인장 및 압축 등방 잔류응력 측정을 위한 누프 압입시험의 응력환산계수 결정

정민재 ( Min Jae Jeong ),김영천 ( Young-cheon Kim ) 한국부식방식학회 2021 Corrosion Science and Technology Vol.20 No.6

Instrumented indentation testing has been widely used for residual stress measurement. The Knoop indentation is mainly selected for determining anisotropic mechanical properties and non-equibiaxial residual stress. However, the measurement of equibiaxial stress state and compressive residual stress on a specimen surface using Knoop indentation is neither fully comprehended nor unavailable. In this study, we investigated stress conversion factors for measuring Knoop indentation on equibiaxial stress state through indentation depth using finite element analysis. Knoop indentation was conducted for specimens to determine tensile and compressive equibiaxial residual stress. Both were found to be increased proportionally according to indentation depth. The stress field beneath the indenter during each indentation test was also analyzed. Compressive residual stress suppressed the in-plane expansion of stress field during indentation. In contrast, stress fields beneath the indenter developed diagonally downward for tensile residual stress. Furthermore, differences between trends of stress fields at long and short axes of Knoop indenter were observed due to difference in indenting angles and the projected area of plastic zone that was exposed to residual stress.

압입경도 측정을 위한 표면변형 분석기법 비교

이윤희 ( Yun Hee Lee ),김국환 ( Kuk Hwan Kim ),남승훈 ( Seung Hoon Nahm ),권동일 ( Dong Il Kwon ) 대한금속재료학회 ( 구 대한금속학회 ) 2009 대한금속·재료학회지 Vol.47 No.7

Approaches for analyzing indentation hardness are still controversial, although the instrumented indentation technique has been generalized as one powerful method that can record surface deformation behaviors. Material pile-ups around the indenter/surface contact region make the conventional Oliver and Pharr`s analysis on the instrumented indentation curve inaccurate. Thus, in order to prove the validity of the hardness analyses, five approaches were applied to the experimental data obtained from fused quartz and (100) monocrystalline tungsten specimens; an elastic recovery analysis on instrumented indentation curves, three indentation work analyses on the unit plastic volume, and a differentiation analysis on remnant indentation morphologies were tried. Five kinds of indentation hardness overlapped on one result plot showed the validity of each analysis. The modified indentation work approach based on a new definition of plastic volume showed consistent results with those from the Oliver-Pharr`s and image differentiation methods. In the case of pile-up accompanying deformation, the Oliver-Pharr`s and image differentiation methods showed the upper and lower limits of indentation hardness, respectively.

A dual conical indentation technique based on FEA solutions for property evaluation

Hyun, Hong Chul,Kim, Minsoo,Lee, Jin Haeng,Lee, Hyungyil Elsevier 2011 Mechanics of materials Vol.43 No.6

<P><B>Abstract</B></P><P>The sharp indenters such as Berkovich and conical indenters have a geometrical self-similarity so that we can obtain only one parameter from an indentation loading curve, which makes different materials have the same load–displacement relation. Most studies to evaluate elastic–plastic properties by using the geometrical self-similar indenter have therefore tried to use dual/plural indentation techniques, on the basis of the concept of representative strain/stress varying with the indenter angle. However, any suggested representative concept is not universally operative for real materials. In this work, we suggest a method of material property evaluation without using the concept of representative strain. We begin the work by studying the characteristics of load–depth curves of conical indenters via finite element (FE) method. From FE analyses of dual-conical indentation, we investigate the relationships between indentation parameters and load–depth curves. The projected contact diameter is expressed as a function of the indenter angle, tip-radius, and material properties, which allows us to simply predict the elastic modulus. Two mapping functions for two indenter angles (45° and 70.3°) are presented to find the two unknowns (yield strain and strain-hardening exponent) via dual indentation technique. The method provides elastic modulus, yield strength and strain-hardening exponent with an average error of less than 5%. The method is valid for any elastically deforming indenters. We also discuss the sensitivity of measured properties to the load–displacement curve variation, and the difference between conical and Berkovich indenters.</P>

Characteristics of indentation cracking using cohesive zone finite element techniques for pyramidal indenters

Hyun, H.C.,Rickhey, F.,Lee, J.H.,Hahn, J.H.,Lee, H. Pergamon Press ; Elsevier Science Ltd 2014 International journal of solids and structures Vol.51 No.25

During indentation of brittle materials, cracks may be generated around the impression, depending on load conditions, material and indenter geometry. We investigate the effect of indenter geometry (centerline-to-face angle and number of edges) on crack characteristics by indentation cracking test and finite element analysis (FEA). Considering conditions for crack initiation and propagation, an FE model is employed featuring cohesive interfaces in zones of potential crack formation. After verification of the FE model through comparison with experimental results for Vickers and three-sided pyramidal indentation, we study the crack morphology for diverse indenter geometries and establish a relation between the crack length c and the number of indenter edges n<SUB>c</SUB>. Together with a relation between indenter angle ψ and crack length c, we can predict the length of the crack induced by other types of indenter from the crack size obtained with a reference indenter.

Nanoscale indentation and scratching tests of single crystal sapphire using molecular dynamics simulation

Kim, Woo Kyun,Xi, Dalei,Kim, Bo Hyun Elsevier 2019 Computational materials science Vol.170 No.-

<P><B>Abstract</B></P> <P>Sapphire is a crystalline aluminum oxide, which has been used for various applications due to its superior thermal, chemical, mechanical, and optical properties. Even though sapphire is a brittle material, its plastic deformation modes have also been studied for decades, mostly in experiments. In this study, we apply the molecular dynamics simulation method to investigate the atomic-scale deformation mechanisms of single crystal sapphire during the indentation and scratching tests. The indentation simulations are carried out in four crystallographic planes (C, A, M, R) and reveal various slip deformations. In particular, the rhombohedral twin structures are formed in the C-plane indentation, and the R-plane indentation triggers most slip systems including the C-, A-, N-, R-, S-planes. Hardness on the four slip planes is calculated during the indentation test and compared with the experimentally measured values. The scratching tests are performed in six different crystallographic directions at three scratching depths of 10 Å, 20 Å, and 30 Å. The simulation results show the deformation modes similar to those found in the indentation tests. In the scratching tests in the two slip directions of the C-plane the basal slip deformation is observed. The normal and scratching forces that are calculated in the scratching test exhibit the orientation dependence such that the C-plane and A-plane have the largest and smallest forces. The atomic displacements and configurations in the rhombohedral twin and basal slip are discussed.</P> <P><B>Highlights</B></P> <P> <UL> <LI> Indentation/scratching of single crystal sapphire are performed using MD simulations. </LI> <LI> Various deformation modes such as rhombohedral twinning and basal slip are observed. </LI> <LI> Hardness, normal and scratching forces are calculated. </LI> <LI> Atomic displacements and configurations of each deformation mode are discussed. </LI> </UL> </P> <P><B>Graphical abstract</B></P> <P>[DISPLAY OMISSION]</P>

Characterizing elastic constants of anisotropic materials by spherical indentation method

Liao Yanguo,Xie Shuibo 한국물리학회 2023 Current Applied Physics Vol.53 No.-

By the theoretical analysis and the finite element (FE) method, a new model for measuring the elastic constants of transversely isotropic materials has been proposed from spherical indentation. A theoretical analysis of the spherical indentation modulus for the materials is presented. Extensive spherical indentation tests were implemented by three dimensional (3D) FE simulations. By fitting the simulation results, the analytical relationship correlating the elastic parameters with the indentation moduli at three different indentation orientation angles (0◦, 45◦, and 90◦) was set up. The effectiveness of the proposed method was examined by a series of numerical indentation experiments. It is found that the calculated values by the proposed method are well consistent with the input elastic parameters. The sensitivity of the calculated elastic parameters to the experimental data was analyzed. Simultaneously, this method was applied to carbon fiber materials. The results calculated by the method proposed in this paper were compared with results obtained by the theoretical model and experimental measurement to verify the effectiveness of this method. Thus the proposed method is practiced and could be used to identify the elastic properties of transversely isotropic materials.

Estimations of work hardening exponents of engineering metals using residual indentation profiles of nano-indentation

Kim, Byung-Min,Lee, Chan-Joo,Lee, Jung-Min 대한기계학회 2010 JOURNAL OF MECHANICAL SCIENCE AND TECHNOLOGY Vol.24 No.1

This study was designed to predict work hardening exponent n of materials from AFM (atomic force microscope) observations of residual indentation impression in sharp indentations. FE simulations of nano-indentation were performed to 140 combinations to each parameter (elastic modulus E, yield stress ${\sigma}_y$, work hardening exponent n, and Poisson's ratio ${\nu}$) expressing elastic-plastic behaviors of universal engineering metals. Using the results from FE simulations and dimensional analysis, dimensionless functions were established to correlate residual indentation profiles with the work hardening exponent. This function was examined with nano-indentation, tensile test, and AFM observations after indentation for two materials (Al6061-T6 and copper).

유한요소해에 기초한 원뿔형 압입 물성평가법

현홍철(Hong Chul Hyun),김민수(Minsoo Kim),이진행(Jin Haeng Lee),이형일(Hyungyil Lee) 대한기계학회 2009 大韓機械學會論文集A Vol.33 No.9

물성치와 하중-변위곡선을 일대일 대응 시킬 수 있는 함수를 생성함으로써, 미지 재료에 대한 압입시험 데이터로부터 바로 재료물성을 찾는 압입물성평가 기법을 제시했다. 원뿔형 압입 유한요소해석으로 압입자 중심각이 압입 하중-변위 곡선에 주는 영향을 살펴 보았다. 이로부터 한 압입자 중심각에 대해 같은 Kick’s law 계수 C를 갖는 두 재료들이 압입자 중심각이 변하면 서로 다른 C 값들을 가짐을 확인했다. 이어 영률, 항복강도, 변형경화지수와 하중-변위곡선 사이의 상관관계들을 분석하고, 항복변형률이 변형경화 지수와 더불어 중요한 변수임을 확인했다. 이 두 특성들을 바탕으로 이중원뿔형 압입 물성평가 수식들을 작성했다. 1회 압입 후 재료의 영률을 평가하고, 두 압입자를 이용해 얻은 하중-변위 곡선들로부터 곡률계수들을 구해 항복변형률과 변형경화 지수를 구했다. 제시된 물성평가법은 압입 하중-변위곡선들로부터, 압입자 물성과 선단반경에 상관없이, 평균 오차 2% 내에서 재료 물성값들을 준다. The sharp indenters such as Berkovich and conical indenters have a geometrical self-similarity in theory, but different materials have the same load-depth curve in case of single indentation. In this study, we analyze the load-depth curves of conical indenter with angles of indenter via finite element method. From FE analyses of dual-conical indentation test, we investigate the relationships between indentation parameters and load-deflection curves. With numerical regressions of obtained data, we finally propose indentation formulae for material properties evaluation. The proposed approach provides stress-strain curve and the values of elastic modulus, yield strength and strain-hardening exponent with an average error of less than 2%. It is also discussed that the method is valid for any elastically deforming indenters made of tungsten carbide and diamond for instance. The proposed indentation approach provides a substantial enhancement in accuracy compared with the prior methods.

Numerical study of the indentation formation of a compound droplet in a constriction

Hoe D. Nguyen,Truong V. Vu,Phan H. Nguyen,Binh D. Pham,Nang X. Ho,Cuong T. Nguyen,Vinh T. Nguyen 대한기계학회 2021 JOURNAL OF MECHANICAL SCIENCE AND TECHNOLOGY Vol.35 No.4

A compound droplet deforming in a constricted tube widely appears in drug delivery and microfluidic devices. In such a constriction, an indentation can present at the trailing surface of the droplet. However, this aspect has not been fully investigated and understood so far. This study focuses on the effects of some dimensionless parameters on the negative curvature, i.e., indentation, at the trailing surface of a compound droplet moving through a constricted tube. The presence of the constriction at the middle of the tube length enhances the droplet indentation. Numerical results were obtained for the capillary number Ca (varied in range of 0.1 - 1.0), the inner-to-outer droplet radius ratio R 21 (varied in range of 0.2 - 0.9), the droplet-to-tube radius ratio R 10 (varied in range of 0.2 - 0.9), the inner-to-outer interfacial tension coefficient ratio σ 21 (varied in range of 0.1 - 6.4), and the normalized depth of the constriction d/R (varied in range of 0.0 - 0.8). The results reveal that the most influencing factor is Ca, increasing its value leads to the increment of the maximum indentation at the trailing surface of the inner and outer droplets. The indentation is also increased with increasing the value of R 10and d/R. In contrast, increasing R 21 results in a decrease in the indentation at the trailing surface of the outer droplet. When increasing σ 21 , the indentation at the trailing surface of the inner one is quickly suppressed, while the outer droplet is minorly affected. We also point out the patterns of the trailing surface of the inner and outer droplets and their transitions from one to the other patterns in the diagrams based on these parameters.

Cohesive Zone Model을 이용한 압입자 형상에 따른 균열특성분석

현홍철(Hong Chul Hyun),이진행(Jin Haeng Lee),이형일(Hyungyil Lee),김대현(Dae Hyun Kim),한준희(Jun Hee Hahn) 대한기계학회 2013 大韓機械學會論文集A Vol.37 No.12

본 연구에서는 유한요소해석과 압입시험으로 압입자 형상이 압입균열특성에 미치는 영향을 조사했다. 본 논문에서는 Lee 등(2012)이 제시한 cohesive zone 모델특성 및 균열생성, 진전을 위한 해석 조건에 기초해 다양한 균열해석을 수행했다. 우선, 사각뿔 및 삼각뿔 압입균열 시험과 해석을 비교해 해석 모델의 유효성을 검증했다. 아울러 비대칭 압입자에 의한 압입시, 압입하부에서 비대칭 균열의 발생 여부를 해석적으로 관찰했다. 최종적으로 압입발생 균열수와 균열길이 관계를 조사했다. 균열수와 균열길이 관계 및 동일 압입자형상(압입자 모서리수)에서 압입자각에 따른 균열길이 변화를 이용하면, 특정 압입자 형태의 압입시험에서 얻은 균열길이 만으로 다양한 압입자 형태의 균열길이를 예측할 수 있다. In this study, we investigated the effect of the indenter geometry on the crack characteristics by indentation cracking test and FEA. We conducted various cohesive finite element simulations based on the findings of Lee et al. (2012), who examined the effect of cohesive model parameters on crack size and formulated conditions for crack initiation and propagation. First, we verified the FE model through comparisons with experimental results that were obtained from Berkovich and Vickers indentations. We observed whether nonsymmetrical cracks formed beneath the surface during Berkovich indentation via FEA. Finally, we examined the relation between the crack size and the number of cracks. Based on this relation and the effect of the indenter angle on the crack size, we can predict from the crack size obtained with an indenter of one shape (such as Berkovich or Vickers) the crack size for an indenter of different shape.