Indentation Load-depth Curves Research Articles

A mechanistic approach to extract the mechanical properties of individual constituents in plasma-sprayed metal matrix composite coatings

Abstract A mechanistic approach to determine the in-situ properties of individual constituents in a plasma sprayed metal matrix composite (MMC) coating was proposed. The approach was based on micro-indentation and inverse analysis techniques. Utilising the indentation data obtained from the micro-indentation experiments, elastic moduli of each constituent were calculated using a well-established method whereas yield strength and hardening exponent were extracted using the inverse procedure based on finite element analysis. Finite element results gave a satisfactory agreement between the numerically simulated and the measured indentation load–depth curves. Further studies using three dimensional finite element analyses of Vickers indentation on the MMC coating based on its actual microstructure also showed that the indentation behaviour of the MMC coatings is strongly dependent on its morphology, volume fraction, size and distribution of the reinforcing phase.

A Method for Estimating Uncertainty of Indentation Tensile Properties in Instrumented Indentation Test

The instrumented indentation test, which measures indentation tensile properties, has attracted interest recently because this test can replace uniaxial tensile test. An international standard for instrumented indentation test has been recently legislated. However, the uncertainty of the indentation tensile properties has never been estimated. The indentation tensile properties cannot be obtained directly from experimental raw data as can the Brinell hardness, which makes estimation of the uncertainty difficult. The simplifying uncertainty estimation model for the indentation tensile properties proposed here overcomes this problem. Though the influence quantities are generally defined by experimental variances when estimating uncertainty, here they are obtained by calculation from indentation load-depth curves. This model was verified by round-robin test with several institutions. The average uncertainties were estimated as 18.9% and 9.8% for the indentation yield strength and indentation tensile strength, respectively. The values were independent of the materials’ mechanical properties but varied with environmental conditions such as experimental instruments and operators. The uncertainties for the indentation yield and tensile strengths were greater than those for the uniaxial tensile test. These larger uncertainties were caused by measuring local properties in the instrumented indentation test. The two tests had the same tendency to have smaller uncertainties for tensile strength than yield strength. These results suggest that the simplified model can be used to estimate the uncertainty in indentation tensile properties.

Material characterization by dual sharp indenters

In a recent study, Le [Le, M.-Q., 2008. A computational study on the instrumented sharp indentations with dual indenters. International Journal of Solids and Structures, 45 (10), 2818–2835.] demonstrated that the yield strength Y can be replaced by the loading curvature C and hence the reduced elastic modulus-loading curvature ratio E ∗ / C and strain hardening exponent n can be used to govern characteristic parameters of indentation load–depth curves. Extending Le’s approach and regarding dimensional analysis, it is found that C / Y and E ∗ / Y can be used to investigate fundamental issues in instrumented sharp indentation. Based on extensive finite element analysis, a set of dimensionless functions are constructed for cone indenters of half included angles of 60° and 70.3°. Dimensionless relationships with respect to dual indenters are further explored. Several features of hardness are also considered. An inverse analysis procedure is suggested to estimate material properties, giving good inverse results for experimental data from the literature and representative materials. Sensitivity of inverse solution are studied and discussed. The results show that the proposed dual indenter method is quite robust and can be applied to a wide range of materials.

Numerical analysis of plastic deformation evolution into metallic materials during spherical indentation process

The present paper deals with the plastic deformation process into metallic materials occurring in the subindenter region during the loading cycle of spherical indentation test. Load–indentation-depth curve and plastic strains field evolution in the region beneath the indenter are examined using finite element analysis (FEA). The FE model was set up and validated by comparison with experimental spherical indentations carried out on two different materials (Al6082-T6, AISI H13) under four different friction conditions, corresponding to friction coefficients equal to 0.0, 0.1, 0.3, and 0.5. It is confirmed that friction effects on load–indentation-depth curves are negligible for the investigated penetration depths, whereas the plastic deformation process is affected by the contact conditions. The investigation shows that, although the L–h curve is not affected by the contact conditions up to medium values of the penetration depth, remarkable effects are produced in the overall plastic core under the indenter. A strong correlation between plastic strains field and friction coefficient is especially observed at low values of this parameter, whereas a saturation of the phenomena is found for medium-high values of the friction coefficient.

Comparison between Berkovich, Vickers and conical indentation tests: A three-dimensional numerical simulation study

Three-dimensional numerical simulations of Berkovich, Vickers and conical indenter hardness tests were carried out to investigate the influence of indenter geometry on indentation test results of bulk and composite film/substrate materials. The strain distributions obtained from the three indenters tested were studied, in order to clarify the differences in the load–indentation depth curves and hardness values of both types of materials. For bulk materials, the differentiation between the results obtained with the three indenters is material sensitive. The indenter geometry shape factor, β, for evaluating Young’s modulus for each indenter, was also estimated. Depending on the indenter geometry, distinct mechanical behaviours are observed for composite materials, which are related to the size of the indentation region in the film. The indentation depth at which the substrate starts to deform plastically is sensitive to indenter geometry.

Safety assessment based on mapping of degraded mechanical properties of materials for power plant pipeline using instrumented indentation technique

The remaining life prediction of those is accomplished by accelerated degradation tests such as creep testing. However, creep testing is both time-consuming and expensive and hence impossible to apply under industrial conditions, where prompt management and analysis are necessary. While residual lifetime predictions and safety assessments of power plant facilities are made using standard mechanical testing methods such as uni-axial tensile and fracture mechanics tests. However, these tests cannot be applied to in-service structure components because of their destructive nature. A nondestructive instrumented indentation technique is thus attractive for investigating the mechanical properties of in-service systems. This technique can measure flow properties by analyzing indentation load-depth curves reflecting the deformation behavior of the material beneath the rigid spherical indenter. In this study, heat treatment was used to produce degraded samples of X20CrMo12.1V and SA-213 T23, materials widely used in power plant pipelines, and their mechanical properties versus degree of degradation were evaluated by instrumented indentation. We assess the degradation of mechanical properties by microstructural analysis and discuss the possibility of appraising the safety of power plant facilities by in-situ monitoring of mechanical properties using instrumented indentation testing.

Application of Instrumented Indentation Technique to Evaluate Residual Stress and Stress Directionality

The instrumented indentation technique (IIT) is a powerful method for evaluating mechanical properties of materials such as elastic modulus, tensile strength, fracture toughness and residual stress. Especially, IIT is a promising alternative to conventional methods of residual stress measurement such as hole drilling, saw cutting, X-ray/neutron diffraction, and ultrasonic methods because of its various advantages of nondestructive specimen preparation, easy process, characterization of material properties on local scales and measurement of in-service structures. Evaluation of residual stress using IIT is based on the key concepts that the deviatoric-stress part of the residual stress affects the indentation load-depth curve and that the quantitative residual stress in a target region can be evaluated by analyzing the difference between the residual stress-induced indentation curve and residual stress-free curve. To verify the applicability of the suggested technique, indentation tests were performed on the welded zone.

A computational study on the instrumented sharp indentations with dual indenters

Finite element analysis was performed to investigate the indentation response of elasto-plastic solids for conical indenters of half included angles of 60° and 70.3°. The interdependence indentation parameters resulting from a single indentation load–depth curve is considered. Regarding dimensional analysis, several dimensionless relationships are constructed as functions of the reduced elastic modulus-loading curvature ratio E ∗/ C and the strain hardening exponent n. Further, the duality between corresponding parameters with dual indenters is explored. Finally, a new method based on dual indenters is proposed to extract the strain hardening exponent and the reduced elastic modulus of an indented material. The accuracy of this method is verified and discussed with experimental data from the literature and representative materials.

An experimental method to determine the contact radius changes during a spherical instrumented indentation

An experimental method to determine contact radius changes during a spherical instrumented indentation test is proposed in this paper. This method is based on the Hertz theory and only depends on the elastic properties of both the indenter and the sample. The programming of several loading, unloading and reloading cycles has allowed the determination of the unloading stiffness changes and consequently the contact radius changes. Numerical results have shown that the proposed method is sensitive to the piling-up or sinking-in. From the contact radius changes we have proposed a new procedure in order to obtain the real indentation load–depth curve from the measured curve. An experimental study has allowed us to validate our procedure during the beginning of the unloading cycle.

A New Method for Nondestructive Evaluation of Mechanical Properties Using Instrumented Indentation Technique

The development of the instrumented indentation test (IIT), which gives accurate measurements of the continuous variation in indentation load as a function of depth, has paved the way to assessing tensile properties and residual stress in addition to hardness by analyzing the indentation load-depth curve. In this study, analytic models and procedures are presented for evaluating tensile flow properties and residual stress states using IIT. Tensile properties were obtained by defining representative stress and strain beneath the spherical indenter. The evaluation of residual stress is based on the concepts that the deviatoric stress part of the residual stress affects the indentation load-depth curve, and that analyzing the difference between the residual stressinduced indentation curve and the residual stress-free curve permits evaluation of the quantitative residual stress in a target region.

A nanoindentation analysis of the influence of lattice mismatch on some wide band gap semiconductor films

Abstract Nanoindentation studies are carried out on epitaxial ZnO and GaN thin films on (0 0 0 1) sapphire and silicon substrates, respectively. A single discontinuity (‘pop-in’) in the load–indentation depth curve is observed for ZnO and GaN films at a specific depths of 13–16 and 23–26 nm, respectively. The physical mechanism responsible for the ‘pop-in’ event in these epitaxial films may be due to the interaction behavior of the indenter tip with the pre-existing threading dislocations present in the films during mechanical deformation. It is observed that the ‘pop-in’ depth is dependent on lattice mismatch of the epitaxial thin film with the substrate, the higher the lattice mismatch the shallower the critical ‘pop-in’ depth.

Residual Stress Estimation with Identification of Stress Directionality Using Instrumented Indentation Technique

The instrumented indentation technique (IIT) has recently attracted significant research interest because it is nondestructive and easy to perform, and can characterize materials on local scales. Residual stress can be determined by analyzing the indentation load-depth curve from IIT. However, this technique using a symmetric indenter is limited to an equibiaxial residual stress state. In this study, we determine the directionality of the non-equibiaxial residual stress by using the Knoop indentation technique. Different indentation load-depth curves are obtained at nonequibiaxial residual stresses depending on the Knoop indentation direction. A model for Knoop indentation was developed through experiments and theoretical analysis.

Stress exponent investigation of β-Sn single crystal by depth-sensing indentation tests

Depth-Sensing Indentation tests with different loading rates were performed on β-Sn single crystal. It was found that variations in indentation load–depth curves were significantly related to loading rates. The creep penetration depths increased with increasing loading rates, although the maximum load and holding time used were the same. Higher loading rates caused larger creep deformation at the same hold time (300 s), as well as larger hardness value. Creep indentation hardness, H, defined from the concept of “ work of indentation” varied with the volume strain occurring during the creep hold time, which is a measure of creep strain rate ε ˙ . Thus, strain rate sensitivity n of the indented material was determined from ln H vs. ln ε ˙ curve. Our results revealed that hardness was linearly dependent on strain rate.

Spherical indentation into elastoplastic materials: Indentation-response based definitions of the representative strain

In the development of a systematic method to determine the mechanical properties of materials using depth-sensing instrumented indentation tests, a key issue is to find the connection between the indentation response and the properties of the indented material. For spherical indentation into power law engineering materials, we showed that this problem can be solved by using the concept of the representative strain. In the present research, using finite element analysis based on the incremental plasticity theory and large deformation formulations, we proposed four indentation-response based definitions of the representative strain. Each of them leads to a simple and explicit expression of the relationship between the material properties (i.e., representative stresses, or reduced modulus and representative stresses) and the directly measurable quantities given by the spherical indentation loading–unloading curves. In addition, the effect of friction on the indentation load–depth curve is further investigated. Based on the results reported in this work, a number of novel approaches to identify the mechanical properties of elastoplastic materials using spherical indentation tests have been established. Numerical experiments were performed to verify the effectiveness of the proposed methods. Experimental uncertainties caused by the effects of the surface roughness and the indenter compliance are also discussed which highlights the precautions of applying the novel methods in practice.

Nanoscale Evaluation of Strength and Deformation Properties of Ultrahigh-Purity Aluminum

In order to investigate the strength and the deformation properties of metals in nearly perfect crystals, the nanoindentation test is performed on aluminum samples with various purities: 99.9999% (6 N), 99.99% (4 N) and 99% (2 N). It is widely known that the strength decreases with increasing purity of metals. On the nanoscale, however, the strength has been revealed to be close to the ideal shear strength, because a nanoscale area is expected to behave as a perfect crystal. In this study, a nanoindentation system that is able to provide indentation load vs penetration depth curves is employed. The experiment is performed on ultrahigh-purity aluminum (99.9999%), and high-purity aluminum (99.99%) and commercial-purity aluminum (99%) so as to discuss the relationship between the purity level and the mechanical properties at room temperature. It is revealed that the penetration depth decreases with increasing purity, and the critical shear stress estimated from the experimental results is close to the ideal shear strength. These results suggest that a perfect crystal is harder than an imperfect crystal. Furthermore, the indentation load vs penetration depth curves indicate a discontinuous deformation of the metals. It is considered that these discontinuities are caused by the existence of impurities or the initiation and the multiplication of dislocations in these samples. [doi:10.2320/matertrans.48.1]

OS5-1-1 Measurement of Stress in Austenitic Stainless Steel by an Indentation Method

Compressive residual stress is introduced into various components by surface modification methods in order to mitigate stress corrosion cracking susceptibility and to improve fatigue strength. There are also some nondestructive evaluation methods of residual stress including X-ray diffraction, neutron diffraction and Barkhausen noise. However, these methods are not suitable for small areas of austenitic stainless steel because it has large grain size and nonmagnetic property. A more reliable method is therefore required to evaluate residual stress in austenitic stainless steel. Recently, much research has focused on an indentation method for the metrology of residual stress. The indentation load-depth curve and impression size obtained from the indentation process can be used to determine residual stress and various mechanical properties such as hardness, the Young's modulus, fracture toughness, yield stress and work hardening exponent of a material. However, these values affect each other and it is necessary to clarify the relations between residual stress and each mechanical property. This study investigates the possibility of separating stress and mechanical properties both experimentally and by numerical calculation using the micro indentation method. For the indentation test using a sharp indenter, it was possible to evaluate stress by comparison of the maximum depth hmax or residual depth hf obtained from the load-depth curve. Furthermore, the 2-dimensional X-ray diffraction method is examined comparatively with the indentation method.

Microindentation of a Zr<SUB>57</SUB>Ti<SUB>5</SUB>Cu<SUB>20</SUB>Ni<SUB>8</SUB>Al<SUB>10</SUB> Bulk Metallic Glass

Using microindentation technique, the indentation behavior of a Zr57Ti5Cu20Ni8Al10 bulk-metallic glass is studied over a range of the indentation load from 200 mN to 5000 mN. For the indentation load larger than 1000 mN, the indentation load-depth curves during unloading display three regions, a) a fast unloading phase at the onset of unloading, b) a linear phase at which the indentation load is proportional to the indentation depth, and c) a slow unloading phase after the linear phase. The size of the linear region increases with the increase in the indentation load, and the slope is independent of the indentation load. The indentation hardness decreases slightly with the increase in the indentation load. The plastic energy dissipated in an indentation cycle is proportional to the 3/2 power of the indentation load. The effect of the indentation loading rate on the indentation behavior is discussed. [doi:10.2320/matertrans.MJ200733]

Feasible Evaluation of Flow Properties and Stress State of Structural Materials Using Instrumented Indentation Tests

Flow properties and stress state are indispensable factors for safety assessment of structural materials in operation, which were evaluated using instrumented indentation tests (IITs). Flow properties were obtained by defining representative stress and strain, and IIT results for 10 steel materials were discussed by comparing with those from uniaxial tensile tests. The indentation load-depth curve is significantly affected by the presence of residual stress, and the stress-induced load change was converted to a quantitative stress value. The stress state of a friction stir-welded joint of API X80 steel was evaluated and compared with that measured by energy-dispersive X-ray diffraction.

A Study of Nano-Indentation Test Using Rhombus-Shaped Cantilever in Atomic Force Microscope

We have designed and fabricated diamond-shaped AFM cantilevers capable of performing multi-functioning tasks by using single crystal silicon (SCS) micromachining techniques. Structural improvement of the cantilever has clearly solved the crucial problems resulted from using conventional simple beam-AFM cantilever for mechanical testing. After forcecalibration of the cantilever, indentation tests are performed to determine the mechanical behaviors in micro/nano-scale as well as topographic imaging. A diamond Berkovich tip of which radius at the apex is approximately 20 nm is attached on the cantilever for the indentation test and 3D topography measurement. The indentation load-depth curves of nano-scale polymeric pattern (PAK01-UV curable blended resin) are measured and surface topography right after indenting is also obtained. Development of this novel cantilever will extend the AFM functionality into the highly sensitive mechanical testing devices in nano/pico scale.

Using the instrumented indentation technique for stress characterization of friction stir-welded API X80 steel

An instrumented indentation technique (IIT) appears to be a promising alternative to conventional stress measurement methods, particularly for welds with rapid microstructural gradients, because it has high spatial resolution and is non-destructive. The technique is used to characterize the residual stress of a friction stir-welded joint of API X80 steel. The indentation load–depth curve is significantly affected by the presence of residual stress and the stress-induced load change at a given penetration is converted to a quantitative stress value through an analytical model. All indentation test results show good agreement with those from an energy-dispersive X-ray diffraction performed to assess the validity of the IIT. In addition, the microstructures in various regions of the friction stir-welded joint and their effects on local microhardness are discussed.