August 2020 Volume 2

between the aspects of the precipitation and the strength. Specifically, the strengthening increment increases with the square root of the volume fraction of the particles, while the strength increase decreases as the real diameter of the particles increases. Precipitation strengthening can be highly desirable in many high-strength applications, and as such, an aging time is often incorporated into the processing of the steel to allow for sufficient precipitation. However, as Figure 7 shows, when too long of a time is allotted for aging, negative effects tend to take place. [6] The precipitates begin to lose coherency with the matrix such that the Friedel mechanism cannot operate, and furthermore the growth of the particles leads to decreasing strengthening increments in the Orowan-Ashby machanism. [6] of the particles (mm). [11] Of importance to note here is the relationships between the aspects of the precipitation and the strength. Specifically, the strengthening increment increases with the square root of the volume fraction of the particles, while the strength increase decreases as the real diameter of the particles increases. Precipitation strengthening can be highly desirable in many high-s reng h applications, and as such, an aging time is often incorporated into the processing of the steel to allow for sufficient precipitation. However, as Figure 7 shows, when too long of a time is allott d for agi g, negative effects tend to take place. [6] The precipitates begin to lose coherency with the matrix such that the Friedel mechanism cannot operate, and furthermore the growth of the particles leads to decreasing strengthening increments in the Orowan-Ashby machanism. [6]

FORGING RESEARCH

Figure 4: Model of dislocation and particle interaction showing glide and climb force directions [9]

Figure 5: Dislocation model showing dislocation movement through (a) dislocation slide and (b) dislocation climb [10] Figure 5: Dislocation model showing dislocation movement through (a) dislocation slide and (b) dislocation climb [10]

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Figure 7: Aging time and particles size influence on precipitation strengthening [6] 2.1.4 Grain-Boundary Strengthening The presence of grain boundaries within a metal provides resistance to the motion of dislocations throughout the structure. While the grain boundary itself has little inherent strength, the boundaries give rise to significant strengthening through interference to slip within and between the grains, such that the strengthening scales with the misorientation across the grain boundary. [6] This strengthening effect increases with the ASTM grain boundary numbers, and thus also scales inversely with the grain size, according to the following equation proposed by Hall and expanded by Petch: [12, 13] σ 0 =σ i +kD- 1/2 (2-3) Where σ 0 is the yield stress, σ i is the friction stress, k is the locking parameter which describes the strengthening contribution of the grain boundaries, and D is the grain diameter. [6] 10 Figure 7: Aging time and particles size influence on precipitation strengthening [6]

Figure 6: Precipitation strengthening relationship with particle volume fraction and size [11] Figure 6 shows the relationship between the strengthening increment due to precipitation and the volume fraction and size of the precipitates. Here is demonstrated the importance of a fine distribution of precipitates, where particles approaching 5nm in diameter contribute very high strength increments exceeding 100MPa at very low volume fractions, while the larger particles at 50nm increase the strength moderately. In the literature [11] the strengthening increment of a particle distribution is described by Δσy= (0.538Gbf 1/2 /X) ln(X/2b) (2-2) Where Δσy is the yield strength change due to precipitation (MPa), G is the shear modulus (MPa), b is the burgers vector (mm), f is the volume fraction of particles, and X is the real (spatial) diameter of the particles (mm). [11] Of importance to note here is the relationships Figure 6: Precipitation strengthening relatio ship w th particle volume fraction and size [11] Figure 6 shows the relationship between the strengthening increment due to precipitation and the volume fraction and size of the precipitat s. Here is d monst ated the importance of a fine distribution of precipitates, where particles approaching 5nm in diameter contribute very high strength increments exceeding 100MPa at very low volume fractions, while the larger particles at 50nm increase the strength moderately. In the literature [11] the strengthening increment of a particle distribution is described by Δ σ y = (0.538G bf 1/2 /X) ln(X/2 b ) (2-2)

FIA MAGAZINE | AUGUST 2020 68 Where Δ σ y is the yield strength change due to precipitation (MPa), G is the shear modulus (MPa), b is the burgers vector (mm), f is the volume fraction of particles, and X is the real (spatial) diameter