A Study to Predict Instrumented Indentation Curve through The Analysis of Entropy Flow At High Temperature

Abstract

Instrumented indentation testing (IIT) can measure many mechanical properties, from basic properties, such as elastic modulus and hardness, to advanced properties, such as tensile properties, fracture toughness, fatigue and creep

this is done by measuring the penetration depth from a material surface of an indenter in loading and unloading. The strongest advantage of instrumented indentation testing over conventional mechanical testing is that the specimen volume required is very small, giving IIT the merits of simplicity, economy, non-destructiveness, and in-field applicability. Thus, instrumented indentation testing can be used for various materials from metal alloys to amorphous materials to bio materials, and it can also be used over a wide range of scales from macro to micro/nano. However, because IIT is a new test method, studies of IIT have focused primarily on validating the testing method itself and correlating its results with those of other testing methods. In addition, studies on IIT have largely been carried out at room temperature

research at high and low temperatures or in corrosive environments are relatively few. The reason for this narrow focus is that, for example, thermal drift (the temperature difference between indenter and specimen) can lead to error in mechanical measurements, making it difficult to ensure stable experimental data. The goal of this thesis was to reduce the error reported in previous research and to develop a high-temperature instrumented indentation system (HTIIS) appropriate for the macro scale in temperatures up to 650°C. This entailed devising a method to determine the accurate contact area. The pileup phenomenon around the indenter in high-temperature IIT was quantified and its physical meaning was analyzed, and a new calibrating factor f(T) was developed to correct for the pileup effect. Conventional high-temperature Vickers testing was conducted to verify the reliability of HTIIS and the use of f(T). However, the difficulty in determining the contact area function is that the experiments must be performed every time at the same temperature: in other words, the contact area calibration function depends on the sample and on the experimental conditions. Therefore, to break away from that empirical study, an additional compensating study was performed. In this compensating study, the relationship of hardness and temperature, that is a modified Westbrooks equation, is newly defined using the shape of existing constitutive equations containing thermodynamic foundation. In the mathematical development here, the physical meaning of each parameter is considered. Thus the indentation contact depth for penetration can be expressed as a function of the indentation variables and temperature. In addition, the contact area using the newly defined equation is compared to that from conventional optical observations. And, to ensure the validity of that compensating study results, hardness values for the same materials obtained from a different institution are compared with hardness results from this study. This sequence of studies suggests a general equation to calculate the contact area and hardness at high-temperatures. However, high-temperature indentation and material behavior cannot be fully elucidated by these mechanical approaches because the specimens are affected by heat energy. Therefore, a theoretical thermodynamic consideration of heat was necessary. First, the concept of indentation work as defined by Cheng and Cheng can be extended to resilience as a mechanical parameter, and its relationship with stiffness, which can be obtained from the unloading curve in IIT, was investigated. In addition, the relationship was explored between stiffness and internal energy, which is a thermodynamic parameter. The relationship between the stiffness and Helmholtz free energy can be investigated by analyzing the entropy flow during loading and unloading in high-temperature IIT. That is, after indentation, the entropy contributing to elastic recovery of the impression mark is calculated, and it is confirmed that the mechanical factor and the thermodynamic factor can be combined through entropy. these Hence the load-depth (L-h) curve at high temperature can be predicted by the change in the indentation depth according to the temperature and the stiffness-Helmholtz relationship. A calibration method for the predicted L-h curve is suggested using the maximum IIT load measurable at room temperature. The predicted high-temperature L-h curve is verified by comparison with the L-h curve measured at the actual temperature. This thesis provides a new perspective on the analysis of the indentation load-depth curve, and posits a mathematical relevance and physical meaning of the parameters that should be considered in high-temperature studies.