Localized Necking Criterion for Strain-Softening Materials

2005 ◽  
Vol 127 (3) ◽  
pp. 273-278 ◽  
Author(s):  
C. L. Chow ◽  
M. Jie ◽  
X. Wu
Keyword(s):  
Strain Softening ◽  
Strain Ratio ◽  
Closed Form Expression ◽  
Forming Limit ◽  
Left Hand ◽  
Localized Necking ◽  
Softening Behavior ◽  
Necking Criterion ◽  
Acoustic Tensor ◽  
The Right

The paper presents the development of a localized necking criterion based on the singularity of acoustic tensor. This criterion is applicable to materials exhibiting strain-softening behavior. The tensor form of the criterion is deployed in simple mathematical expressions, based on which the forming limit diagrams (FLDs) of strain-softening materials can be determined. At the left-hand side of a FLD, or the negative strain ratio region, a closed-form expression of localized band inclination is derived as a function of the strain-ratio value. At the right-hand side of a FLD, or the positive strain ratio regions, the localized band is assumed to be perpendicular to major strain according to the MK [Marciniak and Kuczynski (1967)] model. On both sides of the FLD, the localized necking criteria are analytically expressed by elements of tangent modulus matrix. For the sake of illustration of the proposed criterion, a special case of localized necking employing associative and isotropic plasticity is presented. The material chosen for the illustration is AA-6061 at an elevated temperature. The proposed criterion is also applicable to the formability of other metals at high temperatures and other strain-softening materials such as rocks.

Damage-coupled FLD of Sheet Metals for Warm Forming and Nonproportional Loading

2011 ◽  
Vol 20 (8) ◽  
pp. 1243-1262 ◽  
Author(s):  
M. Jie ◽  
C. L. Chow ◽  
X. Wu
Keyword(s):  
Evolution Equation ◽  
Damage Evolution ◽  
Strain Softening ◽  
Forming Limit ◽  
Sheet Metals ◽  
Nonproportional Loading ◽  
Damage Evolution Equation ◽  
Localized Necking ◽  
Loading Paths ◽  
Necking Criterion

A method of forming limit prediction for sheet metals at high temperatures and under nonproportional loading is presented. The method takes into account the strain-softening behaviors of the material at elevated temperatures. A localized necking criterion based on an isotropic damage-coupled acoustic tensor is developed and employed to determine the forming limits of strain-softening materials. The damage evolution equation is developed within the thermo-mechanical framework. A closed-form expression of the forming limit strains is derived by coupling the damage evolution equation into the localized necking criterion. A computer program, incorporating the incremental theory of plasticity, the damage evolution equation and the localized necking criterion, is developed to compute the forming limit strains under several nonproportional loading paths. A series of the uniaxial tensile tests is performed to measure the relevant mechanical properties of AA6061 at the elevated temperature of 450°C. The material damage variables are determined from the measured elastic modulii from a series of loading and unloading paths. The damage evolution equation of AA6061 at 450°C is formulated based on the test data. The computed limit strains are compared with the test results under various loading paths and a good agreement is observed. It is found that the critical damage value is independent on the stress states and loading paths. It may be concluded that the application of the material damage as a reliable criterion of localized necking including the nonproportional loading cases.

Prediction of Forming Limit of Sheet Metal Based on Stören-Rice Model

2011 ◽  
Vol 221 ◽  
pp. 205-210
Author(s):  
Wei Gang Guo ◽  
Jia Ming Chen ◽  
Hui Min Li ◽  
Li Dong Shao
Keyword(s):  
Experimental Data ◽  
Sheet Metal ◽  
Calculation Result ◽  
Anisotropy Parameter ◽  
Yield Function ◽  
Limit Strain ◽  
Forming Limit ◽  
Left Hand ◽  
A Value ◽  
The Right

On the basis of Storen-Rice model, the limit strain formula is derived by introducing the plasticity constitutive relation coupling Logan-Hosford yield function. Limit strain of AL6111-T4 and AL2028 is calculated and compared with experimental data. The effect of index a of yield function, anisotropy parameter r on the calculation result is discussed. Index a has a significant effect on the right hand side(RHS) limit strain, while it has less relation with left hand side(LHS) limit strain. The RHS limit strain is smaller while a-value gets larger. Good correlation between the calculation result and experimental data is indicated when a-value equals to 4. The RHS limit strain is smaller while r gets larger when a equals to 2, while it has less relation with r when a equals to 4 or 6.

Study on Instability and Forming Limit of Sheet Metal under Stretch-Bending

2014 ◽  
Vol 611-612 ◽  
pp. 84-91 ◽  
Author(s):  
Bo Hou ◽  
Emin Semih Perdahcıoğlu ◽  
A.H. van den Boogaard ◽  
Daniela Kitting
Keyword(s):  
Tensile Stress ◽  
Sheet Metal ◽  
Stress Gradient ◽  
Sheet Thickness ◽  
Forming Limit ◽  
Localized Necking ◽  
Stretch Bending ◽  
Element Simulation ◽  
Deformation Stages ◽  
Necking Criterion

Under stretch-bending conditions, a significant tensile stress gradient through sheet thickness is induced, especially for a small punch radius. The traditional instability theories were developed assuming a uniform tensile stress / strain distribution through thickness; hence, may lead to unreliable prediction of stretch-bending formability. In this study, the instability behavior of sheet metal under stretch-bending is analyzed via FE-simulation of an Angular Stretch-Bend Test (ASBT). In order to reflect the influence of bending, contact normal stress etc., solid elements are used in the simulation. Three deformation stages are identified: (a). stable deformation; (b). strain localization through sheet thickness; (c). localized necking. Based on the instability characteristics, a localized necking criterion is proposed for predicting forming limits of sheet metal under stretch-bending. By combining the proposed criterion and solid element simulation, good agreement between numerical and experimental results is indicated. This work provides a new approach for predicting stretch-bend formability with sufficient accuracy and convenience.

Limit dome height and failure location of stainless steel tailor-welded blanks

2007 ◽  
Vol 221 (12) ◽  
pp. 1497-1506 ◽  
Author(s):  
M Jie ◽  
C H Cheng ◽  
C L Chow ◽  
L C Chan
Keyword(s):  
Numerical Simulation ◽  
Stainless Steel ◽  
Dome Height ◽  
Forming Limit ◽  
Forming Limits ◽  
Limit Dome Height ◽  
Localized Necking ◽  
Tailor Welded Blanks ◽  
Necking Criterion ◽  
Failure Location

Forming limits of stainless steel tailor-welded blanks (TWBs) are investigated through both testing and numerical simulation. Limit dome height (LDH) tests were performed for 1.2/1.0 mm TWBs with 0°, 90°, 45° weldment orientations and various blank widths. Numerical simulation of the LDH test was conducted with LSDYNA. Since TWB is, in reality, a structure, the forming limits of TWBs in terms of the LDH and failure location should be characterized rather than the conventional forming limit diagrams (FLDs). A localized necking criterion based on the vertex theory was employed to identify the failure sites of TWBs. The localized necking criterion was compiled into a computer program, which processed the output data from LSDYNA. The LDHs and failure locations were computed for various combinations of blank thickness and weldment orientation. The predicted LDH and failure locations were compared with the test results and found to be satisfactory.

scholarly journals Experimental and Numerical Investigations into the Failure Mechanisms of TRIP700 Steel Sheets

Metals ◽  
2018 ◽  
Vol 8 (12) ◽  
pp. 1073 ◽  
Author(s):  
Niloufar Habibi ◽  
Veera Sundararaghavan ◽  
Ulrich Prahl ◽  
Ali Ramazani
Keyword(s):  
Forming Limit Diagram ◽  
Forming Limit ◽  
Failure Behavior ◽  
Damage Initiation ◽  
Localized Necking ◽  
Steel Sheets ◽  
Numerical Studies ◽  
Necking Criterion ◽  
Stress States ◽  
Damage Criteria

The formability and failure behavior of transformation-induced plasticity (TRIP) steel blanks were investigated through various stress states. The forming limit diagram (FLD) at fracture was constructed both experimentally and numerically. Numerical studies were performed to evaluate the applicability of different damage criteria in predicting the FLD as well as complex cross-die deep drawing process. The fracture surface and numerical results reveal that the material failed in a different mode for different strain path. Therefore, the Tresca model, which is based on shear stress, accurately predicted the conditions where shear had a profound effect on the damage initiation, whereas Situ localized necking criterion could calculate the conditions in which localization was dominant.

scholarly journals Experimental and Numerical Investigations into the Failure Mechanisms of TRIP700 Steel Sheets

2018 ◽  
Author(s):  
Niloufar Habibi ◽  
Veera Sundararaghavan ◽  
Ulrich Prahl ◽  
Ali Ramazani
Keyword(s):  
Forming Limit Diagram ◽  
Forming Limit ◽  
Failure Behavior ◽  
Damage Initiation ◽  
Localized Necking ◽  
Steel Sheets ◽  
Numerical Studies ◽  
Necking Criterion ◽  
Stress States ◽  
Damage Criteria

The formability and failure behavior of TRIP steel blanks were investigated through various stress states. The forming limit diagram (FLD) at fracture is constructed both experimentally and numerically. Numerical studies are performed to evaluate the applicability of different damage criteria in predicting the FLD as well as complex cross-die deep drawing process.  The fracture surface and numerical results revealed that the material failed in a different mode for different strain path. Therefore, Tresca model which is based on shear stress accurately predicted the conditions where shear had the profound effect on the damage initiation, whereas Situ localized necking criterion was able to calculate the conditions which localization was dominant.

Editorial Note

1946 ◽  
Vol 11 (1) ◽  
pp. 2-2
Keyword(s):  
Editorial Note ◽  
Speech Sounds ◽  
Left Hand ◽  
Hand Column ◽  
Right Hand ◽  
Infant Speech ◽  
The Right

In the article “Infant Speech Sounds and Intelligence” by Orvis C. Irwin and Han Piao Chen, in the December 1945 issue of the Journal, the paragraph which begins at the bottom of the left hand column on page 295 should have been placed immediately below the first paragraph at the top of the right hand column on page 296. To the authors we express our sincere apologies.

Is the Future the Right Time?

2010 ◽  
Vol 57 (4) ◽  
pp. 308-314 ◽  
Author(s):  
Marc Ouellet ◽  
Julio Santiago ◽  
Ziv Israeli ◽  
Shai Gabay
Keyword(s):  
Auditory Task ◽  
English Speakers ◽  
Visual Modality ◽  
Opposite Pattern ◽  
Time Line ◽  
Temporal Reference ◽  
Left Hand ◽  
Reading Direction ◽  
Mental Time Line ◽  
The Right

Spanish and English speakers tend to conceptualize time as running from left to right along a mental line. Previous research suggests that this representational strategy arises from the participants’ exposure to a left-to-right writing system. However, direct evidence supporting this assertion suffers from several limitations and relies only on the visual modality. This study subjected to a direct test the reading hypothesis using an auditory task. Participants from two groups (Spanish and Hebrew) differing in the directionality of their orthographic system had to discriminate temporal reference (past or future) of verbs and adverbs (referring to either past or future) auditorily presented to either the left or right ear by pressing a left or a right key. Spanish participants were faster responding to past words with the left hand and to future words with the right hand, whereas Hebrew participants showed the opposite pattern. Our results demonstrate that the left-right mapping of time is not restricted to the visual modality and that the direction of reading accounts for the preferred directionality of the mental time line. These results are discussed in the context of a possible mechanism underlying the effects of reading direction on highly abstract conceptual representations.

scholarly journals Hand Preference and Performance in Basketball Tasks

2019 ◽  
Vol 16 (22) ◽  
pp. 4336 ◽  
Author(s):  
Emanuela Gualdi-Russo ◽  
Natascia Rinaldo ◽  
Alba Pasini ◽  
Luciana Zaccagni
Keyword(s):  
Professional Training ◽  
Factor Model ◽  
Hand Preference ◽  
Control Group ◽  
Basketball Players ◽  
Confirmatory Factor Analyses ◽  
Left Hand ◽  
Confirmatory Factor ◽  
And Performance ◽  
The Right

The aims of this study were to develop and validate an instrument to quantitatively assess the handedness of basketballers in basketball tasks (Basketball Handedness Inventory, BaHI) and to compare it with their handedness in daily activities by the Edinburgh Handedness Inventory (EHI). The participants were 111 basketballers and 40 controls. All subjects completed the EHI and only basketballers filled in the BaHI. To validate the BaHI, a voluntary subsample of basketballers repeated the BaHI. Exploratory and confirmatory factor analyses supported a two-factor model. Our results show that: (i) Handedness score (R) in daily actions did not differ between basketball players (R by EHI = 69.3 ± 44.6) and the control group (R by EHI = 64.5 ± 58.6); (ii) basketballers more frequently favored performing certain sport tasks with the left hand or mixed hands (as highlighted by R by BaHI = 50.1 ± 47.1), although their choice was primarily the right hand in everyday gestures; and (iii) this preference was especially true for athletes at the highest levels of performance (R by BaHI of A1 league = 38.6 ± 58.3) and for those playing in selected roles (point guard’s R = 29.4 ± 67.4). Our findings suggest that professional training induces handedness changes in basketball tasks. The BaHI provides a valid and reliable measure of the skilled hand in basketball. This will allow coaches to assess mastery of the ball according to the hand used by the athlete in the different tasks and roles.

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