Temporal and Spatial Detection of the Onset of Local Necking and Assessment of its Growth Behavior

This study proposes a method for the temporal and spatial determination of the onset of local necking determined by means of a Nakajima test set-up for a DC04 deep drawing and a DP800 dual-phase steel, as well as an AA6014 aluminum alloy. Furthermore, the focus lies on the observation of the progress of the necking area and its transformation throughout the remainder of the forming process. The strain behavior is learned by a machine learning approach on the basis of the images when the process is close to material failure. These learned failure characteristics are transferred to new forming sequences, so that critical areas indicating material failure can be identified at an early stage, and consequently enable the determination of the beginning of necking and the analysis of the necking area. This improves understanding of the necking behavior and facilitates the determination of the evaluation area for strain paths. The growth behavior and traceability of the necking area is objectified by the proposed weakly supervised machine learning approach, thereby rendering a heuristic-based determination unnecessary. Furthermore, a simultaneous evaluation on image and pixel scale is provided that enables a distinct selection of the failure quantile of the probabilistic forming limit curve.

Characterisation of Diffuse and Local Necking of Aluminium Alloy Sheets using DIC Technique

This paper introduces a new method for the characterisation of the boundary of diffuse and local necking based on DIC measurements during tensile tests. A series of images illustrate the extension of diffuse necking and show the occurrence of local necking as well. The evaluation of strain distribution gives the exact description of processes using both time dependent and non-dependent methods.

Conversion of engineering stresses to Cauchy stresses in tensile and compression tests of thermoplastic polymers

Thermoplastic polymers exhibit non-isochoric behaviour during tensile and compression testing as well as particular deformations like local necking (tension) or buckling (compression). A method for the determination of Cauchy stresses from tensile and compression tests is presented, that considers the actual deformations of the test specimens. The exact geometry of the specimens in the respective present configuration is determined in photographs, which are taken continuously throughout the test. The engineering stresses at several time points are converted into Cauchy stresses using newly developed formulas in consideration of the actual specimen geometry. For validation finite element analyses of the tensile and compression tests are performed using the identified stress-strain curves. The numerical results show good agreement with the experiments for the tested polymers. Thus a method for conversion of engineering to Cauchy stresses in tensile and compression tests could be established considering the non-isochoric deformation in plasticity. With this method “true” stress-strain curves as input for finite element material models can be identified for arbitrary materials.

Modelling of Forming Limit Strains of AA5083 Aluminium Sheets at Room and High Temperatures

Present work analyses mathematical modelling to predict the onset of localized necking and rupture by shear in industrial processes of sheet metal forming of aluminium alloy 5083 such as biaxial stretching and deep drawing. Whereas the AA5083 sheet formability at room temperature is moderate, it increases significantly at high temperature. The Forming Limit Curve, FLC, which is an essential material parameter necessary to numerical simulations by FEM, of AA 5083 sheet was assessed experimentally by tensile and Nakajima testing performed at room and 400°C temperatures. Tensile test specimens at 0o, 45o and 90o to the direction of rolling (RD) and Nakazima type specimens at 0o RD of aluminium AA5083 were fabricated. Simple tensile tests at room and 400°C temperatures were performed to obtain the coefficients of plastic anisotropy and material strain and strain rate hardening behavior at different temperatures. Nakazima biaxial tests at room and high temperature, employing spherical punch were carried out to plot the limit strains in the negative and positive quadrant of the Map of Principal Surface Limit Strains, MPLS, of aluminium AA5083 sheet. The “Forming Map of Principal Surface Limit Strains”, MPLS, shows the experimental FLC which is the plot of principal true strains in the sheet metal surface (ε1,ε2), occurring at critical points obtained in laboratory formability tests or in the fabrication process of parts. Two types of undesirable rupture mechanisms can occur in sheet metal forming products: localized necking and rupture by induced shear stress. Therefore, two kinds of limit strain curves can be plotted in the forming map: the local necking limit curve FLC-N and the shear stress rupture limit curve FLC-S. Localized necking is theoretically anticipated to occur by two mathematical models: Marciniak-Kuczynski modelling, hereafter M-K approach, and D-Bressan modeling. Prediction of limit strains are presented and compared with the experimental FLC. The shear stress rupture criterion modeling by Bressan and Williams and M-K models are employed to predict the forming limit strain curves of AA5083 aluminium sheet at room and 400°C temperatures. As a result of analysis, a new concept of ductile rupture by shear stress and local necking are proposed. M-K model has good agreement with both D-Bressan models.

Experimental Waviness Evolution of Interstitial Free - IF Steel Sheet under Biaxial Stretching

The purpose of present study is to present experimental results and a mathematical model for the evolution of surface waviness parameters with plastic strain of Interstitial Free - IF steel sheet under uniaxial and biaxial stretching tests. Roughness and waviness are very important quality parameters to be evaluated in sheet metal forming. Various waviness profile parameters such as the arithmetic average waviness Wa, the total height peak-valley waviness Wt, maximum peak height Pp and maximum valley depth Pv were measured during uniaxial and biaxial tests. Tensile test specimens at 0º, 45º and 90º to the direction of rolling and Nakazima type specimens of IF steel were fabricated. After preparing the test specimens, incremental simple tensile and Nakazima biaxial tests with flat punch were performed to characterize the negative and positive quadrant of the Map of Principal Surface Limit Strains, MPLS, of IF steel sheet. Measurements of waviness parameters of the specimen surface at incremental plastic strain stages were performed at the same surface site. Also, during the uniaxial and biaxial tests, the following plastic strains were calculated from printed circular mesh at each incremental step: ε1longitudinal major strain and ε2transverse minor strain. From these data, curves of waviness parameters versus equivalent strain were plotted to obtain a phenomenological equation of 4th or 3rd degree polynomial type. Furthermore, the growth rates of Wa and Wt parameters with the equivalent plastic strain were assessed. From the growth rate curves, it was possible to verify how the sheet thickness imperfections evolves during straining, being possible to predict the influence of plastic strain on the waviness values of IF steel sheets. From the analysis of Wa and Wt growth rates during straining, it was possible to proposed a criteria for the onset of local necking or limit strains in the MPLS. The waviness parameters Wt is the best for characterizing the onset of local necking in sheet metal forming.

Experimental Detection of the Onset of Local Necking in an Aluminium Sheet

Forming limit diagrams (FLDs) are widely used to assess metal sheet formability. Experimental FLDs are obtained by performing formability tests and determining failure strains. The standard method for detection of forming limits is based on the spatial distribution of the strains and requires formation of a single local neck. Some aluminium alloys, such as AA6016, have a tendency to form multiple strain localizations in formability tests, which can be interpreted as multiple local necks. Thus, use of the standard method is questionable for these aluminium alloys. The present paper presents an alternative, digital-image-correlation-based method for experimental detection of the onset of local necking in an aluminium sheet. The method is based on monitoring the sheet-thickness evolution, and is developed to be user independent and resistant to noise in the measurements. The method can be used in combination with different types of formability tests. The main requirement is that digital image correlation is used for strain measurements. Here, the method is initially tested on uniaxial tension tests of AA6016 aluminium alloy sheets and then extended to formability tests.