Determination of post-necking stress-strain relationship for zirconium low-oxidation based on actual cross-section measurements by DIC

Kim, Min‐Soo; Gu, Bonjoon; Hong, Seokmoo

doi:10.1007/s12206-020-0913-x

Cited by 15 publications

(7 citation statements)

References 17 publications

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“…It is noted that the generalized flow model of Equation ( 10) with (11) automatically satisfies the necking conditions and that there are N unknowns. The simplest way to determine them is to make the generalized flow model pass the NÀ1 selected points of strain and flow stress, i.e., (ε i , σ i ), called the blending points on the flow curve, which produce a set of NÀ1 linear equations formulated as follows…”

Section: General Bfm Using Ffmsmentioning

confidence: 99%

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General Blending Approach of Fundamental Cold Flow Models for an Almost Complete Cold Flow Model in Terms of Tensile Test

Byun

Jee

Lee³

et al. 2023

steel research int.

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The importance of two major issues in obtaining an almost complete cold flow model (ACCFM) from a tensile test, that is, the necking conditions (including the Considère condition and tensile strength) and several selected representative flow points in both pre‐ and postnecking strain hardening regions, is emphasized. It is shown using the AISI 1010 steel for automatic multistage cold forging (AISI 1010 equivalent) that all the traditional fundamental flow models (FFMs) such as the Ludwik, Voce, Hollomon, and Swift models cannot simultaneously satisfy the two major issues. A general blended flow model (BFM) is proposed, which is a linear combination of known basis blending functions satisfying the necking conditions. The number of basis blending functions is unconstrained. The constants of the linear combination, called blending coefficients, are calculated by a set of linear equations to meet the selected representative flow points. Numerous combinations of basis flow functions are tried. It has been shown that there is no interpolation case among all the obtained BFMs but that there are a few ACCFM‐acceptable cases among them, which are based on the extrapolation of the basis blending functions.

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Section: General Bfm Using Ffmsmentioning

confidence: 99%

“…A lot of research attempts to acquire flow stress at large strain have been made for several decades, [4] which was driven by the need for precision simulation of industrial forming processes, full material information for crack or crash simulation, [9] development of measurement system technologies including DIC, [10][11][12][13] etc.…”

Section: Introductionmentioning

confidence: 99%

General Blending Approach of Fundamental Cold Flow Models for an Almost Complete Cold Flow Model in Terms of Tensile Test

Byun

Jee

Lee³

et al. 2023

steel research int.

View full text Add to dashboard Cite

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“…Additionally, ε eq also increases if the anisotropy is considered, except for the specimen with w = 25 mm, which indicates an improvement in the formability. As the stress–strain relationship of ZIRLO™ from necking to fracture does not follow the empirical equation proposed by Swift [ 10 ], Hollomon [ 31 ], and Voce [ 32 ], the error may be large when converting from the FLD-based forming limit stress curve [ 14 ]. Therefore, this study only deals with TFD conversion.…”

Section: Tfd With Anisotropymentioning

confidence: 99%

“…Previous studies have shown that various empirical stress–strain relations such as the Swift and Voce models can effectively extrapolate the actual stress–strain curve up to failure, which has been verified by a bulge test [ 13 ]. However, Kim et al [ 14 ] showed that the stress–strain relationship of ZIRLO™ materials can be expressed using an empirical stress–strain relationship until diffusion necking but cannot be expressed by extrapolation after that point. Therefore, when the path-independent strain/stress-based forming limit criterion is calculated to avoid the strain path dependence of the FLD, inherent calculation errors can arise owing to the selection of the yield criterion and hardening law.…”

Section: Introductionmentioning

confidence: 99%

Determination of the Forming Limit for a ZIRLO™ Sheet with High Anisotropy

Kim

Hong

2020

Materials

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In this study, the experimental two-dimensional forming limit diagram (FLD) data for a ZIRLO™ sheet, which is used in nuclear fuel rod support grids, were converted and presented as a triaxiality failure diagram (TFD). Most previous studies assumed ZIRLO™ to be isotropic when calculating the effective stress and strain. However, for highly anisotropic materials, the anisotropy should be considered for calculations of effective stress and strain; hence, in this study, they were calculated by introducing the normal anisotropy coefficient. To obtain this parameter of the ZIRLO™ specimens, tensile tests were performed on specimens with 0°, 45°, and 90° angles with respect to the rolling direction. It was observed that the average normal anisotropy coefficient measured during the tests was 4.94, which is very high. The von Mises isotropic and Hill 48 anisotropic yield criterion were applied to the FLD data that were experimentally determined using a limit dome height test and were converted into effective stress and effective strain. When the FLD is converted to TFD, the curve will increase in the top-right direction if the r-value is greater than 1, and this become more severe as the r-value increases. The TFD, which was converted considering the anisotropy, is almost the same to the TFD obtained using the digital image correlation method in the tensile tests of four specimens with different stress states. If anisotropy is not considered, then the formability is normally underestimated. However, a highly accurate TFD can be obtained with the method proposed in this study.

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“…However, the related experiment should be carefully conducted, and its results are more or less inaccurate [9]. The traditional experimental approaches were already replaced by the digital image correlation (DIC) techniques [24][25][26][27] that freed the researchers from the difficulty in measuring the geometric features such as the curvature of the necking profile. Even though the DIC techniques have many strong points of acceptable accuracy, flexibility and applicability, the analytical or numerical approaches cannot be underestimated if their accuracy is superior to the experimental methods.…”

Section: Introductionmentioning

confidence: 99%

A Novel Flow Model of Strain Hardening and Softening for Use in Tensile Testing of a Cylindrical Specimen at Room Temperature

2021

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We develop a new flow model based on the Swift method, which is both versatile and accurate when used to describe flow stress in terms of strain hardening and damage softening. A practical issue associated with flow stress at room temperature is discussed in terms of tensile testing of a cylindrical specimen; we deal with both material identification and finite element predictions. The flow model has four major components, namely the stress before, at, and after the necking point and around fracture point. The Swift model has the drawback that not all major points of stress can be covered simultaneously. A term of strain to the third or fourth power (the “second strain hardening exponent”), multiplied and thus controlled by a second strain hardening parameter, can be neglected at small strains. Any effect of the second strain hardening exponent on the identification of the necking point is thus negligible. We use this term to enhance the flexibility and accuracy of our new flow model, which naturally couples flow stress with damage using the same hardening constant as a function of damage. The hardening constant becomes negative when damage exceeds a critical value that causes a drastic drop in flow stress.

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Determination of post-necking stress-strain relationship for zirconium low-oxidation based on actual cross-section measurements by DIC

Abstract: Determination of post-necking stress-strain relationship for zirconium low-oxidation based on actual cross-section measurements by DIC.

Cited by 15 publications

References 17 publications

General Blending Approach of Fundamental Cold Flow Models for an Almost Complete Cold Flow Model in Terms of Tensile Test

General Blending Approach of Fundamental Cold Flow Models for an Almost Complete Cold Flow Model in Terms of Tensile Test

Determination of the Forming Limit for a ZIRLO™ Sheet with High Anisotropy

A Novel Flow Model of Strain Hardening and Softening for Use in Tensile Testing of a Cylindrical Specimen at Room Temperature

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