Results & Discussion
Material characterization
The microstructure of extrusion plane is shown in Fig. 3. It is seen
from this figure that the micostrcture is composed of grains with
different sizes having an average of \(9.52\pm 1.89\) \(\mu\)m. This
structure is commonly observed in magnesium ZK60 alloy41–43. The pole figures in Fig. 4 show that the
majority of basal planes are aligned with the extrusion direction.
Mechanical
characterization
A representative monotonic tensile stress-strain curve for the material
is shown in Fig. 5. According to Fig. 5, it can be seen that the
material exhibits conventional power-type hardening. This is expected
because it is known that the major plastic deformation mechanism is
slipping when a tensile loading is applied parallel to the extrusion
direction 44. Mangesium exhibits distinct
characteristics than conventionl material such as steel and aluminum
alloys due to the closed-packed hexagonal
lattice structure. Because of
limited slip system and depending on the loading orientation, Mg may
deforms plastically under slipping and/or twinning44–47. In the case of wrought Mg alloys (extruded,
rolled or forged) that possess strong texture with basal planes parallel
to the working direction and the c-axis normal to it48,49. Tensile loading along the working direction
only activates slip mechanisms resulting in a power hardening behavior13. In particular, because basal planes (\(0002\)) can
accommodate only 8% elongation, prismatic slip
(\(10\overset{\overline{}}{1}0\)) is also activated and becomes the
dominant to accommodate additional strain reaching to 20%50. The average and the standard deviation of the
mechanical properties obtained from testing two specimens are listed in
Table 2.
Selected load-extension curves for the tensile tests on U and V notched
specimens are shown in Figs. 6 and 7, respectively. A summary of the
fracture load for these is listed in Table 3. It can be seen from Table
3 that the obtained fracture loads from the duplicates are consistent
with a standard deviation between 0.02 and 1.75 kN. In addition, the
effect of stress triaxiality can also be observed from the U-notch
experiment that generally shows that fracture load increases as the
notch root radius decreases 51. In addition, notch
strengthing is observed in ductile materials. Peron et al tested
additively manufactured Ti-6Al-4V notched specimen using electron beam
melting (EBM) process 52. The authors explained that
the stress triaxialily and constaint effects due to elastic stress state
in the bulk of the sample are contributing to the rise of the fracture
load, i.e. notch strengtthing, for specimens with sharper notches.
However, it is noted from Figs. 6 and 7 that the relationship between
notch acuity or notch sharpness and fracture load does not always hold.
To illustrate, U5 specimen has less acuity than U3 or U4 but it actually
has comparable fracture load them. Similarly, the fractur load for
V-notch specimens with notch angle of 35 is lower than that for
60 and 90. Because the main aim of the study is to predict the
fracture load of U and V notched ZK60-T5 speciems using SED method it is
out of the scope to invesitage the triaxiality and the notch strengthing
mechanism of this material.
SED predictions
Due to the unavailability of fracture toughness for the studied
material, Eq. 2 cannot be used to evaluate the critical radius.
Therefore, in these conditions, an empirical approach can be a good
solution for determining the critical radius 10,30.\(R_{c}\) can be empirically determined considering the fact that the
critical strain energy density value, \(W_{c}\), is independent of the
acuity and shape of the notch, but it only depends on the material.
Therefore, the SED of any notched geometry can be measured for different
radii of the control volume, and the value of the radius at which the
measured SED matches the critical one found from Eq. 1 (1.105
MJ/m3) corresponds to the value of control volume
measured with the critical radius, \(R_{c}\).
To do so, we considered the U-notched specimen with 1.5 mm radius and we
leveraged on numerical analyses by using the finite element (FE) code
ANSYS to evaluate the SED. The SED values can be directly derived from
FE models, and they are mesh-independent as reported in Ref53. Axisymmetric linear elastic 2D analyses were
performed (the 8-nodes axisymmetric element plane 83 was selected for
these analyses). Due to the double symmetry of the geometry, only one
quarter of the specimen was modeled. Symmetric boundary conditions were
used for vertical and horizontal symmetry lines of the models as shown
in Fig. 8. Fig. 9 plots the SED as a function of different values of the
control volume and compares it with the critical SED value, \(W_{c}\).
It can be seen that the intersection is closed to 1.3 mm, and from a
more detailed analysis where the value of the radius was varied from
1.25 mm and 1.35 mm with a step of 0.01 mm, the critical radius was
found to be 1.31 mm.
Table 4 summarizes the outlines of the experimental, numerical, and
theoretical findings for the tested ZK60 notched samples, except for U
notched samples with 1.5 mm radius since it was used to measure the
critical radius. In particular, the table summarizes the experimental
stresses to failure (\(P_{i}\) with \(i=1,\ 2,\ 3\)) for every notched
geometry compared with the theoretical value (\(P_{\text{th}}\)) based
on the SED evaluation. The tables also give the SED value as obtained
directly from the FE models of the ZK60 samples by applying to the model
the average experimental stress \(p\). The last columns of the table
report the relative deviations between experimental and theoretical
stresses. As widely discussed in previous contributions31,54,55, acceptable engineering values range between
-20% and +20%. As visible from the table, this range is satisfied for
the great majority of the summarized test data.
The results are also given in a graphical form in Figs. 10a to 10d for
the different notch geometries. The experimental values of the failure
stresses (dots) have been compared with the theoretical predictions
based on the constancy of the SED in the control volume (line). The
plots are given for the notched ZK60 samples as a function of the notch
tip radius \(\rho\). The trend of the theoretically predicted failure
stresses is in good agreement with the experimental ones.
A synthesis in terms of the square root of the local energy averaged
over the control volume (or radius \(R_{c}\)), normalized with respect
to the critical energy of the material as a function of the notch tip
radius is shown in Fig. 11. The plotted parameter is proportional to the
fracture load 18,30. The new data are plotted together
independently of the notch geometries. The aim is to investigate the
influence of the notch tip radius on the fracture assessment based on
SED. From the figure, it is clear that the scatter of the data is very
limited and almost independent of the notch radius, as already verified
in other contributions 56,57. All the values fall
inside a scatter ranging from 0.8 to 1.2 with the majority of the data
inside 0.9–1.1 and only one value outside the range from 0.8 to 1.2.
The synthesis confirms also the choice of the control volume which seems
to be suitable to characterize the material behavior under pure mode I
loading. The scatter of the experimental data presented here is in good
agreement with the recent database in terms of SED reported in Ref31.
Fractography
The morphology of fracture surface obtained from the tested specimens
are represented in Fig. 12. According to Fig. 12, the unnotched
specimens showed a large area from the fracture surface edge toward the
center of net section influenced by shear failure. These shear lips were
also observable in U-notched specimens, however, their size seemed to be
limited only to an area close to the specimen’s surface. Finally, the
presence of shear lips in V-notched specimens could not be seen in the
low magnification of images obtained by the microscope. Therefore,
(FE-SEM) analyses were performed on the tested specimens to study their
failure mechanisms in more details. Figs. 13 to 15 show the typical
fracture surfaces of the unnotched, the U-notched (\(\rho\ =\ 1.5\)mm) and the blunted V-notched (\(2\alpha\ =\ 35\), \(\rho\ =\ 0.4\)mm) specimens observed by FE-SEM. For the sake of brevity FE-SEM results
from the notched specimens with highest notch acuities are presented and
compared to the unnotched specimens. The fracture surfaces of the tested
specimens with different geometries consist of shear lips on the area
close to the edge of the fracture surface and a plateau in the center of
fractured area, representing the tensile failure in this region. The
shear lips follow the direction of maximum shear stress at \(45\), while
the plateau is perpendicular to the loading direction. This morphology
of the fracture surface is common among the ductile materials undergoing
fibrous and shear failure mechanisms at the same time.
The observed shear lips were characterized by shear dimples. The size of
these shear lips tends to decrease by increasing the notch acuity,
having the largest and smallest width in the unnotched specimens and
V-notched specimens of \(35\) opening angle and \(0.4\) mm tip radius
(See Figs. 13a, 14a, and 15a). The smaller shear lips in the notched
specimens represent the localized plastic deformation in these parts,
resulting in lower ductility of the part under tensile loading and
consequently reduced elongation at failure. This is in agreement with
the experimental data obtained from the tensile tests. The presence of
secondary cracks was detected in notched specimens. Secondary crack
origins arise where the local stress concentration due to the presence
of material inhomogeneities meets the intensified stress field ahead of
the primary crack. The higher stress level at the vicinity of the notch
together with the stress triaxiality in this region can be considered as
sources for the higher appearance of these secondary cracks in the
notched specimens.
The center part of the fracture surface is characterized by a mixture of
both cleavage facets and dimple-like fracture features describing the
mixed ductile/brittle nature of fracture in the tested specimens.
Presence of secondary phase particles rich in Zn and Zr with an average
size of \(5.2\ \pm\ 2.1\) \(\mu\)m was more evident in this region of
the fracture surface (see Figs. 13f, 14f, and 15f). Due to local stress
concentration around the secondary phase particles, void formation under
tensile loading is more probable to occur from these sites. Similar
morphology of fracture features was observed for both unnotched and
notched specimens.