Strain and interface energy of ellipsoidal inclusions subjected to volumetric eigenstrains: shape factors

Thermodynamic modeling of the development of non-spherical inclusions as precipitates in alloys is an important topic in computational materials science. The precipitates may have markedly different properties compared to the matrix. Both the elastic contrast and the misfit eigenstrain may yield a remarkable generation of elastic strain energy which immediately influences the kinetics of the developing precipitates. The relevant thermodynamic framework has been mostly based on spherical precipitates. However, the shapes of actual particles are often not spherical. The energetics of such precipitates can be met by adapting the spherical energy terms with shape factors. The well-established Eshelby framework is used to evaluate the elastic strain energy of inclusions with ellipsoidal shapes (described by the axes a, b, and c) that are subjected to a volumetric transformation strain. The outcome of the study is two shape factors, one for the elastic strain energy and the other for the interface energy. Both quantities are provided in the form of easy-to-use diagrams. Furthermore, threshold elastic contrasts yielding strain energy shape factors with the value 1.0 for any ellipsoidal shape are studied.

Evolution of Transformation Strain During Partial Transformation Cycling of an NiTi Shape Memory Alloy

This paper deals with how the magnitude of transformation strain changes on partial transformation cycling of an NiTi shape memory alloy. A near-equiatomic NiTi shape memory alloy was allowed to undergo partial thermal cycling keeping the stress constant at 100 MPa for various upper cycle temperatures (between austenite start and austenite finish), using a custom-built thermomechanical cycling test setup. The displacement and the temperature of the sample during cycling were measured using a LASER extensometer and an optical pyrometer, respectively. The test results show that the recovery strain and thermal hysteresis width decrease with increasing number of cycles during partial cycling. In addition, martensite start and martensite finish temperatures increase during the initial cycles, whereas austenite start and austenite finish temperatures decrease during the initial cycles, followed by their saturation.

Morphology and Crystallography Analyses of HSLA Steels with Hardenability Enhanced by Tailored C–Ni Collocation

High hardenability is of great importance to ultra-heavy steel plates and can be achieved by tailoring the composition of steel. In this study, the continuous cooling transformation (CCT) curves of two high-strength low-alloy (HSLA) steels (0.16C-0.92Ni steel and 0.12C-1.86Ni steel) were elucidated to reveal the significance of C–Ni collocation on hardenability from the perspective of morphology and crystallography. At a low cooling rate (0.5 °C/s), the 0.12C-1.86Ni steel showed higher microhardness than 0.16C-0.92Ni steel. The microstructure in 0.16C-0.92Ni steel was mainly granular bainite with block-shaped martensite/austenite islands (M/A islands), while that in 0.12C-1.86Ni steel was typically lath bainite with film-shaped M/A islands, denoting that the 0.12C-1.86Ni steel is of higher hardenability. Moreover, the 0.12C-1.86Ni steel exhibited a higher density of block boundaries, especially V1/V2 boundaries. The higher density of block boundaries resulted from the weakened variant selection due to the larger transformation driving force and more self-accommodation of transformation strain induced by the reduced carbon and increased nickel content.

A Computational Scheme for Evaluating the Stress Field of Thermally and Pressure Induced Unconventional Reservoir

The fluid flow connecting the hydraulic fracture and associated unconventional gas or oil reservoir is of great importance to explore such unconventional resource. The deformation of unconventional reservoir caused by heat transport and pore pressure fluctuation may change the stress field of surrounding layer. In this paper, the stress distribution around a penny-shaped reservoir, whose shape is more versatile to cover a wide variety of special case, is investigated via the numerical equivalent inclusion method. Fluid production or hydraulic injection in a subsurface resource caused by the change of pore pressure and temperature within the reservoir may be simulated with the help of the Eshelby inclusion model. By employing the approach of classical eigenstrain, a computational scheme for solving the disturbance produced by the thermally and pressure induced unconventional reservoir is coded to study the effect of Biot coefficient and some other important factors. Moreover, thermo-poro transformation strain and arbitrarily orientated reservoir existing within the surrounding layer are also considered.

A Crystal Plasticity Simulation on Strain-Induced Martensitic Transformation in Crystalline TRIP Steel by Coupling with Cellular Automata

In transformation-induced plasticity (TRIP) steel, the strain-induced martensitic transformation (SIMT) has a close relationship with the shear band formation. At a small length scale such as that of a crystal, the explicit analysis of the shear band structure with the formed microstructure is quite important for an adequate understanding of the SIMT. Here, a study on the microstructures formed by SIMT, related to shear band formation in both single and polycrystal TRIP steels, is presented. The constitutive equation for single crystal TRIP steel considering the transformation strain on each variant system is derived based on a rate-dependent crystal plasticity theory. To express the martensitic transformation, the cellular automata approach, including a transformation criterion acting as a local rule, is introduced. Numerical simulation is conducted with patterning processes of the martensitic phase at an infinite medium under the plane strain tension. It is found that the similar distributions of the plastic strain and the martensitic phase are dependent on the initial crystal orientation and appear as the shear band structures. In addition, the sizes of embryo and cell strongly influence the shear band formation and the martensitic volume fraction of crystal TRIP steel.

On the Decrease in Transformation Stress in a Bicrystal Cu-Al-Mn Shape-Memory Alloy during Cyclic Compressive Deformation

The evolution of the inhomogeneous distribution of the transformation stress (σs) and strain fields with an increasing number of cycles in two differently orientated grains is investigated for the first time using a combined technique of digital image correlation and data-driven identification. The theoretical transformation strains (εT) of these two grains with crystal orientations [5 3 26]β and [6 5 11]β along the loading direction are 10.1% and 7.1%, respectively. The grain with lower εT has a higher σs initially and a faster decrease in σs compared with the grain with higher εT. The results show that the grains with higher σs might trigger more dislocations during the martensite transformation, and thus result in greater residual strain and a larger decrease in σs during subsequent cycles. Grain boundary kinking in bicrystal induces an additional decrease in transformation stress. We conclude that a grain with crystal orientation that has high transformation strain and low transformation stress (with respect to loading direction) will exhibit stable transformation stress, and thus lead to higher functional performance in Cu-based shape memory alloys.

Recent Developments in Small-Scale Shape Memory Oxides

This review presents an overview of the developments in small-scale shape memory materials: from alloys to oxides and ceramics. Shape memory oxides such as zirconia, different ferroelectric perovskites and VO2-based materials have favorable characteristics of high strength, high operating temperature and chemical resistance, which make this class of shape memory materials interesting for special applications, e.g., in harsh environments or at the nanoscale. Because of the constraint and mismatch stress from neighboring grains in polycrystalline/bulk oxides, the transformation strain of shape memory oxides is relatively small, and micro-cracks can appear after some cycles. However, recent progress in shape memory oxide research related to small-scale approaches such as decreasing the amounts of grain boundaries, strain-engineering, and application in the form of nanoscale thin films shows that some oxides are capable to exhibit excellent shape memory effects and superelasticity at nano/micro-scales. The materials systems ZrO2, BiFO3, and VO2 are discussed with respect to their shape memory performance in bulk and small-scale.