Strengthening Mechanisms of Metals: Part One

---

Understanding Polycrystalline Metal Behavior

The simplifications that result from single-crystal conditions materially assist in describing deformation behavior in terms of crystallography and defect structure. However, with the exception of solid-state electronic devices, single crystals are rarely used for engineering applications due to limitations involving their strength, size, and production capabilities. Commercial metal products invariably consist of a tremendous number of individual crystals or grains, forming what engineers call polycrystalline aggregates.

The individual grains within polycrystalline aggregates do not deform according to the relatively simple laws that describe plastic deformation in single crystals. This complexity arises from the restraining effect of surrounding grains, which creates a network of interactions that significantly influences the overall mechanical behavior of the material.

The purity and method of preparation determine the initial dislocation density and substructure of these materials. These variables introduce sufficient complexity that mechanical behavior cannot generally be predicted with high precision as a function of strain, strain rate, temperature, and stress rate. However, this complexity becomes advantageous when engineers seek to produce materials with the highest strength and usefulness.

To achieve superior mechanical properties, metallurgists employ several strategies. Fine grain size is often desired for high strength applications, while large additions of solute atoms increase strength and create new phase relationships. Fine particles may be incorporated to enhance strength, and phase transformations can be utilized to achieve remarkable strength improvements. These various strengthening mechanisms represent the foundation of modern alloy design and are essential for understanding polycrystalline material behavior.

Grain Boundaries and Their Role in Deformation

Understanding Grain Boundary Structure

The boundaries between grains in polycrystalline aggregates represent regions of disturbed lattice structure, typically only a few atomic diameters wide. In most cases, the crystallographic orientation changes abruptly when passing from one grain to the next across the grain boundary. The ordinary high-angle grain boundary represents a region of random misfit between adjoining crystal lattices, creating zones of high energy and structural disorder.

As the difference in orientation between grains on each side of the boundary decreases, the state of order within the boundary increases correspondingly. For the limiting case of low-angle boundaries, where the orientation difference across the boundary may be less than one degree, the boundary consists of a regular array of dislocations arranged in a predictable geometric pattern.

Mechanical Strengthening from Grain Boundaries

Direct evidence for the mechanical strengthening effect of grain boundaries comes from carefully controlled experiments on bicrystals. In these studies, researchers systematically varied the orientation difference between longitudinal grain boundaries while maintaining other variables constant. The results demonstrated that yield stress of bicrystals increased linearly with increasing misorientation across the grain boundary.

Particularly revealing was the extrapolation to zero misorientation angle, which gave a value close to that of the yield stress of a single crystal. These results strongly suggest that simple grain boundaries possess little inherent strength. Instead, the strengthening due to grain boundaries results from mutual interference to slip within the grains, creating a complex network of constraints that impede dislocation movement.

Low-Angle Grain Boundaries and Substructure

A definite substructure can exist within grains that are surrounded by high-energy grain boundaries. These subgrains are separated by low-angle boundaries where the difference in orientation across the boundary may be only a few minutes of arc or, at most, a few degrees. Because of this small orientation difference, special X-ray techniques are required to detect the existence of such substructure networks.

The presence of subgrain boundaries creates additional obstacles to dislocation movement, contributing to the overall strengthening of the material. This substructure often develops during thermomechanical processing and can be controlled to optimize mechanical properties.

Strain Aging Phenomena

Strain aging represents a distinctive type of behavior usually associated with the yield-point phenomenon. In this process, the strength of a metal increases while ductility decreases upon heating at relatively low temperatures after cold-working. This phenomenon occurs when interstitial atoms, such as carbon or nitrogen in steel, migrate to dislocations during the aging treatment.

The migration of these atoms creates atmospheres around dislocations, effectively pinning them in place and requiring higher stresses to initiate plastic deformation. This mechanism explains why materials often exhibit higher yield strengths after being stored at room temperature following cold deformation, a phenomenon known as natural aging.

Solid-Solution Strengthening Mechanisms

Fundamental Principles

The introduction of solute atoms into solid solution within the solvent-atom lattice invariably produces an alloy that is stronger than the pure metal. This strengthening occurs through two primary types of solid solutions, each with distinct characteristics and strengthening mechanisms.

When solute and solvent atoms are roughly similar in size, the solute atoms occupy lattice points in the crystal lattice of the solvent atoms, creating what metallurgists call substitutional solid solution. Alternatively, when solute atoms are significantly smaller, they may occupy interstitial positions between the regular lattice sites.

Strengthening Effectiveness

Solute atoms fall into two broad categories regarding their relative strengthening effect. Atoms that produce non-spherical distortions, such as most interstitial atoms, demonstrate a relative strengthening effect per unit concentration of approximately three times their shear modulus. In contrast, solute atoms that produce spherical distortion, such as substitutional atoms, exhibit relative strengthening of about one-tenth of the shear modulus.

Interaction Mechanisms

Solute atoms can interact with dislocations through several distinct mechanisms, each contributing differently to the overall strengthening effect:

Long-range interactions include elastic interaction, modulus interaction, and long-range order interaction. These mechanisms are relatively insensitive to temperature and continue to operate effectively up to approximately 0.6 times the melting temperature.

Short-range interactions encompass stacking-fault interaction, electrical interaction, and short-range order interaction. These constitute short-range barriers that contribute strongly to flow stress primarily at lower temperatures.

The elastic interaction occurs when the strain field around a solute atom interacts with the strain field of a dislocation, creating either attractive or repulsive forces depending on the relative size of the solute atom. The modulus interaction arises from differences in elastic moduli between solute and solvent atoms, while order interactions relate to the tendency of atoms to arrange in specific patterns.

Strengthening from Fine Particles

Dispersion Hardening

Small second-phase particles distributed throughout a ductile matrix represent a common and highly effective source of alloy strengthening. In dispersion hardening, hard particles are mixed with matrix powder and consolidated using powder metallurgy techniques. This approach allows for the creation of materials with exceptional high-temperature stability and strength.

The effectiveness of dispersion hardening stems from the fact that the second phase typically has very little solubility in the matrix, even at elevated temperatures. Additionally, there is generally no coherency between the second-phase particles and the matrix, which means the particles maintain their distinct identity and strengthening effect over a wide range of temperatures.

Precipitation Hardening Fundamentals

Precipitation hardening, also known as age hardening, represents one of the most important strengthening mechanisms in modern metallurgy. This process involves solution treating and quenching an alloy in which a second phase is in solid solution at elevated temperature but precipitates upon quenching and aging at lower temperature.

For precipitation hardening to occur effectively, the second phase must exhibit specific solubility characteristics. It must be soluble at elevated temperatures but demonstrate decreasing solubility with decreasing temperature. This requirement places limitations on the number of useful precipitation-hardening alloy systems, but those that meet these criteria can achieve remarkable strength improvements.

Coherency and Lattice Matching

A critical distinction between precipitation and dispersion hardening lies in the relationship between the particles and the matrix. In precipitation-hardening systems, there is typically atomic matching, or coherency, between the lattices of the precipitate and the matrix. This coherency creates strain fields that significantly contribute to strengthening.

In contrast, dispersion-hardened systems generally exhibit no coherency between second-phase particles and the matrix. While this might seem disadvantageous, it actually provides superior thermal stability since the particles resist growth or overaging to a much greater extent than coherent precipitates.

Guinier-Preston Zones and Precipitation Processes

The general requirement for precipitation strengthening of supersaturated solid solutions involves the formation of finely dispersed precipitates during aging heat treatments. These treatments may include either natural aging at room temperature or artificial aging at elevated temperatures.

The aging process must occur not only below the equilibrium solvus temperature but also below a metastable miscibility gap called the Guinier-Preston zone solvus line. The supersaturation of vacancies created during quenching allows diffusion, and thus zone formation, to occur much faster than expected from equilibrium diffusion coefficients.

During the precipitation process, the saturated solid solution first develops solute clusters, which then become involved in the formation of transitional precipitates. These Guinier-Preston zones are typically in the size range of tens of angstroms in diameter and represent essentially distorted regions of the matrix lattice rather than discrete particles of a new phase having a different lattice structure.

As completely coherent structures with the matrix, GP zones impose local but often large strains on the surrounding material. These mechanical strains, combined with the presence of locally solute-rich and sometimes ordered lattice regions, account for large changes in mechanical properties before any long-range microstructural changes become apparent.

The GP zones are characteristically metastable and dissolve in the presence of more stable precipitates. This dissolution causes precipitate-free, visibly denuded regions to form around stable precipitate particles. The final structure consists of equilibrium precipitates, which do not contribute as significantly to hardening as the intermediate GP zones.

Particle-Dislocation Interaction Mechanisms

Particle Shearing Mechanisms

When particles are small and relatively soft, dislocations can cut and deform the particles during plastic deformation. Six properties of the particles affect the ease with which they can be sheared, each representing a distinct strengthening mechanism:

• Coherency strains represent one of the most significant strengthening mechanisms. Mott and Nabarro recognized that the strain field resulting from the mismatch between a particle and the matrix would be a source of strengthening. The increase in yield stress is given by the relationship Δσ ≈ 2Gεf, where f represents the volume fraction of the dispersed phase and ε measures the strain field intensity.
• Stacking-fault energy effects become important when particles have structures that give rise to extended dislocations. For this mechanism to operate effectively, the particle must possess a structure that promotes the formation of stacking faults when sheared by dislocations.
• Ordered structure strengthening proves responsible for the excellent high-temperature strength of many superalloys. When particles have an ordered structure, anti-phase boundaries are introduced when they are sheared by dislocations. The strengthening model for ordered particles depends critically on the details of particle size and spacing.
• Modulus effects arise when there are significant differences in elastic moduli between the particles and the matrix. This difference creates additional resistance to dislocation movement through the particle.
• Interfacial energy and morphology considerations become important when the energy required to create new particle-matrix interfaces during shearing contributes significantly to the overall resistance.
• Lattice friction stress represents the basic resistance to dislocation movement within the particle itself, which may differ substantially from that in the matrix.

These various mechanisms often operate simultaneously, and their relative contributions depend on factors such as particle size, volume fraction, coherency, and temperature. Understanding these interactions is crucial for designing alloys with optimal combinations of strength, ductility, and thermal stability.

The complexity of polycrystalline metal strengthening mechanisms demonstrates why modern alloy development requires careful consideration of multiple factors. From grain boundary effects to sophisticated precipitation reactions, each mechanism contributes to the overall performance of engineering materials. The continued development of stronger, more reliable metals depends on our growing understanding of these fundamental strengthening processes and their interactions within complex microstructures.