Bogdan Raniecki

Thermodynamics of isotropic pseudoelasticity in shape memory alloys

The thermodynamic theory of the pseudoelastic behaviour of SMA is generalized to include new observed effects in isotropic solids. It has been shown that macroscopic eigenstrain due to martensitic phase transitions (p.t.) is a homogeneous function of the stress of order zero, provided that partial thermodynamic equilibrium occurs. The specific form of the Gibbs potential is presented and new conditions for the initiation of p.t. are derived. They are expressed in terms of the temperature, second and third invariants of the stress deviator. The thermostatic properties and phenomenological constants are found for a NiTi alloy using experimental data reported in the literature. The theoretical and experimental results are compared for simple tension compression and pure shear.

Pseudoelastic behaviour of shape memory alloy beams under pure bending: experiments and modelling

Abstract The moment–curvature hysteresis loops (for single cycle) under pure bending were experimentally determined for Cu–Al–Be single crystal, Ni–Ti and Cu–Zn–Al polycrystal samples using specially designed device. The comparison with the theoretical loops is presented for linear strain-hardening and ideal pseudoelasticity models discussed in (Int. J. Mech. Sci. 2001;43:1339). All theoretical constants were determined using simple-tension data and thermodynamical identities. The tensile–compression dissymmetry effect is accounted for and non-linear differential equation describing the motion of neutral plane is derived for beams with arbitrary symmetric cross-section. The evidence of dissymmetry effect in Cu–Al–Zn is provided by application of metallographical and mechanical techniques. But the experiments and modelling have shown that the tension/compression asymmetry has in fact little influence on the moment–curvature responses on SMA beams.

On the uniqueness problem in coupled thermoplasticity

Abstract Rate equations of coupled thermoplasticity are derived assuming that the total strain rate is composed of elastic and plastic terms and accounting for coupling effects such as heat of dissipation, piezocaloric effect, in both mechanical and temperature equations. Local and global uniqueness conditions are presented and its engineering significance is discussed.

On the thermodynamic driving force for coherent phase transformations

Abstract Using the basic principles of continuum thermodynamics the notion of the thermodynamical driving force for coherent phase transformations is introduced. The new representations of thermodynamical driving force are derived. It is shown that thermodynamical driving force reaches an extremum at any dynamically admissible phase amplitude, provided that two phase solids exhibit instantaneous elasticity. The possible interpretation of macroscopic thermodynamical driving force for martensitic transformation is presented.

Anatomization of hysteresis loops in pure bending of ideal pseudoelastic SMA beams

Abstract The results of qualitative analysis of the variation of stress and the phase content distribution in arbitrary symmetric cross-section of the beam are discussed for single bending cycle. The explicit analytical equations for the moment–curvature hysteresis loop are derived. The interrelation between formation of characteristic points on this diagram and movement of the beam planes separating the regions occupied by single phase (austenite or martensite) and their mixture (austenite and martensite) in the course of phase transitions is discussed. It is shown that at such mobile surfaces the gradient of macroscopic stress suffers jump discontinuity. The dimensionless bending diagrams (nomograms) for rectangular beams are constructed. They enable rough quantitative estimation of some basic design parameters without recourse to the computer-aided numerical calculations. One-dimensional Muller–Xu thermodynamic theory of ideal pseudoelasticity is used as the theoretical foundation for the analysis. The theory is briefly discussed and its generalization that accounts for the tension–compression asymmetry effect is presented.

A derivation of the uniqueness conditions in coupled thermoplasticity

Abstract This article presents the proof of local and global uniqueness conditions in rate independent coupled thermoplasticity. The mathematical structure of rate equations which account for all coupling effects was discussed in [1] where uniqueness conditions were stated without proof and discussed for some particular cases.

Variational principles in uncoupled thermoplasticity

Abstract Stress-rate and strain-rate variational principles are derived for a viscoplastic material characterized by additive elastic and inelastic strain rates. Elastic, viscous and plastic properties are assumed to be temperature dependent but all coupling effects are neglected.

The Equilibrium Motion of the Martensitic Interface in Thick-Walled Infinite Austenitic Plate

i) Consider the microregion R(t) subdivided (in actual configuration) by strong discontinuity interface S(t) into parent-phase portion R 1(t) (high-temperature phase-austenite (A)) and product phase portion (low temperature phase-martensite (M)) R 2 ·A → M phase transition (p.t.) is regarded as the coherent one, i.e., displacement and temperature T are continuous, whereas deformation gradient F, velocity v, and Cauchy’s stress σ experience jump discontinuities at S(t). The jump in some physical quantity ψ at the interface is denoted by [ψ]= ψ1 — ψ2, where indexes 1 and 2 indicate a property of parent phase and product phase, respectively. When, at generic instant t, the reference configuration is so chosen that the parent phase particles are identified by their position in the current configuration at that time (region R 1) then the geometric and kinematical compatibilities relations become {fy(1)|46-1} and, for a quasistatic situation, the equation of balance of internal energy u, mechanical equilibrium equation, and Clausius-Duhem inequality at the interface S can be written in the following form [1] {fy(2)|46-2} {fy(3)|46-3}

On The Mechanics of Solidification

This note is devoted to the discussion of possible boundary conditions that should be satisfied by a solution of the first-order rate boundary-value problem on the moving solid-liquid interface. They account for the jump of the mass density at the interface - the factor that affects the transient and residual stresses that may develop in castings and ingots at early stage of the solidification process. The phase stresses in an e l a s t i c solidifying sphere are also discussed.