Perry H. Leo

Transient heat transfer effects on the pseudoelastic behavior of shape-memory wires

Abstract Experimental results of a displacement-controlled elongation of a shape-memory wire of nickel-titanium are presented. It is observed that the hysteretic strain-stress curves depend strongly on the strain rates at which the wire is extended. A theoretical model is proposed to explain this phenomenon. This model couples the fully time-dependent heat transfer in the wire to its quasi-static mechanical behavior through the temperature dependence of the transformation stress of the alloy. It accounts quantitatively for experimentally observed changes in the pseudoelastic hysteresis. The model presented here is different from others proposed in the literature, as it does not make use of a kinetic relation and accounts for the observed changes in the pseudoelastic hysteresis without parameter fitting. The results show that a model consisting of a single moving austenite-martensite interface is sufficient to predict the response of the wire over several decades of strain rate.

Overview no. 86: The effect of surface stress on crystal-melt and crystal-crystal equilibrium

Abstract The effect of surface stress on the equilibrium conditions at crystal-melt, coherent crystal-crystal and greased crystal-crystal interfaces is investigated by using a variational method to test for equilibrium. In all three cases, the interface between the phases is modelled as a Gibbsian dividing surface, and the excess internal energy associated with the interface is allowed to depend on both the deformation of the interface and the crystallographic normal to the interface. The position of an interface can vary due to both deformation at the interface and transformation between the two phases at the interface (accretion), and so we define a special variation that accounts for both. Thus, surface stress appears explicitly in both the force and energy balances at crystal-melt and coherent crystal-crystal interfaces. In particular, an interfacial strain energy term appears in the energy balance at these interfaces; this term gives the energy of deforming the interface against the force associated with the surface stress, and is a new result from this analysis. Anisotropy also appears in this energy balance through a term that can be expressed by using Cahn and Hoffmans ξ-vector. Finally, it is shown that a greased crystal-crystal system differs from crystal-melt and coherent crystal-crystal systems in that two independent deformations and crystallographic normals can be defined at a greased interface. However, by partitioning the excess energy associated with a greased interface between these deformations and normals, one can reduce the equilibrium conditions at a greased interface to those that obtain if the two crystals would interact only through a thin fluid layer at the interface.

A diffuse interface model for microstructural evolution in elastically stressed solids

Abstract We present a diffuse interface (DI) model for capturing microstructure formed during the coarsening of a two dimensional, elastically stressed binary alloy. The DI model is based on a generalized Cahn–Hilliard free energy; evolution occurs to lower the free energy. Using a matched asymptotic expansion, we show that the DI model converges to a well-studied sharp interface system as the thickness of the diffuse interface approaches zero. Numerical simulations confirm this equivalence. We develop pseudo-spectral numerical methods to solve the DI system and we carefully investigate the dependence of results on numerical parameters. The DI model is used to follow microstructural evolution through topological transitions such as particle merging and vanishing. We show that in isotropic media, elastic inhomogeneity may lead to interesting topology changes such as a reversal of the roles of the precipitate and matrix phases.

The use of shape memory alloys for passive structural damping

Experimental results on the dynamics of a beam constrained by shape memory wires are presented. It is observed that the damping increases significantly when the shape memory wires are stressed such that they lie within the pseudoelastic hysteresis loop. Theoretical models of the inner hysteresis loop are considered, and modal analysis is used to obtain the dynamic response of the system. Simulations of the system using these models give theoretical values of damping which agree well with those observed experimentally. The proposed models of the pseudoelastic hysteresis loop are adequate for providing an estimate of the initial increase of damping due to the use of prestressed shape memory wires in structures. These results demonstrate that pseudoelasticity of shape memory wires can be used to augment passive damping significantly in structural systems.

The Effect of Surface Stress on Crystal-Melt and Crystal-Crystal Equilibrium

The effect of surface stress on the equilibrium conditions at crystal-melt, coherent crystal-crystal and greased crystal-crystal interfaces is investigated by using a variational method to test for equilibrium. In all three cases, the interface between the phases is modelled as a Gibbsian dividing surface, and the excess internal energy associated with the interface is allowed to depend on both the deformation of the interface and the crystallographic normal to the interface. The position of an interface can vary due to both deformation at the interface and transformation between the two phases at the interface (accretion), and so we define a special variation that accounts for both. Thus, surface stress appears explicitly in both the force and energy balances at crystal-melt and coherent crystal-crystal interfaces. In particular, an interfacial strain energy term appears in the energy balance at these interfaces; this term gives the energy of deforming the interface against the force associated with the surface stress, and is a new result from this analysis. Anisotropy also appears in this energy balance through a term that can be expressed by using Cahn and Hoffman’s ξ-vector. Finally, it is shown that a greased crystal-crystal system differs from crystal-melt and coherent crystal-crystal systems in that two independent deformations and crystallographic normals can be defined at a greased interface. However, by partitioning the excess energy associated with a greased interface between these deformations and normals, one can reduce the equilibrium conditions at a greased interface to those that obtain if the two crystals would interact only through a thin fluid layer at the interface.

A microstructural model for the elastic response of articular cartilage

A model of articular cartilage is developed in which the continuum stiffness tensor is related to the tissues microstructure. The model consists of bilinear elastic fibers embedded in an elastic matrix. Homogenization techniques are used to relate this level of organization to the macroscopic response of the tissue. The model includes the effects of spatial orientation of fibers, pre-stress in the fibers and matrix resulting from matrix swelling, slipping at the interface between the fibers and the matrix, fiber buckling in compression, and deformation-induced fiber reorientation. The model predicts increased axial stiffness with increasing stretch due to fiber reorientation, reduced axial and shear stiffness with slipping between fiber and matrix and a sensitivity of the tissue response to the swelling pressure in the matrix, the matrix modulus and the bonding of the fiber matrix interface.

Relative roles of vascular and airspace pressures in ventilator-induced lung injury.

ObjectiveTo determine whether elevations in pulmonary vascular pressure induced by mechanical ventilation are more injurious than elevations of pulmonary vascular pressure of similar magnitude occurring in the absence of mechanical ventilation. DesignProspective comparative laboratory investigation. SettingUniversity research laboratory. SubjectsMale New Zealand white rabbits. InterventionsThree groups of isolated, perfused rabbit lungs were exposed to cyclic elevation of pulmonary artery pressures arising from either intermittent positive pressure mechanical ventilation or from pulsatile perfusion of lungs held motionless by continuous positive airway pressure. Peak, mean, and nadir pulmonary artery pressures and mean airway pressure were matched between groups (35, 27.4 ± 0.74, and 20.8 ± 1.5 mm Hg, and 17.7 ± 0.22 cm H2O, respectively). Measurements and Main Results Lungs exposed to elevated pulmonary artery pressures attributable to intermittent positive pressure mechanical ventilation formed more edema (6.8 ± 1.3 vs. 1.1 ± 0.9 g/g of lung), displayed more perivascular (61 ± 26 vs. 15 ± 13 vessels) and alveolar hemorrhage (76 ± 11% vs. 26 ± 18% of alveoli), and underwent larger fractional declines in static compliance (88 ± 4.4% vs. 48 ± 25.1% decline) than lungs exposed to similar peak and mean pulmonary artery pressures in the absence of tidal positive pressure ventilation. ConclusionsIsolated phasic elevations of pulmonary artery pressure may cause less damage than those occurring during intermittent positive pressure mechanical ventilation, suggesting that cyclic changes in perivascular pressure surrounding extra-alveolar vessels may be important in the genesis of ventilator-induced lung injury.

The effect of elastic fields on the morphological stability of a precipitate grown from solid solution

Abstract A system that consists of a misfit precipitate transforming from an infinite matrix is analyzed to determine the effect of elastic fields on a morphological stability analysis. Elastic fields enter the analysis through the boundary condition that sets the solute concentration at the interphase interface. Elastic fields influence the stability results when the shear modulus of the precipitate is different from that of the matrix; they act to stabilize the interface and favor spherical growth shapes if the shear modulus of the precipitate is greater than that of the matrix, and to destabilize the interface and favor non-spherical growth shapes in the alternative case. These elastic effects are especially pronounced at small supersaturations. For the case of a hard precipitate growing in a soft matrix, elastic fields can, at small supersaturations, absolutely stabilize the interface against any given perturbation wavelength. In the absence of capillarity, elastic fields spoil the shape preserving growth of an ellipsoidal precipitate, a solution found by Ham when both capillarity and elastic fields vanish. When a precipitate is undergoing unstable growth, elastic fields shift the value of the fastest growing harmonic such that stabilizing elastic fields favor long wavelength perturbations and relatively smooth growth shapes, while destabilizing elastic fields favor short wavelength perturbations and relatively rough growth shapes.

Quasi-static extension of shape memory wires under constant load

The transformation of nickel-titanium (NiTi) shape memory wires under constant load is studied by hanging a mass from the end of the wire and measuring the subsequent elongation. The experimental relationship between the weight of the mass and the elongation rate is compared with the theoretical model of Leo, Shield and Bruno. In displacement controlled experiments this model was shown to predict accurately the rate effects due to heat transfer at austenite-martensite interfaces in the wire. In the load controlled case these rate effects are manifest as a relationship between the elongation rate and the applied load. Very good agreement between the model and the experiments is found in the load controlled case. It is also observed that the load controlled experiments damage the wire when sufficiently large loads are applied.

Fracture of shape memory CuAlNi single crystals

The fracture behavior of shape memory CuAlNi single crystals loaded in tension is studied. Specimens cut from a single crystal are notched and loaded in tension until final fracture. Eight different crystallographic orientations of the notch and tensile axes are considered. The stress field at the notch tip triggers a cubic to orthorhombic phase transition in the crystal, which results in a set of twinned martensite plates emanating from the notch tip. As loading increases, a crack forms and grows off the notch tip, with the martensite plates continuing to appear at the growing crack. Details of the crack growth depend strongly on both the type of singular microstructures that forms and how this microstructure interacts with the growing crack. In one group of orientations a distinct transformation zone forms along one flank of the crack and the motion of this zone is directly connected to the crack growth. In a second group of orientations, the microstructure formation is not as strongly tied to the crack. Interestingly, in all specimens studied, the final crack direction is approximately 80° from the direction of the martensite plates.