Research Papers

On the Evaluation of Stress Triaxiality Fields in a Notched Titanium Alloy Sample Via Integrated Digital Image Correlation

[+] Author and Article Information
Dominik Lindner, Florent Mathieu, François Hild, Cuong Ha Minh

ENS Cachan/CNRS/Université Paris Saclay,
61 Avenue du Président Wilson,
Cachan Cedex F-94235, France

Olivier Allix

ENS Cachan/CNRS/Université Paris Saclay,
61 Avenue du Président Wilson,
Cachan Cedex F-94235, France
e-mail: allix@lmt.ens-cachan.fr

Olivier Paulien-Camy

Turbomeca (SAFRAN Group),
Avenue Joseph Szydlowski,
Bordes F-64511, France
e-mail: olivier.paulien@turbomeca.fr

1Present address: Turbomeca (SAFRAN Group), Avenue Joseph Szydlowski, Bordes F-64511, France.

2Corresponding author.

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received January 8, 2015; final manuscript received April 26, 2015; published online June 3, 2015. Assoc. Editor: A. Amine Benzerga.

J. Appl. Mech 82(7), 071014 (Jul 01, 2015) (10 pages) Paper No: JAM-15-1010; doi: 10.1115/1.4030457 History: Received January 08, 2015; Revised April 26, 2015; Online June 03, 2015

This paper presents a coupled experimental/numerical procedure to evaluate triaxiality fields. Such a type of analysis is applied to a tensile test on a thin notched sample made of Ti 6-4 alloy. The experimental data consist of digital images and corresponding load levels, and a commercial code (abaqus) is used in an integrated approach to digital image correlation (DIC). With the proposed procedure, samples with complex shapes can be analyzed independently without having to resort to other tests to calibrate the material parameters of a given constitutive law to evaluate triaxilities. The regularization involved in the integrated DIC (I-DIC) procedure allows the user to deal with experimental imperfections such as cracking of the paint and/or poor quality of the speckle pattern. For the studied material, different hardening postulates are tested up to a level of equivalent plastic strain about three times higher than those achievable in a tensile test on smooth samples. Different finite element (FE) discretizations and model hypotheses (i.e., 2D plane stress and 3D simulations) are compared.

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Fig. 1

Triaxiality field obtained by 3D FE elastoplastic simulations on the final sample geometry. Three midsection cuts are shown.

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Fig. 2

Sample geometry (nominal dimensions in millimeter)

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Fig. 3

Longitudinal response of the specimen at macroscopic and mesoscopic scales. Net section stress versus engineering strain for two different gage lengths L0.

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Fig. 4

Longitudinal displacements (expressed in pixels) measured via Q4-DIC when εmacro = 0.072

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Fig. 7

Longitudinal nominal strain field for a Q4-DIC analysis when εmacro = 0.072

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Fig. 6

Mean dimensionless correlation residuals for all the analyze sequence via Q4-DIC (solid line) and I-DIC-3D-f (dashed line)

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Fig. 5

Normalized gray level residual field ϕ for a Q4-DIC analysis when εmacro = 0.072

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Fig. 12

Comparison between measured and identified (via I-DIC-3D-f) load levels. The dashed–dotted line corresponds to the maximum load level (Fmax).

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Fig. 11

Absolute difference of normalized gray level residuals between a Q4-DIC and an I-DIC-3D-f analysis when εmacro = 0.072

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Fig. 10

Longitudinal nominal strain field for an I-DIC-3D-f analysis when εmacro = 0.072

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Fig. 9

Normalized gray level residual field ϕ for an I-DIC-3D-f analysis when εmacro = 0.072

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Fig. 8

Longitudinal displacements (expressed in pixel) measured via I-DIC-3D-f when εmacro = 0.072

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Fig. 15

Comparison of the calibrated hardening curve with the results of Ref. [20] (thin solid line: extrapolated values). For the present work, the dashed line corresponds to Voce's model shown in Fig. 14, the solid line to a calibration up to the maximum load level (Fmax) and subsequently extrapolated.

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Fig. 14

True equivalent stress/plastic strain curves determined for the three chosen hardening postulates

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Fig. 13

Identification, correlation, and equilibrium residuals with I-DIC-3D-f

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Fig. 17

Von Mises' equivalent plastic strain maps for two different locations when εmacro = 0.072: (a) external surface and (b) midsection plane

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Fig. 18

Triaxiality maps for two different locations when εmacro = 0.004 (i.e., elastic regime): (a) external surface and (b) midsection plane

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Fig. 19

Triaxiality maps for two different locations when εmacro = 0.072 (i.e., plastic regime): (a) external surface and (b) midsection plane

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Fig. 20

Triaxiality history for four different points either located at the notch tip or in the center of the considered surfaces (i.e., external plane or midsection plane)

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Fig. 16

Von Mises' equivalent stress maps in the elastic regime εmacro = 0.004 (a) and fully developed elastoplastic step εmacro = 0.072 (b)



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