The strengthening or weakening of polycrystals due to the presence of grain boundaries

Dislocation Mechanics of High-Rate Deformations

“…The weakening is generally accounted for on an analogous constitutive equation basis to that described for grain boundary weakening at higher temperatures. [114] The behavior is described with a general equation of the form [5,115] de=dt ð Þ¼ AD L Gb=k B T ð Þb=' ð Þ p r=G ð Þ q : ½21…”

Origin of the twinning to slip transition with grain size refinement, with decreasing strain rate and with increasing temperature in magnesium

“…It must be emphasized here that in a large majority of the studies aimed to analyze the influence of grain size on the mechanical behavior of Mg alloys [5][6][7][8][9][10][11][12][13][14][15][16][17][18][20][21][22][23]43,[51][52][53][54] the samples with different d values are first processed by rolling or extrusion at moderate to elevated temperatures to avoid cracking, and then annealed to reach the desired average grain size value. Unavoidably, these processing routes lead to well known deformation textures, which have been exhaustively characterized [5].…”

“…The effect of grain size on twinning in magnesium at room temperature and quasi-static rates is still under debate [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20]. First, although it is generally accepted that grain refinement gives rise to larger increases in the yield stress (r y ) when twinning is the main deformation mechanism than when dislocation slip prevails [6][7][8], several conflicting views have been put forth regarding the nature of such grain size dependence.…”

“…First, although it is generally accepted that grain refinement gives rise to larger increases in the yield stress (r y ) when twinning is the main deformation mechanism than when dislocation slip prevails [6][7][8], several conflicting views have been put forth regarding the nature of such grain size dependence. On the one hand, the grain size effect on yielding during twin-dominated straining has been modeled using a Hall-Petch (HP) type relation (r y = r 0 + -kd n ), where r 0 , the lattice friction stress, and k, the HP slope, vary widely with composition, texture, temperature and processing method [6][7][8][9][10][11][12][13][14][15]. This approach has, however, been recently called into question by a systematic statistical analysis of a large number of crystallites in a rolled high purity Mg polycrystal by Beyerlein et al [16], who found no influence of grain size on whether or not at least one twin appeared in a specific grain.…”

Grain size dependence of the activation parameters for plastic deformation: Influence of crystal structure, slip system, and rate-controlling dislocation mechanism

“…Both investigators attributed the stress-grain size dependence now known as the Hall-Petch (H-P) relation to a predicted influence of dislocation pileups being held up at polycrystal grain boundaries. Ronald W. Armstrong, in whose honor the symposium on "Dynamic Deformation: Constitutive Modeling, Grain Size and Other Effects" was held, has been s ϭ s 0 ϩ k l Ϫ1/2 one of the active protagonists of the pile-up model for the H-P equation and through his extensive work with colleagues [7][8][9][10][11][12] has demonstrated its validity not only to steels and bcc materials but also for a variety of fcc and hcp metals and alloys.…”