Xiaodong Hou

Grain size and sample size interact to determine strength in a soft metal

Understanding the strengthening of small-scale materials and structures is one of the key issues in nanotechnology. Many theories exist, each addressing a small domain of experimentally observed size effects and invoking different mechanisms. Measurements of the stress–strain relationship of nickel foils in flexure by the load–unload method provide strikingly accurate data from the elastic region through the yield point and to high plastic strain. The data show that the effects on the rate of work-hardening due to crystallite size and sample size interact, whereas in existing theories they should be independent. Existing theories cannot be complete. The symmetry of the dependence of flow stress on grain size and structure size suggests that strengthening effects are due to a finite strained volume, however this is delimited.

Study of the interaction between the indentation size effect and Hall–Petch effect with spherical indenters on annealed polycrystalline copper

Methods to obtain tensile stress–strain properties of materials from a practically non-destructive indentation test are of great industrial interest. Nanoindentation is a good candidate. However, to do this successfully, indentation size effects must be accounted for. An indentation size effect with spherical indenters has been shown for a range of fcc metals with relatively large grain size (Spary et al 2006 Phil. Mag. 86 5581–93); the increase in yield stress being proportional to the inverse cube root of indenter radius. Here, we investigate these differences further and present results for the indentation size effect with spherical indenters on Cu samples with a range of different grain sizes from 1 µm to single crystal. The important experimental control parameter, of the relative size of the indentation compared with the grain size, is also explored by using indenters of different radii on the different grain sized samples. When the grain size, d, is less than 6 times the radius of the projected contact area, a, a Hall–Petch-like behaviour is observed superimposed on the indentation size effect. For d > 6a the indentation size effect dominates. The two effects may be combined by addition in quadrature. This new parametric function is able to predict the indentation pressure in annealed copper given input values of indenter radius and grain size.

Indentation size effect at the initiation of plasticity for ceramics and metals

In nanoindentation, the plasticity size effect has been observed for several years, where a higher hardness is measured as contact size decreases. For spherical indenters, Lim and Chaudhri (1999 Phil. Mag. 79 2979) first showed that the entire flow curve appears at higher contact pressures for smaller radius indenters in copper. However, few papers have reported the initial yield size effect due to the difficulty in defining the yield point. Recently, Spary et al (2006 Phil. Mag. 86 5581) demonstrated that the initial yield strength of metals increases linearly with inverse cube root of indenter radius, by nanoindentation together with finite elemental modelling. Here, we use a clear method to determine the onset of plasticity in spherical nanoindentation without the uncertainties of modelling. This enables us to measure the yield pressure of tungsten metal and a series of ceramics with a high degree of accuracy and over a large range of indenter radii (hundreds of nanometres to several tens of micrometres). Our data of all ceramics and metals show clearly that there is a significant yield strength enhancement, which is inversely proportional to the cube root of the indenter radius. Normalizing the data for each material by its yield pressure for an infinite radius indenter, we find that the data for metals and ceramics fall on lines of different slope, indicating that material parameters influence the indentation yield strength size effect as well as the geometrical size effect.

Micromechanical testing with microstrain resolution.

Simple test equipment has been developed for studying the elastic limit and plastic deformation of thin metal wires and thin foils (down to 10 μm) under torsion, tension, and bending. Using load-unload methods and gauge lengths up to 1 m, plastic strain as low as 10(-6) can be measured accurately.

Exploiting interactions between structure size and indentation size effects to determine the characteristic dimension of nano-structured materials by indentation

It was shown that yield (or flow) stress is determined by a critical dimension and the reciprocal sum of component critical dimensions (such as indentation size, structure size and dislocation density) combine into a single critical dimension as predicted by slip distance theory (Hou et al 2012 Acta. Mater. 60 4128). This suggests that ?length determines strength? and all lengths contribute at all times to the critical value. We have already shown that Cu hardness increases when grain size falls below six times the indentation contact radius (Hou et al 2008 J. Phys. D: Appl. Phys. 41 074006). In this paper, we test the inverse case (indent size greater than grain size), by indenting two different metallic glasses (NiAl and ZrTiAlCuBe). We show that the indentation size effect (ISE) does indeed become observable even when the indent size is larger than the grain size by up to an order of magnitude. The indentation depth (size) at onset of the ISE is proportional to the characteristic structure size of these nano-structured materials and suggests a novel use of ISE as a determinant of structure size. These findings have implications for the design of hardness reference blocks and the use of hardness mapping to determine materials property variations.

Yield and plastic flow of soft metals in small volumes loaded in tension and flexure

Theories of small-scale plasticity often invoke effects of strain gradient, and this is best tested by comparison of experimental stress–strain data obtained with and without well defined strain gradients. We provide new results to add to the body of data for 25–150-µm Cu wires in tension, 10–125-µm Cu and Ni foils in flexure and 10–125-µm Ni foils in tension, and test whether the data can adequately discriminate between the theories. What the collected data shows is that there are size effects in yield strain, as well as in the strain-hardening behaviour in the low-strain and high-strain regimes. Within the experimental scatter, the data is largely consistent with theories that invoke, and those that do not invoke, effects of strain gradients. The tension data in particular are too scattered, and the differences in the theoretical predictions are not sufficiently stark, to discriminate between the theories. However, we find that the flexure data for Cu and Ni agree within experimental error, indicating that material-specific properties such as elastic moduli and stacking fault energies are not involved in the size effect.

Direct measurement of surface shape for validation of indentation deformation and plasticity length-scale effects: a comparison of methods

It is ironic that recent developments in instrumented indentation, such as the drive to obtain tensile properties from indentation data and to understand length-scale effects in plasticity, have seen a return to direct imaging of indentations. Significant uncertainties in contact size arise when using contact mechanics calculations that do not take into account the lateral dilation of elastic recovery (Hou et al 2008 J. Phys. D: Appl. Phys. 41 074006) and important sink-in and pile-up contributions to the contact response (Lim and Chaudhri 1999 Phil. Mag. A 79 2979–3000). High resolution, direct measurement avoids these problems. Accurate wear volume and coating thickness measurements obtained by cap grinding methods also depend on high accuracy and low uncertainty direct measurement methods. The use of metrological atomic force microscopy to measure and certify the shape of indenters is well established (Aldrich-Smith et al 2005 Z. Metallk. 96 1267–71) and is essential for valid mechanical property measurement by instrumented indentation. In this paper, we consider indent measurement and compare three direct measurement techniques: optical microscopy, metrological atomic force microscopy (AFM) and confocal laser scanning microscopy (CLSM). We compare the relative merits and uncertainties of various 2D and 3D analysis methods with a new analysis method of differentiating 3D data obtained from AFM and CLSM. This new method has the lowest uncertainty (2.8% for a 50 µm diameter indent at the 95% confidence level). Better still, it enables objective measurements of indent size that avoid the issues caused by difficult-to-standardize parameters (such as illumination angle, contrast and brightness settings), which strongly affect manual estimates of the edge position of an indentation/crater (Gee et al 2002 NPL Measurement Good Practice Guide No 57).

The interaction between Lateral size effect and grain size when scratching polycrystalline copper using a Berkovich indenter

Abstract It has been reported previously that, for single and polycrystalline copper (fcc), the indentation size effect and the grain size effect (GSE) can be combined in a single length-scale-dependent deformation mechanism linked to a characteristic length-scale calculable by a dislocation-slip-distance approach (X. D. Hou and N. M. Jennett, ‘Application of a modified slip-distance theory to the indentation of single-crystal and polycrystalline copper to model the interactions between indentation size and structure size effects,’ Acta Mater., Vol. 60, pp. 4128–4135, 2012). Recently, we identified a ‘lateral size effect (LSE)’ in scratch hardness measurements in single crystal copper, where the scratch hardness increases when the scratch size is reduced (A. Kareer, X. D. Hou, N. M. Jennett and S. V. Hainsworth ‘The existence of a lateral size effect and the relationship between indentation and scratch hardness’ Philos. Mag. published online 24 March 2016). This paper investigates the effect of grain size on the scratch hardness of polycrystalline copper with average grain sizes between 1.2 and 44.4 μm, when using a Berkovich indenter. Exactly the same samples are used as in the indentation investigation by Hou et al. (‘Application of a modified slip-distance theory to the indentation of single-crystal and polycrystalline copper to model the interactions between indentation size and structure size effects,’ Acta Mater., Vol. 60, pp. 4128–4135, 2012). It is shown that, not only does the scratch hardness increase with decreasing grain size, but that the GSE and LSE combine in reciprocal length (as found previously for indentation) rather than as a superposition of individual stresses. Applying the same (as indentation) dislocation-slip-distance-based size effect model to scratch hardness yielded a good fit to the experimental data, strongly indicating that it is the slip-distance-like combined length-scale that determines scratch hardness. A comparison of the fit parameters obtained by indentation and scratch on the same samples is made and some distinct differences are identified. The most striking difference is that scratch hardness is over four times more sensitive to grain size than is indentation hardness.

The existence of a lateral size effect and the relationship between indentation and scratch hardness in copper

Abstract Indentation size effects (ISEs) are well known in static indentation of materials that deform by dislocation-based mechanisms. However, whilst instrumented indentation techniques have become rapidly established as a means of determining the near-surface mechanical properties of materials, scratch testing has been much less widely used. Hardness is used in wear models as a proxy for the yield stress, and the design of materials and hard coatings has often sought to exploit size-derived performance enhancements through length-scale engineering. Yet, it is not known directly whether (or not) length-scale effects also apply to scratch (and thus wear) performance at small scales, or what the functional form of this effect is. This work directly demonstrates that there is a lateral size effect (LSE) and shows that there are questions to be answered if the use of hardness as an indicator of wear performance is to remain valid. We report on constant load scratch experiments using a Berkovich indenter on single-crystal, annealed copper, using a range of applied normal forces and compare results from three scratch hardness calculation methods to indentation hardness (ISO 14577:2002) measured on the same sample at the same loads. Scratch tests were performed with the Berkovich indenter aligned either edge forward or face forward to the scratch direction. In all cases, we demonstrate that there is a very significant (approximate factor of two) effect of scratch size (an LSE) on scratch hardness. The results also show that the deformation mechanisms occurring in scratch tests are different to those occurring beneath a static indentation and that different mechanisms dominated for different stylus orientations (face-forward vs. edge-forward orientation). This is, to our knowledge, the first direct demonstration of an LSE akin to the ISE in metallic materials. The results have significant implications for using static indentation as a predictor of deformation during wear processes.

Size effect in the initiation of plasticity for ceramics in nanoscale contact loading

In nanoindentation, the plasticity size effect has been observed for several years, where a higher hardness is measured as indenter size decreases. In this paper, we report the size effect on the initiation of plasticity in ceramics by using spherical indenters. Here, we show a clear method that is able to determine the details of the onset of plasticity in nanoindentation. This enables us to measure the yield pressure with a high degree of accuracy and over a large range of indenter radii (hundreds of nanometers to several tens of micrometers). Our data shows clearly that there is a significant yield strength enhancement, which is inversely proportional to the cube root of the indenter radius. Also after normalization by the bulk yield strength, the increase in yield strength with decreasing indenter radius is shown to follow a single relation for all the ceramics studied in agreement with recent results for metals [1], and consistent with critical thickness theory for the initiation of yielding over a finite volume.