Structural Nanomaterials Part 1 (Nanotechnology)

INTRODUCTION

By definition, structural materials are used for mechanical strength at room and elevated temperatures, to withstand cyclical loading and for wear and fracture resistance. Structural nanomaterials (with grain sizes less than 100 nm) are distinguished by unusually high strength, hardness, and wear resistance as well as good fatigue resistance, fracture toughness, and extensive high-temperature formability. However, commercial applications have only begun to tap the potential of high-strength parts (e.g., nearly 1 GPa in nano-Al alloys, known as GIGAS,[1] and high-strength nano-SiC springs). More commonly, they are used as thermal barrier coatings, or in friction-resistant and wear-resistant rotating parts (e.g., sleeves or bearings).

Nanomaterials used for structural applications may have nanometer size in one dimension (1D), two dimensions (2D), or three dimensions (3D). Generally, 1D nanomaterials are wires, 2D refers to coatings and films, and 3D solids are used to make bulk parts. In this entry, bulk or 3D materials are emphasized, but some 1D and 2D nanomaterials used for their mechanical properties are also presented.

FABRICATION OF NANOSTRUCTURED MATERIALS

Processing

The primary challenge in producing bulk nanostructures is to create and to maintain grain sizes less than 100 nm in defect-free, sizable, reproducible, and reliable parts. To date, the processing of raw nanomaterials (powders and thin films) has progressed farther than the formation of bulk parts. Nanosize powders of metals, ceramics, polymers, and composites are now available, sometimes in tonnage quantities. All of these nanostructured powders may be used for processing 2D and 3D parts.

The most common techniques to produce 2D parts are thermal spraying and electrodeposition (ED). The former includes arc, flame, plasma, detonation gun, and high-velocity oxyfuel spraying to produce metal, alloy, ceramic, and composite coatings.[2] In the spraying process, the fine microstructure develops when molten or semimolten particles rapidly solidify as they are deposited onto a substrate. Electrodeposition techniques include both electroplating and electroforming, and are typically applied to a limited number of metals, although some ceramics and composites have been also obtained.[3] Although electroplating is typically used for coatings, electroforming is a cost-effective method for free-standing ultrathin foils or thick structures, wires, plates, and complex shapes. Grain size is controlled by enhanced nucleation by charge transfer at the electrode surface, high deposition rates, and the inhibition of grain growth by using additives. Electrode-position can be used to control grain boundary type and to achieve nanocrystalline structures with a relatively narrow grain size distribution and with few pores. Electrodepo-sition and sputtering also may be used to produce nanolayered materials.

Generally, the processing methods for bulk nanoma-terials involve one or two steps. The more commonly used two-step methods consist of producing nanomaterials in a powder form and subsequently consolidating them to a final 3D part. These methods offer the greatest versatility in the shape, size, and weight of the final bulk parts. All powder processing methods have been applied to sinter nanostructured powders and many of them have achieved final grain sizes less than 100 nm.[4] The challenge is to fully densify nanopowders without losing the initial metastable features (nanoscale grain size and, sometimes, metastable phases). The consolidation methods use a full range of temperature and pressure conditions from conventional pressureless sintering to high pressure and shock consolidation. Inert gas condensation (IGC) of powders followed by densification has been a widely used technique to process bulk nanocrystalline materials. Most of these methods leave processing flaws, including incomplete densification, poor interparticle bonding, cracks, or trapped gases.

The one-step methods include severe plastic deformation (SPD), crystallization of amorphous bulk parts, and ED. Severe plastic deformation comprises variants such as equal-channel angular forming and high-pressure torsion straining. Generally, SPD results in grain sizes greater than 100 nm, which are known as ultrafine-grained structures. However, smaller grain sizes (down to 20 nm) have occasionally been achieved.[5] Intense plastic deformation has also been used to produce in situ fiber or lamellar composites. A novel intense deformation process based on ball milling with in situ densification (BMID) was recently reported by Koch.[6]

The crystallization of bulk amorphous alloys to form nanophases occurs on controlled thermal processing.[7] The most challenging step is the formation of bulk amorphous precursors using slow cooling rates similar to conventional casting processes, to enable the fabrication of sizeable parts. This has been achieved in a few metal-based systems (Zr, Mg, and, partially, Al). Next, controlled direct or stepwise devitrification takes place at temperatures within the supercooled liquid region, or close to the onset of crystallization. The resultant structures are typically multiphase alloys formed by the precipitation of nanoscale metastable (metal-based or quasi-crystalline) or stable (intermetallic) phases in an amorphous matrix. The type and the size of nano-crystalline components vary with alloy chemistry and processing conditions.

Dependence of Properties on Processing

Most processing methods result in some imperfections in the final bulk part. In conventional materials, well-established standards control flaw size and distribution, resulting in a negligible effect on mechanical properties. However, such flaws have a more critical effect on the mechanical properties of nanomaterials, and are different in nature and size than in conventional materials. The most common imperfections in nanocrystalline bulk materials are pores, trapped gases, impurity contamination, cracks, imperfect bonding, surface defects, residual stresses, and texture. Although some defects are common to several techniques (e.g., contamination, surface defects, or pores), texture is typical in ED, residual stresses are most severe in SPD, and incomplete bonding and densification are observed in powder consolidation and thermal spraying. Defect characterization in nanomater-ials is a relatively new field, and appropriate guidelines are definitely required.

The most detailed defect characterization has been carried out for the flaws specific to the two-step powder consolidation methods, particularly pores that result from incomplete densification.[8,9] At small grain sizes (less than 10 nm), a density shortfall may also originate from the high volume of low-density grain boundaries. Van Swygenhoven et al.[10] calculated densities of 97% for a 10- to 12-nm grain size Ni and 95.2% for a 3.4-nm grain size Ni. Experiments confirmed a 97.6% density value measured by a high-precision Archimedes method in 10-nm grain size samples produced by IGC.[11]

Processing flaws in nanomaterials have an adverse effect on mechanical properties. The modulus of elasticity or Young’s modulus E is a reflection of interatomic bonding and is largely dependent on defects. The low experimental E values reported in early studies of nano-crystalline materials have been unquestionably attributed to defects such pores, poor grain-to-grain bonding, or deficiencies in measuring techniques.[9,12] More recent experimental measurements on low-defect nanomaterials demonstrate that grain size has a negligible effect on Young’s modulus.[13] Simulations also showed no variation in Young’s modulus down to a grain size of 10 nm.[14] Below this limit, when the slightly lower-density grain boundary volume becomes predominant, the modulus decreases with decreasing grain size. Some calculated values are as low as about 75% of the modulus of bulk metals at 3-6 nm grain size.[14,15]

All other mechanical properties, including strength, hardness, and ductility, are sensitive to microstructure and are even more adversely affected by defects. Ample evidence exists for inferior strength and ductility values, particularly in tensile testing, because of pores and trapped gases, cracks, imperfect bonding, and surface defects. Agnew et al.[8] Sanders et al.[9] Legros et al.[13] and Nieman et al.[16] carefully documented the dependence of strength and ductility on processing flaws in metals. He and characterized the variation of hardness with porosity in the Fe3Al intermetallics. Hardness values were reported to double by processing improvements to produce dense metals.[9] The reduction of the surface imperfections has been shown to increase the tensile strength by up to a factor 4 by preventing premature fracture.[16] Consequently, reduced size specimens (e.g., micro and miniature tensile and bend specimens) have been used to lower the defect probability.[13,18,19] The elimination of some defects by annealing can also increase the strength of metals[20,21] and intermetallics[20-23] by decreasing porosity, relaxing the grain boundary structure toward equilibrium, or reducing internal stresses.

As is detailed in ”Strength and Ductility,” ductility is the property most affected by processing flaws. The lack of good interparticle bonding is the major cause of brittle failure in consolidated samples tested in tension or bending.[9,24,25] As an example, 80-nm Fe3Al produced by shock wave consolidation of mechanically alloyed powders displayed brittle behavior in tension but a large plastic strain in compression (true plastic strain of 1.4).[26] Similar to strength, an improvement in ductility was reported after annealing at low temperatures without altering the grain size (e.g., an increase from 2% to 7.3% in 30-nm Cu) because of grain boundary relaxation.[27] Electrodeposition yields better ductilities than powder consolidation because of reduced porosity and good interparticle bonding. However, some ductility problems have been noted when using grain growth inhibitors, or because of texture development. Throughout this entry, an effort has been made to exclude materials with significant processing deficiencies, when these are reported.

Fig. 1 Effects of grain size distributions on mechanical properties. (From Refs. [14] and [21].) (a) Comparison of grain size values given by TEM and XRD in IGC copper. The open circles are the relative number of grains in a given size range. The solid and dotted lines indicate the log-normal fits of the data points as number-fraction and volume-fraction curves, respectively. (b) Effects of the standard deviation size Slnv on the grain size distribution and (c) on stress-strain curves for the same average grain size (d=20 nm). The IGC Cu is heavily twinned and the ”grain size” value actually refers to the twin size.

In conventional materials, it is acceptable to use average grain size to characterize mechanical properties. This approach is not appropriate in nanomaterials because of the size dependence of the deformation behavior. For instance, some large recrystallized 1-5 mm size grains enabled larger ductility values in nano-Cu vs. nano-Ni, which had fewer such recrystallized grains and was consequently brittle.[13] All processing methods result in a distribution of grain sizes. In nanomaterials, grain size measurements are commonly carried out by X-ray diffraction (XRD) and transmission electron microscopy (TEM). Transmission electron microscopy enables a direct measurement of grain sizes and grain size distribution. In contrast, XRD techniques provide only an average grain size, the value of which also depends on the specific method used [e.g., Scherrer, Warren-Averbach (W-A), or Williamson-Hall].[28] Average TEM grain size and X-ray results are in good agreement when the grain size distribution is narrow and XRD corrections are made (Fig. 1a). Log-normal distributions of grain sizes are usually used. When grain size distribution is described by volume fractions, the peak value may be quite different from the TEM number fraction and XRD values (Fig. 1a). Volume fractions more realistically reflect the effect of large grains, which may be predominant on mechanical properties.[21] The standard deviation of the volume fraction also affects the grain size distribution (Fig. 1b) and, consequently, the mechanical properties (Fig. 1c).

STRENGTH AND DUCTILITY

The general description of the mechanical behavior in tension is given in Fig. 2.[29] Brittle materials are characterized by a linear elastic stress (s)-strain (e) response and fracture with no plastic deformation (Fig. 2a). Ductile materials yield beyond the elastic region and then fracture after a certain elongation (Fig. 2b). Fig. 2b defines the yield strength (sy), tensile strength (sUTS), and elongation to fracture (ef). In the plastic region, work hardening is expressed using a true strain value e by:

where K is a constant and n is the strain hardening exponent. Strain or work hardening is attributed to the generation and interaction of the dislocations. It controls the amount of uniform elongation at stresses larger than yield strength sy. A dimensional instability in tension, or necking, typically starts to develop at maximum load.

Fig. 2 Stress-strain curves for brittle (a) and ductile (b) materials. The slope of the linear portion of the s-e plot defines the elastic modulus by the Hooke’s law (s=Ee).

Grain size refinement results in the classical grain boundary strengthening (expressed in terms of yield strength sy but also valid for sUTS or hardness H), which is described by the Hall-Petch (H-P) relationship:[29]

where s0 is the friction stress to move dislocations, k is a material-dependent and temperature-dependent constant, and d is grain size.

The H-P relationship can be rationalized by two basic dislocation descriptions: 1) the dislocation pile-up model, in which yielding occurs as a result of stress concentrations caused by pileups (Fig. 3a); and 2) the dislocation network model, in which the slip is because of dislocations emitted by grain boundaries (Fig. 3b). A third model developed by Meyers and Ashworth[29] is a variant of the dislocation emission model with localized plastic flow at a work-hardened grain boundary layer (Fig. 3c). Plastic deformation occurs when the applied stress exceeds the higher-flow stress of the grain boundary region. The resulting grain size dependence of the yield strength is the sum of d~1/2 and dT1 dependencies:

where k is a different constant from k. The second term is dominant at large grain sizes, whereas the third term becomes important at small grain sizes. All models assume conventional dislocation generation and mobility.

Strength of Nanostructured Materials

By extrapolating the grain size to the nanometer range, both strengthening and an increase in ductility were predicted.[30] Experimentally, this prediction has been observed for a number of materials (Fig. 4).

According to the H-P relationship, a 1000-fold reduction in grain size from microns to nanometers yields more than a 30-fold increase in strength, provided that the same dislocation mechanisms are operational. Experimentally, strength or hardness was found to increase by a factor of 5-10 by reducing the grain size from microns down to the 30- to 50-nm level.[9,25,31] Similar high-strength values for nanocrystalline metals and alloys were observed in compression, or by hardness measurements, in which processing defects are less detrimental than in tension. Yield strengths greater than 1 GPa were found in Pd (40-50 nm), and yield strengths close to 1 GPa were found in Cu (20 nm).[9] Ball-milled and densified Fe (24 nm) had a true compressive strength of approximately 3 GPa,[24] whereas IGC-processed 21-nm Ni failed in compression at more than 2.1 GPa.[21]

Fig. 3 Dislocations models to explain the H-P behavior developed by: (a) Cottrell (dislocation pile-up); (b) Li (dislocations generated at ledges in grain boundaries); and (c) Meyers and Ashworth.

Fig. 4 Strength-ductility values of nanostructured materials (filled symbols) compared to conventional counterparts (open symbols: circles—dispersion-strengthened Al alloys; triangles— cold-worked steels).

Often the spread of experimental data is quite large, but reasonable H-P correlations at the smallest grain sizes have been revealed (i.e., stronger materials at smaller grain size) (Fig. 5). Deviations from H-P strengthening, where the slope decreases or the curve flattens, also have been reported, usually at grain sizes smaller than about 30 nm (Fig. 5b and c).[24,32] An inverse H-P effect, in which strength decreases at the smallest grain sizes, has been reported in alloys such as Ni-P.[33] This effect was most often reported in specimens annealed to increase the initial small grain size in metals or intermetallics.[20,22] Generally, these results must be treated with caution because either processing artifacts may not have been completely eliminated, or other processes (e.g., precipitation of a second phase in Ni-P alloys or in mechanically alloyed Fe) may have interfered with the measurements.[24,33]

Various mechanisms have been proposed to rationalize the deviations from H-P strengthening, such as the breakdown of dislocation pileups, lack of dislocation activity, and increased contributions from diffusional deformation mechanisms (creep and grain boundary slid-ing).[14,21,34,35] Cheng et al.[34] proposed a deformation mechanism map showing the transition from the dislocation mechanisms to intergranular processes. Transmission electron microscopy studies have confirmed the lack of dislocation structure below a critical grain size of 1030 nm.[13,34]

Fig. 5 Grain size dependence of mechanical properties in nanocrystalline metals: (a) Cu (IGC) (From Refs. [9], [21], and [31].); (b) Fe (ball-milled/densified) (From Ref. [24].); and (c) Ni (electrodeposited) (From Ref. [32].). The dotted lines are the H-P extrapolations of coarse grain data.

To explain the H-P behavior, a model based on dislocation generation from grain boundary sources was recently proposed by Cheng et al.[34] The model also predicts the observed tension/compression asymmetry based on the pressure dependence of dislocation self-energy during bowout. Composite models considered grain interior and grain boundary properties, and, sometimes, triple junction lines and quadruple nodes.[21] The width of grain boundary or adjacent area is still under debate, but the maximum yield strength was found at similar grain size value (about 10 nm). Composite models that are more consistent with microstructural results by accounting for a dispersion in grain sizes have been developed.[28,35] These models combine deformation mechanisms that are active in various grain size ranges. Masumara et al.[35] considered a combination of dislocation glide for grains larger than a critical size d* and Coble creep below d*. In the model developed by Mitra et al.[28] the critical grain size d* differentiates grains that undergo plastic deformation (d> d*) from grains that remain elastic (d<d*).[21] The overall calculation was based on the plastic deformation of grains in an elastic matrix that used the mechanics of nondeformable inclusions. The average grain size was given by a volume averaging of the grains, similar to previous work.[35] For the same average grain size, the volume fractions are shown to be greatly influenced by the standard deviation (Fig. 1b). In turn, a larger standard deviation (with more small-size grains deformed by creep) results in softer behavior (Fig. 1c).