Instrumented Spherical Indentation Research Articles

Extraction of Mechanical Properties of Shape Memory Alloys From Instrumented Spherical Indentation

Abstract An approach to infer mechanical properties of shape memory alloys (SMAs) from instrumented spherical indentation records of indenter tip loading force, P, versus the resultant indentation depth, h, during indentation loading and unloading is proposed. The approach is based on (i) a finite element (FE) model for describing the forward problem of determining the indentation response, i.e., the P−h curve, for a given set of SMA mechanical properties, (ii) a computationally efficient Gaussian process surrogate model to replace the costly FE one, and (iii) an iterative solution strategy, which approximates the unknown model parameters from an experimentally determined P−h record and their corresponding probability densities via a Bayesian inference framework and a Markov Chain Monte Carlo sampling strategy. The efficacy of the proposed approach is demonstrated using numerical experiments, i.e., indentation curves generated by evaluating the FE model at points in the parameter space.

A Correction Function to Improve the Accuracy of Measuring Elastic Modulus by Instrumented Spherical Indentation

Abstract Instrumented indentation combined with the classic Oliver–Pharr method has been widely utilized to measure elastic modulus of various materials. However, the elastic modulus measured by instrumented spherical indentation (ISI) is not as accurate as that measured by instrumented sharp indentation, especially at large indentation depth. In this work, the effect of the maximum indentation depth on measurement of elastic modulus by ISI was deeply investigated through finite element simulations and experiments. It was found that errors in measured elastic moduli increase significantly due to the inaccurate estimation of contact radius and excessive increase in initial unloading stiffness as maximum indentation depth increases. A correction function was then proposed to correct the measured elastic modulus. After correction, the errors were effectively reduced to within ±5 % for most cases. This work contributes to discovery of the error source in the measurement of elastic modulus by ISI, thereby improving the measurement accuracy.

Rapid evaluation of trade-offs between strength and impact toughness of wheel steels by instrumented spherical indentation test

In this paper, an improved size-independent instrumented spherical indentation test (ISIT) method was proposed to determine tensile strength and fracture toughness on wheel rims of two different types of wheel steels. Additionally, Charpy impact specimens were taken from three specific positions on the wheel rims and subjected to standard Charpy impact testing. The resulting Charpy impact energy (CVN) were matched with the fracture toughness measured by ISIT (KIc,IT) at the same positions. There was a clear linear correlation between CVN and the square of KIc,IT, which was consistent with the established relationship between both properties as determined by conventional Charpy impact and compact tension tests. Therefore, we expanded the ISIT method to study the impact of cooling rates on the variation of yield strength and Charpy impact energy across the wheel rim. To accomplish this, we designated additional testing points on the wheel rim using the ISIT method. The investigation found trade-offs between strength and impact toughness of wheel steels under different cooling rates. The above findings demonstrated the effectiveness of using the ISIT method, which facilitated high-resolution fracture toughness measurement, to establish accurate correlation between CVN and fracture toughness of wheel steels. Moreover, this ISIT method can be employed to regulate heat treatment of material properties to meet specific application requirements.

On determination of elastic modulus and indentation hardness by instrumented spherical indentation: influence of surface roughness and correction method

Although, surface roughness can influence the determination of elastic moduli and indentation hardness to some extent by instrumented spherical indentation test, limited work has been done to quantitatively reveal and minimize these influences. In the present work, through a large number of finite element (FE) simulations and analyses, we clarified the evolution trend of determined elastic moduli and indentation hardness corresponding to different normalized indentation depths (h/R) and normalized roughness (S q/R). On this basis, an area correction method was proposed to improve the measurement accuracy in the elastic moduli and indentation hardness. The FE results show that, with the newly proposed correction method, the maximum relative error in determined elastic moduli is reduced from about ±7% to ±2%, and that in the determined indentation hardness is reduced from about ±13% to ±5%, when S q/R ≤ 2.2 × 10−3 and h/R = 5%. Applications were then illustrated on four typical metallic materials (i.e., AA 7075, AA 2014, steel 316 L, and copper T2). The experimental results demonstrate that the proposed correction method is able to mitigate the effects of surface roughness on the determination of elastic moduli and indentation hardness to obtain more correct results.

Toward Material Property Extraction from Dynamic Spherical Indentation Experiments on Hardening Polycrystalline Metals

Static indentation and dynamic indentation are reviewed, with a focus on extraction of material properties of isotropic strain-hardening polycrystalline metals that may be rate- and temperature-sensitive. Static indentation is reviewed first, followed by dynamic indentation, since the former is regarded as a specialization of the latter with inertia, rate dependence, and adiabatic heating excluded. Extending concepts from the literature review, a treatment of dynamic indentation using dimensional analysis is forwarded, and a general framework for extraction of material property information (i.e., constitutive model parameters) from instrumented dynamic spherical indentation experiments is set forth. In an example application of the methodology, experimental data obtained from instrumented spherical indentation in a miniature Kolsky bar apparatus are evaluated via dimensional analysis. The substrate material is aluminum alloy Al 6061-T6. Several definitions of indentation strain proposed for static indentation are assessed for dynamic indentation, as are indentation strain rates. While the fidelity of the experimental method and inertial effects could inhibit extraction of elastic properties, extraction of certain plastic constitutive properties may be feasible. Current data are insufficient to enable determination of a complete and unique set of all physical properties. Motivated by the present review and analysis, new experiments and simulations are proposed that would identify influences of material properties, facilitating their extraction from data.

A new instrumented spherical indentation test methodology to determine fracture toughness of high strength steels

A new instrumented spherical indentation test (ISIT) methodology is proposed to determine fracture toughness of metallic materials that their strain hardening can be adequately described by a power-law function. Firstly, tensile properties, including Young’s modulus (E), yield stress (σy) and strain hardening exponent (n) are determined by an improved representative stress–strain method with the Meyer power-law correction. Secondly, by performing dimensional analysis and finite element computation, a new dimensionless function of critical indentation contact pressure (Pmcr) versus tensile properties is developed. To generalize the above dimensionless function to a broad scale of metallic materials, 100 different combinations of tensile properties have been implemented in the finite element computation of spherical indentation tests. Consequently, Pmcr of various tested metallic materials can be calculated conveniently by substituting the corresponding tensile properties into the dimensionless function. The critical indentation depth (hccr) of metallic materials can then be determined by identifying Pmcr on the curve of mean contact pressure versus indentation depth. Finally, fracture toughness is calculated by the concept of indentation energy to fracture at hccr. To demonstrate the repeatability of the above methodology, it has been applied to predict fracture toughness of three different high strength steels by two research groups, independently. The best measurement capacity of the present approach could be optimized in a relative small error, as ±6 % in tensile properties and ±10 % in fracture toughness, that is close to the conventional standard testing results upon multiple samples of the same group.

Anisotropic Mechanical Properties of the Human Uterus Measured by Spherical Indentation.

The mechanical function of the uterus is critical for a successful pregnancy. During gestation, uterine tissue grows and stretches to many times its size to accommodate the growing fetus, and it is hypothesized the magnitude of uterine tissue stretch triggers the onset of contractions. To establish rigorous mechanical testing protocols for the human uterus in hopes of predicting tissue stretch during pregnancy, this study measures the anisotropic mechanical properties of the human uterus using optical coherence tomography (OCT), instrumented spherical indentation, and video extensometry. In this work, we perform spherical indentation and digital image correlation to obtain the tissue's force and deformation response to a ramp-hold loading regimen. We translate previously reported fiber architecture, measured via optical coherence tomography, into a constitutive fiber composite material model to describe the equilibrium material behavior during indentation. We use an inverse finite element method integrated with a genetic algorithm (GA) to fit the material model to our experimental data. We report the mechanical properties of human uterine specimens taken across different anatomical locations and layers from one non-pregnant (NP) and one pregnant (PG) patient; both patients had pathological uterine tissue. Compared to NP uterine tissue, PG tissue has a more dispersed fiber distribution and equivalent stiffness material parameters. In both PG and NP uterine tissue, the mechanical properties differ significantly between anatomical locations.

Evaluation of Non-Equibiaxial Residual Stresses in Metallic Materials via Instrumented Spherical Indentation

Residual stresses, existed in engineering structures, could significantly influence the mechanical properties of structures. Accurate and non-destructive evaluation of the non-equibiaxial residual stresses in these structures is of great value for predicting their mechanical performance. In this work, investigating the mechanical behaviors of instrumented spherical indentation on stressed samples revealed that non-equibiaxial residual stresses could shift the load-depth curve upwards or downwards and cause the residual indentation imprint to be an elliptical one. Through theoretical, experimental, and finite element (FE) analyses, two characteristic indentation parameters, i.e., the relative change in loading curvature and the asymmetry factor of the residual indentation imprint, were found to have optimal sensitivity to residual stresses at a depth of 0.01R (R is the radius of spherical indenter). With the aid of dimensional analysis and FE simulations, non-equibiaxial residual stresses were quantitatively correlated with these two characteristic indentation parameters. The spherical indentation method was then proposed to evaluate non-equibiaxial residual stress based on these two correlations. Applications were illustrated on metallic samples (AA 7075-T6 and AA 2014-T6) with various introduced stresses. Both the numerical and experimental verifications demonstrated that the proposed method could evaluate non-equibiaxial surface residual stresses with reasonable accuracy.

Application of Instrumented Spherical Indentation Technique to Estimate Mechanical Properties of Steels used in Gas Pipelines

Application of Instrumented Spherical Indentation Technique to Estimate Mechanical Properties of Steels used in Gas Pipelines

Spherical indentation method for estimating equibiaxial residual stress and elastic–plastic properties of metals simultaneously

Abstract

Identification of the elastic–plastic constitutive model for measuring mechanical properties of metals by instrumented spherical indentation test

Several methods for determination of elastic–plastic parameters by instrumented spherical indentation tests have been presented in the past few years. Each method was established according to a specific constitutive model. Identification of the constitutive models of new materials has become an indispensable step in order to choose an appropriate indentation method to extract the elastic–plastic parameters. In the present work, the half depth energy accumulation rate and Meyer’s index were related to the elastic–plastic constitutive models via qualitative and numerical analyses. A method for identification of the elastic–plastic constitutive models by instrumented spherical indentation test was proposed.

Prediction of Asymmetric Yield Strengths of Polymeric Materials at Tension and Compression Using Spherical Indentation

Engineering polymers generally exhibit asymmetric yield strength in tension and compression due to different arrangements of molecular structures in response to external loadings. For the polymeric materials whose plastic behavior follows the Drucker–Prager yield criterion, the present study proposes a new method to predict both tensile and compressive yield strength utilizing instrumented spherical indentation. Our method is decomposed into two parts based on the depth of indentation, shallow indentation, and deep indentation. The shallow indentation is targeted to study elastic deformation of materials, and is used to estimate Young's modulus and yield strength in compression; the deep indentation is used to achieve full plastic deformation of materials and extract the parameters in Drucker–Prager yield criterion associated with both tensile and compressive yield strength. Extensive numerical computations via finite element method (FEM) are performed to build a dimensionless function that can be employed to describe the quantitative relationship between indentation force-depth curves and material parameters of relevance to yield criterion. A reverse algorithm is developed to determine the material properties and its robustness is verified by performing both numerical and experimental analysis.

An instrumented spherical indentation study on high purity magnesium loaded nearly parallel to the c-axis

Instrumented spherical indentation has been used to extract information on the deformation behaviour of (0001) oriented grains in commercial purity magnesium. Reproducible discontinuities were found in the loading and the unloading curves and these have been interpreted as the nucleation and growth of {101¯2} extension twins during loading and their subsequent retreat during unloading. Detailed three-dimensional electron backscatter diffraction-based orientation microscopy (3D-EBSD) revealed that the presence of residual deformation twins depended on the depth of the indent. Analysis of residual geometrically necessary dislocation density using the EBSD data showed that residual basal 〈a〉 dislocations were dominant in the deformation zone. The crystallographic misorientation observed below the indent can be rationalized by the presence of these basal 〈a〉 dislocations and this is shown to be consistent with crystal plasticity finite element method calculations. Finally, a schematic view of the different stages of deformation during loading and unloading is proposed to rationalize the experimental observations.

Identification of a damage criterion of a highly porous alumina ceramic

This paper aims at identifying the multiaxial compression behavior of highly porous ceramics used as catalyst supports. For this purpose, instrumented spherical indentation tests are performed, together with uniaxial and hydrostatic compression tests. A transition from a brittle to a damageable behavior with densification of the material is noted when increasing the triaxiality of the test. The collapse of large pores is shown as being responsible for the densification phenomenon, as confirmed by SEM and mercury intrusion porosimetry. A multiaxial damage criterion is proposed and identified thanks to a numerical finite element model.The results described in this paper coupled with a previous work (Staub et al., Oil and gas science and technology 2015, vol 70, n° 3, 475–86) on the behavior of the same material under tension loading, allow for the first time to define a multiaxial criterion both in tension and in compression for highly porous ceramics. These materials are shown to present a typical behavior of dense ceramics in tension, whereas in compression, their behavior is close to that of porous rocks.

Surface residual stress in soda-lime glass evaluated using instrumented spherical indentation testing

Instrumented spherical indentation testing is proposed as a non-destructive way to evaluate surface residual stress in soda-lime glass. 10 μm-deep indentations with a spherical indenter of 250 μm radius do not reduce the strength of 3.5-mm-thick soda-lime glass as measured in four-point bending tests. We find good linearity between the compressive surface residual stress and the force difference at maximum indentation depth in the indentation force–depth curve, while hardness as measured by instrumented spherical indentation testing is independent of compressive surface residual stress introduced by bending and strengthening heat treatment.

Relationships between the work recovery ratio of indentation and plastic parameters for instrumented spherical indentation

Abstract

Evaluation of the material’s damage in gas turbine rotors by instrumented spherical indentation

Experimental indentations are carried out on items of two different materials, taken in several location of various components from high pressure gas turbine rotor which have seen an extensive service. The components object of investigation consisted in 1st and 2nd high pressure turbine wheels made in nickel-base superalloy (Inconel 718), the spacer ring (Inconel 718) and the compressor shaft made in CrMoV low alloy steel (ASTM A471 type10). Aim of the work is to set up the capability of the instrumented spherical indentation testing system to evaluate variations in the material properties due to damage, resulting from temperature field and stresses acting on components during service. To perform this task load-indentation depth curves will be acquired in various zones of the above mentioned components. The analysis of the results has allowed to identify an energy parameter which shows a linear evolution with the mean temperature acting on the components.

An integrated method to determine elastic–plastic parameters by instrumented spherical indentation

Abstract

Metals Identification from Instrumented Spherical Indentation Testing

A new integrated system consisting of a testing machine, denominated Diaptometro, and of an algorithm for metallic materials identification via instrumented spherical indentation testing is presented. The identification is carried out by analyzing the experimental load – penetration depth curve ( curve) from shallow indentation tests, thus preventing any contact condition effects in the material properties estimation. Accuracy in the experimental data collecting and the curve representation were recognized to be the key factors at the basis of reliable and accurate estimations. A new equipment with accuracies of 0.075% and 0.1% for the penetration depth and indentation load respectively was specifically built-up, whereas a four-terms power expansion is proposed for modeling the curve in the identification procedure. Experimental validation campaigns confirm the effectiveness of the adopted solutions.

Extended expanding cavity model for measurement of flow properties using instrumented spherical indentation

We propose an extended expanding cavity model (ECM) in instrumented spherical indentation to evaluate flow properties measured in uniaxial mechanical testing. We describe the mean pressure of the projected surface from radial stress at the hemispherical core boundary with a scaling factor for strain-hardening metals. Plastic constraint factors determined by the strain-hardening exponent, yield strain and scaling factor successfully illustrate flow stress–strain points in uniaxial tension tests. We suggest a novel way to determine the strain-hardening exponent from the ratio of indentation loading slope, and a modified Meyer relation to measure yield strengths.