Force-indentation Depth Curves Research Articles

A new method for determining the ogden parameters of soft materials using indentation experiments

A full understanding of the material properties of skin tissue is crucial for exploring its tribo-mechanical behaviour. It has been widely accepted that the mechanical behaviour of skin tissue for both small and large deformations can be accurately described using a hyperelastic model, such as the one developed by Ogden. However, obtaining these Ogden parameters for in-vivo skin by in-vivo experiments no matter the indentation or suction tests is a significant challenge. The mathematical model used to describe the material behaviour during the test should consider not only the material nonlinearity but also the geometrical confinement of the tissue, the large deformations induced, and the fact that the specimens are relatively thin.A range of contact models is available to describe the contact behaviour during the indentation test. However, none of them can be used for hyperelastic materials with small thickness under large deformations. Simultaneously explaining material nonlinearity and geometric nonlinearity, either through theoretical equations or numerical calculations, poses a significant challenge.In this research, we propose a pragmatic method to obtain Ogden parameters for in-vivo skin tissue by combining experimental indentation results and numerical simulations. The indentation tests were used to obtain the force-indentation depth curves, while the numerical simulations were used to obtain the strain fields. The method assumes the material behaviour of specimens can be linearized in each small deformation increment, and the contact model developed by Hayes can be applied to accommodate each increment. Then, the linear elastic behaviour in each increment can be described by the elastic modulus E which were obtained using Hayes model, and the principal stresses in each increment were subsequently obtained using Hooke's law. By combining all stress fields, overall stress-strain curves can be constructed, from which the hyperelastic Ogden parameters can be obtained. A second numerical simulation of the hyperelastic indentation was then performed using the obtained Ogden parameters, allowing a comparison of the experimental and simulated relationships between force and indentation.

New aesthetic in-house 3D-printed brackets: proof of concept and fundamental mechanical properties

ObjectivesThree-dimensional (3D) printing technology is an emerging manufacturing process for many orthodontic appliances, and the aim of this study was to evaluate the mechanical properties of resin-based materials as alternatives for the in-house preparation of orthodontic brackets.Material and MethodsTwo types of 3D printed resins used for temporary (T) and permanent (P) crown fabrication were included in this study. Ten blocks from each resin were manufactured by a 3D printer and, after embedding them in acrylic resin, the samples were subjected to metallographic grinding and polishing, followed by instrumented indentation testing (IIT). Martens hardness (HM), indentation modulus (EIT), and elastic index (ηIT) were determined with a Vickers indenter recording force-indentation depth curves from each specimen. After calculating descriptive statistics, differences between material types were investigated with Wilcoxon rank sum test accounting for clustering of measurements within specimens at alpha = 5%.ResultsNo statistically significant differences in the mechanical properties of the two tested materials were seen: HM: median 279 N/mm2 (interquartile range [IQR] 275–287 N/mm2) for T and median 279 N/mm2 (IQR 270–285 N/mm2) for P (P value = 0.63); EIT: median 5548 MPa (IQR 5425–5834 MPa) for T and median 5644 (IQR 5420–5850 MPa) for P (P value = 0.84); ηIT: median 47.1% (46.0–47.7%) for T and median 46.0% (IQR 45.4–47.8%) for P (P value = 0.24).ConclusionsUnder the limitations of this study, it may be concluded that the mechanical properties of the two 3D printed resins tested are equal, and thus, no differences in their clinical performance are expected.

In-house 3D-printed aligners: effect of in vivo ageing on mechanical properties.

To investigate alterations in the mechanical properties of in-house three-dimensional (3D) printed orthodontic aligners after intraoral ageing. Sixteen 3D-printed aligners (TC-85DAC resin, Graphy, Seoul, Korea) were used for the purpose of the study, which were divided into 10 control (not used) aligners and 6 materials retrieved from 4 patients after 1-week service (retrieved group). Samples from the control group were analysed by attenuated total reflectance-Fourier-transform infrared (ATR-FTIR) spectroscopy. Samples from control/retrieved groups were embedded resin and subjected to instrumented indentation testing (IIT) to record force-indentation depth curves, calculating the following (as per ISO 14577-1, 2002 standard): Martens hardness (HM), indentation modulus (EIT), and elastic index (ηIT), and the indentation relaxation index (RIT). Differences between control and retrieved 3D-printed aligners were checked with Mann-Whitney/t-tests at an alpha = 5%. ATR-FTIR analysis showed that aligners were made of a vinyl ester-urethane material. The results of the IIT testing were: HM (control: median 91.5 N/mm2, interquartile range [IQR] 88.0-93.0/as-retrieved: median 90.5 N/mm2, IQR 89.0-93.0); EIT (control, mean 2616.3 MPa, standard deviation [SD] 107.0 MPa/retrieved, mean 2673.2 MPa, SD 149.4 MPa); ηIT (control: median 28.6%, IQR 28.2-30.9%/as-retrieved: median 29.0%, IQR 28.7-29.2%); and RIT (control: median 45.5%, IQR 43.0-47.0%/as-retrieved: median 45.1%, IQR 45.0-45.3%). No differences between as-retrieved and control aligners were found for any of the mechanical properties tested (P > 0.05 in all instances). The mechanical properties of the in-house 3D-printed aligners tested were not affected after 1 week in service period.

Simulation of interaction behavior between dislocation and graphene during nanoindentation of graphene/aluminum matrix nanocomposites

Graphene has been thought to be an ideal reinforcement material for metal matrix composite due to its superior mechanical properties and unique two-dimensional geometry. However, the deformation mechanism of graphene/aluminum matrix composite is still unclear. In this paper, molecular dynamics simulation is used to elucidate the evolution details of the dislocation microstructure and the underlying interaction behavior between dislocation and graphene during nanoindentation of the graphene/aluminum matrix composite with various graphene orientations. To this end, four different cases, i.e. the pure aluminum and the graphene/aluminum matrix composite with the graphene orientation of 90°, 45° and 0° are examined, respectively. Based on the force-indentation depth curve, the interaction behavior between dislocation and graphene and its effect on the plastic zone are analyzed. The results indicate that the graphene can act as an effective dislocation motion barrier, and the elastic deformation of graphene can occur locally along the direction of dislocation slip. Using the visualization technique of dislocation extraction algorithm, the nucleation and propagation of dislocation are investigated. The results show that the differences in interaction behavior between dislocation and graphene with various orientations affect the spreading trend of the plastic zone and the blocking strength of graphene to dislocation. For the composite with the graphene orientations of 45° and 0°, the interaction between graphene and dislocation causes the number of dislocations to increase. Additionally, the plastic zone of the composite with the graphene orientation of 45° is tangent to two symmetrical graphene sheets. For the composite with the graphene orientation of 90°, the interaction between graphene and dislocation shortens the total length of the dislocation line, and the volume shrinkage of plastic zone is most significant after indenter retraction. Here, the hardness is also calculated to quantitatively evaluate the influence of graphene orientation on the mechanical properties of graphene/aluminum matrix composite. The hardness of the composite with the graphene orientation of 45° is highest, which is due to the decrease of the volume of the plastic zone and the increase of dislocation number. The decrease of the hardness of the composite with the graphene orientation of 90° is attributed to the reduction of dislocation number in the plastic zone. However, for the composite with the graphene orientation of 0°, the interaction between graphene and dislocation results in the softening effect, because of a wide range of elastic deformation in the graphene plane. The study can provide a certain theoretical guidance for designing and preparing the high-performance graphene/metal matrix composites.

Influence of Plasticity and Friction on the Contact Mechanics of Auxetic Materials

AbstractContact interactions play an important role in the tribological behavior of engineering materials. This paper develops a finite element model to investigate the contact mechanics and stress distribution of auxetic materials, i.e., materials with negative Poisson’s ratio. The model results are compared with numerical and mathematical models for isotropic auxetic polymers. The indentation of auxetic materials is analyzed for the effects of friction, plasticity and allowing separation after contact with a spherical indenter using a commercial software, abaqus. The results are discussed in terms of stress profiles, force-indentation depth curves, plasticity, friction, internal energy, compressibility, sink-in, and the pile-up of material. It is concluded that for purely elastic contact, the indentation resistance increases for auxetic materials and the inclusion of friction shifts subsurface stresses closer to the surface. However, the introduction of plasticity negates the improvement of increased indentation resistance. The pile-up of material around the indent reduces for auxetic materials which makes them more suitable for rolling/sliding contacts. The internal strain energy decreases for purely elastic contact and increases for an elastic/plastic contact.

Size Effects of Hardness and Strain Rate Sensitivity in Amorphous Silicon Measured by Nanoindentation

In this work, dynamic mechanical properties of amorphous silicon and scale effects were investigated by the means of nanoindentation. An amorphous silicon sample was prepared by plasma-enhanced chemical vapor deposition (PECVD). Next, two sets of the samples were investigated: as-deposited and annealed in 500 °C for 1 hour. A three-sided pyramidal diamond Berkovich’s indenter was used for the nanoindentation tests. In order to determine the strain rate sensitivity (SRS), indentations with different loading rates were performed: 0.1, 1, 10, 100 mN/min. Size effects were studied by application of maximum indentation loads in the range from 1 up to 5 mN (penetrating up to approximately one-third of the amorphous layer). The value of hardness was determined by the Oliver–Pharr method. An increase of hardness with decrease of the indentation depth was observed for both samples. Furthermore, the significant dependence of hardness on the strain rate has been reported. Finally, for the annealed samples at low strain rates a characteristic “elbow” during unloading was observed on the force-indentation depth curves. It could be attributed to the transformation of (β-Sn)-Si to the PI (pressure-induced) a-Si end phase.

Quantifying Mechanical Properties of Automotive Steels with Deep Learning Based Computer Vision Algorithms

This paper demonstrates that the instrumented indentation test (IIT), together with a trained artificial neural network (ANN), has the capability to characterize the mechanical properties of the local parts of a welded steel structure such as a weld nugget or heat affected zone. Aside from force-indentation depth curves generated from the IIT, the profile of the indented surface deformed after the indentation test also has a strong correlation with the materials’ plastic behavior. The profile of the indented surface was used as the training dataset to design an ANN to determine the material parameters of the welded zones. The deformation of the indented surface in three dimensions shown in images were analyzed with the computer vision algorithms and the obtained data were employed to train the ANN for the characterization of the mechanical properties. Moreover, this method was applied to the images taken with a simple light microscope from the surface of a specimen. Therefore, it is possible to quantify the mechanical properties of the automotive steels with the four independent methods: (1) force-indentation depth curve; (2) profile of the indented surface; (3) analyzing of the 3D-measurement image; and (4) evaluation of the images taken by a simple light microscope. The results show that there is a very good agreement between the material parameters obtained from the trained ANN and the experimental uniaxial tensile test. The results present that the mechanical properties of an unknown steel can be determined by only analyzing the images taken from its surface after pushing a simple indenter into its surface.

Effect of Pyrolysis Temperature on the Mechanical Response in Partially Pyrolysed Polysiloxanes

The pyrolysis process of polysiloxane resin conducted in the temperature range 400 – 700 °C results in hybrid materials owning some polymeric (thermosetting) behaviour. A certain level of elastic recovery and/or viscoelastic flow showed at various steps of pyrolytic transformation was monitored using the instrumented Vickers hardness method. Determined indentation force-indentation depth curves reflect the mechanical response and the level of the transformation; however, the relaxation behaviour is not covered by this method fully. An extensive indentation relaxation was revealed in the material partially pyrolysed at 400 °C, about 16 % and 8 % when the HV 0.1 and the HV 0.2 loading were applied, respectively. Materials pyrolysed from 500 to 650 °C which exhibited the indentation relaxation below 1 % and the mostly elastic response on the loading were observed. Above the pyrolysis temperature of 600 °C a rapid onset of mechanical properties, namely indentation elastic modulus and hardness, was observed. The short-term indentation relaxation was evaluated via the indentation force relaxation method in the regime of constant indentation depth obtained at the moment of reaching an initial force of 0.981 N or 1.962 N. The obtained indentation force relaxation curves were analysed on the basis of a logarithmic function. The significant effect of the pyrolysis temperature as well as the influence of loaded volume was described.

Nanoindentation and deformation behaviors of silicon covered with amorphous SiO2: a molecular dynamic study.

A fundamental understanding of the mechanical properties and deformation behaviors of surface modified silicon during chemical mechanical polishing (CMP) processes is difficult to obtain at the nanometer scale. In this research, MD simulations of monocrystalline silicon covered with an amorphous SiO2 film with different thickness are implemented by nanoindentation, and it is found that both the indentation modulus and hardness increase with the growing indentation depth owning to the strongly silicon substrate effect. At the same indentation depth, the indentation modulus decreases shapely with the increase of film thickness because of less substrate influence, while the hardness agrees well with the trend of modulus at shallow depth but mismatches at larger indentation depth. The observed SiO2 film deformation consists of densification and thinning along indentation direction and extension in the deformed area due to the rotation and deformation of massive SiO4 tetrahedra. The SiO2 film plays an important role in the onset and development of silicon phase transformation. The thinner the SiO2 film is, the earlier the silicon phase transformation takes place. So the numbers of phase transformation atoms increase with the decrease of SiO2 film thickness at the same indentation depth. It is suggested that the thicker film should be better during CMP process for higher material removal rate and less defects within silicon substrate.

Modeling and experimental verification for non-equibiaxial residual stress evaluated by Knoop indentations

Surface residual stress is usually characterized by two parameters; (1) magnitude and (2) direction of two principal residual stresses. We propose a novel way to evaluate these parameters by instrumented indentation testing (IIT) using a Knoop indenter, which has two-fold symmetry. Non-equibiaxial surface stress causes a shift from residual stress in the force-indentation depth curve of IIT that depends on the Knoop indentation in-plane angle between residual stress and long diagonal of Knoop indenter. We develop a theoretical model to evaluate surface residual stress using only experimental parameters obtained by four Knoop IITs at 45° rotated angles, by introducing mathematical definition of conversion factor, a, which ratio of normal and parallel conversion factors was known as constants (~0.34) on previous studies. We verify this model by Knoop IITs on four metallic cruciform samples in which the surface residual stress is controlled by bending. Experimental results of principal stress and direction show good agreements with applied stress and directions.

Do the mechanical and chemical properties of InvisalignTM appliances change after use? A retrieval analysis.

To investigate the mechanical and chemical alterations of Invisalign appliances after intraoral aging. Samples of Invisalign appliances (Align Technology, San Jose, California, USA) were collected following routine treatment for a mean period of 44±15 days (group INV), whereas unused aligners of the same brand were used as reference (group REF). A small sample from the central incisors region was cut from each appliance and the buccal surface was analysed by attenuated total reflectance-Fourier transform infrared (ATR-FTIR) spectroscopy (n = 5). Then the appliances were cut (n = 25) and embedded in acrylic resin, ground/polished in a grinding polishing machine, and the prepared surfaces were subjected to Instrumented Indentation Testing under 4.9 N load. Force-indentation depth curves were recorded for each group and the following parameters were calculated according to ISO 14577-1; 2002 specification: indentation modulus (E IT), elastic to total work ratio also known as elastic index (ηIT), Martens Hardness (HM), and indentation creep (C IT) The mean values of the mechanical properties were statistically analysed by unpaired t-test (a = 0.05). ATR-FTIR analysis confirmed the urethane based structure of the appliances, without important chemical differences attributed to the aging process. INV group showed significantly lower E IT (REF: 2466±20, INV: 2216±168MPa), HM (REF: 119±1, INV: 110±6 N mm-2) and higher ηIT (REF: 40.0±0.3, INV: 41.5±1.2%), and C IT (REF: 3.7±0.2 INV: 4.0±0.1%). The increase in ηIT indicates that INV is a more brittle than REF, whereas the increase in C IT, a decrease in creep resistance. Despite the lack of detectable chemical changes, intraoral aging adversely affected the mechanical properties of the Invisalign appliance.

Influences of evaluation methods and testing load on microhardness and Young's modulus of ZTA and ATZ ceramics

In this work, microindentation tests under different conditions were performed to determine the influence of indentation load on Young's modulus and microhardness of ZrO2 reinforced with Al2O3 particles (ATZ) and Al2O3 reinforced with ZrO2 particles (ZTA).Microhardness of ATZ and ZTA materials was measured using traditional Vickers and instrumented microhardness methods at 500, 1000, 1500 and 2000mN loads. As for the instrumented method, Vickers microhardness was calculated from the force-indentation depth curves by analyzing the unloading segments, according to the Oliver–Pharr method. In this way the possible differences between the two methods were calculated. Furthermore, Young's modulus at each load was calculated using the instrumental method.The main differences between the two methods were analyzed, and the influence of the load on the definition of Young's modulus in the case of the instrumental method was studied. The results indicated an indentation load effect for both materials, as hardness and Young's modulus increase by decreasing the indentation load.

Instrumented Indentation Testing on Uniaxially Prestressed Steel Samples

Instrumented indentation testing has been carried out on steel samples subjected to uniaxial loading. It is distinguished between purely elastic as well as elasto-plastic loading up to plastic strains of 3%. The experimental approach allows the combination of local in-situ residual stress analyses by means of X-ray diffraction and the subsequent realisation of instrumented indentation testing for the same material volumes beforehand irradiated by the X-rays. The aim of the investigations was to explore a potential correlation between the imposed macroscopic stresses and the characteristic values of instrumented indentation testing evaluated from the measured force-indentation depth curves according to the standard ISO EN 14577. The studies illustrate that results of depth sensing indentation testing have to be handled with care for prestressed material states. The effect of mechanical stresses on the results of instrumented indentation testing is not stringently limited on the hardness measures alone. Other indentation parameters like e.g. the indentation modulus EIT or the elastic part of the indentation work η IT are likewise affected by the prestresses, whereas the impact is in the order of magnitude that it has to be taken into account during interpretation of indentation readings.

Hardness measured with traditional Vickers and Martens hardness methods

Objective To determine the differences, if any, between hardness measured with traditional Vickers and Martens hardness test methods on denture teeth under 2, 10 and 50 N loads. Method Hardness of acrylic resin (VIV), composite resin (ORT) and porcelain (POR) denture tooth materials was measured using a traditional Vickers hardness (HV) method and Martens hardness (HM) method at 2, 10 and 50 N test loads. Vickers hardness was also calculated from the force-indentation depth curves (HVfid) that were recorded during Martens hardness. Indentation creep of the three test materials was also determined during Martens hardness testing. Results HM values were the same irrespective of the test force used. However, HV values were different for the three test forces. ANOVA using Tukey's test of the HM data showed that the hardness of POR was significantly higher than VIV or ORT ( P < 0.001). Moreover, ORT had a significantly higher hardness than VIV ( P < 0.001). The statistical analysis of HVfid data showed similar results. ANOVA of the HV data showed the hardness of VIV to be significantly higher than ORT ( P < 0.001) under 2, 10 and 50 N test load. The HV values for POR under 2 and 10 N test load could not be calculated because of inability to measure the indentation diagonals. Under the 50 N load, the hardness of POR was significantly higher than VIV and ORT. POR had a significantly lower creep value than any other material tested while VIV showed a statistically significantly higher creep than ORT. Significance This study confirms that the visco-elastic recovery of the materials has a very significant effect on the outcome of the hardness tests of denture teeth and the Martens hardness test method has obvious advantages when testing dental materials.

Effect of Applied and Residual Stresses on the Analysis of Mechanical Properties by Means of Instrumented Indentation Techniques

Various methods have been proposed in recent years for the determination of mechanical properties of a material by using instrumented indentation testing. These load and depth sensing indentation techniques imply the measurement of a characteristic load-indentation depth curve by the aid of which numerous materials properties can be extracted. On the other hand in many publications the effect of applied or residual stresses on the results of hardness readings is investigated. Methods are proposed to estimate applied or residual stresses by means of instrumented indentation testing. Based on this obvious inconsistency between these procedures on the use of information of instrumented hardness testing the influence of residual stresses as well as applied stresses on continuous microhardness readings is systematically investigated for steel samples. Experimental investigations were supplemented by finite element simulations of ball indentation tests on equi-biaxially prestressed materials states. These simulations show that the registered force-indentation depth curves as well as the geometry of the indentations are affected by loading and residual stresses in a characteristic way. For hardness values changes of up to 35% are determined with reference to the unstressed initial state.

Determination of elastic and plastic material properties using indentation: Development of method and application to a thin surface coating

The objective of this work is to develop a combined computational–experimental indentation based method to determine the elastic–plastic stress–strain behaviour of a material. Both ultra-micro and nano-indentation is considered and a power-law material strain hardening behaviour is assumed. This paper reports on the results obtained for indentation into AISI 01 heat-treated steel and a MoST™ coating on an AISI 01 steel substrate. In developing the method, the percentage plastic work (PPW) at maximum indentation load and the plastic zone size surrounding an indentation are investigated to ascertain if either can be used in conjunction with a force–indentation depth curve in determining the material properties. It is shown that it is possible to identify the material properties using the plastic zone size but not the PPW. The method is validated experimentally for the AISI 01 steel. It is then used to determine the material properties of the MoST™ coating.

Elastic-Plastic Characterisation of Aluminium Bearing Alloys

A method is proposed to determine the elasto-plastic properties of a thin aluminium alloy lining of a bearing system from micro-indentation tests. This indentation process was modelled using an axi-symmetric FE model which was validated against experimental force-indentation curves from materials with known elasto-plastic properties. A fuller database of force-indentation curves has been generated by running the FE model with a range of elasto-plastic properties. This larger database has been used in adaptive numerical modelling to derive a generic model for the indent size as a function of load, elastic limit, yield strength and strain hardening coefficient and exponent in aluminium alloys. The adaptive numerical model was subsequently used to interpolate between the time-intensive FE results. Based on iterations of the most appropriate adaptive model, the elastic limit, yield strength and strain hardening exponent of a bearing alloy have been determined from the experimental micro hardness force-indentation depth curves for the same material.

Comment on : Energetically evaluated load-indentation measurements of different classes of material by b. Rother

It is shown that the energetically evaluated load-indentation measurement procedure introduced by Rother and Dietrich is equivalent to the analysis of the force-indentation depth-curve by means of the well known Bernhardt formula. A disadvantage of the proposed “differential load feed” (DLF) procedure is that differentation enlarges the scatter of the experimental curves. Deviations of the indenter tip from its ideal shape and surface roughness also influence the experimental results in the case of DLF analysis in a manner as one observes for these methods usually used to analyse force-indentation depth-curves.