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• 1.
KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering.
KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering. KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering. KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering.
Modelling of prismatic grain growth in cemented carbides2019In: INTERNATIONAL JOURNAL OF REFRACTORY METALS & HARD MATERIALS, ISSN 0263-4368, Vol. 78, p. 310-319Article in journal (Refereed)

A mean-field model dealing with prismatic grain growth during liquid phase sintering of cemented carbides with a Co-rich binder is presented. The evolution of the size of an assembly of non-spherical grains is obtained using a Kampmann-Wagner approach and by introducing a constant shape factor between the characteristic lengths of prisms. This factor is a function of interfacial energies of the two kind of facets, basal and prismatic, considered. The growth model is based on three different mechanisms, that can be rate limiting, taking place in series: 2D nucleation of a new atomic layer, mass transfer across the interface and long-range diffusion. The driving force for coarsening is distributed between the different facets. These equations are solved numerically, and the simulation results reveal that the specific abnormal grain growth phenomena experimentally observed in cemented carbides may be reproduced with this new more realistic description of the grain shape contrary to the spherical approach developed in the past. It is also shown that the initial powder size distribution, and more specifically its shape has a strong influence on the distribution of the driving force between the different rate limiting mechanisms and thus on the occurrence of abnormal grain growth. In that case, the self-similarity of the normalized grain size distribution over time is not achieved.

• 2.
KTH, Superseded Departments, Materials Science and Engineering.
Nucleation and growth of martensite in steel1997Doctoral thesis, comprehensive summary (Other scientific)
• 3.
KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Physical Metallurgy.
KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Physical Metallurgy.
Eutectoids with cementite as the major constituent in Fe-C-M alloys2016In: Acta Materialia, ISSN 1359-6454, E-ISSN 1873-2453, Vol. 103, p. 280-289Article in journal (Refereed)

The addition of a third element to hypereutectoid Fe-C alloys may cause inclusions of a minor constituent in the precipitate of cementite from austenite even if the initial austenite is supersaturated only with cementite. Cementite will often become the major constituent of this kind of microstructure. For Fe-C-Cu alloys this has been explained as the result of precipitation from supersaturated cementite. An alternative mechanism could be that the mixture of cementite and a minor constituent forms by simultaneous and cooperative growth of the two phases, i.e., by a reaction that may be regarded as eutectoid. This mechanism has already been applied to explain the occurrence of eutectoid colonies with cementite as the major constituent and a minor constituent for which there was no supersaturation initially. This phenomenon has been observed in hypereutectoid ternary Fe-C alloys with Al, Mn or Si. The necessary requirements on the ordinary isothermal phase diagram are now examined with a graphical method based on the slopes of tie-lines. It predicts the phenomenon in all cases where it has been observed, including Fe-C-Cu and not in the Fe-C-Ni and Fe-C-Cr systems where it has not been observed. The requirements become more evident when the calculated phase equilibria are plotted as an isothermal phase diagram with the alloy content as a function of the carbon activity instead of carbon content. Finally, a comparison is made with bainite in Fe-C alloys where ferrite is the major and cementite the minor constituent. The same two explanations have been proposed for that case.

• 4.
KTH, Superseded Departments, Materials Science and Engineering.
KTH, Superseded Departments, Materials Science and Engineering. KTH, Superseded Departments, Metallurgy.
DICTRA, a tool for simulation of diffusional transformations in alloys2000In: Journal of phase equilibria (Print), ISSN 1054-9714, E-ISSN 1544-1032, Vol. 21, no 3, p. 269-280Article in journal (Refereed)

In the present paper, a general survey of the diffusion-controlled transformations (DICTRA) software is given. DICTRA is an engineering tool for diffusion simulations in multicomponent alloys. The simulations are based on multicomponent diffusion and thermodynamic data, both obtained by analyzing and assessing experimental information. This allows for many different cases to be studied as soon as the underlying data are available. DICTRA is not a complete simulation tool because only geometries that can be transformed into one space variable can be treated, but many well posed problems of practical interest may be solved. The program contains several different models, which are discussed in the present paper. Each model has its own applications and several examples from recent simulations are given in order to demonstrate the usage of the particular models.

• 5.
KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering.
KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering.
Determination of the critical carbon content for growth of acicular ferrite2005In: Solid-Solid Phase Transformations in Inorganic Materials 2005, Vol 1 / [ed] Howe, JM; Laughlin, DE; Lee, JK; Dahmen, U; Soffa, WA, 2005, p. 105-110Conference paper (Refereed)

The critical carbon content for growth of acicular ferrite has been determined in Fe-Ni-C alloys by using a gradient technique. A carbon gradient has been introduced in binary Fe-Ni alloys which are subsequently heat treated isothermally. The carbon content. at the position where acicular ferrite stops growing, is determined by EMPA (Electron Microprobe Analysis) and microstructural examination with LOM (Light Optical Microscopy). At low Ni contents the experimentally determined values for the critical carbon content can be understood from the hypothesis that the growth of acicular ferrite is controlled by carbon diffusion under paraequilibrium conditions and modified with an extra thermodynamic barrier.

• 6.
KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Physical Metallurgy.
KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Physical Metallurgy. KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Physical Metallurgy. KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Physical Metallurgy. KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Physical Metallurgy. KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Physical Metallurgy.
On the Symmetry Among the Diffusional Transformation Products of Austenite2011In: Metallurgical and Materials Transactions. A, ISSN 1073-5623, E-ISSN 1543-1940, Vol. 42A, no 6, p. 1558-1574Article in journal (Refereed)

Information on the diffusional transformation products of austenite in high-carbon steels is reviewed and supplemented with new microscopic studies. A comparison with transformation products in low-carbon steels indicates that there is a symmetry with pearlite in the middle, where ferrite and cementite are equal partners, and with acicular ferrite or cementite on each side. They both form with a surface relief, and at lower temperatures, each one is the leading phase in a eutectoid microstructure, bainite and inverse bainite, respectively. However, there is an asymmetry because at low temperatures bainite appears in high-carbon steels but inverse bainite never appears in low-carbon steels. At a constant high carbon content, there is another kind of symmetry, which is related to temperature. At intermediate temperatures the eutectoid reaction results in spherical nodules in which the cementite constituent originates from Widmanstatten plates. It turns spiky at both higher and lower temperatures with the leading phase in the spikes being cementite at higher temperatures and ferrite at lower temperatures. In the first kind of symmetry, there is an abrupt change among the three reaction products; in the second kind of symmetry, there is a gradual change. Accepting that all the eutectoid microstructures form by diffusion of carbon, one may explain the existence of both symmetries by the variation of the ratio of the supersaturations of ferrite and cementite with carbon content and with temperature.

• 7.
KTH, Superseded Departments, Materials Science and Engineering.
Massive transformation in the Fe-Ni system2000In: Acta Materialia, ISSN 1359-6454, E-ISSN 1873-2453, Vol. 48, no 11, p. 2765-2775Article in journal (Refereed)

The critical limit for the massive gamma-->alpha transformation in the Fe-Ni system has been measured by isothermal heat treatment of diffusion couples. The position of the alpha/gamma interface at the end of the treatment could be identified but some growth occurred during the quench. Growth is probably hindered at the beginning of the quench by a redistribution of Fe and Ni at the interface during the isothermal treatment. During the quench it often happens that the alpha/gamma interfaces develop jagged shapes and even very fine plates although there should usually be no orientation relationship. The critical limit agrees fairly well with classical results for the formation of equiaxed ferrite from continuous cooling of homogeneous specimens. At 1023 K it coincides with the alpha/alpha + gamma phase boundary. At lower temperatures it moves inside the alpha + gamma two-phase field. The driving force for the massive transformation increases at decreasing temperature and the limiting composition never approaches the T-0 line.

• 8.
KTH, Superseded Departments, Materials Science and Engineering.
Nucleation of isothermal martensite2000In: Acta Materialia, ISSN 1359-6454, E-ISSN 1873-2453, Vol. 48, no 11, p. 2777-2785Article in journal (Refereed)

Two methods of evaluating an activation energy for the nucleation of martensite from kinetic information on isothermal martensite are discussed. In both methods the nucleation is described as thermally activated growth of an embryo up to a size where rapid growth can get started. The first method is based on the absolute Value of the rate of reaction at each separate temperature and depends on the neglect of the reverse reaction. The second method is based on the temperature dependence of the rate at low temperatures and includes the reverse reaction and it typically yields a lower activation energy. It can be used to define the region of low net driving force where the reverse reaction, which is neglected in the first method, is important and that method should not be used. A unified description of the nucleation of athermal and isothermal martensite is also presented.

• 9.
KTH, Superseded Departments, Materials Science and Engineering.
KTH, Superseded Departments, Materials Science and Engineering.
Activation energy for isothermal martensite in ferrous alloys1997In: Acta Materialia, ISSN 1359-6454, E-ISSN 1873-2453, Vol. 45, no 2, p. 651-662Article in journal (Refereed)

The experimental information on isothermal α martensite in ferrous alloys is reviewed. From the kinetics one can clearly distinguish between three groups of alloys yielding isothermal martensite. The first group contains high alloy steels with a low Ms temperature. They form isothermal martensite with a temperature dependence corresponding to a very low activation energy, possibly 7 kJ/mol. The second group contains steels with an appreciable amount of carbon. Its rate of formation of isothermal martensite can be explained by assuming that it is triggered by submicroscopic plates of bainite formed with a rate controlled by carbon diffusion. The third group contains Fe---Ni alloys with up to about 25% Ni. There the temperature dependence corresponds to an activation energy of about 80 kJ/mol. It is proposed that their transformation is related to the transformation causing plateau II in experiments with very rapid cooling, a transformation which has previously been proposed to be related to the formation of bainite.

• 10.
KTH, Superseded Departments, Materials Science and Engineering.
KTH, Superseded Departments, Materials Science and Engineering.
Bainite in the light of rapid continuous cooling information1996In: Metallurgical and Materials Transactions. A, ISSN 1073-5623, E-ISSN 1543-1940, Vol. 27, no 6, p. 1501-1512Article in journal (Refereed)

Rapid continuous cooling of pure iron can produce three different transformations yielding acicular structures: Widmanstätten a, lath martensite, and lenticular martensite. The information on their extensions into binary systems with carbon, nickel, and chromium has been reviewed, and admittedly rough methods have been used for estimating growth rates in order to examine the role of diffusion. The effect of alloying elements on their plateau temperatures and growth rates indicates that Widmanstätten a in Fe-C alloys grows under conditions close to local equilibrium for carbon, and it is suggested that the same should hold for edgewise growth of bainite. In Fe-Ni alloys, there are indications that Widmanstätten α grows under a considerable solute drag, an effect which may also occur for bainite. In Fe-Cr alloys, the solute drag effect seems to be weaker but may increase with the carbon content.

• 11.
KTH, Superseded Departments, Materials Science and Engineering.
KTH, Superseded Departments, Materials Science and Engineering.
Driving force for f.c.c.→b.c.c. martensites in Fe-X alloys1997In: Acta Materialia, ISSN 1359-6454, E-ISSN 1873-2453, Vol. 45, no 5, p. 2079-2091Article in journal (Refereed)

Information on Ms, the starting temperature for formation of martensite, is reviewed and one Ms line each for lath and plate martensite are drawn in a number of Fe-X phase diagrams. A reasonable interpretation of the data indicates the possibility that the distance between the two lines may vary linearly with temperature and be independent of the choice of alloying element. Using thermodynamic descriptions of the binary systems, the driving force for the start of the formation of the two kinds of martensite is calculated from the same interpretation of data. When plotted against temperature the results indicate that the driving force for martensite may not be much affected by solution hardening but may mainly be a function of temperature. For plate martensite it may have a fairly constant value of about 2100 J/mol. For lath martensite it may vary linearly, possibly from 500 J/mol at 800°C to 2100 J/mol at 250°C.

• 12.
KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Physical Metallurgy.
KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Physical Metallurgy.
Kinetics of bainite transformation in steels2012In: Phase Transformations in Steels, Elsevier, 2012, Vol. 1, p. 468-501Chapter in book (Refereed)

The main kinetic features of the formation of bainite are discussed, firstly in relation to two incompatible hypotheses for the growth mechanism of bainitic ferrite. One is based on diffusionless growth of bainitic ferrite but diffusional growth of Widmanstätten ferrite. The other is based on the assumption that there is only one kind of acicular ferrite and it grows under simultaneous diffusion of carbon into the interior of the parent austenite. The kinetics of the first stage of bainite formation, the growth of acicular ferrite, is treated in detail because it has been subject to the more intensive research. The kinetics of the reactions by which cementite forms and the subsequent reactions, by which the transformation to bainite is completed, have been subject to less research.

• 13.
KTH, Superseded Departments, Materials Science and Engineering.
KTH, Superseded Departments, Materials Science and Engineering.
Model for nucleation of isothermal martensite2001In: Scripta Materialia, ISSN 1359-6462, E-ISSN 1872-8456, Vol. 45, no 8, p. 917-922Article in journal (Refereed)

Kaufman and Cohen's model for thermally activated growth of preexisting embroys of isothermal martensite was defined with a series of obstacles but they only considered jumps in one direction. Jumps in both directions across obstacles were recently considered and the activation energy for the net reaction was described. That nucleation model is now developed further.

• 14.
KTH, Superseded Departments, Materials Science and Engineering.
KTH, Superseded Departments, Materials Science and Engineering. KTH, Superseded Departments, Materials Science and Engineering.
Critical temperature for growth of martensite1995In: Acta Metallurgica Et Materialia, ISSN 0956-7151, Vol. 43, no 3, p. 945-954Article in journal (Refereed)

Ms may be defined as the temperature below which the formation of martensite starts upon cooling. It may also be useful to define Mg, the temperature below which martensite can grow if it is already nucleated. In order to analyze the mechanism of martensite formation, it is essential to know the difference Mg - Ms. We have tried to evaluate Mg - Ms for an Fe-C alloy with a decarburized surface zone in order to induce nucleation. The samples were studied by means of electron microprobe, serial sectioning and optical microscopy. The results indicate that Mg is surprisingly close to Ms. The possibility that Mg is controlled by growth rather than nucleation is discussed.

• 15.
KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering.
KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering. KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering.
Metallographic evidence of carbon diffusion in the growth of bainite2009In: Acta Materialia, ISSN 1359-6454, E-ISSN 1873-2453, Vol. 57, no 11, p. 3242-3252Article in journal (Refereed)

There are two paradigms regarding the formation of bainite. One is based on the first stage being rapid, diffusionless growth or acicular ferrite and the subsequent formation of carbide occurring by precipitation from the supersaturated ferrite. All assumption that the first stage occurs as a series of subsequent rapid steps resulting in sub-units plays an important role as an explanation of the not so rapid growth observed macroscopically. The other paradigm is based on the first stage being the formation of acicular ferrite under carbon diffusion and on the subsequent growth of carbide and ferrite side by side. Metallographic observations are presented that support the second paradigm. It is difficult to see how they can be accounted for by the first paradigm, in particular the observation of the shapes of sub-units.

• 16.
KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Physical Metallurgy.
KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Physical Metallurgy. KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Physical Metallurgy. KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Physical Metallurgy. KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Physical Metallurgy.
Effect of carbon activity and powder particle size on WC grain coarsening during sintering of cemented carbides2014In: International journal of refractory metals & hard materials, ISSN 0958-0611, E-ISSN 2213-3917, Vol. 42, p. 30-35Article in journal (Refereed)

Liquid-phase sintering is an important step in the production of cemented carbides. During sintering, the average WC grain size increases, leading to a coarser structure, which affects the performance of the final product. The coarsening occurs by dissolution of small grains and growth of large grains. In the present work, the effect of high carbon activity during sintering on the WC grain coarsening has been evaluated using electron backscattered diffraction (EBSD) and the results have been compared with a previous work where sintering was performed at a lower carbon activity. A more homogeneous grain size distribution was observed in alloys sintered at a high carbon activity. In addition, the effect of the initial powder particle size distribution was investigated. It was found that the coarsening rate of a WC powder with an initial small average grain size is significantly higher as compared to the coarsening rate for a powder with a larger initial average grain size. The results obtained emphasize the importance of considering the complete particle size distribution in order to predict coarsening.

• 17.
KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Physical Metallurgy.
KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Physical Metallurgy. KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Physical Metallurgy. KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Physical Metallurgy. KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Physical Metallurgy.
On the three-dimensional structure of WC grains in cemented carbides2013In: Acta Materialia, ISSN 1359-6454, E-ISSN 1873-2453, Vol. 61, no 13, p. 4726-4733Article in journal (Refereed)

In the present work, the size distribution and shape of WC grains in cemented carbides (WC-Co), with different Co contents, have been investigated in three dimensions. Direct three-dimensional (3-D) measurements, using focused ion beam serial sectioning and electron backscattered diffraction (EBSD), were performed and a 3-D microstructure was reconstructed. These measurements were supplemented by two-dimensional (2-D) EBSD and scanning electron microscopy on extracted WC grains. The data from 2-D EBSD collected on planar sections were transformed to three dimensions using a recently developed statistical method based on an iterative inverse Saltykov procedure. This stereological analysis revealed that the assumed spherical shape of WC grains during the Saltykov method is reasonable and the estimated 3-D size distribution is qualitatively in good agreement with the actual distribution measured from 3-D EBSD. Although the spherical assumption is generally fair, the WC grains have both faceted and rounded surfaces. This is a consequence of the relatively low amount of liquid phase during sintering, which makes impingements significant. Furthermore, the observed terraced surface structure of some WC grains suggests that 2-D nucleation is the chief coarsening mechanism to consider.

• 18.
KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Physical Metallurgy.
KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Physical Metallurgy. KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Physical Metallurgy. KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Physical Metallurgy. KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Physical Metallurgy.
Microstructure, grain size distribution and grain shape in WC-Co alloys sintered at different carbon activities2014In: International Journal of Refractory Metals and Hard Materials, ISSN 0958-0611, Vol. 43, p. 205-211Article in journal (Refereed)

The properties of cemented carbides strongly depend on the WC grain size and it is thus crucial to control coarsening of WC during processing. The aim of this work was to study the effect of sintering at different carbon activities on the final microstructure, as well as the coarsening behavior of the WC grains, including the size distribution and the shape of WC grains. These aspects were investigated for five WC-Co alloys sintered at 1410 C for 1 h at different carbon activities in the liquid, in the range from the graphite equilibrium (carbon activity of 1) to the eta (M6C) phase equilibrium (carbon activity of 0.33). The grain size distribution was experimentally evaluated for the different alloys using EBSD (electron backscatter diffraction). In addition, the shape of the WC grains was evaluated for the different alloys. It was found that the average WC grain size increased and the grain size distribution became slightly wider with increasing carbon activity. Comparing the two three-phase (WC-Co-eta and WC-Co-graphite) alloys a shape change of the WC grains was observed with larger grains having more planar surfaces and more triangular shape for the WC-Co-graphite alloy. It was indicated that in alloys with a relatively low volume fraction of the binder phase the WC grain shape is significantly affected by impingements. Moreover, after 1 h of sintering the WC grains are at a non-equilibrium state with regards to grain morphology.

• 19.
KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Physical Metallurgy.
KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Physical Metallurgy. KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Physical Metallurgy.
Influence of nitrogen Gas pressure on the miscibility Gap in the Ti-Zr carbonitride system2012In: International Journal of Refractory Metals and Hard Materials, ISSN 0263-4368, Vol. 32, p. 11-15Article in journal (Refereed)

The microstructure of cemented carbides with a gradient structure at the surface consists of WC, cubic carbonitrides and a binder phase. The carbonitrides can, for example, consist of Ti(C,N)-Zr(C,N) where it is reasonable to believe that there is a miscibility gap with Ti-rich and Zr-rich carbonitrides. In the present work, the effect of the N-2-gas pressure on the equilibrium composition of the miscibility gap in the (Ti,Zr)(C,N) system has been investigated. In the study, the carbonitride system is in equilibrium with: WC, liquid binder, graphite and, N-2-gas of different pressures. Both Fe and Co are used as binder phase to study the effect of the binder phase. The results verify that there is a miscibility gap in the carbonitride system and that the region of the miscibility gap will change when N is introduced. There is a critical N-2-gas pressure lower than 0.1 bar and above that pressure the compositions of the carbonitride are rather constant as a result of the formation of a surface rim.

• 20. Chen, Hao
KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Physical Metallurgy. KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Physical Metallurgy. KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Physical Metallurgy.
Application of interrupted cooling experiments to study the mechanism of bainitic ferrite formation in steels2013In: Acta Materialia, ISSN 1359-6454, E-ISSN 1873-2453, Vol. 61, no 12, p. 4512-4523Article in journal (Refereed)

New interrupted cooling experiments have been designed to study the kinetics of bainitic ferrite formation starting from a mixture of austenite and bainitic ferrite. It is found that the kinetics of bainitic ferrite formation during the cooling stage is determined by the isothermal holding time. The formation rate of bainitic ferrite at the beginning of the cooling decreases with increasing prior isothermal holding time. An unexpected stagnant stage during the cooling stage appears when the isothermal holding time increases to a critical point. There are two reasons for the occurrence of the stagnant stage: (i) a solute spike in front of the interface; and (ii) kinetic transition. A so-called Gibbs energy balance approach, in which the dissipation of Gibbs energy due to diffusion inside the interface and interface friction is assumed to be equal to the available chemical driving force, is applied to theoretically explain the stagnant stage. A kinetics transition from a fast growth mode without diffusion of Mn and Si inside the austenite-bainitic ferrite interfaces to a slow growth mode with diffusion inside the interface is predicted. The stagnant stage is caused by the transition to a slow growth mode. The Gibbs energy balance approach describes the experimental observations very well.

• 21.
KTH, Superseded Departments, Materials Science and Engineering.
KTH, Superseded Departments, Materials Science and Engineering.
Thermodynamic evaluation of the Fe-Mn-Si system and the γ/ε martensitic transformation1993In: Journal of phase equilibria (Print), ISSN 1054-9714, E-ISSN 1544-1032, Vol. 14, no 3, p. 354-363Article in journal (Refereed)

The thermodynamic properties of the Fe-Mn-Si system are analyzed by means of thermodynamic models for the individual phases. Special attention is paid to the γ → ε martensitic transition. A complete set of parameters, from which arbitrary sections of the phase diagram as well as the Ms and As temperatures may be calculated, is given.

• 22.
KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Physical Metallurgy.
KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Physical Metallurgy. KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Physical Metallurgy.
On the Three-Dimensional Microstructure of Martensite in Carbon Steels2012In: Proceedings Of The 1st International Conference On 3D Materials Science, John Wiley & Sons, 2012, p. 19-24Conference paper (Refereed)

The mechanical properties of high-performance steels are often reliant on the hard martensitic structure. It can either be the sole constituent e. g. in tool steels, or it can be part of a multi-phase structure as e. g. in dual-phase steels. It is well-known that the morphology of martensite changes from lath to plate martensite with increasing carbon content. The transition from lath to plate is however less known and in particular the three-dimensional (3D) aspects in the mixed lath and plate region require more work. Here the current view of the 3D microstructure of martensite in carbon steels is briefly reviewed and complemented by serial sectioning experiments using a focused ion beam scanning electron microscope (FIB-SEM). The large martensite units in the Fe-1.2 mass% C steel investigated here are found to have one dominant growth direction, less transverse growth and very limited thickening. There is also evident transformation twinning parallel to the transverse direction. It is concluded that more 3D analysis is required to understand the 3D microstructure of martensite in the mixed lath and plate region and to verify the recently proposed 3D phase field models of martensite in steels.

• 23.
KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Physical Metallurgy.
KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Physical Metallurgy.
Centennial of the Diffusionless Paradigm of Bainite2012In: Metallurgical and Materials Transactions. A, ISSN 1073-5623, E-ISSN 1543-1940, Vol. 43A, no 12, p. 4487-4495Article in journal (Refereed)

The diffusionless growth model of bainite formation was included in an international consensus in 1912 that all transformation products of austenite form by an initial transformation to martensite. The introduction of isothermal treatment revealed that all the products form directly. However, for bainite, the idea of some relation to martensite survived and developed into the diffusionless paradigm. Zener introduced the T (o) concept for predicting the start temperature of lower bainite, but also described diffusional growth of upper bainite. The present description of the diffusionless growth model is now examined and criticized.

• 24.
KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering.
KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Physical Metallurgy. KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Physical Metallurgy.
Do bainitic and Widmanstatten ferrite grow with different mechanisms?2010In: Scripta Materialia, ISSN 1359-6462, E-ISSN 1872-8456, Vol. 62, no 2, p. 75-77Article in journal (Refereed)

Caballero et al. recently presented new evidence for different growth mechanisms of Widmanstatten and bainitic ferrite. Their argument was based on Zener's hypothesis of diffusionless growth of bainitic ferrite. It is now demonstrated that Bhadeshia's model, based on Zener's hypothesis, predicts that some of the new measurements, claimed to fall above B-s and to be due to Widmanstatten ferrite, actually fall within the predicted temperature range of bainite, indicating that they cannot be used as new support for Bhadeshia's model.

• 25.
KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering. Swerim AB, Isafjordsgatan 28A, S-16440 Stockholm, Sweden.
Swerim AB, Isafjordsgatan 28A, S-16440 Stockholm, Sweden.. Swerim AB, Isafjordsgatan 28A, S-16440 Stockholm, Sweden.. KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering.
Formation of Chromium Nitride and Intragranular Austenite in a Super Duplex Stainless Steel2019In: Metallurgical and Materials Transactions. A, ISSN 1073-5623, E-ISSN 1543-1940, Vol. 50, no 12, p. 5594-5601Article in journal (Refereed)

Precipitation of chromium nitrides and formation of intragranular austenite were studied in detail for the super duplex stainless steel grade 2507 (UNS S32750). The situation of multipass welding was simulated by heat treatment at 1623 K (1350 degrees C) and quenching followed by short heat treatments at 1173 K (900 degrees C). The microstructural evolution was characterized using transmission and scanning electron microscopy, electron backscatter, and transmission Kikuchi diffraction, and it was observed that the interior of the ferrite grains contained chromium nitrides after quenching. The nitrides were predominantly of CrN with a cubic halite-type structure and clusters of CrN-Cr2N where rod-shaped trigonal Cr2N particles had nucleated on plates of CrN. After heat treatment for 10 seconds at 1173 K (900 degrees C), the nitride morphology was transformed into predominantly rod-shaped Cr2N, and finely dispersed intragranular secondary austenite idiomorphs had formed in the nitride-containing areas within the ferrite grains. After 60 seconds of heat treatment, both the Cr2N nitrides and the secondary austenite were coarsened. Analysis of electron diffraction data revealed an inherited crystallographic relationship between the metastable CrN and the intragranular austenite. The mechanism of chromium nitride formation and its relation to secondary austenite formation in duplex stainless steels are discussed.

• 26. Hou, Ziyong
KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering. KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering. KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering.
Effect of carbon content on the Curie temperature of WC-NiFe cemented carbides2019In: International Journal of Refractory Metals and Hard Materials, ISSN 0263-4368, Vol. 78, p. 27-31Article in journal (Refereed)

We have investigated the effect of the carbon content on the Curie temperature of a cemented carbide composite material with a Ni-Fe alloy as the binder phase and WC as the hard phase. In the carbon concentration range from 5.72 to 5.83 wt% carbon, which covers the interval where WC coexists with fcc Ni-Fe without other phases (the ‘carbon window’), the Curie temperature rises from 200 to 527 °C. This result indicates the possibility to use the Curie temperature to determine the carbon balance in the system. With thermodynamic calculations and kinetic simulations we can quantitatively establish the correlation between the carbon and tungsten content of the binder phase and the Curie temperature. This strong compositional effect on the Curie temperature is quantitatively very different from the conventional Co-based cemented carbides, with Curie temperatures of about 950–1050 °C.

• 27.
KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Physical Metallurgy.
KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering. KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering. KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering. Sandvik Coromant R&D, SE 126 80 Stockholm, Sweden. KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering.
Evaluating magnetic properties of composites from model alloys – Application to alternative binder cemented carbides2019In: Scripta Materialia, ISSN 1359-6462, E-ISSN 1872-8456, Vol. 168, p. 96-99Article in journal (Refereed)

The magnetic properties of 85Ni-15Fe model alloys containing Co, W and C have been studied with the intent to isolate the influence of alloy chemistry on quality control measurements of alternative binder cemented carbides. The results show a strong influence of dissolved W on the Curie temperature and the saturation magnetization. The amount of dissolved C, and the presence of WC precipitates, on the other hand, is shown to have negligible effect. Furthermore, the magnetic coercivity is indicated to be entirely dominated by the microstructural features and quite insensitive to composition.

• 28.
KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering.
KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering. KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering.
Modelling of the fraction of martensite in low-alloy steels2015In: MATERIALS TODAY-PROCEEDINGS, Elsevier, 2015, Vol. 2, p. 561-564Conference paper (Refereed)

Thermodynamics-based modelling of the fraction of martensite formed upon quenching in low-alloy steels is developed. The adopted modelling approach has two distinct features: 1) it applies the driving force of the transformation, i.e. the difference of Gibbs energy between austenite and martensite, from thermodynamic calculations; 2) it predicts the sigmoidal shape of transformation to capture also the initial 10-20% of martensite formation, which is distinct from some previous modelling using e.g. the Koistinen-Marburger equation. It is found that the general equation can describe the experimental data of martensite fraction versus quenching temperature for plain carbon steels and low-alloy steels well. Furthermore, the only model parameter that is needed is linearly proportional to the martensite start temperature of the steel, which opens the possibility for a thermodynamics-based simple but yet predictive model if it is coupled with the previously developed thermodynamics-based model for the Ms temperature.

• 29.
KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Physical Metallurgy.
KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Physical Metallurgy. Thermo-Calc Software AB, Råsundavägen 18, SE-169 67 Solna, Sweden. KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering. KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Physical Metallurgy.
Experimental Determination and Thermodynamic Modeling of Msσ for a Medium Mn SteelManuscript (preprint) (Other academic)

Medium Mn steels have attracted worldwide interests recent years due to their excellent mechanical properties and low cost. These steels contain large fraction (~30%) of metastable retained austenite and exhibit good elongation due to transformation-induced plasticity (TRIP). In order to obtain the highest elongation, the mechanical stability of austenite, quantified using Msσ, needs to be optimized. Msσ is defined as the highest temperature at which martensite can form under stress without austenite yielding by slip. The present work aims to formulate a model of Msσ which can be used to design medium Mn steels with optimized elongation. In the present work, an Fe–0.18C–5.08Mn (mass %) steel was intercritically annealed at 650 °C. Based on tensile tests at different temperatures using a single specimen method, the Msσ temperatures were experimentally determined to about 0 °C regardless of intercritical annealing time between 15 min and 3 h. Microstructure observations showed that large austenite grains with a globular shape are more transformed than thin-film ones, and thus the former probably governs the determined Msσ. Msσ was further predicted at the crossing point of yielding by martensite formation and by austenite slip; the former was modeled by expanding an existing model of martensite start temperature and the latter by a constitutive model. The predicted Msσ showed reasonable agreement with the determined values. The model also indicated that a large and a small austenite grain have similar Msσ, which could partly explain why the determined Msσ is rather constant regardless of IA time.

• 30.
KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Physical Metallurgy.
KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Physical Metallurgy. KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Physical Metallurgy. KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Physical Metallurgy.
On the tuning of austenite stability in a medium mn trip steel2015In: PTM 2015 - Proceedings of the International Conference on Solid-Solid Phase Transformations in Inorganic Materials 2015, International Conference on Solid-Solid Phase Transformations in Inorganic Materials , 2015, p. 933-934Conference paper (Refereed)
• 31.
KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Physical Metallurgy.
KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Physical Metallurgy. KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Physical Metallurgy. KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Physical Metallurgy.
Inverse Saltykov analysis for particle-size distributions and their time evolution2011In: Acta Materialia, ISSN 1359-6454, E-ISSN 1873-2453, Vol. 59, no 3, p. 874-882Article in journal (Refereed)

In this work a new method for transforming 2-D to 3-D size distributions is proposed. A representation of the 2-D size distributions is constructed from the data of measured radii with a statistical method called the kernel density estimator. The method yields a smooth density estimation that is more accurate than the classic histogram. The 3-D distribution is optimized from the 2-D density estimate in an iterative manner. (C) 2010 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

• 32.
KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Physical Metallurgy.
KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Physical Metallurgy.
Eutectoid Transformations in 4.12 Mass Pct Cr 0.88 Mass Pct C Steel2011In: Metallurgical and Materials Transactions. A, ISSN 1073-5623, E-ISSN 1543-1940, Vol. 42A, no 13, p. 3941-3951Article in journal (Refereed)

The sequence of eutectoid microstructures, obtained by lowering the temperature of the isothermal transformation, was studied in synthetic steel with 4.12 mass pct Cr 0.88 mass pct C. The results were compared with observations on plain carbon steels with 1.65 and 1.67 mass pct C. In both cases, the main features can be explained as an effect of a lowered temperature on the increasing supersaturation of cementite in austenite and an even stronger effect on that of ferrite. One distinction was a continuous change in the pearlite structure toward a more acicular structure. This structure is named acicular pearlite.

• 33.
KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Physical Metallurgy.
KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Physical Metallurgy. KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering. KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Physical Metallurgy.
Direct Observation that Bainite can Grow Below M-S2012In: Metallurgical and Materials Transactions. A, ISSN 1073-5623, E-ISSN 1543-1940, Vol. 43A, no 13, p. 4984-4988Article in journal (Refereed)

In situ simultaneous synchrotron X-ray diffraction and laser scanning confocal microscopy have confirmed that bainite in steels can grow below the martensite start temperature. This observation suggests that the formation curves for bainite in time-temperature-transformation diagrams should be extended below the martensite start temperature. Furthermore, the implication of this observation on the growth mechanism of bainitic ferrite is discussed.

• 34.
KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Physical Metallurgy.
KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Physical Metallurgy. KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Physical Metallurgy. KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Physical Metallurgy.
Thermodynamic Analysis of the Critical Condition for Acicular FerriteArticle in journal (Other academic)
• 35.
KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Physical Metallurgy.
KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Physical Metallurgy. KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Physical Metallurgy.
Kinetic Study of Transformations ofAustenite in a 4.12 mass% Cr 0.88 mass% C SteelManuscript (preprint) (Other academic)
• 36.
KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Physical Metallurgy.
KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Physical Metallurgy.
Trans-interface diffusivity in the Fe-Ni system2007In: Scripta Materialia, ISSN 1359-6462, E-ISSN 1872-8456, Vol. 56, no 1, p. 61-64Article in journal (Refereed)

The trans-interface diffusivity in the Fe-Ni system has been estimated by fitting simulations to experimental data. For diffusion across the alpha/gamma phase boundary, the mobility of species divided by an interfacial thickness of 1 nm, M-k/delta, is approximately 5% of the phase interface mobility M-int at 873 K and 15% at 973 K.

• 37.
KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering.
KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering. KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering.
Modeling C-Curves for the Growth Rate of Widmanstatten and Bainitic Ferrite in Fe-C Alloys2016In: Metallurgical and Materials Transactions. A, ISSN 1073-5623, E-ISSN 1543-1940, Vol. 47A, no 1, p. 19-25Article in journal (Refereed)

When Zener formulated his maximum growth rate criterion for predicting the coarseness of various metallographic objects, he simplified the growth rate equations and predicted that the optimum coarseness should be twice the critical value for which all the driving force would be absorbed by interfacial energy. It is now emphasized that a composition dependence of the diffusion coefficient has a considerable influence and can result in a ratio much larger than two. Various approximations have now been removed from the growth rate equation. When applied to acicular ferrite in the Fe-C system, a C-curve for the growth rate is obtained that resembles the unusually wide C-curve obtained experimentally when information on Widmanstatten ferrite and bainite is combined. It is not necessary to explain that shape as a combination of separate curves for Widmanstatten ferrite and bainite. The main reason for the wide C-curve is the direct effect of the composition dependence of the diffusivity of carbon in austenite.

• 38.
KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering.
KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering. KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering. KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering. KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering.
Use of Fe-C Information as Reference for Alloying Effects on B-S2019In: Metallurgical and Materials Transactions. A, ISSN 1073-5623, E-ISSN 1543-1940, Vol. 50A, no 10, p. 4531-4540Article in journal (Refereed)

Many empirical equations of the variation of the critical temperature with alloy content of the start of bainite formation in steels are available. They are often obtained by regression analysis of measured values for a large number of alloyed steels, usually with several alloying elements. However, such equations differ considerably, especially when applied to pure Fe-C alloys, which results in large differences between reported effects of individual alloying elements since they have not been based on the Fe-C system as a reference. Apparently, for the first time, an empirical equation is now derived by starting with information from Fe-C alloys and low alloy steels and then adding the effect of each alloying element separately, using information from ternary Fe-C-M alloys. Sets of information from the same alloy content but different carbon contents proved particularly useful. Lines connecting such points are regarded as B-S lines for the respective alloy content and the effect of alloying elements was evaluated from their distance from the B-S line for Fe-C alloys. Only under this condition can coefficients for alloying elements be expected to represent the physical effect of the elements. The resulting equation was tested with about 600 experimental B-S temperatures.

• 39.
KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering.
KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering. KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering. KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering.
Diffusion-Controlled Lengthening Rates of Bainitic Ferrite a Part of the Steel Genome2019In: Metallurgical and Materials Transactions. A, ISSN 1073-5623, E-ISSN 1543-1940, Vol. 50A, no 6, p. 2613-2618Article in journal (Refereed)

As a step in the further development of models and databases to support design of new steels, i.e., the steel genome, the growth of bainitic ferrite plates is accounted for by a thermodynamic and kinetic approach. The thermodynamic aspects are represented by CALPHAD databases and a Gibbs energy barrier for growth B-m. Experimental information on ferrite-plate growth rates for a number of Fe-C alloys, some of high-purity, are analyzed in terms of a modified Zener-Hillert model and the barrier as well as some kinetic parameters are evaluated. It is found that the barrier varies in a smooth way with carbon content and lengthening rate. In order to improve the agreement with the experimental information it was necessary to adjust the diffusion coefficient of carbon in austenite at low temperatures. It is concluded that the representation of the experimental data is satisfactory.

• 40.
KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering.
KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering. KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering. KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering. KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering. KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering. KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering.
A comparative study of microstructure and magnetic properties of a Ni–Fe cemented carbide: Influence of carbon content2019In: International Journal of Refractory Metals and Hard Materials, ISSN 0263-4368, Vol. 80, p. 181-187Article in journal (Refereed)

Due to the renewed interest in alternative binders for cemented carbides it is important to understand how the binder composition influences not only mechanical properties but also the microstructure and related measurements for quality control. Microstructure and chemical composition of WC-Co is often evaluated by magnetic measurements. However, when the binder composition deviates significantly from conventional Co-based binders it should not be assumed that the standard measurements can be used to directly evaluate the same parameters. In this paper we investigate the influence of relative C-content on the microstructure and magnetic properties of an alternative binder cemented carbide. It is shown that the saturation magnetization is related to the relative C-content and the magnetic coercivity is related to the microstructure, more specifically to the binder phase distribution, but could not be directly linked to the carbide grain size in the same manner as for standard WC-Co. Furthermore, a direct correlation between Curie temperature and saturation magnetization is observed for this system which means that the Curie temperature potentially could be used for calibration of empirical relations or as a method to accurately determine the binder volume fraction.

• 41.
KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering.
KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering. KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering.
Bridging the Gap Between Bulk Properties and Confined Behavior Using Finite Element Analysis2017In: PROCEEDINGS OF THE 4TH WORLD CONGRESS ON INTEGRATED COMPUTATIONAL MATERIALS ENGINEERING (ICME 2017) / [ed] Mason, P Fisher, CR Glamm, R Manuel, MV Schmitz, GJ Singh, AK Strachan, A, SPRINGER INTERNATIONAL PUBLISHING AG , 2017, p. 103-111Conference paper (Refereed)

Theoretically and empirically based models of materials properties are crucial tools in development of new materials; however, these models are often restricted to certain systems due to assumptions or fitting parameters. When expanding a model into alternative systems it is therefore necessary to have sufficient experimental data. When working with composite or highly confined materials, such as layered structures or coatings, this can be problematic as most available data is on bulk materials. The present work displays the potential of using Finite Element Method (FEM) simulations as a tool to understand experimental observations and expand existing models to new systems using only bulk properties of the constituent phases. The present work focuses on the effect of geometrical constraints on the indentation behavior of elasto-plastic materials as an example on how FEM may be used to better understand experimental observations in composite or layered materials. The results may also be integrated into phenomenological models, expanding their application range.

• 42.
KTH, School of Engineering Sciences (SCI), Mechanics, Physicochemical Fluid Mechanics.
KTH, School of Engineering Sciences (SCI), Mechanics, Physicochemical Fluid Mechanics. KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Physical Metallurgy. KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Physical Metallurgy.
Effect of external loading on the martensitic transformation - A phase field study2013In: Acta Materialia, ISSN 1359-6454, E-ISSN 1873-2453, Vol. 61, no 20, p. 7868-7880Article in journal (Refereed)

In this work, the effect of external loading on the martensitic transformation is analyzed using an elasto-plastic phase field model. The phase field microelasticity theory, incorporating a non-linear strain tensor and the effect of grain boundaries, is used to study the impact of applied stresses on an Fe-0.3%C polycrystalline alloy, both in two and three dimensions. The evolution of plasticity is computed using a time-dependent equation that solves for the minimization of the shear strain energy. Crystallographic orientation of the grains in the polycrystal is chosen randomly and it is verified that the said assumption does not have a significant effect on the final volume fraction of martensite. Two-dimensional (2-D) and three-dimensional (3-D) simulations are performed at a temperature significantly higher than the martensitic start temperature of the alloy with uniaxial tensile, compressive and shear loading, along with hydrostatic stresses. It is found that the 3-D simulations are necessary to investigate the effect of external loading on the martensitic transformation using the phase field method since the 2-D numerical simulations produce results that are physically incorrect, while the results obtained from the 3-D simulations are in good agreement with the empirical observations found in the literature. Finally, it is concluded that the given model can be used to predict the volume fraction of martensite in a material with any kind of external loading.

• 43.
KTH, School of Engineering Sciences (SCI), Mechanics, Physicochemical Fluid Mechanics.
KTH, School of Engineering Sciences (SCI), Mechanics, Physicochemical Fluid Mechanics. KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Physical Metallurgy. KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Physical Metallurgy.
Phase field modeling of martensitic transformation- Effect of grain and twin boundariesManuscript (preprint) (Other academic)

In this work we are presenting, for the first time, the elasto-plastic phase field modeling and simulation of the martensitic transformation in a polycrystalline material including the effect of grain and twin boundaries. The phase field microelasticity theory proposed by Khachaturyan is used to perform 2D and 3D simulations of FCC$\rightarrow$BCT martensitic transformation in an Fe-0.3\%C polycrystalline alloy, incorporating the effect of both coherent and incoherent boundaries. The effect of plastic accommodation is also introduced into the model, by solving a time dependent equation, during the solid-to-solid phase transformation. It is found that the given phase field model, with the effect of grain boundaries, not only respects the morphological features of martensite but it also conforms well with the physics of the problem. Different sets of simulations are performed to validate the model and it is concluded that the given model can correctly predict the evolution of martensitic microstructure in a polycrystal as opposed to the previous models where the effects of grain and twin boundaries are neglected.

• 44.
KTH, School of Engineering Sciences (SCI), Mechanics.
KTH, School of Engineering Sciences (SCI), Mechanics, Physicochemical Fluid Mechanics. KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Physical Metallurgy. KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Physical Metallurgy.
Phase-field modelling of martensitic transformation: the effects of grain and twin boundaries2013In: Modelling and Simulation in Materials Science and Engineering, ISSN 0965-0393, E-ISSN 1361-651X, Vol. 21, no 8, p. 085003-Article in journal (Refereed)

In this work, we present the non-linear elasto-plastic phase-field model and simulation of the martensitic transformation in a polycrystalline material including the effects of grain and twin boundaries. The phase-field microelasticity theory proposed by Khachaturyan is used to perform 2D and 3D simulations of fcc -> bct martensitic transformation in a Fe-0.3%C polycrystalline alloy, incorporating the effect of both coherent and incoherent boundaries. The effect of plastic accommodation is also introduced into the model, by solving a time-dependent equation, during the solid-to-solid phase transformation. It is found that the given phase-field model, with the effect of grain boundaries, not only respects the morphological features of martensite but also conforms well with the physics of the problem. Different sets of simulations are performed to validate the model and it is concluded that the given model can correctly predict the evolution of the martensitic microstructure in a polycrystal, as opposed to previous models where the effects of grain and twin boundaries are neglected.

• 45.
KTH, School of Engineering Sciences (SCI), Mechanics, Physicochemical Fluid Mechanics.
KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Physical Metallurgy. KTH, School of Engineering Sciences (SCI), Mechanics, Physicochemical Fluid Mechanics. KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Physical Metallurgy. KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Physical Metallurgy.
Three dimensional elasto-plastic phase field simulation of martensitic transformation in polycrystal2012In: Materials Science & Engineering: A, ISSN 0921-5093, E-ISSN 1873-4936, Vol. 556, p. 221-232Article in journal (Refereed)

The Phase Field Microelasticity model proposed by Khachaturyan is used to perform 3D simulation of Martensitic Transformation in polycrystalline materials using finite element method. The effect of plastic accommodation is investigated by using a time dependent equation for evolution of plastic deformation. In this study, elasto-plastic phase field simulations are performed in 2D and 3D for different boundary conditions to simulate FCC -> BCT martensitic transformation in polycrystalline Fe-0.3%C alloy. The simulation results depict that the introduction of plastic accommodation reduces the stress intensity in the parent phase and hence causes an increase in volume fraction of the martensite. Simulation results also show that autocatalistic transformation initiates at the grain boundaries and grow into the parent phase. It has been concluded that stress distribution and the evolution of microstructure can be predicted with the current model in a polycrystal.

• 46.
KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Physical Metallurgy.
KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Physical Metallurgy. KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Physical Metallurgy.
Carbide grain growth: the effect of grain size distributionsManuscript (preprint) (Other academic)

It is important to understand the WC grain growth behavior in order to obtain good mechanical properties when manufacturing cemented carbides. In the present study the WC grain growth for dierent initial grain size distributions during sintering is studied theoretically using a model based on three processes; 2-D nucleation of atomic planes, long-range diusion and interface friction. Simulations clearly show that the initial grain size distribution inuences the growth behavior significantly. Bimodal powders show a more dramatic grain growth than powders having a lognormalgrain size distribution.

• 47.
KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Physical Metallurgy.
KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Physical Metallurgy. KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Physical Metallurgy. KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Physical Metallurgy.
Abnormal grain growth in cemented carbides - Experiments and simulations2011In: International journal of refractory metals & hard materials, ISSN 0958-0611, E-ISSN 2213-3917, Vol. 29, no 4, p. 488-494Article in journal (Refereed)

The grain size and the grain size distribution are two of the most important factors when tailoring the mechanical properties of cemented carbides. In the present work the effect on the growth behavior when adding some abnormal grains in an initial fine grained powder is studied. It is clearly seen that abnormal grains in a fine grained matrix lead to faster grain growth and a higher average grain size.

• 48.
KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Physical Metallurgy.
KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Physical Metallurgy. KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Physical Metallurgy. KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Physical Metallurgy.
Carbide grain growth in cemented carbides2011In: Acta Materialia, ISSN 1359-6454, E-ISSN 1873-2453, Vol. 59, no 5, p. 1912-1923Article in journal (Refereed)

Abnormal grain growth is often observed in cemented carbides during sintering, but cannot be understood in terms of the classical LSW