Marciniak Test Research Articles

A methodology for evaluating sheet formability combining the tensile test with the M–K model

This paper proposed an approach for evaluating the sheet formability by combining the tensile test with the finite element Marciniak and Kuczynski (M–K) model. Firstly, the tensile test with a notched specimen was carried out to identify an appropriate constitutive law for an AA5086 sheet. A modified Ludwick's law was used to describe its forming behavior. A technique of digital image correlation associated with a high-speed camera was applied to evaluate specimen's surface strains during the experiments. The inverse analysis was performed to identify the parameter values in the constitutive law. The initial geometrical imperfection factor in the M–K model was determined. Then by using the commercial finite element software ABAQUS, the M–K model was simulated to evaluate numerically the sheet formability of the alloy. By means of a user-defined FORTRAN subroutine UHARD, the constitutive law was implanted into ABAQUS. Different strain states were obtained by changing displacement ratios and forming limit curves (FLCs) of the sheet were determined too. Finally, an experimental procedure based on the modified Marciniak test was carried out and the FLCs were obtained experimentally. The comparison between the numerical and experimental results showed that the approach developed in this paper could give an appropriate prediction of FLCs.

A Comparative Study of Different Necking Criteria for Numerical and Experimental Prediction of FLCs

For sheet metal forming, the determination of the onset of localized necking directly influences the formability evaluation and construction of forming limit curves (FLCs). Several necking criteria in the literature have been proposed and widely used, however, there are some restrictions, e.g., some criteria are suitable for numerical methods but not for the experimental phase. In this study, numerical and experimental procedures are carried out to seek an appropriate necking criterion for the prediction of FLCs. This article begins with the FE modeling of the Marciniak test with ABAQUS. Based on the FE simulation, different necking criteria (global and local ones) are reviewed and analyzed in detail, and the FLCs for a 5086 aluminum sheet are constructed with these criteria. On the other hand, a quasi-static experimental Marciniak test is carried out to study the formability for this given sheet. With a chosen necking criterion, the limit strains are experimentally determined. The comparison between experimental and numerical results shows that the chosen necking criterion could be effective to numerically and experimentally evaluate the global formability of this aluminum alloy on the wide range of strain states.

Influence of the Punch Geometry and Sample Size on the Deep-Drawing Limits in Expansion of an Aluminium Alloy

The effects of punch geometry and sample size on forming limit diagrams in expansion are investigated in the case of a 2024 aluminium alloy. Four configurations were selected: flat punch (Marciniak test) or hemispheric punch and decimetric vs. centimetric tooling dimensions. Both decimetric and centimetric deep-drawing devices are associated with an image correlation tool that allows to identify without any contact the deformation on the surface of planar or non-planar specimens. Strains on the surface of the samples are observed by means of a double numerisation in three dimensions of the sample before and after deformation by using stereoscopic vision and triangulation. Finally, deep-drawing limit of the four configurations are compared in expansion state and with literature. Results mainly show that hemispherical punch is less sensitive to size effect than Marciniak test.

Effect of Strain Paths on Formability Evaluation of TRIP Steels

The Forming Limit Diagrams (FLD) are widely used in the formability analysis of sheet metal to determine the maximum strain, which gives the Forming Limit Curve (FLC). It is well known that these curves depend on the strain path during forming and hence on the test method used to calculate them. In this paper, different stretching tests such as the Nakajima and the Marciniak tests were performed, with different sample geometries to obtain points in different areas of the FLD. An optical analysis system was used, which allows following the strain path during the test. The increasing use of advanced high-strength steels (AHSS) has created an interest in determining the mechanical properties of these materials. In this work, FLCs for a TRIP steel were determined using Nakajima and Marciniak tests, which revealed different strain paths depending on the type of test. Determination of the FLCs was carried out following the mathematical calculations indicated in the ISO 12004 standard and was also compared with an alternative mathematical method, which showed different FLCs. Finally, the tests were verified by comparing the strain paths of the Nakajima and Marciniak tests with a well-known mild steel.

Theoretical and numerical study of strain rate influence on AA5083 formability

With the application of new forming techniques (hydroforming, incremental forming), it is necessary to improve the characterization of the formability of materials and in particular the influence of strain rate. This paper begins with the characterization of material behavior of an aluminum alloy 5083 at high temperatures. To describe its visco-plastic behavior, Swift’s hardening law is used and the corresponding parameter values are identified. Then, two different approaches are introduced to construct FLDs (forming limit diagrams) of this alloy sheet and evaluate the effect of the rate sensitivity index on its formability. The first one is theoretical (the M-K model), and an algorithm is developed to calculate the limit strains by this model. In the second approach, the Marciniak test is simulated with the commercially available finite-element program ABAQUS. Based on FEM results, different failure criteria are discussed and an appropriate one is chosen to determine the onset of localized necking. With the material behavior data corresponding to AA5083 at 150 °C, parametric studies are carried out to evaluate the effect of the strain rate sensitivity index. The comparison of results by these two approaches shows the same tendency that an improvement of the formability with increasing strain rate sensitivity is observed. Finally, by consideration of the compensating effects of the strain hardening and rate sensitivity indices, the FLDs of this sheet at 150, 240 and 300 °C are determined and compared. Results show that the formability of AA5083 seems not to be improved up to a certain temperature (between 240 and 300 °C), above this temperature, the formability is greatly enhanced.

Comparison of the experimental and the numerically predicted mechanical damage in the sheet forming of steel

There is great economical interest in the workability prediction of a material during sheet metal forming. This type of processing involves complex sequences of stress and strain states, and the material workability cannot be evaluated through simple procedures such as tension testing. Under these circumstances, various mechanical tests have been proposed in order to analyze sheet forming. There is also an increasing interest in the description of this process through numerical approaches such as finite element analysis (FEA), which allows the evaluation of the mechanical damage of the material employing various ductile fracture criteria. The present paper presents a comparison between the mechanical damage measured experimentally during the Marciniak test of a steel sheet and the damage predicted by FEA. No clear relationship between the two approaches was found and the FEA results display a fairly high dispersion. It is concluded that the various mechanical damages calculated in the FEA are not directly connected to the experimental damage associated with pore opening and measured through metallographic techniques.

Ｍｇ量の異なる５０００系アルミニウム合金板の成形限界ひずみ

Forming Limit Curves (FLCs) of 5000 series aluminum alloys with different Mg contents, 2.5 and 5.5 mass%, are experimentally determined in detail using the Marciniak test. The forming limit strains of the Al–Mg 5.5% alloy are larger than those of the Al–Mg 2.5% alloy from uniaxial tension to near plane-strain tension regions, whereas the order of formability is reversed in the biaxial stretching region. To evaluate the work-hardening behavior of the test materials under biaxial tension and to determine appropriate anisotropic yield functions, biaxial tensile tests of the test materials are carried out using cruciform specimens. Moreover, forming limit strains of the test materials under proportional loading are calculated using the Marciniak-Kuczyński approach based on a phenomenological plasticity model with non-normality effects [Kuroda and Tvergaard, 2001, J. Mech. Phys. Solids, 49, pp. 1239–1263]. The validity of the phenomenological plasticity analysis is discussed by comparing the observed FLCs with calculated ones.

Effects of fatigue precracking on stretch zone formation : Smith, J., Bassim, M.N. and Liu, C.D. Engng. Fract. Mech. (1995) 52 (3), 401–408

Ductile fracture during biaxial sheet stretching for two types of ferrous alloys and one type of nonferrous pure metal was predicted using the ellipsoidal void model proposed by one of the authors. First, fracture forming limit obtained experimentally by the Nakajima test scarcely differed from that obtained experimentally by the Marciniak test. Next, fracture forming limit obtained by the experiment scarcely depended on the magnitude of prestrain, which was applied to the sheet by rolling, and scarcely depended on the type of prestrain. Since the number of material constants on ductile fracture is only one, the material constant was determined so that the material thickness at fracture calculated from the simulation agreed with that obtained by the experiment. Fracture forming limit calculated using the ellipsoidal void model agreed closely with that obtained by the experiment, whereas fracture forming limit calculated using conventional ductile fracture criteria differed from that obtained by the experiment. Furthermore, fracture forming limit calculated using the ellipsoidal void model and that calculated using the conventional ductile fracture criteria changed drastically when the strain ratio changed across one for simulating biaxial stretching using a prestrained sheet.