**6. Discussion**

The present description of experimental strength measurements involved examples, in turn, of the topics: localized deformations in micro- and nano-indentation tests; tensile or compression tests of whisker, micro-wire, and micro-pillar crystal or polycrystalline specimens; and stress–strain, fracturing, and deformation rate dependencies of micro-to nano-polycrystalline materials. In a number of cases, the micro- or nano-scale properties have been connected with (lower) strength levels normally achieved in conventional bulk materials.

An example of connection between nano-indentation testing incorporated in Figure 1 and technical alloy development has been given in a report on aluminum single crystals by Filippov and Koch [38]. The test method was employed to probe the material anisotropic elastic deformation behavior through testing the diamond pyramid hardness of (100), (110), and (111) crystal surfaces. The research

relates to reference [20] in which a comparison was made between the experiment and simulation of nano-indentations in (111) and (100) α-iron crystal surfaces. At an opposite dimensional scale, an important civil engineering connection spanning nano- to macro-size dimensions was provided by a comparison of the ultrafine steel wire measurements described for the drawn micro-wire strengths presented in Figure 2 and the comprehensive description by Ono [39] of steel wire materials employed in historical and current transportation bridge constructions.

A novel example of exceptionally high strength measurements being made on silicon nano-particles, relating to the results shown in Figure 1, has been reported by Nowak et al. [40]. Near theoretical limiting strength levels were determined by compression of the particles between hardened steel platens. In another study, so-called length-scale 'architectured' polycrystalline copper micro-pillars have been fabricated with an achievement of surprisingly higher strength advantage [41]. Another useful study of micro-pillars has involved the measurement of solute effects in aluminum alloys [42]. Basic features of slip behavior have been reported for Fe-3% Si micro-pillar crystals [43]. Dendrite/nano-structured (high entropy alloy) titanium-based composite material has been investigated in static and dynamic compression tests [44]. The use of probing spherical nano-indentation hardness testing has been applied as far afield as in the evaluation of the elastic modulus and strain energy within the mineral, antigorite, to understand planetary tectonic plate subduction behavior [45], thus spanning the seemingly largest imaginable range in dimensions.

Finally, in discussion, the several examples presented of dislocation mechanics modeling of hardness, stress–strain, fracturing, and strain rate sensitivities of materials at smaller dimensions have focused on particular features accompanying the behavior of single or small groups of dislocations. The higher strength levels and exceptional strain hardening behaviors can be understood in a general manner in terms of the higher values of internal dislocation stresses accompanying smaller dislocation line lengths and smaller separations accompanying subsequent dislocation interactions. Stress levels approaching the theoretical strength are obtained [46], for example, as indicated in Figure 2, for the smallest effective grain size of heavily drawn eutectoid steel wire material [7].
