Further analysis of energy-based indentation relationship among Young’s modulus, nominal hardness, and indentation work

Ma, Dengke; Ong, Chung Wo

doi:10.1557/jmr.2010.0137

Cited by 16 publications

(6 citation statements)

References 15 publications

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“…Other reports on the topic have included investigations of a piecewise description of elastic influence of indenter shape [141] and an effect of surface roughness [142]. Several reports have dealt with the general determination of Young's modulus and separation of Poisson's ratio in E r [143][144][145].…”

Section: Elastic Loading Resultsmentioning

confidence: 99%

Elastic, Plastic, Cracking Aspects of the Hardness of Materials

Armstrong

Elban

Walley

2013

Int. J. Mod. Phys. B

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The hardness properties of materials are tracked from early history until the present time. Emphasis is placed on the hardness test being a useful probe for determining the local elastic, plastic and cracking properties of single crystal, polycrystalline, polyphase or amorphous materials. Beginning from connection made between individual hardness pressure measurements and the conventional stress–strain properties of polycrystalline materials, the newer consideration is described of directly specifying a hardness-type stress–strain relationship based on a continuous loading curve, particularly, as obtained with a spherical indenter. Such effort has received impetus from order-of-magnitude improvements in load and displacement measuring capabilities that are demonstrated for nanoindentation testing. Details of metrology assessments involved in various types of hardness tests are reviewed. A compilation of measurements is presented for the separate aspects of Hertzian elastic, dislocation-mechanics-based plasticity and indentation-fracture-mechanics-based cracking behaviors of materials, including elastic and plastic deformation rate effects. A number of test applications are reviewed, most notably involving the hardness of thin film materials and coatings.

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Section: Elastic Loading Resultsmentioning

confidence: 99%

Elastic, Plastic, Cracking Aspects of the Hardness of Materials

Armstrong

Elban

Walley

2013

Int. J. Mod. Phys. B

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Section: Methodsmentioning

confidence: 99%

“…In addition to empirical and numerical methods, the indentation process has also been extensively studied through analytically derivations, yielding a series of analytical methods. [48][49][50] However, most existing analytical methods suggest stress-strain calculations from merely the indentation load-displacement curve, which may be problematic in the stability of reverse predictions due to the compensation effect. 51,52 On the basis of energy analysis and digital image correlation (DIC) measurements, the Z-W incremental indentation energy method including two analytical models (the incremental model and the energy-based model), which is a calculation method of the equivalent stress-strain relation, was proposed in our previous studies.…”

Section: Methodsmentioning

confidence: 99%

On the evaluation of uniaxial tensile and fracture properties of Ti‐6Al‐4V by spherical indentation tests with different calculation models

Wang

Liu²,

Zheng

et al. 2023

Fatigue Fract Eng Mat Struct

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This study assessed the efficacy of models in predicting uniaxial tensile and fracture properties of Ti‐6Al‐4V (TC4) alloys via spherical indentation tests (SITs). Four models, including one empirical, one numerical, and two analytical, were selected as representatives to evaluate uniaxial tensile properties. A series of experiments were conducted on TC4 alloys obtained from three manufacturing processes: selective laser melting (SLM), forging, and welding. The empirical model underestimated the material's strength, while the other models were mostly conservative, with errors within 10%, acceptable for engineering applications. However, although the incremental model is able to provide a desirable result, it may be inaccurate for calculating the yield strength. Thus, the source of errors in each model was thoroughly investigated through theoretical analysis and finite element calculations. Additionally, based on the results of optimal strength assessment, this study validated the effectiveness of the critical stress model to evaluate the fracture toughness of TC4 alloys.

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“…Apart from the representative stress-strain, the n and E p in the Holloman law may also be directly fitted from the indentation P-h curve. [14][15][16][17][18][19][20][21][22] The principle of this fitting is that the indentation P-h curve is governed by the hardening behavior (n and E p in the Holloman law) of the sample material, and materials with different hardening behaviors will exhibit different P-h curves. Therefore, the optimal material parameters can be fitted from the P-h curves.…”

Section: Introductionmentioning

confidence: 99%

Improving the tensile property calculations with plastic zone radius measurements in depth-sensing spherical indentation tests

Zhang

Shang

et al. 2021

The Journal of Strain Analysis for Engineering Design

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Depth-sensing spherical indentation tests (SITs) have been widely used in tensile property calculations, but the accuracy and reproducibility of calculations may be significantly influenced by displacement measurement errors. Taking two representative tensile property calculation methods as examples, namely the analytical and numerical methods, the rationale as to why accurate and reproducible tensile property calculations cannot be expected from the depth-sensing SITs was discussed in detail. Subsequently, the proportional limit σ0 calculation from plastic zone radius rp measurements, which was analytically developed in the expanding cavity model (ECM) and experimentally measured by digital image correlation (DIC), was introduced to enhance the accuracy and reproducibility of the two representative methods. Principles for setting the strain threshold εth were established, and factors influencing the σ0 calculation from rp measurements were investigated through the optical system, the friction condition, the hardening behaviors of specimen materials, and the indentation depth. Through finite element calculations, it was proven that tensile property calculations at the existence of displacement measurement errors, particularly the constant error from the origin correction, can be significantly improved with the introduction of rp measurements. Similar findings were also observed in experiments on four metals that exhibited different hardening behaviors.

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Further analysis of energy-based indentation relationship among Young’s modulus, nominal hardness, and indentation work

Cited by 16 publications

References 15 publications

Elastic, Plastic, Cracking Aspects of the Hardness of Materials

Elastic, Plastic, Cracking Aspects of the Hardness of Materials

On the evaluation of uniaxial tensile and fracture properties of Ti‐6Al‐4V by spherical indentation tests with different calculation models

Improving the tensile property calculations with plastic zone radius measurements in depth-sensing spherical indentation tests

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