Materials Science of Steel Textbook PDF

Wolfgang Bleck (Ed.) Materials Science of Steel - Textbook for RWTH Aachen University Students  Steel Institute RWTH Aachen University Wolfgang Bleck (Ed.) Materials...

Wolfgang Bleck (Ed.) Materials Science of Steel - Textbook for RWTH Aachen University Students  Steel Institute RWTH Aachen University Wolfgang Bleck (Ed.) Materials Science of Steel Textbook for RWTH Aachen University Students Translated from the German Version by Susan Giffin Edited by (1. Edition) Wolfgang Püttgen Edited by (2. Edition) Piyada Suwanpinij, Yujie Feng, Florian Gerdemann Edited by (3. Edition) Zirong Peng, Yujie Feng, Piyada Suwanpinij Edited by (4. Edition) Wolfgang Bleck, Christiane Beumers, Yidu Di, Wenwen Song At this point, all the other unnamed aiders will be thanked. This book was created as supporting material for the lectures and labatory excersies held at the Steel Institute at Aachen University. It cannot be guaranteed that everything is complete and that there are no printing errors. All rights reserved. No part of the contents of this book may be reproduced or transmitted in any form or by any means. 4. überarbeitete Auflage, 2016 Preface Steel is by far the most significant metallic material group. It contains over 2000 steel grades and offers a wide variety of property combinations to be applied to different uses. Many of these steel grades were recently modified or have been newly developed. Combined with new processing methods, they are an interesting and challenging field for engineers. This book is an introduction to the fundamental laws of material development and should excite students and engineers to further study the field of steels. This book, Materials Science of Steel, Textbook for Students at RWTH Aachen University, introduces the reader to an engineering approach of how to develop steels and finishing processes, of how to achieve desired properties, and of how to appropriately use the material. This book begins by acquainting the reader with the physical and chemical characteristics of the element iron. Important alloying elements for steels are introduced by means of phase diagrams. The microstructure formation is the focus of the chapter “Phase Transformation”. The technical significance and application of these phase transformations are discussed in the chapter “Technical Heat Treatments”. The practical relevance of the introduced physical and chemical phenomena for steel development and application is also explained In many cases, the texts and figures are based on textbooks and scientific publications, which were often modified to better fit the structure of this book and to provide a consistent presentation of the material. A list of the material that was used, as well as that which is recommended, is given at the end of each chapter. In spite of the great care that was taken in compiling this book, there very well may be mistakes, and from the point of view of a student, not all phenomena may be clearly and comprehensively explained. The authors kindly ask for your indulgence in this respect and would greatly appreciate any suggestions to improve this edition. Please send an e-mail with your corrections and suggestions to [email protected] aachen.de. This third edition of this book has been revised for improvement of English translation, for clarity of explanations as well as for an update of graphics and tables. A note to students: not all of the material presented in this book is relevant for the exam. The emphasis and required knowledge will be provided in the lectures, exercises, and laboratory assignments. We hope this book will provide a motivating and stimulating reading experience. Wolfgang Bleck  Contents Contents 1 Terms, Abbreviations, Symbols............................................................................. 1 1.1 Definitions......................................................................................................... 1 1.2 Abbreviations and Symbols.............................................................................. 5 2 The Physical Properties of Iron and Steel.......................................................... 16 2.1 Introduction..................................................................................................... 16 2.2 Crystal Formation........................................................................................... 18 2.2.1 The crystal structure of pure iron........................................................... 18 2.2.2 The influence of foreign atoms on the lattice constant of iron.............. 27 2.2.3 Real Structures........................................................................................ 27 2.3 Thermal Properties.......................................................................................... 29 2.3.1 Changes in volume and length of iron.................................................... 29 2.3.2 Changes in volume and length of steels................................................. 33 2.3.3 Thermal conductivity.............................................................................. 36 2.3.4 Diffusion................................................................................................. 38 2.4 Elastic Properties............................................................................................ 41 2.4.1 Elastic modulus (Young’s modulus) and shear modulus....................... 41 2.4.2 Anelasticity............................................................................................. 46 2.5 Magnetic and Electric Properties.................................................................... 50 2.5.1 Magnetic properties of pure iron............................................................ 50 2.5.2 Magnetic properties of steels.................................................................. 56 2.5.3 Electric properties................................................................................... 59 2.6 Further Readings............................................................................................. 62 3 Iron Alloys.............................................................................................................. 63 3.1 Formation of Alloys........................................................................................ 63 3.1.1 Homogeneous alloy formation by means of interstitial and substitutional solution............................................................................. 64 3.1.2 Heterogeneous alloy formations caused by segregation........................ 66 3.1.3 Superlattices in substitutional solid solutions and the formation of intermetallic phases................................................................................ 67 3.2 Phase Diagrams of Fe alloys........................................................................... 70 Contents 3.2.1 Phase diagrams of binary systems........................................................... 70 3.2.2 Thermophysical basics for the expansion or contraction of the J- field. 71 3.2.3 Expansion of the J-field in iron alloys.................................................... 73 3.2.4 Restriction of the J-field in iron alloys................................................... 74 3.2.5 The iron-carbon phase diagram............................................................... 76 3.2.6 The Phase diagrams of Fe-N and Fe-H................................................... 80 3.2.7 Ternary iron systems............................................................................... 80 3.2.8 The Phase diagram of Fe-C-Cr................................................................ 81 3.2.9 The ternary Fe-Cr-Ni system................................................................... 85 3.3 Segregation...................................................................................................... 88 3.3.1 Segregation processes during solidification........................................... 88 3.3.2 Segregation behavior during dendritic solidification............................. 91 3.3.3 Macrosegregation.................................................................................... 93 3.3.4 Segregation in continuous casting.......................................................... 94 3.3.5 Crystal segregation.................................................................................. 97 3.3.6 Secondary segregation............................................................................. 99 3.3.7 Examination of segregation...................................................................104 3.4 Internal Cleanliness in Steel..........................................................................110 3.4.1 Internal cleanliness................................................................................112 3.4.2 Sulfide inclusions..................................................................................115 3.4.3 Oxide inclusions....................................................................................117 3.4.4 Influence of calcium on the formation of non-metallic inclusions.......119 3.5 Further Readings...........................................................................................123 4 Phase Transformations.......................................................................................125 4.1 Ferritic-Pearlitic Transformation..................................................................128 4.1.1 Morphology...........................................................................................128 4.1.2 Formation of the ferritic microstructure...............................................132 4.1.3 Formation of the pearlitic microstructure: transformation with simultaneous precipitation....................................................................136 4.1.4 Influence of lamellar spacing on mechanical properties......................143 4.1.5 Influence of alloying elements on pearlite formation...........................145  Contents 4.1.6 Special forms of pearlite....................................................................... 148 4.1.7 Application of ferritic–pearlitic steels.................................................. 151 4.2 Martensitic (athermal) Transformation........................................................ 152 4.2.1 Morphology........................................................................................... 152 4.2.2 Formation of the martensitic microstructure........................................ 152 4.2.3 Influence of alloying elements on martensite formation...................... 163 4.2.4 Influence of deformation on martensite formation.............................. 171 4.2.5 Mechanical properties of martensitic steels......................................... 173 4.2.6 Special forms of martensite and martensite formation......................... 177 4.2.5 Application of martensitic steels.......................................................... 179 4.3 Bainitic Transformation................................................................................ 181 4.3.1 Morphology........................................................................................... 181 4.3.2 Formation of the bainitic microstructure.............................................. 184 4.3.3 Temperature range of bainite formation............................................... 190 4.3.4 Influence of alloying elements on bainite formation........................... 193 4.3.5 Widmanstätten ferrite........................................................................... 198 4.3.6 Acicular ferrite...................................................................................... 199 4.3.7 Application of bainitic steels................................................................ 199 4.4 Precipitating from a Supersaturated Solid Solution..................................... 203 4.4.1 Theoretical basics................................................................................. 204 4.4.2 Variables influencing carbide precipitation......................................... 216 4.4.3 Ageing................................................................................................... 219 4.4.4 Application examples........................................................................... 221 4.5 Further Readings........................................................................................... 227 5 Technical Heat Treatments................................................................................ 232 5.1 Hardening...................................................................................................... 236 5.1.1 Definitions............................................................................................ 236 5.1.2 Quenching and tempering..................................................................... 236 5.1.3 Examination of hardenability............................................................... 252 5.1.4 Calculating the hardenability................................................................ 255 5.1.5 Case hardening...................................................................................... 257 Contents 5.1.6 Properties of hardened materials...........................................................262 5.2 Annealing Treatments...................................................................................268 5.2.1 Diffusion annealing...............................................................................268 5.2.2 Coarse grain annealing..........................................................................271 5.2.3 Normalising...........................................................................................273 5.2.4 Soft annealing........................................................................................277 5.2.5 Recrystallisation annealing...................................................................281 5.2.6 Stress-relief annealing...........................................................................289 5.2.7 Combined annealing processes.............................................................290 5.2.8 Wire patenting.......................................................................................291 5.3 Description of Austenite Transformation for Technical Applications.........293 5.4 Time-Temperature-Austenitisation Diagrams (TTA diagrams)...................296 5.4.1 Austenitisation with isothermal heating...............................................299 5.4.2 Austenitisation with continuous heating...............................................302 5.4.3 Influence of austenitisation...................................................................307 5.5 Transformation Diagrams..............................................................................309 5.5.1 Isothermal transformation.....................................................................309 5.5.2 Continuous transformation....................................................................320 5.5.3 Other possibilities for the representation of transformation behavior.324 5.5.4 Influences on the transformation behavior...........................................326 6 Thermomechanical Treatment...........................................................................336 6.1 Terminology..................................................................................................337 6.2 Role of microalloying elements....................................................................339 6.2.1 Solubility behavior of microalloying elements.....................................341 6.2.2 Precipitation kinetics.............................................................................346 6.2.3 Mechanisms of microalloying elements...............................................347 6.2.4 Influence of microalloying elements on austenite grain growth..........350 6.2.5 Influence of microalloying elements on softening behavior................350 6.2.6 Influence of microalloying elements on transformation behavior.......353 6.2.7 Precipitation hardening.........................................................................354 6.3 Factors influencing the TMT of microalloyed steels....................................358  Contents 6.3.1 Austenitisation...................................................................................... 358 6.3.2 Deformation.......................................................................................... 359 6.3.3 Cooling.................................................................................................. 363 6.3.4 Influence of deformation on the JėD transformation......................... 364 6.3.5 Coiling temperature.............................................................................. 365 6.3.6 Summary of the influencing variables.................................................. 366 6.4 Further Readings........................................................................................... 370 7 Index..................................................................................................................... 374  1.1 Definitions 1 Terms, Abbreviations, Symbols 1.1 Definitions The element iron has the symbol Fe (ferrum) and is a transition element in Group VIII of the periodic table of elements. Iron has the atomic number 26 and an atomic mass of 55.8. It is the fourth most common element in the Earth’s crust (5.1 mass-%). The liquid core of the Earth consists predominantly of molten iron. Iron is rarely found as a pure element in the Earth’s crust, but is frequently found bound as an oxide, sulfide, carbonate, or silicate. Elemental iron has a low chemical stability; it is easily oxidised, and directly reacts with most non-metallic elements by forming bonds in which iron assumes an oxidation number of +2 or +3 (and in special cases +6). For example, iron can bond with oxygen to form FeO (+2) and Fe2O3 (+3), as well as Fe3O4 (FeO˜Fe2O3). In the presence of oxygen, water, and electrolytes, a group of electrochemical reactions that fall under the term ‘corrosion’ occur. At its various levels of oxidation, iron can form organometallic bonds with carbon-containing phases. Iron can also form non-stoichiometric bonds (alloys) with most of the metallic elements. The name has its roots in the Illyric word “iser”, which together with the Venetain- Illyric “eisarnon”, in which lies the Indogermanic root “eis”, developed into the Germanic term “isarnan”. Through the movement of languages, the Gothic word “eisarn”, the Old-nordic “isarn”, the German “eisen”, the Dutch “ijzer”, the Swedish “järn”, and the English term “iron” evolved. The scientific name “ferrum” has Latin-Eutruscian roots; the French term “acier” comes from the Latin “acies”, which means sharp. The beginning of the “iron age”, at around 1500 BC, marks the introduction of iron as a useful metal for weapons and kitchen utensils. Before that, iron was sporadically used in precious jewelry. For example, in Troy a piece of golden jewelry was found which had been decorated with the then valuable iron. Egyptian jewelry has also been known to be made of iron. Iron was probably discovered coincidentally while melting copper – possibly because, for example, a supposed copper ore, which in fact was iron ore, was put in the furnace. In this manner, copper itself was most likely accidentally discovered during clay baking. The history of iron production begins with the Hittites, around 2000 BC, in the area known today as Asia Minor. For the first time, the targeted production of iron and its trade products was established and passed down. Through the Phoenicians, Etruscans, and Romans, the art of iron production made its way to the Slovenians and Germans. Iron was mainly won in a one-step process of reducing oxide or 1 1 Terms, Abbreviations, Symbols sulfide ores. The resulting doughy mass, which was mixed with slag, required intensive forging to separate and reduce the slag before it was useable. In Europe, the two-step process was first developed in the 14th century. This process includes the creation of liquid pig iron as an intermediate product, and a subsequent refining process to produce forgeable iron through the oxidation of tramp elements, resulting in the purification of iron and its transformation into steel. Significant advancements were made during the industrial revolution in the second half of the 18th century. The first examples of industrial applications were boilers, train tracks, and bridges. Particularly symbolic are the iron bridge in Coalbrookdale, Great Britain (built in 1779), and the Eiffel tower in Paris (built in 1889). The biological properties of iron distinguish it as a vital mineral for humans and animals. It is the central atom in hemoglobin and myoglobin molecules. Hemoglobin, found in the red blood cells, transports oxygen from the lungs to the body’s cells, and carries carbon dioxide from peripheral cells to the lungs. Myoglobin transports oxygen within muscle fibers. An iron deficiency in humans results in a reduced oxygen supply to the brain, one noticeable symptom of which is tiredness. The iron content of blood is an important factor for performance. Iron can only be absorbed into the body in its ionic form (+2), and in the presence of vitamin C. The term steel is used to identify a material group of which the main element is iron (iron based alloys). Iron forms non-stoichiometric bonds with other metallic and non-metallic elements, which are called alloys. The alloying elements can either replace the iron atoms in the crystal lattice (substitutional), or they can dissolve in the spaces (vacancies) within the crystal lattice (interstitial). About 2000 steels are technically relevant, and usually have several alloying elements along with the element iron. A typical alloying element is carbon, which can be found between 0.0002 and 2.0 mass-% in steels. Cast iron usually has a higher carbon content of around 2.0 to 4.0 mass-%, and is further processed using casting techniques. On the other hand, steels are usually further processed by means of hot deformation. Important reasons why the element iron is universally, technically applicable: x Its abundance (5.1% of the earth’s crust: deposits of >50 mass-% iron can be found worldwide). x Its high melting temperature TL of 1808 K (1535°C): as a result, from room temperature up to around 450°C (= 0.4 TL), no thermally activated microstructural changes take place. Within the technically, well controllable temperature range of 550 to 950°C, heat treatment can be used to activate diffusion processes and to specifically adjust microstructures. 2  1.1 Definitions x Iron has two first order phase transformations in the solid state (A4 and A3- transformations), which allow for the use of different crystal structures in steels. Many properties of the solid can be calculated from the geometry of the body- centered cubic lattice and the face-centered cubic lattice. x A magnetic transformation (A2-transformation, second order phase transformation) allows for materials with diverse electrical and magnetic properties, and leads to useful anomalies, such as those which occur during thermal expansion. x Iron can be alloyed with about 80 other elements that involve mutual solubility or bond formation. Therefore the solution of the foreign atoms can take place interstitially or substitutionally. x In alloys or under high pressure a hexagonal lattice can also emerge besides a body-centered cubic and a face-centered cubic lattice. Apart from paramagnetism and ferromagnetism, antiferromagnetism also occurs. The Curie temperature indicates the transition from ferromagnetism to paramagnetism; while the Néel temperature shows the transition from antiferromagnetism to paramagnetism. The possible crystal structures and the respectively appearing forms of magnetism are summarized in Figure 1.1. Figure 1.1: Crystal structures and magnetism forms in iron and iron alloys. The term material refers to all natural and synthetic substances. The term material is used here to describe a solid aggregate state, from which components and structures can be produced using specific processes. 3 1 Terms, Abbreviations, Symbols A material is distinguished by its technically useful properties, its technical and economical possibilities, as well as its ecological soundness. In materials science, materials are characterised by their crystalline structure, their microstructure (type and distribution of the lattice defects) and their macrostructure (macroscopic appearance). The traditional term ferrous metallurgy describes a scientific field of engineering that deals with the production, processing, and application of iron and steel; ferrous metallurgy is, therefore, a division of materials science. Metallurgy is the science of producing and processing metallic materials; the emphasis is on processing technology. Materials science deals with the technically relevant aspects of the production, processing, and application of materials. The scientific expansion in this field of study began in Germany in the second half of the 19 th century with the appointment of professors of ferrous metallurgy at the Universities of Aachen, Berlin, Clausthal, and Freiberg. 4  1.2 Abbreviations and Symbols 1.2 Abbreviations and Symbols Chapter 2: Physical properties of iron and steel Symbol Unit Definition A °C or K transformation temperature (K = Kelvin) AC °C or K transformation temperature during heating Ar °C or K transformation temperature during cooling a m lattice parameter a1 ° oscillation amplitude 1 a2 ° oscillation amplitude 2 -1 D K linear thermal expansion coefficient B T=Vs m-2 magnetic induction Br T remnant Bs T saturation induction b m atomic spacing bcc - body-centered cubic crystal d m material thickness 'd m thickness difference E MPa Elastic modulus / Young's modulus (MPa = Mega Pascal) e As elementary charge (A s = Ampere Second) H - elongation H1 - elastic elongation percentage H2 - anelastic elongation percentage f s-1 frequency fcc - face-centered cubic crystal G MPa shear modulus -1 J K cubical thermal expansion coefficient J - shear angle 5 1 Terms, Abbreviations, Symbols Symbol Unit Definition -1 H Am magnetic field strength -1 HC Am coercive field strength -1 k JK Boltzmann constant (J = Joule) L V2 K-1 Lorenz constant (V = Volt) l m length / - logarithmic decrement -1 -1 O Wm K thermal conductivity (W = Watt) Ma g absolute atomic mass -1 Mr g mol relative atomic mass μ - Poisson's ratio -1 μ0 Vs Am induction constant μr - relative permeability VR(bcc) % packing density of the bcc-lattice VR(fcc) % packing density of the fcc-lattice r m atomic radius rs m spherical radius of a lattice interstitial site Uth g cm-3 theoretical density -3 U g cm material density Usp = U (T) :cm specific electrical resistance UPh :cm temperature dependent amount of the specific electrical resistance U0 :cm residual resistance V : cm -1 electrical conductivity V MPa normal stress T °C or K temperature TC °C or K Curie temperature TL °C or K melting point (Liquidus temperature) 6  1.2 Abbreviations and Symbols Symbol Unit Definition 'T °C or K temperature difference W MPa shear stress 3 Vat m atomic volume 3 VU m unit cell volume 3 'V m volume difference Chapter 3: Iron alloys Symbol Unit Definition A M-% maximum solubility a mol/l activity co mol/l melt concentration cS mol/l crystal concentration cL mol/l liquid concentration -1 H KJmol enthalpy of solution -1 HD   KJmol enthalpy of solution in ferrite -1 HJ   KJmol enthalpy of solution in austenite k0 - solubility coefficient 1/ko - segregation coefficient P bar partial pressure -1 -1 R J mol K universal gas constant 'S J entropy T °C or K temperature Chapter 4: Phase transformations Chapter 4.1: Ferritic-Pearlitic Transformation Symbol Unit Definition a, b, c m lattice parameters D ° angle between lamella axis and thin section surface CD mass-% carbon concentration of ferrite 7 1 Terms, Abbreviations, Symbols Symbol Unit Definition c C mass-% carbon concentration of cementite J C mass-% carbon concentration of austenite D - diffusion coefficient, D = D0 exp(-Q/RT) 'EV J total gain in enthalpy, in relation to volume 'GB J mol-1 interfacial enthalpy -1 'GV J mol gain in enthalpy through transformation 'HV J m-3 volume enthalpy J - diffusion current O m lamellar spacing (for D =0) OD m lamellar spacing (within angle D) Oa m average lamellar spacing of pearlite Omin m minimum distinguishable lamellar spacing of pearlite Q J activation energy per jump -1 -1 R J mol K gas constant, R = 8.314 J/mol K T °C or K temperature 'T °C or K supercooling TE °C or K equilibrium temperature between two-phases TT °C or K transformation temperature -2 V Jm interfacial energy W m width of lamella x W m s-1 mobility rate x m path z n number of atomic jumps (flips) 8  1.2 Abbreviations and Symbols Chapter 4.2 and 4.3: Martensitic and bainitic Transformation Symbol Unit Definition a, b, c m lattice parameters Ad °C or K decreased austenite start temperature, deformation induced Af °C or K austenite finish temperature As °C or K austenite start temperature B1 - low carbon bainite B2 - upper bainite B3 - lower bainite Bf °C or K bainite finish temperature Bs °C or K bainite start temperature -1 GA J mol enthalpy of volume of austenite -1 GM J mol enthalpy of volume of martensite -1 'G J mol nucleation enthalpy LM - lath martensite Md °C or K increased martensite start temperature, deformation induced Md 30 °C or K increased martensite start temperature, after 30% cold deformation Mf °C or K martensite finish temperature Ms °C or K martensite start temperature PM - plate martensite RA - retained austenite 'T °C or K supercooling Chapter 4.4: Precipitation out of the supersaturated solid solution Symbol Unit Definition B - constant BH - bake-hardening c0 mass-% initial concentration in the matrix on the phase boundary 9 1 Terms, Abbreviations, Symbols Symbol Unit Definition cC/N mass-% equilibrium concentration of carbon or nitrogen in D-iron cc (T) mass-% equilibrium concentration of carbon in D-iron cE mass-% equilibrium concentration with quasi- planar interface, equilibrium concen- tration according to the phase diagram cP mass-% equilibrium concentration within the precipitated carbide cRT mass-% carbon concentration at room temperature c(r) mass-% equilibrium concentration in front of the particles with radius r  cm mass-% concentration in the matrix 2 -1 D cm s diffusion coefficient -1 Hel kJ mol elastic strain energy -1 'gu kJ mol change in free molar volume enthalpy 'GO kJ mol-1 nucleation energy -1 'G(r) kJ mol change in free enthalpy -1 'h kJ mol difference in molar enthalpy -2 -1 jD cm s diffusion current density n - number of atoms n - precipitation exponent N nucleation rate -1 -1 k J mol K Boltzmann constant 3 : m molar volume of particle matter r m nucleus radius r0 m nucleus radius at time t=0 rc m critical radius of nucleus 10  1.2 Abbreviations and Symbols Symbol Unit Definition -1 Q J mol activation energy in order to bring 1 mol of carbon or nitrogen atoms in the D-matrix R J mol-1 K-1 gas constant, R = 8.3143 J mol-1 K-1 R m attainable particle end-radius -1 -1 's J mol K difference in molar entropy -1 V kJ mol specific energy of the DEphase boundary t s time W s time constant T K absolute temperature W precipitated volume fraction x m half of the average particle spacing Chapter 5: Technical heat treatments Chapter 5.1: Hardening Symbol Unit Definition A % fracture elongation Av J notch impact energy b - alloying element regression coefficient for the distance from the face x, (hardenability calculation) b0 - constant (hardenability calculation) Jx HRC hardness, dependent on distance from the surface of the sample K - value, dependent on martensite fraction, used to determine maximum hardness R - hardening degree = actual hardness / maximum possible hardness Rm MPa tensile strength Rp0.2 MPa 0.2% offset yield strength 11 1 Terms, Abbreviations, Symbols Symbol Unit Definition Vbw MPa fatigue strength x mm distance from face (Jominy test) Z % reduction in area Chapter 5.2: Annealing Symbol Unit Definition n - time exponent -1 Q kJ mol activation energy for recrystallisation -1 -1 R J mol K gas constant, R = 8.314 J mol-1 K-1 T °C or K annealing temperature TR °C or K recrystallisation temperature W s recrystallisation time of the JMAK Equation W0 s time constant of the JMAK Equation t s annealing time W(t) - fraction recrystallised Chapter 5.3: Description of the austenite transformation for technical applications Symbol Unit Definition Ac1 °C or K temperature at which formation of austenite begins during heating (temperature of three-phase equilibrium D + J + carbide) Ac1b °C or K for non-alloyed and alloyed steels: temperature at which formation of austenite begins during heating (entering three-phase field D + J+ carbide) 12  1.2 Abbreviations and Symbols Symbol Unit Definition Ac1e °C or K temperature at which first transformation ends during heating, i.e. three phase area (D + J + carbide) is exited and system enters two-phase field (D + J or J + carbide) Ac3 °C or K temperature, during heating, at which transformation from ferrite into austenite ends Acc °C or K temperature at which dissolution of carbides in austenite ends for alloyed steels during heating Accm °C or K temperature at which dissolution of cementite in austenite ends for hyper- eutectoid steels during heating Mf °C or K temperature at which transformation from austenite to martensite is nearly finished during cooling Ms °C or K temperature at which transformation from austenite to martensite begins during cooling Chapter 5.4: TTA phase diagrams Symbol Unit Definition a - constant C % mass content of carbon Mi % mass content of phase i ni - constant TT °C or K transformation temperature Chapter 5.5: TTT phase diagrams Symbol Unit Definition A - initial phase D - material constant 2 -1 D cm s diffusion coefficient 13 1 Terms, Abbreviations, Symbols Symbol Unit Definition G m s-1 growth rate -3 -1 K m t nucleus growth rate Km K/s upper critical cooling rate; only with regard to martensite KP s, minute, hour cooling time which leads to a complete pearlitic microstructure Kf s, minute, hour quickest cooling time for steels to form 1 % proeutectoid ferrite Kk s, minute, hour quickest cooling time for hypereutectoid steels to form 1 % proeutectoid carbide O - cooling parameter Ms °C or K martensite start temperature n - exponent -1 Q J mol activation energy -1 -1 R J mol K general gas constant SV Pm , nm -1 -1 effective grain boundary area per unit volume t s time W - temperature-dependent time constant T °C or K temperature TE °C or K equilibrium temperature TEV °C or K equilibrium temperature of proeutectoid ferrite formation TEP °C or K equilibrium temperature of proeutectoid pearlite formation TEB °C or K equilibrium temperature of proeutectoid bainite formation TEM °C or K equilibrium temperature of proeutectoid martensite formation U - transformation product W Volume-% transformed phase amount 14  1.2 Abbreviations and Symbols Chapter 6: Thermomechanical Treatment Symbol Unit Definition A, B - constants Mcrit - critical degree of deformation K - equilibrium constant Tcr °C or K critical temperature for a complete recrystallisation before precipitation occurs TNR °C or K recrystallisation stop temperature 15 2 The Physical Properties of Iron and Steel 2 The Physical Properties of Iron and Steel 2.1 Introduction The historical significance of iron In the periodic table of elements, iron has the symbol Fe, which is derived from the Latin word ferrum. The significant use of iron is demonstrable from approx. 2000 BC. Seen historically, iron came to be used much later than lead, gold, copper, and tin because of the considerable difficulty involved in processing and handling it. In the beginning, pig iron was extracted from ore in simple, charcoal heated ovens. However, in contrast to other metals, iron’s extreme hardness aroused the interest of the military for its possible technical applications. Weapons made of iron were significantly more robust than those made of bronze. Due to the high costs, however, the Romans were the first people to commonly use iron weapons. Advancements in iron extraction were first achieved in the Middle Ages with the development of the shaft furnace, the predecessor of the present blast furnace. In the 16th century, Agricola (De Re Metallica libri XII) described the different methods of iron production in detail. In the 18 th century, the economic importance of iron increased as a result of improvements in furnaces and the replacement of charcoal with coal and coke. All of the important processes of steel production, including some still in use today, have been developed since the middle of the 19 th century: In 1855 the Bessemer process; in 1864 the open hearth process; in 1877 the Thomas process; and in 1880 the electric process by Siemens. In 1948, Durrer and Hellbrügge developed the surface injection method known as the LD (Linz- Donawitz) process. Sources of iron The universe consists of 0.0014 mass-% iron, thus iron is the 9 th most abundant element in the universe. It is the most important heavy metal and the fourth most common element on Earth after oxygen, silicon, and aluminum. The inner and outer cores (‡ 7000 km) of earth consist essentially of iron. Except for the pure form found in meteors and basalt, iron is only found in bound form in nature. In most cases, it can be found as an oxidised mineral, such as hematite, magnetite, or limonite. In 2003, the largest producers of iron ore were Brazil, China, Russia, Ukraine, Australia, Kazakhstan, and Canada. The largest deposits of iron ore in Europe can be found in Sweden and France. The body of an adult human, with an average weight of 70 kg, contains 4 to 5 g of iron. 70% of the body’s iron can be found in the hemoglobin, 25% in iron containing proteins, and 3.5% in myoglobin. The typical daily allowance for iron 16  2.1 Introduction varies from 5 to 40 mg. Iron is non-toxic; a human would have to consume more than 50 g of iron before it becomes life threatening. Isotopes Iron has four stable isotopes, of which, with a 91.7% share, Fe-56 is the most common. Fe-54 follows with 5.8%, Fe-57 with 2.2%, and Fe-58 with 0.3%. Of the nine radioactive isotopes, Fe-60 and Fe-59 have the longest half-lives, with 300,000 and 2.7 years, respectively. Fe-49 decomposes with a half-life of only 75 ms. The radioactive isotope Fe-59 is used in medicine for diagnostic purposes. The chemical properties of iron are summarised in Table 2.1. Figure 2.1 shows the location of iron and its properties specified in the periodic table of elements. Relative atomic mass 55.847 Ionization energy 7.870 eV Configuration [Ar] 3d6 4s2 Melting point 1808 K Boiling point 3023 K Oxidation numbers 6, 5, 4, 3, 2, 1, 0, -1, -2 Theoretical density 7.87 g/cm3 Atomic radius 124.1 pm (a) Electronegativity 1.8 Ionic radius 67 pm (+3), 82 pm (+2) Table 2.1: Chemical properties of iron. Atomic number Electronegativity 3 Relative atomic mass Theoretical density in g/cm 26 1.8 24 25 55.847 7.87 27 28 Cr Mn 1808 Fe 124.1 Co Ni 3134 7.870 Melting point in K Atomic radius in pm Boiling point in K Ionization energy in eV Figure 2.1: The position of iron in the periodic table of elements. 17 2 The Physical Properties of Iron and Steel 2.2 Crystal Formation 2.2.1 The crystal structure of pure iron A specialty of iron is that it can transform to different crystal structures in the solid state; this behavior is called polymorphism. The polymorphic transformation of pure iron and its alloys makes the application of these materials possible for technological purposes. The temperatures at which the transformations of the crystal structure in pure iron occur can be determined using thermal analysis (Figure 2.2). The transformation points are recognisable as steps in the temperature curve, where the temperature does not change. At the points of transformation there are delays in temperature change during cooling and heating. The transformation temperature A (French, Arrêt) is indicated with an r (French, Refroidir) if it takes place during cooling, and with a c (French, chauffer) if it takes place during heating. The crystallographic structures of pure iron can be divided into D-iron, J-iron and, G-iron. The body-centered cubic (bcc) lattice of D-iron is thermodynamically stable below 911°C. When heated slowly, maintaining near-equilibrium conditions, to temperatures above 911°C (1184 K), the Ac3-temperature, the D-crystal structure transforms into the face-centered cubic (fcc) crystal structure of J-iron. Above 1392°C (1565 K), the Ac4-temperature, the bcc crystal structure reappears as G-iron. This structure is thermodynamically stable until the melting point TL = 1535°C (1808 K) is reached. When cooled at a rate near to thermodynamic equilibrium, the same transformation temperatures apply. However, heating or cooling at a faster rate leads to a hysteresis, which is depicted as superheating or supercooling. A second order transformation, which cannot be directly determined by thermal analysis, takes place at the so called Curie temperature, A2 = 769°C (1042 K). At this temperature, instead of a change in the crystal structure, a change in the magnetic properties takes place. Above the A2-temperature iron is paramagnetic, and below this temperature it is ferromagnetic. On the left-hand side of Figure 2.3 a bcc iron unit cell and on the right-hand side a fcc iron unit cell can be seen. The black dots indicate the position of the Fe-atoms. The distance to the next neighbor is indicated by dashed lines. The lattice constants are given for D-iron at room temperature, and for J-iron at 911°C. The characteristics of these crystal structures will be discussed in detail in the following sections. 18  2.2 Crystal Formation 1800 Liquid 1600 TL = 1536 °C TL = 1536 °C G-iron 1400 Ar4 = 1392 °C Ac4 = 1392 °C Temperature in °C 1200 J-iron 1000 Ar3 = 911 °C Ac3 = 911 °C 800 Ar2 = 769 °C D-iron Ac2 = 769 °C 600 400 Time Figure 2.2: Cooling curve (left) and heating curve (right) of pure iron as determined using thermal analysis; the rate of temperature change is near to thermodynamic equilibrium. D-iron J-iron Lattice constant Lattice constant a (bcc) = 0.286 nm a (fcc) = 0.364 nm at 25 °C at 911 °C Figure 2.3: Crystal structures of pure iron. 19 2 The Physical Properties of Iron and Steel The body-centered cubic lattice According to the point lattice model, the atomic nuclei of the body-centered cubic (bcc) lattice are located at the corners and in the center of the unit cell (Figure 2.4a). According to the ball model (Figure 2.4b), which takes into consideration the expansion of the electron shells, the atoms come into contact along the three- dimensional diagonals. These diagonals through the center of the cell, the cell diagonals , correspond to the closest packed direction of the bcc lattice. The atomic distance b is defined as the distance between two atomic nuclei along the closed packed direction. Figure 2.4c shows the relationship between the atomic distance b, the lattice constant a and the atomic radius r for the bcc lattice of D-iron at room temperature, which can be calculated as follows: a r ˜ 3 1.24 ˜1010 m (2.1) 4 a b 2r ˜ 3 2.48 ˜1010 m (2.2) 2 Since the volume of the unit cell is not completely filled by the atomic spheres, interstitial sites exist in the lattice between the atoms. Altogether, a bcc unit cell contains two full atoms: 1/8 of an atom at each of the eight corners of the cube, and an entire atom in the center. The packing density VR(bcc) can be calculated as follows: 3 4 8 §a · 2 ˜ S ˜ r3 S¨ ˜ 3¸ 3 3 ©4 ¹ S˜ 3 VR( bcc) 68% (2.3) a3 a3 8 The name of the interstitial sites can be derived from the geometric arrangement of their surrounding atoms: octahedral and tetrahedral interstitial sites. An octahedral interstitial site is located in the middle of each face, and at the middle of each edge of the unit cell (Figure 2.5). Each tetrahedral interstitial site is surrounded by two corner atoms and two central atoms. Altogether, in one bcc unit cell there are six octahedral and twelve tetrahedral interstitial sites. The size of the interstitial sites can be calculated as the spherical radius rS that passes directly to the center of the space created by the surrounding atomic spheres. The following applies: rs Octahedral interstitial site: 0.155 Ÿ rs 0.19 ˜1010 m (2.4) r rs Tetrahedral interstitial site: 0.290 Ÿ rs 0.36 ˜1010 m (2.5) r where r = atomic radius of an iron atom. The theoretical density Uth of bcc iron can be calculated using the lattice parameters and the absolute atomic mass Ma of iron. Given the Avogadro constant Na = 6.02 ˜ 20  2.2 Crystal Formation 1023 mol-1 and the relative atomic mass Mr = 55.89 g/mol, the absolute atomic mass Ma of iron in a bcc unit cell can be calculated: Mr Ma 2˜ 18.55 ˜1023 g (2.6) Na In order to calculate the density Uth, the volume of the unit cell VU(bcc) is then substituted into the formula: Ma g U th 7.88 (2.7) VU ( bcc) cm3 The value of the theoretical density corresponds closely to the actual density (7.87 g/cm3) at room temperature. 4r —a a —a —a = 4r a Unit cell of a bcc b Unit cell according to c Geometric relationships point lattice the ball model in the bcc lattice Figure 2.4: Body-centered cubic structure. 21 2 The Physical Properties of Iron and Steel a/2 a—5/4 a—3/2 a—2 a—3/2 Metal atoms Metal atoms Interstitial atoms in Interstitial atoms in octahedral interstitial sites tetrahedral interstitial sites Figure 2.5: Interstitial sites in the body-centered cubic lattice. The face-centered cubic lattice In the face-centered cubic (fcc) lattice, the atomic nuclei are located at the corners and in the center of each face of the unit cell (Figure 2.6a). According to the ball model, the atoms come into contact along the plane diagonals (Figure 2.6b). With the help of Figure 2.6c, the atomic radius r and the atomic distance b can be calculated for the fcc lattice of J-iron at 911°C as follows: a r ˜ 2 1.29 ˜1010 m (2.8) 4 a b ˜ 2 2.57 ˜1010 m (2.9) 2 Altogether, an fcc unit cell contains four full atoms: 1/8 of an atom at each of the eight corners of the cube, and a half of an atom at the center of each of the faces. The packing density VR(fcc) for an fcc unit cell is given by the following: 3 4 §a · 4˜ S ˜¨ ˜ 2¸ 3 ©4 ¹ S˜ 2 VR( fcc ) 74% (2.10) a3 6 As shown in Figure 2.7, an octahedral interstitial site is found at the middle of each unit cell edge, and in the center of the cell. The tetrahedral interstitial sites are found at 1/4 the distance along the three-dimensional diagonal from each corner of the cell. Altogether, there are four octahedral and eight tetrahedral interstitial sites in an fcc unit cell. The sizes of the interstitial sites in the fcc lattice are: 22  2.2 Crystal Formation rs Octahedral interstitial site: 0.41 Ÿ rs 0.53 ˜10 10 m (2.11) r rs Tetrahedral interstitial site: 0.22 Ÿ rs 0.28 ˜10 10 m (2.12) r a —a 4r —a = 4r a Unit cell of the fcc B Unit cell according to c Geometric relationships point lattice the ball model in the fcc lattice Figure 2.6: Face-centered cubic structures. a/2 a—2 a—3/4 a/—2 Metal atoms Metal atoms Interstitial atoms in Interstitial atoms in octahedral interstitial sites tetrahedral interstitial sites Figure 2.7: Interstitial sites in the face-centered cubic lattice. The theoretical density Uth of iron in an fcc cell can be calculated using the absolute mass Ma of the atoms as follows: Mr Ma 4˜ 37.10 ˜1023 g (2.13) Na 23 2 The Physical Properties of Iron and Steel Ma g U th 7.69 (2.14) VU ( fcc ) cm 3 The value of the theoretical density of fcc iron (7.69 g/cm3) agrees approximately with the actual density (7.65 g/cm3) at 911°C. The slightly smaller value for the actual compared to the theoretical density is due to vacancies in the crystal lattice that are not taken into consideration in the calculations. The hexagonal lattice The hexagonal lattice consists of several layers of hexagonal lattice points. As shown in Figure 2.8, the c-axis differs from the a-axis in length. Figure 2.8: Hexagonal structure. The actual unit cell that consists of two atoms is depicted in grey (Figure 2.8, left). However, for a better illustration of a hexagonal structure, three unit cells are usually presented. If all the atoms are the same size, then they touch each other in the hexagonal base plane and in the neighboring planes (Figure 2.8, middle). In this case the c/a ratio can be calculated as follows: c 8 1.63 (2.15) a 3 This structure is called hexagonal close-packed (hcp) and occurs, for instance, in magnesium. This lattice type is very similar to the face-centered cubic lattice. In the fcc lattice the plane containing the three face diagonals also has a hexagonal structure; the fcc lattice also corresponds to a stack of closed-packed planes. However, the two lattices have a different stacking sequence of layers: ABCABC in fcc and ABABAB in hcp. Figure 2.9 shows the interstitial sites in the hexagonal lattice. 24  2.2 Crystal Formation Figure 2.9: Interstitial sites in the hexagonal lattice. Interstitial sites are of vital importance for the formation of iron alloys. Table 2.2 shows the atomic radii of elements that dissolve interstitially. One can see that most of the elements have a radius larger than that of the largest interstitial site. Therefore, when an interstitial element is dissolved in an interstitial site, a lattice distortion results. Hydrogen is the only exception; it fits into the octahedral interstitial sites of the fcc lattice and the tetrahedral interstitial sites of the bcc lattice without causing any distortions. Other interstitially dissolved elements are embedded into the octahedral interstitial sites of the bcc lattice because the distortion energy resulting from the shifting of neighboring atoms to increase the size of the interstitial sites is lower than that of embedding the elements in tetrahedral interstitial sites. The characteristic properties of the bcc and fcc lattices are summarised in Table 2.3. The respective lattice constants are represented by the symbol a. Element Atomic radius in 10-10 m H 0.32 N 0.75 C 0.77 O 0.72 B 0.82 He 0.93 Table 2.2: Atomic radii of interstitially dissolved elements in iron lattices. 25 2 The Physical Properties of Iron and Steel Body-centered Face-centered Hexagonal cube cube Lattice constant a = 2.86˜10-10 m a = 3.64˜10-10 m at room at 911°C temperature Volume of the unit cell a3 a3 2.59·a2·c Number of atoms per 2 4 2 unit cell Number of adjacent 8 12 12 neighboring atoms Distance to adjacent 0.866 a 0.707 a neighboring atoms Number of octahedral 6 4 2 interstitial sites Number of tetrahedral 12 8 4 interstitial sites Size of the octahedral 0.19˜10-10 m 0.53˜10-10 m interstitial sites Size of the tetrahedral 0.36˜10-10 m 0.28˜10-10 m interstitial sites Number of the second 6 6 closest neighbors Distance to the second a a closest neighbors Packing density 68 % 74 % 74% Closed packed direction Closed packed plane {110} {111} (0002) Atomic radius 1.24˜10-10 m 1.29˜10-10 m Atomic distance 2.48˜10-10 m 2.57˜10-10 m Theoretical density 7.88 g/cm3 7.69 g/cm3 Table 2.3: Characteristic properties of the two lattice types of iron. 26  2.2 Crystal Formation 2.2.2 The influence of foreign atoms on the lattice constant of iron The Hume-Rothery rule (15%-rule) is a good approximation for the solubility of foreign atoms in α-iron. It states that the difference between the space required for the dissolved atoms and the space required for the atoms of the matrix crystal must not be greater than 15%. The distance between neighboring atoms serves as a measurement for the required space. The atomic volume of D-iron is small in comparison to most other elements, nearly all alloying elements cause an increase in the volume of the unit cell, with the exception of silicon and phosphorus. Figure 2.10 shows the influence of foreign atoms on the D-iron lattice constant. 0.2874 Zn, Al W 0.2872 Mo Ti V Lattice constant a in 10 m -9 0.2870 Cr Cu Mn Ni 0.2868 Co 0.2866 0.2864 Si P 0.2862 0 2 4 6 8 10 12 Mass-content in % Figure 2.10: Influence of alloying elements on the D-iron lattice constant at room temperature. Foreign atoms are of considerable importance for the crystallographic transformational behavior of iron. They can either account for a delay or acceleration of the DoJ transformation and therefore, for the temperature at which the transformation occurs. The addition of large amounts of alloying elements, such as chromium or nickel, can have the effect that a transformation does not occur over very large temperature ranges. 2.2.3 Real Structures Real crystals are not perfect; rather, they show certain defects. Table 2.4 and Figure 2.11 show typical crystal structural defects of iron and steel, as well as the dimension in which they are found in the lattice. Lattice defects regulate many physical phenomena in metals. For example, the vacancy density is of great 27 2 The Physical Properties of Iron and Steel importance for diffusion; dislocations are significant for plastic deformation, and grain boundaries are important for many mechanical and physical properties. Dimension Type of structural crystal Description defect 0-dimensional point defect vacancy interstitial foreign atom substitutional foreign atom 1-dimensional linear defect dislocation 2-dimensional planar defect grain boundary stacking fault subgrain boundary twin boundary 3-dimensional space defect inclusion precipitate intermetallic phase Table 2.4: Dimensions, types, and descriptions of lattice defects. Figure 2.11: Graphic representation of typical lattice defects. 28  2.3 Thermal Properties 2.3 Thermal Properties 2.3.1 Changes in volume and length of iron The heating of a pure metal generally leads to a steady increase in the lattice constant and, therefore, the volume of the unit cell increases, if no polymorphic changes occur. At normal atmospheric pressure, pure iron undergoes two transformations: the DoJ transformation (bccofcc) at 911°C (A3), and the JoG transformation (fccobcc) at 1392°C (A4). With increasing temperature, the lattice constant a is characterised by three curve segments, each with a different positive slope (Figure 2.12). The difference in the slope of each curve segment is due to the different expansion behaviors of the bcc and fcc crystal lattices. 0.295 0.373 for D- and G-iron in nm 0.293 G 0.371 Lattice constant a Lattice constant a for J-iron in nm DFe JFe Fe 0.291 0.369 0.289 0.367 0.287 0.365 A3 A4 0.285 0.363 0 200 400 600 800 1000 1200 1400 1600 1800 Temperature in K Figure 2.12: Change in the lattice constant a of pure iron with increasing temperature. The linear expansion coefficient D can be calculated as an average expansion coefficient for each temperature range: 1 dl D ˜ (2.16) l dT where l = length and T = temperature. Equation 2.17 is the result of solving the previous equation for the length at a given temperature: l (T ) l 0 ˜ 1  D ˜ 'T (2.17) 29 2 The Physical Properties of Iron and Steel In Table 2.5, the average thermal expansion coefficients for pure iron are listed for different temperature ranges. The linear thermal expansion coefficient D is shown as a function of temperature in Figure 2.13. Lattice type Temperature range Average expansion in °C coefficient D in 10-6K-1 D-Fe 20 – 911 15.3 J-Fe 911 – 1392 22.0 G-Fe 1392 – 1536 16.5 Table 2.5: Average thermal expansion coefficients for pure iron. Figure 2.13: Thermal expansion of pure iron. In the stable range for D-iron, the linear thermal expansion coefficient D rises as the temperature increases. At the Curie temperature TC, an anomaly in form of a decrease in the linear thermal expansion coefficient D occurs due to a change in the magnetic properties from ferromagnetic to paramagnetic. After this, D begins to rise again. In the stable range for J-iron, a constant expansion coefficient D of 22˜10-6 K-1 can be observed. Above the A4-point, in the stable range for G-iron, the expansion coefficient D falls instantaneously to a value of approximately 16.5˜10-6 K-1. The dotted curves show the approximate theoretical progression of the thermal expansion coefficient for fcc iron and paramagnetic bcc iron. At each of the transformation points, the calculated curves join the measured curves. 30  2.3 Thermal Properties The atomic volume changes according to the lattice constant with increasing or decreasing temperatures. The following relationships exist between the lattice constant a and the atomic volume: a3 bcc lattice: Vat (2.18) 2 a3 fcc lattice: Vat (2.19) 4 Figure 2.14 shows the change in the atomic volume of pure iron according to temperature. Analogous to the linear thermal expansion coefficient D, a cubic thermal expansion coefficient J can be calculated as the volume-related differential quotient of the change in volume, dV, and the difference in temperature, dT. 1 dV J ˜ (2.20) V dT For isotropic materials, the cubic thermal expansion coefficient J correlates with the linear thermal expansion coefficient D: J 3 ˜D (2.21) Therefore, the determination of the linear thermal expansion coefficient is sufficient to describe the change in volume. Figure 2.14: Change in the atomic volume of pure iron with temperature. 31 2 The Physical Properties of Iron and Steel Between room temperature and the A3-temperature, the atomic volume increases by approximately 4% and the relative length by about 1.3%. Between room temperature and the melting point, the atomic volume increases by about 7.5% and the relative length by approximately 2.6%. The transformation of D-iron (VR(bcc) = 68%) into the more closed packed J-iron (VR(fcc) = 74%) at the A3-temperature is associated with a decrease in volume and length of about 1% and 0.35%, respectively. The increase in volume at the A4-temperature is only 0.5%, because J- iron has a larger thermal expansion coefficient than D- and G-iron. Table 2.6 helps to clarify the temperature dependence of the lattice constant and density of pure iron. It also shows the results calculated for the relative change in length of a pure iron rod at different temperatures. Temperature Structure Symbol Lattice constant Density Relative length °C - - nm g/cm3 (calculated) 20 bcc D 0.2866 7.88 1 911 bcc D 0.2904 7.57 1.0132 911 fcc J 0.3646 7.65 1.0097 1392 fcc J 0.3688 7.40 1.0211 1392 bcc G 0.2932 7.36 1.0229 1536 bcc G 0.2941 7.29 1.0262 Table 2.6: Lattice constants and densities of pure iron dependent on temperature. A pure iron rod with a length l0 of exactly one meter at room temperature increases in length to 1.0132 m after heating to 911°C (A3-temperature). At the point of transformation, an instantaneous shrinkage of 0.35% to 1.0097 m occurs. As the temperature increases to 1392°C (A4-temperature), the rod expands to a length of 1.0211 m. Due to the reversal of the transformation, an instantaneous expansion of 0.18% to 1.0229 m occurs. At the melting point the rod has a length of 1.0262 m, a total increase of 26 mm from the starting length at room temperature. The formulas to calculate the relative length within the three different temperature ranges are given in Table 2.7. Temperature range in °C Equation (T in °C) 20 – 911 l (T ) l0 ˜ >1  14.8 ˜106 ˜ T  20 @ 911 – 1392 l (T ) l0 ˜1.0097 ˜ >1  23.6 ˜106 ˜ T  911 @ 1392 – 1536 l (T ) l0 ˜1.0229 ˜ >1  22.3 ˜106 ˜ T  1392 @ Table 2.7: Calculating the total expansion of pure iron. 32  2.3 Thermal Properties 2.3.2 Changes in volume and length of steels The thermal expansion of pure ferritic and ferritic-pearlitic steels, as well as quenched and tempered (QT-) steels, is similar to the thermal expansion of D-iron. At room temperature the linear thermal expansion coefficient D of these steels is between 11˜10-6 and 13˜10-6 K-1, similar to that of D-iron. High alloyed austenitic steels exhibit significantly larger linear thermal expansion coefficients. Figure 2.15 shows the dependence of the linear thermal expansion coefficients of ferritic and austenitic steels on different temperatures. In many magnetically ordered J-iron alloys, a volume-magnetostriction appears, whereby, through the transformation of magnetic ordering, a change in the lattice spacing occurs, thereby influencing thermal expansion. In alloys with a sufficiently large positive volume-magnetostriction, the magnetic coupling can compensate for the thermally dependent change in lattice spacing. These so called Invar alloys are characterised by a small and almost constant thermal expansion over a certain temperature range. Classic iron based Invar alloys contain about 36 mass-% nickel and reach thermal expansion coefficients of 1˜10-6 K-1. Superinvars additionally contain cobalt and reach thermal expansion coefficients of approximately 1˜10-7 K-1. Thermal expansion coefficient Din 10-6 K -1 25 Austenitic steels 20 15 Ferritic steels 10 5 0 100 200 300 400 500 600 700 800 Temperature in K Figure 2.15: Thermal expansion coefficients of ferritic and austenitic steels. 33 2 The Physical Properties of Iron and Steel Case study: Invar steel Figure 2.16: Application of Invar steel. Figure 2.16 shows the applications of Invar steel. For the purpose of demonstration, Figure 2.17 shows a comparison between the thermal expansion coefficients of an Invar alloy and a common plain carbon steel. Easily recognisable is the comparatively larger temperature range over which the Invar alloy containing 36 mass-% nickel shows little thermal expansion. Figure 2.18 shows the transition temperatures of the iron-nickle system. Paramagnetic iron-manganese-nickel alloys and iron-chromium-nickel alloys show a thermal expansion behavior contrary to that of Invar alloys. The temperature- dependent change in thermal expansion for each of these alloys is characterised by a maximum. These maxima result from the transition of atoms to a higher energy state, which increases their atomic volume. The maxima also explain the higher expansion coefficient of austenitic chromium-nickel alloys compared to ferritic steels. As a result of this anomaly, face-centered cubic alloys exhibit a relatively large thermal expansion at room temperature. Therefore, alloys with a large expansion, for example, 75% Fe, 19% Ni, 6% Mn, can be used as active components in bi- metallic systems. In Figure 2.19, the thermal expansion coefficient D is graphed against the number of valence electrons per atom, e/a. A maximum of approximately 19˜10-6 K-1 appears at an e/a ratio of 8.3. Alloys with either smaller 34  2.3 Thermal Properties or larger numbers of valence electrons have a smaller thermal expansion at room temperature. Figure 2.17: Linear thermal expansion coefficients of an Invar steel (36% Ni) and a plain carbon steel. Figure 2.18: Transition temperatures of the nickel-iron system 35 2 The Physical Properties of Iron and Steel Figure 2.19: Thermal expansion of various fcc alloy groups at 300 K. 2.3.3 Thermal conductivity Temperature differences in a solid object lead to a flow of heat, which is, above all, dependent on the thermal conductivity of the material. Generally, good electrical conductors also serve as good thermal conductors. Thermal conduction can function on the basis of two fundamental mechanisms; it can occur through oscillations in the lattice, or over free electrons (conducting electrons). The temperature dependence of thermal conductivity O is represented in Figure 2.20. 36  2.3 Thermal Properties Figure 2.20: Thermal conductivity of pure iron dependent on temperature. This temperature dependence is a reflection of the impact of ferromagnetic properties of iron. A large increase in thermal conductivity is associated with the appearance of magnetic ordering below the Curie temperature TC. Since conducting electrons are essentially responsible for thermal conduction at conditions above room temperature, the correlation between thermal conductivity and electrical conductivity can be described by the Wiedemann-Franz-Lorenz Law, which says that the ratio of thermal conductivity O to electrical conductivity V changes proportionally to temperature T. O V ˜ L ˜T (2.22) The Lorenz number L has nearly the same value for all metals and can be determined as follows: k2 L # 3˜ (2.23) e2 where k = Boltzmann constant and e = (element) charge. Above room temperature, the Lorenz number L for pure iron is 3.03. 10-8 V2 K-1. At lower temperatures, the Lorenz constant also becomes temperature-dependent. In addition to electron conductance, the amount of heat transported through lattice oscillations takes on importance with decreasing temperature. The combination of the effects of these two mechanisms and the amount of remaining resistance results in a maximum in thermal conductivity reached at low temperatures, as seen in the inserted graph in the upper right-hand corner of Figure 2.20. The maximum of the thermal conductivity increases with the purity of the crystal. Crystal lattice defects hinder both the electrical conductivity and thermal conductivity. 37 2 The Physical Properties of Iron and Steel 2.3.4 Diffusion Diffusion is identified by a thermally activated transport of atoms in solid and of atoms or molecules in liquid or gas. The diffusional motion of iron atoms in an iron lattice is called self-diffusion; while the diffusional motion of foreign atoms within the atom matrix is called interstitial or substitutional diffusion. The diffusion flux density I (diffusion flux over the cross area A) depends on the number of the moving atoms n in a time period t and is proportional to the concentration gradient dc/dx. The relation is known as First Law of Diffusion: 1 dn dc I ˜ D ˜ (2.24) A dt dx The diffusion constant D has the dimension of m2/s and is described by means of an Arrhenius equation: Q  D D0 ˜ e RT (2.25) with Q = activation energy, R = gas constant, T = absolute temperature, and D 0 = frequency factor. The temperature dependence is a linear Arrhenius plot logD versus 1/T. The Second Law of Diffusion describes the concentration change over time as a function of concentration gradient: dc d 2c D ˜ (2.26) dt dx 2 A specific solution of the differential equation for the one-dimensional diffusion is usually applied to demonstrate the mean diffusion range as a function of temperature and time: X 2Dt (2.27) Important influencing factors of atom diffusibility are summarized in Figure 2.21. 38  2.3 Thermal Properties Figure 2.21: Influencing factors on the diffusion coefficient. Diffusion parameters for the interstitially dissolved C in iron lattices and the self- diffusion parameters for iron are listed in Table 2.8. It becomes apparent that the interstitial atoms can diffuse faster than the substitutional atoms due to the low activation energy. The diffusion rate in body-centered cubic lattice is significantly higher than that in face-centered cubic lattice at the same temperature because of the higher frequency factor. The high frequency factor can be explained by the higher number of the octahedral interstices/interstitial sites and lower pack density in bcc lattice. Table 2.8: Diffusion parameters. The Arrhenius relations of diffusion coefficients for the interstitially dissolved atoms H, C and N and the substitutionally dissolved atoms in bcc iron lattice are shown in Figure 2.22. Especially revealing in this diagram is that the axis label on the right shows the required time for a diffusion range of 20 μm. The range can be considered as a mean distance to a grain boundary; thus it provides a measurement to evaluate if a relevant parameter change can be counted on as a result of diffusion. This can 39 2 The Physical Properties of Iron and Steel occur for instance in the formation of segregation on grain boundaries. It can be inferred from the diagram that the diffusion of hydrogen in pure iron is hardly obstructed. The diffusion of C and N over a distance of 20 μm is effected within several days at slightly elevated temperatures of e.g. 100°C, so that the change of microstructure and properties must be anticipated. The time-dependent phenomena are called aging. For the substitutionally dissolved atoms the diffusion below approx. 550°C can be neglected in a technically relevant period. Figure 2.22: Diffusion coefficient of interstitially and substitutionally dissolved elements in bcc and fcc iron. 40  2.4 Elastic Properties 2.4 Elastic Properties 2.4.1 Elastic modulus (Young’s modulus) and shear modulus When a mechanical force acts on an object, a resistance force is generated in the object, such that the internal and external forces on the object are in equilibrium. The resistance of the object is called stress (in units of area). The kind of stress is defined by forces perpendicular to the surface of interest (normal stress V), and forces acting within the surface of interest (shear stress W). Normal stresses cause a relative change in length H (elongation) of an object. In the case of tensile normal stress, an elongation of the object occurs, while normal stress applied as pressure results in a compression of the object. Shear stress results in a shearing of the object at an angle J. If the object takes on its original shape again after the stress is removed, the object is said to be elastic. If the object does not regain its original shape after the stress has been removed, the object is said to behave plastically. Note that an elastic change in an object is associated with a reversible change in volume, whereas for plastic deformation the law of constant volume applies. The increase in volume of an object under elastic tensile stress should be made clear by the following example. Tensile stress is applied to a round rod with an initial volume of V0. The final volume V1 can be determined with the following calculations. The initial volume V0 of a round rod with a diameter d0 and a length l0 is: S 2 V0 ˜ d 0 ˜ l0 (2.28) 4 The applied elastic tensile stress results in a volume V1, giving consideration to the increase in length and decrease in diameter: S 2 V1 ˜ d 0  'd ˜ l 0  'l (2.29) 4 Ignoring all terms in which 'd and 'l are squared or multiplied with one other, and substituting Vo and H results in the following equation: § 'd 'l · V1 V0 ˜ ¨¨1  2  ¸ V0 ˜ 1  2 ˜ PH  H (2.30) © d 0 l 0 ¸¹ 'd l 0 with Poisson’s number: P ˜ (2.31) d 0 'l 'l and the elongation: H (2.32) l0 Therefore, the change in volume caused by tensile stress is: 41 2 The Physical Properties of Iron and Steel 'V V1  V0 V0 ˜ H ˜ 1  2 ˜ P (2.33) With μFe = 0.235, the increase in volume of an iron object under elastic tensile stress can be calculated. In the elastic zone, many materials show a linear relationship between stress and elastic deformation. Hooke’s Law describes this relationshi