Monitoring Time-Dependent Deformation in Small Volumes
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MONITORING TIME-DEPENDENT DEFORMATION IN SMALL VOLUMES T P Weihs and J B Pethica Department of Materials, Oxford University, Parks Road, Oxford OXI 3PH, England.
ABSTRACT Time-dependent deformation (TDD) in small volumes was monitored using an alternating (AC) force technique and a Nanoindenter. The AC technique provides a continuous measure of contact stiffness during an indentation. By holding the force constant and monitoring the stiffness, the applied pressure and an effective strain rate were measured. Reasonable strain rate sensitivities were obtained for permanent indentations involving significant plastic strains. Time-dependent recovery due to residual strain energy is also reported. For reversible, elastic indentations, TDD was seen when the applied force was held constant. The deformation is attributed to atomic diffusion. INTRODUCTION Indentation testing offers a quick and convenient means for measuring time-dependent properties of materials over a range of temperatures [1-5]. Compared to conventional creep tests, indentation-creep experiments are particularly useful when the testing temperatures are high and when the sample volumes are very small. This paper concerns the latter condition and attempts to show that quantitative measures of TDD can be made from indentations less than 5nm in depth. Most indentation-creep experiments are stress relaxation experiments that utilize spherical, conical, or pyramidal indenters [1-3]. Typically, the force on a tip is held constant and its movement into the sample is monitored by measuring the depth or area of contact. As the depth and area increase, the applied pressure decreases and the stresses in the zone of deformation relax. In other creep experiments, displacement [6] or loading rate [7] are controlled instead of the force. Each technique has particular advantages. For this study, a constant force is applied while stiffness is monitored continuously. In early attempts to quantify time-dependent deformation, the effective stress or applied pressure was measured as a function of time [1,2]. More recently, particularly with the development of depth-sensing instruments, the applied pressure is referred to as an effective stress and it is measured as a function of an effective strain rate [6,7]. The effective stress is simply given by aeff = pressure=
F
(1)
where F is the applied force and A is the projected area of contact. The effective strain rate is slightly more elusive than 0 eff. Generally, it refers to the rate at which the hemispherical plastic
zone under a tip moves radially outward, relative to its current size or scale. For the case of pyramidal or conical tips, the stress fields and displacement fields in these zones are self-similar [2]. They change only in scale and not in shape [2]. Since the depth of an indentation, u, and the radius of contact, a, both measure the scale of an indentation, the effective strain rate is commonly defined [2,4,6,7] as -eff = u u a
(2)
Mat. Res. Soc. Symp. Proc. Vol. 239. @1992 Materials Research Society
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