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.