## Strengthening mechanisms

Mechanisms contributing to the strengthening (increase of strength) of metal materials and effectively impeding dislocation creep.

The strength of a metal material is always closely linked to the dislocations it contains. In order to increase the strength of a material, the movement of dislocations must therefore be impeded or hindered or even prevented entirely. The most important means available for this purpose are briefly described below.

1. Work hardening (nodule formation, strengthening by network formation): Networks of “entangled” dislocations render a material more brittle and hard as they inhibit dislocation movements. Networks are mainly formed when working a material (thus, “work hardening”).

Consequently, it is possible to achieve a significant increase in dislocation by means of cold forming of a material, which in turn causes an enormous increase in dislocation density. The numerous dislocations introduced by forming impede each other’s movement and the material is work-hardened. 2. Grain boundary strengthening (grain refinement, phase boundary hardening): When a migrating dislocation comes into contact with a boundary between two grains misoriented towards each other, periodicity is disrupted and the original glide plane is not continued “seamlessly”. The level of obstruction depends on the size of the misorientation. A small grain can be obtained by targeted heat treatment or treatment of the melt with a grain refinement agent or inoculant. The dependence of yield strength on grain size is governed by the so-called Hall-Petch relationship (eq. 1)

Eq 1:$R = \sigma_0 + \frac{k_y}{\sqrt{d_K}}$

where σ0 is the initial stress for dislocation movement (“frictional stress”), ky is the grain boundary resistance (Hall-Petch constant) and dK is the mean grain diameter. These are constants depending on the material and testing conditions.

3. Solid solution strengthening (alloy hardening, strengthening by incorporation of foreign atoms): Foreign atoms – especially those having considerably varying sizes – interfere with dislocation creep. This effect is even further enhanced by the stress field surrounding the foreign atom and can lead to “pinning” of the dislocation.

The increase in strength by solid solution strengthening can be much more effective than the strengthening achieved by forming or grain refinement. Assuming a linear superposition of the strengths of two elements according to their percentage composition, the actual curve lies well above this line. One example is the Cu-Ni system (Fig. 1) where the elements are completely miscible over the entire concentration range. The incorporation of foreign atoms of other sizes causes tensile and compressive stresses within the crystal lattice impeding the movement of dislocations.

4. Dispersion strengthening: Large dispersed particles represent greater obstacles, creeping being impeded by particles which are close to each other. Further dislocation rings are created (Orowan mechanism). If a metal contains non-metal inclusions, e.g. oxides, these particles interfere with dislocation movements. The only deformation mechanism possible is for the dislocations to bow out between obstacles.

5. Precipitation hardening: Migrating dislocations get stuck on precipitated particles (having another structure). (Example: Cu-Al: solid solution at high temperature, precipitation of particles with Al2Cu structure at low temperatures). Of course, this mechanism is particularly effective in multi-phase materials (see Hardening, Heat treatment of hardenable aluminum casting alloys).

The phase boundary between the precipitation and the matrix can be both incoherent or partly coherent. For dislocations, incoherent phases are like insurmountable grain boundaries which is why these phases are as effective as particles or dispersoids. If a dislocation moves through a coherent precipitation, the particle is sheared since the dislocation displaces the atoms at the other side of the glide plane, as shown in Fig. 2 (Friedel effect). The shearing creates additional phase boundaries the energy of which must be provided by the stresses applied when cutting the particle.

The shear stress during particle shearing is proportional to the root of the particle size but cannot become greater than the Orowan stress as it would then be easier for the dislocation to just bow out between the particles instead of shearing them. This relationship is illustrated in Fig. 3. Therefore, it is easy to understand that there is a certain precipitate size with the particle radius r0 at which maximum strength can be obtained.

6. Tailoring: In multi-phase systems, the targeted generation of microstructures is possible by means of “tailoring” (= treatment at suitable temperature/time) which is defined by the phase chemistry, transformation kinetics, atomic structures and size distribution of the precipitated phases. Example: “steel” (Fe + C) where the coexistence of a number of structural phases (austenite, martensite, ferrite, cementite, etc.), more or less large carbon precipitations, special structures (“martensitestructure) and internal stresses (as well as additives) determine the properties of the relevant steel grade.

7. Transformation hardening: Many compounds undergo phase transformations. Possible coexisting phases result in microstructures inducing hardening.

Combination of mechanisms for increasing strength

• The strength or hardness values which can be achieved in metal materials by the individual mechanisms are limited for both physical and technical reasons.
• For example, in solid solution strengthening, the elements having the greatest strengthening effect are only slightly soluble in the matrix.
• Dislocation hardening is subject to an upper dislocation density. When exceeding this limit, the crystalline structure is lost.
• With grain boundary strengthening, there is a lower grain size limit which cannot be passed by the technical means of grain refinement.
• Particle hardening is limited by the particles having varying sizes. Therefore, the maximum theoretical strength – requiring particles of the critical diameter in narrow distribution and with high density – cannot be achieved.

Literature references:
Riehle M., Simmchen E., Grundlagen der Werkstofftechnik, Deutscher Verlag für Grundstoffindustrie, Stuttgart, 2000.