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Material for May 6th 2010

Structure of the welded jointand Cracking phenomena in steel weld

Dr. Jippei Suzuki

1. Introduction

Fig.A1 The microstructure of steels is determined by the chemical compositions and the heat

cycle (or heating history), and it affects the mechanical properties of steel welds and the

phenomena, shch as cracking, embrittling in the steel welds. Therefore, it is important forwelding engineers to understand the structure in steel welds (Fig.A1).

Major thermal factors controlling microstructure are the peak temperature and the cooling

rate. These factors are determined by the heat balance between the input into and output

from the welded region. The intensity of heating is expressed by welding heat input;

H=EI

v 60

The Hhas the dimension of[joule]

[cm] , and means the energy inputted into the welding beadof unit length (cm). Although there is actually a heat loss due to radiation, this effect is not

considered except the theoretical discussions.

The output of heat is mainly caused by the conduction of heat to the whole base mwtal

plate. It is controlled by some parameters, such as (1) thermal conductivity, (2) plate

thickness, (3) joint type, and (4) preheating temperature.

Fig.A2 Fig.A2 (upper) shows the typical weld. The weld is composed (1) weld metal, (2) heat

affected zone, briefly HAZ and (3) unaffected base metal. Since the weld metal is heated

up to melting range, the heat conduction occurs into the region which dose not melt. The

heat affects the characteristics of the base metal. The region changed by conducting heat

is named the heat affected zone. The influence of conducting heat is decreased with the

distance from the weld metal (unaffected base metal). The boundary between HAZ and

UBM is not clear, because the effect of conducting heat is gradually decreased with the

distance. In the case of steel welds, A1 temperature is the criterion for the boundary.

Fig.A3

Fig.A3 shows the details of the weld.

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2. Dual microstructures of steels

Fig.A4 Fig.A4 shows the microstructures of the weld made by mild steel.

Fig.A5 Fig.A5 shows the microstructures of the weld metal made by mild steel.

In Fig.A4, the test pieces are etched by nital which is the solution of nitric acid with

alcohol. Nital reveals the grain boundary, then it is used for observation of transformed

microstructures. In Fig.A5, the saturated picric acid solution is used to etch the region where

the impurities segregates. In the case of steels, impurities segregates to the grain boundaries

during solidification, then the picric acid reveals the solidification microstructures.

Fig.A6

Fig.A6 shows the equilibrium diagram of Fe-C ststem. The steels solidify at the temper-

ature of about 1500, and solidification structures formed. In region, the microstructure

becomes austenite only. Austenite transforms to various microstructures named the trans-

forming microstructure.

3. Microstructure formed during solidification

Fig.A7 Fig.A7 shows the sequence of solidification of molten metal. At first, the very small

crystal named nuclei forms in liquid metal. The small crystals grow large. The moltenmetal between grains becomes thinner, and finallyit becomes the grain boundaries.

In the growth of nuclei or small grain, the atoms in liquid region is fixed at tthe specified

position in the crystal structure of small grain. The rate of fixing is changed depending on

the crystalline direction.

Fig.A8 The preferential ditrction for growth is [100] of cubic crystal as shown in Fig.A8. the

growing rate in [100] is larger than those of [110], [111], etc.

The derections of [010], [001], [100], [010], [001], are equivalent with [100] in cubic crystal.So, there are six preferential directins during solidification of iron.

Fig.A9 When the pure iron is alloyed by other elements, the liquidus and solidus temperature

rise up or drop down (Fig.A9 upper two figures). The ratio of the solute concentration in

solid iron;CS to that in requid iron; CL ia named the equilibrium coefficient; k0. When the

liquid metal containg solute ofC0 is solidified, it can dissolve the solute of only k0C0. Then

the excess of solute is (1 k0)C0, and it is pushed out into the liquid region. The increase

in solute concentration of the liquid metal occurs at the solid/liquid interface is increased.This phenomenon is expressed by the following differential equation.

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DL2CL

x2+ R

CL

x= 0

where, DL is the diffusion coefficient of solute atom in liquid iron, x is the distance from the

interface, R is the moving rate of solid/liquid interface. The solution of above differentialequation is as follows.

CL = C0

1 +

1 k0k0

exp

RDL

x

(1)

Fig.A10 This increase of solute concentration near the interface occurs only when k0 is smaller

than unity (k0 < 1). Since the concentration of solute atom is high near the interface and

is decreased with the distance from interface, the liquidus temperature will be increased

shown in Fig.A10. The thermal graduent G (actual temperature) is increased linearly and is

lower than the liquidus temperature. The reversal of actual temperature against the liquidus

temperature is the driving force of solidification. This phenomenon is named constitutional

supercooling.

Fig.A11 Fig.A11 shows that the types of solidification microstructures depend on two factors

of the solute concentration and the solidification parameter. The solidfication interface

changes from planar to dendritic, because the constitutional supercooling becomes large with

increasing the solute concentration C0 or the solidification rate R, as shown by equation (2).

Fig.A12 A14 Fig.A12 A14 show the examples of solidification microstructures. The solid crystal grows in the liquid metal in concord with the following rules.

Molten metal solidifies along the direction of maximum thermal gradient.

The solidification rate depends on the crystalline direction. In the case of cubic crystal,

the solid crystal grows in the direction of< 100 >.

Fig.A15 The solidification of the weld pool begins at the boundary between melted- and not melted

zones. This boundary is called the weld bond. The region which is not melted, that is, heat

affected zone, is a solid, therefore, it has a crystalline structure. The molten metal in the

weld pool has no crystalline structure. During solidification, the atoms in molten metal are

set in the crystalline structure. Therefore, two grains have the same crystalline direction.

Such growth that the new cristal has the same structure and the same direction is named

the epitaxial growth.

In crystals of a1 a4, the direction < 100 >, in which the growing rate is maximum,is agreeable to the direction of maximum thermal gradient shown in Fig.A15. Therefore,

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crystals; a1 a4 grow more quickly than the crystals; b1, b2. The growth of b1, b2 will bestopped by the crystals; a1 a4. This phenomenon is named competitive grouth.

Fig.A16

Fig.A16 (upper) shows that the direction of maximum thermal gradient changes, as theweld pool is moving. This direction is perpendicular to the contour line of weld pool. At

the beginning of solidification, this direction is normal to the weld bond, and at the final

stage, it is idential with the welding direction.

As shown in Fig.A16 (lower), the solidification rate R is zero at the beginning and is the

same as the welding speed V. When the contour line inclines to the welding direction by i,

R = Ccosi.

Fig.A17

The crystalline direction of a1 a4 differs from the direction of maximum thermal gradientshown in Fig.A17. New crystal initiates and grows. This crystal is named the stray crystal.

Fig.A18 Fig.A18 shows the shapes depending on the welding conditions.

********** notation ****************************************************

Epitaxy Growth of one crystal on the surface of another crystal in which the growth of the

deposited crystal is oriented by the lattice structure of the substrate.

McGraw-Hill Dictionary of scientific and technical terms

Epitaxy Growth of a crystalline substance on a substrate crystal, in which the substrate determines

the crystal structure adopted. Since crystal structures vary in lattice parameter and crystal type,

quite apart from variations in atomic radius, it is obvious that epitaxial growth must be restricted,

and that considerable stresses may be generated even when it occurs. In general, the two lattices

involved (substrate and deposit) should be reasonably commensurate, the binding energy should

not be too dissimilar, and in ionic substances, the arrangement of positive and negative ions should

be capable of similar alignment.

Macdonald and Evans, The Metals Society, C.R.Tottle, An Encyclopaedia of Metallurgy and Materials

************************************************************************

4. Hot crack

Fig.A19 Hot crack is the weld defect which occurs at elevated temperature, mostly during solidi-

fication of weld pool.

The contour of weld pool is composed of two curves; liquidus and solidus curves shown inFig.A19. In the region between two curves, liquid crystal and molten metal coexist. The hot

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crack may occur, if the distance between two curves is large. This distance is depending on

the difference between liquidus and solidus temperatures, in general, which is increased with

solute concentration, and on the thermal gradient. Therefore, the more solute concentration

is, the more sensitive to hot crack is.

Fig.A20 Borland had proposed the critical solidification range (CSR) shown in Fig.A20. In eutectic

alloy, the solidification begins below solidus curve. In the stage 1, the amount of solid is

small and solid crystals can move freely in the molten metal. In this stage, the hot crack

does not occur. At the coherent temperature, solid crystals contact each other, but liquid

regions are connected three dimensionally. In the stage 2, the hot crack does not occur.

When the metal is cooled below the critical temperature, the amount of solid crystal is large

and the isolated liquid region begins to form. Since these liquid regions are separated from

the weld pool, new liquid can not flow into that region. Therefore, the hot crack may occurin the stage 3. The CSR is the difference between critical temperature and solidus curve.

Fig.A21 Fig.A21 shows the sensitivities to hot crack for several types of alminum alloys.

Fig.A22 In the case of welding the steels, the carbon content is usually lower than 0.5mass%.

Primary crystal is -ferrite, which can contain more impurities, such as P and S, comparing

with -iron. When the carbon content exceeds 0.09mass%, the peritectic reaction occurs

shown in Fig.A22. During this reaction, the austenite (-iron) forms between primary -ferrite and molten iron. Since austenite can not contain the impurities, impurities are

exhausted into molten iron. The concentrations of impurities in remaining liquid will become

large.

Fig.A23 Fig.A23 shows the equilibrium diagrams of Fe-S and Fe-P systems. In these systems,

there exists the substances with low menting point.

5. Microstructure formed during transformation of austenite

Fig.B1 There are two poles, equilibrium and non-equilibrium conditions. From the view point of

equilibrium diagram, that is, true equilibrium condition, there are only two phases, -ferrite

and cementite (Fe3C). In general meaning, the microstructures in equilibrium condition

includes the grain size of and the distribution of cementite shown in Fig.B1.

In non-equilibrium condition, a variety of microstructure are formed depending on the

types of material (chemical compositions) and thermal hystry (especially cooling rate).

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6. The isothermal transformation of steels

Fig.B2 The eutectoid steel heated to the temperature range of transfomes to pearlite which

is mixture of-iron and cementite, if it is cooled slowly. If the -iron of eutectoid steel iscoold down below A1 temperature, and is kept at that temperature, the -iron transforms

to some types of microstructures after somewhat delay of time.

Fig.B2 (right) shows the TTT diagram of eutectoid steel. In equilibrium condition,

the austenite transforms to pearlite just below Ae1. But actually the transformation is

delayed for any time depending on the difference in temperature between A1e and the holding

temperature. After the incubation time, the pearlite begins to form at the Ps curve. Pearlite

reaction finishes at Pf curve. The pearlite is coarse when it forms at the higher temperature

and longer time, while it is fine at lower temperature and shorter time. At about 550,

the incubation time becomes minimum. It is called the nose of TTT curve. When the steelis kept at the temperature below nose temperature, the bainite forms after the incubation

time. The incubation time for bainite is increased with a falling temperature. It is called

the bayof TTT curve. The bainite is divided into upper- and lower-bainites. When the steel

is cooled below Ms temperature, the martensite forms. The amount of martensite depends

on the holding temperature, and does not on the holding time.

Fig.B3 During cooling the austenite of hypo-eutectoid steel (-iron), pro-eutectoid ferrite (-iron)

precipitates at A3

temperature, and the remaining austenite at A1e transforms to pearlite(Fig.B3 (left). In the case of hyper-eutectoid steel, the precipitation of cementite occurs

before pearlite reaction. Therefore, Fs curve is added in TTT diagram of hypo-eutectoid

steel (Fig.B3 right,upper), and Cs curve in TTT diagram of hyper-eutectoid steel (right,

lower).

7. CCT diagram

Fig.B4 In welding, the steel is continuously cooled. Fig.B4 left is TTT diagram of eutectoid

steel. The heat cycle simulated weld heat cycles are drawn by the inclined curve on thetemperature-time diagram. They are different from the cooling curves used for making

TTT diagram which are the vertical line and the horizontal lines on the figure. Fig.B4 right

is continuous cooling trandformation diagram (briefly CCT diagram). The cooling curves of

v1 v4, VI and VII are correspond in both figures. However, the curves in left figure arenot correct, because the cooling curve is limited only to the vertical-horizontal line.

In the right figure, the cooling curves are bended because the horizontal axis of time is

locarithmic scale. In the cooling of v1, v2, pearlite forms as same as isothermal transfor-

mation. In the cooling between VI and VII, pearlite reaction begins, but dose not finish.

Remaining austenite transforms to martensite at the temperature of Ms. In this case, the

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cooling rate is large and the pearlite is extremely fine, thus it is called troostite. When the

cooling rate is larger than VII, all austenite transforms to martensite.

Fig.B5 B7

Fig.B5 B7 show the microstructure of 600MPa class high strength steel. Fig.B8 showsthe microstructure of SM500 steel.

Fig.B9 In the weld metal, the austenite grains are fine columnar shaped. While, in heat affected

zone, austenite grains are coarse polygonal shaped. Two austenite grains are essentially

same except the size and shape (Fig.B9).

In the case of hypo-eutectoid steel, pro-eutectoid ferrite precipitates preferentially at the

austenite grain boundaries.

Fig.B10 Fig.B10 left shows some types of ferrite. The specimens are cooled from austenitizing

temperature to the mentioned temperature along a specified cooling rate, and then rapidly

cooled into water. If the ferrite precipitates during cooling to the mentioned temperature,

we can observe the ferrite precipitated.

As shown in Fig.B10 left, at first, ferrite precipitates at grain boundary (GBF). Ferrite

side plates (FSP) grow from GBF. Very fine ferrite grain (acicular ferrite; AF) precipitate

in the remaining region.

Fig.B10 right shows the acicular ferrite obserbed by optical (upper) and electrom micro-scope (lower). Nucleation of acicular ferrite occurs at the very fine particle of oxide.

Fig.B11 Fig.B11 shows the microstructure of Si-Mn steel containing Ti and B. The oxygen levels

are different. In 60 ppm oxygen, the microstructure is fine ferrite including coarse grain.

In 270 ppm oxygen, the microstructure is fine ferrite only. In 440 ppm oxygen, we find the

coarse ferrite at the grain boundary (GBF) and fine ferrite interior of pre-austenite grain.

Among three oxygen levels, the weld metal containing 270ppm oxygen is most excellent in

toughness.

Fig.B12 B15 Japan Welding Society propose the following classifications. Fig.B12 shows the morphol-

ogy of ferrite in the weld metal and Fig.B13 shows the classification of microstructure in

heat affected zone. Fig.B14 and B15 show the example of microstructures.

8. Heat cycle during welding

Fig.C1 Fig.C1 shows the CCT diagram of 800MPa class high strength steel.

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Fig.C2 Fig.C2 can be drawn from the CCT diagram. In reverse, the figure as Fig.C2 is given

taking the place of writing the numerals for the amounts of microstructures and the hardness.

For using the CCT diagram, we should have the imfomation for cooling cycle.

Fig.C3 Fig.C3 shows the analitical solution for moving heat source. These solutions are useful for

understanding the thermal phenomena quantitatively. However, these solutions are obtained

assuming that many physical values, such as specific heat, thermal conductivity are constant.

Fig.C4 Fig.C4 shows the method for exstimating the cooling rate at 300 prposed by Cottrell.

The formula is experimental expression, therfore, it has no physical meanings. The cooling

rate is controlled by the balance between heat input and output. In this method, weld heatinput is used as the input of heat, and the thermal severity number (TSN; N) is used as the

output of heat. The TSN is determined from the joint configuration and plate thickness by

the unit of 1/4 inch.

Fig.C5 Dr.Inagaki had proposed the method for estimating the cooling time from 800 to 500

or 300. This method covers the wide range welding procedures. The following formula

also is experimental expression.

CT800500 or 300 =KJn

(m o)2

1 + 2

tan1 hho

The cooling time can be calculated easily by using the electric calculator. If there is no

calculator, we can use the nomogram as shown in Fig.C5.

The procedures are as follows.

1. Calculate the heat input; H from the welding current, arc voltage and welding speed.

2. Read the cooling time from 800 to 500 , by the plate thickness, heat input and joint

type, when the initial temperature of plates is room temperature, that is, withoutpreheating.

3. If the preheating is used, read the cooling time by using the axis for preheating from

the preheating temperature and the cooling time without preheating.

Fig.C5 is the nomogram for the shilded metal arc welding. Other nomograms are prepared

for other welding processes.

******************* Problems ***********************

Answer the following questions.

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1. Estimate the microstructure of HAZ of 800 MPa class high strength steel, when it is cooled

for 40 seconds from A3 to 500 .

2. Estimate the cooling time from 800 to 500 with the following welding conditions.

welding joint T type joint of a steel plate of 10mm thickness

welding process shielded metal arc welding

welding current 200 A

arc voltage 24 V

travel speed 4 mm/s

3. Estimate the microstructure and maximum hardness in HAZ of 800 MPa class high strength

steel, when it is welded with the above welding conditions.

4. Determine the preheating temperature to reduce the maximum hardness of HAZ to 300

VHN for the same steel.

****************************************************

9. Effect of heat cycle on toughness of steel welds

Fig.C11 The weld cracks occurs in the weld metal and the heat affected zone. The solidification

structure is concerned with the hot crack. Other metallurgycal factors are alloying elements

and impurities, especially microsegregation of impurities.The harder microstructures such

as martensite and bainite are concerned with the cold cracks. Since these hard structures

are formed during transformation in both of the heat affected zone and the weld metal, cold

cracks occur in both regions. In general, the HAZ is more sensitive to cold crack than the

weld metal.

Transformation microstructure is also concerned with the toughness of the weld.

Fig.C11 left shows the results of Charpy impact test for mild steels. Three curves are

named the Charpy full curve. The absorbed energy at room temperature is relatively large,and it is rapidly decreased with a fall of testing temperature. This phenomenon is observed

remarkably for the body-centered metal such as steels.

Three transition temperatures are defined.

Energy transition temperature; TrE

The absorbed energy of base metal at room temperature is about 14 kg-m/cm2. This

energy is called the shelf energy. The TrE is defined as the temperature which gives a

half of the shelf energy.

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Surface transition temperature; TrS

The percentage of brittle fracture surface is changed when the absorbed energy varies

with testing temperature as shown by the dotted curve. The TrS is defined as the

temperature which gives 50% brittle fracture surface.

Transition temperature which gives a defined absorbed energy; for example, Tr15The Tr15 gives the absorbed energy of 15 ftlb.

The toughness of the steel is evaluated by these transition temperatures. The lower

transition temperature is, the more tough the steel is. In Fig.C11, the base metal is most

tough and its toughness is decreased by heating and rapid cooling. However, the steel cooled

by 50/sec is more tough than that by 23 /sec.

Fig.C11 right shows the effect of cooling rate on the toughness of high strength steel.

The transition temperatures; Tr

S

and Tr15 fall and The absorbed energy is increased, as the

cooling rate is increased. So, rapid cooling is desired for the toughness of low alloying steels.

The Tr15 can be calculated by following formula, when the carbon content is lower than

0.18mass%.

Tr15 = 400Ceq 4

5

m +

2

50

Ceq = C+Mn

40 Ni

25+

Cr

20+

Mo

8

where, m is the amount of martensite (%), and is that of bainite (%).

Fig.C12 Fig.C12 shows the relationship between two transition temperatures calculated and mea-

sured.

The C, Mn, Cr, Mo have positive coefficients in the fomula of carbon equivalent. There-

fore, these elements increase the transition temperature. The Ni decreases the transition

temperature, that is, Ni is useful element for toughness of the steel. The m and have

negative coefficients, therefore, these microstructures decrease the transition temperature.

Although these hard microstructures are poor in general, the amounts of hard microstruc-

tures decrease the transition temperature.

Fig.C13 Fig.C13 (left side) shows the CCT diagrams of four carbon steels. The Ms temperature

is decreased with increasing the carbon content.

Fig,C13 (right) shows the Ms temperature against the carbon content for a variety of

steels containg other alloying elements. The Ms temperature is depending mainly on the

carbon content. In the welding, the martensite is formed with a rapid cooling below the Mstemperature. When the carbon content is smaller than 0.3mass%, the martensite is formed at

higher temperature of 350. While, the martensite is decomposed to ferrite and cementite

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at higher temperature of 350. Therefore, the martensite is formed and decomposed on and

on during weld thermal cycle. This phenomenon is called the Q-tempering. The tempered

martensite is fine grain microstructure and excellently tough.

10. Cold cracking The transformation microstructure is concerned with cold crack of structural steels. Three

major factors affect the sensitivity to cold crack.

1. Hydrogen

i) Type of electrode and welding procedure ii) Welding conditions(diffusion time for hydro-

gen) iii) Post weld heat treatment ; PWHT

2. Restraint stress (residual stress)

i) Joint configuration (position of joint in welded structure) (mainly) plate thickness ii)

Welding conditions

3. Hardened microstructure (martensite) or hardness

i) Chemical compositions (hardenability of steel) CCT diagram, Ceq ii) Cooling rate

(cooling time from A3 to a defined temperature) a. heat input energy used for heating b.

cooling ability plate thickness joint configuration pre-heating difference in temperature

between weld and base metal

Fig.C14 The microstructure of welded joint can be estimated by using the CCT diagram, if we

have. However, the CCT diagram for a steel can be used only for its steel. Therefore, in

many cases, we can not use CCT diagrams.

The hardness is also important as well as the microstructure to predict (or prevent) cold

cracks.

Fig.C15 In 1940 1969, the studies were made concerning the method for estimation of themaximum hardness from the chemical compositions of steel. The maximum hardness can

be estimated by the carbon equivalent Ceq.

Ceq = %C+%Mn

6+

%Ni

15+

%Cr

5+

%Mo

4+

%V

14+

%Cu

13 Hvmax = 1200Ceq200 (IIW)

Ceq = %C +%Mn

6+

%Si

24+

%Ni

40+

%Cr

5+

%Mo

4 Hvmax = 666Ceq +40 (WES)

Fig.C15 shows the relationship between maximum hardness and carbon equivalent.

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The carbon equivalent is obtained for a standard welding condition. Since the welding

condition is kept constant, we can not obtain the information of welding conditions affecting

the hardness.

In 1970

1979, the effect of cooling time was investigated. In general, the hardness of

martensite; HM is controlled only by carbon content, and the hardness of bainite; H B by

carbon and other alloying elements. The hardness of weld is determined by HM, HB and

the cooling time; .

Fig.C16 I recommends the method proposed by Dr.Yurioka (Fig.C16).

Fig.C17 The hardness of the steel Hv is a function ofHM, HB and X parameter. Actually, the

following expression is used.

Hv =HM + HB

2 HMHB

2.2tan1X

where, HM is the hardness of steel, when the steel is rapidly cooled, and HB is that , when

the steel is cooled with relatively slow cooling rate. Quantitative meanings of rapidly and

relatively slow are mentioned later.

The X parameter is expressed as follows.

X= 4

log M

log BM

2

where, is the cooling time from 800 to 500 , and it changes from M to B. If the cooling

time is M, the steel is cooled rapidly, and if= B, the steel is cooled relatively slow.

As the changes from M to B, X parameter changes from 2 to +2 shown in the nextfigure, and the range of the arctangent is about 2.2. Therefore, Hv changes from HM to HBcorresponding to the cooling time, .

It should be noticed that HM, HB, M and B are determined from only chemical com-

positions of the steel, and independent from cooling rate.

HM = 884(%C)

1 0.3(%C)2

+ 294

HB = 145 + 130tanh(2.65CeqII 0.69)

M = exp(10.6CeqI 4.8)

B = exp(6.2CeqIII + 0.74)

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Fig.C18 As shown in Fig.C18, HM is dependent on only carbon content. When the carbon content

is lower than 0.3 mass%, the increase in HM is linear. However, the effect of carbon is

decreased in the high carbon range.

Fig.C19 HB is determined by the second carbon equivalent CeqII, which includes the influences

of some alloying elements. Therefore, HB is dependent on not only carbon but also other

alloying elements.

Fig.C20 Fig.C20 shows the M and B. The M is smaller than B. These values are increased

with the carbon equivalents, which equivalents mean the hardenability of the steel.

In addition, CeqI,CeqII,CeqIII are also determined from the chemical compositions of the

steel.

CeqI = Cp +

%Si

24+

%Mn

6+

%Cu

15+

%Ni

12+

%Mo

4+

%Cr

8+

1 0.16

%Cr

+ H

Cp =

%C if %C 0.3%

%C + 0.25 if %C > 0.3%

H =

0 if %B 1ppm

0.03fn if %B = 2ppm

0.06fn if %B = 3ppm

0.09fn if %B 4ppm

fn =0.02%N

0.02

CeqII

= %C +%Si

24+

%Mn

5+

%Cu

10+

%Ni

18+

%Cr

5+

%Mo

2.5+

%V

5+

%Nb

3

CeqIII = Cp +

%Mn

3.6+

%Cu

20+

%Ni

9+

%Cr

5+

%Mo

5

That is, all parameters except the cooling time can be determined from the chemical

compositions of the steel. The time can be calculated by using the experimental formula

proposed by Dr.Inagaki.

Fig.C21

Fig.C21 shows the comparison of measured hardness with estimated values.

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