Dynamic Indentations Research Articles

Quasistatic and Dynamic Nanoindentation Measurements of Pinus radiata D. Don S2 and CCML Cell Wall Layers

Quasistatic nanoindentation is a proven tool that provides information on the micromechanical behavior of wood cell walls. However, quasistatic tests cannot probe the time-dependent mechanical behavior shown by wood. Nanoindentation dynamic mechanical analysis (nanoDMA) can measure the viscoelastic properties of wood cell walls. This research aimed to study the quasistatic and viscoelastic properties of individual radiata pine wood (Pinus radiata D. Don) cell wall layers. To minimize variability and retrieve both properties at the same locations, a load function composed of a multiload-quasistatic function followed by dynamic reference frequency segments was developed. Nanoindentations were then performed on the S2 layer and compound corner middle lamella (CCML) of unembedded latewood cells. Because the S2 layer is anisotropic, both transverse and longitudinal–tangential wood planes were studied. In the transverse plane, the average results of the quasistatic elastic moduli Es for the S2 layer and CCML were 15.7 GPa and 4.6 GPa, respectively. In the longitudinal–tangential plane, the Es was 3.9 GPa. In the transverse section, the hardness H of the S2 layer and CCML were 331 MPa and 277 MPa, respectively, and in the longitudinal–tangential section H was 244 MPa. To acquire the viscoelastic properties, measurements were made over more than three decades of frequency. An increase of the storage modulus E′, and a reduction of the loss modulus E″ and loss factor tanδ as frequency increased were found in both wood orientations. The quasi-static and dynamic indentations equivalent at 0.1 Hz showed similar values for Es and E′. This study contributes to our knowledge of wood cell wall micromechanical properties.

Quasi-static and dynamic depth-sensing indentation measurements to characterize wear and mar resistance of coating–polymer systems

Abstract Different layers of different thicknesses were coated on the same polymethyl methacrylate (PMMA) substrate. For each of these bilayered systems, quasi-static and dynamic instrumented indentations using continuous stiffness measurement have been made. We verified if data from indentation tests performed on a given sample obey a power law relationship. The aim was to calculate the viscoplasticity index n with sufficient accuracy (by taking into account the viscoelastoplastic properties of the studied samples), since this value is characteristic of the viscoplastic properties of a material and, therefore, allows evaluating the plastic scratch resistance of the surface. Thanks to both indentation methods the viscoplasticity index could be calculated and its value compared to the different bilayered systems one. As n is supposed to be intrinsic to a material, its value should not depend on the characterization technique.

In vivo soft tissue compressive properties of the human hand.

Background/PurposeFalls onto outstretched hands are the second most common sports injury and one of the leading causes of upper extremity injury. Injury risk and severity depends on forces being transmitted through the palmar surface to the upper extremity. Although the magnitude and distribution of forces depend on the soft tissue response of the palm, the in vivo properties of palmar tissue have not been characterized. The purpose of this study was to characterize the large deformation palmar soft tissue properties.MethodsIn vivo dynamic indentations were conducted on 15 young adults (21–29 years) to quantify the soft tissue characteristics of over the trapezium. The effects of loading rate, joint position, tissue thickness and sex on soft tissue responses were assessed.ResultsEnergy absorbed by the soft tissue and peak force were affected by loading rate and joint angle. Energy absorbed was 1.7–2.8 times higher and the peak force was 2–2.75 times higher at high rate loading than quasistatic rates. Males had greater energy absorbed than females but not at all wrist positions. Damping characteristics were the highest in the group with the thickest soft tissue while damping characteristics were the lowest in group with the thinnest soft tissues.ConclusionPalmar tissue response changes with joint position, loading rate, sex, and tissue thickness. Accurately capturing these tissue responses is important for developing effective simulations of fall and injury biomechanics and assessing the effectiveness of injury prevention strategies.

Formation mechanism of hierarchical pattern fabricated by ultrasonic-assisted texturing: dynamic indentation induced pile-up

Ultrasonic-assisted surface texturing can produce surface textures with hierarchical micro/nano-scale structures on metal components. In this work, we prove that the formation of nano-scale structure originates from pile-up produced by ultrasonic dynamic indentation. Both quasi-static and dynamic indentations are performed on pure copper, 316 stainless steel, and pure titanium using an ultrasonic nanocrystal surface modification system. For the first time, it is revealed that ultrasonic dynamic indentation produces significant higher pile-up as compared with that of quasi-static indentation, making nanoscale structure possible. Finite element simulations demonstrate that dynamic indentation produces larger equivalent plastic strain, an indicator for work hardening, in the region close to the edge of the contact interface. It is conjectured that higher degrees of work hardening and dislocation density result in a higher dislocation resistance as compared with quasi-static indentation. The plastic deformation is confined at the contact interface and is then forced to move upward, leading to a significant pile-up.

Static and time-dependent mechanical response of organic matrix of bone

Bone derives its mechanical strength from the complex arrangement of collagen fibrils (type-I primarily) reinforced with hydroxy-apatite (HAp) mineral crystals in extra- and intra-fibrillar compartments. This study demonstrates a novel approach to obtain organic matrix of bone through its demineralization as well as mechanically characterize it at small length scales using static and dynamic indentation techniques. Sample surface preparation protocol used in the present work maintained the surface integrity of demineralized bone samples which resulted sample surface of roughness (RMS) magnitude of approximately 14 nm (averaged over 1 × 1 μm2 area duly verified by atomic force microscope (AFM)). Elemental composition analysis via energy dispersive X-ray spectroscopy (EDX) (for probed depth upto 2 μm) confirmed the complete removal of HAp mineral from bone samples during their demineralization using EDTA leaving collagen molecule assemblies unaffected as represented by Second Harmonic Generation (SHG) imaging. The modulus magnitudes of organic matrix obtained using from quasistatic as well as dynamic indentations (at constant frequency of 30 Hz) as ∼2.6 GPa and 4.5 GPa respectively, demonstrated the influence of loading rate on the estimated mechanical properties. For indentation depth to surface roughness ratio greater than ∼5:1, interestingly, measured material properties of organic matrix were found to depend on increasing magnitude of indentation depth of up to ∼500 nm value which probed from few collagen fibrils to next level of hierarchy i.e. collagen fibers. These findings are very useful to accurately determine the elastic and visco-elastic response of organic matrices of mineralized tissues for various applications including tissue engineering, bio-mimetics, etc.

Amorphization‐induced volume change and residual stresses in boron carbide

AbstractThe residual pressure surrounding quasistatic and dynamic Vickers indentations in boron carbide was quantitatively mapped in 3 dimensions using Raman spectroscopy. These maps were compared against similar maps of amorphization intensity and optical micrographs of deformed regions to determine the roles of amorphization and damage upon indentation‐induced residual stress. Stress relaxation was observed near radial cracks, spalled regions, and graphitic inclusions. A positive correlation was found between high levels of residual stress and the number of amorphized sites detected. Finite element simulations were conducted to model the indentation‐induced residual stress fields in the absence of amorphization and cracking. The simulations underpredicted the average residual pressure observed through Raman spectroscopy, implying that amorphization contributes to increased pressure in the material. This pressure is interpreted as potential evidence of volumetric expansion of the amorphized material which is less ordered and hence exerts compressive forces on the surrounding crystalline matrix.

Characterization and investigation of size effect in nano-impact indentations performed using cube-corner indenter tip

Abstract

Raman spectroscopy mapping of amorphized zones beneath static and dynamic Vickers indentations on boron carbide

Three-dimensional models of amorphized zones beneath quasistatic and dynamic Vickers indentations on boron carbide were constructed using micro-Raman spectroscopy. The square of amorphized zone depth varied linearly with load and the maximum amorphized area occurred beneath the indentation imprint in accord with the maximum shear stress under Hertzian contact. Reduced measurements of amorphization intensity at loads above 10N may be due to a loss of subsurface amorphized material through lateral cracks. Utilizing an expanding cavity model with power-law (n=0.79–0.80) and linear (Ep=0.39–0.45) strain hardening responses, finite element simulations were conducted to determine the critical values of stress and strain required to cause amorphization. These simulations suggest that amorphization may initiate at von Mises stresses and equivalent plastic strains above 6.6GPa and 0.026, respectively. These results may be useful for validating computational models of boron carbide under complex loading scenarios (e.g., ballistic impact).

Microscopic and spectroscopic investigation of phase evolution within static and dynamic indentations in single-crystal silicon

Silicon undergoes multiple phase transformations during indentation, and its final phase depends primarily upon the rate of unloading. In this study, single-crystal silicon was subjected to static and dynamic indentations in order to evaluate the propensity for particular phase transformations as a function of unloading strain rate. Raman spectroscopy and transmission electron microscopy were employed to map the phase distribution within and beneath the indent impression. It was found that silicon behavior is strongly dependent on unloading strain rate, with the preferred final phase switching from crystalline polytypes to nanocrystalline Si. The manuscript provides data in the intermediate strain rate range (103–105s−1) that is not currently available in literature and links published nanoindentation to shock testing results, crucial to predicting material response at a range of strain rates.

Mechanical response of Ti-based bulk metallic glass under static and dynamic indentations

Vickers hardness and plastic deformation of Ti-based bulk metallic glass (Ti-BMG) were investigated under both static and dynamic indentations. Dynamic hardness is obviously greater than that under static indentation, which is attributed to the combination effects of energy barriers and separation of nanocrystallizations from the metallic glass during dynamic indentation. Although dynamic indentation induced more severe deformation than that under static indentation, the deformation characteristics in the two loading cases are nearly the same: both exhibiting semi-circular shear bands on the top surface and a mixture of semi-circular and radial shear bands underneath the indentation tips. The most obvious difference between the two kinds of indentations is that substantial successive shear bands accompanied by numerous shear-offsets formed in dynamic indentation while obviously less shear bands and shear-offsets formed in static indentation.

Characterization of viscoelastic materials by quasi-static and dynamic indentation

This paper describes the experimental measurements of the elastic modulus and hardness of viscoelastic materials under quasi-static and dynamic depth-sensing indentation using a homemade tribology probe microscope (TPM). The indentation measurements were performed using a sapphire sphere tip under various conditions. Materials such as polytetrafluoroethylene, styrene rubber and nitrile rubber were tested in both quasi-static and dynamic experiments. In quasi-static mode, the loading and unloading force curves were obtained from these specimens, and the results show a significant load effect on the measured hardness and elastic modulus. The dynamic indentation tests were conducted under a range of loading forces with various frequencies. The values of storage modulus, loss modulus and damping factor were determined by dynamic indentation. To get an accurate measurement, the stiffness and damping of the instrument were rigorously analyzed. Using dynamic indentation, it was confirmed that the variation in the frequency of the oscillation force has a significant effect on the measured results of the materials. Comparing the results obtained from the quasi-static and dynamic indentations, for the viscoelastic properties, dynamic indentation offers an advantage over the quasi-static method. Collectively, these results clearly demonstrate the capability of our homemade TPM facility to determine the constitutive behavior of viscoelastic solids in the frequency domain.

Static versus dynamic gerbil tympanic membrane elasticity: derivation of the complex modulus

An accurate estimation of tympanic membrane stiffness is important for realistic modelling of middle ear mechanics. Tympanic membrane stiffness has been investigated extensively under either quasi-static or dynamic loading conditions. It is known that biological tissues are sensitive to strain rate. Therefore, in this work, the mechanical behaviour of the tympanic membrane was studied under both quasi-static and dynamic loading conditions. Experiments were performed on the pars tensa of four gerbil tympanic membranes. A custom-built indentation apparatus was used to perform in situ tissue indentations and testing was done applying both quasi-static and dynamic sinusoidal indentations up to 8.2Hz. The unloaded shape of the tympanic membrane was measured and used to create specimen-specific finite element models to simulate the experiments. The frequency dependent Young's modulus of each specimen was then estimated by an inverse analysis in which the error between experimental and simulated indentation data was optimised for each indentation frequency separately. Using an 8μm central region thickness, we found Young's moduli between 71 and 106MPa (n = 4) at 0.2Hz indentation frequency. A standard linear viscoelastic model and a viscoelastic model with a continuous relaxation spectrum were used to derive a complex modulus in the frequency domain. Due to experimental limitations, the indentation frequency upper limit was 8.2Hz. The average relative modulus increase in this domain was 14% and the increase was the strongest below 6Hz.

Rate Sensitive Indentation Response of a Coarse‐Grained Magnesium Aluminate Spinel

The effect of loading rate on indentation hardness, brittleness, and fracture modes during static and dynamic Vickers indentation of a transparent coarse grain (250 μm average grain size) polycrystalline magnesium aluminate spinel was investigated. Static hardness was measured using a conventional Vickers tester while the dynamic hardness was measured using a custom test fixture based on split Hopkinson pressure bar technique with the capability to produce single indentations at strain rates of roughly 103 s−1. Static and dynamic hardness values as well as characteristic fracture response are compared at a range of indentation loads. It was found that Vickers micro hardness increased by an average of 5% over the entire load range, while the calculated brittleness factor increased when subjected to dynamic indentation loads. Static and dynamic indentations were found to produce radial and lateral cracks with evidence of spall appearing only during dynamic loading. Dynamic indentations also revealed an increased level of transgranular cracking, whereas intergranular cracking was more dominant during static indentations. Indentation cracks generated due to static indentations placed in the vicinity of a grain boundary deflected along a grain boundary, whereas these cracks cut across the grain boundary into the neighboring grain during dynamic indentations. Static and dynamic indentations that were placed directly on grain boundaries generated intergranular (grain boundary) cracks that were on average 18% longer than accompanying intragranular cracks. The implications of these fracture modes on dynamic impact response of polycrystalline spinel are discussed.

Static and dynamic indentation response of basal and prism plane sapphire

Static and dynamic indentation experiments are conducted on sapphire along the c[0 0 0 1] and a [ 1 1 2 ¯ 0 ] crystallographic axes to determine the loading rate dependence on its mechanical response. Static hardness is measured using a conventional Vickers tester while the dynamic hardness is measured using a custom test fixture based on split Hopkinson pressure bar technique with the capability to produce single indentations at strain rates of roughly 10 3 s −1. Static and dynamic hardness values as well as characteristic fracture response for both axes are compared at a range of indentation loads. The results indicate that dynamic hardness increases by 10% and 12% over static hardness for basal and prism plane sapphire, respectively. Observed crack orientations due to indentation of the a- and c-planes are consistent with the expected location of twinning or slip on the r ( 0 1 1 ¯ 2 ) , ( 1 1 ¯ 0 2 ) , ( 1 ¯ 0 1 2 ) and c ( 0 0 0 1 ) planes for both static and dynamic indentations. Prism slip is also suspected to interact with rhombohedral twinning systems to create a weakened zone oriented along the c-axis. Static indentations yielded well defined crystallographically oriented cracks with repeated directional switchbacks indicating a zone of competition between the two crack systems. Dynamic indentations, on the other hand, resulted in shorter and less jagged cracks accompanied by increased localized spalling beneath each indentation site as compared to the static indentations. This mode of fracture would suggest a shift in energy dissipation mechanism from crystal axis oriented long crack propagation under static loading to micro cracking that is independent of crystallographic orientation under higher strain rate events.

Inelastic deformation under indentation and scratch loads in a ZrB 2–SiC composite

Inelastic deformation features induced in an ultra-high temperature ceramic composite, ZrB 2–SiC, due to static indentation (rate of deformation of the order of 10 −5 s −1), dynamic indentation (rate of deformation of the order of 10 3 s −1), and high-velocity scratch (500 mm/s) experiments are presented. It was found that this ceramic composite has up to 30% higher dynamic hardness compared to static hardness. Dynamic indentations resulted in extensive transgranular microcracking within the indented regions compared to static indentations. In addition, significant plastic deformation features in terms of slip-line formation were observed within statically and dynamically indented regions. The high-velocity scratch studies revealed extensive transgranular microcracking perpendicular to the scratch direction and slip-lines in and around the scratch path. Preliminary transmission electron microscopy (TEM) observations from regions of slip-lines surrounding the scratch grooves revealed dislocation activity in the composite.

Recent Advances in Dynamic Indentation Fracture, Impact Damage and Fragmentation of Ceramics

In this feature article, dynamic indentation‐induced deformation and fracture phenomena in brittle solids are related to the deformation behavior and fracture patterns evolved during dynamic impact on structural ceramics. Examples of indentation‐induced localized amorphization in boron carbide (B4C) and differences in fracture characteristics due to static and dynamic indentations on B4C and zirconium diboride–silicon carbide (ZrB2–SiC) ceramic composite are presented. These features are compared with the fracture patterns evolved during the high‐velocity ball impact on SiC. The influences of processing‐induced (inherent) flaws and deformation‐induced flaws on fracture initiation in a brittle material are discussed. Recent developments in analytical modeling of indentation‐ and impact‐induced damage in ceramics and computational efforts on fracture and fragmentation response of ceramics are thoroughly reviewed. Finally, some future research directions are identified.

Evolution of shear bands in bulk metallic glasses under dynamic loading

Shear band spacing in Zr-based bulk metallic glasses (BMGs) under dynamic loads is found to vary with position and local strain rate in the indented region. To investigate the dependence of shear band evolution characteristics on local strain rate and normal stress, a micromechanical model based on momentum diffusion is proposed. The thermo-mechanical model takes into account the normal stress dependence of yield stress, the free volume theory and the associated viscosity change within the shear band region. Temperature rise is obtained from the balance between the heat diffusion to the adjacent regions from a shear band and the heat generation due to the accumulated plastic work in a shear band. The parametric study has revealed that thermal effects play a minor role when the critical shear displacement is below 10 nm (as in nanoindentation) but become significant when the shear displacement accumulated in a shear band is of the order of hundreds of nanometers (as in uniaxial compression and in dynamic indentations). Finally, it is found that the normal stress plays a crucial role in the deformation behavior of BMGs by not only decreasing the time for shear band formation but also increasing the temperature rise significantly.

Dynamic Indentation Response of Fine‐Grained Boron Carbide

Boron carbide disks with three different grain sizes were consolidated from submicrometer‐sized boron carbide powder using the plasma pressure compaction technique. Static and dynamic indentations were performed to determine their loading‐rate dependence on mechanical properties. Dynamic indentations resulted in a decrease in hardness and fracture toughness, and induced more severe damage compared with static indentations. Using Raman spectroscopy, the mechanism responsible for loss of strength under dynamic loads was identified as the solid‐state structural phase transformation in the dynamically loaded regions. The influence of processing conditions and the resulting microstructure on the observed rate dependency of mechanical properties are discussed.

Dynamic indentation response of ZrHf-based bulk metallic glasses

Static and dynamic Vickers indentations were performed on ZrHf-based bulk amorphous alloys. A decrease in indentation hardness was observed at higher strain rates compared with static indentation hardness. For equivalent loads, dynamic indentations produced more severe deformation features on the loading surface than static indentations. Using bonded interface technique, the induced shear band patterns beneath the indentations were studied. In static indentations, the majority of the deformation was primarily accommodated by closely spaced semicircular shear bands surrounding the indentation. In dynamic indentations two sets of widely spaced semicircular shear bands with two different curvatures were observed. The observed shear band patterns and softening in hardness were rationalized based on the variations in the confinement pressure, strain rate, and temperature within the indentation region during dynamic indentations. It is also proposed that free volume migration and formation of nano-voids leading to cracking are favored due to adiabatic heating and consequently cause the observed softening at high strain rates.

Quasi-static and dynamic depth-sensing indentation measurements to characterize wear and mar resistance of coating–polymer systems

Abstract Different layers of different thicknesses were coated on the same polymethyl methacrylate (PMMA) substrate. For each of these bilayered systems, quasi-static and dynamic instrumented indentations using continuous stiffness measurement have been made. We verified if data from indentation tests performed on a given sample obey a power law relationship. The aim was to calculate the viscoplasticity index n with sufficient accuracy (by taking into account the viscoelastoplastic properties of the studaed samples), since this value is characteristac of the viscoplastic properties of a materaal and, therefore, allows evaluating the plastic scratch resistance of the surface. Thanks to both indentation methods the viscoplasticity index could be calculated and its value compared to the different bilayered systems one. As n is supposed to be intrinsic to a material, its value should not depend on the characterization technique.