General methodology to estimate the dislocation density from microhardness measurements
Graphical Abstract
Introduction
Plastic properties of metals such as work hardening and ductility are intrinsically related to the content and type of microstructural defects. Understanding the influence of these defects is essential to understanding the materials' mechanical response under different loading conditions [1]. For instance, it is widely accepted that dislocations have the major influence on the mechanical plastic response. However, determining dislocation density in metals is one of the classical problems in materials science, and efforts to tackle this problem have been under development for many decades. Transmission Electron Microscopy (TEM) is generally used to estimate dislocation density directly [2], [3], [4]. However, the area analysed by TEM is typically very small, this leads to local observations rather than bulk measurements [5], [6], [7]. Another methodology to quantify dislocation density is by analysing the broadening of peaks in X-ray diffraction (XRD) measurements. However, XRD cannot distinguish between phases that have similar lattice parameters, such as the ferrite and martensite phases in iron [8]. As a result, alternative approaches which provide bulk and accurate measurements of dislocation density are required.
Two types of dislocations can present during plastic deformation: Statically Stored Dislocations (SSDs), which evolve during uniform plastic deformations (uniform strains), and Geometrically Necessary Dislocations (GNDs) that exist only to accommodate strain gradients. Non-uniform strains take place near crack tips and in the plastic zones of microhardness and nanoindentation [9], [10]. Many studies have shown that hardness in metallic materials in the microhardness and nanoindentation ranges increases considerably with decreasing the indentation depth because of the GNDs [11], [12], [13], [14], [15]. This effect is known as the Indentation Size Effect (ISE) [11]. De Guzman et al. [15] and Stelmashenko et al. [16] proposed a model describing the relationship between the total dislocation density and hardness. This model assumes that hardness results only from dislocations and classifies the hardness based on the indentation depth. Macrohardness results only from the SSDs at relatively large indentation depths, and microhardness results from linear superposition of the GNDs and SSDs at small indentation depths. Graca et al. [7], [17] used this model to estimate the density of SSD. They assumed that the radius of the stored volume of GNDs is larger than the contact radius of indentation by a factor (f). They assumed that f has a constant value of 1.9 [7], [17]. However, it should be noted that their approach is only valid for pure Face-Centred Cubic (FCC) metals, where the material resistance is only generated from dislocations; and assuming f = 1.9 for different types of materials is not always valid as explained by Durst et al. [14]. Consequently, the approach of using microhardness measurements to estimate the density of SSD needs to be revised to become suitable as a general method for estimating the density of SSD for different materials.
In this paper we propose a general approach to estimate the density of SSD in cubic metals, regardless of the degree of purity, using microhardness experimental data. The suitability of the suggested approach was confirmed for pure metals and dual phase Lean Duplex Stainless Steel 2101 alloy (LDSS 2101), which has a 50/50% distribution of ferrite (Body-Centred Cubic (BCC)) and austenite (FCC) phases with a significant alloying content.
Section snippets
Material and Sample Preparation
A 20 mm-thick Lean Duplex Stainless Steel (LDSS 2101) plate obtained from Outokumpo® was used in this study. The plate was hot rolled, heat treated at 1050 °C and then quenched in water. Table 1 shows the full chemical composition of the investigated LDSS 2101. Sample preparation for microstructural examinations and hardness measurements was performed following standard metallographic procedures up to vibratory polishing with 0.02 μm non-crystallizing colloidal silica suspension.
Microstructural Examinations
Microstructural
Proposed Methodology to Estimate Dislocation Density
In order to establish a general method for predicting the density of SSD accurately, it is necessary to consider all factors affecting materials' response. The overall resistance against plastic deformations in metallic materials is the sum of the following strengthening mechanisms [21]: the internal friction stresses (e.g. Peierls barriers), solid solution strengthening, grain boundary strengthening, and dislocation strengthening [22]. By considering all these factors, the total hardness (H)
Initial Microstructural Analysis
EBSD maps (Fig. 5) show that the studied LDSS 2101 has two phases: α-ferrite (BCC) and γ-austenite (FCC). The volume fractions were estimated at 43% and 57% for the ferrite and austenite phases, respectively. The ferrite phase had an average grain size of ~ 75 μm while the average grain size of the austenite phase was ~ 25 μm.
The as-received plate had substructures inside the ferrite phase and high density of annealing twins inside the austenite phase, as shown in Fig. 6. EBSD phase map with Image
Conclusions
A general approach to estimate the density of Statically Stored Dislocations (SSD), using microhardness measurements has been presented. This approach was validated using reported experimental data for pure cubic metals (Ni and W) and our results for Lean Duplex Stainless Steel LDSS 2101. The main conclusions are:
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Microhardness measurements with indentation depths larger than 200 nm were correlated to the dislocation densities via the ISE and microstructural strengthening mechanisms to establish
Acknowledgements
The authors would like to thank Prof. Sean Cadogan in the School of Physical, Environmental and Mathematical Sciences at The University of New South Wales Canberra for his support in performing X-ray diffraction experiments. Dr. Zakaria Quadir at Faculty of Science and Engineering at Curtin University is also acknowledged for his help with EBSD measurements. Moreover, the authors are grateful for the support of A/Prof. Jodie Bradby and Mr. Christopher Tanner in the Department of Electronic
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