3.2. Formability limits
The formability limit by necking (FLC) was determined by means
of sheet formability tests (tensile, Nakazima, bulge and hemispherical
dome tests) that covered strain paths from uniaxial to biaxial
stretching conditions. The procedure utilized for determining the
in-plane strains (ε1, ε2) at the onset of necking involved electrochemical
etching of a grid of overlapping circles with 2 mm initial
diameter on the surface of the test specimens before forming and
measuring the major and minor axes of the ellipses that resulted
from plastic deformation.
The characterization of the formability limits by fracture (FFL
and SFFL) included additional results from double-notched test
specimens loaded in tension and in plane torsion. The latter were
needed to characterize the SFFL because all the remaining sheet
formability tests failed by fracture under crack opening mode I.
The determination ofthe strains atfracture involved measuring the
thickness ofthe specimens before and after fracture at several locations
along the crack in order to obtain the ‘gauge length’ strains.
The gauge length strains were subsequently fitted by two straight
lines; (i) one straight line (FFL) falling from left to right with a slope
‘−0.68’ in agreement with Eq. (7) of Section 2.2 and (ii) another
straight line (SFFL) rising from left to right with a slope equal to
‘+1.39’ in agreement with Eq. (8) of Section 2.2.
The formability limits by necking and fracture of the aluminium
AA1050-H111 sheets with 1 mm thickness are shown in Fig. 4.