**4.3 Age-hardenable alloys**

A very important family of metals is that formed by age-hardenable alloys. Their properties can be tuned by means of heat treatments that usually start with a quenching process of the sample from above the solution temperature. The quenching step is followed by an isothermal annealing that typically lasts for some hours. The variation of mechanical properties is related with the precipitation state developed by the heat treatment. Therefore, deformation that takes place at high temperature is accompanied by an evolution of the precipitation state. The two phenomena are coupled. The deformation slows down due to the presence of atoms in solid solution and coherent precipitates, and the precipitation kinetics is modified

by the presence of the dislocation structure [32]. **Figure 8** shows the structure of

*Back scattered image of a AA2014 powder particle showing the precipitate structure after quenching from*

The formation of dislocation fractal structures with plastic deformation is, as in many others aspects of nature, a widespread phenomenon. It is, in fact, observed under different tensing conditions and metal alloys. This is because metal plasticity

On the temporal scale, the dislocations can move at speeds greater than that of the sound when the dislocation density is low, leading to rapid plastic deformation events (e.g., car accident). On the contrary, deformation under creep conditions can occur in much longer time periods, as long as days, months, or even years (e.g., motion of glaciers). The same concept can be applied to the spatial scale as deformation phenomenon involves entities as small as dislocations and vacancies in the crystal lattice, and, on the other side, this phenomenon takes place at a macroscopic

The behavior of dislocations during strain of metals is very rich and complex because the plasticity phenomenon covers different spatial and temporal scales and there is a very broad range of experimental conditions and alloys. Nonetheless, the existence of fractal structures of dislocations is ubiquitously found when a metal is deformed. This fact greatly encourages the use of fractals to fully describe the

The determination of the fractal dimension of dislocation structures, DF, is conducted from images obtained by different microstructural characterization methods, typically, by TEM. These images must, then, be carefully treated to minimize inaccuracies in the determination of DF. The box counting technique is revealed to be a very suitable and reliable method to determine DF. Although the process is automated in some image analysis applications, the presence of elements different from dislocations (e.g., dots related with other microstructural features)

precipitates in aged AA2014.

*800 K, followed by aging at 523 K for 10 h.*

*Fractal Analysis of Strain-Induced Microstructures in Metals*

*DOI: http://dx.doi.org/10.5772/intechopen.91456*

occurs on several temporal and spatial scales.

scale, meters in size in large components.

phenomenon of plasticity in metals.

can greatly modify the fractal dimension.

**113**

**5. Conclusions**

**Figure 8.**

#### **Figure 8.**

**4.1 Low-temperature dislocation structures**

*Fractal Analysis - Selected Examples*

**4.2 High-temperature dislocation structures**

and 29 MPa is around 5 microns.

**4.3 Age-hardenable alloys**

**Figure 7.**

*29 MPa.*

**112**

crystal strained up to 22.3% at room temperature at 104�s

In **Figure 6**, a bright field TEM image of a commercially pure aluminum single

This figure corresponds to a perpendicular section of the sample with respect to the tensile axis. Dislocations are arranged in a messy way. The subgrain size developed

In **Figure 7**, a detail of a subgrain boundary shows a bright field TEM image of a

A very important family of metals is that formed by age-hardenable alloys. Their

*Bright field image of a subgrain boundary of polycrystalline pure aluminum deformed around 2% at 573 K and*

properties can be tuned by means of heat treatments that usually start with a quenching process of the sample from above the solution temperature. The quenching step is followed by an isothermal annealing that typically lasts for some hours. The variation of mechanical properties is related with the precipitation state developed by the heat treatment. Therefore, deformation that takes place at high temperature is accompanied by an evolution of the precipitation state. The two phenomena are coupled. The deformation slows down due to the presence of atoms in solid solution and coherent precipitates, and the precipitation kinetics is modified

by deformation of this pure metal at room temperature is around 1 micron.

commercially pure polycrystalline aluminum strained around 2% at 573 K and 29 MPa. **Figure 7** corresponds also to a perpendicular section of the sample with respect to the tensile axis. The dislocations are well-ordered in the subgrain boundary. The subgrain size developed by deformation of this pure metal at room 573 K

�<sup>1</sup> strain rate is shown.

*Back scattered image of a AA2014 powder particle showing the precipitate structure after quenching from 800 K, followed by aging at 523 K for 10 h.*

by the presence of the dislocation structure [32]. **Figure 8** shows the structure of precipitates in aged AA2014.
