fingerprints of materials

7/31/2019 Fingerprints of Materials

1/18


2/18

P. Christodoulou et al. / Materials Science and Engineering A 457 (2007) 350367 351

Fig. 1. Hardness density distribution for a single phase material.

points was implemented. The resulting data sets were trans-

formed into continuous microhardness density distributions

using S-Plus software [1,2]. These distributions were the sumof individual microhardness density distributions for each phase

or microstructural component. Using PeakFit software [3] the

peaks were separated and used for further analysis.

Microhardness measurements of a perfectly homogeneous

single phase material would always yield one value (within

equipments measuring accuracy), represented by a vertical line

depicting a density value of one on the hardness density distri-

bution (see Fig. 1). In reality, a single phase metal alloy does

not comprise such homogeneity, there are variations in grain

size, grain orientation, chemical composition, elastic and plas-

tic deformation of various regions of the materials and so on.

All these factors influence the microhardness values at differ-ent locations resulting in a microhardness density distribution

(often Gaussian) as shown in Fig. 1. One would expect such a

distribution to vary depending on the processing history of the

material (as-cast, heat treated, hot rolled, etc.).

Two-phase materials, where each phase varies in micro-

hardness, should result in two distinct microhardness density

Fig. 2. Hardness distribution for a two-phase material.

distribution curves. These curves may or may not overlap

depending on the microhardness differences. Further, if these

twophases donotdevelopadditionalstructural forms(e.g. eutec-

tic or eutectoid) the area under the peak representing one of thephases is expected to be proportional to the phase content. For

example, if there was 70% of phase A and 30% of phase B, one

would expect that after normalisation the area under the distri-

bution curve for phase one would account for 70% of the entire

area and the area under the second curve would account for the

remaining 30% (see Fig. 2). The first peak on Fig. 2 is not part

of any of the two phases; it reflects the presence of oxides, pores

and other inclusions that may be present in the material. It may

also be a result of measuring hardness on the grain boundaries

directly.

However, most of the two or more phase metal alloys

form additional microstructural components. Essentially, theseare spatial arrangements of phases involved, which lead to

unique physical and chemical properties, including hardness.

The following microstructural components are usually present:

primary precipitates (e.g. carbides), eutectic, forms resulting

from eutectoid or other transformations (e.g. perlite) and sec-

ondary precipitates distributed in the primary phase (matrix).

Fig. 3. Example of hardness density distribution analysis.


3/18

352 P. Christodoulou et al. / Materials Science and Engineering A 457 (2007) 350367

Fig. 4. Hardness distribution and numerical results for alloy #5 in the as-cast state.

Fitted parameters

r2 coef det 0.99979664

d.f. adj r2 0.99978198

Fit S.E. 3.6556E05

Fvalue 71393.0879

Peak Type a0 a1 a2

1 Gauss Amp 0.00059655 47.9486321 12.2691203

2 Gauss Amp 0.00036387 104.863587 23.4187213

3 Gauss Amp 0.00149296 164.141910 16.2284467

4 Gauss Amp 0.01314490 250.970324 23.4283062

5 Gauss Amp 0.00178980 315.050380 14.7067200

6 Gauss Amp 0.00077938 360.841214 21.0251870

7 Gauss Amp 0.00033430 487.999718 11.9617422

8 Gauss Amp 0.00033431 965.001055 11.9616167

Peak Type Amplitude Center FWHM Asym50 FW Base Asym10

Measured values

1 Gauss Amp 0.00059655 47.9486321 28.8915704 1 57.83249 1

2 Gauss Amp 0.00036387 104.863587 55.1468743 1 110.388 1

3 Gauss Amp 0.00149296 164.141910 38.2150715 1 76.49542 1

4 Gauss Amp 0.01314490 250.970324 55.1694451 1 110.4331 1

5 Gauss Amp 0.00178980 315.050380 34.6316791 1 69.32252 1

6 Gauss Amp 0.00077938 360.841214 49.5105318 1 99.10564 1

7 Gauss Amp 0.00033430 487.999718 28.1677504 1 56.38362 1

8 Gauss Amp 0.00033431 965.001055 28.1674548 1 56.38303 1

Peak Type Anlytc area % area Int area % Area Centroid Moment2Measured values

1 Gauss Amp 0.01834651 1.83559133 0.01832833 1.83381 47.98963 148.97

2 Gauss Amp 0.02135971 2.13706595 0.02135916 2.13705 104.8661 548.19

3 Gauss Amp 0.06073147 6.07626052 0.06073147 6.07637 164.1419 263.36

4 Gauss Amp 0.77194794 77.2343697 0.77194794 77.2358 250.9703 548.89

5 Gauss Amp 0.06597980 6.60136296 0.06597980 6.60149 315.0504 216.29

6 Gauss Amp 0.04107494 4.10959937 0.04107494 4.10968 360.8412 442.06

7 Gauss Amp 0.01002364 1.00287788 0.01002364 1.0029 487.9997 143.08

8 Gauss Amp 0.01002358 1.00287228 0.01002358 1.00289 965.0011 143.08

Total 0.99948758 100.000000 0.99946886 100


4/18


Distribution of the secondary precipitates is not necessarily

homogeneous throughout the matrix. In fact, there are often dif-

ferent conglomerations of precipitates visible within the matrix,

as well as areas free of precipitates altogether (pure matrix).

Additionally, it is not unusual to detect shifting microhardness

properties of thesame grain in differentplanes, which is a reflec-

tion of the directional anisotropy of a given microstructure. It is

thus expected to observe a complex collection of microhardness

density distribution peaks within the matrix related to its struc-

tural and chemical composition, as well as individual peaks for

each remaining phase/structure (eutectic, carbides, etc.).

Fig. 3 provides an example of such analysis. It shows both

microhardness density distribution as determined by micro-

hardness measurements (dotted outline) and the separated

components (peaks) forming the distribution. The example

assumes Gaussian distribution and illustrates six visible peaks,

where a corresponding microhardness value with the highest

probability (in this case the mean value) is provided for each

peak. The r2 is an estimate of the correlation between calculated

and measured values of the resultant hardness density distribu-tion, while S.E. represents the estimated standard error of the fit

and Fis the F-statistic value estimating the effectiveness of the

fit.

Fig. 3 illustrates a series of peaks related to the com-

plex structure of the matrix and the individual peaks of other

microstructural components. The call-outs describing the var-

ious phases point to the microhardness density distribution

determined directly from hardness measurements and indicate

the presence of phases A, B, C and D. Phase A, comprising the

largest area, represents the matrix, while phases B, C and D may

represent other precipitates or microstructural components. For

example, phase B could be (and most likely is) the reflection ofthe eutectic presence within these alloys, while phases C and D

probably represent the carbide precipitates.

In the present case, the matrix is described by three of the

six peaks. Structure A1 is very likely to correspond to a pure

matrix, structure A2 to be the result of a presence of minor car-

bideprecipitates distributed throughout the matrix, and structure

A3 either results from texture within the matrix, the presence of

areas varying in precipitation density, or different precipitates

altogether.

It is beyond the scope of this article to consider the exact

nature of relations between peaks and matrix microstructure.

However,existence of a correlationbetween these results and the

chemical composition of alloys supporting the above assump-

tions will be demonstrated. Most importantly, this additional

information can be used in specific situations such as those

involving materials performance analysis.

Fig. 4 depicts another example of a numerical and graphi-

cal analysis output. From this, it is clear there is a rather large

quantity of information associated with all alloys tested. For

practical reasons, it is essential such information is transformed

into a small set of indicators/factors, which can be used to com-

parevariousalloysor tofindcorrelationsbetweenmicrohardness

density distribution and the selected materials properties.

3. Results

Table 1 breaks down chemical compositions of the tested

alloys. These are 0.3% C, 18% Cr and 30% Ni cast alloys with

varying amount of Si, Nb, Ti and Al.

For reference purposes, the microstructure of tested alloys

consists of an austenitic matrix and a network of primary and

eutectic precipitates of carbides in the inter-dendritic regions.

The type and morphology of carbides varies with changing

chemical composition. Without the addition of stabilising ele-

ments, the carbides within alloys are of M23C6 nature, while the

simple NbC and TiC carbides are observed in the structure ofthe alloys with Nb and Ti content, respectively. When both Nb

and Ti elements are present, additional (Nb, Ti)C-based com-

plex carbides are also formed. When these alloys are annealed,

secondary M23C6 type carbides precipitate, while MC carbides

Table 1

Chemical composition of the tested alloys (wt.%)

Alloy Si Nb Ti Al C Mn Cr Ni P S Cu

1 1.685 1.750 0.830 0.280 0.270 0.92 17.50 29.30 0.02 0.0090 0.22

2 1.820 0.030 1.000 0.260 0.300 1.05 18.30 29.60 0.02 0.0120 0.21

3 1.815 1.840 0.050 0.021 0.300 0.96 18.20 29.30 0.02 0.0100 0.224 3.995 3.000 0.700 0.110 0.250 0.96 18.20 29.50 0.01 0.0100 0.23

5 1.720 0.100 0.700 0.160 0.350 0.94 18.30 29.20 0.01 0.0100 0.21

6 1.390 1.920 0.050 0.041 0.300 0.91 18.30 29.50 0.02 0.0090 0.19

7 3.110 2.480 1.420 0.240 0.280 1.04 17.80 29.50 0.02 0.0090 0.19

8 1.690 0.030 0.030 0.035 0.260 0.97 17.90 29.20 0.01 0.0090 0.21

9 4.255 1.590 1.070 0.130 0.300 1.02 17.80 29.30 0.02 0.0070 0.21

10 3.535 2.800 0.530 0.160 0.290 1.04 18.30 29.20 0.01 0.0090 0.22

11 1.570 0.550 0.300 0.100 0.330 0.97 18.30 29.40 0.02 0.0120 0.19

12 3.055 1.590 1.220 0.230 0.260 1.04 17.80 29.30 0.02 0.0100 0.19

13 3.530 1.470 0.400 0.120 0.290 0.98 17.90 29.20 0.02 0.0090 0.18

14 1.755 2.060 0.680 0.180 0.360 0.94 18.20 29.20 0.02 0.0100 0.21

15 3.150 1.540 0.370 0.068 0.300 0.89 17.80 29.20 0.02 0.0100 0.20

Average 0.30 0.98 18.04 29.33 0.02 0.01 0.21


5/18


in the presence of Si, undergo partial transformation into phase

G [4].

Based on the above analyses, microhardness and respec-

tive volume fraction has been extracted and tabulated. For all

alloys, 16 subcomponents (F0F15) were found to be consis-

tently determined in terms of varying microhardness value (see

Table 2).

4. Discussion

The average microhardness of the microstructure subcom-

ponents increases from 60 HV for the F0 component, to

2500HV for the F15 component (see Table 2). Both micro-

hardness and volume fraction of each component vary with

an alloys chemical composition. It can be argued that these

(from left to right) describe matrix, eutectic and primary precip-

itates, respectively. Thefirst subcomponents canbe related to the

matrix, thenext ones to theeutectic andthe remainingto primary

precipitates. Without detailed optical and X-ray microstructural

analyses to determine the nature of corresponding subcompo-nents, there is no way to establish a clear boundary in terms of

microhardness between the three structural components of the

alloys. It is proposed that in general there would be four major

subcomponents (see Table 3).

A low alloyed matrix phase (C0). This matrix subcompo-

nent would have microhardness less than 200 HV and would

incorporate low hardness measurements resulting from vol-

ume defects in the form of pores, non-metallic inclusions and

grain boundaries. This would result in a significant variation

of hardness across tested alloys.

Highly alloyed matrix (C1), possibly with precipitates dis-tributed throughout the volume, including precipitates that

are part of the eutectic (transient volumes).

Subcomponents related to the eutectic (C2).

Subcomponents likely related to primary precipitates (C3).

These would have highly varying microhardness, as pre-

cipitate nature changes significantly with varying chemical

composition.

Following the above, the results comprising Table 2 were

transformed to conform to these assumptions and presented in

Table 3 (average weighed hardness and sum of volume frac-

tions, respectively). The results point to an apparent relationship

between chemical compositions, heat treatment, volume frac-

tion of the microstructural subcomponents, and their micro-

hardness.

Multivariate linear regression analysis was implemented to

determine quantitative relations between chemical composition

and the alloys microstructural components volume fraction

and hardness (arbitrary function without an underlying phys-

ical meaning). Since volume fraction and hardness is always

positive, the regression function should also ensure a positive

response. An exponential dependence between volume fraction

and chemical composition was selected in the following form:

Vf= ef(x)

or ln(Vf)= f(x),

HVi= ef(x) or ln(HVi)= f(x)

where Vf is the volume fraction (vol.%); HVi is hardness; f(x)

is the polynomial function of independent variables (chemical

composition in wt.%).

Following these analyses, relationships between selected

mechanical properties, volume and microhardness of micro-structural components (C0C3), and chemical composition of

the alloys were determined using a similar approach. The fol-

lowing mechanical properties were considered (see Table 4):

Yield stressat room temperature (R02) andat 900C (WR02).

Ultimate tensile strength at room temperature (Rm) and at

900 C (WRm).

Elongation at room temperature (A10) andat 900C (WA10).

Fracture toughnessat room temperature (KCV) andat 900C

(WKCV).

The regression analysis was limited to heat-treated alloysas there is an interest in determining relationships between

microstructural composition and mechanical properties of the

alloys following heat treatment. It is established that mechani-

calpropertiesof materialsdepend on theirchemicalcomposition

andprocessing history, which in turn determines themicrostruc-

ture of the material. Here we can study the influence of

microstructural composition (volume fractions) and its micro-

hardness collectively with chemical composition on materials

mechanical properties. Clearly, there remains an information

gap regarding spatial and size distribution of microstructural

components, nonetheless it is a significant leap forward when

compared with the ability to consider only chemical composi-tion and average microhardness of bulk material. Quantitative

metallography can be of some help and will be explored in the

future.

The regression analysis results and associated statistical

information are presented in the appendices. Very high corre-

lations (R20.9999, with one exception of 0.9987, and in case

of the mechanical properties the R20.99999 in all cases) and

low errors (less than 5%) were attained, indicating fundamental

interrelationships between the chemistry, materials history and

microstructuralcomposition of alloys. Only in thecase of micro-

hardnessof componentC3, the selected exponential dependence

could not be obtained at satisfactory correlation and error

levels. Instead, a direct dependency between microhardnessand chemical composition was established (HVw3=f(chemical

composition)).

As expected, the four alloying elements observed (Si, Nb, Ti,

Al) proved strongly influential. Silicon had an extremely pow-

erful influence on matrix properties, while Nb and Ti combined

with C and Cr showed strong influence on eutectic and pre-

cipitates properties (volume fraction and microhardness). An in

depth analysis of the effects of alloying elements will be done

elsewhere for now it suffices to say that volume fraction of the

four microstructural components and their microhardness can

be predicted with confidence based on chemical composition

(within the studied range of the alloying elements).


6/18

Table 2

Hardness (HVi) and volume fraction (Vi) of each microstructural component (upper table for as-cast alloys and lower table for heat treated alloys)

Alloy Low alloyed matrix C0 Matrix C1 Eutectic related C2 Precipitates C3

F0 F1 F2 F3 F4 F5 F6 F7 F8 F9 F10 F11 F12

HVc0 Vc0 HVc1 Vc1 HVc2 Vc2 HVc3 Vc3 HVc4 Vc4 HVc5 Vc5 HVc6 Vc6 HVc7 Vc7 HVc8 Vc8 HVc9 Vc9 HVc10 Vc10 HVc11 Vc11 HVc12

Cast

1 127 1.1 265 47.4 325 37.9 438 5.8 515 1.9 715 1.0 921 3.0 1149 1.0

2 61 3.0 196 16.1 293 60.7 374 17.8 494 1 .3 731 1.0

3 97 10.2 160 5.7 242 72.3 337 3.6 380 5.4 464 0.9 557 1.0 783 1.0

4 160 3.5 275 55.7 374 31.0 695 4.5 944 4.2 1330

5 48 1.8 105 2.1 164 6.1 251 77.2 315 6.6 361 4.1 488 1.0 965 1.0

6 81 5.3 179 16.6 348 68.6 463 2.9 535 3.6 696 2.0 802 1.0

7 96 1.4 205 15.1 276 39.7 348 27.2 563 8.0 699 3.0 810 3.6 1371

8 128 3 .4 244 30.0 329 60.5 418 3 .1 543 2.0 677 1.0

9 84 8.5 323 69.5 452 3.6 549 11.4 791 4.1 1044 2.0 1371

10 129 5.4 183 4.0 253 73.9 391 7.3 469 3.3 603 1.0 677 2.0 748 1.0 1217

11 99 0.9 204 6.0 254 6.0 343 64.6 415 18.5 525 2.0 700 1.0 1330

12 55 2.7 247 71.1 347 10.3 437 6.6 560 1.4 675 5.7 810 0.3 881 1.0

13 88 2.8 167 2.8 291 17.2 317 61.9 470 6.3 591 2.0 765 2.0 883 1.0 1330

14 111 2.1 189 5.9 269 65.0 345 15.6 442 4.4 574 2.0 677 1.0 836 2.0 1126 2.0

15 105 0.8 168 7.1 260 72.1 325 5.9 402 10.2 471 0.9 579 2.0

55 102 175 263 333 380 456 558 694 787 905 1106 1325

Alloy Low alloyed matrix C0 Matrix C1 Eutectic related C2 Precipitates C3

F0 F1 F2 F3 F4 F5 F6 F7 F8 F9 F10 F11 F12

HVw0 Vw0 HVw1 Vw1 HVw2 Vw2 HVw3 Vw3 HVw4 Vw4 HVw5 Vw5 HVw6 Vw6 HVw7 Vw7 HVw8 Vw8 HVw9 Vw9 HVw10 Vw10 HVw11 Vw11 HVw12

Heat treated

1 103 1.0 213 7.6 273 11.9 300 68.3 404 1.9 471 6.3 580 1.1 644 0.9 1102 1.0

2 93 3.4 178 22.4 272 57.2 358 10.3 434 2.7 574 2.0 765 1.0 1102 1.0

3 32 0.8 143 10.9 174 5.3 248 56.6 343 19.2 462 4.1 585 1.3 653 1.7

4 149 1.7 285 18.9 352 36.4 411 13.7 456 9.3 663 12.7 758 1.9 890 1.3 1182 1.0 1330

5 108 5.6 206 16.8 245 22.6 300 45.2 376 5.6 473 2.1 620 1.9

6 144 20.6 203 8.5 275 54.2 421 15.8 531 0.9

7 115 9.4 156 1.5 248 47.3 332 28.6 440 1.8 530 4.7 671 3.6 805 0.9 1235 2.0

8 60 13.9 124 2.5 259 72.2 296 8.7 419 1.8 579 1.0

9 86 2.6 221 7.8 378 61.0 551 20.2 784 2.2 911 2.2 1184 1.0 1331

10 190 8.6 304 50.3 437 29.4 654 2.4 789 4.3 1149 1.0 1371

11 144 10.4 308 60.4 341 6.7 417 16.7 626 3.1 763 1.9 1030 1.0

12 140 2.2 223 7.7 297 63.8 385 13.9 493 5.6 565 3.1 628 2.9 1003 1.0

13 90 10.5 190 12.3 290 64.5 544 6.2 616 1.5 761 0.9 1118 1.0

14 61 0.8 189 5.7 281 47.4 370 38.6 385 2.0 630 2.7 735 1.8

15 65 0.6 148 11.3 232 55.4 241 10.7 303 14.5 406 2.5 526 2.0 731 1.0 1371

54 122 198 265 326 394 454 556 640 766 901 1123 1351


7/18


Table 3

Hardness and volume distribution of major microstructural components

Alloy Cast

C0 C1 C2 C3

HVc0 Vc0 HVc1 Vc1 HVc2 Vc2 HVc3 Vc3

1 127 1.1 292 85.3 457 7.6 1018 6.0

2 175 19.2 293 60.7 382 19.1 731 1.0

3 120 15.9 246 75.9 415 7.2 783 1.0

4 160 3.5 275 55.7 374 31.0 869 9.7

5 130 10.0 256 83.8 386 5.1 965 1.0

6 156 21.9 348 68.6 503 6.5 731 3.0

7 195 16.5 305 66.9 563 8.0 965 8.6

8 128 3.4 301 90.5 467 5.1 677 1.0

9 84 8.5 323 69.5 526 15.0 944 7.1

10 152 9.4 253 73.9 431 11.6 960 5.0

11 191 6.9 335 70.6 426 20.5 1015 2.0

12 55 2.7 260 81.4 459 8.0 982 7.9

13 128 5.6 311 79.1 499 8.3 1191 7.0

14 169 8.0 284 80.6 483 6.3 922 5.1

15 162 7.9 265 78.0 434 13.1 1609 1.0

AVG 142 290 454 958

Alloy Heat treated

C0 C1 C2 C3

HVw0 Vw0 HVw1 Vw1 HVw2 Vw2 HVw3 Vw3

1 200 8.6 296 80.2 470 9.3 883 1.9

2 167 25.8 285 67.5 493 4.7 934 2.0

3 148 17.0 272 75.9 493 5.4 653 1.7

4 149 1.7 329 55.3 429 23.1 859 19.8

5 181 22.4 282 67.9 403 7.8 620 1.9

6 161 29.1 275 54.2 427 16.7 NA 0.0

7 121 11.0 280 75.9 505 6.5 862 6.6

8 69 16.4 263 80.9 477 2.8 NA 0.0

9 187 10.4 378 61.0 551 20.2 1113 8.410 190 8.6 304 50.3 437 29.4 1151 11.7

11 144 10.4 308 60.4 395 23.3 738 5.9

12 204 9.9 297 63.8 436 22.5 726 3.9

13 144 22.8 290 64.5 544 6.2 1447 6.4

14 174 6.5 321 86.0 385 2.0 823 5.5

15 216 67.3 277 25.2 459 4.5 1237 3.0

AVG 164 297 460 926

Table 4

Selected mechanical properties of the heat treated alloys

Alloy R02 (MPa) Rm (MPa) A10 (%) KCV (J/cm2) WR02 (MPa) WRm (MPa) WA10 (%) WKCV (J/cm2)

1 186.3 418.2 6.7 31.9 57.9 98.7 22.9 39.82 236.4 389.0 6.4 39.0 68.7 108.9 30.4 42.5

3 231.9 429.2 6.3 31.7 74.8 119.1 23.4 37.7

4 263.9 455.5 4.4 25.0 56.2 103.5 29.2 25.5

5 242.6 428.3 6.3 37.0 72.6 111.0 24.3 42.6

6 239.1 459.0 8.8 34.3 80.5 120.3 20.7 53.4

7 251.4 373.0 1.7 18.8 66.4 127.4 17.9 23.2

8 253.5 467.8 6.7 40.9 78.9 118.7 24.5 45.8

9 241.3 356.2 3.4 23.4 50.8 96.8 24.2 27.0

10 233.8 353.8 3.9 23.6 49.9 98.6 20.9 28.6

11 245.5 442.7 6.6 41.4 82.3 134.7 16.3 47.3

12 208.8 330.5 3.9 26.2 52.5 101.2 17.9 29.3

13 224.7 456.1 9.9 46.7 58.4 94.3 31.0 48.9

14 225.1 439.0 9.0 42.5 62.6 104.8 33.4 52.6

15 226.9 447.7 9.7 44.0 62.6 103.9 23.9 43.0


8/18


Inallcasesa significant influenceonmechanical properties of

volume fraction and microhardness of the microstructural com-

ponents was observed along with significant effects of chemical

composition. The extremely high correlation and exceptionally

low errors indicate strong relationships between mechanical

properties on the one hand, and volume fraction and micro-

hardness of microstructural components as well as chemical

composition of the alloys on the other. Therefore, the following

can be confidently stated.

Based on chemical composition we can predict volume frac-

tion of the constituent microstructural components and their

microhardness. This, in conjunction with chemical composi-

tion, allows mechanical properties of the alloys studied to be

determined fairly accurately.

It is beyond the scope of this article to analyse in great depth

the developed relationships and cross check with other analyses

suchas X-raydiffraction, optical quantitative metallographyand

microhardness measurements of selected microstructural com-

ponents.However, for illustration purposestheequationforyield

stress at room temperature (R02, see Table A9) will be brieflydiscussed

ln(R02) = 0.050Vw0+ 0.048Vw1+ 0.048Vw2

+0.0709Vw3+ 0.000488HVw2 0.000137

HVw3+ 2.63 108 HV32 + 0.02801Nb2

0.1170Nb+ 0.2959 Ti2 0.4125 Ti

+1.7127 C

From the above equation it can be said that each of the

microstructure constituents contribute proportionally to their

volume fraction (the biggest being alloyed matrix and eutectic).This contribution is enhanced by microhardness of the eutec-

tic (HVw2), while increasing microhardness of the precipitates

(whichis an indication of thechangingnatureof theprecipitates)

has a deteriorating effect. Also, there appear to exist optimum

levels of Nb and Ti that maximise yield stress. However, this

needs to be considered in conjunction with volume fraction of

microstructural components as these also depend on chemical

composition. To achieve this, a series of equations should be

formulated (function to maximise and constraints) to determine

using optimisation procedures whether an optimal composition

for the set of required mechanical properties is attainable.

It is worth noticing that similar results could be achieved byusing quantitative X-ray analysis [5]. However, this approach

is much more difficult as it requires intricate (not always easily

available) information about phase components. It seems that

combining the two analysis tools with quantitative metallogra-

phywillyielda powerfuland comprehensivemeans formaterials

analysis.

5. Conclusions

A new microstructural analysis tool based on microhardness

measurements has been developed and presented. It appears

capable of uniquely describing materials in terms of microhard-

ness density distribution, which can then be used to determine

volume fraction and average microhardness of microstructural

components.

It has been shown that high quality (in the sense of correla-

tions and accuracy) quantitative relationships between chemical

composition and microstructural properties (as determined by

the analysis) can be achieved. Further, relationships between

microstructure, chemical composition and selected mechani-

cal properties can be developed. It follows that combining

the two sets of relationships (microstructurechemical com-

position and microstructuremechanical propertieschemical

composition) an in depth analysis of relationships between

chemical composition and mechanical properties can be carried

out.

It appears that the microhardness analysis presented offers

a relatively easy way to accomplish the complex task of pre-

dicting mechanical properties of materials based on chemical

composition for a given processing.

Appendix A. Regression analysis results

A.1. Linear multivariate modellingabbreviations

To increase clarity the results of the regression analysis are

presented in table form. The following abbreviations are used:

log natural logarithm function

d.f. degrees of freedom

standard deviation on the equations response scale

r.sq square of the correlation coefficientCALL expression for the equation, where denotes the

functional dependence between the left side (the

response) and right side (independent variables, alloy-

ing elements); the sign : denotes multiplication

(interaction between two variables). I() denotes iden-

tity function that is used internally by the software for

evaluating expressions. Thus I(Si2) is the same as Si2,

orI(((C)/(Nb))2) is the sameas (C/Nb)2. (1) indicates

that intercept is equal zero (no intercept)

value value of the coefficients for the respective independent

variables in the equation

S.E. standard error for a given coefficient

tvalue Student tvalue for a given coefficientPr(>|t|) probability that for a given t value the coefficient is

equal zero (insignificant effect)

sum of sq sum of squares

mean sq mean value of sum of squares

Fvalue value of the Fishers test

Pr(F) probability that for a given Fvalue the considered vari-

able has zero (insignificant) contribution.

A.2. Volume fraction

See Tables A1A4.


9/18


Table A1

Volume fraction for C0 microstructural component

CALL

lm log(Vw0)Nb+Ti+Cr+Fe+log(I((C)/(Cr)))+I(Ni2) +I((C)/(Cr))+I(I((C)/(Si))2)+ Ti:Cr+ Si:Fe+ Nb:log(I((C)/(Cr)))+ Nb:Ti + Nb:Cr 1

row.names Value S.E. tvalue Pr(>|t|)

Coefficients

Nb 30.591323 2.467706 12.396664 0.006444

Ti 99.259423 1.815902 54.661213 0.000335

Cr 10.367372 0.165921 62.483847 0.000256

Fe 10.190755 0.081474 125.079141 6.40E05

log(I((C)/(Cr))) 155.279701 1.144282 135.700545 5.40E05

I(Ni2) 0.104586 0.002115 49.453508 0.000409

I((C)/(Cr)) 9818.588833 78.042079 125.811472 6.30E05

I(I((C)/(Si))2) 57.436742 2.578585 22.27452 0.002009

Ti:Cr 6.301932 0.103762 60.734257 0.000271

Si:Fe 0.23436 0.001979 118.417655 7.10E05

Nb:log(I((C)/(Cr))) 1.347527 0.102639 13.128799 0.005752

Nb:Ti 0.206821 0.013207 15.660157 0.004053

Nb:Cr 0.792291 0.114958 6.891989 0.020411

0.012978 NA NA NA

r.sq 0.999997 NA NA NA

row.names d.f. Sum of sq Mean sq Fvalue Pr(F)

Analysis of variance

Nb 1 59.641305 59.641305 354125.415 3.00E06

Ti 1 8.570229 8.570229 50886.47694 2.00E05

Cr 1 34.81712 34.81712 206729.6634 5.00E06

Fe 1 0.323476 0.323476 1920.669004 0.00052

log(I((C)/(Cr))) 1 0.069186 0.069186 410.799122 0.002425

I(Ni2) 1 0.484405 0.484405 2876.197907 0.000348

I((C)/(Cr)) 1 0.443368 0.443368 2632.537006 0.00038

I(I((C)/(Si))2) 1 2.637793 2.637793 15662.12225 6.40E05

Ti:Cr 1 0.205554 0.205554 1220.495013 0.000818Si:Fe 1 2.665877 2.665877 15828.87459 6.30E05

Nb:log(I((C)/(Cr))) 1 0.056282 0.056282 334.181324 0.002979

Nb:Ti 1 0.034777 0.034777 206.493492 0.004808

Nb:Cr 1 0.008 0.008 47.499517 0.020411

Residuals 2 0.000337 0.000168 NA NA

Table A2


CALL

lm log(Vw1)Si+Nb+Cr+Ni+Fe+Nb:Ni+Si:Nb+Si:Ni+Nb:Cr+Ti:Cr


Coefficients

(Intercept) 999.777498 31.000082 32.250802 6.00E06

Si 61.478523 3.414741 18.00386 5.60E05

Nb 78.275569 3.637342 21.51999 2.80E05

Cr 9.246534 0.298245 31.003136 6.00E06

Ni 13.873398 0.432768 32.057349 6.00E06

Fe 8.282341 0.277617 29.833688 8.00E06

Nb:Ni 1.942818 0.104818 18.535184 5.00E05

Si:Nb 0.40945 0.018761 21.824024 2.60E05

Si:Ni 1.843364 0.115083 16.01768 8.90E05

Nb:Cr 0.761204 0.067167 11.33297 0.000346

Ti:Cr 0.564654 0.019782 28.543259 9.00E06

0.027015 NA NA NA



10/18


Table A2 (Continued)



Si 1 0.179544 0.179544 246.007857 9.70E05

Nb 1 0.003404 0.003404 4.664183 0.096925Cr 1 0.018011 0.018011 24.678414 0.007664

Ni 1 0.007624 0.007624 10.446652 0.031911

Fe 1 0.178697 0.178697 244.848286 9.70E05

Nb:Ni 1 0.061934 0.061934 84.861075 0.000772

Si:Nb 1 0.000788 0.000788 1.080229 0.357341

Si:Ni 1 0.078538 0.078538 107.61204 0.000488

Nb:Cr 1 0.103469 0.103469 141.771474 0.000285

Ti:Cr 1 0.594605 0.594605 814.717631 9.00E06

Residuals 4 0.002919 0.00073 NA NA

Table A3


CALL

lm log(Vw2)Si+Cr+I(Cr2)+Nb+Ti+log(I((C)/(Cr)))+I(Ti2)+ Ti:Cr 1


Coefficients

Si 0.531748 0.11229 4.735483 0.002119

Cr 11.38901 1.182861 9.62836 2.70E05

I(Cr2) 0.568066 0.058186 9.762952 2.50E05Nb 0.550525 0.120745 4.559399 0.002607

Ti 212.806018 23.809414 8.937894 4.50E05

log(I((C)/(Cr))) 5.143122 0.97753 5.261347 0.001172

I(Ti2) 3.337254 0.558581 5.974522 0.000556

Ti:Cr 11.574035 1.300106 8.902379 4.60E05

0.280226 NA NA NA




Si 1 71.204338 71.204338 906.752631 0

Cr 1 3.406404 3.406404 43.378904 0.000308

I(Cr2) 1 0.541149 0.541149 6.891273 0.034154

Nb 1 0.190737 0.190737 2.428946 0.163074

Ti 1 0.058788 0.058788 0.748638 0.415573


log(I((C)/(Cr))) 1 0.662052 0.662052 8.430914 0.022868

I(Ti2) 1 0.087199 0.087199 1.110435 0.326996

Ti:Cr 1 6.22343 6.22343 79.252358 4.60E05

Residuals 7 0.549687 0.078527 NA NA


11/18


Table A4


CALL

lm log(Vw3) log(Al)+I((C)/(Ti))+ Al+ log(Ti)+ log(Fe) + Ti+I((C)/(Ti)):log(Al)+I((C)/(Ti)):log(Fe)+ Al:log(Fe)+I((C)/(Ti)):log(Ti)


Coefficients

(Intercept) 256.088745 16.157542 15.849487 9.30E05

log(Al) 4.625657 0.428653 10.791141 0.000418

I((C)/(Ti)) 136.173345 6.993815 19.470538 4.10E05

Al 651.497393 79.179895 8.228066 0.001189

log(Ti) 2.344309 0.597771 3.921749 0.017222

log(Fe) 64.493814 4.305391 14.97978 0.000116

Ti 2.361372 0.631308 3.740446 0.020113

I((C)/(Ti)):log(Al) 2.056596 0.065923 31.196727 6.00E06

I((C)/(Ti)):log(Fe) 35.825226 1.986633 18.033136 5.60E05

Al:log(Fe) 164.73605 20.47168 8.047022 0.001295

I((C)/(Ti)):log(Ti) 3.073436 0.207698 14.797631 0.000121

0.06913 NA NA NA




log(Al) 1 23.241029 23.241029 4863.25095 0

I((C)/(Ti)) 1 35.283766 35.283766 7383.227566 0

Al 1 1.089047 1.089047 227.886053 0.000112

log(Ti) 1 0.650128 0.650128 136.041085 0.000309

log(Fe) 1 1.350978 1.350978 282.696015 7.30E05

Ti 1 1.320794 1.320794 276.379928 7.70E05

I((C)/(Ti)):log(Al) 1 6.82561 6.82561 1428.278098 3.00E06

I((C)/(Ti)):log(Fe) 1 1.360613 1.360613 284.712092 7.20E05

Al:log(Fe) 1 0.004774 0.004774 0.998878 0.374142

I((C)/(Ti)):log(Ti) 1 1.046437 1.046437 218.969878 0.000121

Residuals 4 0.019116 0.004779 NA NA

Table A5

Hardness of C0 microstructural component

CALL

lm log(HVw0)Si+Nb+Ti+Fe+I(I((C)/(Ti))2) +I(Si2)+log(Nb)+I(Cr2)+ Ti:Fe+ Si:Ti+ Nb:log(Nb) 1


Coefficients

Si 0.848168 0.082276 10.30877 0.0005

Nb 1.432943 0.163379 8.770649 0.000932

Ti 33.306471 1.538345 21.650844 2.70E05

Fe 0.119999 0.010358 11.584767 0.000317

I(I((C)/(Ti))2) 0.024937 0.002287 10.901503 0.000402

I(Si2) 0.289269 0.0231 12.522723 0.000234

log(Nb) 0.506211 0.064708 7.823002 0.001441

I(Cr2) 0.007238 0.001548 4.676608 0.009472

Ti:Fe 0.622629 0.028252 22.038114 2.50E05

Si:Ti 1.776184 0.116218 15.283152 0.000107

Nb:log(Nb) 0.212479 0.074257 2.861399 0.045865

0.025175 NA NA NA



12/18





Si 1 339.180836 339.180836 535177.9262 0

Nb 1 0.73282 0.73282 1156.283125 4.00E06

Ti 1 1.899333 1.899333 2996.870692 1.00E06

Fe 1 43.424614 43.424614 68517.71243 0

I(I((C)/(Ti))2) 1 0.537226 0.537226 847.663851 8.00E06

I(Si2) 1 0.007348 0.007348 11.593792 0.027153

log(Nb) 1 0.009674 0.009674 15.264645 0.0174438

I(Cr2) 1 0.00352 0.00352 5.554652 0.077932

Ti:Fe 1 0.223796 0.223796 353.118196 4.70E05

Si:Ti 1 0.143302 0.143302 226.108987 0.000114

Nb:log(Nb) 1 0.005189 0.005189 8.187604 0.045865

Residuals 4 0.002535 0.000634 NA NA

Table A6


CALL

lm log(HVw1) Si+Nb+Cr+Fe+I(Si2)+ log(Ti)+ log(Si) + Si:log(Ti) 1


Coefficients

Si 2.134921 0.961995 2.219264 0.061944

Nb 0.121283 0.022847 5.308422 0.001113

Cr 0.126808 0.033867 3.744248 0.007222

Fe 0.104124 0.014581 7.141188 0.000187

I(Si2) 0.24281 0.085695 2.833417 0.025282

log(Ti) 0.008922 0.038832 0.22975 0.824855

log(Si) 2.443218 1.309833 1.86529 0.104397

Si:log(Ti) 0.046 0.019852 2.317136 0.05362

0.0394 NA NA NA




Si 1 426.820222 426.820222 274954.5826 0

Nb 1 0.559062 0.559062 360.143874 0

Cr 1 58.172673 58.172673 37474.42628 0

Fe 1 0.028576 0.028576 18.408228 0.003609

I(Si2) 1 0.01827 0.01827 11.76917 0.010976

log(Ti) 1 0.074899 0.074899 48.249338 0.000222

log(Si) 1 0.001952 0.001952 1.257706 0.299078

Si:log(Ti) 1 0.008335 0.008335 5.369119 0.05362

Residuals 7 0.010866 0.001552 NA NA

Table A7


CALLlm log(HVw2) Si+Nb+C+Cr+Ni+log(I((C)/(Ti))) +I(Al2)+Nb:C 1


Coefficients

Si 0.278574 0.033576 8.296903 7.20E05

Nb 0.248116 0.136916 1.812175 0.112855

C 5.040324 1.183285 4.259603 0.003748

Cr 0.245647 0.058191 4.221371 0.00393

Ni 0.282206 0.033096 8.526988 6.10E05

log(I((C)/(Ti))) 0.255808 0.037596 6.804094 0.000252

I(Al2) 8.933878 1.462583 6.108286 0.000487

Nb:C 1.038008 0.464585 2.234272 0.060588

0.036376 NA NA NA



13/18





Si 1 494.418133 494.418133 373656.6002 0

Nb 1 0.461261 0.461261 348.598228 0

C 1 64.022906 64.022906 48385.32356 0

Cr 1 3.953503 3.953503 2987.86053 0

Ni 1 0.184913 0.184913 139.747963 7.00E06

log(I((C)/(Ti))) 1 0.029087 0.029087 21.982205 0.002238

I(Al2) 1 0.047075 0.047075 35.576756 0.000562

Nb:C 1 0.006605 0.006605 4.991972 0.060588

Residuals 7 0.009262 0.001323 NA NA

Table A8


CALL

HVw3Si+Nb+Ti+Cr+Fe+I(Cr2) +I(I((C)/(Si))2) +I(Ti2) +I(I((C)/(Cr))2)+C+Si:Ti+Ti:Cr+Si:Nb 1


CoefficientsSi 1542.184313 47.959154 32.156204 0.000966

Nb 2002.956319 43.825787 45.702689 0.000478

Ti 50630.758565 1387.765570 36.483654 0.000750

Cr 11392.691153 251.858609 45.234472 0.000488

Fe 1906.160803 39.461400 48.304440 0.000428

I(Cr2) 315.798658 7.347174 42.982330 0.000541

I(I((C)/(Si))2) 43881.687615 1123.381906 39.062128 0.000655

I(Ti2) 678.250362 31.264292 21.694090 0.002118

I(I((C)/(Cr))2) 30559747.607236 1681834.032040 18.170489 0.003015

C 41518.142630 2968.722628 13.985188 0.005074

Si:Ti 552.456689 17.917693 30.833026 0.001050

Ti:Cr 2846.510871 77.999344 36.494036 0.000750

Si:Nb 16.427385 4.941069 3.324662 0.079792

7.949860 NA NA NA




Si 1 10553256.72 10553256.72 166981.1755 6.00E06

Nb 1 5851.497967 5851.497967 92.586586 0.010629

Ti 1 56245.43967 56245.43967 889.955573 0.001122

Cr 1 32270.50981 32270.50981 510.607086 0.001953

Fe 1 971.342249 971.342249 15.369272 0.059333

I(Cr2) 1 4391.239953 4391.239953 69.481339 0.014089

I(I((C)/(Si))2) 1 448.329988 448.329988 7.093798 0.116784

I(Ti2) 1 483258.2763 483258.2763 7646.458069 0.000131

I(I((C)/(Cr))2) 1 589212.3263 589212.3263 9322.938825 0.000107

C 1 43589.33184 43589.33184 689.701583 0.001447

Si:Ti 1 22522.12799 22522.12799 356.361217 0.002794Ti:Cr 1 83855.87844 83855.87844 1326.827682 0.000753

Si:Nb 1 698.576509 698.576509 11.053377 0.079792

Residuals 2 126.400556 63.200278 NA NA

Table A9

Yield stress at room temperature (R02) as function of microstructural and chemical composition

CALL

lm log(R02)Vw0+ Vw1+HVw2+ Vw2+HVw3+ Vw3+Nb+ Ti+ C+I(Ti2) +I(Nb2) +I(HVw32) 1


Coefficients

Vw0 0.050447 0.000269 187.204163 0

Vw1 0.048363 0.000294 164.371812 0


14/18




HVw2 0.000488 4.10E05 11.798301 0.001309

Vw2 0.048137 0.000273 176.530078 0

HVw3 0.000137 1.10E05 12.193866 0.001187

Vw3 0.07096 0.000602 117.794653 1.00E06

Nb 0.117014 0.004543 25.757382 0.000128

Ti 0.412528 0.014804 27.866835 0.000101

C 1.712759 0.046811 36.588992 4.50E05

I(Ti2) 0.295947 0.010228 28.935577 9.10E05

I(Nb2) 0.028074 0.001876 14.963134 0.000648

I(HVw32) 2.63E08 7.90E09 3.3282 0.044779

0.003838 NA NA NA

r.sq 1 NA NA NA



Vw0 1 258.316364 258.316364 17533134.24 0

Vw1 1 178.054351 178.054351 12085377.75 0

HVw2 1 5.625469 5.625469 381826.798 0

Vw2 1 3.195897 3.195897 216920.4021 0

HVw3 1 0.056517 0.056517 3836.041955 9.00E06

Vw3 1 0.739913 0.739913 50221.3401 0

Nb 1 0.013174 0.013174 894.212549 8.20E05

Ti 1 3.00E05 3.00E05 2.061339 0.246589

C 1 0.018072 0.018072 1226.632142 5.10E05

I(Ti2) 1 0.011938 0.011938 810.320512 9.50E05

I(Nb2) 1 0.00327 0.00327 221.925824 0.000656

I(HVw32) 1 0.000163 0.000163 11.076913 0.044779

Residuals 3 4.40E05 1.50E05 NA NA

Table A10

Yield stress at 900 C (WR02) as function of microstructural and chemical composition

CALL

lm log(WR02)HVw0+Vw1+Si+I(Vw22)+Vw2+I(1/(HVw3)) + HVw3 +I(1/(C)) + HVw0:C+ Vw1:Si


Coefficients

(Intercept) 6.650373 0.040639 163.644154 0

HVw0 0.001625 0.000232 6.999824 0.002192

Vw1 0.004036 0.000286 14.134486 0.000145

Si 0.047351 0.007289 6.496529 0.002896

I(Vw22) 0.000557 1.40E05 38.951135 3.00E06

Vw2 0.013553 0.000468 28.942802 8.00E06

I(1/(HVw3)) 0.001669 3.30E05 50.35335 1.00E06

HVw3 0.000185 4.00E06 41.956049 2.00E06

I(1/(C)) 0.373903 0.013526 27.643056 1.00E05

HVw0:C 0.017394 0.000834 20.844406 3.10E05

Vw1:Si 0.000752 0.000107 7.032001 0.002155

0.001932 NA NA NA

r.sq 0.999962 NA NA NArow.names d.f. Sum of sq Mean sq Fvalue Pr(F)


HVw0 1 0.118711 0.118711 31811.56228 0

Vw1 1 0.001137 0.001137 304.699706 6.30E05

Si 1 0.23786 0.23786 63740.71091 0

I(Vw22) 1 0.004551 0.004551 1219.685028 4.00E06

Vw2 1 0.010365 0.010365 2777.477269 1.00E06

I(1/(HVw3)) 1 0.008871 0.008871 2377.163874 1.00E06

HVw3 1 0.003184 0.003184 853.109608 8.00E06

I(1/(C)) 1 0.010478 0.010478 2807.842281 1.00E06

HVw0:C 1 0.001618 0.001618 433.5125 3.10E05

Vw1:Si 1 0.000185 0.000185 49.449043 0.002155



15/18


Table A11

Ultimate tensile strength at room temperature (Rm) as function of microstructural and chemical composition



HVw0 1 517.881769 517.881769 2687690.165 0

Vw0 1 0.01304 0.01304 67.677119 0.00119

Vw1 1 21.597211 21.597211 112084.6801 0

Vw2 1 4.191071 4.191071 21750.71575 0Vw3 1 1.077479 1.077479 5591.874973 0

Ti 1 0.063943 0.063943 331.847515 5.30E05

I(HVw02) 1 0.00249 0.00249 12.92438 0.022859

I(1/(HVw2)) 1 0.008223 0.008223 42.677887 0.002836

HVw0:Vw1 1 0.024211 0.024211 125.650814 0.000361

HVw0:Vw2 1 0.006495 0.006495 33.706644 0.004379

Vw0:Vw2 1 0.001857 0.001857 9.639857 0.036053

Residuals 4 0.000771 0.000193 NA NA

CALL

lm log(WRm)HVw0 + Si+ log(HVw0)+I(HVw02)+Vw1+I(HVw32) +I(Vw32) + 1 cbind(WRm= MP.df[, WRm], HT.ccn.df)

F statistic value= 77730.61295, numdf 8, dendf 7


Coefficients

HVw0 0.027795 0.001988 13.980777 2.00E06

Si 0.079952 0.015692 5.095078 0.001407

log(HVw0) 1.708268 0.043802 38.999374 0

I(HVw02) 4.30E05 5.00E06 7.978474 9.30E05

Vw1 0.005054 0.000591 8.552277 5.90E05

I(HVw32) 0 0 8.39169 6.70E05

I(Vw32) 0.000756 0.000115 6.586949 0.000308


Table A12

Ultimate tensile strength at 900

C (WRm) as function of microstructural and chemical compositionCALL

lm log(WRm)HVw0 + Si+ log(HVw0)+I(HVw02)+Vw1+I(HVw32) +I(Vw32) + Si:log(Vw3) 1


Coefficients

HVw0 0.027795 0.001988 13.980777 2.00E06

Si 0.079952 0.015692 5.095078 0.001407

log(HVw0) 1.708268 0.043802 38.999374 0

I(HVw02) 4.30E05 5.00E06 7.978474 9.30E05

Vw1 0.005054 0.000591 8.552277 5.90E05

I(HVw32) 0 0 8.39169 6.70E05

I(Vw32) 0.000756 0.000115 6.586949 0.000308

Si:log(Vw3) 0.024783 0.003822 6.484306 0.000339

0.02304 NA NA NAr.sq 0.999989 NA NA NA



HVw0 1 313.010038 313.010038 589629.9937 0

Si 1 1.542081 1.542081 2904.881165 0

log(HVw0) 1 15.463757 15.463757 29129.721 0

I(HVw02) 1 0.038717 0.038717 72.93225 6.00E05

Vw1 1 0.014045 0.014045 26.45701 0.001333

I(HVw32) 1 0.014209 0.014209 26.766707 0.00129

I(Vw32) 1 0.006426 0.006426 12.10554 0.010276

Si:log(Vw3) 1 0.022321 0.022321 42.046218 0.000339

Residuals 7 0.003716 0.000531 NA NA


16/18


Table A13

Elongation at room temperature (A10) as function of microstructural and chemical composition

CALL

lm log(A10)Vw1+HVw2+Vw2+HVw3+Vw3+Ti+C+I(Vw02) +I(1/(HVw1)) + Vw0+I(1/(Ti))+ Vw1:Vw3 + Vw2:Ti 1


Coefficients

Vw1 0.171633 0.000762 225.213079 2.00E05HVw2 0.011216 8.90E05 126.28491 6.30E05

Vw2 0.134002 0.00089 150.526647 4.40E05

HVw3 0.000865 1.40E05 61.101118 0.000268

Vw3 0.065038 0.002073 31.368707 0.001015

Ti 1.048054 0.012172 86.100139 0.000135

C 15.148203 0.08961 169.046618 3.50E05

I(Vw02) 0.001102 8.00E06 142.035043 5.00E05

I(1/(HVw1)) 1802.012882 10.868802 165.796824 3.60E05

Vw0 0.261548 0.001318 198.468982 2.50E05

I(1/(Ti)) 0.00524 0.000715 7.326765 0.018124

Vw1:Vw3 0.001164 3.80E05 30.597925 0.001066

Vw2:Ti 0.002387 0.000498 4.796904 0.040817

0.003713 NA NA NA




Vw1 1 42.598259 42.598259 3090156.152 0

HVw2 1 1.834693 1.834693 133091.9884 8.00E06

Vw2 1 0.077135 0.077135 5595.504557 0.000179

HVw3 1 0.005646 0.005646 409.558876 0.002433

Vw3 1 0.225936 0.225936 16389.80395 6.10E05

Ti 1 1.754432 1.754432 127269.7524 8.00E06

C 1 0.915662 0.915662 66423.77561 1.50E05

I(Vw02) 1 0.243122 0.243122 17636.5291 5.70E05

I(1/(HVw1)) 1 0.001081 0.001081 78.452807 0.01251

Vw0 1 0.996135 0.996135 72261.47837 1.40E05

I(1/(Ti)) 1 0.006926 0.006926 502.397808 0.001985

Vw1:Vw3 1 0.013246 0.013246 960.885924 0.001039Vw2:Ti 1 0.000317 0.000317 23.010287 0.040817


Table A14

Elongation at 900 C (WA10) as function of microstructural and chemical composition

CALL

lm log(WA10)Vw2+I(Vw32) +I(Ti2)+ log(Ti) +I(HVw32)+C+log(Si)+I(Nb2)+ log(HVw3)+ Vw2:C+ Ti:log(HVw3) 1


Coefficients

Vw2 0.128963 0.004478 28.798743 9.00E06

I(Vw32) 0.001881 7.50E05 25.018903 1.50E05

I(Ti2)

0.718015 0.042406

16.93183 7.10E

05log(Ti) 0.436711 0.010965 39.828023 2.00E06

I(HVw32) 0 0 27.613905 1.00E05

C 6.978825 0.120024 58.145196 1.00E06

log(Si) 0.434188 0.024941 17.408292 6.40E05

I(Nb2) 0.029256 0.002068 14.148109 0.000145

log(HVw3) 0.021797 0.001457 14.956858 0.000116

Vw2:C 0.460194 0.014765 31.167742 6.00E06

Ti:log(HVw3) 0.305277 0.011308 26.996544 1.10E05

0.011656 NA NA NA




Vw2 1 94.166469 94.166469 693087.7129 0

I(Vw32) 1 0.239087 0.239087 1759.739776 2.00E06


17/18




I(Ti2) 1 10.424839 10.424839 76729.30272 0

log(Ti) 1 27.355742 27.355742 201344.7985 0

I(HVw32) 1 10.645921 10.645921 78356.5246 0

C 1 6.887299 6.887299 50692.16769 0

log(Si) 1 0.009083 0.009083 66.855692 0.001218I(Nb2) 1 0.046779 0.046779 344.306775 5.00E05

log(HVw3) 1 0.02406 0.02406 177.090995 0.000184

Vw2:C 1 0.484119 0.484119 3563.227958 0

Ti:log(HVw3) 1 0.09902 0.09902 728.813401 1.10E05

Residuals 4 0.000543 0.000136 NA NA

Table A15

Fracture toughness at room temperature (KVC) as function of microstructural and chemical composition

CALL

lm log(KCV)HVw2+ Vw2 + HVw3+ Nb+ Ti+ log(Nb) + log(C)+ Vw3 + HVw0+ HVw2:HVw3 + HVw2:Nb + Vw2:log(C)


Coefficients(Intercept) 4.487551 0.008311 539.959368 3.00E06

HVw2 0.002945 1.80E05 161.102782 3.90E05

Vw2 0.030717 0.000431 71.313991 0.000197

HVw3 0.001874 6.00E06 297.400569 1.10E05

Nb 0.981808 0.002679 366.445905 7.00E06

Ti 0.248427 0.00051 487.103051 4.00E06

log(Nb) 0.114402 0.000418 273.874131 1.30E05

log(C) 0.835761 0.004967 168.274781 3.50E05

Vw3 0.003563 9.70E05 36.894088 0.000734

HVw0 0.000295 1.00E05 30.115229 0.001101

HVw2:HVw3 5.00E06 0 342.646505 9.00E06

HVw2:Nb 0.002878 6.00E06 444.846854 5.00E06

Vw2:log(C) 0.037465 0.000373 100.571071 9.90E05

0.000575 NA NA NA




HVw2 1 0.043343 0.043343 131233.5362 8.00E06

Vw2 1 0.357375 0.357375 1082062.274 1.00E06

HVw3 1 0.012597 0.012597 38142.3278 2.60E05

Nb 1 0.225693 0.225693 683354.0243 1.00E06

Ti 1 0.295872 0.295872 895841.9697 1.00E06

log(Nb) 1 0.011756 0.011756 35594.51727 2.80E05

log(C) 1 0.01056 0.01056 31973.83961 3.10E05

Vw3 1 0.000877 0.000877 2654.168743 0.000377

HVw0 1 0.002022 0.002022 6123.152477 0.000163

HVw2:HVw3 1 0.058261 0.058261 176403.11 6.00E06

HVw2:Nb 1 0.06383 0.06383 193265.8097 5.00E06

Vw2:log(C) 1 0.003341 0.003341 10114.54032 9.90E05Residuals 2 1.00E06 0 NA NA

Table A16

Fracture toughness at 900 C (WKVC) as function of microstructural and chemical composition

CALL

lm log(WKCV)Vw0+Vw1+Vw2+I(HVw02)+ log(Vw2)+I(Vw12) +I(C2)+Ti+log(Vw0)+I(Ti2)+ Vw1:log(Ti) + Vw2:log(Vw2) 1


Coefficients

Vw0 0.04839 0.000644 75.10713 5.00E06

Vw1 0.087421 0.002141 40.835982 3.20E05

Vw2 0.562229 0.020774 27.063947 0.000111


18/18




I(HVw02) 5.00E06 1.00E06 8.61852 0.003285

log(Vw2) 1.37143 0.045409 30.201424 8.00E05

I(Vw12) 0.000333 2.00E05 16.97169 0.000446

I(C2) 2.716264 0.212326 12.792871 0.001031

Ti 0.887369 0.072294 12.274456 0.001165

log(Vw0) 0.059745 0.009517 6.277516 0.008162

I(Ti2) 0.116978 0.036211 3.230439 0.0482

Vw1:log(Ti) 0.004552 0.000145 31.471761 7.00E05

Vw2:log(Vw2) 0.113904 0.004751 23.973393 0.000159

0.009306 NA NA NA




Vw0 1 120.481613 120.481613 1391184.731 0

Vw1 1 75.706776 75.706776 874175.8 0

Vw2 1 2.211015 2.211015 25530.28787 1.00E06

I(HVw02) 1 0.012479 0.012479 144.098424 0.001244

log(Vw2) 1 0.071561 0.071561 826.299631 9.20E05

I(Vw12) 1 0.060211 0.060211 695.244335 0.00012I(C2) 1 0.093624 0.093624 1081.062152 6.20E05

Ti 1 0.165061 0.165061 1905.933441 2.60E05

log(Vw0) 1 0.072814 0.072814 840.77275 9.00E05

I(Ti2) 1 0.062089 0.062089 716.930674 0.000114

Vw1:log(Ti) 1 0.084843 0.084843 979.666227 7.20E05

Vw2:log(Vw2) 1 0.049773 0.049773 574.723558 0.000159

Residuals 3 0.00026 8.70E05 NA NA

A.3. Hardness

See Tables A5A8.

A.4. Mechanical properties

See Tables A9A16.

References

[1] M. John, Chambers, Trevor J. Hastie, Statistical Models in S, Chapman &

Hall Inc., 1993, ISBN 0-412-04261-4.

[2] John M. Chambers, Programming With Data. A Guide to the S Lan-

guage, Hamilton Printing Co., Rensselaer, NY, 1998, ISBN 0-387-

91577-X.

[3] Users Manual, PeakFitPeakSeparation andAnalysisSoftware, SPSSInc.,

1997, ISBN 1-56827-183-2.[4] B. Piekarski, M. Garbiak, Metalurgija 41 (2) (2002) 7782.

[5] P. Christodoulou, N. Calos, Mater. Sci. Eng. A 301 (2001) 103117.

fingerprints of materials

Documents