Elsevier

Scripta Materialia

Volume 44, Issue 12, 8 June 2001, Pages 2713-2719
Scripta Materialia

Numerical investigations of pyramid indentation on powder compacts

https://doi.org/10.1016/S1359-6462(01)00964-2Get rights and content

Introduction

The strength of powder metallurgy compacts correlate strongly with its density. Hence precise evaluation of density variations in powder compacts are of utmost importance. The basic assumption in hardness testing is that the material is homogeneous but in powder compacts the voids are generally present throughout the material in a variety of shapes, sizes and also in clusters. One simple method to obtain density distribution is by sectioning the specimens into small pieces and determining the density of each piece. This method is complicated, time consuming and results in destruction of the component. Other methods involve the use of radiography, ultra violet light rays, image analysis etc. These techniques require expensive equipment. The most common method adopted in shop floor is the use of hardness measurements for determining the density distribution in compacted specimens [1].

Spherical ball indentations have been used 2, 3 to obtain the density distribution within the compact. Rockwell hardness testing produces large indentation hence not commonly used to determine the density distribution except for obtaining the overall density of compact. Vickers hardness measurement is generally used to evaluate the density distribution within the compact 1, 4. Various loads have been applied for hardness testing of powder compacts. Shamasundar et al. [5] have suggested that the load applied should be such that the indentation produced is larger than the average particle size. Irrespective of the load applied, significant scatter has been observed in Vickers hardness measurement of powder compacts 6, 7. The scatter in the data needs to be investigated, as the current requirement of high quality load bearing parts require very tight control over density distribution.

Deformation behaviour at a larger scale may not be much affected by this non-uniform void distribution. In the case of focussed local deformation, where the behaviour of a very small volume dominates the process, like hardness measurement, the non-uniformity will affect the local ductility 8, 9. Although hardness measurements in powder compacts have been used extensively, very little effort has been made to understand the influence of the presence of non-uniform voids on the measurements

Analytical studies on indentation process have been presented by Chen and Engel [10] for punch contact in layered media and by King [11] for thin films on substrates. These solutions are applicable only for elastic deformation. Johnson [12] has proposed semi-empirical relations for indentation process. Finite element method has been used to perform elasto-plastic analysis of spherical indentation 13, 14 and wedge indentation 15, 16. Bhattacharya and Nix [17] and Blanchard [18] have presented finite element studies for conical indentation. These studies mainly concentrated on the load-depth response during the process. Bhattacharya and Nix [17] approximated pyramid indentation as conical and performed axisymmetric analysis. Three dimensional FE analysis of pyramid indentation process has been performed by Giannakopoulos et al. [19] The influence of strain hardening and yielding stress on deformation during indentation has been examined and proved to be in good agreement with experimental results. Giannakopoulos and Larsson [20] have also extended their studies with the materials modelled according to the Drucker-Prager elasto-plastic law and provided valuable information regarding indentation of pressure sensitive hard materials and ceramics. Finite element simulation of indentation process on porous solids has been presented by Fleck et al., [21]. The effect of porosity upon the indentation resistance and the plastic deformation at the indentation zone have been explored. They performed two-dimensional analysis of conical indentation based on Gurson’s porous plasticity theory.

In the present study a detailed three dimensional finite element analysis of pyramid indentation process has been performed with the aim (1) to provide a better understanding of the deformation behaviour including compaction and pile-up of material and (2) to bring out the effect of random voids on the hardness measurement. These results have been compared with experimentally determined values.

Section snippets

Experiments

Hardness measurements have been made on specimens with different densities made from iron powder compacted quasistatically. Cylindrical specimens of 20mm diameter with compacted heights less than 7.5mm were used. The heights were kept small so as to keep the density variation within the compact as low as possible. The specimens were sintered and carefully sectioned longitudinally along the diameter by thin diamond wheel cutter. Hardness measurements have been made by using a digital Vickers

Results and discussion

Hardness values in N/mm2 obtained from experiments and numerical simulation are shown in Figure 2. Significant scatter can be observed in experimentally determined values. The voids present in the compact may affect the local deformation and hence cause variation in the hardness value obtained. Hardness values obtained by numerical simulation for Case 1 gives the upper bound of the experimental values. This may be due to the fact that the constitutive model does not account for the

Conclusions

Three-dimensional analysis of the pyramid indentation process has been performed using Finite element method. The results from simulation showed good correlation with the experimentally determined values. The presence of non-uniform size and distribution of voids in powder compacts has been found to affect the hardness values obtained. Hence large scatter in data can be taken to be a measure of uniformity of void distribution. Material densification occurs in the plastic deformation zone during

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