Dislocation theory is used to invoke a strain gradient theory of rate independent plasticity. Hardening is assumed to result from the accumulation of both randomly stored and geometrically necessary dislocation. The density of the geometrically necessary dislocations scales with the gradient of plastic strain. A deformation theory of plasticity is introduced to represent in a phenomenological manner the relative roles of strain hardening and strain gradient hardening. The theory is a non-linear generalization of Cosserat couple stress theory. Tension and torsion experiments on thin copper wires confirm the presence of strain gradient hardening. The experiments are interpreted in the light of the new theory.

Strain gradient plasticity: Theory and experiment

A balanced mechanics-materials approach and coverage of the latest developments in biomaterials and electronic materials, the new edition of this popular text is the most thorough and modern book available for upper-level undergraduate courses on the mechanical behavior of materials To ensure that the student gains a thorough understanding the authors present the fundamental mechanisms that operate at micro- and nano-meter level across a wide-range of materials, in a way that is mathematically simple and requires no extensive knowledge of materials This integrated approach provides a conceptual presentation that shows how the microstructure of a material controls its mechanical behavior, and this is reinforced through extensive use of micrographs and illustrations New worked examples and exercises help the student test their understanding Further resources for this title, including lecture slides of select illustrations and solutions for exercises, are available online at wwwcambridgeorg/97800521866758

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Mechanical Behavior of Materials

Strain gradient plasticity

A Strain Gradient Theory of plasticity is introduced, based on the notion of statistically stored and geometrically necessary dislocations. The strain gradient theory fits within the general framework of couple stress theory and involves a single material length scale l. Minimum principles are developed for both deformation and flow theory versions of the theory which in the limit of vanishing l, reduce to their conventional counterparts: J2 deformation and J2 flow theory. The strain gradient theory is used to calculate the size effect associated with macroscopic strengthening due to a dilute concentration of bonded rigid particles; similarly, predictions are given for the effect of void size upon the macroscopibic softening due to a dilute concentration of voids. Constitutive potentials are derived for this purpose.

A phenomenological theory for strain gradient effects in plasticity

Magnesium alloys have received an increasing interest in the past 12 years for potential applications in the automotive, aircraft, aerospace, and electronic industries. Many of these alloys are strong because of solid-state precipitates that are produced by an age-hardening process. Although some strength improvements of existing magnesium alloys have been made and some novel alloys with improved strength have been developed, the strength level that has been achieved so far is still substantially lower than that obtained in counterpart aluminum alloys. Further improvements in the alloy strength require a better understanding of the structure, morphology, orientation of precipitates, effects of precipitate morphology, and orientation on the strengthening and microstructural factors that are important in controlling the nucleation and growth of these precipitates. In this review, precipitation in most precipitation-hardenable magnesium alloys is reviewed, and its relationship with strengthening is examined. It is demonstrated that the precipitation phenomena in these alloys, especially in the very early stage of the precipitation process, are still far from being well understood, and many fundamental issues remain unsolved even after some extensive and concerted efforts made in the past 12 years. The challenges associated with precipitation hardening and age hardening are identified and discussed, and guidelines are outlined for the rational design and development of higher strength, and ultimately ultrahigh strength, magnesium alloys via precipitation hardening.

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Nicholson, Robin, Sir

Papers

Strengthening methods in crystals