Goal theories

Several general reviews about this topic have been published by several authors [2].

A. Mechanical Properties

The mechanical properties of steels are determined by their constitutional and structural parameters. The important mechanical properties considered in this section are:

Yield strength ss (if there is no yield phenomenon during deformation test, the flow stress, or proof stress spis used instead).

Ultimate strength or tensile strength su.

Ductility, characterized by two parameters, et, the strain to fracture, and eu, maximum uniform strain prior to plastic instability.

Toughness, usually characterized by the Charpy Shelf Energy (CSE) value and by the impact transition temperature (ITT) ; in fracture mechanics, it is measured by crack opening displacement (COD).

Fatigue, a failure mode under cyclic stress.

1. Strength, Ductility and Toughness

a. Microstructure Composed of Polygonal Ferrite (Annealed and Normalized Low-Carbon Steels). For mild strip steels, IF steels, micro-alloyed high strength low alloy (HSLA) steels, polygonal ferrite is the basic and the predominant microstructural consti-tuents. The mechanical properties of the steel are basically determined by the properties of the ferrite intrinsically.

The yield strength of ferrite is determined by a number of factors, namely, its lattice friction stress (so), solid solution strengthening (ss), precipitation strengthening (sp), dis-location and substructure strengthening (sd), texture strengthening (st) and last, but the most influential, grain refining strengthening (sg).

(1) STRENGTH. (a) Intrinsic Lattice Friction Stress (so). This term is the origin of the strength of steels. It comes from the bonding force between atoms in the lattice. Friction

stress of ferrite is determined by the shear modulus (m) of iron, it measures the resistance to the movement of dislocations in the periodic field of the crystal lattice due to the intera-tomic interaction potential barriers. Assuming a sinusoidal force–displacement relation-ship, s_o may be expressed approximately as

soffi 2m expð2pw=bÞ ffi 10^3 ð1Þ

in which w¼a=(1n), and is the width of dislocation, b is Burgers’ vector. so is basically determined by the shear modulus of the base metal of the alloy. For ferrite, mFe¼8.310¹¹dyne=cm², then socan be calculated as about 83 MN=m². For all kinds of steels, it is nearly of the same value. It changes slightly either with the microstructure resulting from different processing parameters, or from alloying or heat treatment.

(b) Solid Solution Strengthening (ss). Unlike Al-, Ti- and Cu- alloys, solid solution strengthening is not the main method to increase the strength of carbon-, low alloy-and medium-alloy steels. Generally speaking, the mechanism which plays the role in solid solution strengthening is different in different alloys and at different temperatures, namely, it may be due to the misfit of atomic size, chemical locking, different in elastic modulus, change in electronic structure of the dislocation core, local ordering or clustering, long range order in intermetallic compounds, etc. For carbon- and low- and medium-alloy steels, solid solution strengthening is caused by the interaction of solute atoms and dislo-cations.

For both substitutional and interstitial solid solutions, solutes of different atomic size dissolved in body centered cubic iron produce localized strain fields which interact with those of the dislocations. The size misfit can be represented by

ds¼ ð1=aÞðda=dcÞ ð2Þ

where a is the lattice parameter of ferrite, in which the solute atoms are distributed ran-domly, the misfit produces interaction forces on dislocation that are to be summed statistically. Taking the flexibility of the dislocation into account, Mott and Nabarro first carried out the calculation and the result predicts the strengthening effects of magnitude

mðdsÞ⁴⁼³c^1=22=3 ð3Þ

c¹⁼²applies to very dilute solutions, c²⁼³applies to more concentrated solutions. m is the shear modulus of the alloy.

For steel, the effect of solid solution strengthening is less effective than that of pre-cipitation strengthening or that of transformation strengthening. The lattice distortion caused by solid solution usually impairs the toughness. It is also limited by the solid solu-bility limit of the solute in the matrix metals.

The solid solution strengthening coefficients of the common alloying elements used in steel are listed in Table 1 [3–5]. The elements most commonly used in carbon-, low- and medium-alloy steels are phosphorus, manganese and silicon, though boron may also be used in IF steels. Carbon and nitrogen are the most potent solid solution strengthening elements but substantial quantities of these elements in solution are not normally used because they lead to deleterious room temperature strain aging. Very small quantities in solution are used to give bake hardening.

Solid solution strengthened steels usually have a minimum yield stress in the range 220–300 N=mm², though higher strength may be obtained depending on the processing facilities available. Phosphorus is the element most commonly used for fairly low increase in strength, since it is relatively cheap and gives a higher increase in strength per unit

addition than manganese or silicon. Phosphorus addition is usually restricted to well below 0.1% to avoid problems with welding and because phosphorus may lead to second-ary cold work embrittlement (SCWE) of IF steel. SCWE is a phenomenon which leads to brittle fracture after the steel has previously received strain. A very small addition of boron, such as 0.0005%, is sufficient to reduce the tendency to SCWE [6]. The strengthen-ing by phosphorus is often supplemented first by manganese and then by silicon.

An advantage of solid solution strengthening steels is that they retain the general characteristics of the mild steel from which they are derived, good formability and the strain ratio of thickness to width. Furthermore, there is less loss in strength from the hot-rolled to the cold-rolled and annealed condition.

For structural steels containing up to 0.25% and 1.5% Mn, the microstructure is ferriteþ pearlite. When pearlite is less than 1=5 by volume fraction in the microstructure, pearlite has no effect on syof the steel. The solid solution principle is also valid for the ferrite in these steels. The solid solution effects of the common alloying elements are illu-strated in Fig. 1 [7].

Additions of up to about 0.1% P are incorporated in the higher strength rephosphor-ized grades that are used in the automotive body panel. But phosphorus is not used as a strengthening agent per se in structural steels. Phosphorus is added to the weathering grades because of its beneficial effect on atmospheric corrosion resistance. Silicon and manganese are cost effective as solid solution strengtheners in low-carbon structural steel, but silicon is added to steel primarily as a deoxidizing agent.

The following equation indicates approximately how the tensile strength of a batch-annealed solid solution strengthened AK strip steels varies with the steel composition (wt%) [8]:

s_u¼ 270 þ 441½O þ 64½Mn þ 98½Si þ 930½P ð4Þ

Another equation is as follows [9]:

s_u¼ 292 þ 563½C þ 678½P þ 18½Mn þ 90½Si  1534½S ð5Þ An equivalent equation for a continuously annealed steel is as follows [10]:

su¼ 477 þ 918½P þ 48½Mn þ 127½Si  0:019 ðT^CÞ ð6Þ where T 8C is the annealing temperature.

Table 1 Solid Solution Strengthening Coefficient

Solute

Solution strengthening coefficient (A), MNm^2(wt%)^1

C and N 5544

Solid solution strengthened steels are usually based on titanium, niobium or tita-nium plus niobium IF ultra-low-carbon steels but with sufficient phosphorus, manga-nese, silicon or boron to give the strength required. Figure 2 is a plot of properties vs.

[Si]þ [Mn] þ 10[P] for niobium bearing ULC IF steels. These curves suggest that the increase in strength from manganese is equivalent to that from silicon and that the effect of phosphorus is 10 times as great. The ratio of the true strain in width direction to the true strain in the thickness (r value) decreases most for manganese and least for phos-phorus. Figure 3 gives the effect of solid solution additions to titanium steel, in this case, the effect of silicon is greater than that of manganese as it is in an AK steel [10]. Figure 4 shows that the decrease in elongation is greatest for phosphorus addition and least for silicon. Boron imparts solid solution strengthening to titanium treated IF steel, even though boron has high affinity for nitrogen, in this case, nitrogen is precipitated as tita-nium nitride.

(c) Precipitation Strengthening (sp). The effect of precipitation strengthening is stronger than that of solid solution strengthening for steels. Both strip and structural grades of steel may be precipitation strengthened by the addition of elements such as tita-nium, niobium, and vanadium, and these elements may have an additional effect on strength by leading to grain refinement. These elements are strong carbide and nitride formers which may be partially or completely dissolved at the slab reheating stage prior to hot rolling and which may then be reprecipitated into a fine form on subsequent cool-ing and transform to ferrite. The degree of strengthencool-ing is dependent on both fraction and size of the precipitates; finer precipitates produce a greater effect. Coarse precipi-tates, which are not dissolved at the slab reheating stage, are ineffective as strengthening agents.

For quench aged carbides and precipitated carbonitrides in Nb, V and Ti added steels, the strengthening effect can be expressed by the modified Ashby–Orowan relation-ships [12,13]:

where f¼ the volume fraction of precipitate, x
¼the mean planar intercept diameter of the precipitates. Figure 5 shows the dependence of precipitation strengthening on precipitate size (x
) and volume fraction ( f ) according to the Ashby–Orowan model, compared with Figure 1 Solid solution strengthening effects in ferrite–pearlite steels. (From Ref. 7.)

Figure 2 Mechanical properties of ULC continuously annealed Nb bearing steel vs. [Si]þ[Mn]þ 10[P]. (From Ref. 11.)

Figure 3 Increase in tensile strength of ULC Ti bearing steel vs. content of solid solution elements.

(From Ref. 10.)

experimental observations for a given micro-alloying addition [14]. A simplified approach leads to an easily manipulated relationship:

sprecipitate¼ Bð% soluteÞ ð8Þ

The values of B in Table 2 have been published in Ref. [3].

Variation of the value of B below the maximum depends on:

(i) Whether some precipitation occurs in the austenite prior to ferrite transformation, especially during controlled rolling; if it occurs, it will decrease the value of B.

(ii) The temperature at which the precipitates are formed.

(iii) The extent to which the precipitates may overage during subsequent cooling.

(iv) Between 7508C and 6508C, with decreasing transformation temperature spincreases linearly with a decrease in transformation temperature; it amounts to 20 MN=m²=108C.

(v) sp increases to a maximum value with increasing cooling rate; if precipitation is suppressed by faster cooling, spwill decrease.

(vi) Tempering may be used to reactivate the precipitate process if such suppression occurs.

The solubility product for the precipitate is important, since it determines the amount of precipitate that can be taken into the solution at any temperature and consequently the volume fraction that may be subsequently reprecipitated in a fine form.

The temperature dependence of the solubility product is generally represented by an equa-tion of the form:

log½x½y ¼ A=T þ B ð9Þ

where [x] and [y] are the weight percentage of elements in solution, T is the temperature in degree Kelvin, and B is a constant. Table 3 gives the solubility products for a number of compounds in austenite.

Figure 6 shows the solubility of NbC and VN in austenite at various temperatures [17].

A number of precipitates are solid soluble in each other and the precise composition of such precipitates depends on the composition of the austenite matrix with which they are in equilibrium, as well as on the temperature. For example, niobium carbonitride Figure 4 Deterioration of elongation by solid solution elements. (From Ref. 10.)

has a wide range of solid solubility; the ratio of carbon to nitrogen in the precipitate in equilibrium at a given temperature could be calculated for different amounts of carbon, nitrogen, and niobium in the steel [18].

It is assumed that a precipitate with the formula NbCxN1xis in equilibrium with a matrix based on the reaction:

Nbsolþ xCsolþ ð1  xÞNsol¼ NbCxN1x ppt ð10Þ

The solubility product K for this reaction is written as

½Nb½C^x½N^1x=½NbCxN_1x ¼ K ð11Þ

where [NbCxN_1x] is the activity of the carbonitride which is taken as unity. It is also assumed that the activity of NbC in the precipitate is x and the effective activity of NbN in the precipitate was 1x and the separate solubility product equations for the equi-librium between the matrix and NbC and NbN, respectively, are:

½Nb½C=x ¼ K1 ð12Þ

½Nb½N=1  x ¼ K2 ð13Þ

Figure 5 Ashby–Orowan model compared with experimental observations. (From Ref. 14.)

Table 2 The Coefficient (B) of Precipitation Strengthening Solute and

precipitate

Bmax

(MN=m²=wt%)

Bave

(MN=m²=wt%)

Solute concentration (wt%)

V as V₄C₃ 1000 500 0–0.15

V as VN 3000 1500 0–0.06

Nb as Nb (CN) 3000 1500 0–0.05

Ti as TiC 3000 1500 0.03–0.18

where K1and K2are the solubility product for the pure carbide and nitride, respectively, at the desired temperature. For a given steel composition and temperature, these equations could be solved to give a value of x. The model was later developed further to involve more than one precipitate [19] and a number of computer programs able to predict the Table 3 Temperature Dependence of Solubility Product (wt%) for Carbides, Nitrides,

Carbonitride [15], Sulfides and Carbosulfides [16]

Solubility product (K ) Log₁₀K Solubility product (K) Log₁₀K

[B][N] 13970=Tþ5.24 [V][N] 7700=Tþ2.86

[Nb][N] 10150=Tþ3.79 [V][C]^0.75 6500=Tþ4.45

[Nb][C]^0.87 7020=Tþ2.81 [Ti][S] 16550=Tþ6.92

[Nb][C]^0.7[N]^0.2 9450=Tþ4.12 [Ti][C]¹⁼²[S]^0.5 15350=Tþ6.32

[Ti][N] 15790=Tþ5.40 [Mn][S] 9020=Tþ2.93

[Ti][C] 7000=Tþ2.75

Figure 6 Solubility of NbC and VN in austenite. (From Ref. 17.)

equilibrium conditions for a series of multi-component systems have now been developed.

These programs can be used to predict the amounts of titanium, niobium, carbon, nitro-gen, and sulfur, etc., retained in solution in equilibrium at any temperature as well as the amounts and composition of the precipitates.

Micro-alloyed steels are essentially low-carbon–manganese steels alloyed with the addition of the strong carbide or nitride-forming elements niobium, titanium or vanadium, separately or together, and are often known as high strength low alloy (HSLA) steel. In the hot-rolled condition, they usually have a yield stress in the range of 300 up to 500 or 600 N=mm². The upper limit of the potential yield stress range is usually lower for a cold-rolled and annealed product, depending on the processing given.

The alloying elements have widely differing effects [20] due to the different solubility of their carbides and nitrides in both austenite and ferrite, due to their different precipita-tion kinetics. They increase the strength both by precipitaprecipita-tion when sufficient carbon (nitrogen for vanadium steels) is present in the steel and grain refinement; but the grain refinement itself may arise from several mechanisms. In ferrite–pearlite steels, the systems of commercial significance are those involving niobium, vanadium, and titanium. These elements have only a limited solubility in steels due to their strong affinity for carbon and nitrogen. They are added to steels in small amounts, e.g., up to about 0.06% Nb or 0.15% V. At the slab or bloom reheating temperature of 12508C, a substantial amount of niobium will be taken into solution. Nb(C, N) will precipitate at the auste-nite–ferrite interface during transformation, called interphase precipitation, which leads to a substantial strengthening. But when reheating to a typical normalizing temperature of 9208C, very little Nb(C, N) will dissolve and virtually no precipitation strengthening can take place. The undissolved particles will act as pinning agents, restricting austenite grain growth and leading to the formation of a fine ferrite grain size. Therefore, the reheat-ing temperature controls the potential for precipitation strengthenreheat-ing and the strength increases progressively as the temperature raises from 9208C to 12508C. Vanadium dis-solves more easily than niobium and a complete solution of V4C3would be expected to occur in commercial grades of structural steel at a typical normalizing temperature, e.g.

9208C. For the dissolution of VN, slightly higher temperatures are required; at 9208C, VN can act as a grain refining agent. Aluminum is a powerful nitride former, in the pre-sence of 0.04% Al, significant vanadium will go into the solution at 9208C and be available for the precipitation of V4C3on transformation to ferrite. Vanadium steels provide signi-ficant precipitation strengthening effect, i.e., up to 150 N=mm²per 0.10% V.

Another instance of the application of precipitation strengthening is the micro-alloy-ing forgmicro-alloy-ing steel. Historically, after the methods of alloy reduction and substitution had largely been exhausted, attention was turned to potential savings in manufacturing costs and particularly in the area of heat treatment. Traditionally, components such as crank shaft and connecting rods are cooled to room temperature after the forging operation, only to be reheated to a temperature of about 8508C prior to oil quenching. Tempering at 550–6508C then produces tensile strengths in the range 800–1100 N=mm². In the mid-1970s, a micro-alloy-medium carbon steel (49MnVS3) was manufactured in Ger-many; after air cooling from the forging operation, heat treatment was eliminated. Since then, a major effort has been devoted to the development of micro-alloy forging steels in Europe, Japan, and China.

As indicated earlier, niobium, titanium, and vanadium are used as micro-alloying elements in low-carbon steels; high soaking temperature must be employed in order to achieve a substantial solution of Nb(CN) , TiC, and TiN. Vanadium is the most suitable micro-alloying element for medium-carbon steels due to its high solubility in austenite

regardless of carbon content. Vanadium carbonitride precipitates in both the proeutectoid ferrite and ferrite lamellae of the pearlite on cooling from the solution treatment tempera-ture [21]. Vanadium content in the range 0.05–0.2% is employed depending upon the levels of strength required. Figure 7 illustrates the tensile properties of these grades that increase progressively with the vanadium content. Nitrogen content influences the level of precipi-tation strengthening. The tensile strength of these steels can be expressed as a function of (Vþ 5  N) % [22]. In order to intensify the strengthening effect up to 0.02%, Ni is incor-porated in the steels.

One of the disadvantages of these micro-alloy steels is that they display significantly lower levels of toughness than the traditional quenched and tempered martensitic grades.

The low impact strength is related to the coarse pearlitic structure but this effect is exacer-bated by precipitation strengthening. Whereas this problem has been overcome in struc-tural steel plates with the use of low temperature finishing (controlled rolling), there is little scope for the adoption of this practice in dropping the forging operation due to the metal flow=die filling problems that occur at low forging temperatures.

The impact strength of these grades can be improved by lowering the carbon content and increasing the manganese, vanadium, and nitrogen content to compensate the loss in strength. Its practice in Sweden and Germany has shown that an improvement in tough-ness can also be obtained by increasing the silicon content. But grain refining by the addi-tion of titanium in pursuit of higher impact strength has been given attenaddi-tion. The stoichiometric level required for reaction with nitrogen in TiN and the growth of particles are also minimized by rapid solidification from the liquid state; then the finely dispersed particles of TiN present at the normal soaking temperature for forging, namely 11508C, will refine the austenite grain size [21]. In practice, the titanium additions are restricted to levels of about 0.01% and the need for rapid solidification is generally satisfied by con-tinuous casting.

Figure 7 Effect of V on the tensile properties of air cooled 0.45% C, 0.9% Mn steel. (From Ref. 5.)

The formations of TiN for grain refinement can reduce the level of available nitrogen for precipitation strengthening by V(CN). However, this problem can be overcome by adjusting nitrogen such that free nitrogen exceeds 0.006%.

(d) Dislocation and Substructure Strengthening (sd). Dislocations are introduced into ferrite by cold working, by controlled rolling at low temperatures, or by decreasing the trans-formation temperature. The complete processing will result in a substantial increase in strength. The strengthening effect due to dislocation is related to the dislocation density r,

s_d¼ amb ffiffiffirp

ð14Þ s_dis the stress increase due to cutting forest dislocations, m shear modulus, b Burgers’ vector of dislocation, and a is a constant.

The measurement of dislocation density is a sophisticated and time consuming work using the transmission electron microscope. As subgrain boundaries formed after

The measurement of dislocation density is a sophisticated and time consuming work using the transmission electron microscope. As subgrain boundaries formed after

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