On Establishing Elastic–Plastic Properties of a Sphere by Indentation Testing

Instrumented indentation is a popular technique for determining mechanical properties of materials. Currently, the evaluation techniques of instrumented indentation are mostly limited to a flat substrate being indented by various shaped indenters (e.g., conical or spherical). This work investigates the possibility of extending instrumented indentation to non-flat surfaces. To this end, conical indentation of a sphere is investigated where two methodologies for establishing mechanical properties are explored. In the first approach, a semi-analytical approach is employed to determine the elastic modulus of the sphere utilizing the elastic unloading response (the “unloading slope”). In the second method, reverse analysis based on finite element analysis is used, where non-dimensional characteristic functions derived from the force–displacement response are utilized to determine the elastic modulus and yield strength. To investigate the accuracies of the proposed methodologies, selected numerical experiments have been performed and excellent agreement was obtained

On the Uniqueness and Sensitivity of Indentation Testing of Isotropic Materials

Instrumented indentation is a popular technique to extract the material properties of small scale structures. The uniqueness and sensitivity to experimental errors determine the practical usefulness of such experiments. Here, a method to identify test techniques that minimizes sensitivity to experimental erros is in indentation experiments developed. The methods are based on considering “shape functions,” which are sets of functions that describe the force–displacement relationship obtained during the indentation test. The concept of condition number is used to investigate the relative reliability of various possible dual indentation techniques. Interestingly, it was found that many dual indentation techniques can be as unreliable as single indentation techniques. Sensitivity analyses were employed for further understanding of the uniqueness and sensitivity to experimental errors of indentation techniques. The advantage of the Monte Carlo approach over other procedures is established. Practical guidelines regarding the selection of shape functions of force–displacement relationship and geometric parameters, while carrying out indentation analysis are provided. The results suggest that indentation experiments need to be very accurate to extract reliable material properties

Conical Indentation of a Viscoelastic Sphere

Instrumented indentation is commonly used for determining mechanical properties of a range of materials, including viscoelastic materials. However, most—if not all—studies are limited to a flat substrate being indented by various shaped indenters (e.g., conical or spherical). This work investigates the possibility of extending instrumented indentation to nonflat viscoelastic substrates. In particular, conical indentation of a sphere is investigated where a semi-analytical approach based on “the method of functional equations” has been developed to obtain the force–displacement relationship. To verify the accuracy of the proposed methodology selected numerical experiments have been performed and good agreement was obtained. Since it takes significantly less time to obtain force–displacement relationships using the proposed method compared to conducting full finite element simulations, the proposed method is an efficient substitute of the finite element method in determining material properties of viscoelatic spherical particles using indentation testing

Aspects of Experimental Errors and Data Reduction Schemes From Spherical Indentation of Isotropic Materials

Sensitivity to experimental errors determines the reliability and usefulness of any experimental investigation. Thus, it is important to understand how various test techniques are affected by expected experimental errors. Here, a semi-analytical method based on the concept of condition number is explored for systematic investigation of the sensitivity of spherical indentation to experimental errors. The method is employed to investigate the reliability of various possible spherical indentation protocols, providing a ranking of the selected data reduction protocols from least to most sensitive to experimental errors. Explicit Monte Carlo sensitivity analysis is employed to provide further insight of selected protocol, supporting the ranking. The results suggest that the proposed method for estimating the sensitivity to experimental errors is a useful tool. Moreover, in the case of spherical indentation, the experimental errors must be very small to give reliable material properties

Aspects of Experimental Errors and Data Reduction Schemes From Spherical Indentation of Isotropic Materials

Sensitivity to experimental errors determines the reliability and usefulness of any experimental investigation. Thus, it is important to understand how various test techniques are affected by expected experimental errors. Here, a semi-analytical method based on the concept of condition number is explored for systematic investigation of the sensitivity of spherical indentation to experimental errors. The method is employed to investigate the reliability of various possible spherical indentation protocols, providing a ranking of the selected data reduction protocols from least to most sensitive to experimental errors. Explicit Monte Carlo sensitivity analysis is employed to provide further insight of selected protocol, supporting the ranking. The results suggest that the proposed method for estimating the sensitivity to experimental errors is a useful tool. Moreover, in the case of spherical indentation, the experimental errors must be very small to give reliable material properties