Brown University School of Engineering

Joint Materials/Solid Mechanics Seminar Series: “Material Instabilities: Twin Motion, Shear Bands, and Voids”

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Monday, April 14, 2014 4:00pm - 5:00pm

T.W. Wright, Adjunct Research Professor, Johns Hopkins University. Material failure is generally preceded by some kind of material instability, but the contrary is only sometimes true. An elastic instability initiates dislocation or twinning activities, but these are regarded as mechanisms of plastic deformation, not failure. Phase transformation is another example of material instability that is not necessarily associated with failure. However, void initiation and growth often is a predecessor of failure, as are cleavage and amorphization. This talk will focus on three specific instances of instability in solid materials for which the author has had some experience. A virtual work argument applied to finite elastic deformation arrives at a familiar stability criterion for bulk materials under pressure. Boundary constraints (as noted by Hill) and also cases with strong shear components require consideration of incremental rotation as well as strain. The same virtual work approach, when applied to a volume of material that contains a planar interface, yields three competing stability inequalities that must all hold simultaneously if the material is to be stable. The bulk inequality applies to the material on either side of the interface, and a third inequality applies to the surface itself, but the terms in the inequality require interpretation. Application to an ideal twin boundary in an fcc material, using additional data from molecular dynamics, confirms the validity of the continuum inequality. Adiabatic shear is a form of material instability in plastically deforming materials that often precedes failure. Bands form when local thermal softening caused by plastic working exceeds the ability of thermal conductivity to remove sufficient heat. In a fully formed band the material rapidly loses shear strength along a plane in the material, which in turn causes material unloading adjacent to the band. A fully formed band, where heat conduction away from the band is nearly in balance with heat generation within the band, is not adiabatic at all. The extreme concentration of the band, however, can be useful in asymptotic modeling of its structure, which in turn exposes various important nondimensional parameters. Void nucleation and growth is a form of internal rupture that often leads to total failure. It is most easily visualized as a bifurcation under tensile pressure. A growth law, first developed for elastic materials, can be adapted for elastic/plastic deformation. When further coupled to statistical distributions of potential initiation sites, the driving tensile pressure increases until growth of porosity accelerates, causing tension to peak and then drop rapidly. The peak tensile pressure, which is an indication of spall strength, naturally shows considerable sensitivity to rate of loading. Current research (under Prof. KT Ramesh at JHU) is exploring and refining this description by exploring the effects of various metallurgical features.