Plastic Deformation During Indentation Of Crystalline And Amorphous Materials

Abstract

Indentation hardness, H, has been widely used to characterize the mechanical properties of materials for more than a century because of the following advantages of this technique; (1) it requires small sample and (2) the test is non destructive in nature. Recent technological advances helped in the development of instrumented indentation machines which can record the load, P, vs. displacement, h, data continuously during indentation with excellent load and displacement resolutions. From these, H and the elastic modulus, E, of the indented material can be obtained on the basis of the ‘contact area’ of the indentation at the maximum load. The estimation of true contact area becomes difficult during ‘pile-up’ and ‘sink-in’, commonly observed phenomena while indentation of a low and high strain hardened materials. In order for the better understanding of these phenomena it is important to understand the plastic flow distribution under indenters. It is also important for the prediction of elastic-plastic properties from the P-h data. Recently, there have been considerable theoretical and simulation efforts on this front with a combination of dimensional analysis and finite element simulations. One of the important input parameter for the dimensional analysis is the ‘representative strain’ under the indenter, which is a strong function of the indenter geometry. However there is no comprehensive understanding of the representative strain under the indenter despite several studies till date. One objective of the present thesis is to conduct an experimental analysis of the plastic flow during the sharp indentation. The plastic zone size and shape under conical indenters of different apex angles in a pure and annealed copper were examined by employing the subsurface indentation technique to generate the hardness map. From these isostrain contours are constructed joining the data having similar strain values. The following are the key observations. (1) The plastic strain contours are elliptical in nature, spreading more along the direction of the indenter axis than the lateral direction. (2) The magnitude of the plastic strain in the contact region decreases with increasing the indenter angle. (3) The strain decay in the indentation direction follow a power-law relation with the distance. The estimated representative strains under the indenters, computed as the volume average strain within the elastic-plastic boundary, decreases with increasing indenter angle. We also performed finite element simulations to generate plastic flow distribution under the indenter geometries and compared with the experimental results. The results suggest that the experimental and computed average strains match well. However, the plastic strain contours do not, suggesting that further detailed understanding of the elasto-plastic deformation underneath the sharp indenter is essential before reliable estimates of plastic properties from the P-h curves can be made routinely. The second objective of this thesis is to understand plastic flow in amorphous alloys. It is now well established that plastic deformation in metallic glasses is pressure sensitive, owing to the fundamentally different mechanisms vis-à-vis the dislocation mediated plastic flow in crystalline metals alloys. Early work has shown that the pressure sensitivity of amorphous alloys gets reflected as high constraint factor, C (hardness to yield stress ratio), which sometimes exceed 3.0. In this thesis, we study the temperature dependence of pressure sensitive plastic flow in bulk metallic glasses (BMGs) using C as the proxy for the pressure sensitivity. Experiments on three different BMGs show that C increases with temperature hence the pressure sensitivity. In addition we have carried out finite element simulations to generate P-h curves for different levels of pressure sensitivities and match them with the experimental curves that are obtained at different temperatures. Simulations predict that higher pressure sensitivity index values are required to match the experimental curves at high temperatures confirming that the pressure sensitivity increases with increasing temperature. The fundamental mechanisms responsible for the increase in pressure sensitivity are discussed in detail. Finally we pose a question, is the increase in pressure sensitivity with temperature is common to other amorphous materials such as strong amorphous polymers? In order to answer this question we have chosen PMMA, a strong amorphous polymer. In this study also we have taken C as a proxy to index the pressure sensitivity. Indentation stress-strain curves are constructed at different temperature using spherical indentation experiments. The C values corresponding to different temperatures are determined and plotted as a function of temperature. It is found that C increases with temperature implying that the pressure sensitivity of amorphous polymers also increases with temperature. The micro-mechanisms responsible for the increase in pressure sensitivity are sought.