Diffuse necking and localized necking under plane stress

1989 ◽  
Vol 111 ◽  
pp. 1-7 ◽  
Author(s):  
Jianshe Lian ◽  
Dajun Zhou
Keyword(s):  
Plane Stress ◽  
Localized Necking ◽  
Diffuse Necking

scholarly journals Prediction of necking in thin sheet metals using an elastic–plastic model coupled with ductile damage and bifurcation criteria

2017 ◽  
Vol 27 (6) ◽  
pp. 801-839 ◽  
Author(s):  
Yasser Bouktir ◽  
Hocine Chalal ◽  
Farid Abed-Meraim
Keyword(s):  
Plane Stress ◽  
Thin Sheet ◽  
Three Dimensional ◽  
Ductile Damage ◽  
Forming Limit ◽  
Sheet Metals ◽  
Forming Limit Diagrams ◽  
Plastic Model ◽  
Elastic Plastic ◽  
Localized Necking

In this paper, the conditions for the occurrence of diffuse and localized necking in thin sheet metals are investigated. The prediction of these necking phenomena is undertaken using an elastic–plastic model coupled with ductile damage, which is then combined with various plastic instability criteria based on bifurcation theory. The bifurcation criteria are first formulated within a general three-dimensional modeling framework, and then specialized to the particular case of plane-stress conditions. Some theoretical relationships or links between the different investigated bifurcation criteria are established, which allows a hierarchical classification in terms of their conservative character in predicting critical necking strains. The resulting numerical tool is implemented into the finite element code ABAQUS/Standard to predict forming limit diagrams, in both situations of a fully three-dimensional formulation and a plane-stress framework. The proposed approach is then applied to the prediction of diffuse and localized necking for a DC06 mild steel material. The predicted forming limit diagrams confirm the above-established theoretical classification, revealing that the general bifurcation criterion provides a lower bound for diffuse necking prediction, while the loss of ellipticity criterion represents an upper bound for localized necking prediction. Some numerical aspects related to the prestrain effect on the development of necking are also investigated, which demonstrates the capability of the present approach in capturing the strain-path changes commonly encountered in complex sheet metal forming operations.

Experimental Investigation on the Instability of Al Sheet in Hydraulic Bulging Based on ESPI

2011 ◽  
Vol 264-265 ◽  
pp. 84-89
Author(s):  
Yan Liu ◽  
Zhong Jin Wang
Keyword(s):  
Strain Rate ◽  
Strain Localization ◽  
Speckle Pattern ◽  
Electronic Speckle Pattern Interferometry ◽  
Three Dimension ◽  
Full Field ◽  
Localized Necking ◽  
Diffuse Necking ◽  
Fringe Patterns ◽  
Hydraulic Bulging

Electronic speckle pattern interferometry (ESPI) was applied to hydraulic bulging to analyze the entire deformation process, especially the instability evolution of Al 1060 sheet. Speckle patterns of the specimens were captured continuously to record the deformation fields. The development of full-field strain rate during bulging was represented by the fringe patterns real-timely. The emergence of the defect and its subsequent transformation into groove and crack were revealed clearly by the aberration region in the fringe patterns. The onset of diffuse necking and localized necking were determined by the strain rate distribution curves calculated based on the fringe patterns. Results indicate that ESPI is a satisfying method to analyze the instability and fracture of sheet metals even in three dimension deformation. The growth of micro-crack caused a banded weak region. Diffuse necking occurred in the weak region due to strain localization. A groove generated in the banded weak region and then extended along the length direction. The remarkable strain localization in the groove indicated the onset of localized necking. The thickness of the groove decreased quickly and finally caused fracture. The accurately and quickly determined necking strains would lead to a safer FLD.

Computing cell tractions from particle displacements on silicone rubber substrata

1994 ◽  
Vol 52 ◽  
pp. 162-163
Author(s):  
Tim Oliver ◽  
Akira Ishihara ◽  
Ken Jacobsen ◽  
Micah Dembo
Keyword(s):  
Plane Stress ◽  
Linear Elasticity ◽  
Silicone Rubber ◽  
Mathematical Analysis ◽  
Elastic Recovery ◽  
Video Images ◽  
Cell Traction Forces ◽  
Latex Beads ◽  
Cell Traction ◽  
Better Than

In order to better understand the distribution of cell traction forces generated by rapidly locomoting cells, we have applied a mathematical analysis to our modified silicone rubber traction assay, based on the plane stress Green’s function of linear elasticity. To achieve this, we made crosslinked silicone rubber films into which we incorporated many more latex beads than previously possible (Figs. 1 and 6), using a modified airbrush. These films could be deformed by fish keratocytes, were virtually drift-free, and showed better than a 90% elastic recovery to micromanipulation (data not shown). Video images of cells locomoting on these films were recorded. From a pair of images representing the undisturbed and stressed states of the film, we recorded the cell’s outline and the associated displacements of bead centroids using Image-1 (Fig. 1). Next, using our own software, a mesh of quadrilaterals was plotted (Fig. 2) to represent the cell outline and to superimpose on the outline a traction density distribution. The net displacement of each bead in the film was calculated from centroid data and displayed with the mesh outline (Fig. 3).

Improved Compliance Solutions for C(T), SE(B) and Clamped SE(T) Specimens Including Side-Grooves, Varying Thicknesses and 3-D Effects

2014 ◽  
Author(s):  
Gustavo Henrique B. Donato ◽  
Felipe Cavalheiro Moreira
Keyword(s):  
Crack Growth ◽  
Plane Strain ◽  
Plane Stress ◽  
Potential Drop ◽  
Crack Size ◽  
Growth Conditions ◽  
Size Estimation ◽  
Unloading Compliance ◽  
Integrity Assessments ◽  
Elastic Unloading

Fracture toughness and Fatigue Crack Growth (FCG) experimental data represent the basis for accurate designs and integrity assessments of components containing crack-like defects. Considering ductile and high toughness structural materials, crack growing curves (e.g. J-R curves) and FCG data (in terms of da/dN vs. ΔK or ΔJ) assumed paramount relevance since characterize, respectively, ductile fracture and cyclic crack growth conditions. In common, these two types of mechanical properties severely depend on real-time and precise crack size estimations during laboratory testing. Optical, electric potential drop or (most commonly) elastic unloading compliance (C) techniques can be employed. In the latter method, crack size estimation derives from C using a dimensionless parameter (μ) which incorporates specimen’s thickness (B), elasticity (E) and compliance itself. Plane stress and plane strain solutions for μ are available in several standards regarding C(T), SE(B) and M(T) specimens, among others. Current challenges include: i) real specimens are in neither plane stress nor plane strain - modulus vary between E (plane stress) and E/(1-ν2) (plane strain), revealing effects of thickness and 3-D configurations; ii) furthermore, side-grooves affect specimen’s stiffness, leading to an “effective thickness”. Previous results from current authors revealed deviations larger than 10% in crack size estimations following existing practices, especially for shallow cracks and side-grooved samples. In addition, compliance solutions for the emerging clamped SE(T) specimens are not yet standardized. As a step in this direction, this work investigates 3-D, thickness and side-groove effects on compliance solutions applicable to C(T), SE(B) and clamped SE(T) specimens. Refined 3-D elastic FE-models provide Load-CMOD evolutions. The analysis matrix includes crack depths between a/W=0.1 and a/W=0.7 and varying thicknesses (W/B = 4, W/B = 2 and W/B = 1). Side-grooves of 5%, 10% and 20% are also considered. The results include compliance solutions incorporating all aforementioned effects to provide accurate crack size estimation during laboratory fracture and FCG testing. All proposals revealed reduced deviations if compared to existing solutions.

scholarly journals A Study of Yielding and Plasticity of Rapid Prototyped ABS

Mathematics ◽  
2021 ◽  
Vol 9 (13) ◽  
pp. 1495
Author(s):  
Dan-Andrei Șerban ◽  
Cosmin Marșavina ◽  
Alexandru Viorel Coșa ◽  
George Belgiu ◽  
Radu Negru
Keyword(s):  
Experimental Data ◽  
Stress State ◽  
Plastic Flow ◽  
Plane Stress ◽  
Yield Criterion ◽  
Numerical Analyses ◽  
Flow Potential ◽  
Stress States ◽  
State Configuration

In this article, the yielding and plastic flow of a rapid-prototyped ABS compound was investigated for various plane stress states. The experimental procedures consisted of multiaxial tests performed on an Arcan device on specimens manufactured through photopolymerization. Numerical analyses were employed in order to determine the yield points for each stress state configuration. The results were used for the calibration of the Hosford yield criterion and flow potential. Numerical analyses performed on identical specimen models and test configurations yielded results that are in accordance with the experimental data.

The Exact One-Dimensional Theory for End-Loaded Fully Anisotropic Beams of Narrow Rectangular Cross Section

2001 ◽  
Vol 68 (6) ◽  
pp. 865-868 ◽  
Author(s):  
P. Ladeve`ze ◽  
J. G. Simmonds
Keyword(s):  
Cross Section ◽  
Plane Stress ◽  
Rectangular Cross Section ◽  
Dimensional Theory ◽  
Explicit Formulas ◽  
Cross Sectional ◽  
Rectangular Shape ◽  
One Dimensional ◽  
Anisotropic Elastic ◽  
Derivatives Of

The exact theory of linearly elastic beams developed by Ladeve`ze and Ladeve`ze and Simmonds is illustrated using the equations of plane stress for a fully anisotropic elastic body of rectangular shape. Explicit formulas are given for the cross-sectional material operators that appear in the special Saint-Venant solutions of Ladeve`ze and Simmonds and in the overall beamlike stress-strain relations between forces and a moment (the generalized stress) and derivatives of certain one-dimensional displacements and a rotation (the generalized displacement). A new definition is proposed for built-in boundary conditions in which the generalized displacement vanishes rather than pointwise displacements or geometric averages.

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