Micropillar Compression Experiments Research Articles

Unifying the size effect observed in micropillar compression experiments

ABSTRACT Micropillar compression experiments show size effect, σp/μ = A(d/b)n , where σp , is the flow stress, μ is the resolved shear modulus, d is the pillar diameter and b is Burgers’ vector. With fcc metals n ≈ –0.67 and A ≈ 0.7; however, with bcc metals there is greater variation, with n closer to zero. Here we propose a different but similar empirical relation of σp/μ = σb/μ + A’(d/b)n’, where σb is a size independent resistance stress. In which case there must be a strong correlation between the original constants, A and n. This hypothesis is found to be true for the published data from a large number of bcc metals, ionic solids that possess the rock salt crystal structure, and some covalent bonded semiconductors. This correlation is shown to predict a universal power law with the exponent in the range, −1.0 < n’ < −0.5, and with A’ close to 1. These values are very similar to the empirical relation that can be used to describe the behaviour of fcc metals tested in micropillar compression with σb = 0. This universality of the empirical relation provides strong evidence for a common mechanism for the micropillar size effect across a range of materials.

Understanding the damage initiation and growth mechanisms of two DP800 dual phase grades

Dual phase (DP) steels are amongst the most widely used structural steels for automotive applications. It is essential to understand the damage initiation and damage growth in these high strength steels and further shed light on improving mechanical properties. In this work, two DP800 dual phase grades are investigated, which exhibit identical ultimate tensile stress but significantly different elongation in the uniaxial tensile test. To explain the difference in ductility, particularly described by uniform elongation, we investigate the damage initiation and growth mechanisms by analyzing microstructural changes upon deformation, such as voids, dislocation structures and the grain morphology. Furthermore, ferrite micropillars in pre-strained samples are tested in situ to capture the strain hardening capability of ferrite. We found that the DP steel with harder martensite and softer ferrite exhibits more damage initiation sites after deforming to an identical strain. However, void growth is much slower compared to the DP steel grade with fewer initiation sites. We explain the suppressed void growth by significant strain-hardening of ferrite surrounding the voids, which is observed in the micropillar compression experiments. The improved strain hardening of ferrite originates primarily from the difference in chromium content considering the negligible influence of dispersed particles.

In situ study on enhanced plastic deformability of Lanthanum-doped Bismuth ferrite processed by flash sintering

BiFeO3 is a promising multiferroic material for versatile device applications due to its co-existence of magnetic (i.e., antiferromagnetic) and ferroelectric ordering at room temperature. While its functional properties have been extensively investigated, the exploration of its mechanical behavior was limited mostly to the thin-film form of BiFeO3. In this work, we conducted in situ micropillar compression experiments to investigate the deformation behavior of La-doped BiFeO3 (La-BFO) samples processed by both conventional and flash sintering methods. The conventionally sintered La-BFO exhibited limited deformability at room temperature and 450 °C. In contrast, the deformability of the flash-sintered La-BFO specimens was substantially improved by nearly 100% at both testing temperatures. Detailed post-mortem studies suggest that preexisting dislocations and wide anti-phase boundaries introduced during flash sintering can toughen flash-sintered La-BFO by easing dislocation migration and ferroelastic domain switching. This study provides a fresh perspective to design an advanced multifunctional system with improved mechanical properties.

Effect of sub-zero temperatures on activation of basal slip, tension twinning and pyramidal slip in magnesium using micropillar compression

In this paper, the effect of sub-zero temperatures on the activation of basal <a> slip, {101‾2} tension twinning and <c+a> pyramidal slip in pure magnesium was investigated systematically at the micron length scale using micropillar compression. The micropillar compression was performed inside an SEM on selected grains of commercially pure polycrystalline magnesium between room temperature and ~ −94°C. A cryo-stub was designed and successfully employed to perform micropillar compression experiments below room temperature. Post-mortem SEM and TEM showed activation of basal <a> slip in [112‾1] oriented micropillars, {101‾2} tension twinning in [13‾20] oriented micropillars and <c+a> pyramidal slip in [0001] oriented micropillars. CRSSs were derived from the stress-strain curves as a function of test temperature for the three deformation modes. The CRSSbasal increased with decrease in test temperature for micron-sized pillars in comparison to an opposite trend for CRSSpyra: CRSStwin showed no change from room temperature to ~ −94°C.

Application of a nanoindentation-based approach for parameter identification to a crystal plasticity model for bcc metals

The application of an inverse method for determining the parameters of a crystal plasticity constitutive law of a body-centered-cubic (BCC) single phase material is presented. Nanoindentation is used as the primary experimental input. An objective function, based on the deviation between the experimentally measured imprint and the simulated one, is minimized by a differential evolution algorithm to obtain the best fitting crystal plasticity parameters. To aid the identification procedure additional experimental data is used: the upper bounds and the ratios of the critical resolved shear stresses of the three slip plane families in BCC are estimated from micropillar compression experiments and used as a constraint in the optimization. The effect of the imposed constraints and the chosen strategy for mapping experimental to simulated displacements is presented and discussed. The validation of the method is done in the macroscopic regime by comparing an experimental tensile test with a simulated one using the obtained crystal plasticity parameters. Accurate results are achieved from two different indents. Therefore, the method is a promising path for determining crystal plasticity parameters in the case where a direct fitting from a macroscopic stress–strain curve is not possible, i.e. in the case of multi-phase materials.

Mechanical properties and strengthening mechanism of Ni/Al nanolaminates: Role of dislocation strengthening and constraint in soft layers

This work focuses on the mechanical properties and strengthening mechanism of Ni/Al nanolaminates, where dislocation strengthening and constraint dominate in the soft Al nanolayers. Nanoindentation and micropillar compression experiments highlight a constrained plasticity of Al nanolayers, which endows Ni/Al nanolaminates with a strain hardened behavior. Plasticity of Ni/Al nanolaminate begins with yielding of Al, and the Al yield strength depends on the individual layer thickness. Based on an inverse methodology, the Al yield strength as a function of Al grain size is determined. The results evidence a significant strengthening in the Al nanolayers. Specially, when Al layer thickness decreases from ≈110 nm to ≈16 nm, its yield strength is increased for ≈68 %, from ≈0.69 GPa to ≈1.16 GPa. The strengthening rule follows a confined layer slip model that is developed based on confining of single dislocation loops in nanolayers. Both the dislocation strengthening and the constraint effects in the Al layers contribute to a more sensitivity of Ni/Al strength with the variation of Al layer thickness, instead of Ni layer thickness. The work may forward the fundamental understanding in the strengthening mechanism and mechanical behavior of metallic nanolaminates with large elastoplastic mismatch.

Simultaneous high strength and mechanical stability of bcc Nb/Mg nanolaminates

While bimetallic nanocomposites have demonstrated extraordinary – three to even ten-fold – gains in strength with decreasing layer thickness, their strengths tend to plateau beyond a critical layer thickness. More disappointingly, such increases in strength are almost always accompanied by a decrease in their strains to failure (ductility). In this work we report simultaneous improvements in both strength and mechanical stability of Nb/Mg nanolaminates with decreasing layer thicknesses, a trend seldom reported in nanolaminates consisting of pure metals. Using micro-pillar compression and nanoindentation experiments we show that physical vapor deposited (PVD) Nb/Mg nanolaminates that contain a body center cubic (bcc) Mg pseudomorphic phase demonstrate a >60% increase in strength and a >80% increase in strain to failure over those containing the hexagonal close packed (hcp) Mg phase. Instead of a strength plateau, the hcp-to-bcc phase transition in Mg results in a renewed strengthening regime in the nanolaminate caused by the change to a coherent interface from an incoherent one, along with a concurrent increase in strain-to-failure due to the introduction of a more plastically isotropic bcc material from an anisotropic hcp structure. Using high resolution transmission electron microscopy (HR-TEM) we also demonstrate the presence of a thin layer of bcc Mg at the Nb/Mg interface at larger layer thicknesses when Mg is predominantly hcp. Our results suggest that the increases in strain to failure in the Nb/Mg nanolaminates with decreasing layer thicknesses can be corelated to the approximate volume fraction of the pseudomorphic bcc Mg present in the layers.

Chemical-element-distribution-mediated deformation partitioning and its control mechanical behavior in high-entropy alloys

• Effect of chemical heterogeneities on plasticity and strength is studied using atomic simulations in high-entropy alloys. • Elemental anisotropy/difference factor is proposed, and then used to evaluate the short range order and predict the HEA properties. • Elemental anisotropy factor for optimal high performance is accurately estimated by machine learning. • By a machine learning approach coupled with MD simulations, elemental anisotropy ranges from 2.9 to 3. The chemical element distributions always strongly affect the deformation mechanisms and mechanical properties of alloying materials. However, the detailed atomic origin still remains unknown in high-entropy alloys (HEAs) with a stable random solid solution. Here, considering the effect of elemental fluctuation distribution, the deformation behavior and mechanical response of the widely-studied equimolar random CoCrFeMnNi HEA are investigated by atomic simulations combined with machine learning and micro-pillar compression experiments. The elemental anisotropy factor is proposed, and then used to evaluate the chemical element distribution. The experimental and simulation results show that the local variations of chemical compositions exist and play a critical role in the deformation partitioning and mechanical properties. The high strength and good plasticity of HEAs are obtained via tuning the chemical element distributions, and the optimal elemental anisotropy factor ranges from 2.9 to 3 using machine learning. This trend can be attributed to the cooperative mechanisms depending on the local variational composition: massive partial dislocation multiplication at an initial stage of plastic deformation, and the inhibition of localized shear banding via the nucleation of deformation twinning at a later stage. Using the new insights gained here, it would be possible to create new metallic alloys with superior properties through thermal-mechanical treatment to tailoring the chemical element distribution.

Rate-dependent mechanical behavior of single-, bi-, twinned-, and poly-crystals of CoCrFeNi high-entropy alloy

While considerable effort is made to understand the solid solution strengthening on the deformation behavior of high-entropy alloys (HEAs), relatively little attention is paid to the role of microstructural interfaces, especially twin boundaries (TBs), on the strain-rate sensitivity (SRS) of them. To address this, we have conducted micropillar compression experiments on single-, bi-, and twinned-crystals of CoCrFeNi HEA and compared the results with those obtained with uniaxial tensile and compression tests on polycrystalline bulk samples. Results show that SRS, as well as the yield strength and plastic flow behavior, in single crystals are orientation dependent due to the differences in the maximum Schmid factors. While the high-angle grain boundaries arrest dislocation motion, TBs allow for dislocation transmission through them, which result in distinct mechanical responses. While the bi-crystal's deformation behavior is controlled by the ‘hard’ grain, twinned crystals exhibit an ‘averaged’ response. The large diversity of the reported SRS values in face centered cubic HEAs could be due to the varying fractions and thus contributions of annealing twins in the tested samples.

Mechanics of micropillar confined thin film plasticity

Micropillar compression experiments probing size effects in confined plasticity of metal thin films, including the indirect imposition of ‘canonical’ simple shearing boundary conditions, show dramatically different responses in compression and shear of the film. The Mesoscale Field Dislocation Mechanics (MFDM) model is confronted with this set of experimental observations and shown to be capable of modeling such behavior, without any ad-hoc modification to the basic structure of the theory (including boundary conditions), or the use of extra fitting parameters. This is a required theoretical advance in the current state-of-the art of strain gradient plasticity models. It is also shown that significantly different inhomogeneous fields can display qualitatively similar size effect trends in overall agreement with the experimental results. The (plastic) Swift and (elastic) Poynting finite deformation effects are also demonstrated.

Plasticity of Metal-Organic Framework Glasses.

Metal-organic framework (MOF) glasses provide new perspectives on many material properties due to their unique chemical and structural nature. Their mechanical properties are of particular interest because glasses are inherently brittle, which limits their applications as structural materials. Here we perform strain-rate-dependent uniaxial micropillar compression experiments on agZIF-62, agZIF-UC-5, and agTIF-4, a series of MOF glasses with different substituting linker molecules, and find that these glasses show substantial plasticity, at least on the micrometer scale. At a quasi-static strain rate of 0.001 s-1, the micropillars yielded at approximately 0.32 GPa and subsequently deformed plastically up to 35% strain, irrespective of the type of substituting linker. With increasing strain rate, the yield strength of agZIF-62 evolved with the strain-rate sensitivity m = 0.024 to reach a yield strength of 0.44 GPa at a strain rate of 510 s-1. On the basis of this relatively low strain-rate sensitivity and the absence of serrated flow, we conclude that structural densification is the predominant mechanism that accommodates such extensive plasticity.

Microstructural origin of the anisotropic flow stress of laser powder bed fused AlSi10Mg

The microstructural origin of anisotropy in the yield stress and ultimate tensile strength of AlSi10Mg tensile specimens produced by laser powder bed fusion (LPBF) is revealed using a combination of micropillar compression tests and microstructure-based numerical simulations. Uniaxial tensile tests demonstrate that specimens with tensile axis parallel to the build direction (vertical specimen) exhibit a higher yield stress and ultimate tensile strength than those perpendicular to the build direction (horizontal specimen). Micropillar compression experiments and a microstructure-based crystal plasticity model together confirm that the anisotropy has its origin in an elongated Al-Si cellular network (nominally 0.7 µm × 1.4 µm with long axis aligned with the build direction) within individual grains. A multiscale microstructure-based model predicts the mechanical properties of LPBF AlSi10Mg tensile specimens by accounting for the hierarchical microstructural features across length scales, which include the Al-Si network, the crystallographic grain structure, and the differences in microstructure between melt pool interiors and melt pool boundaries. The multiscale model over-estimates the yield stress, but correctly predicts the ultimate tensile strength and the anisotropy in the flow strength of tensile specimens. The model is used to computationally predict new microstructures driven by composition and processing parameters for LPBF AlSi10Mg alloys with improved mechanical properties.

Microscale compressive behavior of hydrated lamellar bone at high strain rates

The increased risk of fracture in the elderly associated with metabolic conditions like osteoporosis poses a significant strain on health care systems worldwide. Due to bone's hierarchical nature, it is necessary to study its mechanical properties and failure mechanisms at several length scales. We conducted micropillar compression experiments on ovine cortical bone to assess the anisotropic mechanical response at the lamellar scale over a wide range of strain rates (10−4 to 8·102 s−1). At the microscale, lamellar bone exhibits a strain rate sensitivity similar to what is reported at the macroscale suggesting that it is an intrinsic property of the extracellular matrix. Significant shear band thickening was observed at high strain rates by HRSEM and STEM imaging. This is likely caused by the material's inability to accommodate the imposed deformation by propagation of thin kink bands and shear cracks at high strain rates, leading to shear band thickening and nucleation. The post-yield behavior is strain rate and direction dependent: hardening was observed for transverse oriented micropillars and hardening modulus increases with strain rate by a factor of almost 2, while axially oriented micropillars showed strain softening and an increase of the softening peak width and work to ultimate stress as a function of strain rate. This suggests that for compression at the micrometer scale, energy absorption in bone increases with strain rate. This study highlights the importance of investigating bone strength and post-yield behavior at lower length scales, under hydrated conditions and at clinically relevant strain rates. Statement of significanceWe performed micropillar compression experiments of ovine cortical bone at two different orientations and over seven orders of magnitude of strain rate. Experiments were performed under humid condition to mimic the natural conditions of bone in a human body using a newly developed micro-indenter setup. The strain rate sensitivity was found to be of a similar magnitude to what has been reported for higher length scales, suggesting that the strain rate sensitivity is an intrinsic property of the bone extracellular matrix. In addition, localized shear deformation in thick bands was observed for the first time at high strain rates, highlighting the importance of investigating bone under conditions representative of an accident or fall at several length scales.

Thermal activation process of plastic deformation in Fe–18Cr single-crystal micropillars with high-density dislocations

Micropillar compression testing was performed on bcc solid-solution single-crystal micropillars with two diameter (d) ranges (2–3 and 5–6 μm) prepared on the surfaces of fully annealed and subsequently 10% cold-rolled 18Cr ferritic steel specimens. This was done to investigate the effect of initial dislocations on the plastic deformation of micron-sized crystals. The 10% cold rolling process significantly increased the stress level (provided by an activated single slip system) required to initiate slip in the annealed micropillars with different diameter ranges. In the case of the annealed micropillars, the strain-rate sensitivity (m) of the yield stress becomes lower for larger specimens (the m value decreased from 0.12 to 0.04). However, the 10% cold-rolled micropillars exhibited a much lower strain-rate sensitivity regardless of the specimen size. The activation volume (v*) of the annealed micropillars showed a significant specimen size dependency (v*∝d1.47), consistent with published data on the micropillar compression experiments of single-crystals of the bcc metals and alloys. For the 10% cold-rolled micropillars, the high v* values (88b3 and 112b3) showed a slight dependency on the specimen size (v*∝d0.33). The v* values appeared somewhat higher but were equivalent to those of bulk-size specimens, suggesting that the initial high-density dislocations would provide sufficient sources for dislocation multiplication in the micron-sized specimens under compression. The observed high v* values might be associated with the strong dislocation interactions in the α-(Fe, Cr) solid-solution matrix.

A Calibration Method of Micropillar Compression Testing for Taper and Eccentricity Induced Errors

Errors induced by pillar taper and eccentric load in micropillar compression experiments have seldom been investigated, although they significantly affect the measurement accuracy, especially in the testing of specimens in a micrometer and nanometer size. A novel calibration method related to stress–strain responses in micropillar compression testing was proposed in this study to eliminate this kind of errors. Axial load and eccentric load were applied to high-entropy alloy (HEA) pillars with taper angles of 1°, 2°, and 3°, respectively, and the measured stress–strain curves were corrected by the proposed calibration method. The results revealed that the difference of the corrected curves with different tapers or eccentricities was smaller than the measured curves. The errors induced by the taper and eccentric load increased with the taper angle and eccentricity. In addition, the difference between measured and corrected flow stresses increased with the taper angle, which was essentially consistent with the results from the calibration method.

Uniaxial compression of [001]-oriented CaFe2As2 single crystals:the effects of microstructure and temperature on superelasticity Part I: Experimental observations

Micropillar compression experiments on [001]-oriented CaFe2As2 single crystals have recently revealed the existence of superelasticity with a remarkably high elastic limit of over 10%. The collapsed tetragonal phase transition, which is a uni-axial contraction process in which As-As bonds are formed across an intervening Ca-plane, is the main mechanism of superelasticity. Usually, superelasticity and the related structural transitions are affected strongly by both the microstructure and the temperature. In this study, therefore, we investigated how the microstructure and temperature affect the superelasticity of [001]-oriented CaFe2As2 micropillars cut from solution-grown single crystals, by performing a combination of in-situ cryogenic micromechanical testing and transmission electron microscopy studies. Our results show that the microstructure of CaFe2As2 is influenced strongly by the crystal growth conditions and by subsequent heat treatment. The presence of Ca and As vacancies and FeAs nanoprecipitates affect the mechanical behavior significantly. In addition, the onset stress for the collapsed tetragonal transition decreases gradually as the temperature decreases. These experimental results are discussed primarily in terms of the formation of As-As bonds, which is the essential feature of this mechanism for superelasticity. Our research outcomes provide a more fundamental understanding of the superelasticity exhibited by CaFe2As2 under uni-axial compression.

Statistics of dislocation avalanches in FCC and BCC metals: dislocation mechanisms and mean swept distances across microsample sizes and temperatures

Plastic deformation in crystalline materials consists of an ensemble of collective dislocation glide processes, which lead to strain burst emissions in micro-scale samples. To unravel the combined role of crystalline structure, sample size and temperature on these processes, we performed a comprehensive set of strict displacement-controlled micropillar compression experiments in conjunction with large-scale molecular dynamics and physics-based discrete dislocation dynamics simulations. The results indicate that plastic strain bursts consist of numerous individual dislocation glide events, which span over minuscule time intervals. The size distributions of these events exhibit a gradual transition from an incipient power-law slip regime (spanning approx 2.5 decades of slip sizes) to a large avalanche domain (spanning approx 4 decades of emission probability) at a cut-off slip magnitude {s}_{mathrm{c}}. This cut-off slip provides a statistical measure to the characteristic mean dislocation swept distance, which allows for the scaling of the avalanche distributions vis-à-vis the archetypal dislocation mechanisms in face-centered cubic (FCC) and body-centered cubic (BCC) metals. Our statistical findings provide a new pathway to characterizing metal plasticity and towards comprehension of the sample size effects that limit the mechanical reliability in small-scale structures.

Uniaxial Compression of [001]-Oriented CaFe 2As 2 Single Crystals: The Effects of Microstructure and Temperature on the Superelasticity, Part I: Experimental Observations

Micropillar compression experiments on [001]-oriented CaFe 2 As 2 single crystals have recently revealed the existence of superelasticity with a remarkably high elastic limit over 10%. The collapsed tetragonal phase transition, which is a uni-axial contraction process in which As-As bonds are formed across an intervening Ca-plane, is the main mechanism of superelasticity. Usually, superelasticity and the related structural transitions are affected strongly by both the microstructure and the temperature. In this study, therefore, we investigated how the microstructure and temperature affect the superelasticity of [001]-oriented CaFe 2 As 2 micropillars cut from solution-grown single crystals, by performing a combination of in-situ cryogenic micromechanical testing and transmission electron microscopy studies. Our results show that the microstructure of CaFe 2 As 2 is influenced strongly by the crystal growth conditions and by subsequent heat treatment. The presence of Ca and As vacancies and FeAs nanoprecipitates affect the mechanical behavior significantly. In addition, the onset stress for the collapsed tetragonal transition decreases gradually as the temperature decreases. These experimental results are discussed primarily in terms of the formation of As-As bonds, which is the essential feature of this mechanism for superelasticity. Our research outcomes provide a more fundamental understanding of the superelasticity exhibited by CaFe 2 As 2 under uni-axial compression.

Design of a V–Ti–Ni alloy with superelastic nano-precipitates

Stress-induced martensitic transformations enable metastable alloys to exhibit enhanced strain hardening capacity, leading to improved formability and toughness. As is well-known from transformation-induced plasticity (TRIP) steels, however, the resulting martensite can limit ductility and fatigue life due to its intrinsic brittleness. In this work, we explore an alloy design strategy that utilizes stress-induced martensitic transformations but does not retain the martensite phase. This strategy is based on the introduction of superelastic nano-precipitates, which exhibit reverse transformation after initial stress-induced forward transformation. To this end, utilizing ab-initio simulations and thermodynamic calculations we designed and produced a V45Ti30Ni25 (at%) alloy. In this alloy, TiNi is present as nano-precipitates uniformly distributed within a ductile V-rich base-centered cubic (bcc) β matrix, as well as being present as a larger matrix phase. We characterized the microstructure of the produced alloy using various scanning electron microscopy (SEM) and transmission electron microscopy (TEM) methods. The bulk mechanical properties of the alloy are demonstrated through tensile tests, and the reversible transformation in each of the TiNi morphologies were confirmed by in-situ TEM micro-pillar compression experiments, in-situ high-energy diffraction synchrotron cyclic tensile tests, indentation experiments, and differential scanning calorimetry experiments. The observed transformation pathways and variables impacting phase stability are critically discussed.

Low-temperature rheology of calcite

SUMMARY Low-temperature plastic rheology of calcite plays a significant role in the dynamics of Earth's crust. However, it is technically challenging to study plastic rheology at low temperatures because of the high confining pressures required to inhibit fracturing. Micromechanical tests, such as nanoindentation and micropillar compression, can provide insight into plastic rheology under these conditions because, due to the small scale, plastic deformation can be achieved at low temperatures without the need for secondary confinement. In this study, nanoindentation and micropillar compression experiments were performed on oriented grains within a polycrystalline sample of Carrara marble at temperatures ranging from 23 to 175 °C, using a nanoindenter. Indentation hardness is acquired directly from nanoindentation experiments. These data are then used to calculate yield stress as a function of temperature using numerical approaches that model the stress state under the indenter. Indentation data are complemented by uniaxial micropillar compression experiments. Cylindrical micropillars ∼1 and ∼3 μm in diameter were fabricated using a focused ion beam-based micromachining technique. Yield stress in micropillar experiments is determined directly from the applied load and micropillar dimensions. Mechanical data are fit to constitutive flow laws for low-temperature plasticity and compared to extrapolations of similar flow laws from high-temperature experiments. This study also considered the effects of crystallographic orientation on yield stress in calcite. Although there is a clear orientation dependence to plastic yielding, this effect is relatively small in comparison to the influence of temperature.