossRef  Google Scholar 

  6. Kuwabara, T., Kuroda, M., Tvergaard, V., Nomura, K.: Use of abrupt strain path change for determining subsequent yield surface: experimental study with metal sheets. Acta Mater. 48(9), 2071–2079 (2000)

    CrossRef  Google Scholar 

  7. Makinde, A., Thibodeau, L., Neale, K.W.: Development of an apparatus for biaxial testing using cruciform specimens. Exp. Mech. 32(2), 138–144 (1992)

    CrossRef  Google Scholar 

  8. Makris, A., Vandenbergh, T., Ramault, C., Van Hemelrijck, D., Lamkanfi, E., Van Paepegem, W.: Shape optimisation of a biaxially loaded cruciform specimen. Polym. Test. 29(2), 216–223 (2010)

    CrossRef  Google Scholar 

  9. Shiratori, E., Ikegami, K.: Experimental study of the subsequent yield surface by using cross-shaped specimens. J. Mech. Phys. Solids 16(6), 373–394 (1968)

    CrossRef  Google Scholar 

  10. Tiernan, P., Hannon, A.: Design optimisation of biaxial tensile test specimen using finite element analysis. Int. J. Mater. Form. 7(1), 117–123 (2014)

    CrossRef  Google Scholar 

  11. Yu, Y., Wan, M., Wu, X.-D., Zhou, X.-B.: Design of a cruciform biaxial tensile specimen for limit strain analysis by FEM. J. Mater. Process. Technol. 123(1), 67–70 (2002)

    CrossRef  Google Scholar 

  12. Problem FAC-2. http://www.afgrow.net [Online]. http://www.afgrow.net/applications/DTDHandbook/Examples/page1_1.aspx. Accessed 2 Mar 2015

  13. Williams, M.L.: On the stress distribution at the base of a stationary crack. J. Appl. Mech. 24, 111–114 (1957)

    Google Scholar 

  14. Irwin, G.R.: Analysis of stresses and strains near the end of a crack transversing a plate. J. Appl. Mech. 24, 361–364 (1957)

    Google Scholar 

  15. Sanford, R.J.: A critical re-examination of the westergaard method for solving opening-mode crack problems. Mech. Res. Commun. 6(5), 289–294 (1979)

    CrossRef  MATH  Google Scholar 

  16. Barber, J.R.: Plane strain and plane stress. In: Barber, J.R. (ed.) Elasticity, 3rd edn, pp. 40–41. Springer, New York (2010)

    CrossRef  Google Scholar 

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Correspondence to G. M. Hommer .

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Hommer, G.M., Stebner, A.P. (2016). Development of a Specimen for In-Situ Diffraction Planar Biaxial Experiments. In: Beese, A., Zehnder, A., Xia, S. (eds) Fracture, Fatigue, Failure and Damage Evolution, Volume 8. Conference Proceedings of the Society for Experimental Mechanics Series. Springer, Cham. https://doi.org/10.1007/978-3-319-21611-9_6

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  • DOI: https://doi.org/10.1007/978-3-319-21611-9_6

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-21610-2

  • Online ISBN: 978-3-319-21611-9

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