Stress-induced Phase Transformation Research Articles

A unique three-stage dependence of yielding behavior and strain-hardening ability in Ti-10V-2Fe-3Al alloy on phase fraction

Ti-10V-2Fe-3Al alloy represents one of the most widely adopted metastable β titanium alloys, the mechanical properties of which were influenced by several factors, including the grain size, phase fraction, precipitates, etc. In this study, we systematically investigated the effect of phase fraction on the tensile properties of equiaxed α+β dual-phase microstructures in Ti-10V-2Fe-3Al alloy. It is revealed that there existed a unique three-stage dependence of yielding behavior and strain-hardening ability on the phase fraction in this alloy. The change in β phase fraction (fβ) and corresponding phase composition not only determined the mechanical stability of β phase via equilibrium Mo content, but also altered the relative nano-hardness between the two phases by solid solution hardening. Specifically speaking, when fβ was larger than 80%, the β phase generally exhibited stress-induced martensitic phase transformation (SIMT) during loading. However, the β phase stability was continuously enhanced with decreasing fβ, leading to a progressive transition from double-yielding to single-yielding behavior. At 60% ≤ fβ < 80%, despite of the basically suppressed SIMT, there was a clear strain partitioning between the two phases due to a relatively large nano-hardness difference. This helped to maintain a reasonable strain-hardening ability by promoting geometrically necessary dislocations (GNDs) near the interphase boundaries. With further decrease of the β phase fraction (fβ < 60%), the nano-hardness of the two phases became much closer and as a result, the strain-hardening abilities were substantially deteriorated due to a lack of strain partitioning. Also, both the yield and ultimate tensile strength became much less dependent on the β phase fraction for microstructures in this region.

Immunity of Al0.25CoCrFeNi high-entropy alloy to hydrogen embrittlement

The influence of hydrogen via electrochemical charging on the mechanical behavior of the cryo-rolled and annealed Al0·25CoCrFeNi high entropy alloy (HEA) through tensile experiments was investigated. The results indicated that the Al0·25CoCrFeNi alloy mainly composed of FCC phase has immunity to electrochemical hydrogen embrittlement. Analysis on the fracture surfaces revealed that hydrogen permeates into a shallow depth and transforms the deformation mechanism. The deformation twins and stress-induced phase transformation (FCC-to-HCP) are introduced in the surface near fracture of tensile sample when the Al0·25CoCrFeNi alloy is not charged by hydrogen. After hydrogen charging, the dissolved hydrogen decreases the stacking fault energy and promotes the planar dislocation slip, resulting in the enhancement of strength and ductility in Al0·25CoCrFeNi HEA.

Phase transformation in Fe–Mn–Si SMA/WC composite coating developed by laser cladding

A Fe–Mn–Si shape memory alloy/nano-WC (SMA/WC) coating was prepared by laser cladding on the surface 304 stainless steel. The phase composition, stress-induced phase transformation mechanism, microstructure, microhardness and wear resistance were analyzed by X-ray diffraction (XRD), scanning electron microscopy (SEM), transmission electron microscopy (TEM), microhardness tester and friction tester, respectively. Results show that γ austenite, ε martensite and Fe6W6C phase appear in the composite coating, and the coating is composed of planar crystals, cell crystals, fine dendritic crystals and fine equiaxed grains from binding zone to surface region. The residual stress leads to the entanglement and accumulation of dislocations in the austenite grain boundaries, which in turn induce martensite deformation. The martensite phase of the annealed composite coating disappeared, and the microstructure showed austenite morphology. The SMA/WC coating has higher microhardness and excellent wear resistance due to the occurrence of γ austenite → ε martensite transformation. Furthermore, the addition of WC increases the microhardness of the coating by more than 2 times, and reduces the friction coefficient and the wear loss by about 1/4 and 2/3 respectively.

Crystal plasticity finite element simulation of NiTi shape memory alloy under canning compression based on constitutive model containing dislocation density

Crystal plasticity finite element (CPFE) simulation is employed for revealing plastic deformation mechanism of NiTi shape memory alloy (SMA) under canning compression at 400 °C, where only B2 austenite phase exists and it presents plastic deformation by dislocation slip without stress-induced martensite phase transformation and deformation twinning. Statistically stored dislocation (SSD) and geometrically necessary dislocation (GND) densities are incorporated into crystal plasticity constitutive model for strain gradient. Texture evolution, stress and strain fields, SSD and GND densities are obtained on the basis of CPFE simulation. With progression of plastic deformation, γ-fiber (<111>) texture is gradually strengthened, which is further validated by the experimental data. Heterogeneous plastic deformation of NiTi polycrystalline cylinder model subjected to canning compression is illustrated by distribution of stress and strain based on all the slip systems, where stress concentration mainly emerges near the grain boundaries and large strain appears in the core location of NiTi polycrystalline cylinder. SSD density and GND density exhibit a heterogeneous distribution in the similar manner. Both SSDs and GNDs aggregate near the grain boundaries. SSD density increases with increasing plastic strain, whereas GND density decreases with increasing plastic strain. In addition, the total dislocation density increases with the increase of plastic strain. The developed CPFE model is an effective tool for simulating plastic deformation of NiTi SMA in the appropriate temperature range where dislocation slip is responsible for plastic deformation and work hardening is dominant during plastic deformation.

Effect of deep rolling on subsurface conditions of CoCr28Mo6 wrought alloy to improve the wear resistance of endoprostheses

Wear of orthopaedic endoprostheses is associated with adverse local and systemic reactions and can lead to early implant failure. Manufacturing determines the initial subsurface microstructure of an alloy that influences the implant's wear behaviour. Therefore, this study aims at generating enhanced wear resistances by a modification of the surface and subsurface microstructure of a CoCr28Mo6 wrought alloy by applying deep rolling.The state of the art was investigated by means of eleven retrieved CoCr28Mo6 hip implant components from different manufacturers with respect to their subsurface microstructure and micro hardness profiles. CoCr28Mo6 wrought alloy samples (DIN EN ISO 5832–12) were aged at 750 °C for 24 h and/or plastically deformed by deep rolling with varying axial forces (170 N, 230 N and 250 N). The samples were metallographically prepared and investigated using optical and scanning electron microscopy with EDS and EBSD, micro hardness testing, XRD and tribological testing.The retrieved implant components revealed that, independent of the manufacturer, neither the head nor the stem trunnion exhibited a defined subsurface condition. The dominant phase within the implants was face-centered cubic (fcc). Some implants exhibited single hexagonal close-packed (hcp) grains due to a stress-induced phase transformation. The initial CoCr28Mo6 wrought alloy had a fcc crystal structure. After isothermal aging, the matrix entirely transformed to a hcp structure. In the initial fcc-condition, deep rolling generated a plastically deformed surface layer within the first 100 μm and stress-induced phase transformation to hcp was observed. Micro hardness gradients were present in the subsurface of up to 600 μm depth and exhibited a maximum increase of 34% by deep rolling in comparison to the initial fcc-matrix. This trend was confirmed by a correlated increase in residual compressive stresses. In tribological tests under serum lubrication, the modified samples generated lower wear in comparison to the contemporarily used fcc-matrix samples. This study demonstrates that deep rolling is an effective processing to modify the subsurface of a biomedical CoCr28Mo6 wrought alloy in order to increase the wear resistance. The intentional transformation from the fcc to the hcp phase induced by deformation offers great potential for implant application.

Orientation-dependent plastic deformation mechanisms and competition with stress-induced phase transformation in microscale NiTi

Understanding the orientation-dependent deformation behavior of NiTi shape-memory alloys at small length scales is of importance for designing nano- and micro-electromechanical systems. However, a complete understanding of the orientation- and size-dependent competition between the various modes of slip, deformation twinning, and martensitic transformation in NiTi shape-memory alloys is still lacking, especially in micron-scale specimens. In the present study, we perform micro-compression tests on [001]- and [112]-oriented micro-pillars of a solutionized Ti-49.9at.% Ni alloy. Post-mortem TEM analysis of the deformed pillars reveal that the operating plastic deformation modes are {011}<100> slip and {114}<221¯> deformation twinning, which compete with the martensitic transformation, depending on the crystal orientation. Furthermore, in both experiments and molecular dynamics simulations, we consistently find residual B19′ martensite in a herringbone microstructure composed of finely spaced (001)B19′ compound twins instead of the generally assumed [011]B19′ type II twins common in bulk samples, suggesting that the operative martensitic transformation mode may be size-dependent. Schmid factors in compression are calculated for all commonly reported slip, deformation twinning, and martensitic transformation modes as a function of crystallographic orientation, which rationalize the orientation-dependent competition between these deformation modes.

Toughening cemented carbides by phase transformation of zirconia

Yttria partially stabilized zirconia was introduced into WC-Co cemented carbides to enhance their mechanical performance. The hardness and fracture toughness were improved simultaneously with the addition of ZrO2. Particularly, the fracture toughness of the cemented carbides was significantly enhanced. The mechanism was mainly attributed to the stress-induced phase transformation of tetragonal ZrO2 to monoclinic ZrO2. This phase transformation introduced a compressive stress field and deflected the micro-cracks. In addition, the ZrO2 particles dispersed homogeneously in the WC skeleton and had good interfacial bonding with both WC and Co phases, which was beneficial to the mechanical properties of the cemented carbides. This study provides a new promising approach to break the trade-off between the hardness and fracture toughness of cemented carbides to achieve excellent comprehensive mechanical properties. The new strategy will be also promising to be applied in a variety of cermets or ceramic-based composites.

Modeling of Superelastic–plastic Behavior of Porous Shape Memory Alloys Incorporating Void Shape Effects

A new constitutive model for describing the superelastic–plastic behavior of porous shape memory alloys (SMAs) is proposed. The model incorporates the influences of void shape and hydrostatic pressure as well as the elastic modulus mismatch between austenite and martensite. In addition, the interactions between plastic strain and transformation strain are considered via the plastic back stress. The porous SMAs are considered as two-phase composites with the dense SMA matrix and the second phase representing ellipsoidal voids. Based on Gurson’s formulation, the transformation and plastic flow potentials accounting for the transformation–plasticity coupling are developed. The numerical results present good agreement with available experimental data for various levels of porosity, which proves that the model is capable of capturing stress-induced phase transformation and plastic deformation of porous SMAs. Using the proposed model, the influence of plastic strain on reverse transformation and the effects of porosity and void shape on the pseudoelastic and plastic behavior of porous SMAs are investigated.

The Plastic Deformation Mechanisms of hcp Single Crystals with Different Orientations: Molecular Dynamics Simulations

The deformation mechanisms of Mg, Zr, and Ti single crystals with different orientations are systematically studied by using molecular dynamics simulations. The affecting factors for the plasticity of hexagonal close-packed (hcp) metals are investigated. The results show that the basal <a> dislocation, prismatic <a> dislocation, and pyramidal <c + a> dislocation are activated in Mg, Zr, and Ti single crystals. The prior slip system is determined by the combined effect of the Schmid factor and the critical resolved shear stresses (CRSS). Twinning plays a crucial role during plastic deformation since basal and prismatic slips are limited. The twinning is popularly observed in Mg, Zr, and Ti due to its low CRSS. The twin appears in Mg and Ti, but not in Zr because of the high CRSS. The stress-induced hcp-fcc phase transformation occurs in Ti, which is achieved by successive glide of Shockley partial dislocations on basal planes. More types of plastic deformation mechanisms (including the cross-slip, double twins, and hcp-fcc phase transformation) are activated in Ti than in Mg and Zr. Multiple deformation mechanisms coordinate with each other, resulting in the higher strength and good ductility of Ti. The simulation results agree well with the related experimental observation.

Comparison of optical and crystal properties of three translucent yttria-stabilized tetragonal zirconia polycrystals with those of lithium disilicate glass-ceramic material

Background/purposeAmong the ceramic materials used for all-ceramic crowns, zirconia has high biocompatibility and favorable mechanical properties, but its main drawbacks include low translucency and stress-induced phase transformation. To stabilize high-strength tetragonal zirconia polycrystal (TZP), 3–5 mol% yttria is usually added to prepare yttria-stabilized TZP (Y-TZP). In this study, the optical properties of three commercial Y-TZP ceramics were compared with those of the clinically available glass-ceramic material of lithium disilicate, and the relationship between translucency and crystal properties was analyzed in vitro. Materials and methodsTwelve 5-mm-thick standardized disks were prepared from three Y-TZP ceramics and one lithium disilicate block. Absolute translucency was measured using a spectrophotometer with an integrating sphere. X-ray diffraction was used to quantify the main structural parameters (i.e., preferred plane, quantitative phase, and grain size) of Y-TZP crystals. ResultsThe product-dominated phase of Y-TZP exhibited a tetragonal lattice pattern, and the preferred planes had minor variations. The diffraction patterns of the three Y-TZP ceramics demonstrated minor effects on translucency, without significant differences (p > 0.05). The grain size of 54–70 nm was negatively related to translucency in Y-TZP. Lithium disilicate specimens had significantly higher translucency than the three Y-TZP specimens (p < 0.001). ConclusionGrain size reduction played an essential role in developing highly translucent Y-TZP ceramics. The three Y-TZP ceramics were essentially opaque but exhibited poorer translucency than lithium disilicate in terms of esthetics.

Tentative Confinement of Ionic Liquids in Nylon 6 Fibers: A Bridge between Structural Developments and High-Performance Properties

A reversible confinement of ionic liquid (IL) among the amide segments has been carried out for the preparation of high-modulus and high-strength aliphatic semicrystalline nylon 6 fibers. In this research work, the suppression or the weakening of the hydrogen bonds during the conventional low-speed melt spinning process is followed by a hot-drawing stage and a subsequent IL extraction of the IL out of the 2% wt IL-confined fibers and an immediate thermal stabilization process for the improvement of the properties of the pristine nylon 6 fibers. The resulted crystal structural developments of the IL-confined fibers are attributed to ultimate molecular orientations, which have contributed to the developments of the overall fiber properties. Here, the influences of the IL on the γ and the α crystal phases, the γ-α transition, the morphological properties, and the tensile properties are investigated. The FTIR reported, experimentally, additional peaks at 1237 cm–1 for the γ crystal phase and at 1417 and 1476 cm–1 for the α crystal phase, in conformity with the theoretical computations. The XRD demonstrated that the conventional low-speed melt spinning can successfully be used to prepare as-spun IL-confined fibers having highly improved properties. The so prepared as-spun IL-confined fibers are found to have a γ phase structure that has a small crystal size and high crystal perfections. Fortunately, the γ-to-α crystal phase transition for the IL-confined nylon 6 fibers can be acquired during the hot-drawing stage (stress-induced phase transformation). Furthermore, the IL extraction process followed by a thermal stabilization process, interestingly, has led to significant increases in both of the tensile strengths and the tensile moduli of the reverted nylon 6 fibers. The values that are found are 8.46 cN/dtex for the tensile strength and 39.09 cN/dtex for the tensile modulus. The structure–property relationships between the IL-confined and the reverted nylon 6 fibers have also been discussed.

On equilibrium two-phase microstructures at plane strain

Stress-induced phase transformations in linear elastic solids are considered for the case of plane strain on the basis of a previously developed procedure that includes finding the optimal composite microstructures which provide the exact lower bound of the energy and the equilibrium new phase volume fraction that satisfies the thermodynamic equilibrium condition. Stress–strain diagrams are constructed for various deformation paths on which phase transformations are controlled by average strains or by different components of average strain and average stresses. Strain hardening and strain softening effects are demonstrated on the path of the transformation. In the case of mixed strain-stress control, regimes for which the minimizing volume fraction does not correspond to any optimal microstructure, or optimal microstructures which could not satisfy the thermodynamic equilibrium condition with respect to the new phase volume fraction, are presented. It is shown that this leads to the incompleteness of a gradual phase transformation, jump-like transformation behavior, and jump in stress. An indifferent equilibrium regime is also discussed.

Mechanical (compressive) form of driving force triggers the phase transformation from β to ω & α’’ phases in metastable β phase-field Ti-5553 alloy

Most of the structural alloys’ applications are under static, dynamic, and cyclic forms of loading. Ti-5553 alloy in the beta phase field is being investigated to confirm the mechanism of deformation and phase transformation upon quasi-static and dynamic compression. The Ti-5553 alloy was heat-treated at 900 °C (almost 50 °C above beta transus temperature) for one hour of soaking time followed by air quenching to achieve a fully β phase field. After that, Dynamic compression (DC) by Split Hopkinson Pressure Bar (SHPB) and Quasi-static compression (QSC) were performed at a strain rate of ̴103/s and 10−3/s, respectively. Recovered specimens were thoroughly examined by using different tools, such as an Optical microscope (OM), Scanning electron microscope (SEM), High-resolution transmission electron microscope (HRTEM), and Electron backscatter diffraction (EBSD) to get the reliable data for justification of logical conclusions. It is found that the dominating mode of deformation was dislocation slip along with twinning ({332} <113>) to some extent in both of QSC and DC, but sliding & spalling of the grain boundary is observed more in the former. Stress-induced phase transformation, i.e., β to α’’ and β to ω, took place in the grains saturated with dislocation slips, where the former transformation occurred simultaneously with {332} <113> twinning, while β to ω transformation was completed when a set of two adjacent (110)ᵦ planes covered ±1/6th of the total separation distance between two (next to each other) (111)ᵦ planes, by equal but opposite shear in (111)ᵦ direction, and it caused 3% shrinkage of two closed packed (110)ᵦ planes after transformation.

Overcoming the strength-ductility trade-off of an aluminum matrix composite by novel core-shell structured reinforcing particulates

The trade-off between strength and ductility of particulate reinforced metal matrix composites (PRMMCs) has been a longstanding puzzle. Here we propose an effective strategy to surmount the inverse relationship between strength and ductility of an A356 Al alloy based PRMMC by in situ synthesizing novel reinforcing particulates with a special core-shell (CS) structure. Such structure features a Ti core inside a dual-layer shell: the inner layer has a nano-grained (~130 nm) heterogeneous structure, and the outer layer possesses a composite structure composed of a (Al,Si)3Ti substrate with dense dispersion of nanoparticles. As a result, the obtained composite reinforced with such CS reinforcing particulates (CS composite) achieves an unprecedented tensile elongation to failure of 8.3 ± 0.8% and a uniform elongation of 7.1 ± 0.6%, which nearly triples that of the same alloy based composite reinforced with monolithic (Al,Si)3Ti particulates (monolithic composite) and equivalent to corresponding matrix alloy while maintaining high ultimate tensile strength of 373 ± 8.8 MPa and yield strength of 268 ± 7.9 MPa, equivalent to monolithic composite simultaneously. This special architecture of shell renders itself a high capability of stress bearing and good toughness, and the nanoparticles in outer layer further slower crack development, which significantly postpone crack formation in shell. Subsequent propagation of cracks in Ti core is also constrained remarkably by the transformation-induced plasticity effect occurred ahead of crack tips resulting from stress-induced phase transformation of hcp-Ti into fcc-Ti. These factors lead to highest work hardening rate that undergoes a long plateau and thus overcome the strength-ductility trade-off of A356 alloy based PRMMC.

Role of trivalent Bi/Tm partial substitution on active operable slip systems in Bi-2212 crystal structure

This study delves into three main subjects: (I) A strong definition on the variation of fundamental key mechanical design performance and general mechanical characteristic features founded on the formation of active operable slip systems and elimination of structural problems in the Tm substituted Bi-site Bi2.1-xTmxSr2.0Ca1.1Cu2.0Oy (0.00 ≤ x ≤ 0.30) ceramic materials; (II) Preference of propagation of cracks and dislocation movements (III) An examination of differentiation in the load-independent microhardness parameters in the saturation limit regions with the Bi/Tm partial replacement. It is found that all the mechanical performance (mechanical strength, stiffness, durability and resistant towards to the failure by fatigue) properties considerably improve with the increment in the Bi/Tm substitution level up to x = 0.07 due to the augmentation in the new active operable slip systems and crystallinity quality of Bi2.1Sr2.0Ca1.1Cu2.0Oy (Bi-2212) system. Accordingly, in case of the optimum Bi/Tm substitution the propagation of dislocation and crack movements is more and more easily controlled in the Bi-2212 ceramic system. However, the excess Tm concentrations in the ceramic system make the stress-induced phase transformation remarkably activate as a consequence of the degradation in the crack orientation and geometry. Hence, any deformation at even lower applied test loads is much more permanent and non-recoverable due to the enhancement of unconstrained dislocation motions and especially entanglement of cracks and dislocations. This fact is also confirmed from the reduction of typical indentation size effect (ISE) behavior in the event of excess Tm concentration. To conclude, the optimum Bi/Tm partial replacement in the Bi-2212 crystal structure is successful to improve the economic lives of Bi-2212 inorganic ceramics in the new, novel, innovative, feasible and potential design areas for the universe economy.

Phase Stability and Deformation Behavior of TiZrHfNbO High-Entropy Alloys

Strengthened by Oxygen doping, the single-phase body-center-cubic (BCC) TiZrHfNbO refractory high-entropy alloys (HEAs) become strong and ductile. However, phase stability at intermediate temperature and the effects of Oxygen addition on the deformation behavior during tensile tests need to be well understood. In the present work, the phase decomposition of (TiZrHfNb)100-xOx HEAs with Oxygen doping in the range of x=0, 0.5, 1, 1.5, 2 was examined at 873 K. The formation of hexagonal-close-packed (HCP) solid-solution precipitates in submicron size, enriched with Hf, Zr and O elements, were investigated by a combination of X-ray diffraction, transmission electron microscopy and atom probe tomography. Tensile tests of alloys annealed at both 1273 K and 873 K were conducted. It was found that doping Oxygen increased the yield strength and maintained ductility for alloys annealed at 1273 K, while formation of HCP precipitates after annealed at 873 K deteriorates the plasticity significantly. To unveil the deformation behaviors, in situ synchrotron X-ray diffraction experiments were applied in the current research. The single-crystal elastic constants and shear elastic anisotropy of HEAs with and without Oxygen doping were calculated and found similar to those of “Gum Metal” Ti alloy. Yet current HEAs possess higher BCC phase stability than “Gum Metal”, and no stress-induced phase transformation was detected during deformation.

Stress-induced phase stabilization and transformation in equiatomic CuZr B19’ martensite: A DFT study

The stress-induced martensitic transformation of CuZr-based alloy takes an indispensable part in its shape memory effect and plasticity improving. CuZr–B19’ phase as an unstable martensite product of CuZr–B2 austenite has been widely reported by experimental and DFT methods. However, the instability of B19’ structure ignored in theoretical calculation drives it transform into B33 phase after structural relaxation, which makes computational properties of B19’ phase untrusted. Therefore, in this work, we prevented B19’ phase from relaxation phase transition by applying external force to supply a reliable structure for its subsequent properties calculations. In addition, a reversible phase transition between phases B19’ and B33 was found and the theoretical value of transformation stress was determined. The changes of elastic modulus, formation enthalpy and electronic property of two phases (B33 and B19’) under various pressures were compared and analyzed. The results aforementioned justify that CuZr–B33 is an indirect martensite product of CuZr–B2 phase, which explains why some peoples observed B33 phase in experiments, while others did not.

Ferroelastic and plastic behaviors in pseudo-single crystal micropillars of nontransformable tetragonal zirconia

The orientation-dependent micromechanical properties of nontransformable tetragonal (t’) zirconia, which underwent a diffusionless transformation from the fluorite cubic phase and does not exhibit a stress-induced phase transformation, were characterized via pseudo-single crystal micropillar compression and electron microscopy. The t’ zirconia sample was obtained via atmospheric plasma spraying of 4.5 mol% yttria-stabilized zirconia (YSZ) powders into liquid nitrogen and consolidated into a bulk state via hot pressing at 1100°C. Dense and cylindrical micropillars were fabricated using a focused ion beam from pseudo-single crystalline regions, which exhibited a nanodomain microstructure of three t’ variants partitioned by {1 0 1}c twin boundaries with 90° symmetry. These micropillars were compressed using a flat-end diamond indenter. Near-<0 0 1>c compressions were attributed to ferroelastic domain switching and subsequent {1 0 1}c and/or {1 1 1}c hard slips. In ferroelastic deformation, a certain t’ variant diminished, and a binary domain microstructure developed with c axes perpendicular to the compressive direction. Near-<1 1 1>c compressions were governed by {0 0 1}c soft slips accompanied by strain hardening with negligible ferroelasticity, which resulted in buckling deformation with rotational kinking. In both the hard- and soft-slip orientations, ferroelastic toughening was observed with certain t’ variants awaken around the crack tips. Contrarily, cleavage fractures subsequent to yielding were observed in near-<1 0 1>c compressions. In the cubic counterpart with a domain-free microstructure (8.0 mol% YSZ), ferroelastic toughening was not observed. Hence, it is viewed as the origin of enhanced toughness in t’ zirconia.

Phase field modelling of fracture and fatigue in Shape Memory Alloys

We present a new phase field framework for modelling fracture and fatigue in Shape Memory Alloys (SMAs). The constitutive model captures the superelastic behaviour of SMAs and damage is driven by the elastic and transformation strain energy densities. We consider both the assumption of a constant fracture energy and the case of a fracture energy dependent on the martensitic volume fraction. The framework is implemented in an implicit time integration scheme, with both monolithic and staggered solution strategies. The potential of this formulation is showcased by modelling a number of paradigmatic problems. First, a boundary layer model is used to examine crack tip fields and compute crack growth resistance curves (R-curves). We show that the model is able to capture the main fracture features associated with SMAs, including the toughening effect associated with stress-induced phase transformation. Insight is gained into the role of temperature, material strength, crack density function and fracture energy homogenisation. Secondly, several 2D and 3D boundary value problems are addressed, demonstrating the capabilities of the model in capturing complex cracking phenomena in SMAs, such as unstable crack growth, mixed-mode fracture or the interaction between several cracks. Finally, the model is extended to fatigue and used to capture crack nucleation and propagation in biomedical stents, a paradigmatic application of nitinol SMAs.

Study of the Fracture Behavior of Tetragonal Zirconia Polycrystal with a Modified Phase Field Model.

The superior fracture toughness of zirconia is closely correlated with stress-induced martensitic phase transformation around a crack tip. In this study, a modified phase field (PF) model coupling phase transformation and fracture is proposed to study the fracture behavior and toughening effect of tetragonal zirconia polycrystal (TZP). The stress-induced tetragonal to monoclinic (t–m) phase transformation around a static or propagating crack is characterized with PF simulations. It is shown that the finite size and shape of the transformation zone under different loads and ambient temperatures can be well predicted with the proposed PF model. The phase transformation may decrease the stress level around the crack tip, which implies the toughening effect. After that, crack propagation in TZP is studied. As the stress field is perturbed by the phase transformation patterns, the crack may experience deflection and branching in the propagation process. It is found that the toughness of the grain boundaries (GBs) has important influences on the crack propagation mode. For TZP with strong GBs, the crack is more likely to propagate transgranularly while, for TZP with weak GBs, intergranular crack propagation is prevalent. Besides that, the crystal orientation and the external load can also influence the topology of crack propagation.