On the extraction of yield stresses from micro-compression experiments

Highlights

• Digital image correlation used to aid analysis of micro-compressive loading curves.

• Linking of deformation events to features in loading curve via strain comparison.

• Elimination of systematic errors related to micro-compression test setup.

• Substantial reduction of uncertainty of CRSS values extracted.

Abstract

It is widely stated that yield stress extraction from micro-compression testing can be unreliable due to factors such as the pillar taper, pillar-punch misalignment and lateral displacement for example through discrete slip events. This study reports on how these factors can be eradicated when using digital image correlation based strain mapping. This approach is demonstrated through a conventional micropillar compression experiment using the hexagonal MAX phase system Cr₂AlC. The use of this approach enables the uncertainty of the extracted yield stress values to be significantly reduced and effectively increases the precision of critical resolved shear stress extraction for basal plane slip from ±52% to ±4% of the mean value. The findings suggest that the statistical variations commonly observed in micro-compression tests may frequently be linked to systematic errors in the stress measurements taken, and that precise evaluation of deformation statistics can only be facilitated if the pillar deformation morphology is closely monitored.

Introduction

Micropillar compression, also referred to as micro-compression, is widely used in the analysis of small-scale deformation. Its range of application includes the study of mechanical size effects and microplasticity in metals [[1], [2], [3], [4], [5], [6], [7], [8], [9], [10], [11], [12], [13], [14]], the determination of mechanical properties of thin films and small sample volumes [[15], [16], [17]] and the evaluation of the governing deformation mechanisms in multiphase materials [[18], [19], [20], [21], [22]]. The method has also gained increased popularity in assessing the deformation behaviour of brittle materials, as the small length scales allow plasticity to be studied through the suppression of brittle fracture [[23], [24], [25], [26], [27], [28], [29]].

Typically, a micro-compression specimen is prepared by focused ion beam (FIB) milling in the form of a cylindrical or cuboidal pillar with a diameter or side length < 10 μm. This specimen is further compressed using a nanoindenter in combination with a flat punch that is of greater diameter than the micropillar. The micro-compression test yields load displacement data that is clearly separated into an elastic region and a region of plastic flow. This data is usually converted to a standard uniaxial stress-strain curve using the pillar cross section and height as reference [1]. An often-observed characteristic of the micro-compressive loading curve is a form of jerky plastic flow, which arises as a result of stochastic deformation events within the pillar [[1], [2], [3]]. If compression is carried out in load-controlled mode, i.e. under constant loading rate, this effect manifests itself as strain bursts in the loading curve [[1], [2], [3], [4], [5], [6], [7], [8], [9], [10],14,17,[24], [25], [26]]. Each strain burst evolves at constant stress, and individual bursts are separated by short elastic loading intervals. If the test is performed in displacement-controlled mode (i.e. under constant displacement rate), as has become common practice for better test control, serrated yielding is observed instead [11,[13], [14], [15],18,21,22,[26], [27], [28], [29], [30], [31], [32]]. Here, the strain bursts develop into yield drops with an upper and lower yield stress, with mainly elastic loading again being observed between individual yield drops.

The micro-compression method was first designed to allow for eased extraction of yield stresses and critical resolved shear stresses from small scale testing [1]. Yet, there are several factors that might induce errors into these stress measurements. For example, although the majority of micro-compression experiments refer to a tapered specimen due to most pillars being prepared using perpendicular ion beam impact, the conversion from micro-compressive load to stress data is carried out using a fixed cross-sectional area. However, for a 3:1 aspect ratio pillar, a taper of as low as 3° can already lead to a discrepancy of 15% between stresses calculated using the middle and top cross section as reference, increasing to 30% when considering bottom and top [32]. A similar problem arises as there is often not enough clarity regarding the choice of the yield point for yield stress extraction. Commonly, similar to a macroscopic uniaxial test, the 0.2% or 1% elasticity limit is taken as the yield stress reference [2,15,22]. Where jerky flow is observed, it is argued that the yield stress should be taken directly as the onset stress of the first strain burst or yield drop [10,17,25,26]. However, it is possible that the measurement of a distinct first strain burst or yield drop is impeded by misalignment between punch and pillar, in which case the flow stress at an elevated total strain (2–5%) is chosen as reference [4,5,[7], [8], [9],11,13]. Yet, here it is often argued that pillar deformation at such elevated strains can be severely influenced by lateral displacement (due to generation of few discrete slip events [32,33]), or alternative deformation mechanisms (e.g. slip on softer slip systems [34]). Such ambiguity can be detrimental, especially where the results of compression testing are compared (e.g. for room and high temperature testing) or where material behaviour is modelled based on micro-compression testing (e.g. crack evolution, microplasticity).

On the basis of a conventional micro-compression experiment, the current study presents an alternative analysis procedure for micro-compressive yield and critical resolved shear stress (τ_CRSS) determination, based on area-sensitive strain mapping of the pillar via sequential digital image correlation (DIC) [35]. It is demonstrated that the more detailed picture of the pillar deformation morphology facilitated by DIC is crucial for the accurate interpretation of micro-compressive loading curves and the precise extraction of flow stresses on this basis. The material chosen for investigation was a Cr₂AlC MAX phase. Plasticity in this hexagonal system is dominated by easy basal plane slip – studies in textured macroscopic samples showed the corresponding resolved shear yield stresses to be as low as 77 MPa [36,37]. Slip on prismatic or pyramidal slip systems is widely acknowledged to be significantly harder and has only been reported when subjected to extreme stress states during indentation testing [38]. This deformation behaviour is exploited in the current study as it can be assumed that only one slip system (basal plane slip) will be activated during compression, which significantly eases interpretation.