Micro-cantilever Bending Tests Research Articles

Two scale models for fracture behaviours of cementitious materials subjected to static and cyclic loadings

This study employs a lattice fracture model to simulate static and fatigue fracture behaviour of Interfacial Transition Zone (ITZ) at microscale and mortar at mesoscale. The heterogeneous microstructure of ITZ and mesostructure of mortar are explicitly considered in the models. The initial step involves calibrating and validating the microscopic model of the ITZ through micro-cantilever bending tests. Subsequently, this validated ITZ model serves as a constitutive law to simulate the fracture behavior of mortar at the mesoscale using an uncoupled upscaling method. The influence of microstructural features, such as w/c ratio and microscopic roughness, on the fracture behaviour of ITZ is investigated. Moreover, the effect of ITZ properties and stress level on the fracture performance and fatigue damage evolution of mortar is also studied. The simulation results for both the ITZ and mortar demonstrate good agreement with experimental results. The proposed two models provide insights into the fracture mechanisms and fatigue damage evolution in cementitious materials subjected to static and cyclic loadings.

Deformation Behavior and Fracture Strength of Single‐Crystal 4H‐SiC Determined by Microcantilever Bending Tests

In this study, the deformation behaviors and mechanical properties of 4H‐SiC single crystals are investigated using microcantilever beam specimens with two different sizes, A and B (A < B). Tensile stress is applied along <20> direction. Plastic deformation, or nonlinearity, is observed in the stress–strain curves, and yield stress, or proportional limit, coincides between the two specimens at ≈25 ± 2 GPa. Scanning transmission electron microscopy and transmission electron microscopy studies show that the plastic deformation is due to dislocation activities; multiple‐dislocation pileup areas are observed in both the specimens. Assuming {100}/<110> prismatic slip which most plausibly occurs in the <20> stress application, the critical resolved shar stress is estimated to be 10.9 GPa, which agrees well with the previous studies. Measured fracture strength is 41.9 ± 2.8 and 33.5 ± 2.4 GPa for the A and B, respectively. Dislocation–fracture relationship is discussed on the basis of dislocation‐based fracture mechanics, etc. It is suggested that cracks form within the multiple‐dislocation pileup area, by interaction with dislocation pileups, and act as fracture origins. A's strength is close to an ideal tensile strength of 4H‐SiC in the <110> direction, 47–55 GPa.

Microscopic mechanical properties of silicon nitride ceramics corroded in sulfuric acid solution

The microscopic mechanical properties including the bending strength and Young’s modulus for Si3N4 ceramics doped with Y2O3 and Al2O3 which was immersed in 5 wt% sulfuric acid solution using microcantilever beam specimens was investigated in comparison with the macroscopic results obtained in conventional three-point bending tests. Both the properties sharply dropped in very short periods of the corrosion in the microcantilever tests, resulting from the dissolutions of yttrium and aluminum ions of grain boundary glass networks, followed by the hydration. After the drops at the beginning of the corrosion, they showed little degradation afterwards. The degradation behaviors of the mechanical properties are basically the same as those in conventional macroscopic approaches; however, they changes appear in very short periods of the corrosion in the microcantilever bending tests. This study also verified that a small difference of a ratio of sintering additives results in different grain boundary strengths of Si3N4 ceramics.

Effect of Strain Gradient on Elastic and Plastic Size Dependency in Polycrystalline Copper

This study unveils the presence of size effect not only in the plastic regime but also in the elastic regime under strain gradient. This discovery emerges from a comprehensive set of experiments encompassing micro-cantilever bending and micro-pillar compression tests. Subsequent finite element analysis serves to not only expose the limitation of classical continuum theory but also to effectively demonstrate the enhanced predictive capabilities of couple stress theory in both elastic and plastic size effects. To incorporate couple stress theory, a systematic and rigorous finite element analysis-based optimization was devised to determine length scale parameters, which are additional material properties in couple stress theory. The resulting length scale parameters for polycrystalline copper were found to be 0.536 and 0.669µm in the elastic and plastic regimes, respectively. The study also explores the physical interpretation of these length scale parameters in both regimes.

Micro- and macro-scale strength properties of c-axis aligned hydroxyapatite ceramics

In this study we first investigated the strength of grains, i.e., single crystals, and grain boundaries (micro-scale strength) of hydroxyapatite ceramics in different crystal orientations, using microcantilever bending tests. The specimens were prepared from two types of hydroxyapatite ceramics; one is that with uniaxially aligned c-axes of grains and the other with randomly oriented ones. Both the grain and grain boundary strengths were slightly higher in tensile stress application parallel to c-axis than in the perpendicular in the aligned material. These strengths, however, were substantially higher than those of the randomly oriented one. Then, three-point bending tests were conducted to determine the polycrystalline strength (macro-scale strength) for the above two types of hydroxyapatite ceramics. While the strength values were comparable in tensile stress applications parallel and perpendicular to c-axis in the aligned material, that of the randomly oriented one is again significantly lower than them. In particular, the strength of the grain boundary was higher when the angle between the c-axis of the two hydroxyapatite grains divided by the boundary was close to 0 or 90°. The effects of the grain orientation and alignment on the mechanical properties were discussed on the basis of both the micro-scale and macro-scale results. These results indicate that selective formation of high-strength grain boundaries due to c-axis alignment of hydroxyapatite grains is effective in improving the mechanical properties of bulk ceramics, such as macroscopic strength and fracture toughness.

Measuring microscale mechanical properties of PVdF binder phase and the binder-particle interface using micromechanical testing

In this study, we developed a robust methodology for extracting the mechanical properties of individual components in complex systems such as Li-ion battery electrodes and provided quantitative values that can be used as input for modelling and lifetime estimation of Li-ion batteries. We employed micromechanical testing techniques, including micropillar compression, microcantilever bending, and nanoindentation, to measure the mechanical properties of the PVdF binder phase in the active layer. We discovered that nanoindentation tends to overestimate the modulus due to uncertainty associated with the test volume and initial large compression strains, while the micropillar compression technique provides more accurate modulus data with a narrower spread. Additionally, the yield stress of the binder phase can be evaluated using micropillar compression. Our obtained modulus values were in the range of 2.5–4.4 GPa, and the yield stress was in the range of 162–270 MPa. By microcantilever bending tests, we determined that the binder–particle interface often fails before the binder itself, suggesting that the interface significantly influences the failure mechanics. Overall, our results indicate that the microcantilever bending tests provide moduli estimates that agree with those obtained from micropillar compression tests. We also qualitatively examined the binder-particle and binder-current collector interfaces, further emphasising the significance of our methodology and the obtained quantitative values.

Structural and stress state dependence of small-scale deformation in bulk metallic glass

Bulk Metallic Glasses (BMGs) are attractive for myriad structural applications at multiple length scales (nano-micro-macro) but show limited bulk plasticity due to the tendency for shear localization. However, there is limited understanding of the effect of structural state and stress state on the small-scale deformation behavior of BMGs. Here, the micro-scale deformation behavior of a model Ni-based BMG was studied in as-cast and corresponding relaxed state under multiaxial nano-indentation, uniaxial micro-pillar compression, and micro-cantilever beam bending. The relaxed BMG showed 6 % higher hardness, 22 % higher yield strength, and 26 % higher bending strength compared to its as-cast counterpart. The increase in hardness, yield strength, and bending strength for the relaxed alloy compared to its as-cast counterpart demonstrates the relation of intrinsic free volume present in a BMG to its resistance for initiation of plastic events at this scale. Both the as-cast and corresponding relaxed samples showed stable notch opening and blunting during micro-cantilever bending tests rather than unstable crack propagation. However, pronounced notch weakening was observed for both the structural states, with the bending strength lower by ∼ 25 % for the notched samples compared to the un-notched samples. This work may stimulate further investigations into the deformation behavior of BMGs in response to complex stress states pertinent to real-world structural applications at small scale.

Influence of the aspect ratio of the micro-cantilever on the determined Young’s modulus using the Euler-Bernoulli equation

Micro-cantilever bending experiments can be used to determine fundamental material properties, such as fracture stress and fracture toughness. Furthermore, the Young’s modulus can be calculated from the slope of the load-displacement curve using the classical Euler-Bernoulli equation. However, in literature it can be frequently found that applying this technique, the Young’s modulus is significantly underestimated, especially when using micro-cantilevers with aspect ratios (bending length/width) < 6. In order to investigate the influence of the aspect ratio on the determination of the Young’s modulus, SiO2 and single crystalline α-Al2O3 micro-cantilevers with aspect ratios ranging from ∼ 3.5–6.5 were fabricated using focused ion beam milling and tested with a nanoindenter system. In addition to the quasi-static tests, dynamic micro-cantilever bending tests were performed by using an excitation frequency on top of a quasi-static loading and the results of both techniques were compared to each other. Finally, finite element analysis was used to simulate the static-micro-cantilever bending experiments and investigate the influence of shear deformation, flexing of the support and the geometry of the micro-cantilever on the load-displacement curves.

Mechanical properties of the W coating and interface of vacuum-plasma-sprayed W–ferritic steel joints under shear and bending loads

Vacuum plasma spraying (VPS) is a prospective technology for the fabrication of tungsten-coated ferritic steel (W-steel), which is the main candidate for plasma-facing components (PFCs) of fusion reactors. PFCs are subjected to harsh service environments; therefore, the mechanical properties of W-steel joints must be evaluated. However, detailed studies on the mechanical properties of W-steel joints are still limited because of the limited thickness of the tungsten-coating layer. In this study, high-grade W-steel joints were fabricated using a VPS system. The mechanical properties of the W coating and W–steel interface were evaluated using micro-double-notch compression and micro-cantilever bending tests. The ultimate shear strength of the interface area exhibited a large scatter (~0.84–3.54 GPa), which was similar to that of the W layer (~1.2–3 GPa) and higher than that of the reduced-activation ferritic/martensitic steel (F82H) substrate (~0.6 GPa). The bending test indicated that the interface exhibited good bending performance and that its nominal fracture strength was higher than that of the W coating, which may be attributed to the ductile nature of the F82H region at the interface. The fracture microstructure elucidated the importance of improving the mass densities of W coatings to improve the mechanical performance of vacuum-plasma-sprayed W–steel joints. Effective bonding of a W/F82H interface and the adjacent F82H substrate via VPS results in high strength and ductility of the interface area, and hence the W–steel joint, against shearing and bending loads.

In-situ micro-cantilever bending studies of a white etching layer thermally induced on rail wheels

A complex and untraceable mechanical and thermal loading situation in rolling-sliding contacts can lead to the formation of white etching layers (WELs), depicting critical crack initiation sites. For our detailed studies, to obtain a holistic view of the microstructural characteristics and micro-mechanical properties, we prepared a WEL on a decommissioned (after 200,000 km service life) rail wheel by laser surface treatments with a defined energy input. This WEL is predominantly martensitic down to a depth of 30–40 μm, after which a transition to the deformed ferritic-pearlitic microstructure of the hypoeutectoid rail wheel steel is present. The martensitic region is with 6.98 ± 0.68 GPa significantly harder than the transition zone (5.17 ± 0.39 GPa) and the deformed ferritic-pearlitic base material (3.30 ± 0.33 GPa). In-situ V-notched micro-cantilever bending experiments of the martensitic (and thus most brittle) region show crack initiation and propagation – mostly along the boundaries of the martensitic grains – besides a plastic behavior. Applying the elastoplastic fracture mechanics allows to derive the local fracture toughness KIQ, which is 16.4 ± 1.2 MPam1/2 for this martensitic region of the WEL. The results outpoint the application of micro-cantilever bending tests in addition to hardness testing as a promising tool to discuss the relationship of microstructural characteristics with its micro-mechanical properties.

The effects of radiation-induced grain subdivision and dislocations on the fracture properties of uranium dioxide

Microcantilever bending tests were applied on uranium dioxide samples irradiated by 84 MeV Xe ions. Depending on the initial grain sizes, different levels of grain subdivision and dislocation development were observed near the irradiated surface. These radiation damage features were shown to degrade the fracture properties of both samples. The fundamental aspects of the radiation-microstructure-property relationships were discussed in this paper, taking a holistic consideration of the microcantilever bending data, fractography and microstructures. The separate effects of the irradiation-induced grain subdivision and dislocations on the fracture initiation and propagation of uranium dioxide were discussed. It was observed that radiation-induced dislocations and grain subdivision, without the presence of Xe bubbles co-located with the defects, cause reductions in the Young's modulus, fracture strain, and fracture stress, and a transition to intergranular fracture.

Microscale fracture toughness degradation of notched solder microcantilevers under varied accelerated aging process

Experimental fracture mechanics at the microscale became an indispensable tool for understanding and analyzing the solder joint degradation in microelectronics packaging, which is facing severe temperature swings and is prone to failure due to the delamination induced by the microcracks. In this work, we studied the fracture behavior of the widely used Sn-based solder on microscale with the notched microcantilevers fabricated using the focused ion beam (FIB) milling. The microcantilever bending tests were performed to demonstrate the fracture process by the nanoindentation system. Besides, the continuous stiffness measurement (CSM) for the dynamic stiffness was applied to assess the crack behavior. Crack resistance was obtained from the J-Δa curves and the fracture toughness was calculated from the bending tests based on the elastic-plastic fracture mechanics. The results indicated that the fracture toughness decreased after the thermal cycling test. Compared to the specimen without aging, the resistance to rupture decreases rapidly and tends to a low variation against the increased aging cycles. Moreover, the grain orientations and dislocation densities were analyzed using electron back-scatter diffraction (EBSD). It was found that the dislocation density and misorientations of the aged specimens correlated closely to fracture toughness. Furthermore, the stress distribution of the crack tip and the deformation in the plastic zone were analyzed by the finite element simulations. This work provided new insight into the degradation of fracture and deformation behavior of solder material on microscale and revealed the relationship of crack resistance and thermal cycling aging.

A Study of the High-Temperature Strength of Titanium Alloys Using Nanoindentation and Micro-cantilever Bending Tests

A Study of the High-Temperature Strength of Titanium Alloys Using Nanoindentation and Micro-cantilever Bending Tests

Nanoindentation and micro-cantilever testing for understanding cold-dwell sensitivity of heat-resistant titanium alloys

The mechanism of cold-dwell fatigue of the Ti alloys Ti-6242S and IMI 834 was investigated by measuring their local strain-rate sensitivities using nanoindentation analysis, electron backscatter diffraction, and energy-dispersive X-ray spectroscopy. In addition, microcantilever bending tests involving a load-holding-induced change in plastic strain near grain boundaries were conducted to investigate the plastic behavior of the alloys. The difference in the strain-rate sensitivity exponent between soft and hard grains was large in Ti-6242S and small in IMI 834, although slips were generated in the hard grains of both IMI 834 and Ti-6242S by activated slips in the soft grains during the microcantilever bending tests. The hardness of IMI 834 varied with its Al concentration, whereas no Al-concentration-dependent changes in hardness were observed in Ti-6242S. These results suggest that the stress redistribution was caused by differences in the concentrations of solid elements and the crystal orientation of the hard and soft grains.

Hydrogen assisted intergranular cracking of alloy 725: The effect of boron and copper alloying

To overcome the Hydrogen embrittlement (HE) susceptibility of the standard Alloy 725 (Mod A), two alloys with minor alloying modifications with B (Mod B) and B+Cu (Mod C) were produced. Then, the intergranular cracking susceptibility was investigated on bi-crystal beams by electrochemical in situ micro-cantilever bending test. The atom probe tomography and first principles calculations were employed to capture and calculate the grain boundary (GB) segregation and its effect on the GB cohesion. Cross-sectional view of the bent beams showed the superior resistance of Mod B against HE by facilitating the GB dislocation transfer/generation. While bending Mod A sample in hydrogen environment leads to form a sharp intergranular cracking, Mod B showed some nano-voids/cracks mostly in dislocation slip bands and rarely in GB path. However, a reduction of strength was observed in load-displacement (L-D) curves of Mod B. The addition of Cu, although not participated in GB segregation, compromised the lost strength of Mod B. In Mod C, after bending in H-charged condition, the nano-voids were formed in GB, but no load drop in L-D curves nor crack propagation in post-deformation observations was detected. The micro-alloying proposed in this study could be an important contribution to the future developing of H resistant alloys via GB segregation engineering.

Role of grain boundaries in hydrogen embrittlement of alloy 725: single and bi-crystal microcantilever bending study

In situ electrochemical microcantilever bending tests were conducted in this study to investigate the role of grain boundaries (GBs) in hydrogen embrittlement (HE) of Alloy 725. Specimens were prepared under three different heat treatment conditions and denoted as solution-annealed (SA), aged (AG) and over-aged (OA) samples. For single-crystal beams in an H-containing environment, all three heat-treated samples exhibited crack formation and propagation; however, crack propagation was more severe in the OA sample. The anodic extraction of H presented similar results as those under the H-free condition, indicating the reversibility of the H effect under the tested conditions. Bi-crystal micro-cantilevers bent under H-free and H-charged conditions revealed the significant role of the GB in the HE of the beams. The results indicated that the GB in the SA sample facilitated dislocation dissipation, whereas for the OA sample, it caused the retardation of crack propagation. For the AG sample, testing in an H-containing environment led to the formation of a sharp, severe crack along the GB path. • Single crystal (SC) and bi crystal (BC) in situ cantilever bending test is used. • SC of over-aged sample experienced severe cracking than the aged sample. • Load drop for SC over aged cantilevers occurs at lower distance than aged sample. • Bi crystal cantilever of over-aged was more resistant than aged sample. • Grain boundary in solution annealed cantilever mitigated the risk of embrittlement.

Assessment of hydrogen embrittlement on advanced high strength steels revealed by in-situ electrochemical micro-cantilever bending test

In the current study, the hydrogen-induced embrittlement on advanced high strength steels (AHSSs) is evaluated by in-situ electrochemical microcantilever bending (IECB) tests. Microcantilevers of 1200 M and 1400 M steels were bent while hydrogen charged inside a miniaturized electrochemical cell and then compared to bent-cantilevers in the air. The results of bending experiments and post-mortem evaluation of the bent-cantilevers showed that the plastic deformation occurred for the bent-cantilevers in the air. At the same time, the reduction of yield stress and the formation of hydrogen-enhanced cracking happened for the hydrogen-charged cantilevers. The results indicated that the microcracks are initiated and propagated adjacent to the clamped boundaries of the cantilevers, where the stress intensity is topmost. This finding is demonstrated by created step-wise cracks in 1400 M representative bent cantilever. The results show that the hydrogen-enhanced dislocation nucleation and hydrogen-reduced dislocation mobility are responsible for plastic deformation and hydrogen-enhanced cracking behavior. • The effect of hydrogen on advanced high strength steels was evaluated by micro-cantilever bending tests. • Plastic deformation occurred for the bent-cantilevers in the air. • Hydrogen assisted cracking happened due to hydrogen dislocation interactions. • Cracks were initiated and propagated beside the clamped boundaries of the cantilevers.

Micro-cantilever bending tests for understanding size effect in gradient elasticity

Higher-order deformation theories, such as the couple stress and strain gradient theory, have been widely used to predict the mechanical behavior of micro/nano-scale structures. In this paper, the additional length scale parameter introduced in the couple stress theory is measured by performing bulk-scale tensile and micro-scale cantilever bending experiments. Bulk-scale characterization provided microstructural information of the polycrystalline copper plate along with macroscopic mechanical properties. Micro-scale cantilevers with thicknesses ranging from 1.6 µm to 8.6 µm were fabricated within the copper plate using femtosecond laser machining followed by focused ion beam milling. Line load was applied on these samples utilizing a nanoindenter. Finite element analysis was performed to exclude the effect of substrate deformation. The measured effective elastic modulus increases from 94 GPa to 215 GPa with decreasing thickness. The increase of the bending rigidity is analyzed based on the couple stress theory, and the length scale parameter is measured as 0.78 µm. The physical origin of the length scale parameter is discussed by considering mobile dislocations escaping via the free surfaces during loading.

Fracture behavior and deformation-induced structure changes of a Ti-based metallic glass using micro-sized cantilevers

Micro-cantilever bending tests are performed to quantify the fracture toughness and reveal the deformation mechanism of a Ti-based metallic glass. Plastic deformation is localized in shear bands initiating from the roots of the notches of the cantilevers. Although the load-displacement curves show considerable ductile failure characteristics, the notch fracture toughness values that obtained from the bending tests are extremely low (∼4.7 MPa m). Size dependent fracture is thought to be observed, where the fracture toughness increases with decreasing the uncracked ligament size of the cantilevers. TEM bright field images show that the shear bands with the width of 4–7 nm present brighter contrast. The regions in vicinity of the shear bands show dark zones (ranging from 3 to 5 nm in size) surrounded by continues bright zones. Cu nanocrystals are found not only inside the shear bands, but also around them. The free volume theory together with the simulation results is applied to explain the formation of shear bands in this Ti-based metallic glass during the bending deformation. The observed Cu nanocrystals are thought to be formed as a consequence of plastic-deformation-assisted crystallization. It is suggested that local atomic rearrangements lead to shifting of Cu nanocrystals towards more stable positions and cause the formation of Cu nanocrystals in regions subjected to high shear stress field.

Determination of fracture toughness of a platinum-modified nickel aluminide coating by micromechanical testing

The fracture toughness of an industry benchmark platinum-modified nickel aluminide coating (RT22LT) is determined by microcantilever bending tests. Cantilevers are prepared in three microstructurally-different zones across the coating cross-section by focused ion beam machining and then bent in-situ by a nanoindenter in a scanning electron microscope. Elastic-plastic fracture mechanics, combined with finite element analysis, are implemented to compute the fracture toughness. It is found that the fracture toughness of the coating varies through its thickness: the middle zone has the highest toughness (7.62 MPam), followed by the surface zone (6.59 MPam), and the interdiffusion zone has the lowest toughness (4.89 MPam). The main reason for such difference is the amount of plastic deformation prior to fracture and its corresponding contribution to the energy release rate vary from zone to zone. Observations of fracture surface show that fracture in the β-phase matrix is predominantly transgranular. However, the fracture morphology depends on the precipitate content of each zone and a higher precipitate content gives rise to more interfacial decohesion between the β-matrix and the precipitates. Analysis of microstructural-compositional features and their correlation with the plastic component of the energy release rate suggests that the precipitate content plays a major role in variation of the fracture toughness between the three zones. The fracture behaviours of the coating are compared with those reported in the literature and their difference is rationalised by the Weibull analysis.