For Effective Dispersion Strengthening the Dispersed Phase Should Be Continuous

Dispersion Hardening

Dispersion hardening or strengthening is a technique whereby hard or soft external particles are introduced into the aluminium alloy matrix.

From: Surface Engineering of Light Alloys , 2010

Precipitation Hardening

R.E. Smallman , A.H.W. Ngan , in Modern Physical Metallurgy (Eighth Edition), 2014

13.4.4 Dispersion hardening

In dispersion hardening it is assumed that the precipitates do not deform with the matrix and that the yield stress is the stress necessary to expand a loop of dislocation between the precipitates. This will be given by the Orowan stress

(13.10) $\tau =\alpha \mu b/L$

where L is the separation of the precipitates. As discussed above, this process will be important in the later stages of precipitation when the precipitate becomes incoherent and the misfit strains disappear. A moving dislocation is then able to bypass the obstacles, as shown in Figure 13.8(b), by moving in the clean pieces of crystal between the precipitated particles. The yield stress decreases as the distance between the obstacles increases in the over-aged condition. However, even when the dispersion of the precipitate is coarse a greater applied stress is necessary to force a dislocation past the obstacles than would be the case if the obstruction were not there. Some particle or precipitate strengthening remains but the majority of the strengthening arises from the dislocation debris left around the particles giving rise to high work hardening.

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Strengthening mechanisms in steel for creep and creep rupture

F. Abe , in Creep-Resistant Steels, 2008

9.2.2 Precipitation or dispersion hardening

Precipitation or dispersion hardening is one of the important strengthening mechanisms in creep-resistant steels at elevated temperature. To achieve enough strengthening using this effect, engineering creep-resistant steels usually contain several kinds of precipitate particles in the matrix and at grain boundaries: carbonitrides such as M ₂₃C₆, M₆C, M₇C₃, MX and M₂X, where M denotes the metallic elements, C are the carbon atoms and X are the carbon and nitrogen atoms, intermetallic compounds such as the Fe₂(Mo,W) Laves phase, Fe₇W₆ μ-phase, χ-phase and so on, and a metallic phase such as Cu. In a special case of oxide dispersion strengthened (ODS) steels, fine particles of alloy oxides such as Y₂O₃ are dispersed in the matrix by mechanical alloying. A dispersion of fine precipitates stabilizes free dislocations in the matrix and sub-grain structure, which enhances dislocation hardening and sub-boundary hardening.

Several mechanisms have been proposed for the threshold stress, corresponding to the stress needed for the dislocation to pass through precipitate particles, for example, in the Orowan mechanism, local climb mechanism, general climb mechanism and Srolovitz mechanism, see Fig. 9.2. ⁸ The Orowan stress σ_or is given by:

9.2. Schematic drawings of a dislocation passing through particles. (a) Orowan mechanisms, (b) Srolovitz mechanism, (c) general climb mechanism and (d) local climb mechanism.

[9.1] ${\sigma }_{\mathrm{or}}=0.8MGb/\lambda$

where M is the Taylor factor (= 3), G is the shear modulus, b is the Burgers vector and λ is the mean interparticle spacing. ³ Typical values of the volume fraction, diameter and spacing of the major particles contained in tempered martensitic high Cr steels after tempering are listed in Table 9.1, together with the Orowan stress estimated from the values of interparticle spacing. ³

Table 9.1. Volume fraction, diameter and spacing of each kind of precipitate in high Cr ferritic steel, together with Orowan stress estimated from the values of interparticle spacing

Particle	Volume fraction V(%)	Diameter d p(nm)	Spacing σp(nm)	Orowan stress σor (MPa)
Fe2(W, Mo)	1.5	70	410	95
M23C6	2	50	260	150
MX	0.2	20	320	120

The coarsening of fine precipitates of M₂₃C₆, MX and Fe₂(W, Mo) Laves phase and the dissolution of fine MX to form massive precipitates of Z phase, which have been observed in 9–12Cr steels during creep, cause an increase in λ in Equation(9.1) and hence a decrease in Orowan stress over long periods of time. ^{3 , 4} The coarsening and dissolution of fine precipitates sometimes takes place preferentially in the vicinity of grain boundaries during creep, which promotes the formation of localized weak zone and promotes localized creep deformation near grain boundaries. ^{9 , 10} This results in premature creep rupture and is time and temperature dependent.

The strengthening mechanisms caused by a dispersion of oxide particles were examined for a 13Cr–3   W–0.5Ti–0.4Y₂O₃ ODS steel with ferrite matrix at 650   °C, by comparing the threshold stress measured by a stress abruptly loading test (SAL test) with the calculated Orowan and void-hardening stresses, σ_or and σ_V. ¹¹ Figure 9.3(a) shows the relationship between the creep stress and strain upon loading for the ODS steel at 650   °C, using the time elapsed after applying the stress as a parameter. The Orowan and void-hardening stresses are calculated to be 135–192 and 114–163   MPa, respectively, from the histogram for size distribution of Y₂O₃ particles in the steel (Fig. 9.3(b)). These values are also shown in Fig. 9.3(a). The threshold stress, caused by the dislocation passing through the oxide particles, just after loading (at t = 100   ms) is measured to be 175   MPa as shown by arrow A in Fig. 9.3(a), which agrees with the calculated Orowan stress. As the time elapses to 4   s, the threshold stress decreases to 150   MPa as shown by arrow B, which agrees with the calculated void-hardening stress. This suggests that the originating mechanisms of the threshold stress come from the Srolovitz mechanism in this steel. According to the Srolovitz mechanism, ¹² when the matrix-particle interface is incoherent, the normal traction of dislocation stress field on the particle surface is relaxed by interface sliding and volume diffusion and the dislocation is attracted to the particle, see Fig. 9.2(b). After the relaxation is completed, the particles are felt by dislocations as voids and the threshold stress should be equal to the void-hardening stresses. In Fig. 9.3(a), the time of 1–4   s required for the change from the Orowan stress to the void-hardening stress corresponds for the time necessary to the full relaxation. The Srolovitz mechanism was also confirmed for the threshold stress in high-temperature deformation of Al–1.5Be and Al–0.7Mn alloys containing incoherent precipitate particles. ¹³

9.3. (a) Relationship between creep stress and instantaneous strain at 650   °C and (b) size distribution of Y₂O₃ particles in a 13Cr–3   W–0.5Ti– 0.4Y₂O₃ ODS steel.

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METALLIC COMPOSITE MATERIALS

T.W. CLYNE , in Physical Metallurgy (Fourth Edition), 1996

1. Introduction

Reinforced materials based on metals have long been of technological significance. Dispersion hardened metals and precipitation hardening systems were both developed several decades ago. For both dispersion hardening and precipitation hardening, strengthening is due to dislocation motion in the metal being impeded by the presence of small, hard particles. This mechanism operates efficiently only when they are very closely spaced (<1 μm apart). These materials would not, however, generally be classified as true composites. While there is no universally accepted definition of a composite, it is commonly assumed that it is only when load transfer between matrix and reinforcement is significant that the term can properly be applied. When a composite is subjected to an external load, the matrix is relieved of a substantial proportion of that load by the presence of the reinforcement. On this basis, conventional dispersion and precipitation hardened systems are not composites, since they typically contain only around 1% or less of second phase and at such levels the reinforcing constituent cannot significantly reduce the stress borne by the matrix.

Interest in genuine metal matrix composites (MMCs), such as aluminium or copper reinforced with 30–70% of continuous tungsten or boron fibres, grew rapidly in the 1960s. As with most polymeric composites, an applied load is largely borne by the fibres in such a material and the matrix microstructure and strength are relatively unimportant. While commercial interest in such systems has fluctuated somewhat since that period, the attraction of strongly enhanced stiffness and creep resistance has ensured that research activities have continued, particularly for titanium matrices. The main problems concern fabrication difficulties and cost, although issues such as interfacial chemical reactions and their effects on properties have also received attention. The most popular reinforcement in such cases is currently silicon carbide monofilament with various surface coatings.

Discontinuously reinforced metal composites were developed during the 1980s, with attention focussed on Al-based matrices reinforced with SiC particles, or Al ₂ O ₃ particles or short fibres. A combination of good properties, low cost and high workability has made them attractive for many applications. These materials fall somewhere between the dispersion-strengthened and fibre-strengthened extremes. They differ from dispersion hardened systems in having large (∼1–100 μm diameter) reinforcing particles, which contribute negligible Orowan strengthening, and in containing a relatively high (5–40%) volume fraction of reinforcement, such that load transfer from the matrix is significant. However, unlike long fibre reinforced systems, the matrix does bear a substantial load and its strength is important. These distinctions are highlighted by the schematic plots ( Clyne and Withers [1993]) shown in fig. 1, which illustrate how strengthening is strongly dependent on reinforcement size for dispersion and precipitation hardened metals, but is sensitive to reinforcement content and aspect ratio for MMCs. In some cases, both types of mechanism may be significant, as with particle reinforcement of age-hardening alloys. Furthermore, the reinforcement may itself give rise to both types of strengthening, directly by load transfer and indirectly by stimulating changes in matrix microstructure.

Fig. 1. Depiction ( Clyne and Withers [1993]) of strengthening (and stiffening) as a function of inclusion shape, size and volume fraction. (a) Matrix strengthening dominates for dispersion and precipitation hardening systems, with the inclusions constituting too low a volume fraction to carry a significant proportion of the load. (b) Strengthening and stiffening in MMCs are primarily a consequence of load transfer to the reinforcement, which is dependent on volume fraction and aspect ratio.

In this review, a summary is given of the main factors responsible for the thermomechanical characteristics of MMCs. Since the production of material with suitable microstructure is central to any attempt to optimise such characteristics, this is preceded by an outline of the processing methods developed for MMCs.

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Microstructure control in creep–age forming of aluminium panels

L. Zhan , ... D. Balint , in Microstructure Evolution in Metal Forming Processes, 2012

Modelling of material strength increment

As discussed before, the strength of the workpiece material increases during the artificial-ageing process. The main contribution to the increment of material strength is from solute hardening and dispersion hardening. The contribution to the strength due to solute hardening, discussed by Shercliff and Ashby (1990), is given by

[11.4] $\Delta {\sigma }_{\text{SS}}=c_3{\overline{c}}^{2/3}$

where $\overline{c}$ is the mean concentration of solute atoms in the aluminium matrix and c ₃ is related to the size, modulus and electronic mismatch of the solute atoms.

The contribution to the strength due to a volume fraction f of precipitates of mean radius r _p depends on the type of dislocation interaction. For shearing of precipitates by dislocations, it is described by

[11.5] $\Delta {\sigma }_{\text{ps}}=c_4{f}^{1/2}{r}_{\text{p}}^{1/2}$

while for precipitates which are bypassed by dislocations, it is described by

[11.6] $\Delta {\sigma }_{\text{pb}}=c_5\frac{f^{1/2}}{r_{\text{p}}}$

where c ₄ and c ₅ are constants for a given alloy system. By substituting Eq. 11.2 into both Eq. 11.5 and Eq. 11.6, and introducing P _p for normalization (where P/P _p = 1 at peak strength), for precipitate growth at constant volume fraction, Eqs 11.5 and 11.6 can be rewritten as

[11.7] $\Delta {\sigma }_{\text{ps}}=2S_0{\left(\frac{P}{P_{\text{p}}}\right)}^{1/6}\text{and}\Delta {\sigma }_{\text{pb}}=2S_0{\left(\frac{P}{P_{\text{p}}}\right)}^{-1/3}$

Here, all the unknown constants are combined into a single parameter S ₀, with dimensions of strength. A convenient mathematical form for defining the net contribution of precipitation to the strength is given by

[11.8] $\Delta {\sigma }_{\text{ppt}}={\left[\frac{1}{\Delta {\sigma }_{\text{ps}}}+\frac{1}{\Delta {\sigma }_{\text{pb}}}\right]}^{-1}$

Substituting from Eq. 11.7,

[11.9] $\Delta {\sigma }_{\text{ppt}}=\frac{2S_0{(P/P_{\text{p}})}^{1/6}}{1+{(P/P_{\text{p}})}^{1/2}}$

At the peak strength, P/P _p = 1 and the precipitate strength is S ₀.

The net contribution to the yield strength σ _Y of a material subjected to artificial ageing is given by

[11.10] ${\sigma }_{\text{Y}}={\sigma }_{\text{SS}}+{\sigma }_{\text{ppt}}$

In the modelling approach discussed above, the thermodynamics and kinetics of solution heat treatment, precipitation and coarsening have been established and the interaction between dislocations and the strength-giving precipitates has been elucidated. However, all proposed models are capable only of modelling the static ageing effect (stress-free ageing); there is as yet no overall model available that can predict the dynamic ageing behaviour (i.e. age hardening related to the creep strain rate) during CAF. During CAF, as the creep deformation increases, the dislocation density increases, and this will enhance or accelerate the age-hardening mechanism (Poole et al., 1997). Thus the development of unified constitutive equations that can model both static and dynamic ageing effects (i.e. so-called 'creep-ageing' behaviour) is a must for better prediction of material behaviour during CAF.

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The historical development of phase transformations understanding in ferrous alloys

R.E. Hackenberg , in Phase Transformations in Steels: Fundamentals and Diffusion-Controlled Transformations, 2012

1.4.3 Precipitation and tempering

The modification of ferrous alloys due to minor second phase particles, whether carbonitrides, intermetallics, or oxides, became increasingly well known and understood in the second period. This was exploited for both dispersion hardening and for austenite grain size control purposes. The awareness of optimal particle size and spacing relationships, and the kinetics of the Ostwald ripening (second-phase particle coarsening) of such dispersions provided a key understanding that gave focus for optimal alloy and processing design. Speich and Clark (1965) and Edmonds and Honeycombe (1978) survey the entire range of precipitation in ferrous alloys.

Martensite tempering provides an example of the variety of decomposition paths available when starting from highly supersaturated, highly defective microstructures. The three classical stages of tempering – (1) transition carbide formation, (2) decomposition of retained austenite, and (3) further relief of martensite's carbon supersaturation to form cementite in a BCC matrix – were illuminated by a series of systematic studies (Roberts et al., 1953; Lement et al., 1954, 1955; Werner et al., 1957). A fourth stage of tempering, alloy carbide precipitation, was identified in 'secondary-hardening' steels (Kuo, 1953, 1956). Other subtle phenomena have been observed that alter the condition of martensite during the quench or natural aging, such as autotempering, Zener ordering, clustering, segregation, and spinodal decomposition (reviewed by Cohen, 1962, Owen, 1992 and Taylor and Cohen, 1992).

Classical precipitation hardening was first observed in an aluminum alloy by Wilm in 1906. Once Merica et al. (1920) identified the phase diagram prerequisite (decreasing solid solubility with decreasing temperature), a plethora of other alloys had been successfully precipitation hardened (Newkirk, 1968). Age-hardening in dozens of iron-based alloys had been identified by the early 1950s (Geisler, 1951; Hardy and Heal, 1954). The nature of the precipitating particles and their cluster and transition-phase precursors became clearer with the advent of TEM in the 1950s and atom probe two decades later. Two instances of precipitation in ferrous alloys will be briefly mentioned.

Classical continuous precipitation from alpha-iron solid solutions has been demonstrated in many systems such as Fe-Mo (Geisler, 1951; Speich and Clark, 1965). Studies of Fe₃C and Fe₄N precipitation from alpha-iron (Wert, 1949) using internal friction helped motivate the first quantitative theories of precipitation kinetics (Zener, 1949; Wert and Zener, 1950; Ham, 1958, 1959).

Maraging steels first emerged around 1960 (Decker and Floreen, 1988). Since they are hardened by intermetallic precipitation instead of carbide precipitation, these alloys are compositionally distinct from other high-strength steels by their negligibly low level of carbon and their high alloy content (~18   wt% Ni, in addition to Mo, Ti, Co, and W). Fine-scale Guinier–Preston zones and intermetallic particles evolve out of the supersaturated martensitic matrix during aging, producing an extraordinary combination of ultrahigh strength and toughness. Since these precipitates are composed solely of slower-diffusing substitutional elements, they resist coarsening much better than carbides. Moreover, dimensional stability and weldability are robust from an industrial perspective.

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Material standards, designations and alloys

Gene Mathers , in The Welding of Aluminium and its Alloys, 2002

3.4.1.2 Aluminium-manganese alloys (3XXX series)

When iron is present as an impurity the solubility of manganese in aluminium is very low. The rate of cooling from casting or welding is sufficiently rapid for some manganese to be left in supersaturated solution. Further processing to provide a wrought product causes the manganese to precipitate as FeMnAl₆ , this precipitate giving an increase in strength due to dispersion hardening. Any uncombined iron and silicon impurities may be present as an insoluble Al-Fe-Mn-Si phase.

The weld zones are similar to those seen in pure aluminium, the only major difference being the composition of the precipitates. The heat of welding has the same effect on the structure as on pure aluminium, with the precipitates arranged along the grain boundaries and a loss of strength in the annealed regions of cold worked alloys.

The 3103 (AlMn1)alloy is more hot short (see Section 2.5) than pure aluminium, despite having a similar freezing range. In practice, however, hot cracking is rarely encountered. Those alloys containing copper (alloy 3003) or magnesium (alloys 3004, 3005 and 3105) are more sensitive to hot cracking. Weld cracking may be sometimes encountered when autogenous welding but this is easily prevented by the use of an appropriate filler metal composition.

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Magnesium alloys for aerospace structures

In Introduction to Aerospace Materials, 2012

10.2.3 Strengthening of magnesium alloys

Pure magnesium does not have sufficient strength or corrosion resistance to be suitable for use in aircraft. Magnesium has a hexagonal close packed (hcp) crystal structure. As mentioned in chapter 4, hcp crystals have few slip systems (three) along which dislocations can move during plastic deformation. As a result, it is not possible to greatly increase the strength of hcp metals by work-hardening. For example, annealed magnesium has a yield strength of about 90   MPa, and heavy cold-working of the metal only increases the strength to about 115   MPa. Another consequence of the hcp structure is the mechanical properties of wrought magnesium alloys are anisotropic and are different dependent on the loading direction. Owing to the anisotropy, the compressive yield strength of wrought magnesium alloys can be 30–60% lower than the tensile yield strength.

There are two broad classes of magnesium alloys that are strengthened by cold working or solid solution hardening combined with precipitation hardening. As mentioned, it is difficult to greatly increase the strength of magnesium by cold working owing to the hcp crystal structure, and therefore the majority of magnesium alloys used in aerospace applications are strengthened by the combination of solid solution and precipitation hardening. The strength properties of magnesium are improved by a large number of different alloying elements, and the main ones are aluminium and zinc. Other important alloying elements are zirconium and the rare earths. Rare earths are the thirty elements within the lanthanide and actinide series of the Periodic Table, with thorium (Th) and neodymium (Nd) being the most commonly used as alloying elements.

A problem with magnesium, however, is that the addition of alloying elements provides only a relatively small improvement to the strength properties. Compared with the annealed pure metal, the increase in yield strength of magnesium owing to alloying is typically in the range of 20 to 200%. In comparison, the alloying of annealed aluminium increases the yield strength by more than 1000% and the strength of annealed titanium is improved by up to 700%. The low response of magnesium to strengthening by alloying and work-hardening, together with low elastic modulus, ductility and corrosion resistance, are important reasons for the low use of this material in modern aircraft.

The majority of alloying elements used in magnesium increase the strength by solid-solution hardening and dispersion hardening. The alloying elements react with the magnesium to form fine intermetallic particles that increase the strength by dispersion hardening. The three most common intermetallic particles have the chemical composition: MgX (e.g. MgTl, MgCe, MgSn); MgX ₂ (e.g. MgCu₂, MgZn₂); and Mg₂X (e.g. Mg₂Si, Mg₂Sn). These compounds are effective at increasing the strength by dispersion hardening, but they reduce the fracture toughness and ductility of magnesium. For example, the Mg–Al–Mn and Mg–Al–Zn alloys used in aircraft form particles (Mg₁₇Al₁₂) at the grain boundaries which lower the toughness and ductility.

Magnesium alloys must be heat treated before being used in aircraft to minimise the adverse effects of the intermetallic particles on toughness. This involves solution treating the magnesium at high temperature to dissolve the intermetallic particles in order to release the alloying elements into solid solution. The material is then thermally aged to maximise the tensile strength by precipitation hardening. A typical heat-treatment cycle involves solution treating at about 440   °C, quenching, and then thermally ageing at 180–200   °C for 16–20   h. These heat-treatment conditions are similar to those used to strengthen age-hardenable aluminium alloys. However, the response of magnesium to precipitation hardening is much less effective than aluminium. Only relatively small improvements to the tensile strength of magnesium alloys are gained by precipitation hardening. This is because the density and mobility of dislocations in magnesium is relatively low owing to the small number of slip systems in the hexagonal crystal structure.

The precipitation processes that occur in most magnesium alloys during thermal ageing are complex. In chapter 8, it is mentioned that aluminium alloys undergo the following transformation sequence in the age-hardening process: supersaturated solid solution → GP1 zones → GP2 zones → coherent intermetallic precipitates → incoherent intermetallic precipitates. Some magnesium alloys also undergo this sequence of transformations during ageing whereas other alloys form precipitates without the prior formation of GP zones. The types of precipitates that develop are obviously dependent on the composition and heat-treatment conditions. Precipitates in Mg–E–Zr alloys, such as WE43 used in helicopter transmissions, are Mg₁₁NdY and/or Mg₁₂NdY compounds. Precipitates in Mg–Zn alloys, such as ZE41 that is also used in helicopter transmissions, are coherent MgZn₂, semicoherent MgZn₂, and incoherent Mg₂Zn₃ particles. Several magnesium alloys used in aircraft contain aluminium, such as QE21 that is used in aircraft gearboxes. The main precipitate formed in Mg–Al alloys is Mg₁₇Al₁₂, which is effective at increasing strength. Figure 10.2 shows the effect of aluminium content on the tensile properties of a fully heat-treated Mg–Al–Zn alloy. The yield and ultimate tensile strengths increase with the aluminium content owing to solid solution hardening and precipitation hardening. When the aluminium content exceeds 6–8%, the ductility is reduced owing to embrittlement of the grain boundaries by Mg₁₇Al₁₂ particles and, for this reason, the aluminium concentration is kept below this limit.

10.2. Effect of aluminium content on the tensile properties of a heat treated magnesium alloy.

Two important alloying elements used in magnesium are zirconium and thorium. Zirconium is used for its ability to reduce the grain size. Cast magnesium has a coarse grain structure which results in low strength owing to the weak grain boundary hardening effect. Zirconium is used in small amounts (0.5% to 0.7%) to refine the grain structure and thereby increase the yield strength. In the past, thorium was often used to reduce the grain size and, for many years, magnesium–thorium alloys were used in components for missiles and spacecraft. However, thorium is a radioactive element that poses a health and environment hazard and, therefore, its use has been phased out over the past twenty years and it is now obsolete as an alloying element.

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Design Environments and Systems

Michael F. Ashby , ... Daniel L. Schodek , in Nanomaterials, Nanotechnologies and Design, 2009

Metal-matrix nanocomposites

Metals are the most dominant material used in mechanical applications in any industry. Traditional metallurgy has gone extremely far in providing designers with an amazing array of high-performance metals. There are already many superb ways of making metals stronger (e.g., alloying, work hardening, and dispersion hardening; see Section 4.3). As extensively discussed in Section 7.1, many extremely high performance alloys are based on nanoscale dispersions of particles. Nano is by no means new to the metallurgist. Still, there are always demands for stronger, stiffer, or harder materials or materials with particular kinds of stress-strain deformation characteristics for special applications (e.g., energy absorption). Metal-matrix nanocomposites provide an improved way of meeting these needs.

The properties of many common metals can be greatly enhanced by the addition of relatively small amounts of nanomaterials—normally in the form of nanoparticles, nanowires, and nanotubes. The basic matrix can be any of several metals or alloys. For many applications, normally a low-weight ductile matrix is desirable. These, in turn, can be combined with ceramic second-phase reinforcements that can help increase the modulus and strength values. As discussed in Section 7.8, various metals (aluminum, copper, titanium) have been reinforced with carbides, borides, nitrides, and oxides. Depending on the quantity of reinforcement used and the uniformity of distribution, mechanical properties such as strength, wear resistance, and creep resistance can be adjusted to meet the requirements of the design. Carbon nanotubes (CNTs) have also been used in metal-matrix nanocomposites, with observed improvements in yield stress, maximum strength, and hardness. Amounts of second-phase reinforcing used are normally relatively small. Typically, amounts on the order of 0.5% to 2% of dispersed nanomaterials by weight can lead to enhancements in mechanical strengths.

Metals such as aluminum are widely used. Aluminum-based metal-matrix composites are extremely interesting because of their low density and high specific strength. Metal-matrix nanocomposites are particularly interesting for the aerospace and automotive industries as well as for other structural applications.

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Strengthening of metal alloys

In Introduction to Aerospace Materials, 2012

4.5 Summary

The design ultimate load limit (defined by the yield strength) of metal alloys used in aircraft structures and engines is increased by numerous mechanisms that occur at the atomic, nanometre, micrometre, microstructural and millimetre scales. The main strengthening mechanisms of structural materials such as aluminium, titanium and steel are strain hardening, grain boundary hardening, solid solution strengthening and precipitation hardening. Nickelbased superalloys used in jet engines are also strengthened by dispersion hardening. The common feature of these various strengthening processes is that they operate by restricting or stopping the movement of dislocations and, therefore, the applied stress needed to induce plastic flow increases resulting in a corresponding increase in strength.

Dislocations have a strong influence on the yield strength, ultimate strength, ductility, fatigue strength, toughness and creep resistance of metals. The strength properties increase whilst the ductility decreases with increasing concentration of dislocations. The dislocation density in high-strength metals is typically in the range of 10¹² to 10¹⁴ per cubic centimetre.

The strengthening mechanism of strain hardening involves plastic deformation (cold working) of the metal during fabrication of the aircraft component to create a high density of dislocations. Forging processes such as extrusion, rolling and stamp forming are used to plastically deform and shape the metal. During processing a high concentration of dislocations is created and they become entangled, thus causing a restriction of dislocation slip, which increases the strength properties (but lowers ductility and toughness).

The strength properties are increased by solid solution strengthening, which is achieved by the addition of soluble alloying elements to the base metal. Impurity elements in the metal can also cause solid-solution strengthening. The solute elements occupy interstitial or substitutional lattice sites in the crystal structure of the host metal, depending on their atomic size and electron valence number. The interstitial and substitutional atoms induce a localised elastic strain field in the surrounding lattice owing to the mismatch between their atomic size and the size of the base metal atoms. This strain field repulses the movement of dislocations, and thereby raises the strength properties. The strengthening effect increases with the atomic size difference between the solute and solvent atoms as well as the solubility limit of the solute.

The strength properties are increased by grain boundary hardening, which requires the grain size of the metal to be as small as possible. This mechanism operates by grain boundaries impeding the movement of dislocations, thereby raising the yield strength. The strength improves when the grain size is reduced because the distance that dislocations must travel to reach a grain boundary is shortened. The grain size in aerospace metals is controlled in several ways, including rapid cooling of the metal during casting, addition of grain refining elements, and thermomechanical processing during fabrication of the metal components. The average grain size in aerospace structures is typically in the range of one micrometre to several hundred micrometres. An advantage of the grain boundary hardening process is that yield strength is improved without any significant reduction to toughness or ductility, unlike the other strengthening processes. Grain boundary hardening is not normally used to strengthen jet engine materials because a high density of grain boundaries accelerates high-temperature creep deformation.

Dispersion hardening involves the inclusion of small, hard particles in the metal, thus restricting the movement of dislocations, and thereby raising the strength properties. This strengthening process is applied to nickel-based superalloys used in jet engine components. Tiny ceramic oxide particles resist dislocation slip, even at high temperatures. The particles also improve the high-temperature creep strength by pinning grain boundaries which restricts sliding.

Precipitation hardening is an important strengthening mechanism in most types of aerospace metals. Precipitates form in the metal when the concentration of the alloying element exceeds its solid solubility limit in the base metal. Precipitation hardening is achieved by thermomechanical processing (often called thermal ageing), which involves dissolving the alloying elements into solid solution at high temperature, quenching, and then thermally ageing the metal under controlled temperature and time conditions to create a fine dispersion of incoherent intermetallic precipitates in the base metal. The precipitates restrict the movement of dislocations and thereby increase strength. Maximum strengthening is achieved at the point when the precipitates transform from coherent to incoherent particles. The strength properties are reduced by 'over-ageing' caused by coarsening of the precipitate particles, and this must be avoided during thermomechanical processing.

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Creep, Fatigue and Fracture

R.E. Smallman , A.H.W. Ngan , in Modern Physical Metallurgy (Eighth Edition), 2014

15.3.2 Void nucleation and growth during ductile failure

The nucleation of voids often takes place at inclusions and the surrounding dislocation structure leads to a local rate of work hardening higher than the average. The local stress on reaching some critical value σ _c will cause fracture of the inclusion or decohesion of the particle–matrix interface, thereby nucleating a void. The critical nucleation strain ε _n can be estimated and lies between 0.1 and 1.0 depending on the model. For dispersion hardening materials where dislocation loops are generated the stress on the interface due to the nearest prismatic loop, at distance r, is µb/r, and this will cause separation of the interface when it reaches the theoretical strength of the interface, of order γ _w/b. The parameter r is given in terms of the applied shear strain ε, the particle diameter d and the length k equal to half the mean particle spacing as r=4kb/εd. Hence, void nucleation occurs on a particle of diameter d after a strain ε, given by

(15.14) $\epsilon =4k{g}_{\mathrm{w}}/\mu db$

Any stress concentration effect from other loops will increase with particle size, thus enhancing the particle size dependence of strain to voiding.

Once nucleated, the voids grow until they coalesce to provide an easy fracture path. A spherical-shaped void concentrates stress under tensile conditions and, as a result, elongates initially at about C(≈2) times the rate of the specimen, but as it becomes ellipsoidal the growth rate slows until finally the elongated void grows at about the same rate as the specimen. At some critical strain, the plasticity becomes localized and the voids rapidly coalesce and fracture occurs. The localization of the plasticity is thought to take place when the voids reach a critical distance of approach, given when the void length 2h is approximately equal to the separation, as shown in Figure 15.20. The true strain for coalescence is then

Figure 15.20. Schematic representation of ductile fracture. (a) Voids nucleate at inclusions. (b) Voids elongate as the specimen extends. (c) Voids coalesce to cause fracture when their length 2h is about equal to their separation.

After Ashby et al. (1979).

(15.15) $\epsilon =(1/C)\ln [\alpha (2l-2r_{\mathrm{v}})/2r_{\mathrm{v}}]\approx (1/C)\ln [\alpha (1/f_{\mathrm{v}}^{1/2}-1)]$

where α≈1 and f _v is the volume fraction of inclusions.

Void growth leading to failure will be much more rapid in the necked portion of a tensile sample following instability than during stable deformation, since the stress system changes in the neck from uniaxial tension to approximately plane strain tension. Thus the overall ductility of a specimen will depend strongly on the macroscopic features of the stress–strain curves which (from Considère's criterion) determines the extent of stable deformation, as well as on the ductile rupture process of void nucleation and growth. Nevertheless, Eq. (15.15) reasonably describes the fracture strain for cup and cone failures.

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