Characterisation of local deformations in deep-drawing sheet steel 
Michael Nimz', Stefan Jung?, Clemens Miiller!, Oliver Pompe’ 
! Institute of Materials Science, 2 Institute for Production Engineering and Forming Machines, 
Darmstadt University of Technology 
Introduction 
Simulation of strain distributions during deformation of metal parts as, for example, during deep- 
drawing of sheets became feasible by numerical techniques. To check the accuracy of the 
assessment of local strain in work pieces undergoing large variations of material flow, experimental 
methods are required by which a precise quantification of the strain in small areas is possible. A 
useful and well-known method to quantify local strain is to measure the deformation of a grid 
imprinted on the surface (1). In this paper, methods using inherent patterns (surface structure and 
microstructure) are described with respect to local resolution and accuracy. 
Experimental 
A commercial ferritic deep-drawing sheet steel (DC 05) with regular surface structure elements 
(RSSE) acting as lubricant pockets imprinted during rolling was used. In the as-received state the 
RSSE are circles with an inner diameter of about 180 pm. In order to obtain a series of samples 
with defined levels of strain, uniaxial tensile test were carried out. 
Surface roughness was quantitatively characterised with a contact stylus instrument (Hommel T20). 
At each level of strain an area of 1 x 1 mm? (250 lines, each with 800 points) was scanned three 
times. A specific software (Topograf developed at the authors’ laboratory (2)) was used to reduce 
the data to 250 x 250 pixels. This matrix was filtered with a “least error square”-filter to subtract the 
waviness of the specimen from the topographic information of interest. 23 different 3D roughness 
parameters defined in (3, 4) and used for describing the surface topography of deep-drawing steels 
(5) were calculated using Topograf. 
The inner diameter of the RSSE was measured before and after deformation parallel to the direction 
of applied stress with a Quantimet system (Leica). The mean size of grains visible on the polished 
and etched steel surface was measured by the linear intersection method (see, for example (6)). The 
line spacing was chosen as 160 pm. The mean linear intercepts before and after deformation, L and 
Lo, were determined parallel to the direction of applied stress. 
Superposition of images of same location before and after deformation was carried out for the 
structured surface as well as for the polished and etched surface. The image of the initial state was 
stretched interactively in the direction of applied stress and compressed in the perpendicular 
direction until an optimum fit with the image of the deformed state was obtained. As this fit is 
checked by visual inspection on the screen of the image analyser, the accuracy depends somewhat 
on the experience of the operator. 
Methods and results 
Five different ways of determining local strain described in the following were developed and 
tested. 
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