Transformation Volume Change Research Articles

Indentation-induced martensitic transformation in SMAs: Insights from phase-field simulations

Direct experimental characterization of indentation-induced martensitic microstructures in pseudoelastic shape memory alloys (SMAs) is not possible, and thus there is a lack of evidence and understanding regarding the microstructure pattern and related features. To fill this gap, in this work we employ the phase-field method to provide a detailed and systematic analysis of martensitic phase transformation during nanoindentation. A recently-developed finite-element-based computational model is used for this purpose, and a campaign of large-scale 3D simulations is carried out. First, the orientation-dependent indentation response in CuAlNi (a widely studied SMA) is examined. A detailed investigation of the predicted microstructures reveals several interesting features, some of them are consistent with theoretical predictions and some can be (to some extent) justified by experiments other than micro/nanoindentation. The results also highlight the key role of finite-deformation effects and elastic anisotropy of the phases on the model predictions. Next, a detailed study of indentation-induced martensitic transformation in NiTiPd (a potential low-hysteresis SMA) with varying Pd content is carried out. In terms of hysteresis, the results demonstrate the prevailing effect of the transformation volume change over phase compatibility in the conditions imposed by nanoindentation and emphasize on the dominant role of the interfacial energy at small scales. Results of such scope have not been reported so far.

On the evolving nature of c/a ratio in a hexagonal close-packed epsilon martensite phase in transformative high entropy alloys

Activation of different slip systems in hexagonal close packed (h.c.p.) metals depends primarily on the c/a ratio, which is an intrinsic property that can be altered through alloying addition. In conventional h.c.p. alloys where there is no diffusion-less phase transformation and associated transformation volume change with deformation, the c/a ratio remains constant during deformation. In the present study, c/a ratio and transformation volume change of h.c.p. epsilon martensite phase in transformative high entropy alloys (HEAs) were quantified as functions of alloy chemistry, friction stir processing and tensile deformation. The study revealed that while intrinsic c/a is dependent on alloying elements, c/a of epsilon in transformative HEAs changes with processing and deformation. This is attributed to transformation volume change induced dependence of h.c.p. lattice parameters on microstructure and stress state. Lower than ideal c/a ratio promotes non-basal pyramidal 〈c + a〉 slip and deformation twinning in epsilon phase of transformative HEAs. Also, a unique twin-bridging mechanism was observed, which provided experimental evidence supporting existing theoretical predictions; i.e., geometrical factors combined with grain orientation, c/a ratio and plastic deformation can result in characteristic twin boundary inclination at 45–50°.

Effect of cooling rate on microstructural evolution and hardness of self-shielded arc weld deposits containing 1 wt% aluminium

The self-shielded arc welding is based on the presence of flux elements that protect the weld from oxygen and nitrogen. The hardfacing alloy investigated contained about 1 wt% Al to prevent weld porosity by combining with oxygen and nitrogen. Thermodynamic calculations of the phase equilibria for the alloy predicted a weld metal microstructure consisting of δ-ferrite and austenite at high temperatures. Since the alloy had a high hardenability, the austenite transformed to martensite on cooling to provide a hardfacing deposit microstructure that is resistant to metal-to-metal wear. Nevertheless, the high Al content ensured that δ-ferrite was present as the minor microstructural component in all of weld deposits examined. The cooling rate after welding is a key variable that influences the volume fractions of δ-ferrite and martensite in the weld deposit. Dilatometric studies reported in this paper show that increasing the cooling rate of samples subjected to a weld thermal cycle designed to simulate the effect of pre-heat resulted in increases in volume percentage martensite, the magnitude of the transformation volume change and the MS temperature. Using a pre-heat temperature higher than MS resulted in the isothermal formation of bainite, as well as martensite on subsequent cooling. Despite the multiphase microstructure of bainite, martensite and δ-ferrite, the weldment hardness was considerably more uniform than for deposits produced using lower temperature, conventional, pre-heats. In general, deposition at the higher temperature served the purpose of normalising the hardness by reducing differences in dislocation density and carbide precipitation throughout the various regions of the weld deposit.

XRD study of the kinetics of β ↔ α transformations in tin

The transformation kinetics of βSn (white tin) to and from αSn (grey tin) are studied by synchrotron X-ray diffraction of seeded powder samples of 99.99% Sn. An analysis of thermal expansion behaviour revealed that the volume change of transformation increases as the temperature decreases. The βSn → αSn transformation was well described by Johnson–Mehl–Avrami kinetics with an Avrami exponent of 3, which was confirmed to be due to three-dimesional growth from pre-existing nuclei by a microstructural study. The αSn → βSn transformation exhibited a decreasing Avrami exponent from ∼4 to ∼1 during the transformation. Time–Temperature–Transformation curves are plotted from the isothermal transformation data and are compared with past work.

Study on Nanometric Machining Mechanism of Monocrystalline Silicon by Molecular Dynamics

A three-dimensional model of molecular dynamics (MD) was employed to study the nanometric cutting mechanism of monocrystalline silicon. The model included the utilization of the Morse potential function to simulate the interatomic force between the workpiece and the tool, and the Tersoff potential function between silicon atoms. Amorphous phase transformation and chip volume change are observed by analyses of the snapshots of the MD simulation of the nanometric cutting process, energy and cutting forces. Dislocations and elastic recovery in the deformed region around the tool do not appear. Cutting forces initiate the amorphous phase transformation, and thrust forces play an important role in driving the further transformation development. Nanometric cutting mechanism of monocrystalline silicon is not the plastic deformation involving the generation and propagation of dislocations, but deformation via amorphous phase transformation.

A mathematical approach to transformation toughening in bulk metallic glasses

A mathematical framework used to describe transformation toughening in zirconia-based ceramics is adapted to apply to transformation toughening in bulk metallic glass matrix composites . The method is applied to the Cu 47.5 Zr 47.5 Al 5 bulk metallic glass, showing that the low volume change of transformation in this alloy leads to negligible toughening via the proposed mechanism. An alternative mechanism for toughening is presented, whereby shear bands propagate more easily in the early stages of advance.

On the Measurement of Residual Stress in Induction Hardened Parts

It is well known that induction surface heating followed by rapid quenching generally increases the fatigue life of steel components subjected to bending loads by significantly postponing the micro-crack nucleation and propagation processes. The phase transformation volume change combined with severe thermal gradients leave a hard surface layer under relatively high and deep compressive residual stresses. In this paper, residual stress measurements are done on induction hardened AMS6414 martensitic steel (aerospace grade of AISI4340) cylinders using two techniques: the so-called contour method and X-ray diffraction. For both methods, induction hardened parts raise many challenges. The contour method hardly describes high stress gradients near the surface while the diffraction technique accuracy appears limited considering the strong microstructural variation and the high depth of the stresses to be measured. For the contour method, a CMM and an optical pen using the confocal chromatic imaging principle were used to measure the surface after precision WEDM cutting. The effect of data filtering and smoothing on the calculated stresses are discussed. For X-ray analysis, the effect of stress relaxation during layer removal and analysis technique is explained. The difference between the residual stress measurements done with the two techniques is discussed with emphasis on both the surface and the in-depth measurements.

On the volume change in Co–Ni–Al during pseudoelasticity

CoNiAl alloys are a new class of shape memory alloys, which exhibit pseudoelastic strains as high 6% over a broad range of temperatures. Based on the crystallographic lattice constants, a substantial volume change upon transformation is expected at the mesoscopic level, yet it has not been measured previously. Transformation strains are established in three mutually orthogonal directions in the [001]-oriented CoNiAl single crystals under compression. Experiments reveal that the transformation volume change is approximately 2% based on determination of strains on transformed and untransformed locations. Despite the high volumetric strain, the pseudoelastic stress–strain response represents full recoverability with small stress hysteresis. Additional factors that influence pseudoelasticity behavior are discussed particularly the Md−Af interval and the flow resistance, which are both higher for CoNiAl compared to other shape memory alloys.

Effect of Si on the reversibility of stress-induced martensite in Fe–Mn–Si shape memory alloys

Fe–Mn–Si is a well-characterized ternary shape memory alloy. Research on this alloy has consistently shown that the addition of 5–6 wt.% Si is desirable to enhance the reversibility of stress-induced martensite vis-à-vis shape memory. This paper examines the effect of Si on the morphology and the crystallography of the martensite in the Fe–Mn–Si system. It is concluded that the addition of Si increases the c/ a ratio of the martensite, reduces the transformation volume change and decreases the atomic spacing difference between the parallel close-packed directions in the austenite–martensite interface (habit) plane. It is proposed that, in addition to austenite strengthening, Si enhances reversibility by reducing the volume change and the interfacial atomic mismatch between the martensite and the austenite. Although shape memory is improved, transformation reversibility remains limited by the necessary misfit dislocations that accommodate the atomic spacing differences in the interface.

Thermal and stress-induced martensitic transformations in quaternary Ni 50Mn 37(In, Sb) 13 ferromagnetic shape memory alloys

This study investigated the martensitic transformation and the mechanical behaviour of quaternary Ni 50Mn 37In 13− x Sb x ( x = 0, 2, 6, 8, 10) Heusler alloys. Substitution of Sb for In was found to reduce the orthorhombic distortion of the martensite form the L2 1 austenite, but increased the transformation volume change. The critical temperatures of the transformation are found to decrease nearly linearly with increasing valence electron concentration caused by Sb substitution for In, with a linearity coefficient of ∼15 K per at% of Sb. The transformation latent heat and the transformation entropy change decreased with increasing Sb content, with two different composition dependencies in concentration ranges of 0 < x < 6 and x > 6. This is attributed to different magnetic states of the martensite. A recoverable transformation strain of 0.46% was obtained in the polycrystalline Ni 50Mn 37In 3Sb 10 alloy. An effect of stress-induced martensite stabilization was observed in the Ni 50Mn 37In 7Sb 6 sample.

Brillouin scattering studies of liquid argon at high temperatures and high pressures

Brillouin scattering measurements were performed on liquid argon in a diamond anvil cell at various solidification points up to 503 K. With the measured results from the 60 degree platelet- and 180 degree back-scattering geometries, the sound velocity, refractive index, experimental equation of state, and adiabatic bulk modulus of liquid argon as a function of pressure were determined. The discrepancy between experimental and previous calculated equation of state indicates that the many-body contribution to the density of liquid argon increases with increasing pressure and decreases with increasing temperature. By analyzing the Brillouin spectra in the coexistence of liquid and solid phase regions, the volume change and latent heat of solid-liquid transformation along the equilibrium curve have been also obtained for the first time.

Mechanical strength of thermally aged Sn-3.5Ag/Ni-P solder joints

This work presents an investigation on the influence of the solder/under bump metallization (UBM) interfacial reaction to the tensile strength and fracture behavior of Sn-3.5Ag/Ni-P solder joints under different thermal aging conditions. The tensile strength of Sn-3.5Ag/Ni-P solder joints decreases with aging temperature and duration. Four types of failure modes have been identified. The failure modes shift from the bulk solder failure mode in the as-soldered condition toward the interfacial failure modes. Kirkendall voids do not appear to affect the tensile strength of the joint. The volume change of Ni-P phase transformation during the thermal aging process generates high tensile stress inside the Ni-P layer; this stress causes mudflat cracks on the remaining Ni-P coating and also leads to its delamination from the underlying Ni substrate. In general, interfacial reaction and the subsequent growth of Ni3Sn4 intermetallic compound (IMC) layer during solid-state reaction are the main reasons for the decrease of tensile strength of the solder joints. The current study finds there is an empirical linear relation between the solder joint strength and the Ni3Sn4 intermetallic compound (IMC) thickness. Therefore, the IMC thickness may be used as an indication of the joint strength.

Compressive Thermal Yielding Leading to Hydrogen Cracking in a Fired Cannon

Investigation of environmental cracking of a 1100-MPa yield strength A723 steel cannon tube subjected to prototype firings is described. Metallographic results show cracking of the steel beneath a 0.12-mm protective layer of chromium. Cracks undermine and remove sections of chromium and lead to localized erosion that ruins the cannon. Key features of the firing thermal damage and cracking are: (i) recrystalization of the chromium to a depth of up to 0.08 mm; (ii) steel transformation to 0.19 mm below the chrome surface; (iii) two different periodic arrays of cracks normal to the hoop and axial directions, with mean depths of 0.23 and 0.46 mm, respectively. Time-temperature-depth profiles for the firing cycle were derived via bi-material finite difference analysis of a semi-infinite solid which incorporated cannon combustion gas temperatures and material properties that vary as a function of temperature. The temperature and depth associated with the steel transformation were used to solve iteratively for the convective heat transfer coefficient. This value was further confirmed by the depths of chromium recrystalization and of the crack arrays in the two orientations. A profile of maximum temperature versus depth is used to determine the near-bore applied and residual stress distributions within the tube. The measured volume change of steel transformation is used to determine an upper limit on applied and residual stresses. These stresses are used to determine crack-tip stress intensity factors for the observed crack arrays, and hence provide some explanation for the differential depths of cracking. The near-bore temperature and residual stress distributions are used to help determine the cause of hydrogen cracking and measures to prevent cracking. Compressive yielding due to thermal loading produces near-bore tensile residual stresses, and thereby causes hydrogen cracking. Prevention of cracking is discussed in relationship to hydrogen crack growth rate tests of alternative alloys and coatings.

Polymorphic transformations between olivine, wadsleyite and ringwoodite: mechanisms of intracrystalline nucleation and the role of elastic strain

AbstractKinetic models and rate equations for polymorphic reconstructive phase transformations in polycrystalline aggregates are usually based on the assumptions that (a) the product phase nucleates on grain boundaries in the reactant phase and (b) growth rates of the product phase remain constant with time at fixed P-T. Recent observations of experimentally-induced transformations between (Mg,Fe)2SiO4 olivine (α) and its high pressure polymorphs, wadsleyite (β) and ringwoodite (γ), demonstrate that both these assumptions can be invalid, thus complicating the extrapolation of experimental kinetic data. Incoherent grain boundary nucleation appears to have dominated in most previous experimental studies of the α–β–γ transformations because of the use of starting materials with small (&lt;10–20 µm) grain sizes. In contrast, when large (0.6 mm) olivine single crystals are reacted, intracrystalline nucleation of both β and γ becomes the dominant mechanism, particularly when the P-T conditions significantly overstep the equilibrium boundary. At pressures of 18–20 GPa intracrystalline nucleation involves (i) the formation of stacking faults in the olivine, (ii) coherent nucleation of γ-lamellae on these faults and (iii) nucleation of β on γ. In other experiments, intracrystalline nucleation is also observed during the β-γ transformation. In this case coherent nucleation of γ appears to occur at the intersections of dislocations with (010) stacking faults in β, which suggests that the nucleation rate is stress dependent. Reaction rims of β/γ form at the margins of the olivine single crystals by grain boundary nucleation. Measurements of growth distance as a function of time indicate that the growth rate of these rims decreases towards zero as transformation progresses. The growth rate slows because of the decrease in the magnitude of the Gibbs free energy (stored elastic strain energy) that develops as a consequence of the large volume change of transformation. On a longer time scale, growth kinetics may be controlled by viscoelastic relaxation.

Atomistic simulation study of the effect of martensitic transformation volume change on crack-tip material evolution and fracture toughness

The effect of the sign of the F.C.C.→B.C.C. martensitic transformation volume change in Fe-20Ni on material evolution in a region surrounding the crack tip and the accompanying change in the fracture resistance of the material have been investigated using molecular dynamics simulations. The interaction between atoms has been modeled using the embedded atom method (EAM) interatomic potentials. To obtain both the positive and the negative values of the transformation volume change, small adjustments had to be made in the EAM functions. These changes did not significantly affect of the key materials properties, such as the relative thermodynamic stability of the F.C.C. and B.C.C. structures, elastic constants, (11 2 ̄ ) bcc twin boundary energy, (10 1 ̄ ) fcc /(1 2 ̄ 1) bcc interfacial energy, etc. The simulation results show that the sign of the transformation volume change has a profound effect on the material evolution and the path of the advancing crack. When the volume change is negative, the region ahead of the crack tip undergoes the transformation only after the other regions around the crack tip have already transformed. The crack tip undergoes a significant blunting and tends to stay on the original crack plane. In sharp contrast, when the volume change is positive, the region ahead of the crack tip transforms first and significant decohesion along the F.C.C./B.C.C. interfaces takes place. Consequently the crack tends to branch out. The effect of material evolution at the crack tip on the ability of the material to withstand further fracture has been quantified by calculating the Eshelby's F 1 conservation integral. The sign of the transformation volume change is found to have a major effect on the change of the F 1 integral with the simulation time.

The influence of material anisotropy on transformation induced plasticity in steel subject to martensitic transformation

A simplified micromechanical model adapted to martensitic transformation is applied to describe transformation induced plasticity (TRIP) in steel. The accommodation of the transformation volume and shape change is performed by plastification considering Hill's anisotropic yield condition. Both a uniaxial and a triaxial loadstress state are investigated. A generalized TRIP-term is developed in the sense of an “extended” Greenwood and Johnson (1965, Proc. R. Soc. London A 283, 430-422) relation.

Design of TiAlV β phase for transformation toughening of γ-titanium aluminide

A thermodynamic analysis is developed to determine the chemical composition of the TiAlV β phase for dispersed phase transformation toughening of γ-titanium aluminide. The analysis takes into account the fact that maximum transformation toughening is associated with an optimum level of thermodynamic stability of the β phase with respect to martensitic transformation and with a large positive value of teh β phase → martensite transformation volume change. In addition, to prevent deleteriouss interfacial reactions, the two phases β and γ are required to be in chemical equilibrium. Available thermodynamic and lattice parameter data are used to determine a range of chemical compositions of the β phase which ensures maximum transformation toughening. It is found that this range is sufficiently close to the β−( β+ γ) phase boundary and hence guarantees chemical compatibility between the two phases.

A study of β → α″ martensitic transformation volume change in TiAlV alloys

The effect of alloy chemistry on the sign and the magnitude of a volume change accompanying β → α″ martensitic transformation in the TiAlV system is explored using X-ray diffraction. The transformation volume change is found to vary between −4.5 and +4.5%. Alloys within the composition range characterized by a large, positive (> +4%) volume change are further studied to explore their potential for dispersed-phase transformation toughening of γ-titanium aluminide. They are found to be reasonably chemically compatible with the γ phase. However, stability of the β phase in these alloys is low, causing martensite to form on quenching to room temperature. It was concluded that, due to insufficient stability of the β phase, these alloys are not suitable for dispersed-phase transformation toughening of γ-titanium aluminide.

Effect of iron additions on β-phase stability with respect to α″-martensite in V-28Al-17Ti(wt.%)

The effect of iron additions (up to 7 wt.%) on the β b.c.c.-phase stability with respect to α″ orthorhombic-martensite and the corresponding transformation volume change in V-28Al-17Ti (wt.%) alloy has been studied using optical microscopy and X-ray diffraction. It was found that iron additions stabilize the β phase while the volume change remains positive and relatively high (3–4%). Using a liquid nitrogen refrigeration treatment and introducing cracks into the materials to further test β-phase stability, and carrying out a thermodynamic analysis, it was found that an addition of 5 wt.% of iron gives rise to the optimum level of stability of the β phase. This, in turn, should ensure maximum transformation toughening effects when this alloy is used as a dispersed phase within a γ titanium aluminide matrix.

Optimization of ti- al- v beta phase for dispersed phase transformation toughening of gamma titanium aluminides

The most important factors affecting the dispersed-phase transformation toughening in the gamma- TiAl intermetallic by a dispersion of the beta phase are the stability of the dispersion, the transformation volume change and the β/γ chemical compatibility. A thermodynamics-based, computer-aided analysis was used to design an optimum composition of the β-phase dispersion for the crack-tip transformation toughening. It is found that such an optimum composition exists in the ternary Ti- Al- V system.