Necking phenomenon based on the Aramis system

Abstract

In this study, the necking three-dimensional strain on minimum cross-section at room temperature was performed experimentally and analytically. A modified strain assumption was applied to overcome significant errors in calculating necking strain by Bridgman assumption. Then, one relatively simple strain distribution function was deduced based on equilibrium equation of necking element. To obtain the parameters in this function, the monotonic tensile tests in two kinds of carbon structure steels Q235 and Q345 were carried out. Meanwhile, the Aramis system based on digital image correlation method was adopted to measure the surface axial strain and deformation parameters during the loading process. The experimental and numerical results were compared with the traditional Bridgman strain assumption. The maximum axial strain calculation error the strain distribution function and experiment value was less than 8%, which was obviously less than that calculated by Bridgman assumption. Additionally, the variation law of the three-dimensional strain calculated by this function was consistent with that obtained by the macroscopic analysis of fracture surface. The application of traditional Bridgman formula can be expanded by this study. Meanwhile, it can provide a new idea to study the stress distribution characteristics and better understanding of ductile materials’ deformation properties.

Keywords

Necking ductile fracture Aramis system carbon structural steels modified strain model

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References

Besson

Cailletaud

Chaboche

. Non-linear mechanics of materials, Solid Mechanics and its Applications. Netherlands: Springer, 2010, pp. 341–369.

Volk

Hora

. Evaluation of experimental forming limit curves and investigation of strain rate sensitivity for the start of local necking, College Park, MD: American Institute of Physics, 2011, pp. 99–106.

Min

Stoughton

Carsley

et al.

A method of detecting the onset of localized necking based on surface geometry measurements. Exp Mech 2016; 57: 1–15.

Gorji

Manopulo

Hora

. Numerical investigation of the post-necking behavior of aluminum sheets in the presence of geometrical and material inhomogeneities. Int J Solids Struct 2016; 102–103: 56–65.

Bridgman

. Studies in large plastic flow and fracture, Cambridge: Harvard University Press, 1964.

Zhou

Hayden

Gao

. An investigation of the strain rate and temperature effects on the plastic flow stress and ductile failure strain of aluminum alloys 5083-H116, 6082-T6 and a 5183 weld metal. Proc IMechE, Part C: J Mechanical Engineering Science 2013; 195: 883–895.

Gao

Zhang

Roe

. A study on the effect of the stress state on ductile fracture. Int J Damage Mech 2009; 19: 75–94.

Senthil

Iqbal

Chandel

. Study of the constitutive behavior of 7075-T651 aluminum alloy. Int J Impact Eng 2017; 108: 171–190.

Miloud

Imad

Benseddiq

et al.

A numerical analysis of relationship between ductility and nucleation and critical void volume fraction parameters of GTN model. Proc IMechE, Part C: J Mechanical Engineering Science 2013; 227: 2634–2646.

10.

Bao

Wierzbicki

. On fracture locus in the equivalent strain and stress triaxiality space. Int J Mech Sci 2004; 46: 81–98.

11.

Ren

Nyhus

. A special notched tensile specimen to determine the flow stress-strain curve of hardening materials without applying the Bridgman correction. Eng Fract Mech 2017; 179: 225–239.

12.

Tvergaard

. Necking in tensile bars with rectangular cross-section. Comput Method Appl M 1993; 103: 273–290.

13.

Zhang

Ødegård

Søvik

. A study on determining true stress–strain curve for anisotropic materials with rectangular tensile bars. Int J Solids Struct 2001; 38: 4489–4505.

14.

Zhang

Hauge

Ødegård

. Determining material true stress–strain curve from tensile specimens with rectangular cross-section. Int J Solids Struct 1999; 36: 3497–3516.

15.

Cai

Bao

. Analysis of material necking and breaking behavior based on stress triaxiality. Mech Strength 2015; 182: 1152–1158.

16.

Butcher

Chen

Worswick

. Integration of a particle-based homogenization theory into a general damage-based constitutive model to improve the modelling of void nucleation to coalescence. Acta Mech 2013; 224: 139–156.

17.

Sjöberg

Marth

Kajberg

. Experimental characterisation of the evolution of triaxiality stress state for sheet metal materials. Eur J Mech - A/Solid 2017; 66: 279–286.

18.

François

Pineau

Zaoui

. Mechanical behaviour of materials. Vol 2: Fracture mechanics and damage, Netherlands: Springer, 2013, pp. 1298–1305.

19.

Barton

Sturges

Mirza

et al.

Deformation and fracture modeling techniques to take account of strain-rate behaviour and stress state. J Phys IV 1991; 3: 931–936.

20.

Zavaliangos

Anand

. Thermo-elasto-viscoplasticity of isotropic porous metals. J Mech Phys Solid 1993; 41: 1087–1118.

21.

Chen

. Study on metal fracture, Beijing: Metallurgical Industry Press of China, 1978.

22.

Xie

Zhang

Chen

et al.

Updating of the stress triaxiality by finite element analysis. J Vib Shock 2012; 32: 8–14.

23.

Jiang

. Modified GTN model for a broad range of stress states and application to ductile fracture. Eur J Mech - A/Solid 2016; 57: 132–148.

24.

Peter

. Digital imaging technique in experimental stress analysis. Opt Eng 1982; 21: 427–431.

25.

Yamaguchi

. A laser-speckle strain gauge. J Phys E: Sci Instrum 2000; 14: 1270–1270.

26.

The Standardization Administration of China. GBT228.1-2010 Metallic materials-tensile testing-Part 1: method of test at room temperature, Beijing: Standard Press of China, 2011.

27.

Jiang W. Study of ductile fracture based on meso-damage mechanisms. PhD Thesis, Northwestern Polytechnical University, China, 2016.

28.

Bao

Wierzbicki

. A comparative study on various ductile crack formation criteria. J Mater Sci 2004; 126: 314–324.