Strain gradient plasticity

A mechanism-based theory of strain gradient plasticity (MSG) is proposed based on a multiscale framework linking the microscale notion of statistically stored and geometrically necessary dislocations to the mesoscale notion of plastic strain and strain gradient. This theory is motivated by our recent analysis of indentation experiments which strongly suggest a linear dependence of the square of plastic flow stress on strain gradient. While such linear dependence is predicted by the Taylor hardening model relating the flow stress to dislocation density, existing theories of strain gradient plasticity have failed to explain such behavior. We believe that a mesoscale theory of plasticity should not only be based on stress–strain behavior obtained from macroscopic mechanical tests, but should also draw information from micromechanical, gradient-dominant tests such as micro-indentation or nano-indentation. According to this viewpoint, we explore an alternative formulation of strain gradient plasticity in which the Taylor model is adopted as a founding principle. We distinguish the microscale at which dislocation interaction is considered from the mesoscale at which the plasticity theory is formulated. On the microscale, we assume that higher order stresses do not exist, that the square of flow stress increases linearly with the density of geometrically necessary dislocations, strictly following the Taylor model, and that the plastic flow retains the associative structure of conventional plasticity. On the mesoscale, the constitutive equations are constructed by averaging microscale plasticity laws over a representative cell. An expression for the effective strain gradient is obtained by considering models of geometrically necessary dislocations associated with bending, torsion and 2-D axisymmetric void growth. The new theory differs from all existing phenomenological theories in its mechanism-based guiding principles, although the mathematical structure is quite similar to the theory proposed by Fleck and Hutchinson. A detailed analysis of the new theory is presented in Part II of this paper.

Mechanism-based strain gradient plasticity— I. Theory

A microbend test method for measuring the plasticity length scale

Aluminium matrix composites (AMCs) refer to the class of light weight high performance aluminium centric material systems. The reinforcement in AMCs could be in the form of continuous/discontinuous fibres, whisker or particulates, in volume fractions ranging from a few percent to 70%. Properties of AMCs can be tailored to the demands of different industrial applications by suitable combinations of matrix, reinforcement and processing route. Presently several grades of AMCs are manufactured by different routes. Three decades of intensive research have provided a wealth of new scientific knowledge on the intrinsic and extrinsic effects of ceramic reinforcement vis-a-vis physical, mechanical, thermo-mechanical and tribological properties of AMCs. In the last few years, AMCs have been utilised in high-tech structural and functional applications including aerospace, defence, automotive, and thermal management areas, as well as in sports and recreation. It is interesting to note that research on particle-reinforced cast AMCs took root in India during the 70’s, attained industrial maturity in the developed world nd is currently in the process of joining the mainstream of materials. This paper presents an overview of AMC material ystems on aspects relating to processing, icrostructure, roperties and applications.

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Aluminium matrix composites: Challenges and opportunities

Microstructurally inhomogeneous composites: Is a homogeneous reinforcement distribution optimal?

Particle reinforced metal matrix composites are now being produced commerically, and in this paper the current status of these materials is reviewed. The different types of reinforcement being used, together with the alternative processing methods, are discussed. Depending on the initial processing method, different factors have to be taken into consideration to produce a high quality billet. With powder metallurgy processing, the composition of the matrix and the type of reinforcement are independent of one another. However, in molten metal processing they are intimately linked in terms of the different reactivities which occur between reinforcement and matrix in the molten state. The factors controlling the distribution of reinforcement are also dependent on the initial processing method. Secondary fabrication methods, such as extrusion and rolling, are essential in processing composites produced by powder metallurgy, since they are required to consolidate the composite fully. Other methods, suc...

D. J. Lloyd

Papers

Particle reinforced aluminium and magnesium matrix composites