Theoretical study on nanoindentation hardness measurement of a particle embedded in a matrix

The finite element method was used to simulate indentation tests on a particle embedded in a matrix, to investigate the influence of the properties of the particle and the matrix, and the indentation depth on the measured hardness. The particle’s work-hardening exponent and the mismatch in particle and matrix yield strength have a significant influence on the measured hardness. A particle-dominated indentation depth was identified, within which the measured nanoindentation hardness agrees very well with the true hardness of the particle material. Numerical results from the simulations of a wide range of material properties determined that the measured hardness is within 5% difference of the particle’s true hardness when the indentation depth is less than 13.5% of the particle’s radius. The results can be used in practice as a guideline to measure the hardness of a particle embedded in a matrix and provides the theoretical basis to develop a particle-embedded method to measure the hardness of individual particles.     

Resonant ultrasound spectroscopy – a tool to probe magneto-elastic properties of ferromagnetic shape memory alloys

Resonant ultrasound spectroscopy (RUS) was used to investigate the changes of elastic properties induced by magnetic field in magnetic shape memory alloys Ni-Mn-Ga and Co-Ni-Al. In contrast to large magneto-elastic response of Ni₂MnGa austenite, there is only very weak response of Co-Ni-Al. This indicates that the austenite phase of Ni-Mn-Ga can have a privileged position and this may be a reason for the existence of magnetic shape memory effect. In contrast to austenite, the magneto-elastic response in Ni-Mn-Ga martensite is very small with large damping due to existence of twin boundaries. The measurement showed that RUS can be a powerful method to probe magneto-elastic properties of shape memory alloys.     

Alternate stresses and temperature variation as factors of influence of ultrasonic vibration on mechanical and functional properties of shape memory alloys

It is known that the main factors in a variation in the shape memory alloy properties under insonation are heating of the material and alternate stresses action. In the present work the experimental study of the mechanical behaviour and functional properties of shape memory alloy under the action of alternate stresses and varying temperature was carried out. The data obtained had demonstrated that an increase in temperature of the sample resulted in a decrease or increase in deformation stress depending on the structural state of the TiNi sample. It was shown that in the case of the alloy in the martensitic state, a decrease in stress was observed, and on the other hand, in the austenitic state an increase in stress took place. It was found that action of alternate stresses led to appearance of strain jumps on the strain–temperature curves during cooling and heating the sample through the temperature range of martensitic transformation under the constant stress. The value of the strain jumps depended on the amplitude of alternate stresses and the completeness of martensitic transformation. It was shown that the heat action of ultrasonic vibration to the mechanical behaviour of shape memory alloys was due to the non-monotonic dependence of yield stress on the temperature. The force action of ultrasonic vibration to the functional properties was caused by formation of additional oriented martensite.     

Analysis of the substrate effects of strain-hardening thin films on silicon under nanoindentation

Mechanical properties of thin films on substrates can be evaluated directly through nanoindentation. For a comprehensive study, thin films should be characterized via Young’s modulus, yield stress and strain-hardening exponent at constant temperature. In this paper, we evaluate these effects of thin films on silicon substrate through finite element analysis. Thin films, from soft to hard relative to the silicon substrate, are investigated in three categories: soft films on hard substrates, soft to hard films on no elastic mismatch substrates, and hard films on soft substrates. In addition to examining the load-displacement curve, the normalized hardness versus normalized indentation depth is checked as well to characterize its substrate effect. We found that the intrinsic film hardness can be acquired with indentation depths of less than 12% and 20% of their film thickness for soft films on hard substrates and for soft to hard films on no elastic mismatch substrates, respectively. Nevertheless, nanoindentation of hard films on soft substrates cannot determine the intrinsic film hardness due to the fact that a soft substrate cannot support a hard film. By examining the von Mises stresses, we discovered a significant bending phenomenon in the hard film on the soft substrate. PACS 61.43.Bn; 62.20.-x; 68.03.Hj; 68.05.Cf; 68.08.De     

Softening micromechanical constitutive model of stress induced martensite transformation for NiTi single crystal shape memory alloy

Based on the assumption of laminated microstructure, a micromechanical model of stress induced martensite transformation for NiTi shape memory alloys single crystal is proposed. Elasticity anisotropy and different proper-ties for two phases are considered. Martensite volume fraction is chosen as the internal variable that controls the phase transformation quantitatively. An effective macroscopic elasticity matrix based on the different elasticity characteristics of each phase and the martensite volume fraction are obtained with the help of the perfect interfa-cial relationships. A phase transformation driving force is derived to construct the transformation criterion. The model corresponds to a non-convexity free energy function during phase transformation, so softening behavior can be well simulated by the model. A numerical simulation is implemented for the uniaxial loading of NiTi single crystal alloy according to the model, and simulation results are proved by experimental results of polycrystal with strong {111} texture. Superelasticity, Anisotropy, the evolution of microstructure and softening behavior can be well simulated.     

Numerical simulation of flat-tip micro-indentation of glassy polymers: Influence of loading speed and thermodynamic state

Flat-tip micro-indentation tests were performed on quenched and annealed polymer glasses at various loading speeds. The results were analyzed using an elasto-viscoplastic constitutive model that captures the intrinsic deformation characteristics of a polymer glass: a strain-rate dependent yield stress, strain softening and strain hardening. The advantage of this model is that changes in yield stress due to physical aging are captured in a single parameter. The two materials studied (polycarbonate (PC) and poly(methyl methacrylate) (PMMA)) were both selected for the specific rate-dependence of the yield stress that they display at room temperature. Within the range of strain rates experimentally covered, the yield stress of PC increases linearly with the logarithm of strain rate, whereas, for PMMA, a characteristic change in slope can be observed at higher strain rates. We demonstrate that, given the proper definition of the viscosity function, the flat-tip indentation response at different indentation speeds can be described accurately for both materials. Moreover, it is shown that the model captures the mechanical response on the microscopic scale (indentation) as well as on the macroscopic scale with the same parameter set. This offers promising possibilities of extracting mechanical properties of polymer glasses directly from indentation experiments.     

Mechanism of the shape memory effect in martensitic alloys: an assessment

The (one-way) shape memory effect is a phenomenon that when a martensitic alloy is deformed in a martensitic state it recovers its original shape upon heating to the parent phase. This is a universal effect for certain martensitic alloys. We will assess the mechanism of the effect critically and select the essential factors which govern the effect. We try to understand it from a unified view, invoking the group–subgroup symmetry relation between the parent and martensite phase, along with analysis of reversible twinning modes in martensite. By such an assessment, we will show why typical shape memory alloys, such as Ti–Ni, Cu–Al–Ni etc., exhibit good shape memory characteristics, while others, such as ferrous alloys, do not. Thus, we will show that most of the shape memory characteristics of various martensitic alloys can be understood consistently from such an approach.     

On the uniqueness and sensitivity issues in determining the elastic and plastic properties of power-law hardening materials through sharp and spherical indentation

A systematic study of the uniqueness, reversibility and sensitivity issues associated with seven indentation-based methods of property extraction demonstrates that: (i) The indentation algorithms generally identify the elastic and plastic properties of materials uniquely for most materials. (ii) The indentation forward algorithms (wherein the indention responses are determined from the elastic and plastic properties of the indented materials) and the reverse algorithms (wherein the elastic and the plastic properties of materials are extracted from the indentation responses) are distinct for each indentation method and are internally consistent in that the differences in the elastic and plastic properties determined through the reverse analysis and the ‘true’ material properties are generally small for a large number of materials, for each of the seven methods. (iii) While the differences in the indentation response parameters predicted by each of the seven indentation methods (for a particular material) could be small, there could be considerable dispersion in the elastic and plastic properties predicted by the reverse algorithms of the seven methods (for a particular set of indentation response parameters). (iv) In the forward analysis, small uncertainties in the elasto-plastic properties lead to small uncertainties in the predictions of the indentation response of materials. The sensitivity distribution is generally heterogeneous and symmetric across positive and negative variations in the material elasto-plastic properties. (v) In the reverse analysis, the elastic modulus exhibits low sensitivity, while the yield strength and the strain-hardening exponent generally exhibit high sensitivity to uncertainties in the indentation response parameters. The sensitivity distribution is heterogeneous and asymmetric across positive and negative variations in the indentation response parameters. (vi) The representative stresses are fairly robust to uncertainties in the indentation response parameters. Consequently, dual sharp and spherical indentation methods, which identify multiple representative stresses, exhibit reduced sensitivity in the determination of the plastic properties.     

Identification of epsilon martensite in a Fe-based shape memory alloy by means of EBSD

Ferrous shape memory alloys (SMAs) are often thought to become a new, important group of SMAs. The shape memory effect in these alloys is based on the reversible, stress-induced martensitic transformation of austenite to epsilon martensite. The identification and quantification of epsilon martensite is crucial when evaluating the shape memory behaviour of this material. Previous work displayed that promising results were obtained when studying the evolution of the amount of epsilon martensite after different processing steps with Electron BackScatter Diffraction (EBSD). The present work will discuss in detail, on the one hand, the challenges and opportunities arising during the identification of epsilon martensite by means of EBSD and, on the other hand, the possible interpretations that might be given to these findings. It will be illustrated that although the specific nature of the austenite to epsilon martensite transformation can still cause some points of discussion, EBSD has a high potential for identifying epsilon martensite.     

Reversible and irreversible martensitic transformations in Fe-Pd and Fe-Pd-Co alloys

Ferromagnetic Fe-Pd shape memory alloys (SMA) undergo a martensitic phase transformation during cooling from a parent FCC phase to a tetragonal FCT martensite. This transformation is thermoelastic and reversible giving rise to the shape memory effect. On further cooling an irreversible FCT to BCT transformation occurs that makes impossible the memory effect. Nevertheless, the transformation from reversible to irreversible phase has been not complete since a volume fraction of reversible phase in the alloy is retained even after cooling below the temperature of appearance of the irreversible phase. The addition of Co lowers the temperature of the reversible and irreversible phase transformations but also reduces the amount of transformed irreversible martensite after cooling to 10 K.     

Mechanical Characterization of Protein Crystals

The mechanical properties (critical stress intensity factor, hardness and Young's modulus) of 4 crystalline materials (two proteins, lysozyme and glucose isomerase and two non‐proteins, glutamic acid and potassium sulphate) were measured with an indentation technique. It was found that the mechanical properties of lysozyme crystals depend on their state – dried, partly dried and moisture saturated – and their surroundings. The hardness, Young's modulus and the critical stress intensity factor of lysozyme crystals were observed to be much lower than those for the tested non‐proteins, leading to the conclusion that crystalline lysozyme is comparatively more fragile and softer. In combination the mechanical properties of lysozyme and the non‐proteins indicated that these materials were fairly brittle. Mechanical properties for crystals of the other protein, glucose isomerase, could not be quantified by indentation. However, qualitatively crystalline glucose isomerase was found to be more ductile and less fragile than crystalline lysozyme. The experimental findings were interpreted in terms of relative susceptibility to attrition and secondary nucleation in stirred industrial crystallizers.     

Electronic structures and magnetisms of the Co_2TiSb_(1-x)Sn_x(x= 0, 0.25, 0.5) Heusler alloys: A theoretical study of the shape-memory behavior

The total energy, electronic structures, and magnetisms of the Al Cu2Mn-type Co2TiSb1-xSnx(x = 0, 0.25, 0.5) with the different lattice parameter ratios of c/a are studied by using the first-principles calculations. It is found that the phase transformation from the cubic to the tetragonal structure lowers the total energy, indicating that the martensitic phase is more stable and that a phase transition from austenite to martensite may happen at a lower temperature. Thus, a ferromagnetic shape memory effect can be expected to occur in these alloys. The Al Cu2Mn-type Co2TiSb1-xSnx(x = 0, 0.25, 0.5) alloys are weak ferrimagnets in the austenitic phase and martensitic phase.     

Crystallographic patterns of the shape memory effect in non-ordered solid solutions

A method is proposed to estimate the possibility of achieving shape memory effects in martensite alloys with disordered lattices. The analysis of orientational relationships between the lattices of austenite and martensite allows one to detect those which are able to form self-accommodation complexes, an important part of the memory effect mechanism. This method has been applied to the Ti₄₈Zr₄₈Nb₄ alloy in which two martensite phases are formed: hexagonal α′ and orthorhombic α″ martensites.     

Ginzburg-Landau theory and solitary waves in shape-memory alloys

A one-dimensional dynamic Ginzburg-Landau theory of the martensitic phase transition in shape-memory alloys is established. The nonlinear equations of motion yield solitary wave solutions of kink and of soliton type. The kink solutions which cannot move without external force represent single domain walls either between austenite and martensite or between two martensite variants. The soliton solutions correspond to a matrix of austenite or of martensite containing a moving sheet of the other phase. The velocity of the solitons depends on their amplitude. In the static case they reduce to the critical nucleus. The energy of each type of solitary waves is calculated.     

The ALICE experiment at the LHC

A free-energy function is constructed, which couples strain and magnetic moments in ferromagnetic shape memory alloys. The associated Gibbs function is used to calculate time-dependent transition probabilities between martensite variants in a magnetic field under applied stress. By keeping track of the variant fractions, the evolution of strain and magnetization is determined. The simulation model is built in a finite element program for structural analysis, in order to simulate magnetic field-dependent strain and magnetization characteristics of a test actuator. The influence of material parameters and sample geometry is discussed.     

Shape memory effect and superelasticity in a strain glass alloy

The shape memory effect and superelasticity are usually found in alloys exhibiting spontaneous martensitic transformation. Thus it is hard to imagine that such interesting effects can appear in a system without a martensitic transformation. In this Letter we show shape memory and the superelasticity effect in a nonmartensitic Ti48.5Ni51.5 alloy, which has no martensitic transformation but undergoes a "strain glass" transition. In situ x-ray diffraction experiment showed that the shape memory and superelasticity in strain glass stem from a stress-induced strain glass to martensite transformation and its reverse transformation. The new shape memory and superelasticity in strain glass extends the regime of the shape memory effect and superelasticity and may lead to novel applications.     

Rapidly solidified ferromagnetic shape memory alloys

Ferromagnetic shape memory alloys have been manufactured by various techniques involving rapid solidification. Bulk alloys have been obtained by extracting the melted alloy in especially designed copper molds; glass coated wires have been obtained by drawing the melt from glass recipients followed by water cooling and ribbons have been fabricated by melt-spinning. Microstructural observations show particular solidification aspects of fractured areas, while ferromagnetic behavior has been detected in glass coated wires obtained by rapid solidification. The martensitic microstructure was observed on Co-Ni-Ga rapid solidified bulk alloys and Fe-Pd ribbons. The memory effect was detected using a Vibran system that allows the detection of the phase transition for the ribbons and by visual observation for other specimens. The conclusions of the observations are related to the comparison between the ferromagnetic behaviors of shape memory alloys solidified using different techniques.     

Magnetic glass in shape memory alloy: Ni(45)Co(5)Mn(38)Sn(12)

The first order martensitic transition in the ferromagnetic shape memory alloy Ni(45)Co(5)Mn(38)Sn(12) is also a magnetic transition and has a large field induced effect. While cooling in the presence of a field this first order magnetic martensite transition is kinetically arrested. Depending on the cooling field, a fraction of the arrested ferromagnetic austenite phase persists down to the lowest temperature as a magnetic glassy state, similar to the one observed in various intermetallic alloys and in half doped manganites. A detailed investigation of this first order ferromagnetic austenite (FM-A) to low magnetization martensite (LM-M) state transition as a function of temperature and field has been carried out by magnetization measurements. Extensive cooling and heating in unequal field (CHUF) measurements and a novel field cooled protocol for isothermal MH measurements (FC-MH) are utilized to investigate the glass like arrested states and show a reverse martensite transition. Finally, we determine a field-temperature (HT) phase diagram of Ni(45)Co(5)Mn(38)Sn(12) from various magnetization measurements which brings out the regions where thermodynamic and metastable states coexist in the HT space, clearly depicting this system as a 'magnetic glass'.