Determining the exponent of the unloading curve when flattening a sphere

To study the flattening of the sphere, it is proposed to use the kinetic indentation diagram by the plane. Given the known values of the reduced elastic modulus, applied force, maximum and residual deformation, it is possible to determine the contact area. It is indicated that in this regard, the exponent of the unloading curve of a pre-loaded sphere with a flat rigid surface plays an important role. The analysis of methods for determining the unloading curves of unloading for the finite element models, taking into account strain hardening, is carried out. It is shown that dependences of the unloading curves during flattening on the relative indentation in the form and the range of values differ from the similar ones during indentations of the sphere. The dependence between the exponents of the unloading curves for the force and for the area is determined. The range of correct use of the results of the finite element analysis of a hemisphere for rough surfaces is indicated. The exponent of the unloading curve after flattening the spherical segment from the half-space property is determined.

EVALUATION OF THE ELASTIC COMPLIANCE OF THE HARDNESS TESTER IN KINETIC INDENTATION TESTS

When determining the mechanical properties of materials in kinetic indentation tests using indentation diagrams, careful consideration of the elastic compliance of the device, i.e., the hardness tester, is required. The determined values of the Young's modulus of the tested material substantially depend on the reliability of the method of evaluation and accounting for the elastic compliance. Therefore, verification of the test techniques based on kinetic indentation should be carried out using the materials with the known, but rather different values of the Young's modulus. Successful experience has been gained to date in the evaluating and accounting for the elastic compliance of the device upon kinetic indentation of the materials by a diamond pyramid which is reflected in the relevant standards. However, there is no way of transferring this experience to the kinetic indentation by a steel or carbide ball without additional research and experimental verification. We proposes a technique for estimating the elastic compliance of a hardness tester using a kinetic ball indentation diagram based on the G. Hertz equation for the case of elastic contact of a ball with a plane. A linear correlation has been determined between the additional elastic deformations of the device and indentation load, which is characteristic of each device and independent on the ball diameter. The obtained dependence allows for correct consideration of the elastic compliance of the device using software applications in recording and processing the ball indentation diagrams. Experiments have been carried out to determine the hardness and the Young's modulus through ball instrumented indentation of different materials (steel, aluminum alloy, magnesium alloy, and titanium alloy) using the existing and developed methods of taking into account the elastic compliance of the device. The coincidence or proximity of the values of the Young's modulus of the same material determined from the ball indentation diagrams and sample tensile tests is considered the main criterion proving the accuracy of the technique. The advantages and shortcomings of the known and proposed procedures are discussed along with practical recommendations for their applications.

Energy Approach to Material Hardness Determination

Energy hardness is defined as energy density of material plastic displacement from the initial surface level. It is convenient to determine it from the kinetic indentation diagram constructed in the coordinates , where is a relative load, is a relative penetration of a spherical indenter. It dhould be note that a relative energy density is equal to multiplied by the parameter where varies within a narrow range for constructional materials used in machine building. A mean relative error in finding energy hardness by this approach does not exceed 5%. It is shown that for the majority of mechanical engineering materials energy hardness is intermediate between plastic hardness and Meyer’s hardness.