Jiujiang Zhu

A thermodynamic constitutive model for stress induced phase transformation in shape memory alloys

In this paper a thermodynamic constitutive model is developed for stress induced phase transformation in single crystalline and polycrystalline shape memory alloys (SMAs). Volume fractions of different martensite variants are chosen as internal variables to describe the evolution of microstructure state in the material. This model is then used in prediction the transformation behavior of a SMA (Cu-Al-Zn-Mn) under complex thermomechanical load (including complete and incomplete transformation in mechanical cycling, and proportional/non-proportional loading)

To predict the behavior of shape memory alloys under proportional load

In this paper, a simple method is proposed to predict the mechanical behavior of shape memory alloys (SMAs) in stress induced phase transformation (proportional load, constant temperature). This method is based on the transformation strain in the phase transformation and an assumption that the driving energy for the phase transformation is a constant. Given conditions that the temperature is kept constant, the applied load is proportional and the hardening behavior is similar, if the behavior of a SMA under a given applied stress state, for instance, uni-axial tension, is known (from either experiment or analysis), one may easily predict the response of other stress states. A few case studies including single crystalline and textured/non-textured polycrystalline SMAs demonstrate the capability of this method.

Description of deformation in shape memory alloys from DO3 austenite to 18R martensite by group theory

Abstract This paper provides a clear and simple group theory description of deformation in shape memory alloys (SMAs) from DO 3 austenite to 18 R martensite. The 24 elements in the point group of austenite P 24 correspond to 24 martensite habit plane variants. After one pair of vectors (the normal vector of the habit plane and the corresponding shape strain vector) are obtained, the other 47 pairs (including the inverse pairs) can be produced by operations of P 24 and inverse through centre I on the original pair. As point group P 4 is a subgroup of P 24 , operations of P 4 and I on one pair of vectors results in 8 pairs of vectors, which belong to the same basal plane. Point group P 2 is a regular subgroup of P 24 . Phase transformation eigenstrain C is invariant in the operation of group P 2 . There are 12 elements in L 12 , which is the left co-set of P 2 in P 24 , and they correspond to 12 different phase transformation eigenstrains in 18 R Martensite. The point group S 4 is also a subgroup of P 24 , and stands for the self-accommodation group in 18 R Martensite. 4 pairs of vectors in this self-accommodation group S 4 cluster along direction i 1 − i 2 / 2 . All 48 pairs of vectors can be generated by applied left co-set operations and I on these clustered pairs.

Energy Conversion in Shape Memory Alloy Heat Engine Part I: Theory

Shape Memory Alloy (SMA) can be easily deformed to a new shape by applying a small external load at low temperature, and then recovers its original configuration upon heating. This unique shape memory phenomenon has inspired many novel designs. SMA based heat engine is one among them. SMA heat engine is an environment-friendly alternative to extract mechanical energy from low-grade energies, for instance, warm wastewater, geothermal energy, solar thermal energy, etc. The aim of this paper is to present an applicable theoretical model for simulation of SMA-based heat engines. First, a micro-mechanical constitutive model is derived for SMAs. The volume fractions of austenite and martensite variants are chosen as internal variables to describe the evolution of microstructure in SMA upon phase transition. Subsequently, the energy equation is derived based on the first thermodynamic law and the previous SMA model. From Fourier’s law of heat conduction and Newton’s law of cooling, both differential and integral forms of energy conversion equation are obtained.

Energy conversion in shape memory alloy heat engine part II: simulation

In this paper, a theoretical model proposed in Part I (Zhu et al., 2001a) is used to simulate the behavior of a twin crank NiTi SMA spring based heat engine, which has been experimentally studied by Iwanaga et al. (1988). The simulation results are compared favorably with the measurements. It is found that (1) output torque and heat efficiency decrease as rotation speed increase; (2) both output torque and output power increase with the increase of hot water temperature; (3) at high rotation speed, higher water temperature improves the heat efficiency. On the contrary, at low rotation speed, lower water temperature is more efficient; (4) the effects of initial spring length may not be monotonic as reported. According to the simulation, output torque, output power and heat efficiency increase with the decrease of spring length only in the low rotation speed case. At high rotation speed, the result might be on the contrary.

Cellular modelling of electrical remodelling in two different models of human atrial myocytes

Changes in action potentials of atrial myocytes and various ionic channels induced by chronic atrial fibrillation (AF) have been described in the human. The mechanisms underlying the AF-induced action potential duration (APD) shortening have not been clearly identified. In this study we modify two different computational models of electrical activity of human atrial myocytes by incorporating chronic AF induced changes in several of the ionic channels systems found in myocytes. We examine the ionic mechanisms underlying the AF induced APD reduction and the relative roles of different remodeled ionic channels in producing the APD reduction. In both models we have found that AF induced changes in the ionic channel conductances and kinetics are able to reproduce the APD reduction seen experimentally. AF-induced down regulation of L-type Ca current is insufficient to account for the observed APD reduction, but up regulation of I/sub Kl/ has a much greater influence.

Saltation in wind blown sand

The Boltzmann equation of the sand particle velocity distribution function in wind-blown sand two-phase flow is established based on the motion equation of single particle in air. And then, the generalized balance law of particle property in single phase granular flow is extended to gas-particle two-phase flow. The velocity distribution function of panicle phase is expanded into an infinite series by means of Grad’s method and the Gauss distribution is used to replace Maxwell distribution. In the case of truncation at the third-order terms, a closed third-order moment dynamical equation system is constructed. The theory is further simplified according to the measurement results obtained by stroboscopic photography in wind tunnel tests.

Theory of phase transformation and reorientation in single crystalline shape memory alloys

A constitutive model, based on an (n + 1)-phase mixture of the Mori-Tanaka average theory, has been developed for stress-induced martensitic transformation and reorientation in single crystalline shape memory alloys. Volume fractions of different martensite lattice correspondence variants are chosen as internal variables to describe microstructural evolution. Macroscopic Gibbs free energy for the phase transformation is derived with thermodynamics principles and the ensemble average method of micro-mechanics. The critical condition and the evolution equation are proposed for both the phase transition and reorientation. This model can also simulate interior hysteresis loops during loading/unloading by switching the critical driving forces when an opposite transition takes place.

On interface crack propagation with variable velocity for longitudinal shear problems

The antiplane strain problem of straight interface crack propagation between two elastic half-spaces under arbitrary variable loading is considered. The crack edge is specified as an arbitrary smooth function of time. It is assumed that the crack speed is less than the smaller of the shear wave velocities of two media. An integral transform method and factorization technique are used to solve the problem. The solutions are worked out for semi-infinite crack and finite crack problems. The dynamic stress intensity factors at the crack tip of the moving interface crack are given and it is found that the stress intensity factor of the interface crack is slightly higher than that in the homogeneous medium with slower shear wave velocity.

Computational study of the relative contribution of channel and gap junction remodelling on human atrial conduction during fibrillation

Chronic atrial fibrillation (AF) induces remodelling of both channel conductance and intercellular coupling in the human atrium. Effects of these changes and their relative contributions to atrial impulse conduction during fibrillation are unknown. In this study we constructed a virtual human atrial strand by incorporating the Nygren et al model of human atrial action potential into a 1-dimensional reaction diffusion partial differential equation. Experimental data on AF-induced changes of human atrial ionic channel conductances and kinetics and gap junction coupling were incorporated into a model to investigate their contributions and relative importance on conduction velocity (CV) at different rates. At low rates (stimulus interval SI>270 ms), AF-induced channel or gap junction remodelling reduced CV significantly. At high rates (SI<270 ms), channel remodelling increased CV while gap junction remodelling reduced the CV. When combined, channel and gap junction remodelling reduced CV additively. Spatial heterogeneities in gap junction coupling can produce intermittent conduction block.