Knowledge of the mechanical behaviour of materials is essential in materials science and applied mechanics. At small sizes, this behaviour shows significant departures from the classical elastic-plastic model. The strength of a material increases either when the structure is small or when only a small volume is under strain: the so called size effect. Intrinsic size effects arise due to microstructural constraints, such as grain size or second phase particle precipitation. Extrinsic size effects are caused by dimensional constraints. These extrinsic constraints might be due to small sample size, where dislocation motion and other physical mechanisms are affected by the presence of a surface or interface, or due to small strained volume, where the dimensional constraint arises from the testing system. Generally, both sample size and strained volume constrain deformation. Interactions between intrinsic and extrinsic size effects are particularly interesting, though current understanding of this topic is limited. The purpose of the present review is to survey small scale strengthening phenomena and to assess the merits of classical and current mechanisms proposed to explain these effects. Practical applications of size effects are briefly reviewed.

A previous paper reported the development and application of novel step-scan photoacoustic fourier transform infrared spectroscopy (SSPA-FTIR) and confocal Raman microscopy (CRM) quantification methods in polymer coating degradation depth profile study [1]. The degradation trends obtained using the two techniques are consistent and suggest the coating surface is more likely to undergo accelerated degradation. A degradation mechanism was also proposed. Moreover, the difference in signal origins of the two techniques was also explained. It was then concluded that CRM has higher depth resolution than SSPA-FTIR in depth profiling polymer coating. Although the CRM quantification method developed in the previous paper is suitable for monitoring the degradation depth profile in polymeric coatings with high depth resolution, data collection at individual sampling depth is time consuming. This paper introduces a model that can be used to predict degradation depth profile in the polymer coating with over 60% reduction in CRM data collection.

A polyester-melamine coating was exposed to accelerated weathering (i.e., cycle of high UV followed by condensation). The degradation depth profile in the coating was investigated using non-destructive step-scan photoacoustic fourier transform infrared spectroscopy (SSPA-FTIR) and confocal Raman microscopy (CRM). The degradation at different sampling depths was then evaluated following the method developed in this work. The results obtained using the two techniques correlate well with each other and suggest coating surface is more likely to undergo moisture enhanced photo-oxidation degradation. This may be due to the higher moisture level near the coating surface. It is also found that melamine side chains degrade prior to the melamine ring. The quantification methods developed in this work were found to be very suitable to monitor the degradation depth profile in polymeric coatings.

Under the inhomogenous stress field set up by nanoindentation, the smaller the extent of the stress field the greater the yield pressure. When the specimen contains a thin layer of softer material, the yield pressure is reduced if plasticity initiates in the soft material. A series of specimens with the soft layer at different depths enables the depth at which plasticity initiates to be mapped. InGaAs lattice-matched to InP is used, and the soft layer is 320nm of strained-layer InGaAs superlattice. Under nanoindentation, we find that plastic yield initiates throughout a region ranging from 300nm to over 1um depending on the indenter tip radius. The region matches the depth range over which the stress exceeds the yield stress of the InGaAs. Thus a requirement for yield is an overload, or excess stress, throughout a finite volume.

Melamine is a common crosslinker widely used in the coil coating industry to crosslink hydroxyl functional polyesters. Theoretically, melamine can also self-condense with the consequence regions with higher crosslink density build up in the coating. Although the melamine self-condensation has been studied, most of works were based on melamine segregation on the coating surface; the existence of melamine self-condensation has only been modelled rather than observed. Utilising confocal Raman microscopy and nanoindentation, the regions with higher melamine concentration were clearly observed and characterised for the first time.It is primarily found from this work that the regions with higher melamine concentration show unique optical features. Those regions are also harder than the normal coating regions at a temperature above T-g; this suggests the cross-linking density in melamine-enriched region is very high, as expected. Moreover, the pigment concentration in the melamine-enriched regions is much lower (or even zero). A possible mechanism was also proposed in this paper. (C) 2010 Elsevier B.V. All rights reserved.

Critical thickness theory explains an excess yield stress in thin films inversely proportional to the film thickness. However, in other contexts, an excess yield stress is often observed which is proportional to the inverse square-root of a relevant dimension. Work-hardening coefficients show both inverse and inverse square-root behaviours. We review recent experimental work which has demonstrated these effects unambiguously, and discuss the extent to which they can be theoretically understood.

Small-scale mechanical behaviour shows significant departures from classical elastic-plastic theory. In a remarkable number of instances, the strength of a material appears to scale as the reciprocal square root of the smallest length scale. There are several recent experimental and modeling results in the literature that show an interaction between dimensional (extrinsic) size and microstructural (intrinsic) size effects. In this paper, we present a mechanical model that naturally produces the inverse square root strengthening and derive an expression for the effective length when both the extrinsic and intrinsic size effects are significant. The theory fits well to data from a wide range of deformation geometries and includes the interaction between the microstructural and dimensional size effects. Furthermore, this approach is able to predict the size effect under uniform deformation without strain gradient.

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.

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.

Understanding the finite volume throughout which plastic deformation begins is necessary to understand the mechanics of small-scale deformation. In indentation using spherical indenters, conventional yield criteria predict that yield starts at a point on the axis and at a depth of half the contact radius. However, Jayaweera et al (Proc. Roy. Soc. 2003) [4]concluded that yield occurs over a finite volume at least 100 nm thick. Semiconductor superlattice structures, in which the stress and thickness of individual layers can be varied and in which known internal stresses can be incorporated, open up new possibilities for investigation that cannot be achieved by varying external stresses on a homogenous specimen. We have designed samples with bands of highly strained InGaAs superlattice, which are essentially bands of low yield-stress material devoid of other metallurgical artifacts. These bands are placed at different depths in a series of samples. Spherical indenters with a range of radii were used to determine the elastic-plastic transition, The stress field from different sized indenters interacts with the low yield-stress material at different depths below the surface to map out the size of the initial yield volume.

Methods to obtain tensile stress-strain properties of materials from a practically non-destructive indentation test are of great industrial interest. Nano-Indentation is a good candidate; however, to do this successfully, indentation size effects must be accounted for. Many indentation size effects, such as strain gradient plasticity and micro-pillar experiments [1], show a size dependence proportional to the inverse square root of a length scale, in common with Hall-Petch behavior. Recently, however, the indentation size effect from small radius spherical indenters has been shown, for a range of fcc metals, not to follow a Hall-Petch-like relationship but to be proportional to the inverse cube root of indenter radius [2]. Here, we investigate these differences further and present results for the indentation size effect with spherical indenters on copper samples that have been engineered to have different grain sizes. The important experimental control parameter of the relative size of the indentation compared to the grain size is also explored since the cross over from grains significantly smaller than the contact radius to grains significantly larger than the contact radius occurs at different length scales in each sample. A thorough understanding of the various length-scale effects in the different test methods (e.g. the indentation size effect and grain size effect in indentation), is essential if a relationship, robust enough for industrial application, is to be defined to obtain tensile properties from an essentially non-destructive indentation test.

The strength of a material increases either when the structure is small or when only a small volume is under strain. The term 'size effect' covers generically all the ways in which this may happen. One manifestation of the size effect is in epitaxial growth of strained layers, for which critical thickness theory provides a satisfactory explanation. We have extended critical thickness theory to the bending and torsion of foils and wires of soft metals, and have built instruments for measuring the stress-strain curves of soft metal foils with unprecedented accuracy to test this. Experimentally, semiconductor epitaxial growth provides structures with tailored internal strain distributions, ideal for helping to understand these problems. We have found that internal strains can reduce the strength of a superlattice by a factor of two at room temperature, but on the other hand can increase the strength by a factor of a hundred at high temperature. Nanoindentation on the semiconductor structures also reveals the size effect very clearly. All of these effects are clearly related to the finite volume required for the initiation of plasticity. New data is crucial to reconciling the various theoretical approaches to these problems. (C) 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.