The Strengthening Of Metals

Precipitation or age hardening was discovered by Alfred Wilm in Germany in 1906. He attempted to harden an alloy of essentially aluminum-2 atom percent copper in an analogous way to steels by a quenching treatment. The specimen was initially soft, but the hardness increased with time at room temperature after the quench.
Later, the hardening is attributed to a precipitation effect. This was extremely important for development of a whole host of precipitation-hardened alloys. The solubility of copper in aluminum decreases markedly on cooling and that quenching gives a supersaturated solid solution. The change in solubility with temperature in the terminal solid solution is typical for age-hardening systems.

Precipitation or age hardening was discovered by Alfred Wilm in Germany in 1906. He attempted to harden an alloy of essentially aluminum-2 atom percent copper in an analogous way to steels by a quenching treatment. The specimen was initially soft, but the hardness increased with time at room temperature after the quench.

Merica, Waltenberg and Scott first attributed the hardening to a precipitation effect. This was an extremely important paper for it pointed the way to development of a whole host of precipitation-hardened alloys. They correctly pointed out that the solubility of copper in aluminum decreases markedly on cooling and that quenching gives a supersaturated solid solution.

The change in solubility with temperature in the terminal solid solution is typical for age-hardening systems. At room temperature the stable state of an aluminum-2 atom percent copper alloy is an aluminum-rich solid solution (α) and an intermetallic phase with a tetragonal crystal structure having nominal composition CuAl2 (θ). According to the suggestion of these authors, fine particles of θ (and similar precipitates in other systems) form during aging. These were visualized to lie astride and key the slip planes, a proposal put forth by Jeffries and Archer.

However, with the treatment to give maximum hardness, in general precipitate particles are not visible with the highest-resolution light microscope. When the particles are visible the alloy has overaged. Not only is the hardness less in the overaged state but usually the alloy is very much less ductile compared to maximum hardness.

The mystery was solved first in aluminum-copper alloys independently by Guinier and Preston in 1937 by careful X-ray diffraction work. Diffuse scattering occurs outside but associated with the Bragg reflections of the solid solution, and these are due to regions in the matrix solid solution enriched in solute atoms. Small solute-enriched regions in a solid solution where the lattice is identical or somewhat perturbed from that of the solid solution are called Guinier-Preston zones.

Precipitation in Al-Cu Alloys

In aluminum-2 atom percent copper, four different precipitates occur and each may be made to form by controlling the heat treatment. The occurrence of metastable precipitates is quite common in precipitation-hardening alloys. Typical system for describing in details the sequence of events is aluminum-copper although the phenomena mentioned here occur in many other systems.

Guinier-Preston zones of the first kind (GP-I) are plates of copper atoms one or two atoms thick and commonly 25 atoms in diameter oriented parallel to {100} planes in the aluminum-rich matrix. Since the sizes of copper and aluminum atoms differ by about 12 per cent, the lattice is distorted in the regions of the zones. As a matter of fact, the zones here form as thin platelets to minimize strain energy. They form parallel to {100} because the elastic modulus is least in this direction. GP-I forms at room temperature and is the first precipitate to form at 100°C. It is not stable at 210°C; GP-1 formed at a lower temperature rapidly dissolves in about 30 seconded if the metal is heated to 210°C. This is called reversion or retrogression.

Guinier-Preston zones of the second kind (GP-II) are thicker (10 atoms) and of larger diameter (75 atoms) than GP-I, but they are not just big GP-I precipitates. In GP-II an ordering of aluminum and copper atoms occurs to give an average composition of about Cu2Al5. GP-II is the second precipitate to form at, say, 130°C or the first at 210°C. The strongest aluminum-2 atom percent copper at room temperature contains mainly GP-II.

θ’ is a third metastable precipitate. It has the nominal composition CuAl2 and is tetragonal with a lattice distorted from θ so that it may form nearly coherently or epitaxially with the aluminum-rich matrix. It forms in the matrix in a Widmenstatten pattern. The arrangements of atoms in the interface or habit plane are nearly identical in θ’ and the matrix. θ’ begins to form later than GP-II at 130 or 210°C.

Actually all types of precipitates may give hardening but GP zones and ordinary precipitates with some degree of coherency give greater hardening. In some systems, maximum precipitate on hardening occurs with GP zones (aluminum-copper and aluminum-zinc); in some systems maximum hardening occurs with a coherent ordinary precipitate (nickel-titanium, aluminum; nickel, chromium-titanium, aluminum; and aluminum-silver).

Guinier divides GP zones into two classes: ideal and nonideal. The atomic sizes of zinc and silver differ little from that of aluminum. With these, the lattice of the aluminum-rich matrix is not distorted very much in the region of the zones, which are spherical in shape. These are classed as ideal zones. The zones in aluminum-copper are an example of nonideal zones.

An important consideration is why metastable precipitates such as GP zones and θ’ should form at low temperatures, rather than the stable precipitate. The answer lies in the theory of nucleation and diffusion-controlled growth. In these cases a large surface energy exists between the stable phase and the matrix, but the GP zone is a perturbation of the matrix and the surface energy is small, indention is difficult for the former, easy for the latter. Very little diffusion is required to nucleate a GP zone. A large number of small part ides are able to form during the quench from the solution-treating temperature and on the subsequent low-temperature precipitation heat treatment. Quenched-in vacancies play an important role in facilitating diffusion.

If extra vacancies are present -- they may be put in by quenching, irradiation or cold work -- diffusion processes take place at very low temperatures. Some age-hardening alloys (copper-beryllium) do not develop full hardness unless they are cold-worked before aging. The free energy of the system may, of course, be further lowered if the metastable precipitate is replaced by the stable (or a more stable) precipitate. This occurs if the temperature is raised.

Interaction of Dislocation and Precipitate

Discussion about the various precipitates in aluminum-copper showed that the problem which must be considered to understand precipitation hardening is the interaction of a dislocation with a field of obstacles. The obstacles of primary interest here are precipitates defined broadly to include Guinier-Preston zones and metastable second phases as well as stable phases.

Consider a row of such obstacles and a dislocation moving on a slip plane. For slip to occur, the dislocation must either move around the particles or through the particles. An active dislocation will select from the various paths available to it the path where the least energy is expanded.

The dislocation may avoid the particles or obstacles by leaving the slip plane in the vicinity of each particle, or it may avoid the particles by the Orowan mechanism. In this mechanism, the dislocation bends between the particles leaving a dislocation ring about each particle. In either case, energy must be supplied to increase the total length of dislocation line; the stress required is, neglecting a numerical factor, roughly (Gb)/ L where G is the shear modulus, b is the Burgers vector, and L is the spacing between obstacles.

Cutting of Particles by Dislocations

In all age-hardened or precipitation-hardened alloys, the particles are generally cut during plastic deformation when the metal is aged to maximum hardness; avoiding of the particles corresponds to the overaged state.

For a dislocation to move through a particle, energy must be supplied for three basic processes, which may be involved in the cutting.

  • First, if the particle is formed by a solid-state reaction or if there is a difference in coefficient of expansion, there may be elastic misfit stresses between the particle and the matrix since the particle will generally occupy a different volume than the parent phase it replaced.
  • Second, the surface area of the particle is increased by cutting it and slipping the two halves.
  • Third, the flow stress for moving a dislocation inside the particle may be larger than that in the matrix.
However, we will first briefly mention dislocation pinning effects due to the presence of particles. Dislocations may catalyze precipitation, and then precipitates may form at dislocations. This is thought to be the source of the yield drop commonly observed in iron and mild steel. Yield-drop effects are not commonly observed in precipitation-hardened alloys with GP zones or with a general distribution of precipitates.

Strengthening by Elastic Misfit Stresses

The importance of elastic misfit strains in age hardening has long been recognized going back to Rosenhain. Transition phases such as θ’ in aluminum-copper or γ’ in nickel-base alloys form with close matching across the habit or interface plane. The lattice must be strained to give matching.

Very large equivalent stresses may be computed if the mismatch is assumed to be taken up completely by strain. Recently was shown that the maximum precipitation hardening in nickel-base aluminum-titanium alloys from γ’ occurs at the proportion of aluminum to titanium giving the largest difference in lattice parameter between the precipitate (at large particle size) and matrix.

The dislocation theory of the strengthening from misfitting precipitates is due to Mott and Nabarro. Consider first that particles are so closely spaced that the dislocation must move essentially as a rigid line, that is, the maximum bending of the dislocation between particles is negligible.

The minimum radius of curvature to which a dislocation may be bent under the applied stress is larger than the spacing between particles on the slip plane. Depending on the relative orientation of the dislocation and precipitate, the internal stress will aid dislocation motion or hinder dislocation motion. The sum-total effect on a length of dislocation which is long compared to the spacing is zero; no strengthening is predicted to a first approximation.

The situation is analogous to a solid solution. Second, Mott and Nabarro considered the case where the particle spacing is not negligible compared to the minimum radius of curvature of the dislocation, but are of the same order of magnitude. The dislocation will tend to be wavy, assuming a position in the stress fields of the particles, which minimizes the total self-energy of the dislocation. The dislocation does not assume exactly the position corresponding to the minimum self-energy per unit length, but the dislocation is shortened a little by the line tension of the dislocation.

Strengthening from Modulus Change

It was pointed out that variation of the elastic module between the precipitate and matrix may be a source of strengthening. A general theory of stresses about particles must include misfit as well as variation in the elastic module. Further, the self-energy of the dislocation depends on G; therefore, if G of the particle is larger than that of the matrix, an extra stress will be required to force the dislocation through the particle.

The point values of the module will be functions of local composition since the module are related to the second derivatives of the interatomic interaction energies with respect to interatomic distance. Anisotropy in the elastic constants must also be taken into consideration.

August, 2005
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