Papers by Keyword: Necking

Abstract: The study of localized necking based on strain analysis using Digital Image Correlation (DIC) is the most widely used technique in sheet metal forming to study the FLD (Forming Limit Diagram). However, due to the heat generated by plastic deformation during the forming operations, another way is to analyze the temperature field of the specimen during the test by using Digital Infrared Thermography (DIT). A series of Nakazima tensile tests of high-strength low-alloy steel were tested using DIC and DIT synchronized systems. In this study, a thermomechanical numerical model was developed in ABAQUS/Standard in order to study the energy balance between the different effects of heat generation by plastic deformation, and transient conductive and convective heat transfers through the sample and to the environment. Analysis of the predicted energy balance during the tests allowed to understand the temperature evolution observed both at the beginning and at the development of the unstable necking until fracture. The numerical results are consistent with the analysis obtained from experimental temperature field, making feasible the use of DIT systems to study new necking detection criteria.

Abstract: Forming limit curves (FLCs) are important to predict failure against biaxial deformation in sheet metal forming. Particularly crucial is the detection and evaluation of the stable/instable transition which indicates necking and ultimately leads to rupture. In the past, it has been observed that specific processes, in particular free-form bending processes, might not be predicted well by conventionally evaluated FLCs, i.e. the Nakajima experiment, where tapered sheet metal specimens are stretched over a hemispherical punch until material failure. In the present study, FLCs are evaluated from such Nakajima tests and from notched tension tests (NTT) highlighting large differences in between both results. The differences in between the evaluation methodologies are discussed with respect to contact and bending strain in the forming zone. The FLCs of three tested sheet metal materials are compared to fracture strain resulting from an incremental bending process with free forming zone demonstrating an increased failure prediction accuracy by the NTT FLCs than by the conventional ones. In the light of these results, it is therefore encouraged to critically assess the application of FLCs obtained from NTTs to various free-form bending processes.

Abstract: With the goal to define a cost-effective and efficient process to identify adequate materials for sheet metal forming processes, it is crucial to evaluate the formability of materials. Forming limit curves (FLC) are used to analyze the forming and failure limits of sheet metals and dependence of the major (φ₁) and minor strain (φ₂) from the uniaxial stress-strain area through the plane-strain point to the biaxial strain area. According to ISO 12004-2, the FLC is performed by Nakajima or Marciniak tests. Due to the experimental setup and the preconditions, pre-stretching occurs in the specimens and bending and friction effect are the result. The determination of the onset of necking (FLC) results mathematically from a “best-fit inverse parabola” on section lines. In addition, the failure point, i.e. the maximum strain value one frame before failure, is also analyzed. In contrast, tensile, notched tensile and hydraulic bulge tests, which together have a potential to map an alternative FLC, exhibits a linear strain path evolution. The behavior of the various strain paths of Nakajima and the alternative methods are examined for necking and cracking. Furthermore, the fracture surfaces are investigated by confocal laser scanning microscopy to identify influences of the different FLC methods on the fracture mechanics. FLCs were conducted with the Nakajima and the alternative FLC characterization method for a ductile steel (DX54D). To ensure transferability, the tensile tests are also performed with a high-strength steel (DP800). The FLC of the ductile steel, generated through the alternative method, exhibits a similar shape to the Nakajima generated FLC with the advantage of a constant strain rate leading to linear strain paths and a lower number of tests. The same results are achieved for the uniaxial strain tests with DP800.

Abstract: This paper investigates the post necking phenomenon in mild steel using six different hardening laws (Hollomon, Swift, Ludwik, Ghosh, Voce and Hockett-Sherby) by extrapolation method. This is carried out through the finite element simulation on tensile deformation of a mild steel specimen under quasi-static condition. Reference flow curves are obtained analytically and found helpful for the numerical simulation. The material parameters of the above hardening laws are evaluated by curve fitting method based on the pre necking experimental data and their suitability is examined before and after necking.

Abstract: A many-body interatomic potential for metallic nanowires within the second-moment approximation of the tight-binding model (the Cleri-Rosato potential) was employed to carry out three dimensional molecular dynamics simulations. Molecular dynamics simulation results for metallic nanowires at various temperature are presented. The stress–time and stress length curves for nanowires are simulated. The breaking and yield stress of nanowires are dependent on the Volume and temperature. The necking, Plastic deformation, slipping domain, twins, clusters, microspores and break-up phenomena of nanowire are demonstrated. Stress decreases with increasing nanowire volume and temperature. The final breaking position occurs at the central part of the nanowire when it is short, as the nanowire length increases the breaking position gradually shifts to the ends.

Abstract: Strain localization in low carbon steel DC04 undergoing uniaxial tension is investigated by Electronic Speckle Pattern Interferometry (ESPI). The necking in the sheet specimens occurs by forming two narrow crossing bands. A model of strain rate distribution is used to extract quantitative information about the localization bands, such as bandwidths, bands orientations and their maximum strain rates. Thus, their evolutions are followed from the diffuse necking up to the rupture. The influence of specimen geometry on localization phenomenon is studied.

Abstract: The influence of the crystallographic orientation, the level of axial strain and the test temperature on the progressive cross-section ellipticity of single crystal samples under uniaxial tension is analyzed in order to improve axial strain measurement in experiments. The direct three-dimensional finite element modeling of elasto-plastic deformation process of single-crystal initially cylindrical samples is used with taking into account finite strains, slip mechanisms and necking.

Abstract: Generally, the forming limit diagram is widely applied to predict the sheet necking and fracture in the conventional sheet forming process. In recent years, the fact that the forming limit is much higher using Incremental sheet forming (ISF) than that obtained in conventional sheet forming, has become a research hotspot in forming mechanism of local forming process. In this paper, the geometrical imperfection in the thickness was presumed to represent local weakening zone and the BAMMAN_DAMAGE material model which using void to describe non homogenization caused by geometric imperfection, were used respectively to investigate the effect of geometry imperfection on the sheet forming limit. Based on the W.C. Emmens’ experiment, the reason and mechanism of enhancement of forming limit during incremental forming was studied through the numerical simulation method. And the variations of stress and strain during the forming process were also studied.

Abstract: In conventional analysis of instability, a rough prediction of uniform deformation was obtained due to taking material parameters as constants. In this study, the constitutive equation with varying parameters for Zn-5%Al alloy at 340 °C is employed to predict the critical values of uniform strain in tension based on Considere criterion and Hart criterion, respectively. It should address the factor of strain rate in the characterization of the capability of uniform deformation on superplastic alloys, or for that matter, on any rate-dependent material. Comparison and analysis indicated that the results on Hart criterion have the better predictability of uniform deformation than Considere criterion. The Considere criterion is dependent on strain path, while Hart crtierion is merely dependent on the values of strain and strain rate in tension, and is independent on the strain path or the deformation condition or the deformation history. Therefore, the uniform strain vs. strain rate relation can be taken as a quantitative reference for designing a reasonable strain path during superplastic forming with increase of formability and reduction of forming time.

Abstract: This article deals with numerical simulation of necking. It draws the attention onto the importance of the description of strain-hardening and the effects on the evolution of necking. In order to compare necking evolution in relation with different plasticity models, a tracking procedure which consists in determining the evolution over time of discharged volumes of the sample is adopted. Models that take into account physical phenomena at the microscopic level and especially the heterogeneities of materials from a mechanical point of view seem well suited to fit experimental evidence connected to necking.