Technology & Engineering
Necking Engineering
Necking engineering is a phenomenon that occurs when a material undergoes deformation under tension until it reaches its maximum tensile strength and then begins to narrow or "neck" down. This process is important in understanding the behavior of materials under stress and is used in the design of structures and products.
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3 Key excerpts on "Necking Engineering"
eBook - PDFStructural Crashworthiness and Failure
Proceedings of the Third International Symposium on Structural Crashworthiness held at the University of Liverpool, England, 14-16 April 1993
- N. Jones, T. Wierzbicki, N. Jones, T. Wierzbicki(Authors)
- 1993(Publication Date)
- CRC Press(Publisher)
They also allow a clear understand-ing of the effect of geometry in some problems where localization analyses or perturbation analyses using more elaborate descriptions of material behaviour are difficult to handle. From a mathematical point of view, the onset of necking is associated with the bifurcation of the problem in velocities. Stated differently, this means that either unloading or continued plastic deformation can occur beyond some point corresponding to a condition of neutral loading, where material strain-hardening capacity just balances geometrical softening. 2.1 Considere’s Analysis for Diffuse Necking in Tensile Bars The analysis of Considere 1 deals with the usual uniaxial tensile test of a long bar. In a one-dimensional analysis, the onset of a neck affecting the cross-sectional area of the specimen occurs at the point of maximum load. The condition of instability, d (oA) = 0, where o is the axial Cauchy stress and A is the cross-sectional area, can be expressed as 7 + T -or, with dA/A = —de resulting from the condition of plastic incompressibility, y = l (2) where y = d In a/de is the work-hardening coefficient and e is the logarithmic axial strain. For the power-type stress-strain law a = KeN (where N is the work-hardening exponent and K is a constant) the condition ( 2 ) becomes e = N (3) This form of instability is called diffuse necking. In the absence of more refined modeling, it should be noted that the spread of the neck along the tensile axis is unspecified. A parameter of paramount importance for the post-uniform behaviour is the material strain-rate sensitivity, often characterized by the strain-rate sensitivity coefficient m = 3 In a/din be, where e is the axial strain rate. Positive m -values bring 134 G. Ferron & A. Zeghloul about a stabilizing effect in the load equilibrium equation, leading to less non-uniform strain distributions and increased ductilities as m increases (see e.g. the localization analysis of Hutchinson and Neale5).
eBook - PDF- H. Kardestuncer(Author)
- 2000(Publication Date)
- North Holland(Publisher)
Unification of Finite Element Methods H. Kardestuncer (Editor) 0 Elsevier Science Publishers B.V. (North-Holland), 1984 249 CHAPTER 1 1 THE NUMERICAL ANALYSIS OF NECKING INSTABILITIES A. Needleman Some i s s u e s a r i s i n g i n the f i n i t e element a n a l y s i s of necking i n s t a b i l i t i e s a r e addressed within the context of s p e c i f i c problems. In addition t o analyses based on c l a s s i c a l Mises type c o n s t i t u t i v e laws, we discuss numerical solutions using c o n s t i t u t i v e r e l a t i o n s that more accurately model p l a s t i c s l i p processes and progressive rupture on the microscale. f i n i t e element solutions based on these nonclassical c o n s t i t u t i v e r e l a t i o n s t o reproduce e s s e n t i a l features of the development of f a i l u r e i n the necked down region. We i l l u s t r a t e the a b i l i t y of 1. INTRODUCTION When a d u c t i l e metal is deformed past the maximum load point i n tension, t h e deformations l o c a l i z e i n t o a neck-like region. F a i l u r e ultimately occurs within t h i s neck, although the mode of f a i l u r e is both material and geometry dependent. Necking has a l s o come t o be used a s a generic term denoting any t e n s i l e i n s t a b i l i t y t h a t leads to localized thinning. Necking i n s t a b i l i t i e s play an important r o l e i n s e t t i n g deformation and s t r e s s patterns i n material t e s t i n g s i t u a t i o n s , i n l i m i t i n g d u c t i l i t y i n sheet forming operations and i n s e t t i n g macroscopic conditions f o r d u c t i l e rupture. Hence, there is strong motivation f o r developing a quantatative description of necking phenomena. Much progress toward t h i s end has been made i n t h e past decade o r so and numerical solutions have played a major r o l e i n t h i s development. Here, no attempt is made t o give an extensive review of t h e subject.
- M. Predeleanu, P. Gilormini(Authors)
- 1997(Publication Date)
- Elsevier Science(Publisher)
The paper closes with a numerical and experimental study of the necking of rectangular strips in several Marciniack's experiments. 1. INTRODUCTION There are several ways to achieve analysis of necking occurrence in sheet-metal forming. One way consists to carded out a conventional F.E. simulation and by postprocessing the F.E. results, in using a theoretical or experimental necking criterion, to detect the zones where risks of necking can occur. It is the approach we have employed in [1] and [2] introducing the concept of Forming Limit Stress Surfaces for anisotropic sheets. It has been found that the Forming Limit Stress Diagrams are much more intrinsic that the conventional F. L. Strain Diagrams strongly influenced by the strain path which may vary significantly from the direct strain path in the case of complex sheet-metal forming processes. If experimental F.L.D. are not available , the strains of elements calculated in every steps by F.E. analysis are compared with the necking limits obtained by formulas based on plastic-instability theories such that the StorSn-Rice criterion [3]. However, many Limiting Dome Height (L.D.H.) tests [4] on steel-sheets have shown that theoretical formulas give smaller heights than the measured values, except for aluminum alloys. On the other-hand, a large number of macroscopic fracture criteria for failure which occurs after necking have been evaluated by Doege and co-workers [5],[6], consisting of products, integrals and sums of macroscopic stresses and strains. To determine the values of these criteria at the onset of failure, both experiments and F.E. simulations are needed. When applying these criteria, it was found that the main factor affecting the accuracy is the mode in which failure takes place, mainly under deep-drawing or under stretching conditions.
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