Determining the elastic-plastic properties of metallic materials through instrumented indentation

En los últimos años, y asociado al desarrollo de la tecnología MEMS, la técnica de indentación instrumentada se ha convertido en un método de ensayo no destructivo ampliamente utilizado para hallar las características elástico-plásticas de recubrimientos y capas delgadas, desde la escala macroscópica a la microscópica. Sin embargo, debido al complejo mecanismo de contacto debajo de la indentación, es urgente proponer un método más simple y conveniente para obtener unos resultados comparables con otras mediciones tradicionales. En este estudio, el objetivo es mejorar el procedimiento analítico para extraer las propiedades elástico-plásticas del material mediante la técnica de indentación instrumentada. La primera parte se centra en la metodología llevada a cabo para medir las propiedades elásticas de los materiales elásticos, presentándose una nueva metodología de indentación, basada en la evolución de la rigidez de contacto y en la curva fuerza-desplazamiento del ensayo de indentación. El método propuesto permite discriminar los valores de indentación experimental que pudieran estar afectados por el redondeo de la punta del indentador. Además, esta técnica parece ser robusta y permite obtener valores fiables del modulo elástico. La segunda parte se centra en el proceso analítico para determinar la curva tensión-deformación a partir del ensayo de indentación, empleando un indentador esférico. Para poder asemejar la curva tension-deformación de indentación con la que se obtendría de un ensayo de tracción, Tabor determinó empíricamente un factor de constricción de la tensión () y un factor de constricción de la deformación (). Sin embargo, la elección del valor de y necesitan una derivación analítica. Se describió analíticamente una nueva visión de la relación entre los factores de constricción de tensión y la deformación basado en la deducción de la ecuación de Tabor. Un modelo de elementos finitos y un diseño experimental se realizan para evaluar estos factores de constricción. A partir de los resultados obtenidos, las curvas tension-deformación extraidas de los ensayos de indentación esférica, afectadas por los correspondientes factores de constricción de tension y deformación, se ajustaron a la curva nominal tensión-deformación obtenida de ensayos de tracción convencionales. En la última parte, se estudian las propiedades del revestimiento de cermet Inconel 625-Cr3C2 que es depositado en el medio de una aleación de acero mediante un láser. Las propiedades mecánicas de la matriz de cermet son estudiadas mediante la técnica de indentación instrumentada, haciendo uso de las metodologías propuestas en el presente trabajo. In recent years, along with the development of MEMS technology, instrumented indentation, as one type of a non-destructive measurement technique, is widely used to characterize the elastic and plastic properties of metallic materials from the macro to the micro scale. However, due to the complex contact mechanisms under the indentation tip, it is necessary to propose a more convenient and simple method of instrumented indention to obtain comparable results from other conventional measurements. In this study, the aim is to improve the analytical procedure for extracting the elastic plastic properties of metallic materials by instrumented indentation. The first part focuses on the methodology for measuring the elastic properties of metallic materials. An alternative instrumented indentation methodology is presented. Based on the evolution of the contact stiffness and indentation load versus the depth of penetration, the possibility of obtaining the actual elastic modulus of an elastic-plastic bulk material through instrumented sharp indentation tests has been explored. The proposed methodology allows correcting the effect of the rounding of the indenter tip on the experimental indentation data. Additionally, this technique does not seem too sensitive to the pile-up phenomenon and allows obtaining convincing values of the elastic modulus. In the second part, an analytical procedure is proposed to determine the representative stress-strain curve from the spherical indentation. Tabor has determined the stress constraint factor (stress CF), and strain constraint factor (strain CF), empirically but the choice of a value for and is debatable and lacks analytical derivation. A new insight into the relationship between stress and strain constraint factors is analytically described based on the formulation of Tabor’s equation. Finite element model and experimental tests have been carried out to evaluate these constraint factors. From the results, representative stress-strain curves using the proposed strain constraint factor fit better with the nominal stress-strain curve than those using Tabor’s constraint factors. In the last part, the mechanical properties of an Inconel 625-Cr3C2 cermet coating which is deposited onto a medium alloy steel by laser cladding has been studied. The elastic and plastic mechanical properties of the cermet matrix are studied using depth-sensing indentation (DSI) on the micro scale

Conventional Vickers and true instrumented indentation hardness determined by instrumented indentation tests

We evaluate Vickers hardness and true instrumented indentation test (IIT) hardness of 24 metals over a wide range of mechanical properties using just IIT parameters by taking into account the real contact morphology beneath the Vickers indenter. Correlating the conventional Vickers hardness, indentation contact morphology, and IIT parameters for the 24 metals reveals relationships between contact depths and apparent material properties. We report the conventional Vickers and true IIT hardnesses measured only from IIT contact depths; these agree well with directly measured hardnesses within ±6% for Vickers hardness and ±10% for true IIT hardness

Effective indenter radius and frame compliance in instrumented indentation testing using a spherical indenter

We introduce a novel method to correct for imperfect indenter geometry and frame compliance in instrumented indentation testing with a spherical indenter. Effective radii were measured directly from residual indentation marks at various contact depths (ratio of contact depth to indenter radius between 0.1 and 0.9) and were determined as a function of contact depth. Frame compliance was found to depend on contact depth especially at small indentation depths, which is successfully explained using the concept of an extended frame boundary. Improved representative stress-strain values as well as hardness and elastic modulus were obtained over the entire contact depth

A method for measuring the contact area in instrumented indentation testing by tip scanning probe microscopy imaging

The determination of the contact area is a key step to derive mechanical properties such as hardness or an elastic modulus by instrumented indentation testing. Two families of procedures are dedicated to extracting this area: on the one hand, post mortem measurements that require residual imprint imaging, and on the other hand, direct methods that only rely on the load vs. the penetration depth curve. With the development of built-in scanning probe microscopy imaging capabilities such as atomic force microscopy and indentation tip scanning probe microscopy, last generation indentation devices have made systematic residual imprint imaging much faster and more reliable. In this paper, a new post mortem method is introduced and further compared to three existing classical direct methods by means of a numerical and experimental benchmark covering a large range of materials. It is shown that the new method systematically leads to lower error levels regardless of the type of material. Pros and cons of the new method vs. direct methods are also discussed, demonstrating its efficiency in easily extracting mechanical properties with an enhanced confidence

Hall-Petch strengthening of the constrained metallic binder in WC-Co cemented carbides: Experimental assessment by means of massive nanoindentation and statistical analysis

WC–Co cemented carbides are geometrically complex composites constituted for two interpenetrating networks of the constitutive ceramic and metal phases. Accordingly, assessment of microstructural effects on the local mechanical properties of each phase is a challenging task, especially for the metallic binder. In this work, it is attempted by combining massive nanoindentation, statistical analysis, and implementation of a thin film model for deconvolution of the intrinsic hardness and flow stress of the metallic phase. Plotting of yield stress values as a function of the binder mean free path results in a Hall-Petch strengthening relationship with a slope (ky) of 0.98 MPa m1/2. This value points out the effectiveness of WC–Co phase boundaries as strong obstacles to slip propagation; and thus, for toughening of the brittle phase (WC) by means of crack-bridging ductile (Co) reinforcement.Peer ReviewedPostprint (author's final draft

Constitutive modelling and mechanical characterization of aluminium-based metal matrix composites produced by spark plasma sintering

Spark plasma sintering has been applied to the production of aluminium-based functionally graded material systems to be used in abrasive and high temperature conditions. The overall mechanical properties of these metal matrix composites were determined during the optimization phases of the production process by a fast and reliable identification procedure based on instrumented indentation, which can be easily performed on small specimens. The experimental information gathered from conical (Rockwell) indentation was used as input data for the calibration of the material parameters entering the elastic–plastic Drucker–Prager constitutive model. Eventually, the so identified material parameters were used to predict the result of pyramidal (Vickers) indentation, in order to validate the model selection and the output of the identification procedure. The good matching between modelling and experimental results for the different test configurations confirmed the soundness of the considered approach, especially evidenced on the light of the strong influence on the overall mechanical characteristics of the material microstructure and defectiveness resulting from the production process, which prevent the use of classical homogenization rules to evaluate the macroscopic material properties

Development of instrumented indentation test model for fracture toughness evaluation and cryogenic test application

학위논문 (박사) -- 서울대학교 대학원 : 공과대학 재료공학부, 2020. 8. 권동일.Structural integrity assessment is to evaluate the condition of a structure or component before it is destroyed. To manage the structural integrity, an engineer must consider the presence of flaws, designed stress and material properties in the structures. But the most important factor is the mechanical properties of a material firstly, such as strength, hardness, or fracture toughness. In many cases, structural failures arise from the change of mechanical properties of the material due to degradation or embrittlement so that it is required to, if possible, measure in-situ mechanical properties of in-service structural components for structural integrity assessment. There are various mechanical properties, however, among them, fracture toughness, the resistance to crack propagation, is one of the most important mechanical properties for fracture mechanical analysis on structural integrity. But the standard fracture toughness test is a destructive method and requires complex shapes and test procedures, making it nearly impossible to measure the fracture toughness of an in-service structures. For this reason, a nondestructive tool to measure in-situ mechanical properties as well as fracture toughness has required and developed to improve the reliability of structural integrity assessment. Instrumented indentation testing can be considered one of solutions in this issue because it is developed for nondestructive testing of in-field structures. Many researchers have worked to estimate fracture toughness of metallic materials using instrumented indentation testing, trying to develop theoretical or experimental models. The study on the prediction of fracture toughness through the instrumented indentation test started from methods of generating cracks, but the study on the metallic materials that does not occur crack was expanded. In the fact that the crack does not occur in the metallic material, the study has been divided into mechanical model and fracture energy model, but in both cases, many assumptions and empirical correlations have been used. In this study, indentation fracture toughness models are introduced. Among them, flat tip fracture toughness estimation model is selected due to its simple test method and derivation of the fracture mechanics situation. Since the previous approach was focused on being somehow phenomenal in the method of determining fracture toughness, this approach was tired to determine the fracture toughness in an indentation situation by adapting fracture mechanics. According to fracture mechanisms, two distinct indentation fracture toughness models, ductile fracture model and brittle fracture model, are modified. In ductile fracture model, in order to match the stress state beneath an indenter with that ahead of a crack tip, fully plastic state at fracture in ligament of cracked round bar test specimen, crack initiation point is determined at the point which fully plastic zone is developed beneath the indenter. In brittle fracture, it is noted that brittle fracture does not involve plasticity, and the crack initiation point in the indentation test is determined using small scale yielding condition at which plastic deformation energy is minimal. By using the flat punch indenter, due to the geometry of the indenter, one normalized curve not dependent on the size of indenter radius can be obtained and this can be converted to any other sized indentation load-depth curve. Thus, for those two model, the indenter size with a radius corresponding to 1T thickness can be determined, and the fracture toughness can be calculated from the load-displacement curve of that size. To verify developed models, experimental results are compared with standard J test results and it is confirmed that these results match well within 20% error range in both two models. In addition, since, it is very important in practical structures to ensure fracture toughness at cryogenic temperatures, cryogenic indentation system was developed. The system was designed and improved by referring to the previous environmental indentation test and conventional environmental facilities. The developed system was applied to materials used in nuclear power plant structures, and compared with the fracture toughness values obtained from the master curve method.구조 건전성 평가는 구조물이나 부품이 파괴를 방지하기 위해 그 구조물이나 부품의 상태를 평가하는 것인데, 구조물의 건전성을 관리하기 위해, 공학자들은 결함의 유무, 설계 응력, 기계적 특성 등을 파악하고자 한다. 그러나 그 중에서도 가장 중요한 요인은 구조물의 기계적 특성으로 강도, 경도 또는 파괴인성 등이 이에 속한다. 구조물이나 설비의 많은 파손 케이스에 있어, 대다수의 파손은 재료의 열화나 취화에 의해 발생하기 때문에, 구조 건전성 평가 시 가동중인 구조물 재료의 기계적 특성을 평가하는 것이 요구된다. 다양한 기계적 특성 중에서도 균열에 대한 저항성의 척도로 표현되는 파괴인성이 구조 건전성 평가의 파괴 역학 분석에 있어 가장 중요한 특성이다. 그러나, 표준에서 제시하고 있는 파괴인성 시험방법은 복잡한 형상과 시험 절차를 요구하고 있기 때문에 가동중인 구조물에 대해 실험을 수행하기에는 거의 불가능하다. 이런 이유에서 비파괴적인 기법을 통해 운용중인 구조물의 기계적 특성을 평가가 요구되고 또 구조 건전성 평가의 신뢰도를 높이고자 연구가 진행되고 있다. 연속압입시험법은 비파괴적으로 가동 중인 구조물에 실험이 가능하여 다양한 기법들 중에서도 가장 유망한 시험법으로 알려져 있다. 이에, 많은 연구자들이 연속압입시험을 통한 파괴인성 예측 연구를 위해 장비와 이론을 개발하고 있다. 이러한 연구는 처음 군열을 직접적으로 발생시키는데서부터 출발하였으나, 결국 대다수의 금속소재들에서는 균열이 발생하지 않기 때문에, 금속소재들을 대상으로 연구가 확장되었다. 금속소재들에서 압입시험 중 균열이 발생하지 않기 때문에 연구는 각각 기계적인 모델링와 파괴 에너지 모델로 나뉘어져 있으나 두 모델에서 모두 실험적인 관계식이나 많은 가정을 포함할 수 밖에 없는 한계가 있었다. 본 연구에서는 압입시험을 통한 파괴인성 예측 모델을 제안하였다. 과거의 많은 연구들이 있었으나, 실험의 간단함과 파괴 역학과의 유사성을 유도할 수 있는 끝이 평평한 플랫 펀치 압입자가 채택되었다. 과거의 플랫펀치 연구에서는 다소 현상적인 측면에서 파괴인성을 예측하고자 하였기 때문에 본 연구에서는 보다 파괴역학적인 관점에서 균열 개시시점을 결정하고자 하였다. 파괴 거동에 따라 모델을 연성 파괴 모델과 취성 파괴 모델로 나누었다. 연성 파괴 모델에는 압입자 하부와 균열 팁 앞에서의 유사한 응력 상태를 연결하기 위해, 플랫 펀치 압입자로 시험을 했을 때 압입자 하부에 발생하는 완전 소성 영역과 균열 앞에서의 소성역이 발생하는 것을 관계 지어 균열 개시 시점을 결정하였다. 취성 파괴 모델에서는 소성이 고려되지 않고, 균열 앞에서의 소성 변형에너지가 최소가 되는 소성역이 소규모 항복 조건이 적용되는 것을 통해 균열 개시시점을 결정하였다. 플랫 펀치 압입자를 사용하면, 압입자의 자기 유사성에 의해 압입자 사이즈에무관한 하나의 일반화곡선을 얻을 수 있고, 그로부터 다른 반지름 사이즈의 하중-변위 곡선을 얻을 수 있다. 그러므로 두 모델에 대해 표준의 파괴인성 시험에 주로 사용되는 1T 두께에 대응하는 압입자 사이즈를 결정하여 이 때의 하중-변위 곡선을 통해 파괴인성을 결정할 수 있다. 제안된 모델을 검증하기 위해 J test 파괴인성 결과와 비교하여 두 모델 모두 20% 내외의 오차 범위를 가지는 것을 확인하였다. 또한, 파괴인성의 주요한 영향인자인 온도 영향을 확인하기 위해 극저온 압입시스템을 개발하였다. 기존의 극저온 환경 시험들을 조사하였고, 이를 바탕으로 극저온 압입시험을 도입하였고, 원자력 발전소 구조물에 쓰인 소재를 수급하여 파괴인성 마스터 커브법의 시험결과와 비교하였다.Chapter 1. Introduction 1 1.1. Object of this Thesis 2 1.2. Outline of the Thesis 6 Chapter 2. Research Background 7 2.1. Fracture Mechanics 8 2.1.1. Overview 9 2.1.2. Stress analysis of cracks 13 2.1.3. Fracture toughness parameters 23 2.1.4. Fracture toughness test 34 2.2. Instrumented Indentation Technique 45 2.2.1. Introduction 45 2.2.2. Indentation tensile properties 47 2.2.3. Evaluation of residual stress 51 2.3. Indentation fracture toughness 59 2.3.1. Introduction 59 2.3.2. Indentation cracking method 60 2.3.3. Spherical indenter model 63 2.3.4. Flat indenter model 74 Chapter 3. Theoretical Modeling 82 3.1. Introduction 83 3.2. Ductile Fracture Model 85 3.3. Brittle Fracture Model 88 3.4. Size adjustment 90 Chapter 4. Experimental Verification 99 4.1. Materials and Methods 100 4.2. Results 103 Chapter 5. Extension to cryogenic environment 119 5.1. Introduction 120 5.2. Development of cryogenic indentation system 121 5.3. Application 125 Chapter 6. Conclusions 134 Reference 137 Abstract in Korean 145 List of publications 148Docto

Representative Stress-Strain Curve by Spherical Indentation on Elastic-Plastic Materials

Tensile stress-strain curve of metallic materials can be determined by the representative stress-strain curve from the spherical indentation. Tabor empirically determined the stress constraint factor (stress CF), ψ, and strain constraint factor (strain CF), β, but the choice of value for ψ and β is still under discussion. In this study, a new insight into the relationship between constraint factors of stress and strain is analytically described based on the formation of Tabor’s equation. Experiment tests were performed to evaluate these constraint factors. From the results, representative stress-strain curves using a proposed strain constraint factor can fit better with nominal stress-strain curve than those using Tabor’s constraint factors

Indentation Modulus, Indentation Work and Creep of Metals and Alloys at the Macro-Scale Level: Experimental Insights into the Use of a Primary Vickers Hardness Standard Machine

open5In this work, the experimental method and the calculation model for the determination of indentation moduli, indentation work, and indentation creep of metallic materials, by means of macroscale-level forces provided by a primary hardness standard machine at the National Institute of Metrological Research (INRIM) at the at room temperature were described. Indentation moduli were accurately determined from measurements of indentation load, displacement, contact stiffness and hardness indentation imaging and from the slope of the indentation unloading curve by apply-ing the Doerner-Nix linear model; indentation work, representing the mechanical work spent dur-ing the force application of the indentation procedure, was determined by calculating the areas un-der the loading–unloading indentation curve, through fitting experimental data with a polynomial law. Measurements were performed with a pyramidal indenter (Vickers test). The applied force was provided by a deadweight machine, and the related displacement was measured by a laser inter-ferometric system. Applied forces and the occurring indentation depths were simultaneously meas-ured: the resulting loading–unloading indentation curve was achieved. Illustrative tests were per-formed on metals and alloy samples. Discussion and comments on the suitability of the proposed method and analysis were reported.openAlessandro Schiavi, Claudio Origlia, Alessandro Germak, Andrea Prato, Gianfranco GentaSchiavi, Alessandro; Origlia, Claudio; Germak, ALESSANDRO FRANCO LIDIA; Prato, Andrea; Genta, Gianfranc

Determination of the mechanical properties of amorphous materials through instrumented nanoindentation

A novel methodology based on instrumented indentation is developed to determine the mechanical properties of amorphous materials which present cohesive-frictional behaviour. The approach is based on the concept of a universal hardness equation, which results from the assumption of a characteristic indentation pressure proportional to the hardness. The actual universal hardness equation is obtained from a detailed finite element analysis of the process of sharp indentation for a very wide range of material properties, and the inverse problem (i.e. how to extract the elastic modulus, the compressive yield strength and the friction angle) from instrumented indentation is solved. The applicability and limitations of the novel approach are highlighted. Finally, the model is validated against experimental data in metallic and ceramic glasses as well as polymers, covering a wide range of amorphous materials in terms of elastic modulus, yield strength and friction angle