Singular Integral Equations. By N.I. Muskhelishvili. Translated fromthe 2nd Russian edition by J.R.M. Radok. Pp. 447. F1. 28.50. 1953. (Noordhoff, Groningen)

Twinning-induced plasticity (TWIP) steels

During the past decade considerable research efforts have been directed towards achieving balanced engineering properties of two-phase γ-titanium aluminide alloys for future applications as structural materials. For optimization of mechanical properties such as yield and creep strengths, tensile ductility and fracture resistance, a basic understanding of the temperature dependent micromechanisms of plasticity and fracture, and their interplay with various microstructural constituents is required. In this review article, the current knowledge on dislocation types and slip systems, the development of deformation substructures, factors controlling the mobility and multiplication of dislocations, interface related plasticity, solid solution and precipitate strengthening mechanisms as well as microscopic aspects of creep and fracture will be addressed. These topics will be related to specific microstructures and associated engineering properties.

Microstructure and deformation of two-phase γ-titanium aluminides

The effect of interfaces on mechanical properties is considered. Elastic and plastic compatibilities at boundaries are treated. Specific influences at both low and high temperatures are discussed, with emphasis on dislocation mechanisms and the atomic scale structure of boundaries.

The influence of grain boundaries on mechanical properties

Refining a metal’s grain size can result in dramatic increases in strength, and the magnitude of this strengthening increment can be estimated using the Hall–Petch equation. Since the Hall–Petch equation was proposed, there have been many experimental studies supporting its applicability to pure metals, intermetallics and multi-phase alloys. In this article, we gather the grain-size strengthening data from the Hall–Petch studies on pure metals and use this aggregated data to calculate best estimates of these metals’ Hall–Petch parameters. We also use this aggregated data to re-evaluate the various models developed to physically support the Hall–Petch scaling.

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Six decades of the Hall–Petch effect – a survey of grain-size strengthening studies on pure metals

Calculations involving pile ups of dislocations, both analytical and numerical, using either discrete dislocations or continuous distribution of dislocations of infinitesimal Burgers vectors, are reviewed in the light of their effects on the relation between yield or flow stress and grain size. The limitations of the pileup models are discussed and some nonpileup theories of yielding are critically reviewed also. More critical experiments are still needed to reveal the fundamental mechanicm of yielding.

The role of dislocations in the flow stress grain size relationships

The elastic energyE of a straight glide dislocation in bec crystals is analyzed as a function of crystal orientation. Approximate energy functions are obtained for dislocations on the 110, 112, and 123 slip planes. Regions of instability for glide dislocations are found to exist only in highly anisotropic crystals, Li, Na, K, and β-brass. The Peierls stresses op and the widths of edge and screw dislocations are also analyzed. For most common bec crystals, the following inequalities hold: E(110) < E(123) < E(112) for edge dislocations,op(110) <op(112) <op(123) for both edge and screw, and (op)e < (op)s between the edge and screw on the same slip plane, where the subscript p stands for Peierls, e for edge, s for screw, and the superscripts refer to the slip planes.

Y. T. Chou

Papers

The role of dislocations in the flow stress grain size relationships

Energy, stability, and peierls stress of glide dislocations in anisotropie BCC crystals

Effect of grain boundary dislocations on the slope of the Hall-Petch relation