Limit strains in the processes of stretch-forming sheet metal
TL;DR: In this paper, a theoretical analysis of the process of the generation of the groove based on anisotropic plasticity theory is presented, and the system of equations derived was solved numerically with the aid of a computer, which enabled the limiting strain of the sheet metal to be determined as a function of the material.
About: This article is published in International Journal of Mechanical Sciences.The article was published on 1967-09-01. It has received 1814 citations till now. The article focuses on the topics: Forming limit diagram & Groove (music).
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TL;DR: In this article, an anisotropic plane stress yield function based on interpolation by second order Bezier curves is proposed, which can be used to describe, e.g., the yield stress and R-value as a function of the loading direction more accurately than with other common analytical yield functions.
238 citations
01 Jan 1978
TL;DR: In this paper, a localization-band bifurcation analysis is carried out and the influence of geometric imperfections is analyzed using the longwavelength approximation treated in Part I. The main emphasis in this Part is on comparisons between the corresponding predictions of flow theory and deformation theory.
Abstract: Various factors affecting the prediction of limit strains in biaxially-stretched sheets are studied. Time-independent material behavior is assumed, and both the flow theory of plasticity as well as a finite-strain version of deformation theory are considered. A localization-band bifurcation analysis is first carried out. The influence of geometric imperfections is then analyzed using the long-wavelength approximation treated in Part I. We also discuss the predicted forming limit curves and comment on their relation to published experimental data. The main emphasis in this Part, however, is on comparisons between the corresponding predictions of flow theory and deformation theory.
234 citations
TL;DR: In this article, the authors show that the strain to initiate failure in a range of structural steels is co-related by the state of stress for both axisymmetric and plane states of strain.
Abstract: U sing plane strain and axisymmetric notched tensile specimens in combination with finite deformation stress analysis, the strain to initiate failure in a range of structural steels is shown to be co-related by the state of stress for both axisymmetric and plane states of strain. The implications of this result for ductile failure terminated by flow localisation is discussed in the light of the theoretical work on localised flow.
229 citations
01 Jan 1971
TL;DR: In this article, the authors present a treatment of metallographically ductile fracture in a treatise on brittle fracture is the frequently brittle nature of structures made of materials that are metallurgically and micrographically ductile.
Abstract: The rationale for treating what is metallographically ductile fracture in a treatise on brittle fracture is the frequently brittle nature of structures made of materials that are metallurgically and micrographically ductile. An introduction sets the theme of this chapter as the relation between the microstructural features of such fracture observed by the metallographer and the quantitative analysis of the accompanying stress and strain field which is treated by the stress analyst. As background for the stress analysis, both on a large scale and at the microscopic level, the fundamental equations of the statics of solids are reviewed in Sect. II, with attention being given to the idealization of behavior into elastic, plastic, or viscoelastic types, which, in actual materials, are more or less intermixed. The next section turns to criteria of fracture as judged from metallographic observations, quantitatively developed by whatever continuum theories are available. The mechanics and fracture criteria are then brought to bear on the modes of inelastic fracture for which the most complete stress and strain analyses are available: fully plastic fracture in torsion, plane-strain tension, and plane-stress tension. With the fully plastic modes of fracture as a contrast with the more frequently considered elastic modes, we next turn, in Sect. V, to elastic-plastic fracture, which exhibits some of the characteristics of the two different idealized modes. After a brief mention of results in viscoelastic crack propagation, we give recommendations for further research, from the points of view of the scientist, the designer, and the metallurgist, and conclude with a summary in the form of a tentative and approximate reduction to practice of the ideas of this chapter.
228 citations
TL;DR: In this paper, an uncoupled non-associated fracture model is proposed which makes use of a stress state dependent weighting function and an anisotropic plastic strain measure, which is obtained from applying the von Mises equivalent plastic strain definition after the linear transformation of the plastic strain tensor.
222 citations
Cites background from "Limit strains in the processes of s..."
...K model (Marciniak and Kuczynski, 1967) for sheet metal forming....
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...(2009) covers the porous plasticity models, phenomenological models and the M–K model (Marciniak and Kuczynski, 1967) for sheet metal forming....
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References
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TL;DR: In this paper, conditions for instability of plastic strain under plane stress for a material conforming to the Mises-Hencky yield condition and strain-hardening according to a unique relationship between root-mean-square values of shear stress (q) and incremental strain (δψ).
Abstract: This paper examines the conditions for instability of plastic strain under plane stress for a material conforming to the Mises-Hencky yield condition and strain-hardening according to a unique relationship between root-mean-square values of shear stress (q) and incremental strain (δψ).
If, under fixed loading conditions, the material undergoes a strain increment which is consistent with the applied stress system, the conditions are stable or unstable according as the increment in representative yield stress is greater or less than the increment in representative induced stress.
The strain at which instability arises is found in terms of the biaxial stress ratio p2/p1 under different conditions of applied loading, and the effect is demonstrated of strain-hardening according to an empirical relation of the type q = c (a + ψ)n.
The analysis is also applied to certain cases of non-uniform stress distribution. In the case of the hydrostatic bulge results are obtained showing a critical thinning ranging from 26 per cent for a non-hardening material to about 45 per cent for typical strain-hardening materials, values in general agreement with experimental data. Conditions over the punch head in the pressing of a cylindrical shell are discussed but computations are not attempted.
1,604 citations
TL;DR: In this article, explicit formulae are obtained for the stresses in a metal diaphragm which is bulged plastically by lateral pressure, and the predicted influence of work-hardening on the shape of the profile, and on the relation between polar strain and curvature, agree well with experimental data.
Abstract: Summary Explicit formulae are obtained for the stresses in a metal diaphragm which is bulged plastically by lateral pressure. The predicted influence of work-hardening on the shape of the profile, and on the relation between polar strain and curvature, agrees well with experimental data. A simple expression is developed for the instability strain.
262 citations