Several multi-axial testings setups have been developed to study deformation of sheet metal, e.g. bulge pressure tests [6, 7], hemi-spherical punch (i.e. Nakazima) tests [2, 8], cruciform tests [9–11], flat punch (i.e. Marciniak) tests [12, 13], multiaxial compression tests
[14, 15], electromagnetic forming tests [16, 17] (Fig. 1). Each of these techniques have specific strengths and weaknesses regarding the degree of the control of the stress state, the quality of information provided, practicality, etc. The minimum requirement for any methodology for real-time mechanical-microstructural characterization of multi-axial deformation in a miniaturized configuration, is to:
avoid constraining the physical deformation and failure mechanisms of the sheet being tested to allow characterization of “true” microstructural mechanisms,
operate safely within the vacuum chamber of a SEM to allow for in situ visualization and local strain mapping,
produce the required level of load and displacement to reach sheet metal failure.
In this section, these methods are comparatively analyzed for their potential as a miniaturized setup. Where required, results from finite element simulations are presented. Note that all simulations mentioned in this work are modeled with an isotropic elasto-plastic material model of high-quality deep-drawing steel, for which the elastic and plastic material properties are determined from tensile tests (Fig. 2). The sheet is modeled using solid axisymmetric elements, a four node quadrilateral element with bilinear interpolation, while the punch and the two clamps are modeled as rigid bodies. For friction the coulomb model is used, and the coefficients of friction are varied between 0 and 1.
Commonly used methodologies such as the compression test and the hemi-sphere punch test exert the required force through direct contact with the test piece. This makes the observed material behavior heavily dependent on the degree of friction, the level of influence of which is difficult to assess in small-scale tests. For instance, finite element simulations show that the location of fracture in the hemi-sphere punch test is directly related to the level of friction between the punch and the sheet metal being pressed (Fig. 3(a)). Similar concerns hold for the compression test, for which a direct view of observation in SEM is also not possible. For the hemi-sphere punch test the imposed strain path is further complicated due to the existence of a bending component, which increases with the miniaturization of the punch (Fig. 3(b)). As a result of these complications, characterization of the microstructural mechanisms using the hemi-sphere punch test and the compression test is not trivially possible.
Contact related problems are not an issue for bulge tests, electromagnetic forming tests or cruciform tests. However, for the former two cases, operation within SEM is not possible, due to the required fluid pressure (that is released upon sheet metal fracture) and strong magnetic field, respectively. The cruciform test, on the other hand, is an interesting candidate for miniaturization, and upon initial consideration there seems to be no direct influence of boundary conditions on the region of interest (i.e. center of the cruciform). However, finite element simulations carried out with the same material model used in Fig. 3 revealed that reaching high levels of deformation in the center of the cruciform is not possible, unless the thickness in the center is significantly reduced to a bowl-profile with the central thickness approximately ~20% of that of the as-received sheet (Fig. 4(a–c)). It was reported earlier that such a thickness reduced geometry may be manufactured by electro-discharge machining or electro-chemical machining, ensuring that the failure is forced to occur at the center (Fig. 4(b)) . Unfortunately, it is well-known that industrial sheet metals have a non-homogeneous microstructure distribution along the thickness direction. Removing layers from top and bottom of the sheet render the probed microstructure not representative anymore for the as-received sheet metal. Furthermore, it is questionable whether the real material failure behavior is properly probed, since the center of the bowl, with the smallest thickness, is forced to fracture first (Note that in case of a bowl with a flat base, the fracture always occurs at the edge of the flat base, see Fig. 4(b)). Due to these reasons, the cruciform test is also regarded as unsuited for investigating large deformation induced macro and microstructural phenomena in sheet metal.
Finally, in the Marciniak test, the load is transferred from a flat punch to the specimen via a so-called ‘washer’ plate, which has an opening window in the middle under the region of interest. Hence, there are no friction effects in this gauge region of the specimen. Both the specimen and the washer are drawn simultaneously, the latter at a larger velocity due to the opening in the center. This creates the main difference from a typical deep drawing experiment, as the resulting relative velocity between the specimen and the washer in the Marciniak test creates friction forces on the specimen in the opposite direction of those that occur in a normal deep-drawing experiment without a washer (Fig. 5).
This reversed friction force in the Marciniak test limits the level of deformation of the regions where there is contact between the washer and the sheet and, as shown by the finite element simulation in Fig. 6, allows the largest deformation and failure to occur at the center, where there is no contact, making the test fundamentally different from a standard punch test. As a result of the absence of contact a true in-plane deformation occurs and inhomogeneous material deformation is not artificially enforced. Accordingly, this test is perfectly suitable for characterizing microstructural mechanisms and, therefore, regained a lot of interest recently [18–21]. Furthermore, the Marciniak tests can be carried out safely in SEM since there is no influence on the working principles of electron microscopy. All these considerations qualify the Marciniak test as the most suitable candidate for a in situ miniaturized multi-axial deformation test, however, the challenge lies in miniaturization of the Marciniak setup.