A mechanism in which a dislocation bows out between hard particles it cannot cut, passes them and leaves a dislocation loop around each particle. The stress required is inversely proportional to the particle spacing.
Japanese name: オロワン機構
Orowan mechanism appears in 3 practice questions across 1 topic, including Strengthening mechanisms and dislocations.
If hard particles that a dislocation cannot cut lie on the slip plane, the dislocation is caught on them and bows out between neighboring particles. A dislocation has a line tension (about Gb²/2) that tends to shorten it, so stress is needed to make the bow larger. Once the bow passes a semicircle, the segments wrapping around each side of a particle meet behind it and annihilate, the dislocation moves on, and a dislocation loop is left around the particle. The shear stress needed to pass in this way is Δτ ≈ Gb/L (L is the particle spacing), called the Orowan stress.
At a constant volume fraction f, the particle spacing L is roughly proportional to the particle radius r and inversely proportional to √f. So the more numerous and finer the dispersed particles, the smaller L and the larger the Orowan stress. When precipitates coarsen as aging proceeds, the spacing widens and the strength falls even though the volume fraction does not change; this is the softening of overaging. Small coherent particles early in precipitation, on the other hand, are easier to cut than to bypass, so they strengthen by shearing rather than by the Orowan mechanism. The strength is greatest at the size where shearing and bypassing change over.
The Orowan loops left around particles exert a repulsive stress on the next dislocations, effectively enlarging the particles and making the next passage harder. Alloys containing hard particles therefore tend to work-harden strongly, and when the load is reversed the stress from the loops assists deformation, so the Bauschinger effect is also large. Dispersion strengthening by oxide particles, overaged precipitates and much of the strengthening of steels containing carbides rely on this mechanism. At high temperature dislocations can climb over the particles, so the strengthening effect becomes smaller.
Answer: B. About 228 MPa
Δτ = 26×10⁹ × 0.286×10⁻⁹/(100×10⁻⁹) ≈ 7.4×10⁷ Pa, about 74 MPa. Converting to the increase in the yield stress of a polycrystal means multiplying by the Taylor factor, Δσ = 3.06 × 74 ≈ 228 MPa. About 74 MPa leaves the value as a shear stress and forgets M, and about 24 MPa divides by M. The expression comes from the line tension of a dislocation, about Gb²/2, and the fact that a dislocation can pass once it has bowed out into a semicircle between precipitates. At the same volume fraction, finer particles have a smaller spacing L, so the Orowan stress is larger. More precise expressions include a factor for the dislocation character and particle size and a logarithmic term, which give values smaller than this estimate.
Because the line tension depends on the dislocation character (edge or screw) and on the shape of the bowed dislocation, and it also depends logarithmically on the particle size. The more accurate Orowan–Ashby expression gives values smaller than the Gb/L estimate.
With particles that require a large stress for dislocations to cut them, such as particles incoherent with the matrix, hard oxides and carbides, and precipitates that have grown large. Small coherent precipitates are usually sheared by dislocations.
Make the particles finer and more numerous to narrow their spacing. Halving the particle size at the same volume fraction roughly halves the spacing and roughly doubles the Orowan stress.
At the same volume fraction, finer particles have a smaller spacing L, so the Orowan stress is larger.
In an aluminum alloy, the increase in shear stress due to t…Once precipitates become large, it becomes easier for dislocations to bow out between them and pass, leaving loops (the Orowan mechanism), and that stress is inversely proportional to the precipitate spacing, so it falls as the particles coarsen.
As precipitates grow during aging, the strength rises to a …Hard, incoherent particles are not sheared by dislocations and strengthen through the Orowan mechanism.
Which statement about dispersion strengthening with oxide p…Dislocation Taylor factor Dispersion strengthening Ostwald ripening Creep Precipitation hardening Bauschinger effect Critical resolved shear stress Peierls stress Schmid factor