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Der Artikel präsentiert eine umfassende Studie zur Frakturcharakterisierung von Einkristallspinellen mittels Transmissionselektronenmikroskopie (TEM). Zunächst werden die Vorteile und Herausforderungen mechanischer Tests im kleinen Maßstab diskutiert, insbesondere für Materialien, bei denen die Präparation von Großproben schwierig ist. Die Studie verwendet Partikelverfolgung (PT), um vollflächige Deformationskarten zu erhalten, die sich mit Problemen im Zusammenhang mit Bilddrift und Rauschen in TEM-Umgebungen befassen. Die Forschung konzentriert sich auf Spinell MgAl2O4, ein sprödes keramisches Material, das in hochbelasteten Anwendungen wie ballistischen Fenstern und IR-Fenstern für Flugzeuginstrumente verwendet wird. Die experimentellen Methoden umfassen die Präparation einkristalliner Spinellproben mit eingebauten Kerben und deren Beladung im TEM mit Hilfe eines Pikoindenters. Die PT-Ergebnisse werden in Verbindung mit Simulationen der Finite-Elemente-Methode (FEM) analysiert, um die Bruchzähigkeit des Materials zu quantifizieren und die Beiträge der Frakturen der Modi I und II zu bewerten. Der Artikel unterstreicht die Effektivität von PT bei der Erfassung von Ganzfeldbewegungen und die Bedeutung von FEM-Simulationen bei der Verifizierung experimenteller Daten. Die Ergebnisse liefern wertvolle Einblicke in das mechanische Verhalten von Einkristallspindeln unter Bruchbedingungen und tragen zur Entwicklung zuverlässigerer Techniken zur Charakterisierung von Materialeigenschaften bei.
KI-Generiert
Diese Zusammenfassung des Fachinhalts wurde mit Hilfe von KI generiert.
Abstract
Background
Characterizing deformation and failure mechanisms through small-scale testing has helped in the fundamental understanding of material response, and direct loading in a transmission electron microscope (TEM) has played a large role in this effort. However, crystalline materials exhibit incoherent scattering within the TEM and the resulting intensity variations inhibit direct optical metrology.
Objective
In this work, we seek to both validate an in situ optical full-field metrology method in the TEM for use with crystalline materials, and measure fracture properties of a MgAl2O4spinel single crystal at the microscale.
Methods
Microscale single edge notch bend beams were machined from a spinel single crystal and loaded in the TEM. In situ imaging of a nanoscale speckle pattern allowed use of particle tracking (PT) to extract full-field measurements of the displacement field. A numerical analysis methodology was then used to obtain mixed mode stress intensity factor values.
Results
A discrepancy between PT and far-field actuator measurements of applied displacement was found (about a maximum of 35% difference), indicating the advantage of using near-field optical measurements in the TEM. For such small-scale testing it is also generally unavoidable to introduce asymmetry in loading. However, the PT results allowed measurement of both KI and KII, which were found to be at the time of crack initiation KIC = 1.51± 0.03 MPa∙m0.5, KIIC = 0.04± 0.002 MPa∙m0.5, respectively.
Conclusions
The application of PT enables full-field deformation measurements on crystalline materials deformed in the TEM. The effectiveness of the inverse property extraction was demonstrated by good agreement between the full-field PT measurements and FEM results. The MgAl2O4 spinel toughness values extracted also agreed well with previous literature results.
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Introduction
Small-scale mechanical testing provides opportunities to probe the mechanical response of isolated microstructural constituents and defects and characterize deformation and failure mechanisms relatively directly [1‐3]. Such testing has been used to isolate the properties of the grain boundaries from the lattice in polycrystals [4‐6] or probe the importance of lattice dislocation content [7, 8] or sample scale [9, 10] on mechanical response. Small-scale testing also provides an ability to assess the mechanical properties of materials for which bulk specimen preparation is challenging. For example, characterizing the properties of new ceramic materials, such as new refractory high entropy materials, can be challenging [11], since preparing bulk specimens free of pores and defects often requires long processing development time. Sampling small defect free regions via small scale testing circumvents such limitations.
The validity of mechanical properties calculated from small-scale mechanical tests tends to be sensitive to non-ideal conditions that bulk testing standards are designed to avoid. For example, at small scales, large friction effects at contacts may be unavoidable, conditions such as plane stress or plane strain may be impossible to achieve, and specimens must often take on non-ideal geometries, making them susceptible to unintended deformational modes [2, 12]. Furthermore, calibration of small-scale testing instrumentation presents challenges and can introduce another potential source of systematic errors. Non-idealities could, in theory, be accounted for in data analysis if they are accurately quantified. Small-scale experiments, however, often rely on far-field load-displacement measurements that provide insufficient data for associated analyses. System compliance effects on the far-field measurements can be exacerbated at small scales when utilizing test specimens cut from their surrounding or loaded using a small-scale apparatus. Full-field measurements derived from digital image correlation (DIC) applied to scanning electron microscope (SEM) micrographs provide one route to address this issue [13, 14]. Scan artifacts require that such data be corrected prior to analysis but typically require several assumptions about sample drift and the reproducibility of scan noise and hysteresis. Global imaging, such as obtained via transmission electron microscopy (TEM), offers an alternative approach that does not require image correction [15‐19].
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TEM imaging can also be used in a complementary manner to obtain information about deformation mechanisms, such as the motion of dislocations [6], the growth of cracks [20], or the rotation of grains [21‐23]. Unfortunately, crystalline samples exhibit incoherent scattering within the TEM resulting from diffraction, which causes the background intensity of the material to be sensitive to small strains, rotations, or defect motion. This inhibits image correlations based on intensity and makes TEM images of crystalline materials not well suitable for DIC analysis. However, particle tracking (PT) can be employed to determine full-field deformations. It has been demonstrated that DIC and PT both produce sub-pixel displacement resolution from amorphous samples tested in the TEM [16‐18, 24, 25]. Thus, PT should serve as a basis for obtaining full-field deformation maps from crystalline grains mechanically tested within the TEM. These amorphous samples exhibit electron irradiation induced creep that results in large deformations. Brittle crystalline ceramics not subject to creep will exhibit considerably lower strains to failure and present a greater challenge to the application of PT.
To assess the viability of employing PT to provide full-field displacement mapping, this work considers fracture of MgAl2O4 spinel. This spinel material serves as an important transparent structural material in applications such as ballistic windows, IR windows for aircraft instrumentation, and high strength window materials for periscopes. As MgAl2O4 spinel tends to fail at low strains, this brittle material serves as a challenging model material for PT in the TEM. TEM-based small-scale fracture experiments have previously been performed on MgAl2O4 spinel. This work uses PT to better understand how non-ideal loading conditions are manifest in the displacement response. The PT results are then used in conjunction with a finite element method (FEM) analysis to account for the mode I and mode II contributions to fracture.
Experimental Methods
In this work, 0.5 mm thick [100] single-crystal MgAl2O4 wafers, obtained from MTI Corporation, were used. The material was cut to an in-plane size of 3 mm × 2 mm using a low-speed diamond saw and was then polished at 45° relative to the surface until a sharp edge was formed whose width was only several microns. The primary goal of this polishing procedure was decreasing the sample thickness prior to focused ion beam (FIB) milling. Subsequently, diamond polishing was performed on lapping films to a final grit of 1 μm. Gold nanoparticles were then deposited on the surface to serve as the PT pattern. As detailed in [16‐18], a 3 nm thick gold film was sputtered onto the initial substrate surface and then annealed at 900 °C for 1 hour to induce nanoparticle formation via de-wetting.
A spinel beam sample with two built-in ends and a straight notch was then prepared using FIB milling. Figure 1 shows an SEM image of the plan view of a manufactured beam with a notch placed at its midpoint. The length (L) and width (w) of the beam are shown in the figure, and typically were around L ~ 20 µm and w ~ 2 µm, while the thickness was nominally around t ~ 450 nm. More details about the FIB techniques followed can be found in [16, 18].
Fig. 1
Plan view of machined beam containing a single edge notch. Thickness, t, of the beam is out of the page. The nanoparticle pattern has been deposited on the back surface and is not visible in this image
TEM loading experiments were performed in a JEOL 2010 LaB6 TEM. All samples were loaded using a Bruker PI 95 Picoindenter with a 1 μm diameter flat diamond tip [16‐18]. The beam samples were loaded in nominally symmetric bending as illustrated in Fig. 1 by the loading arrow denoted as Force F, but under displacement control with a target displacement rate of 1 nm/s. Note that the actual applied displacement typically exceeds the target value set in the control software, as was determined after data analysis by PT. TEM images (2004 × 1336 pixel2) were acquired from a CCD camera (Gatan, Orius SC 1000 A) at an acquisition rate of 1 frame per second. Particle tracking was carried out using the Trackmate module [26] available in the open-source Fiji ImageJ software [27]. The Trackmate module provides displacement information by first identifying particles in each image according to the manually-assigned estimated particle diameter, and then linking the tracked particles in each image restricted by a maximum linking distance specified by the user. According to the particles shown in the TEM images, two input parameters for PT are particle diameter d = 26 pixels (41 nm), and maximum linking distance Dmax = 5 pixels (8 nm) which is smaller than the spacing between particles.
The TEM environment can be quite harsh and, as mentioned above, this often makes optical measurements in the TEM challenging and thus prone to uncertainties in the resulting measurements. Possible sources of additional error in the TEM include: damage to the pattern by the electron beam incident on the sample, thermal drift and temperature fluctuations at the nanometer length scale, variability in camera imaging including any intensity scaling performed by the TEM camera, vibratory noise, electron beam intensity variation, and interaction of the electron beam with the material under observation. In detailed studies we conducted in [16] and [18] we studied the effect of many of these parameters on measurement accuracy and resolution. In [16, 18] several different combinations of TEM/camera systems were used to study both noise and image drift. Image drift, from all sources, was considered to be the portion of measurement in baseline (i.e., no loading) tests associated with rigid body motion, and the residual measurement once rigid body drift was removed was considered as originating from the remaining noise sources lumped together. It was found in [18] that image drift was the predominant source of “error” and image drift was seen to increase over time (generally linearly with time). As long as a fixed part of the sample was visible, image drift could be removed from the PT results. Typically, this was done by referring everything to the substrate (visible in Fig. 1). Remaining noise levels on average were seen to be about ±1 nm for most microscope/camera combinations. Electron beam irradiation induced deformation is also a potential source of error. It is well established that such effects can influence the response of a number of materials including amorphous glasses, organic materials, thin films, MEMS etc. [28‐32]. In our prior work in [17] for amorphous SiO2 this effect was discussed in detail. However, for crystalline spinel damage mechanisms are significantly different and this material does not exhibit any measurable creep in the TEM environment [28]. Consequently, unlike in [17], we did not include any time-dependent beam irradiation effects in the present analysis described below.
Numerical Modeling and Data Analysis
In these single edge notch bending (SENB) experiments we aimed at quantifying the material fracture toughness from the analytical fitting of the displacement field before crack initiation. Note that we will use here the terminology “fracture toughness” to denote the conditions at incipient crack initiation in this configuration rather than the standardized material property of plane strain facture toughness discussed in ASTM E399. An FEM study using ANSYS [33] was performed to compare with the full-field displacements measured by particle tracking and extract fracture toughness. As expected, only linear load-displacement data were seen in the experiments, as will be illustrated below, so the numerical analysis was limited to elastic, but anisotropic, deformation. The FEM modelled a [100] elastically anisotropic single crystal, and used as the three independent components of the material stiffness matrix elastic constants C11 = 301 GPa, C12 = 162 GPa, and C44 = 148 GPa taken for cubic spinel from the literature [34]. A 3D model was created according to the geometric dimensions measured from the FIB images for each individual sample tested/analyzed. The model was meshed using the SOLID186 element with global mesh size = 0.2 μm and refinement of 0.025 μm around the notch tip. Figure 2 shows an example of the mesh used in plan view and extruded through the thickness in 8 layers. A close-up of the refined mesh near the notch is also shown in the figure, with the definition of axes used also shown (note that the positive y-direction is along the notch line and the x-direction is perpendicular to the notch).
Fig. 2
FEM model of the SENB sample with the global mesh size = 0.2 μm and the refinement mesh size = 0.025 μm around the notch tip. The loading offset in the case shown here deviated from the notch tip δ ≈ 0.2 μm
The beam was uniformly loaded near the midspan, with an applied force as measured during the experiments and over a loading area equal to the width of the indenter tip (red arrows in Fig. 2). The precise location of contact with the indenter tip, and consequently the loading application span in the model, was determined from the experimental images. The point of contact is apparent from so-called ‘bend contours’ that form concentrically around the point of contact that derive from diffraction effects imposed by the stress field within the crystal. In many cases it was not at a position exactly symmetrically opposed to the notch tip but had an offset δ. Hence the wording loaded “near the midspan” rather than “at the midspan”. Typically, δ was around 200 nm, and since this loading asymmetry may be sufficient to cause deviation from pure mode I and introduce a (much smaller) mode II component, we will refer to this configuration as “opening-dominated”. Note that any misalignment in cutting the sample along the [100] direction may also introduce mode mixity in the problem, further necessitating a mixed mode analysis. Finally, fixed ends on both the left and right sides of the beam were set as boundary conditions, and the top and bottom surfaces in the 3D model were kept traction free. As the beam is fairly long compared to its width and thickness, the mesh in Fig. 2 is truncated and shows only the FEM loading, boundary conditions, and final meshing (after a convergence study in [17]) that contains 23,160 elements in total.
Regarding the extraction of stress intensity factors in single crystal spinel, Liu et al. [35] presented an asymptotic solution of a semi-infinite crack tip field for orthotropic materials and used it to extract mixed mode stress intensity factors from optical interferometric data. The notch tip radius of curvature depends on the FIB probe size at current densities sufficient to mill through the sample in a reasonable amount of time. This leads to a curvature at the notch tip which has been modeled as seen in Fig. 2. In addition, the ligament amount was controlled by the beam width and notch length, with the configuration used having a notch to width ratio of about 0.2. Here we use the PT measurement and FEM results to fit the analytical displacement solution shown below, following [35], in order to extract stress intensity factor values and evaluate the significance of mode mixity. As discussed in [35], and using the results presented there, the near tip displacement field can be obtained in terms of potentials Φ1 and Φ2 by
In equation (2), \({\text{K}}_{\text{I}}\) and \({\text{K}}_{\text{II}}\) are stress intensity factors for mode I and mode II, which will be determined by fitting to either experimental or numerical displacement field values. In addition, and keeping in mind that the notation in [35] differs from the present notation in that the direction of \({\text{x}}_{1}\) and \({\text{x}}_{2}\) coordinate axes in [35] are aligned with the -y and x axes in Fig. 2,
where \({\text{b}}_{\text{ij}}\) are components of material compliance matrix, which can be derived from the inverse of the stiffness matrix. Note that MgAl2O4 has a cubic crystal structure, thus \({\text{b}}_{11}\) = \({\text{b}}_{22}\) for spinel.
Results and Discussion
Experimental Results
Figure 3 shows the far-field applied displacement-time, load-time, and the load-displacement plots as recorded by the Picoindenter used in the TEM. Figure 4 shows four selected in situ TEM images acquired at the times denoted by the labels (1–4) in the load-time plot in Fig. 3. The gold nanoparticles are visible in the images of Fig. 4 as dark speckles. Load point 1 corresponds to the onset of contact between sample and indenter tip, at which point the load signal begins increasing as seen in Fig. 3. Note that when the sample and indenter are well aligned the nanoscale point of contact is small and thin in z making it highly electron transparent. For this reason, the images in Fig. 4 appear to show a gap between the indenter and sample. If there is no small bright line “gap” between indenter and sample it is usually because the indenter has slid either behind or in front of the sample surface. This image at point 1 was considered as the undeformed state and was used as the reference image for PT measurements. Images at load points 2 and 3 were selected as deformed state images, with point 3 corresponding to the frame just before the onset of fracture, i.e., at incipient failure, where the displacement data typically show an artificial spike (top plot in Fig. 3). After the sudden load drop, the image at point 4 corresponds to a frame after failure. Since the load drop happened within 1 second in most cases, the TEM image at point 4 is usually one frame after the image at point 3, while load-displacement data were acquired at higher sampling rates, as can be seen in the numerous data points between 3 and 4 in load-time plot of Fig. 3. Loading data and images were also recorded after the failure point 4. After initial failure, in the bending configuration, the load continues increasing with a weak nonlinearity. In this work, we performed analysis only until the failure load point 3.
Fig. 3
Displacement-time history (top), load-time history (middle), and load-displacement data (bottom) recorded by the Picoindenter. Note that loading was under constant displacement rate control and the upward spike in the applied displacement data occurs at the instant of failure. Numbers in the load-time plot denote points where selected images from those taken will be presented
We performed PT on the TEM image sequence obtained, where 274 trajectories were successfully tracked throughout loading. The raw PT results show the displacements of particles in the images, but they contain rigid body motion (e.g., image drift, TEM stage drift, etc.) apart from the true sample deformation. To remove this rigid body motion, the material not directly deformed by the indentation loading was considered to have zero displacement. Specifically, the material seen in the upper right-hand corner of each image in Fig. 4 lies below the deforming beam and is mostly disconnected from it. The rigid translation was measured as the average displacements of particles in that region, and this displacement vector was subtracted from the remaining field measured by PT. The plot on the left of Fig. 5 shows the time evolution, though color coding, of trajectories measured by PT during elastic loading with the origin aligned to the notch tip at the initial frame. From two selected enlarged trajectories shown in the magnified inset plot, we can visualize the noise level involved as the small perturbations in the PT trajectories. The dual-axis plot in Fig. 6 shows the u and v displacements measured by PT as a function of time for the selected trajectory near the loading region marked by an “x” in Fig. 5. Note the significant difference in magnitude, and hence signal-to-noise-ratio, between u and v measurements. As this is a linear elastic loading situation, we would expect linear variations of these quantities with time. Thus, we can estimate the noise level by performing a polynomial fitting of the u and v displacements for each trajectory, then calculating the maximum difference between PT and fitting results. This calculation yielded a standard deviation of 0.003 μm as “error” ranges for the PT displacement measurement in this set-up.
Fig. 5
PT displacement history measurement in a SENB configuration. Particle trajectories are shown as function of time throughout the elastic part of the loading, through the color coding of each trajectory. An expanded view of two trajectories of the boxed region in the main figure is shown in the inset on the right
Time history of measured vertical y-displacement (v) and horizontal x-displacement (u) at the location marked by “x” in Fig. 5. Note the difference in orders of magnitude between u and v, as expected since loading is applied along the y-direction
Note that although displacement control was used in the experiment, the measured applied load was input into the FEM as the loading boundary condition. Thus, the motion of the loading point measured through PT can be compared to the far-field measurement and to the FEM result in order to investigate any systematic errors in the Picoindenter far-field displacement measurement resulting from system compliance or calibration issues. The displacement at the midpoint of the loading area defined in the FEM (numerically equal to the average of nodal displacement in the loading area) is compared with the experimental measurement from the indenter tip and PT at approximately equivalent positions in Fig. 7. Figure 7 shows that the FEM results exhibit a larger (~30–35%) displacement than the indenter tip measurement but agree with the (independent) PT measurement. The motion of the indenter tip is generated by a voltage applied to a piezoelectric control with a calibration factor, which is applied at the terminating end of the indenter rod. The discrepancy between the far-field and PT results could represent a compliance issue or, more likely since the FEM values are larger, a calibration issue. Regardless, the results indicate the value of the PT measurement in obtaining more accurate displacement information.
Fig. 7
Loading point displacement measurements from the indenter and PT compared with FEM results
In addition to data at the point of load application, full-field displacement results from both PT and FEM were also compared to more closely illustrate the deformations occurring in the notched beam. Figure 8(a) shows a quiver plot of FEM and PT results at the loading instant just before crack initiation at maximum load (i.e., point 3 in Fig. 3). A good agreement between the two is observed over most of the near-tip area observed. The top and bottom beam surfaces are illustrated by dashed lines and the notch tip by the black dot at (0,0). These results at maximum load will be fit to the analytical models described above, equations (1) – (4), to obtain the “fracture toughness” values of KIC and KIIC. However, the analytical model produces no displacement at (0, 0) so Fig. 8(b) shows the same data as in Fig. 8(a) but with the notch-tip displacement now being set to 0. Figure 8(b) now clearly illustrates the opening deformation around the notch which was not as obvious in Fig. 8(a). Note that in Fig. 8(b), since the displacements relative to the notch tip position are smaller in magnitude, the arrow size is magnified five times for better visualization. From the comparison in Fig. 8(b), we can now observe some discrepancies between FEM and PT results, especially near the notch tip where the PT signal is now comparable to the noise level. Overall, however, the FEM results still capture the elastic mechanical behavior in the bending test.
Fig. 8
Comparison between PT and FEM results at incipient crack initiation: (a) raw displacement results, (b) opening displacement results by fixing the motion at the notch tip. The dashed lines represent the top and bottom of the sample as measured in the initial frame. The black dot located at the origin indicates the location of the notch tip. The blue-boxed region is used for the analytical fitting
The PT results for u, v displacements are fit to equation (1). Since the analytical equations are derived based on the asymptotic configuration, we selected the near-tip region (blue-boxed area in Fig. 8(b)) for fitting The resultant mode I and mode II fracture toughness values, defined as the values extracted by this fitting procedure at peak load, are KIC = 1.1 MPa∙m0.5, KIIC = 0 MPa∙m0.5 from fitting u, and KIC = 1.66 MPa∙m0.5, KIIC = 0.06 MPa∙m0.5 from fitting v (Table 1). Substituting these values back in equation (1), the fitting results were plotted using black arrows in Fig. 9. Even though the magnitudes between PT and analytical results are comparable in the blue-boxed area, the arrow orientations do not align well, in large part because noise in the PT data, especially for u (see Fig. 6). From the comparison outside of the blue-boxed region (recall the fit was performed only on PT data inside the blue box) we can see that generally the further away from the notch tip a point is, the larger the discrepancy in terms of both arrow magnitude and orientation. Thus from Fig. 9 it appears that the region of validity of the asymptotic field is limited near the tip, at best. The mode II values extracted from both the u and v components of displacement are small compared to the mode I values, at least two orders of magnitude lower, indicating a mode I (opening mode) dominated field.
Table 1
Results of KIC and KIIC derived from different fitting data
Fitting data
KIC (MPa∙m0.5)
KIIC (MPa∙m0.5)
PT data (blue-boxed area)
1.1 (fitting u)
1.66 (fitting v)
0 (fitting u)
0.06 (fitting v)
FEM data (blue-boxed area)
1.51
0.04
FEM data (green-boxed area)
1.53
0.05
Fig. 9
Comparison between PT and analytical results fitted with the boxed PT data
Rather than smoothing the experimental data in an arbitrary fashion, we can alternatively use the FEM results to directly perform the same fitting procedure. The FEM results will have a denser data resolution and no noise effect when compared to PT. And since they overall compare reasonably well with the experimental PT-measured data (Fig. 8(b), should produce more reliable KIC and KIIC values. Using data within the same blue-boxed area shown in Figs. 8(b) and 9, FEM u, v fitting produced similar toughness values (< 0.01 MPa∙m0.5 difference) of KIC = 1.51 MPa∙m0.5, KIIC = 0.04 MPa∙m0.5 (Table 1). Figure 10 shows the comparison between FEM (red) and analytical results (black), where the effective zones for asymptotic solutions can be better discriminated. Good agreement is observed within the green-boxed region in Fig. 10, which is behind the notch tip (y > 0) with significant opening deformation. Ahead the notch tip, however, FEM and analytical results show qualitative differences in the displacements. FEM shows a clockwise “rotational” deformation since the notch was not machined perfectly at the midspan of the beam length, and the loading area was not perfectly aligned with the notch tip in x-direction but with a small offset to the left (the δ shown in Fig. 2). These alignment offsets were measurable in the FIB and TEM images, and were therefore included in the FEM. Even though the finite sample geometries limit the effective zone, fitting within the green-boxed region still produces similar results for the FEM data in Fig. 10: KIC = 1.53 MPa∙m0.5, KIIC = 0.05 MPa∙m0.5. Table 1 shows the KIC and KIIC results for different fitting methods.
Fig. 10
Comparison between FEM and analytical results fitted with the FEM data
In the FEM analysis load was applied perpendicular to the sample’s bottom surface. However, small angle off-axis non-ideal loading could occur due to the nature of the indenter which can undergo some lateral motion via pivoting. To investigate this effect on the values of KIC and KIIC extracted, we performed simulations within ± 10° of in-plane loading angle offset. The fitting results show a maximum difference of ± 0.03 MPa∙m0.5 (2%) for KIC, and ± 0.002 MPa∙m0.5 (4%) for KIIC. The true non-ideal loading angle would be smaller than 10°, since the tip can only pivot approximately 200 \(\mu m\) across a total length of the order of cm. Therefore, this should be considered an overestimate of the potential error. Overall, the fracture toughness calculated indicates mode I dominated response. The value of KIC = 1.53 MPa∙m0.5 agrees well with the microscale testing result in the SEM by [4], but is slightly larger than the bulk testing results of [36, 37]. Discrepancies between material properties measured from experiments at different length scales have been reported previous in literature, e.g., [38].
Summary and Conclusions
In this paper, we performed in situ single-edge notched beam bending experiments on [100] single crystal MgAl2O4 samples in the TEM. Full-field displacements were derived by measuring the trajectories of gold nanoparticles on the surface using PT. Through FEM simulation and analytical fitting, the stress intensity factor of the material under the opening dominated failure was determined. The effectiveness of the inverse property extraction was verified by an agreement between the full-field PT and FEM results. The values of fracture toughness extracted in this work agreed well with the previous literature results. The additional information derived experimentally can verify confidence in the FEM simulation and enhance the reliability of material property characterization. The application of PT enables full-field measurement on crystalline materials deformed in the TEM.
Acknowledgements
This work was carried out in the Materials Research Laboratory Central Research Facilities, University of Illinois. Funding for this research was provided by the National Science Foundation (grant No. CMMI 18-25466). The authors acknowledge Dr. Honghui Zhou, Dr. Waclaw Swiech and Dr. Changqiang Chen for help with FIB, and TEM loading experiments.
Declarations
Conflict of Interest
The authors declare that they have no conflict of interest.
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Die im Laufe eines Jahres in der „adhäsion“ veröffentlichten Marktübersichten helfen Anwendern verschiedenster Branchen, sich einen gezielten Überblick über Lieferantenangebote zu verschaffen.
