Interplay of martensitic phase transformation and plastic slip in polycrystals

Inspired by key experimental and analytical results regarding Shape Memory Alloys (SMAs), we propose a modelling framework to explore the interplay between martensitic phase transformations and plastic slip in polycrystalline materials, with an eye towards computational efficiency. The resulting framework uses a convexified potential for the internal energy density to capture the stored energy associated with transformation at the meso-scale, and introduces kinetic potentials to govern the evolution of transformation and plastic slip. The framework is novel in the way it treats plasticity on par with transformation.

We implement the framework in the setting of anti-plane shear, using a staggered implicit/explict update: we first use a Fast-Fourier Transform (FFT) solver based on an Augmented Lagrangian formulation to implicitly solve for the full-field displacements of a simulated polycrystal, then explicitly update the volume fraction of martensite and plastic slip using their respective stick-slip type kinetic laws. We observe that, even in this simple setting with an idealized material comprising four martensitic variants and four slip systems, the model recovers a rich variety of SMA type behaviors. We use this model to gain insight into the isothermal behavior of stress-stabilized martensite, looking at the effects of the relative plastic yield strength, the memory of deformation history under non-proportional loading, and several others.

We extend the framework to the generalized 3-D setting, for which the convexified potential is a lower bound on the actual internal energy, and show that the fully implicit discrete time formulation of the framework is governed by a variational principle for mechanical equilibrium. We further propose an extension of the method to finite deformations via an exponential mapping. We implement the generalized framework using an existing Optimal Transport Mesh-free (OTM) solver. We then model the $\alpha$--$\gamma$ and $\alpha$--$\varepsilon$ transformations in pure iron, with an initial attempt in the latter to account for twinning in the parent phase. We demonstrate the scalability of the framework to large scale computing by simulating Taylor impact experiments, observing nearly linear (ideal) speed-up through 256 MPI tasks. Finally, we present preliminary results of a simulated Split-Hopkinson Pressure Bar (SHPB) experiment using the $\alpha$--$\varepsilon$ model.

Solid particle erosion of boronized steels

Boronizing is a thermochemical diffusion-based process for producing iron boride layers in the surface of steel components. The boride layer is wear resistant and is very hard. Large residual stresses are found to exist in the surface layers, which are a function of substrate steel composition and heat treatment. By slow cooling from the boronizing temperature (900°C), a large compressive stress is developed in the boride layer. Hardening the steel by rapid cooling, either directly from the boronizing treatment or after subsequent austenitizing, develops tension in the coating which causes it to fracture. Tempering of the martensite produces compression in the coating, closing but not welding the cracks. The results of solid particle erosion experiments using silicon carbide, quartz, and glass bead erodents on boronized steels are presented.

The microstructure and mechanical properties of ball-milled stainless steel powder: The effect of hot-pressing vs. laser sintering

The microstructure and mechanical properties of sintered stainless steel powder, of composition AISI 420, have been measured. Ball-milled powder comprising nanoscale grains was sintered to bulk specimens by two alternative routes: hot-pressing and microlaser sintering. The laser-sintered alloy has a porosity of 6% and comprises a mixture of delta ferrite and tempered martensite, and the relative volume fraction varies along the axis of the specimen due to a thermal cycle that evolves with progressive deposition. In contrast, the hot-pressed alloy has a porosity of 0.7% and exhibits a martensitic lath structure with carbide particles at the boundaries of the prior austenite grains. These differences in microstructure lead to significant differences in mechanical properties. For example, the uniaxial tensile strength of the hot-pressed material is one-half of its compressive strength, due to void initiation at the carbide particles at the prior austenite grain boundaries. Nanoindentation measurements reveal a size effect in hardness and also reveal the sensitivity of hardness to the presence of mechanical polishing and electropolishing. © 2011 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Formation of Fe-N films containing Fe6N2 phase by ion beam assisted deposition

Fe-N films were deposited on Si(100) and GaAs(100) substrates at room temperature by ion beam assisted deposition under various N/ Fe atomic arrival ratio, 0.09, 0.12, 0.15. The results of X-ray diffraction indicated that the film deposited at 0.12 of N/Fe arrival ratio contained a considerable fraction of the Fe16N2 phase which had grown predominantly in the [001] orientation. For the larger N/Fe arrival ratio, a martensite phase with 15 at.% nitrogen was obtained. It was found that a lower deposition temperature (<200 degrees C) was necessary for the formation of the Fe16N2 phase.

Nitride-strengthened reduced activation ferritic/martensitic steels

Two nitride-strengthened reduced activation ferritic/martensitic (RAFM) steels with different Mn contents were investigated. The experimental steels were designed based on the chemical composition of Eurofer 97 steel but the C content was reduced to an extremely low level. Microstructure observation and hardness tests showed that the steel with low Mn content (0.47 wt.%) could not obtain a full martensitic microstructure due to the inevitable δ-ferrite independent of cooling rate after soaking. This steel showed similar room temperature strength and higher strength at 600 °C, but lower impact toughness, compared with Eurofer 97 steel. Fractography of the Charpy impact specimen revealed that the low room temperature toughness should be related to the Ta-rich inclusions initiating the cleavage fracture. The larger amount of V-rich nitrides and more dissolved Cr in the matrix could be responsible for the strength being similar to Eurofer 97 steel. In the second steel developed from the first steel by increasing the Mn content from 0.47 wt.% to 3.73 wt.%, a microstructure of full martensite could be obtained.

Effect of Carbon Reduction on the Toughness of 9CrWVTaN Steels

Nitride-strengthened, reduced activation, martensitic steel is anticipated to have higher creep strength because of the remarkable thermal stability of nitrides. Two nitride-strengthened, reduced activation martensitic steels with different carbon contents were prepared to investigate the microstructure and mechanical property changes with decreasing carbon content. It has been found that both steels had the microstructure of full martensite with fine nitrides dispersed homogeneously in the matrix and displayed extremely high strength but poor toughness. Compared with the steel with low carbon content (0.005 pct in wt pct), the steel with high carbon content (0.012 pct in wt pct) had not only the higher strength but also the higher impact toughness and grain coarsening temperature, which was related to the carbon content. On the one hand, carbon reduction led to Ta-rich inclusions; on the other hand, the grain grew larger when normalized at high temperature because of the absence of Ta carbonitrides, which would decrease impact toughness. The complicated Al2O3 inclusions in the two steels have been revealed to be responsible for the initiated cleavage fracture by acting as the critical cracks.

Hot deformation characteristics of a nitride strengthened martensitic heat resistant steel

Constitutive equations including an Arrhenius term have been applied to analyze the hot deformation behavior of a nitride-strengthened (NS) martensitic heat resistant steel in temperature range of 900–1200 °C and strain rate range of 0.001–10 /s. On the basis of analysis of the deformation data, the stress–strain curves up to the peak were divided into four regions, in sequence, representing four processes, namely hardening, dynamic recovery (DRV), dynamic strain induced transformation (DSIT), and dynamic recrystallization (DRX), according to the inflection points in ∂θ/∂σ∂θ/∂σ and ∂(∂θ/∂σ)/∂σ∂(∂θ/∂σ)/∂σ curves. Some of the inflection points have their own meanings. For examples, the minimum of ∂θ/∂σ∂θ/∂σ locates the start of DRV and the maximum of it indicates the start of DRX. The results also showed that the critical strain of DRX was sensitive to ln(Z) below 40, while the critical stress of DRX was sensitive to it above 40. The final microstructures under different deformation conditions were analyzed in terms of softening processes including DRV, DRX, metadynamic crystallization (MDRX) and DSIT.

Analysis of deformation behavior and workability of advanced 9Cr-Nb-V ferritic heat resistant steels

Hot compression tests were carried out on 9Cr–Nb–V heat resistant steels in the temperature range of 600–1200 °C and the strain rate range of 10−2–100 s−1 to study their deformation characteristics. The full recrystallization temperature and the carbon-free bainite phase transformation temperature were determined by the slope-change points in the curve of mean flow stress versus the inverse of temperature. The parameters of the constitutive equation for the experimental steels were calculated, including the stress exponent and the activation energy. The lower carbon content in steel would increase the fraction of precipitates by increasing the volume of dynamic strain-induced (DSIT) ferrite during deformation. The ln(εc) versus ln(Z) and the ln(σc) versus ln(Z) plots for both steels have similar trends. The efficiency of power dissipation maps with instability maps merged together show excellent workability from the strain of 0.05 to 0.6. The microstructure of the experimental steels was fully recrystallized upon deformation at low Z value owing to the dynamic recrystallization (DRX), and exhibited a necklace structure under the condition of 1050 °C/0.1 s−1 due to the suppression of the secondary flow of DRX. However, there were barely any DRX grains but elongated pancake grains under the condition of 1000 °C/1 s−1 because of the suppression of the metadynamic recrystallization (MDRX).

Constitutive modeling, microstructure evolution, and processing map for a nitride-strengthened heat-resistant steel

A constitutive equation was established to describe the deformation behavior of a nitride-strengthened (NS) steel through isothermal compression simulation test. All the parameters in the constitutive equation including the constant and the activation energy were precisely calculated for the NS steel. The result also showed that from the stress-strain curves, there existed two different linear relationships between critical stress and critical strain in the NS steel due to the augmentation of auxiliary softening effect of the dynamic strain-induced transformation. In the calculation of processing maps, with the change of Zener-Hollomon value, three domains of different levels of workability were found, namely excellent workability region with equiaxed-grain microstructure, good workability region with “stripe” microstructure, and the poor workability region with martensitic-ferritic blend microstructure. With the increase of strain, the poor workability region first expanded, then shrank to barely existing, but appeared again at the strain of 0.6.

Microstructure, mechanical properties and fractography of heat-treated manganese steel

A Fe-8.46%Mn-0.24%Nb-0.038%C (wt.%) manganese steel was investigated. The steel has a 100% bcc structure after heat treatment at 850°C for 1.5 h, water quenching or air cooling. Martensite interlocked microstructure consisting of fine martensite plates/needles with different spatial orientations was found. Austenite forms, in small amounts, after a 600°C reheating treatment. Scanning electron microscopy images and energy dispersive spectrometry of the fracture surfaces revealed both ductile and brittle types of failure and precipitates. Deep quenching after the heat treatments does not change the phase composition or the hardness. NbC is formed in the steel, in high number densities. It plays a role in the impact fracture process, by acting as void nucleation sites, facilitating ductile fracture with dimples appearing on the fracture surface.

Microstructural evolution and mechanical properties of short-term thermally exposed 9/12Cr heat-resistant steels

The microstructural evolution during short-term (up to 3000 hours) thermal exposure of three 9/12Cr heat-resistant steels was studied, as well as the mechanical properties after exposure. The tempered martensitic lath structure, as well as the precipitation of carbide and MX type carbonitrides in the steel matrix, was stable after 3000 hours of exposure at 873 K (600 °C). A microstructure observation showed that during the short-term thermal exposure process, the change of mechanical properties was caused mainly by the formation and growth of Laves-phase precipitates in the steels. On thermal exposure, with an increase of cobalt and tungsten contents, cobalt could promote the segregation of tungsten along the martensite lath to form Laves phase, and a large size and high density of Laves-phase precipitates along the grain boundaries could lead to the brittle intergranular fracture of the steels.

The impact toughness of a nitride-strengthened martensitic heat resistant steel

The nitride-strengthened martensitic heat resistant steel is precipitation strengthened only by nitrides. In the present work, the effect of nitride precipitation behavior on the impact toughness of an experimental steel was investigated. Nitrides could hardly be observed when the steel was tempered at 650°C. When the tempering temperature was increased to 700°C and 750°C, a large amount of nitrides were observed in the matrix. It was surprising to reveal that the impact energy of the half-size samples greatly increased from several Joules to nearly a hundred Joules. The ductile-brittle transition temperature (DBTT) was also discovered to decrease from room temperature to −50°C when the tempering temperature was increased from 650°C to 750°C. The nitride precipitation with increasing tempering temperature was revealed to be responsible for the improved impact toughness.

Martensitic transitions and the nature of ferromagnetism in the austenitic and martensitic states of Ni-Mn-Sn alloys

Structural and magnetic transformations in the Heusler-based system Ni0.50Mn0.50¿xSnx are studied by x-ray diffraction, optical microscopy, differential scanning calorimetry, and magnetization. The structural transformations are of austenitic-martensitic character. The austenite state has an L21 structure, whereas the structures of the martensite can be 10M , 14M , or L10 depending on the Sn composition. For samples that undergo martensitic transformations below and around room temperature, it is observed that the magnetic exchange in both parent and product phases is ferromagnetic, but the ferromagnetic exchange, characteristic of each phase, is found to be of different strength. This gives rise to different Curie temperatures for the austenitic and martensitic states.

Microstructure and magnetic properties of Ni50 Mn37 Sn13 Heusler alloy ribbons

The Heusler alloy Ni50 Mn37 Sn13 was successfully produced as ribbon flakes of thickness around 7-10 μm melt spinning. Fracture cross section micrographs in the ribbon show the formation of a microcrystalline columnarlike microstructure, with their longer axes perpendicular to the ribbon plane. Phase transition temperatures of the martensite-austenite transformation were found to be MS =218 K, Mf =207 K, AS =224 K, and Af =232 K; the thermal hysteresis of the transformation is 15 K. Ferromagnetic L 21 bcc austenite phase shows a Curie point of 313 K, with cell parameter a=0.5971 (5) nm at 298 K, transforming into a modulated 7M orthorhombic martensite with a=0.6121 (7) nm, b=0.6058 (8) nm, and c=0.5660 (2) nm, at 150 K

Experimental and computational investigation of the roll forming process

One of the first questions to consider when designing a new roll forming line is the number of forming steps required to produce a profile. The number depends on material properties, the cross-section geometry and tolerance requirements, but the tool designer also wants to minimize the number of forming steps in order to reduce the investment costs for the customer. There are several computer aided engineering systems on the market that can assist the tool designing process. These include more or less simple formulas to predict deformation during forming as well as the number of forming steps. In recent years it has also become possible to use finite element analysis for the design of roll forming processes. The objective of the work presented in this thesis was to answer the following question: How should the roll forming process be designed for complex geometries and/or high strength steels? The work approach included both literature studies as well as experimental and modelling work. The experimental part gave direct insight into the process and was also used to develop and validate models of the process. Starting with simple geometries and standard steels the work progressed to more complex profiles of variable depth and width, made of high strength steels. The results obtained are published in seven papers appended to this thesis. In the first study (see paper 1) a finite element model for investigating the roll forming of a U-profile was built. It was used to investigate the effect on longitudinal peak membrane strain and deformation length when yield strength increases, see paper 2 and 3. The simulations showed that the peak strain decreases whereas the deformation length increases when the yield strength increases. The studies described in paper 4 and 5 measured roll load, roll torque, springback and strain history during the U-profile forming process. The measurement results were used to validate the finite element model in paper 1. The results presented in paper 6 shows that the formability of stainless steel (e.g. AISI 301), that in the cold rolled condition has a large martensite fraction, can be substantially increased by heating the bending zone. The heated area will then become austenitic and ductile before the roll forming. Thanks to the phenomenon of strain induced martensite formation, the steel will regain the martensite content and its strength during the subsequent plastic straining. Finally, a new tooling concept for profiles with variable cross-sections is presented in paper 7. The overall conclusions of the present work are that today, it is possible to successfully develop profiles of complex geometries (3D roll forming) in high strength steels and that finite element simulation can be a useful tool in the design of the roll forming process.