Multiple bifurcations and local energy minimizers in thermoelastic martensitic transformations

Thermoelastic martensitic transformations in shape memory alloys can be modeled on the basis of nonlinear elastic theory.Microstructures of fine phase mixtures are local energy minimizers of the total energy.Using a one-dimensional effective model,we have shown that such microstructures are inhomogeneous solutions of the nonlinear Euler-Lagrange equation and can appear upon loading or unloading to certain critical conditions,the bifurcation conditions.A hybrid numerical method is utilized to calculate the inhomogeneous solutions with a large number of interfaces.The characteristics of the solutions are clarified by three parameters：the number of interfaces,the interface thickness,and the oscillating amplitude.Approximated analytical expressions are obtained for the interface and inhomogeneity energies through the numerical solutions.

Isothermal and athermal martensitic transformations of ceria cerla doped zilrconian

Martensitic transformation behavior was studied for zirconia containing 4%～10% CeO2 (in mole fraction) by using a dilatometric method. The Ms (Martensite start temperature) decreased near linearly with increasing CeO2. Different transformation modes were observed depending on the composition and cooling rate. ZrO2 containing 6% CeO2 showed isothermal transformation behavior, whereas ZrO2 containing 9% and 10% CeO2 showed athermal transformation behavior. However, ZrO2 containing 8% CeO2 showed either isothermal or athermal transformations behavior depending on the cooling rate. A TTT (Time-Temperature-Transformation) diagram was proposed for ZrO2 containing 8% CeO2.

Mssbauer and electron microscopy study of martensitic transformations in an Fe-Mn-Mo alloy

The kinetic,morphological,crystallographic,and magnetic characteristics of thermally induced martensites in Fe-13.4wt% Mn-5.2wt%Mo alloy were investigated by scanning electron microscopy（SEM）,transmission electron microscopy（TEM）,and M（o｜¨）ssbauer spectroscopy.The experimental results reveal that two types of thermal-induced martensites,e（hcp） andα＇（bcc） martensites,are formed in the as-quenched condition,and these transformations have athermal characters.Mo addition to the Fe-Mn alloy does not change the coexistence ofεandα＇ martensites with the Mn content between 10wt%and 15wt%.Besides,M（o｜¨）ssbauer spectra reveal a paramagnetic character with a singlet for theγ（fcc） austenite andεmartensite phases and a ferromagnetic character with a broad sextet for theα＇ martensite phase. The volume fraction ofα＇ martensite forming in the quenched alloy is much more than that of theεmartensite.

Effect of Compressive Deformation on Lenticular and Thin Plate Martensitic Transformations

The effect of compressive deformation tested above the M_s temperature on the martensite morphology in Fe-Ni-C alloys has been studied.In the Fe-30Ni-0.12C alloy,the M_s temperature is -50℃ The cylindrical specimens were compressively deformed at -40℃.The strain rates were 10,20,30 and 40%.X-ray analysis and metallographic examination showed that no strain-induced martensite was found.After quench- ing to -53℃,some thin plates and unusual morphologies of lenticular martensites with bent and/or broken mid-ribs were observed.In the Fe-30Ni-0.34C alloy,the M_s temperature is -120℃.Compressive deformation with different strain rates were carried out at room temperature. After quenching to the liquid nitrogen temperature, some bent thin plate matensites(unbroken)occur- red.The transformed twins in bent plate were also bent and nearly parallel to the γ-α'interfaces. Orientation relationship between austenite and bent martensite has been examined by means of trans- mission electron microscope.It was proved that these unusual morphologies are inherent in the compressive pre-deformed austenite.

CALORIMETRY OF PARTIAL MARTENSITIC TRANSFORMATIONS

Partial thermoelastic martensitic transformations have been studied by calorimetry on CuAlNi single crystals with special methods. The chemical enthalpy change, the elastic energy stored at the interfaces or inside of the martensite and the energy dissipated in acoustic emission were calculated for a partial transformation; the relationship among them was studied based on measured latent heat and transformation temperatures. The influence of specimen shape on the stored elastic energy was evaluated and discussed.

Microstructure and martensitic transformation in quaternary NiTiHfV alloy

The effect of age hardening on the microstructure,martensitic transformation behavior,and shape memory properties of the(Ni_(50)Ti_(30)Hf_(20))_(95)V_(5)alloy was investigated by scanning electron microscopy,transmission electron microscopy,X-ray diffraction,differential scanning calorimetry,microhardness,and bending tests.The results demonstrate a significant influence of V addition on the microstructure of the alloy.V addition leads to the formation of a(Ni,V)_(2)(Ti,Hf)-type Laves phase,which coexists with B19'martensite at room temperature.Aging at 550℃results in precipitation hardening due to the formation of nano-scale orthorhombic H-phase,with the peak hardness observed after 3 h of aging.The alloy at peak hardness state exhibits higher transformation strain and lower unrecovered strain compared to the solution-treated sample.The aged sample achieves a maximum transformation strain of 1.56%under 500 MPa.

Description of martensitic transformation kinetics in Fe-C-X(X = Ni,Cr,Mn,Si) system by a modified model

Controlling the content of athermal martensite and retained austenite is important to improving the mechanical properties of high-strength steels,but a mechanism for the accurate description of martensitic transformation during the cooling process must be addressed.At present,frequently used semi-empirical kinetics models suffer from huge errors at the beginning of transformation,and most of them fail to exhibit the sigmoidal shape characteristic of transformation curves.To describe the martensitic transformation process accurately,based on the Magee model,we introduced the changes in the nucleation activation energy of martensite with temperature,which led to the varying nucleation rates of this model during martensitic transformation.According to the calculation results,the relative error of the modified model for the martensitic transformation kinetics curves of Fe-C-X(X = Ni,Cr,Mn,Si) alloys reached 9.5% compared with those measured via the thermal expansion method.The relative error was approximately reduced by two-thirds compared with that of the Magee model.The incorporation of nucleation activation energy into the kinetics model contributes to the improvement of its precision.

Pre-existing orthorhombic embryos-induced hexagonal-orthorhombic martensitic transformation in MnNiSi_(1-x)(CoNiGe)_x alloy

The thermal-elastic martensitic transformation from high-temperature Ni_(2)In-type hexagonal structure to low-temperature TiNiSi-type orthorhombic structure has been widely studied in MnMX(M=Ni or Co,and X=Ge or Si)alloys.However,the answer to how the orthorhombic martensite nucleates and grows within the hexagonal parent is still unclear.In this work,the hexagonal-orthorhombic martensitic transformation in a Co and Ge co-substituted MnNiSi is investigated.One can find some orthorhombic laths embedded in the hexagonal parent at a temperature above the martensitic transformation start temperature(M_(s)).With the the sample cooing to M_(s),the laths turn broader,indicating that the martensitic transformation starts from these pre-existing orthorhombic laths.Microstructure observation suggests that these pre-existing orthorhombic laths do not originate from the hexagonal-orthorhombic martensitic transformation because of the difference between atomic occupations of doping elements in the hexagonal parent and those in the preexisting orthorhombic laths.The phenomenological crystallographic theory and experimental investigations prove that the pre-existing orthorhombic lath and generated orthorhombic martensite have the same crystallography relationship to the hexagonal parent.Therefore,the orthorhombic martensite can take these pre-existing laths as embryos and grow up.This work implies that the martensitic transformation in MnNiSi_(1-x)(CoNiGe)_(x) alloy is initiated by orthorhombic embryos.

Effect of Multiple Martensitic Transformations on Structure of Fe-Ni Alloys

Effect of multiple direct and reverse martensitic transformations on fragmentation of austenitic grains in Fe-Ni alloys have been studied by X-ray diffraction and scanning electron microscopy. An ultra-fine structure was formed by fragmentation inside austenitic grains due to progressing misorientation of austenitic sub-grains during multiple γ-α-γ-martensitic phase transitions. An increase in the number of γ-α-γ-transformations increases misorientation angle between austenitic sub-grains and leads to transformation of an austenitic single crystal into a textured polycrystal. It has been shown that multiple γ-α-γ-martensitic phase transitions change the mechanism of internal stress relaxation from dislocation-based to deformation twinning.

Transformation of the TiNi Alloy Microstructure and the Mechanical Properties Caused by Repeated B2-B190' Martensitic Transformations

The influences of thermal cycling treatment in the temperature range of B2-B19 martensitic transformations（-150 to 150 °C） on the Ti Ni alloy structure and properties were studied. Different states named the initial coarse-grained（CG） state, the ultrafine-grained（UFG） state after ECAP（with a grain size of 200 nm）, the state after ECAP and cold upsetting by 30% were considered. The results show that the microhardness and the strength increase in all the three states.According to the XRD analysis, a more significant increment in the dislocation density, resulting from thermal cycling, is observed in the UFG alloy than in the CG alloy.

First-principles calculations of Ni–(Co)–Mn–Cu–Ti all-d-metal Heusler alloy on martensitic transformation,mechanical and magnetic properties

The martensitic transformation,mechanical,and magnetic properties of the Ni_(2)Mn_(1.5-x)Cu_(x)Ti_(0.5) (x=0.125,0.25,0.375,0.5) and Ni_(2-y)Co_(y)Mn_(1.5-x)Cu_(x)Ti_(0.5)[(x=0.125,y=0.125,0.25,0.375,0.5) and (x=0.125,0.25,0.375,y=0.625)]alloys were systematically studied by the first-principles calculations.For the formation energy,the martensite is smaller than the austenite,the Ni–(Co)–Mn–Cu–Ti alloys studied in this work can undergo martensitic transformation.The austenite and non-modulated (NM) martensite always present antiferromagnetic state in the Ni_(2)Mn_(1.5-x)Cu_(x)Ti_(0.5) and Ni_(2-y)Co_(y)Mn_(1.5-x)Cu_(x)Ti_(0.5) (y<0.625) alloys.When y=0.625 in the Ni_(2-y)Co_(y)Mn_(1.5-x)Cu_(x)Ti_(0.5) series,the austenite presents ferromagnetic state while the NM martensite shows antiferromagnetic state.Cu doping can decrease the thermal hysteresis and anisotropy of the Ni–(Co)–Mn–Ti alloy.Increasing Mn and decreasing Ti content can improve the shear resistance and normal stress resistance,but reduce the toughness in the Ni–Mn–Cu–Ti alloy.And the ductility of the Co–Cu co-doping alloy is inferior to that of the Ni–Mn–Cu–Ti and Ni–Co–Mn–Ti alloys.The electronic density of states was studied to reveal the essence of the mechanical and magnetic properties.

Real-time monitoring dislocations,martensitic transformations and detwinning in stainless steel:Statistical analysis and machine learning

Acoustic emission(AE)of 316 L stainless steel with of low Ni content shows,under tension,simultaneously three avalanche processes.One avalanche process relates to the movement of dislocations,the others to martensitic transformations and detwinning/twinning.Detwinning/twinning occurs predominantly at the early stage of the plastic deformation while martensitic transformations only become observable after large plastic deformation.All processes coincide during deformation with variable effect on AE.An excellent fingerprint for the detection of the coincidence between the several mechanisms is the observation of multivalued E~A^(2) correlations.AE signals from moving dislocations decay more slowly(~7×10^(-3)s)and show long avalanche durations.In contrast,AE signals during martensitic transformations and detwinning/twinning decay rapidly(<4×10^(-4) s)and show short avalanche durations.They can be distinguished by different energy exponents of their avalanches.The energy distributions of the mechanisms differ because energies are defined as the integral over the squared AE amplitudes,where the integration extends over the avalanche durations.A combination of statistical analysis with Convolutional Neural Network calculations provides an accurate and straightforward method for online,non-destructive avalanche monitoring of strain-induced martensitic transformations in 316 L steel under high strain.

Machine learning-assisted efficient design of Cu-based shape memory alloy with specific phase transition temperature

The martensitic transformation temperature is the basis for the application of shape memory alloys(SMAs),and the ability to quickly and accurately predict the transformation temperature of SMAs has very important practical significance.In this work,machine learning(ML)methods were utilized to accelerate the search for shape memory alloys with targeted properties(phase transition temperature).A group of component data was selected to design shape memory alloys using reverse design method from numerous unexplored data.Component modeling and feature modeling were used to predict the phase transition temperature of the shape memory alloys.The experimental results of the shape memory alloys were obtained to verify the effectiveness of the support vector regression(SVR)model.The results show that the machine learning model can obtain target materials more efficiently and pertinently,and realize the accurate and rapid design of shape memory alloys with specific target phase transition temperature.On this basis,the relationship between phase transition temperature and material descriptors is analyzed,and it is proved that the key factors affecting the phase transition temperature of shape memory alloys are based on the strength of the bond energy between atoms.This work provides new ideas for the controllable design and performance optimization of Cu-based shape memory alloys.

Martensitic transformation and magnetic properties of aged Ni-Fe-Ga-Ti shape memory alloy

This article reports the effect of ageing on the microstructure, martensitic transformation, magnetic properties, and mechanical properties of Ni51FelsGa27Ti4 shape memory alloy. There are five specimens of this alloy aged at 573 up to 973 K for 3 h per each. This range of ageing temperature greatly affects the microstructure of the alloy. As the ageing temperature increased from 573 up to 973 K, the microstructure of Ni51FelsGa27Ti4 alloy gradually changed from the entirely martensitic matrix at 573 K to the fully austenitic microstructure at 973 K. The volume fraction of precipi- tated Ni3Ti particles increased with the ageing temperature increasing from 573 to 773 K. Further increasing the ageing temperature to 973 K decreased the content of Ni3Ti in the microstructure. The martensitic transformation tempera- ture was decreased steadily by increasing the ageing temperature. The magnetization saturation, remnant magnetization, and coercivity increased with the ageing temperature increasing up to 773 K. A further increase in ageing temperature decreased these raagnetic properties. Moreover, the hardness values were gradually increased at first by increasing the ageing temperature to 773 K, and then dramatically decreased to the lowest value at 973 K.

Martensitic stabilization and defects induced by deformation in TiNi shape memory alloys

Martensitic stabilization caused by deformation in a TiNi shape memory alloy was studied.Special attention was paid to the deformed microstructures to identify the cause of martensitic stabilization.Martensitic stabilization was demonstrated by differential scanning calorimetry for the tensioned TiNi shape memory alloy.Transmission electron microscopy revealed that antiphase boundaries were formed because of the fourfold dissociation of [110]B19＇ super lattice dislocations and were preserved after reverse transformation due to the lattice correspondence.Martensitic stabilization was attributed to dislocations induced by deformation,which reduced the ordering degree of the microstructure,spoiled the reverse path from martensite to parent phase compared with thermoelastic transformation,and imposed resistance on phase transformation through the stress field.

Electronic transport evolution across the successive structural transitions in Ni_(50-x)Fe_xTi_(50) shape memory alloys

TiNi-based shape memory alloys have been extensively investigated due to their significant applications,but a comprehensive understanding of the evolution of electronic structure and electrical transport in a system with martensitic transformations(MT) is still lacking.In this work,we focused on the electronic transport behavior of three phases in Ni_(50-x)Fe_xTi_(50)across the MT.A phase diagram of Ni_(50-x)Fe_xTi_(50) was established based on x-ray diffraction,calorimetric,magnetic,and electrical measurements.To reveal the driving force of MT,phonon softening was revealed using first-principles calculations.Notably,the transverse and longitudinal transport behavior changed significantly across the phase transition,which can be attributed to the reconstruction of electronic structures.This work promotes the understanding of phase transitions and demonstrates the sensitivity of electron transport to phase transition.

Mechanisms of strength-plasticity enhancement and stress-induced phase transition in a medium-carbon low-alloy steel

A medium-carbon low-alloy steel with designed chemical composition was investigated.The steel exhibits an excellent product of strength and elongation value of 31,832 MPa%through quenching and partitioning treatment,with a tensile strength of 1413 MPa and elongation of 22%.X-ray diffraction analysis and transmission electron microscopy characterizations confirm that the retained austenite in the specimens undergoes stress-induced phase transformation to the martensite and hexagonal phases,namely the transformation-induced plasticity(TRIP)effect is triggered.This TRIP effect,triggered by the stress-induced phase transition of retained austenite,is responsible for the excellent mechanical properties obtained in the steel.For further investigating the stress-induced phase transition mechanism,thermodynamic methods are applied.Gibbs free energy of face-centered cubic-Fe,ε-Fe,ω-Fe and body-centered cubic-Fe associated with the stress-induced phase transition was calculated using molecular dynamics simulations,and a calculation method of strain energy in thermodynamic units for the stress-induced martensitic transformation is presented.The final results reveal the process and thermodynamic mechanism of stress-induced martensitic transformation in medium-carbon steels,in which the hexagonal phase can participate in the process as an intermediate product.

Effects of Cu on the martensitic transformation and magnetic properties of Mn_(50)Ni_(40)In_(10) alloy

The structures, the martensitic transformations, and the magnetic properties are studied systematically in Mn50Ni40-xCuxIn10, Mn50-xCuxNi40In10, and Mn50Ni40In10-xCux alloys. The partial substitution of Ni by Cu reduces the martensitic transformation temperature, but has little influence on the Curie temperature of austenite. Comparatively, the martensitic transformation temperature increases and the Curie temperature of austenite decreases with the partial replacement of Mn or In by Cu. The magnetization difference between the austenite phase and the martensite phase reaches 70 emu/g in Mn50Ni39Cu1In10; a field-induced martensite-to-austenite transition is observed in this alloy.

Effect of solution treatment on the martensitic transformation behavior of a Ni_(43)Co_7Mn_(39)Sn_(11) polycrystalline alloy

The effect of solution treatment on the martensitic transformation behavior of a Ni43Co7Mn39Sn11 polycrystalline alloy fabricated by an arc melting method was investigated by scanning electron microscopy（SEM）, energy-dispersive X-ray spectroscopy（EDS）, and differential scanning calorimetry（DSC）. The examination indicates the presence of severe chemical segregation in the dendritic as-cast structure because of solidification. This chemical segregation completely impedes the intrinsic martensitic transformation. Annealing at 1223 K for 24 h is identified as the threshold annealing condition to eliminate the microstructural segregation and begin the martensitic transformation, as indicated by a broad and obscure feature. Annealing at 1273 K for 24–48 h is found to be effective at promoting notably the martensitic transformation, but the martensitic transformation exhibits a multiple-step feature. Complete homogeneity is achieved by annealing at 1273 K for 72 h, which produces a sharp, single-step martensitic transformation. The microstructural evolution and the valence electron concentrations of alloys（e/a ratio） are evaluated, which are reflective of the degree of compositional homogeneity of alloys, confirming that high annealing temperature and long holding time are vital to reveal the intrinsic martensitic behavior of this alloy. The adequately homogenized alloy displays a martensitic transformation at 292 K and an enthalpy of 11.2 J/g.

Effect of annealing temperature on martensitic transformation of Ti_(49.2)Ni_(50.8) alloy processed by equal channel angular pressing

The effect of annealing temperature on the martensitic transformation of a Ti49.2Ni50.8 alloy processed by equal channel angular pressing （ECAP） was investigated by X-ray diffraction （XRD）, transmission electron microscopy （TEM） and differential scanning calorimetry （DSC）. The as-ECAP processed and subsequently annealed Ti49.2Ni50.8 alloys consist of B2 parent phase, Ti4Ni2O phase and B19′ martensite at room temperature. Upon cooling, all samples show B2→R→B19′ two-stage transformation. Upon heating, when the annealing temperature is less than 400℃, the samples show B19′→R→B2 two-stage transformation; when the annealing temperature is higher than 500 ℃, the samples show B19′→B2 single-stage transformation. The B2-R transformation is characterized by wide interval due to the dislocations introduced during ECAP.