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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15 Dec 1996-Materials Science and Engineering A-structural Materials Properties Microstructure and Processing
TL;DR: In this paper, the effect of different types of defects on the tensile behavior of an Al 7Si 0.4Mg casting alloy was studied and the experimental results were in agreement with the predictions of a simple analysis based on models for the growth of a plastic instability in a tensile sample.
Abstract: Samples containing either entrapped dross and oxide films, gas porosity or small drilled holes have been used to study the effect of different types of defects on the tensile behaviour of an Al 7Si 0.4Mg casting alloy. The tensile properties show little or no correlation with the bulk porosity content, especially in the case of samples containing dross and oxide films. In contrast, the decrease in tensile ductility and strength correlates with the area fraction of defects in the fracture surface of the samples. The experimental results are in agreement with the predictions of a simple analysis based on models for the growth of a plastic instability in a tensile sample.
265 citations
TL;DR: In this paper, a phenomenological flow theory of plasticity is proposed which models time-independent incremental behavior at a corner of the yield surface of a polycrystalline metal.
Abstract: A class of phenomenological flow theories of plasticity is proposed which models time-independent incremental behavior at a corner of the yield surface of a polycrystalline metal. The proposal is consistent with the physical theories of plasticity based on single crystal slip. Conditions for convexity, ensuring invertibility of the incremental relations, are derived. The simplest candidate, called J 2 corner theory, coincides with the J 2 deformation theory of plasticity for nearly proportional stress increments and incorporates a smooth transition to elastic unloading for increasingly non-proportional increments. The theory is applied to the bifurcation and imperfection-sensitivity analysis of necking in a thin sheet. For this example, like many others involving bifurcation in the plastic range, the corner theory appears to circumvent some of the difficulties associated with use of the standard phenomenological plasticity laws.
260 citations
TL;DR: In this article, a concise review of different proposed phenomenological equations that describe the behavior of sheet metals and their influence on theoretical forming limits is presented, and geometrical features of yield surface shapes necessary to achieve high formability are discussed.
258 citations
TL;DR: In this article, a micromechanics model based on the theoretical framework of plastic localization into a band introduced by Rice is developed, which consists of a planar band with a square array of equally sized cells, with a spherical void located in the centre of each cell.
256 citations
Cites methods from "Limit strains in the processes of s..."
...Building on the work by Marciniak and Kuczynski (1967), Rice (1977) presents a general framework for imperfection based localization analysis, as is also discussed in Needleman and Tvergaard (1992)....
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TL;DR: In this paper, the authors investigated the possibility that ductile fracture occurs by the McClintock-Berg mechanism of localization of deformation within a narrow shear band, owing to the progressive softening of the material by increasing porosity due to void growth.
Abstract: This paper investigates the possibility that ductile fracture occurs by the McClintock-Berg mechanism of localization of deformation within a narrow shear band, owing to the progressive softening of the material by increasing porosity due to void growth. The ductility predicted for a macroscopically homogeneous sample of a voided material is shown to be unrealistically large and hence an initial inhomogeneity of properties is considered, in the sense of an analysis by Marciniak and Kuczynski in the related problem of local necking in sheet metals. General conditions for a localization bifurcation with an initial inhomogeneity (imperfection), concentrating deformation to allow localization within it, are derived. The initial imperfection is taken in the form of a void-containing, thin slice of a material and is assumed to have a void volume fraction slightly larger than the outside of the imperfection. Elastic-plastic constitutive rate relations for void-containing materials proposed by Gurson are adopted to the conditions for the localization bifurcation. The critical conditions are analyzed numerically to discuss the sensitivity of localization conditions to an initial imperfection, in consideration of the implications for the theory of ductile fracture. The results suggest that the existence of an initial imperfection makes it possible for localization to occur at a reasonable strain, and the predictions from this analysis seem broadly consistent with reported experimental observations.
240 citations
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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