Interactive effect of indenter size and specimen thickness in Hertzian indentation test

Indentation size effect in nanohardness

Indentation tests have been used to measuring the strength and hardness of materials. Moreover, micro and nanoindentation have become major tools for investigating the micromechanical properties of small scale volumes. However, it is well-known that the micro and nanoindentation hardness of materials shows the strong size effect. But the classical continuum plasticity can't predict these size effects in micro/nano scale, since the constitutive equation of the classical mechanics doesn't include the internal length as a parameter for the deformation. In this paper, modified strain gradient theory is proposed based on the nonhomogeneity of polycrystalline metallic materials. When the grains of crystalline metals deform, overlaps and voids appear at the grain boundary. These overlaps and voids can be corrected by the GNDs. By taking into account the nonhomogeneity of polycrystalline materials, the density of the GNDs due to the deformation is calculated. Consideration of the GNDs on the grain boundary gives a relationship between the size effect and the hardness. This relationship can explain the indentation size effects in micro/nano scale. Using the proposed model, analysis of the effect of indent size and grain size under the nanoindentation test of polycrystalline materials is carried out.

Indentation size effect: an improved mechanistic model incorporating surface undulation and indenter tip irregularity

Effects of microstructure and specimen thickness on the fatigue crack closure in Al-Li 8090 alloy

This research investigates deformation behavior of polystyrene (PS) as a thermoplastic resist material for the thermal nanoimprint lithography (T-NIL) process. Molecular dynamics modeling was conducted on a PS substrate with dimensions 58 × 65 × 61 Å that was imprinted with a rigid, spherical indenter. The effect of indenter size, force, and imprinting duration were evaluated in terms of indentation depth, penetration depth, recovery depth, and recovery percentage of the polymer. The results show that the largest indenter, regardless of force, has the most significant impact on deformation behavior. The 40 Å indenter with a 1 µN of force caused the surface molecules to descend to the lowest point compared to the other indenters. An increase in indenter size resulted in higher penetration depth, recovery depth, and recovery percentage. Higher durations of imprint cycle (400 fs) resulted in plastic deformation of the PS material with minimal recovery (4 Å). The results of this research lay the foundation for explaining the effect of several T-NIL process parameters on virgin PS thermoplastic resist material.

Indenter size effect on the reversible incipient plasticity of Al (001) surface is studied by quasicontinuum simulations. Results show that the incipient plasticity under small indenter, the radius of which is less than ten nanometers, is dominated by a simple planar fault defect that can be fully removed after withdrawal of the indenter; otherwise, irreversible incipient plastic deformation driven by a complex dislocation activity is preferred, and the debris of deformation twins, dislocations, and stacking fault ribbons still remain beneath the surface when the indenter has been completely retracted. Based on stress distributions calculated at an atomic level, the reason why the dislocation burst instead of a simple fault ribbon is observed under a large indenter is the release of the intensely accumulated shear stress. Finally, the critical load analysis implies that there exists a reversible-irreversible transition of incipient plasticity induced by indenter size. Our findings provide a further insight into the incipient surface plasticity of face-centered-cubic metals in nano-sized contact issues.

Several attempts have been made over recent years to understand indentation size effect (ISE). The theoretical models, based essentially on strain gradient plasticity theories, such as the Nix–Gao model, predict that ISE is caused by an increase in the density of dislocations as the indentation size decreases. Molecular dynamics simulation results tend to confirm this fact, but the truth is that very few experimental studies exist on the direct observation of how dislocations are generated and accommodated in the vicinity of nanoindentations. In this study, using a Ni transmission electron microscopy thin foil as model material, we show that when the material is submitted to atomic force microscopy-based nanoindentation a high dislocation density zone is generated at the centre of the indented region, and that prismatic loop and helical dislocations are emitted sidewards from the central region of the nanoindentation along the ⟨1 1 0⟩ directions. Moreover, we show that the dislocation array formed during the nanoindentation process is far from the ideal model proposed by Nix and Gao, based on load axi-centred dislocation loops. With this study we aim at contributing to a better comprehension of ISE mechanisms in ductile metals.

The Knoop microhardness anisotropy profile was determined for the basal plane of a Czochralski grown alumina single crystal for indentation test loads from 100 through 1000 g. Microhardness maxima occur at low indentation test loads for the long axis of the Knoop indenter parallel to the 〈2[Onemacr][Onemacr]0〉. Minima exist for the long axis parallel to the 〈10[Onemacr]0〉. This low indentation test load profile is attributed to slip on the primary slip system, the (0001)〈[Onemacr][Onemacr]20〉, as previously noted by Brookes and co‐workers. The degree of the microhardness anisotropy decreases for higher indentation test loads. This results from the activation of multiple slip systems to accommodate the greater amounts of plastic flow required by the larger indentation sizes. The microhardness profile becomes more uniform with increasing indentation test load until the Knoop microhardness approaches a test‐load‐independent, orientation‐independent microhardness of 1167 ± 34 kg/mm2. The indentation size effect (ISE) was further investigated through lubricated indentation hardness measurements. Lubrication of the test specimen surface significantly reduces the ISE. Results indicate that friction between the test specimen surface and the indenter facets is a major portion of the ISE.

The increasing hardness with decreasing penetration depth, referred to as indentation size effect (ISE) was previously investigated experimentally and theoretically by many researchers, however the mechanisms responsible for ISE are still being discussed. Generally, ISE is related to the density of geometrically necessary dislocation stored within a small volume beneath the indenter tip. In this study ISE is investigated experimentally in a single crystal copper using spherical indenter tips of different radii. Some new aspects of ISE are shown: a qualitative change of shape of residual impression (pile-up/sink-in pattern) when tip radius or load is modified, an increase of maximum pop-in load with decrease of tip radius as well as the well-known increase of hardness when tip radius decreases are analyzed. As we observe a difference of the residual imprint morphology which depends on tip radius and load, we apply two methods of hardness estimation: true hardness and nominal hardness. The former is determined on the basis of direct measurement of the contact area while accounting for a specific pile-up pattern, while the latter is determined by measuring the contact area using residual penetration depth. We show that hardness–tip radius relationship has a linear form for the nominal hardness and bilinear form for the true hardness.

The measuring method of CTOD, the effects of notch position, heat treatment, specimen thickness and test temperature on CTOD and the CTOD design curves are examined using a 200 mm thick, mild steel plate and its welded joint. The CTOD measuring method of BS5762 is confirmed. The effect of specimen thickness on CTOD is established. The CTOD design curve which significantly depends on the gage length for measuring strain must be established by taking into account actual conditions such as variance of strength as in welded joint. INTRODUCTION The development of tough steels and sound design practice have led to the safety of offshore structures. The use of thicker plates and the increasingly severe operating and environmental conditions, however, require more intensive effort for safety assurance. The use of fracture mechanics is one of such efforts. Though the linear elastic fracture mechanics is clearly established and its application is easy, it cannot be applied in general to offshore structures because the materials used are tough. The non-linear elastic-plastic fracture mechanics, therefore, is widely used for designing and safety evaluation of offshore structures. The most typical fracture parameter is crack tip opening displacement (CTOD). The CTOD concept, however, is based on the experimental results obtained with materials as thick as up to 50 mm in general. Since heavier section steel plates and their welded joints are used in construction of offshore structures, the CTOD concept must be reexamined from the view points of measurement and application. The present paper examines the measuring method of CTOD, the effect of notch position, heat treatment, specimen thickness and test temperature on CTOD and the CTOD design curve using a 200 mm thick, mild steel plate and its narrow gapped submerged arc welded joint. EXPERIMENTAL PROCEDURE MATERIALS TESTED The materials tested were a 200 mm thick steel plate (BS4360-43E) and its narrow gapped submerged arc welded joint. The chemical composition and mechanical properties of the steel are listed in Table 1. The welding conditions are listed in Table 2.Table 3 shows the chemical composition and mechanical properties of weld metal. FRACTURE TOUGHNESS TEST Figure 1 shows the dimensions of three point bend specimens and test conditions. The specimens with reduced thickness were cut from the mid thickness portion of the original plate and its welded joint. The test and measurement of CTOD were carried out according to BS5762[1]. Figure 2 illustrates the procedure for determining rotational factor for three point bend test. The rotational factor was determined geometrically using five clip gages mounted on each specimen. The wide plate tensile test was performed with four specimens whose geometries are shown in Fig. 3. One specimen was of base metal with surface notch. Three specimens were notched in fusion line; one with surface notch and two with through thickness notches.

The Adductor Sling Technique for Pediatric Medial Patellofemoral Ligament Reconstruction Better Resists Dislocation Loads When Compared With Adductor Transfer at Time Zero in a Cadaveric Model

The aim of the submitted work is to study the relationship between the local deformation and the indentation size effect (ISE). A local value of reduction of the area (Z) was used as the measure of the deformation. Applied loads in the micro-hardness test ranged between 0.09807 to 0.9807 N. The micro-hardness was measured on the cross section in the longitudinal axis of the fractured sample after the uniaxial tension test. The material of the sample was 99.5% aluminium. The influence of both load and deformation on the ISE was evaluated by the analysis of variance (ANOVA). The influence of the load was also evaluated by Meyer’s index n, PSR method, and Hays–Kendall approach. The influence of both factors on the measured value of micro-hardness and therefore on the ISE is statistically significant. The ISE is normal in the areas with high deformation, on the contrary, in areas with low deformation, it has a “reverse” character. The difference between load independent “true hardness” and measured micro-hardness HV0.05 increases with increasing deformation.

Constant load indentation creep and load relaxation tests were performed on several FCC Al, Ag, and Ni metals that exhibit indentation size effect (ISE) to examine the coupled relationship between the activation volume V* at specific loads, the dislocation density ρ, and the dislocation velocity (v) from kinetics-based perspective. The influence of the ISE on the dislocation velocity and the activation volume is thoroughly examined using the two independent indentation creep and load relaxation experiments. This study is carried out based on the general experimental and theoretical hypothesis that the ISE is driven by a dislocation mechanism, specifically the increase in the geometrically necessary dislocation density at shallow depth of indentation due to the presence of a large strain gradient. Geometrically necessary dislocations dominate the material’s propensity to work harden when their density exceeds the density of statistically stored dislocations and are primarily considered responsible for the size effects observed in indentation. Based on the preestablished bilinear behavior and the decrease in the activation volume with hardening due to dislocation–dislocation interaction in indentation creep experiments by Elmustafa and Stone, 2003, we demonstrate that the dislocation velocity exhibits a bilinear behavior when plotted vs hardness using the Orowan’s relation. Ag and Ni distinctively depict a bilinear behavior in the dislocation velocity with hardness, whereas Al exhibited a rather linear behavior. This can be explained by the fact that aluminum’s work-hardening rate is higher due to the increase in the rate and intensity of cross-slip and dislocation climbing.

BackgroundCeramic veneers are a common option for enhancing dental aesthetics by improving tooth form, shade, and function. Preparation design is considered a critical factor in the success of dental veneers, as it influences the failure load and fatigue survival of posterior minimally invasive ceramic veneer restorations. The purpose of the study is to compare the failure load and mode after fatigue among three types of veneer preparation designs for restoring premolars.Methods64 human premolars were equally divided into four groups. Group 1 had a buccal preparation depth of 0.7 mm; Group 2 had an additional reduction of the buccal cusp; Group 3 had a mesio-occluso-distal box with dimensions of 2 mm wide and 3 mm deep. The remaining sound teeth served as the control group. Monolithic lithium disilicate restorations were cemented onto the prepared teeth with adhesive cement and then exposed to dynamic fatigue and thermocycling. Each specimen underwent a single load-to-failure test, and the discrepancy in failure load before and after fatigue was computed.ResultsNo significant differences in initial failure load were observed among the four groups evaluated (p <.075). A significant drop in failure load was observed in all groups after fatigue (P = 0.012). The failure loads of Groups I and II were significantly lower than those of Group III and the control (P < 0.05).” Nevertheless, after fatigue, statistically significant differences were detected (p <.013) as fatigue caused a substantial drop in failure load among all groups.ConclusionsWithin the limitations of this study, fatigue significantly reduced failure load in all groups. Veneer preparation design influenced post-fatigue strength, with more conservative designs showing better resistance. These findings underscore the impact of fatigue on structural integrity and the importance of tooth preparation design on fatigue resilience.

Four-point bending behaviors of CFRP trapezoidal corrugated sandwich plates