On the Fracture Toughness of Pseudoelastic Shape Memory Alloys

Abstract

A finite element analysis of quasi-static, steady-state crack growth in pseudoelastic shape memory alloys is carried out for plane strain, mode I loading. The crack is assumed to propagate at a critical level of the crack-tip energy release rate. Results pertaining to the influence of forward and reverse phase transformation on the near-tip mechanical fields and fracture toughness are presented for a range of thermomechanical parameters and temperature. The fracture toughness is obtained as the ratio of the far-field applied energy release rate to the crack-tip energy release rate. A substantial fracture toughening is observed, in accordance with experimental observations, associated with the energy dissipated by the transformed material in the wake of the growing crack. Reverse phase transformation, being a dissipative process itself, is found to increase the levels of toughness enhancement. However, higher nominal temperatures tend to reduce the toughening of an SMA alloy-although the material's tendency to reverse transform in the wake of the advancing crack tip increases-due to the higher stress levels required for initiation of forward transformation.

On the Effect of Latent Heat on the Fracture Toughness of Pseudoelastic Shape Memory Alloys

“…3. A discrep ancy between the calculated SMA stress field and the mode I elastic asymptotic A'-field was also observed in the isothermal case [15]. A possible reason, as explained in Ref.…”

“…2(a) and 2(b), respectively. For the specific combination of parameters (As -Ms)/(To -Ms) and (Af -As)/(7o -Afs), reverse phase transformation take pla ces in the wake of the growing crack due to nonproportional load ing experienced in those material regions [15]. The temperature increase under adiabatic conditions (Fig.…”

“…[15], intro duced by the energy balance equation. The latter parameter (MS+AS)/(T0 -Ms) is the normalized approximation of the equi librium temperature Teq = (Ms + As)/2.…”

“…[15]. In general, under nominal isothermal conditions, reverse transforma tion, which may occur due to unloading in the wake of the grow ing crack, distinguishes the fracture toughening response of pseudoelastic SMAs from that of other dissipative materials, such as conventional elastic-plastic materials and ferroelastics.…”

A Constitutive Model for Isothermal Pseudoelasticity Coupled with Plasticity

“…For steady state, the I-integral is always path-independent and for ferroelastic and ferroelectric materials can be used to determine the ratio of the crack tip energy release rate to the far-field applied energy release rate. This procedure has been used by Landis [18] for ferroelastic materials, Wang and Landis [38,39] for ferroelectric materials, and Baxevanis et al [40,41] for pseudoelastic materials. For the material properties listed in Table 1 with plastic deformation turned off, the computed ratio of the far-field steady-state energy release rate to the crack tip energy release is,…”