Uniaxial compression and spherical indentation behavior of porous copper

Bodapati, Bolla Reddy and Bhattacharjee, Pinaki Prasad (2019) Uniaxial compression and spherical indentation behavior of porous copper. PhD thesis, Indian institute of technology Hyderabad.

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Abstract

The plastic flow behavior of materials is normally determined on the basis of uniaxial tensile/compressive tests. However, the use of this technique is not straightforward in case of coatings or when the volume of the material available for testing is very small. Indentation technique (especially with a spherical ball or spherical tip as the indenter) is a good alternative for determining the plastic flow behavior of coatings and thin films and also to understand the behavior of individual phases in multi-phase alloys. While the indentation technique is simple, fast and relatively inexpensive, it poses a significant challenge in terms of data analysis compared to uniaxial testing. The primary origin of such a challenge is linked to the fact that the stress fields underneath the indent are not uniform and the measured response is an aggregate of the complex tri-axial stress field. In spite of this challenge, the pioneering work of David Tabor presented a simple methodology to relate the spherical indentation and uniaxial response of bulk materials. Tabor first demonstrated that the hardness (H) and corresponding contact radius (a) at a given load using a spherical indenter of radius R, can be converted to uniaxial plastic flow stress-strain data using the conversion factor C (called constraint factor) for converting the hardness to equivalent uniaxial flow stress and the second conversion factor q (called Tabor coefficient) for converting a/R, which was taken as a measure of indentation strain, to uniaxial plastic equivalent strain. Given the fact that indentation occurs under multiaxial stress state, it is rather surprising that one can easily obtain the uniaxial plastic flow stress-strain from hardness data using the two conversion factors mentioned above. However, repeated indentation experiments on a wide range of metallic materials have demonstrated the validity of the approach. Of the two conversion factors, factor C has a sound theoretical basis while on the other hand, the Tabor coefficient has no theoretical basis and many investigators have felt that it is an empirical fitting parameter. Besides, most of the prior work involves assumptions about one of the conversion factors to calculate the other. Furthermore, the validity of such an approach for porous materials and the new scaling relationships and deformation behavior that arises due to the porosity has not been systematically studied. In view of the above, a systematic study has been carried out to understand the influence of porosity on the post-yield behavior of porous copper. As a first step towards synthesizing porous samples, an electrolytic copper powder having an average size of 67 µm was selected to generate porous Cu samples. Spark Plasma Sintering (SPS) technique was employed to generate sintered porous Cu samples with different levels of porosities. In order to generate samples with the required amount of porosity, the process parameters in SPS were optimized. During the process of optimization, sintered compacts were also heat treated to attain a fully annealed condition irrespective of their initial porosity. Standard Archimedes principle was used to measure the density and thereby the porosity in the sintered samples. The samples were designated on the basis of a rounded off value of maximum porosity attained for a given process parameter. For example, Cu2 refers to the Cu sample with a porosity range from 1 – 2.3% while Cu with 24.1 – 25% porosity was designated as Cu25. Uniaxial compression and spherical indentation tests on samples having different levels of porosity were carried out using Universal Testing Machine (UTM) at room temperature. All the tests were conducted at constant crosshead speed of 0.2 mm/min. During uniaxial compression, the Digital Image Correlation (DIC) technique was employed to measure the displacements. Samples having porosities in the range 2 – 25% were compressed to three different levels of strain, i.e., 0.08, 0.17 and 0.26. During the compression process, the load was obtained from the load cell and displacements were obtained from crosshead and DIC. The load-displacement data was converted to true stress-true strain data for Cu2, Cu4, Cu9, Cu15, Cu19 and Cu25 samples. The stress-strain curve shifts downwards with increasing porosity. The porosity evolution for samples with different initial porosity can be normalized by dividing the porosity values at various strain levels by their initial porosity, wherein the normalized porosity for all the samples irrespective of initial porosity falls on a single linear curve with a negative slope. This reduction in porosity leads to correct the stress values calculated using the standard procedure. Also, the instantaneous strain hardening rate (

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