Haasen Plot Activation Analysis of Constant-Force Indentation Creep in FCC Systems
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1049-AA10-03
Haasen Plot Activation Analysis of Constant-Force Indentation Creep in FCC Systems Vineet Bhakhri, and Robert J. Klassen Mechanical & Materials Engineering, The University of Western Ontario, London, N6A 5B9, Canada ABSTRACT An analysis of the length-scale and temperature dependence of Haasen plots obtained from constant-force nano- and micro-indentation creep tests are reported here. The operative deformation mechanism for all the systems studied involved dislocation glide limited by dislocation-dislocation interactions. Our findings illustrate the potential usefulness of Haasen plot activation analysis for interpreting data from constant-force pyramidal indentation creep tests.
INTRODUCTION The use of Haasen plot activation analysis to characterize the operative plastic deformation mechanisms in materials subjected to uniaxial loading is well established [1-5]. This type of analysis involves plotting the experimentally determined inverse activation area 1 ∆a of the deformation process versus the applied shear stress τ. The resulting “Haasen plot” gives information on the operative mechanism of plastic deformation. Linear trends of 1 ∆a and τ indicates that dislocation glide in the test material is being limited by dislocation/dislocation interactions (i.e. the Cottrell-Stokes law is maintained) while nonlinear trends arise from the cumulative effect of several types of obstacles or to a changing microstructural state within the sample during the test. The application of Haasen plot activation analysis to interpret indentation creep test data is very attractive from the view point of understanding local variations in plastic deformation across complex microstructures [6]. Indentation test data are, however difficult to interpret due to the complex stress and strain states within the indentation plastic zone. During a Constant Force (CF) pyramidal indentation test the indenter applies a high local stress state, represented by the average indentation stress σ ind , to the indented sample. The sample creeps and this causes the indentation depth h to increase. Since the indentation force is held constant σ ind decreases as h increases. The average indentation stress σ ind and local indentation strain rate ε&ind can be expressed, for a Berkovich indenter, as
σ ind =
F h& and ε&ind = αA(h) h
(1)
where α is an empirically derived function accounting for the sink-in/pile-up effects around the indenter and A(h) is the area function of the indenter probe. Both σ ind and ε&ind are average values
representing the complex distribution of ε& and σ within the indentation plastic zone. We can represent these distributions by an equivalent average indentation shear stress, τ ind and an equivalent average indentation shear strain rate γ&ind as
τ ind =
σ ind 3 3
and γ&ind = 3ε&ind =
3h& h
(2)
Since the local stress around the indentation is very large, the underlying deformation mechanism, in most ductile metals, is one involving obstacle-limited dislocation glide. The relationship between γ&ind and τ ind f
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