AXIALLY LOADED STAINLESS STEEL COMPRESSION MEMBERS

A Thesis Presented to The Academic Faculty

By

Fulvio E. Jaramillo

In Partial Fulfillment of the Requirements for the Degree Master of Science in Civil Engineering

Georgia Institute of Technology December 2006

AXIALLY LOADED STAINLESS STEEL COMPRESSION MEMBERS

Approved by: Dr. Abdul-Hamid Zureick, Advisor School of Civil Engineering Georgia Institute of Technology Dr. Leroy Z Emkin School of Civil Engineering Georgia Institute of Technology Dr. Lawrence F. Kahn School of Civil Engineering Georgia Institute of Technology

Date Approved: 08/24/2006

iii

TABLE OF CONTENTS Page LIST OF TABLES

v

LIST OF FIGURES

vii

SUMMARY

ix

CHAPTER 1 MATERIALS

1

1.1 Introduction

1

1.2 Materials Specifications

2

1.3 Stress-Strain relationship for stainless steel

18

1.4 Coupon test of 304L stainless steel material

23

2 AXIALLY COMPRESSED STAINLESS STEEL MEMBERS

3

38

2.1 Introduction

38

2.2 Cold formed stainless steel

38

2.3 Hot-rolled and built-up stainless steel elements

56

2.4 Available design guidelines

62

EXAMPLES

67

3.1 ASCE LRFD (2002)

68

3.2 Euro Inox (1994)

75

3.3 Winter –Curve

78

3.4 Curves superposition

82

4 CONCLUSIONS

83

REFERENCES

85

iv

LIST OF TABLES Table 1.1: Austenitic grades – Chemical composition

5

Table 1.2: Austenitic grades – Mechanical properties

9

Table 1.3: Ferritic grades – Chemical composition

12

Table 1.4: Ferritic grades – Mechanical properties

13

Table 1.5: Martensitic grades – Chemical composition

14

Table 1.6: Martensitic grades – Mechanical properties

15

Table 1.7: Duplex grades – Chemical composition

16

Table 1.8: Duplex grades – Mechanical properties

17

Table 1.9: Stainless steel - representative values for yield stress in tension and compression and modulus of elasticity

19

Table 1.10: Compressive test lengths

24

Table 1.11: Compression test data

28

Table 2.1: Section properties, Johnson & Winter (1966)

39

Table 2.2: Critical column stresses vs. slenderness, Johnson & Winter (1966)

40

Table 2.3: Mechanical properties, Johnson & Winter (1966)

45

Table 2.4: Test materials – Mechanical properties, Bredenkamps et al. (1992)

57

Table 2.5: I section Dimensions, Bredenkamps et al. (1992)

58

Table 2.6: Mechanical properties, Bredenkamps et al. (1992)

58

Table 2.7: Experimental and analytical column strength 140x70x4.5x3.5 I-sections, Bredenkamps et al. (1992)

60

Table 2.8: Experimental and analytical column strength 1840x970x6.0x4.5 I-sections, Bredenkamps et al. (1992)

60

Table 2.9: Values of α and λo for flexural, torsional and torsional-flexural buckling 65

v

Table 3.1: Stress σ (ksi) vs. strain ε

69

Table 3.2: Tangent modulus Et (ksi) vs. stress F (ksi)

71

Table 3.3: Determination of Pcr (Kips), ASCE LRFD (2002)

73

Table 3.4: Evaluation of the flexural buckling strength N b , Rd (kips)

77

Table 3.5: Evaluation of the nondimensional compression strength χ

80

vi

LIST OF FIGURES Page Figure 1.1: Typical strain-stress curve for stainless steel, Bezkorovainy (2003)

18

Figure 1.2: Yield strength determination by using the offset method

23

Figure 1.3: Compression test coupon – dimensions

25

Figure 1.4: Compression test coupon – strain gages

26

Figure 1.5: Compression test, strain-stress curve

30

Figure 1.6: Strain-stress best-fit curve by regression analysis

33

Figure 1.7: Compression test, strain-stress Ramberg-Osgood curve

35

Figure 1.8: Compression test, strain-stress curve, Determination Eo and Fy

37

Figure 2.1: Section dimensions, Johnson & Winter (1966)

39

Figure 2.2: Critical column stress vs. slenderness, Johnson & Winter (1966)

42

Figure 2.3: Critical column stress vs. slenderness, Rasmussen & Rondal (1997)

46

Figure 2.4: Critical column stress vs. effective length, Young & Wibosono (2002)

50

Figure 2.5: Critical column stress vs. effective length, Young & Wibisono (2002)

50

Figure 2.6: Axial load vs. effective length, Young & Liu (2003)

52

Figure 2.7: Non dimensional critical column stress vs. slenderness, Hammer & Petersen (1995)

53

Figure 2.8: Non dimensional critical column stress vs. slenderness, The Steel Construction Institute U.K. (1991)

55

Figure 2.9: Non dimensional critical column stress vs. slenderness, Coetze et al. (1990)

56

Figure 2.10: I section Dimensions

58

vii

Figure 3.1: Stainless steel angle 2”x 2”x ¼”

67

Figure 3.2: Analytical stress-strain curves

70

Figure 3.3: Tangent Modulus

71

Figure 3.4: Nondimensional compression strength χ vs. slenderness λ (ASCE 2002)

74

Figure 3.5: Critical load Pcr vs. length L (ASCE LRFD 2002)

74

Figure 3.6: Nondimensional compression strength χ vs. slenderness λ (Euro Inox 1994)

78

Figure 3.7: Nondimensional compression strength χ vs. slenderness λ (Winter-curve)

81

Figure 3.8: Nondimensional compression strength χ vs. slenderness λ. Superposition of curves

82

viii

SUMMARY

In recent years, the engineering community has focused its attention on selecting durable and low maintenance materials. As a result of recent advances in steel fabrication technologies, stainless steel has risen as a valuable alternative to regular carbon steel for heavy structural elements in addition to the traditional light gage structural elements of common use. The objective of this investigation is to summarize the existing literature concerning on the behavior of cold formed and hot rolled, annealed stainless steel members undergoing axial compression forces. Two documents summarize the existing information taken from testing and general research done until now on the subject: The American Society of Civil Engineers, ASCE standard, SEI/ASCE 8-02 and Design Manual for Structural Stainless Steel, Nickel Development Institute, Euro Inox (1994), the last is based on the Eurocode 3 (1993).

ix

CHAPTER 1 MATERIALS 1.1 Introduction In recent years, the engineering community has focused its attention on selecting durable and low maintenance materials. As a result of recent advances in steel fabrication technologies, stainless steel has risen as a valuable alternative to regular carbon steel for heavy structural elements in addition to the traditional light gage structural elements of common use. The objective of this investigation is to summarize the existing literature concerning on the behavior of cold formed and hot rolled, annealed stainless steel members undergoing axial compression forces. Stainless steel is the common name applied to a range of iron-based alloys whose prime corrosion-resistant element is chromium. The term stainless implies a resistance to staining, rusting, and pitting in the air. In general, stainless steel contains Chromium, Magnesium, Sulfur, Scandium, Nickel and other elements. In order for the material to be considered stainless steel, the minimum chromium content must be approximately 11% and the maximum must be around 30%. Carbon content usually ranges from 0.02 to 0.12%. Stainless steels have room temperature yield strengths that range from 205 MPa (30 Ksi) to more than 1725 Mpa (250 Ksi). Stainless steel can be used in applications in which operating temperatures around 750ºC (1400ºF) are common, although sometimes they are used with operating temperatures as high as 1090ºC (2000ºF). Several stainless steel types were developed because other ferrous alloys such as regular carbon steel

1

lacked sufficient corrosion or oxidation resistance as service temperatures increased. At the other extreme of temperatures some stainless steel types maintain their toughness and other mechanical properties down to temperatures approaching absolute zero. The three basic stainless steel type were initially developed between 1910 and 1915. Harry Brearley from England developed the 0.35% carbon, 14% chromium alloy that is known today as S40200 (type 402). Concurrently, similar developments were achieved in America and Germany with alloys known as S41000 (type 410) and S30200 (type 302). These developments were the beginning of a family of alloys, which have enabled the advancement, and growth of a number of industries, mainly chemical processing and power generating systems, upon which our technological society is based. The subsequent development of several important subcategories of stainless steels, named the ferritic, austenitic, martensitic, and duplex grades, are based on compositional, micro structural, and crystallographic factors that will be presented in connection with their mechanical and chemical effects. 1.2 Materials Specifications: There are over 100 wrought stainless steel alloys. Such alloys can be classified according to three general systems: 1. Metallurgic structure: Austenitic, Ferritic, Martensitic and Duplex. 2. The AISI (American Iron and Steel Institute) numbering system: The AISI number contains three digits and designates a specified composition range. The austenitic series begins with the number 3, the manganese-substituted austenitic steel begins with a 2 and both ferritic and martensitic classes begin with the number 4.

2

3. The Unified Numbering System: this was developed by the American Society for Testing Materials (ASTM) and the Society of Automotive Engineers (SAE) for all commercial metal alloys. This classification uses a five-digit system in which the last three digits correspond to the AISI number. Specifications of the Alloy Casting Institute (ACI) refer exclusively to cast alloys, although the composition of some of the ACI alloys approximate wrought alloy composition. The chemical composition and mechanical properties for each type of stainless steel can be found in the ASTM A 276-05 “Standard Specification for stainless steel bars and shapes.” Such a standard applies to hot-finished or cold-finished bars, except bars for reforging. It includes rounds, square and hexagons, and hot-rolled or extruded shapes, such as angles, tees and channels in the more commonly used types of stainless steels. In addition, the ASTM A 484/A 484M-05 “General requirements for Stainless Steel Bars, Billets and Forgings” contains general requirements that apply to wrought stainless steel bars, shapes, forgings and billets. 1.2.1 Austenitic Stainless steel: The high-temperature form of iron (between 910ºC and 1400ºC, or 1670ºF and 2550ºF) is known as austenite, although strictly speaking the term austenitic also implies carbon in solid solution.

The Austenitic stainless steels have many common

characteristics: 1. They can be hardened by cold working but not by heat treatment. 2. In the annealed condition, all are essentially nonmagnetic, although some may become slightly magnetic by cold working.

3

3. They have excellent corrosion resistance. 4. They have good formability. 5. They increase in strength as result of cold work. Type 304 stainless steel is the most widely used alloy of the austenitic group, with a nominal composition of 18% chromium and 8% nickel. Both chromium and nickel contents can be increased to improve corrosion resistance, and additional elements, most common molybdenum, can be added to further enhance the corrosion resistance. Austenitic stainless steels are found within the major market segment: consumer products, transportation, architecture, food and beverage, chemical and petrochemical, pulp and paper, pharmaceutical and biotechnology (e.g., surgical implants and prosthetic devices, semiconductor, environmental and aerospace). The ASTM A 276-05 “Standard Specification for stainless steel bars and shapes” provides the minimum requirements for chemical composition and mechanical properties for austenitic stainless steels. These requirements are presented in Tables 1.1 and 1.2.

4

5

2.00 5.5-7.5 4.0-6.0 4.0-8.0 7.5-10.0 14.0-15.5 4.0-6.0 7.0-9.0 8.0-10.0 8.0-10.0 11.5-14.5 11.0-14.0 17.0-19.0

0.03 0 0.15 0.15 0.15 0.15 0.120.25 0.06 0.10 0.08 0.04 0.08 0.15 0.15

… 201 … … 202 205

XM-19 …

XM-10

XM-11

XM-29

XM-28 …

S20100

S20161

S20162

S20200

S20500

S20910

S2180

S21900

S21904

S2400

S24100

S28200

N08367

Mg

C

Type

UNS Designation

0.045

0.045

0.060

0.045

0.045

0.060

0.045

0.060

0.060

0.040

0.045

0.060

0.040

P

0.030

0.030

0.030

0.030

0.030

0.030

0.030

0.030

0.030

0.040

0.030

0.030

0.030

S

1.00

1.00

1.00

1.00

1.00

3.5-4.5

1.00

1.00

1.00

2.5-4.5

3.00-4.00

1.00

1.00

Sc

17.0-19.0

16.5-19.0

17.0-19.0

19.0-21.5

19.0-21.5

16.0-18.0

20.5-23.5

16.5-18.0

17.0-19.0

16.5-2.1

15.0-18.0

16.0-18.0

20.0-22.0

Cr

Composition, %

…

0.5-2.5

2.3-3.7

5.5-7.5

5.5-7.5

8.0-9.0

11.5-13.5

1.0-1.7

4.0-6.0

6.0-10.0

4.0-6.0

3.5-5.5

23.5-25.6

Nick

0.75-1.25

…

…

…

…

…

1.5-3.00

…

…

0.50-2.50

…

…

6.0-7.0

Mb

Table 1.1 Austenitic Grades – Chemical composition

0.40-0.60

0.20-0.45

0.20-0.40

0.15-0.40

0.15-0.40

0.08-0.18

0.20-0.40

0.32-0.40

0.25

0.05-0.25

0.08-0.20

0.25

0.18-0.25

N

Cu0.75-1.25

…

…

…

…

…

Cb0.1-0.3

…

…

…

…

…

Cu 0.75

Other Elements

6

0.03 0.08 0.08 0.03 0.03 0.12 0.08 0.05-0.10 2.00 2.00

304Lc

304N

XM-21

304LN

…

305

308

…

309

309S

S30403

S30451

S30452

S30453

S30454

S30500

S30800

S30815

S30900

S30908

17.0-19.0

2.00

0.80

2.00

2.00

2.00

2.00

2.00

2.00

2.00

2.00

0.08

304

S30400

2.00

0.15

302B

S30215

2.00

0.15

302

S30200

Mg

C

Type

UNS Designation

0.045

0.045

0.040

0.045

0.045

0.045

0.045

0.045

0.045

0.045

0.045

0.045

0.045

P

0.030

0.030

0.030

0.030

0.030

0.030

0.030

0.030

0.030

0.030

0.030

0.030

0.030

S

1.00

1.00

1.40-2.0

1.00

1.00

1.00

1.00

1.00

1.00

1.00

1.00

2.00-3.00

1.00

Sc

22.0-24.0

22.0-24.0

20.0-22.0

19.0-21.0

17.0-19.0

18.0-20.0

18.0-20.0

18.0-20.0

18.0-20.0

18.0-20.0

18.0-20.0

17.0-19.0

17.0-19.0

Cr

Composition, %

12.0-15.0

12.0-15.0

10.0-12.0

10.0-12.0

11.0-13.0

8.0-11.0

8.0-11.0

8.0-10.0

8.0-11.0

8.0-12.0

8.0-11.0

8.0-10.0

8.0-10.0

Nick

…

…

…

…

…

…

…

…

…

…

…

…

…

Mb

Table 1.1 (Cont.) Austenitic Grades – Chemical composition

…

…

0.14-0.20

…

…

0.16-0.30

0.10-0.16

0.16-0.30

0.10-0.16

…

…

0.10

0.10

N

…

…

Ce0.03-0.08

…

…

…

…

…

…

…

…

…

…

Other Elements

7 0.08 0.03 0.08 0.08 0.08 0.03 0.03

316Lc

316Ti

316Cb

316N

316LN

…

S31603

S31635

S31640

S31651

S31653

S34565

0.25

316

0.02

0.08

S31600

310Cb

S31040

0.08

314

310S

S31008

0.25

S31400

310

S31000

0.08

…

309Cb

S30940

C

S31254

Type

UNS Designation

5.0-7.0

2.00

2.00

2.00

2.00

2.00

2.00

2.00

1.00

2.00

2.00

2.00

2.00

Mg

0.030

0.045

0.040

0.045

0.045

0.045

0.045

0.045

0.045

0.045

0.045

0.045

0.045

P

0.010

0.030

0.030

0.030

0.030

0.030

0.030

0.030

0.010

0.030

0.030

0.030

0.030

S

1.00

1.00

1.00

1.00

1.00

1.00

1.00

1.50-3.0

0.80

1.50

1.50

1.50

1.00

Sc

23.0-25.0

16.0-18.0

16.0-18.0

16.0-18.0

16.0-18.0

16.0-18.0

16.0-18.0

23.0-26.0

19.5-20.5

24.0-26.0

24.0-26.0

24.0-26.0

22.0-24.0

Cr

Composition, %

16.0-18.0

10.0-13.0

10.0-14.0

10.0-14.0

10.0-14.0

10.0-14.0

10.0-14.0

19.0-22.0

17.5-18.5

19.0-22.0

19.0-22.0

19.0-22.0

12.0-16.0

Nick

4.00-5.00

2.00-3.00

2.00-3.00

2.00-3.00

2.00-3.00

2.00-3.00

2.00-3.00

…

6.0-6.5

…

…

…

…

Mb

Table 1.1 (Cont.) Austenitic Grades – Chemical composition

0.40-0.60

0.10-0.16

0.10-0.16

0.10

0.10

…

…

…

0.18-0.22

…

…

…

…

N

Cb 0.10

…

…

Cb10xC1.10

Tix(C+N)_0.7

…

…

…

Cu0.5_1.0

Cb10xC-1.1

…

…

Cb10xC-1.1

Other Elements

8

…

…

321

…

S31727

S32053

S32100

S32654

317

S31700

…

…

S31654

S31726

348

S34800

…

347

S34700

S31725

Type

UNS Designation

0.02

0.08

0.03

0.03

0.03

0.03

0.08

0.03

0.08

0.08

C

2.00-4.00

2.00

1.00

1.00

2.00

2.00

2.00

2.00

2.00

2.00

Mg

0.030

0.045

0.030

0.030

0.045

0.045

0.045

0.045

0.045

0.045

P

0.030

0.030

0.010

0.030

0.030

0.010

0.030

0.030

0.030

0.030

S

1.50

1.00

1.00

1.00

1.00

1.00

1.00

1.00

1.00

1.00

Sc

24.0-25.0

17.0-19.0

22.0-24.0

17.5-19.0

17.0-20.0

16.0-18.0

18.0-20.0

16.0-18.0

17.0-19.0

17.0-19.0

Cr

Composition, %

21.0-23.0

9.0-12.0

24.0-26.0

14.5-16.5

14.5-17.5

13.5-17.5

11.0-15.0

10.0-14.0

9.0-12.0

9.0-12.0

Nick

7.00-8.00

…

5.00-6.00

3.80-4.50

4.00-5.00

4.00-5.00

3.00-4.00

2.00-3.00

…

…

Mb

Table 1.1 (Cont.) Austenitic Grades – Chemical composition

0.45-0.55

…

0.17-0.22

0.15-0.21

0.10-0.20

0.20

0.10

0.16-0.30

…

…

N

Ti5x(C+N)07 Cb10xC1.10

…

Cu2.8-4.0

…

…

…

…

Cb10xC-1.1 Ta 0.10 Co 0.20

Cb10xC-1.1

Other Elements

Table 1.2 Austenitic grades – Mechanical properties

Tensile Yield Strength, strength, D Min Min Condition Finish Type ksi MPa ksi MPa Austenitic grades- Mechanical Properties Hot-finished N08367 A or coldall 95 655 45 310 finished Hot-finished 201,202 A all 75 515 40 275 or coldfinished Hot-finished S20161 A all 125 860 50 345 or Cold-finished all 125 860 50 345 Hot-finished S20162 A or all 100 690 50 345 cold-finished Hot-finished 205 A all 100 690 60 414 or cold-finished Hot-finished A all 100 690 55 380 or cold-finished Hot-finished Up to (50.28), 135 930 105 725 or inc cold-finished Over 2 to 3 115 795 75 515 (50.8 to 76.2),incl. XM-19 Over 3 to 8 As hot(76.2 to 100 690 60 415 rolled 203.2),incl. Over 2 to 2 ½ (50.80 to 63.5) 90 620 65 450 incl. Over 2 ½ to 3 80 550 55 380 (63.5 to 76.2) incl. Hot-finished S21800 A all 95 655 50 345 or cold-finished Hot-finished XM-10, A or all 90 620 50 345 XM-11 cold-finished Hot-finished XM-29 A all 100 690 55 380 or cold-finished Hot-finished XM-28 A all 100 690 55 380 or cold-finished Hot-finished S24565 A or all 115 795 60 415 cold-finished

9

E

RA

BH

30

50

…

40

45

…

40

40

255

40

40

311

50

60

…

40

50

…

35

55

…

20

50

…

25

50

…

30

50

…

30

40

…

30

40

…

35

55

241

45

60

…

30

50

…

30

50

…

35

40

…

Table 1.2 (Cont.) Austenitic grades – Mechanical properties

Type

Condition

S28200

A

302, 302B, 304, 304LN, 305, 308, 309, 309S, 310Cb, 314, 316, 316LN, 316Cb, 316TI, 317, 321, 347,348,

A

A

304,316 N B

S31726

A

S31727

A

S32053

A

S32654

A

304, 304N, 316, 316N

Hot-finished or cold-finished Hot-finished or

Hot-finished or Cold-finished

304L, 316L

S

Yield strength, Min ksi MPa

E

RA

BH

all

110

760

60

410

35

55

…

all Up to ½ (12.70 ) incl. Over ½ (12.70)

75

515

30

205

40

50

…

90

620

45

310

30

40

…

75

515

30

205

30

40

…

70

485

25

170

40

50

…

90

620

45

310

30

40

…

70

485

25

170

30

40

…

80

550

35

240

30

…

…

125

860

100

690

12

35

…

115

795

80

550

15

35

…

105

725

65

450

20

35

…

100

690

50

345

24

45

…

95

655

45

310

28

45

…

80

550

35

240

40

…

…

80

550

36

245

35

…

217

93

640

43

295

40

…

217

109

750

62

430

40

40

250

95

650

75

515

25

40

…

90

620

65

450

30

40

…

80

550

55

380

30

40

…

Finish

Cold-finished

A

D

Tensile Strength, Min ksi MPa

Hot-finished or cold-finished

all Up to ½ (12.70 ) incl. Over ½ (12.70) all

Up to ¾ (19.05) incl. Over ¾ (19.05) to 1 (25.40) Over 1 (25.40) to 1 ¼ Cold-finished (31.75) Over 1 ¼ (31.75) to 1 ½ (38.10) Over 1 ½ (38.10) to 1 ¾ (44.45) Hot-finished or all cold-finished Hot-finished or all cold-finished Hot-finished or all cold-finished Hot-finished or all cold-finished Up to 2 (50.8) incl. Over 2 to 2 ½ (50.80 to Cold-finished 63.5) incl. Over 2 ½ to 3 (63.5 to 76.2) incl.

10

Table 1.2 (Cont.) Austenitic grades – Mechanical properties

D Type XM-21, S30454, S31654

XM-21, S30454, S31654

S30815

Condition A

B

A

S31254

A

S31725

A

Finish Hot-finished or all cold-finished cold-finished Up to 1 (25.4) incl. Over 1 (25.40) to 1 ¼ (31.75) Over 1 ¼ (31.75) to 1 ½ (38.10) Over 1 ½ (38.10) to 1 ¾ (44.45) Hot-finished all or Cold-finished Hot-finished all or cold-finished Hot-finished or all cold-finished

Tensile Yield strength, Strength, Min Min ksi MPa ksi MPa

E

RA

BH

90

620

50

345

30

50

…

145

1000

125

860

15

45

…

135

930

115

795

16

45

…

135

895

105

725

17

45

…

125

860

100

690

18

45

…

87

600

45

310

40

50

…

87

600

45

310

40

50

…

95

650

44

300

35

50

…

75

515

30

205

40

…

…

D = Diameter or thickness in (mm) E = Elongation 2 in (50 mm) or 4D, min % RA = Reduction of Area, Min % BH = Brinell hardness, max.

1.2.2 Ferritic stainless steel: Ferritic stainless steel has a crystal structure similar to that of iron at room temperature. The ferritic stainless steel is straight-chromium alloy identified by AISI as 400 series that cannot be hardened by heat treatment and only moderately hardened by cold working. They are magnetic, have good ductility and resistance to corrosion and

11

oxidation. Common alloys in the ferritic class contain between 11% and 29% chromium, no nickel, and very little carbon in the wrought condition. Type 430 is the generalpurpose stainless steel of the ferritic group. The 11% ferritic chromium steels, have gained wide acceptance in automotive exhaust systems and containers. The intermediate alloys, with 16-17% chromium, are used primarily as automotive trim and cooking utensils, always in light gages. The high chromium steel, with 18% to 29% chromium content, has been used in applications requiring high resistance to oxidation and corrosion. The ASTM A 276-05 “Standard Specification for stainless steel bars and shapes” contains the requirements for chemical composition and mechanical properties for ferritic stainless steel. These requirements are shown in tables 1.3 and 1.4: Table 1.3 Ferritic grades – Chemical composition UNS Type Designation

C

Mg

P

S

Composition, % Cr Nick

Sc

Mb

N

Other Elements

Ferritic Grades - Chemical composition S40500 S40976

405 …

0.080 1.00 0.040 0.030 1.00 0.030 1.00 0.040 0.030 1.00

11.5-14.5 0.50 … 10.5-11.7 0.75-1.00…

Al 0.10-030 Cb 10x(C+N)0.80 S42900 429 0.120 1.00 0.040 0.030 1.00 14.0-16.0 … … … … S43000 430 0.120 1.00 0.040 0.030 1.00 14.0-18.0 … … … … S44400 444 0.025 1.00 0.040 0.030 1.00 17.5-19.5 1.00 1.75-2.50 0.035 Ti+Cb 0.20+4x(C+N) -0.80 S44600 446 0.200 1.50 0.040 0.030 1.00 23.0-27.0 0.75 … 0.25 … S44627 XM- 0.010 0.40 0.020 0.020 0.40 25.0-27.5 0.50 0.75-1.50 0.015 Cu 0.20 27 Cb 0.05-0.20 S44700 … 0.010 0.30 0.025 0.020 0.20 28.0-30.0 0.15 3.50-4.20 0.020 C+N 0.025 Cu 0.15 S44800 … 0.010 0.30 0.025 0.020 0.20 28.0-30.0 2.00-2.503.50-4.20 0.020 C+N 0.025 Cu 0.15 C = Carbon, Mg = Manganese, P = Phosphor, S = Sulfur, Sc = Silicon, Cr = Chromium, Nick = Nickel, Mb = Molybdenum, N = Nitrogen, Cu = cooper, Cb = Columbium, Ti = Titanium

12

… 0.040

Table 1.4 Ferritic grades – Mechanical properties Tensile Yield Strength, strength, D Conditio Min Min Finish Type n ksi MPa ksi MPa Ferritic Grades - Mechanical properties Hot-finished o all … … … … 405 A cold-finished all … … … … Hot-finished o all 70 480 40 275 429 A cold-finished all 70 480 40 275 Hot-finished or 430 A all 60 415 30 207 cold-finished Hot-finished or S40976 A all 60 415 20 140 cold-finished A Hot-finished all 60 415 45 310 S44400 cold-finished all 60 415 45 310 Hot-finished all 65 450 40 275 446, XM-27 A cold-finished all 65 450 40 275 Hot-finished all 70 480 55 380 S44700 A cold-finished all 75 520 60 415 Hot-finished all 70 480 55 380 S44800 A cold-finished all 75 520 60 415

E

RA

BH

… … 20 16

… … 45 45

207 217 … …

20

45

…

20

45

244

20 16 20 16 20 15 20 15

45 45 45 45 40 30 40 30

217 217 219 219 … … … …

D = Diameter or thickness in (mm) E = Elongation 2 in (50 mm) or 4D, min % RA = Reduction of Area, Min % BH = Brinell hardness, max.

1.2.3 Martensitic stainless steel: The basic martensitic alloy corresponds to S42000 (type 420). This alloy is referred to as martensitic because of its structure in the hardened condition. The term martensite is derived simply from the name of the man, Martens, who first examined metals under the microscope (Davis, 2000). The martensitic stainless steels are commonly found in elevated temperature applications such as steam turbines, jet engines and gas turbines.

13

The ASTM A 276-05 “Standard Specification for stainless steel bars and shapes” contains the requirements for chemical composition and mechanical properties for martensitic stainless steels. Tables 1.5 and 1.6 present these requirements Table 1.5 Martensitic grades – Chemical composition

UNS Type Designation

Composition, % C

Mg

P

S

Sc

Cr

Nick

Mb

N

Other Elements

Martensitic Grades - Chemical composition S40300 S41000

403 0.15 410 0.08-0.15

1.00 1.00

0.0400.030 0.50 11.5-13.0 0.0400.030 1.00 11.5-13.5

… …

… …

… …

…

…

…

S41040

XM-30

0.18

1.00

0.0400.030 1.00 11.0-13.0

S41400

414

0.150

1.00

0.0400.030 1.00 11.5-13.5 1.25-2.50

S41425

…

S41500

…

S42000

420

S42010

…

S43100 S44002 S44003

431 440A 440B

… 1.500.05 0.50-1.000.0200.005 0.50 12.0-15.0 4.0-7.0 2.00 0.500.05 0.50-1.000.0300.030 0.60 11.5-14.0 3.5-5.5 1.00 0.15 min 1.00 0.0400.030 1.00 12.0-14.0 … … 0.400.15-0.30 1.00 0.0400.030 1.00 13.50-15.0 0.35-0.85 0.85 0.20 1.00 0.0400.030 1.00 15.00-17.0 1.25-2.50 … 0.60-0.75 1.00 0.0400.030 1.00 16.00-18.0 … 0.75 0.75-0.95 1.00 0.0400.030 1.00 16.00-18.0 … 0.75

… 0.060.12

… … Cb 0.050.30 … Cu0.30

…

…

…

…

…

…

… … …

… … …

C = Carbon, Mg = Manganese, P = Phosphor, S = Sulfur, Sc = Silicon, Cr = Chromium, Nick = Nickel, Mb = Molybdenum, N = Nitrogen, Cu = cooper, Cb = Columbium, Ti = Titanium

14

Table 1.6 Martensitic grades – Mechanical properties

Type

403, 410 403, 410 XM-30 403, 410 XM-30 414

414 S41425

Tensile Yield strength, Strength, min D Min Condition Finish ksi MPa ksi MPa Martensitic Grades - Mechanical properties Hot-finished o all 70 480 40 275 A cold-finished all 70 480 40 275 Hot-finished o all 100 690 80 550 T cold-finished all 100 690 80 550 Hot-finished all 125 860 100 690 T cold-finished all 125 860 100 690 Hot-finished all 120 830 90 620 H cold-finished All (rounds 120 830 90 620 only) Hot-finished all 70 480 40 275 A cold-finished all 70 480 40 275 Hot-finished A or coldall … … … … finished Hot-finished T or coldall 115 790 90 620 finished Hot-finished T all 120 825 95 655

S41500

T

420

A

S42010

A

431

A

440A, 440B and 440 C

A

Hot-finished or coldfinished Hot-finished cold-finished Hot-finished cold-finished Hot-finished cold-finished Hot-finished cold-finished

E

RA

BH

20 16 15 12 13 12 12

45 45 45 40 45 35 40

… … … … 302 … …

12

40

…

13 12

45 35

235 …

…

…

298

15

45

…

15

45

321

all

115

795

90

620

15

45

295

all all all all all All All All

… … … … … … … …

… … … … … … … …

… … … … … … … …

… … … … … … … …

… … … … … … … …

… .. … .. … .. … ..

241 255 235 255 285 285 285 285

D = Diameter or thickness in (mm) E = Elongation 2 in (50 mm) or 4D, min % RA = Reduction of Area, Min % BH = Brinell hardness, max.

15

1.2.4 Duplex stainless steel: The duplex stainless steel has an annealed structure, which is typically about equal parts of austenite and ferrite. Duplex stainless steel offers several advantages over the common austenitic stainless steel types. The duplex grades are resistant to chloride stress corrosion cracking, have excellent pitting and crevice corrosion resistant and exhibit about twice the yield strength as conventional grades. Type 329 and 2205 are typical alloys. Wrought Duplex stainless steel have found widespread use in a range of industries, particularly the chemical an petrochemical, pulp and paper, power generation, pollution control, marine transportation, and oil and gas industries. The ASTM A 276-05 “Standard Specification for stainless steel bars and shapes” contains the requirements for chemical composition and mechanical properties for duplex (austenitic - ferritic grades) stainless steels. These requirements are summarized in Tables 1.7 and 1.8.

Table 1.7 Duplex grades – Chemical composition UNS Type Designation S31100 S31803 S32101 S32205 S32304 S32506 S32550

Composition, % C

Mg

P

S

Sc

Cr

Nick

Mb

Austenitic-Ferritic Grades - Chemical composition XM-26 0.060 1.00 0.045 0.030 1.00 25.0-27.0 6.0-7.0 … … 0.030 2.00 0.030 0.020 1.00 21.0-23.0 4.5-6.5 2.5-3.5 1.354.00.10-0.80 0.040 0.030 1.00 21.0-22.0 … 0.040 1.70 6.0 … 0.030 2.00 0.030 0.020 1.00 22.0-23.0 4.5-6.5 3.00-3.50 … 0.030 2.50 0.040 0.030 1.00 21.5-24.5 3.0-5.5 0.05-0.60 … 0.030 1.00 0.040 0.015 0.90 24.0-26.0 5.5-7.2 3.0-3.5 …

N

Other Elements

… 0.08-0.20

Ti 0.25 …

0.20-0.25 Cu 0.10-0.80

0.14-0.20 … 0.05-0.20 Cu 0.05-0.60 0.08-0.20 W 0.05-0.30 Cu 0.50-1.00 0.040 1.50 0.030 0.010 1.00 24.0-26.0 6.0- 8.0 3.0-4.0 0.20-0.30 W 0.50-1.00

C = Carbon, Mg = Manganese, P = Phosphor, S = Sulfur, Sc = Silicon, Cr = Chromium, Nick = Nickel, Mb = Molybdenum, N = Nitrogen, Cu = cooper, Cb = Columbium, Ti = Titanium

16

Table 1.8 Duplex grades – Mechanical properties

Type

XM-26 S31803 S32056 S32101 S32205 S32304 S32550 S32550 S32760 S32760

Tensile Yield strength, Strength, D Min Min Condition Finish ksi MPa ksi MPa Austenitic-Ferritic Grades - Mechanical properties Hot-finished or All 90 620 65 450 A cold-finished Hot-finished or A All 90 620 65 448 cold-finished Hot-finished or A all 90 620 65 450 cold-finished Hot-finished or A all 94 650 65 450 cold-finished Hot-finished or A all 95 655 65 450 cold-finished Hot-finished or all 87 600 58 400 A cold-finished Hot-finished or A all 109 750 80 550 cold-finished S cold-finished all 125 860 105 720 Hot-finished or A all 109 750 80 550 cold-finished S cold-finished all 125 860 105 720

D = Diameter or thickness in (mm) E = Elongation 2 in (50 mm) or 4D, min % RA = Reduction of Area, Min % BH = Brinell hardness, max.

17

E

RA

BH

20

55

…

25

…

290

18

…

302

30

…

290

25

…

290

25

…

290

25

…

290

16

…

335

25

…

290

16

…

335

1.3 Stress- strain relationship for Stainless steel The stress-strain relationship for annealed and cold rolled stainless steels is nonlinear. A typical stress-strain curve for stainless steel is shown in Fig. 1.1. It is noted that there is no yield plateau as is the case for carbon steel; the curve reflects a material that behaves in an increasingly non-linear fashion, and the overall ductility is generally very high.

Fig. 1.1 Typical strain-stress curve for stainless steel, Bezkorovainy (2003)

On the other hand, unlike carbon steel there are clear differences associated with the longitudinal tension and compression, as well as with transverse tension and compression. Representative values of yield and ultimate tensile (compressive) stresses and the modulus of elasticity are given in Table1.9.

18

Table 1.9 Stainless steel - representative values for yield stress in tension and compression and modulus of elasticity Yield stress in tension Yield stress in Compression Initial modulus of elasticity

ksi 40 to 55 45 to 65 29,000

MPa 275 to 380 310 to 415 200,000

The standard ASTM E 6-03 “Standard Terminology Relating to Methods of Mechanical Testing” covers the terms shown on Fig. 1.1. Modulus of elasticity (E): the ratio of the stress to corresponding strain below the proportional limit. Proportional limit: The greatest stress which a material is capable of sustaining without any deviation from proportionality of stress to strain. Elastic limit: the greatest stress which a material is capable of sustaining, without any permanent strain remaining upon complete release of the stress. The stress-strain relationship, in the case of stainless steel, does not conform to Hooke’s law throughout the elastic range, but deviates at stresses well below the elastic limit. Therefore, the “modulus of elasticity” is usually taken as the slope of either the tangent to the stress-strain curve at the origin or at a low stress, the secant drawn from the origin to a specified point on the stress-strain curve, or the chord connecting any two specified points on the strain-stress curve. In these cases the modulus is designated as the “tangent modulus,” the “secant modulus,” or the “chord modulus.” Thus, in order to determine mechanical properties for stainless steel, one of the following terms may be used.

19

Initial tangent modulus (Eo): The slope of the stress-strain curve at the origin. Tangent modulus (Et): the slope of the stress-strain curve at any specified stress or strain. Secant modulus (Es): the slope of the secant drawn from the origin to any specified point on the stress-strain curve Chord modulus (Ec): the slope of the chord drawn between any two specified points on the stress-strain curve. In the absence of a yield plateau, it is common practice to use the RambergOsgood (1943) to represent the stress-strain relationship in stainless steel. The equation is expressed in the form:

σ

⎛σ ⎞ ε = + K⎜ ⎟ E ⎝E⎠

n

Eq. 1

Where:

ε = Normal strain σ = Normal Stress E = modulus of elasticity K and n are constants, which are evaluated through two secant yield strengths at slopes of 0.7E and 0.85E, respectively.

K=

20

ε1 ⎛ σ1 ⎞ ⎜ ⎟ ⎝E⎠

n

Eq. 2

⎛ε ⎞ log⎜⎜ 2 ⎟⎟ ⎝ ε1 ⎠ n= ⎛σ ⎞ log⎜⎜ 2 ⎟⎟ ⎝ σ1 ⎠

Eq. 3

Where σ1 and σ2 are the specified yield strengths and ε1 and ε2 the specified strains. The modulus of elasticity, E, is considered constant and equal to the initial value,

E0 . The Ramberg-Osgood formula was modified by Hill (1944), who used two offset yield strength values rather than the secant yield strength value. Hill indicated that the yield strength determined at the 0.2% offset strain, i.e. Fy, might be used for determining the constant K. Thus, the constant K can be expressed as:

K=

0.002 ⎛ Fy ⎜⎜ ⎝ E0

⎞ ⎟⎟ ⎠

Eq. 4

n

Consequently, the original Ramberg-Osgood equation can be written as ⎛σ ε= + 0.002⎜ ⎜F E ⎝ y

σ

⎞ ⎟ ⎟ ⎠

n

Eq. 5

In which:

⎛ 0.002 ⎞ ⎟ log⎜⎜ ε 1 ⎟⎠ ⎝ n= ⎛ Fy ⎞ log⎜⎜ ⎟⎟ ⎝ σ1 ⎠

21

Eq. 6

For cold-formed stainless steel, the constant n has been determined on the basis of the 0.01% offset strength because this value is defined as the proportional limit of the material property. The offset strength method is explained in the ASTM A 370 - 03 “Standard test Methods and definition for mechanical testing of steel products.“ The ASTM A 370 covers procedures and definition for the mechanical testing of wrought and cast steel, stainless steel and related alloy products. The ASTM A 370-03 defines the yield point as the first stress in a material, less than the maximum obtainable stress, at which an increase in strain occurs without an increase in stress. It defines the Yield strength as the stress at which a material exhibits a specified limiting deviation from the proportionality of stress to strain. The deviation is expressed in terms of strain, percent offset, total extension under load, etc. To determine the yield stress by the “offset method” on the stress-strain diagram (Fig. 1.2): 1) Draw line OA as the tangent of the stress strain curve at the origin. 2) From the origin off set the distance Om equal to the specified value of strain usually taken as 0.2%, draw mn parallel to OA. 3) Locate r at the intersection of mn with the stress-strain curve. 4) The point r corresponds to load R, which is taken as the yield strength load. When the yield strength is obtained by this method, the value of offset specified or used is stated in parenthesis after the term yield strength, for example: Yield strength (0.2 % offset) = 52,000 psi (360 MPa)

22

n

A R

Stress

r

Strain o

m

Fig. 1.2 Yield Strength determination by using the offset method 1.4 Coupon test of 304L stainless steel material To illustrate how the strength and modulus properties can be determined for a specific stainless steel, a compressive test was performed on a coupon taken from a hot rolled, 304L stainless steel equal leg angle, following the ASTM E-9-859a “Standard Test Methods of Compression Testing of Metallic Materials at Room Temperature.” The length of the coupon was selected so that buckling was prevented. This is expressed mathematically as follows:

π2 ⋅E ⎛k⋅L⎞ ⎟ ⎜ ⎝ r ⎠

23

2

≥ Fu

Eq. 7

From which:

r = Minimum radii of gyration L = Length of the coupon k = Effective length factor E = Modulus of elasticity Fu = Compression strength From Eq. 1, the coupon length L can be determined as:

L≤

π ⋅r k

⋅

E Fu

Eq. 8

For a coupon size of 0.75” x 0.25”, Equation 8 was computed for various values of k, assuming a conservative ultimate strength of Fu = 110 ksi and estimating the compression elastic modulus to be E = 25,000 ksi. The calculations are presented in Table 1.10

Table 1.10 Compressive test lengths

K 0.5

Fu (ksi) 26 28 30 32 34 36 38 90 100 110

0.6

0.7

0.8

0.9

1

8.74 8.42 8.14 7.88 7.64 7.43 7.24 4.70 4.46 4.25

7.77 7.49 7.24 7.01 6.80 6.60 6.44 4.18 3.96 3.78

7.00 6.74 6.51 6.31 6.12 5.95 5.79 3.76 3.56 3.41

L (in) 14.06 13.55 13.09 12.61 12.23 11.89 11.57 7.52 7.14 6.80

11.66 11.23 10.86 10.51 10.20 9.90 9.64 6.27 5.95 5.67

10.00 9.63 9.30 9.01 8.75 8.49 8.27 5.38 5.10 4.87

24

From a hot rolled, 304L stainless steel equal leg angle 2” x 2” x ¼”, a coupon was cut and machined with the dimensions shown on Fig. 1.3. The coupon was taken longitudinally from the angle.

Fig. 1.3 Compression Test coupon - Dimensions

25

Two back-to-back electronic strain gages were placed at the coupon mid-height, as shown in Fig. 1.4.

Fig. 1.4 Compression Test coupon – Strain gages

Coupon Test: The coupon was tested in a MTS machine following the ASTM E-9-859a “Standard Test Methods of Compression Testing of Metallic Materials at Room Temperature.” Table 1.11 contains the data obtained directly from the test. The first column shows the time at which the test lectures were registered; the second and third columns 26

show the total applied load in pounds and the total displacement in inches. The next two columns contain the strains registered by both back and front strain gages measured on 4

µE units (10 µE = 1 %), The next two columns show the strains expressed in terms of

percentage (%), and finally the last column shows the engineering stress calculated at that moment as the total load divided by the initial cross section area of the test coupon. The aforementioned data are plotted in a typical stress-train curve on Fig. 1.5. Two curves are plotted one for each strain gage, back and front. Finally, and following the ASTM A 370 - 03 “Standard test Methods and definition for mechanical testing of steel products,“ the Eo, E and Fy values are determined according with the offset method graphically represented in Fig 1.5a.

27

Table 1.11 Compression test data WINTCS Test: C:\users\Fulvio\Fulvio-Compression.tcs MEGADAC Test: FULVIO~1 Data Set: 1 Data Type: Raw Data Collected on Thursday, July 14, 2005 at 7:15:45 PM Comments: Exported Fields: 4 Scans: 25240 Scanning Speed: 5.0000 scans/second Duration: 5048.000 seconds

TIME SECONDS 2.00E-01 9.54E+01 1.91E+02 2.86E+02 3.82E+02 4.78E+02 5.73E+02 6.69E+02 7.64E+02 8.60E+02 9.56E+02 1.05E+03 1.15E+03 1.24E+03 1.34E+03 1.43E+03 1.53E+03 1.62E+03 1.72E+03 1.82E+03 1.91E+03 2.01E+03 2.10E+03 2.20E+03 2.29E+03 2.39E+03 2.49E+03 2.58E+03 2.68E+03 2.78E+03

Load lbs 3.44E+01 -5.62E+03 -7.21E+03 -7.47E+03 -7.59E+03 -7.50E+03 -7.45E+03 -7.47E+03 -7.65E+03 -7.69E+03 -7.62E+03 -7.57E+03 -7.50E+03 -7.64E+03 -7.67E+03 -7.02E+03 -7.11E+03 -7.25E+03 -7.37E+03 -7.51E+03 -7.63E+03 -7.48E+03 -7.47E+03 -7.97E+03 -8.27E+03 -8.24E+03 -8.26E+03 -8.33E+03 -8.17E+03 -7.86E+03

Displ in -1.56E-04 -9.38E-03 -1.88E-02 -2.83E-02 -3.81E-02 -4.73E-02 -5.73E-02 -6.66E-02 -7.63E-02 -8.58E-02 -9.53E-02 -1.05E-01 -1.14E-01 -1.24E-01 -1.34E-01 -1.43E-01 -1.53E-01 -1.62E-01 -1.72E-01 -1.82E-01 -1.91E-01 -2.00E-01 -2.10E-01 -2.20E-01 -2.29E-01 -2.39E-01 -2.49E-01 -2.58E-01 -2.68E-01 -2.77E-01

Strain-Front µE 2.92E+00 -1.16E+03 -1.69E+03 -1.92E+03 -1.99E+03 -2.03E+03 -2.06E+03 -2.07E+03 -2.15E+03 -2.21E+03 -2.25E+03 -2.29E+03 -2.32E+03 -2.37E+03 -2.41E+03 -2.45E+03 -2.49E+03 -2.54E+03 -2.59E+03 -2.64E+03 -2.68E+03 -2.74E+03 -2.79E+03 -2.86E+03 -2.94E+03 -3.03E+03 -3.14E+03 -3.25E+03 -3.32E+03 -3.31E+03

28

Strain-Back µE 2.92E+00 -1.14E+03 -1.64E+03 -1.84E+03 -1.91E+03 -1.94E+03 -1.96E+03 -1.99E+03 -2.06E+03 -2.11E+03 -2.15E+03 -2.20E+03 -2.23E+03 -2.29E+03 -2.34E+03 -2.38E+03 -2.43E+03 -2.47E+03 -2.54E+03 -2.59E+03 -2.64E+03 -2.71E+03 -2.76E+03 -2.83E+03 -2.91E+03 -2.99E+03 -3.11E+03 -3.24E+03 -3.29E+03 -3.25E+03

strain % Front Back 0.00 0.12 0.17 0.19 0.20 0.20 0.21 0.21 0.22 0.22 0.22 0.23 0.23 0.24 0.24 0.24 0.25 0.25 0.26 0.26 0.27 0.27 0.28 0.29 0.29 0.30 0.31 0.33 0.33 0.33

0.00 0.11 0.16 0.18 0.19 0.19 0.20 0.20 0.21 0.21 0.22 0.22 0.22 0.23 0.23 0.24 0.24 0.25 0.25 0.26 0.26 0.27 0.28 0.28 0.29 0.30 0.31 0.32 0.33 0.32

Stresses (psi) -0.18 29.96 38.48 39.84 40.46 39.99 39.72 39.83 40.82 40.99 40.66 40.38 39.98 40.73 40.91 37.43 37.91 38.68 39.31 40.08 40.67 39.91 39.83 42.52 44.11 43.94 44.07 44.41 43.58 41.94

Table 1.11 (Cont.) Compression test data

TIME SECONDS 2.87E+03 2.97E+03 3.06E+03 3.16E+03 3.26E+03 3.35E+03 3.45E+03 3.55E+03 3.64E+03 3.74E+03 3.97E+03 4.01E+03 4.07E+03 4.29E+03 4.29E+03 4.29E+03 5.03E+03 5.03E+03 5.03E+03 5.03E+03 5.03E+03 5.03E+03 5.03E+03 5.03E+03 5.03E+03 5.03E+03 5.03E+03 5.03E+03 5.03E+03 5.03E+03 5.03E+03 5.03E+03 5.03E+03 5.03E+03 5.03E+03 5.03E+03 5.03E+03

Load lbs -7.55E+03 -7.48E+03 -7.70E+03 -7.88E+03 -7.83E+03 -7.97E+03 -8.14E+03 -8.14E+03 -8.13E+03 -8.19E+03 -8.22E+03 -8.24E+03 -8.32E+03 -8.40E+03 -8.40E+03 -8.41E+03 -8.30E+03 -8.30E+03 -8.30E+03 -8.29E+03 -8.29E+03 -8.29E+03 -8.29E+03 -8.29E+03 -8.30E+03 -8.30E+03 -8.30E+03 -8.30E+03 -8.31E+03 -8.31E+03 -8.30E+03 -8.29E+03 -8.28E+03 -8.28E+03 -8.28E+03 -8.28E+03 -8.28E+03

Displ in -2.87E-01 -2.96E-01 -3.06E-01 -3.16E-01 -3.25E-01 -3.35E-01 -3.45E-01 -3.54E-01 -3.64E-01 -3.74E-01 -3.97E-01 -4.00E-01 -4.06E-01 -4.29E-01 -4.29E-01 -4.29E-01 -5.00E-01 -5.00E-01 -5.00E-01 -5.00E-01 -5.00E-01 -5.00E-01 -5.00E-01 -5.00E-01 -5.00E-01 -5.00E-01 -5.00E-01 -5.00E-01 -5.00E-01 -5.00E-01 -5.00E-01 -5.00E-01 -5.00E-01 -5.00E-01 -5.00E-01 -5.00E-01 -5.00E-01

Strain-Front µE -3.33E+03 -3.33E+03 -3.35E+03 -3.38E+03 -3.37E+03 -3.40E+03 -3.44E+03 -3.46E+03 -3.47E+03 -3.49E+03 -3.52E+03 -3.54E+03 -3.56E+03 -3.65E+03 -3.65E+03 -3.65E+03 -3.86E+03 -3.86E+03 -3.86E+03 -3.86E+03 -3.86E+03 -3.86E+03 -3.86E+03 -3.86E+03 -3.86E+03 -3.86E+03 -3.86E+03 -3.86E+03 -3.87E+03 -3.86E+03 -3.86E+03 -3.86E+03 -3.86E+03 -3.86E+03 -3.86E+03 -3.86E+03 -3.86E+03

29

Strain-Back µE -3.25E+03 -3.25E+03 -3.26E+03 -3.27E+03 -3.27E+03 -3.28E+03 -3.32E+03 -3.33E+03 -3.34E+03 -3.35E+03 -3.37E+03 -3.38E+03 -3.40E+03 -3.47E+03 -3.47E+03 -3.47E+03 -3.68E+03 -3.68E+03 -3.68E+03 -3.68E+03 -3.68E+03 -3.68E+03 -3.68E+03 -3.68E+03 -3.68E+03 -3.68E+03 -3.68E+03 -3.68E+03 -3.68E+03 -3.68E+03 -3.68E+03 -3.68E+03 -3.68E+03 -3.68E+03 -3.68E+03 -3.68E+03 -3.68E+03

strain % Front Back 0.33 0.33 0.34 0.34 0.34 0.34 0.34 0.35 0.35 0.35 0.35 0.35 0.36 0.36 0.36 0.36 0.39 0.39 0.39 0.39 0.39 0.39 0.39 0.39 0.39 0.39 0.39 0.39 0.39 0.39 0.39 0.39 0.39 0.39 0.39 0.39 0.39

0.33 0.32 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.34 0.34 0.34 0.34 0.35 0.35 0.35 0.37 0.37 0.37 0.37 0.37 0.37 0.37 0.37 0.37 0.37 0.37 0.37 0.37 0.37 0.37 0.37 0.37 0.37 0.37 0.37 0.37

Stresses (psi) 40.27 39.92 41.04 42.01 41.76 42.49 43.41 43.39 43.36 43.68 43.85 43.97 44.37 44.78 44.83 44.85 44.26 44.24 44.24 44.23 44.21 44.19 44.19 44.21 44.26 44.26 44.25 44.26 44.34 44.32 44.29 44.22 44.14 44.16 44.18 44.17 44.14

Fig. 1.5 Compression test, strain-stress curve

30

Determination of modulus of elasticity E and yield strength Fy (at 0. 2 % strain):

Step 1: Determine the best-fit curve following the shape of the Ramberg-Osgood curve. To determine the curve that best fit the data obtained from the compression coupon test a regression analysis is performed using a function model. ⎛σ ε= + 0.002⎜ ⎜F E ⎝ y

σ

⎞ ⎟ ⎟ ⎠

n

Eq. 9

Using the expressions: n

⎛ 0.002 ⎞ 1 ⎟ ; a= ; b=⎜ ⎜ F ⎟ E ⎝ y ⎠

y = ε; x = σ

And by substituting in Eq. 9, the function model is obtained in the following form:

y = a ⋅ x + b ⋅ xn

Eq. 10

The parameters of the regression analysis were found to be: n = 7,

a = 0.003729 and b =5.29x10-13; with a standard error coefficient s = 0.03733 and correlation coefficient of r = 0.9335. Thus, Eq. 10 becomes:

y = 0.003729 ⋅ x + 5.29 × 10 −13 ⋅ x 7

Eq. 11

The standard error of the estimated curve is defined as follows:

n po int s

s=

∑ (y i =1

i

− f ( xi ) )

n po int s − n

31

2

Eq. 12

Where: npoints = Number of points yi = Data points f(xi) = denotes the value calculated from the regression model n = number of parameter The standard error of the estimated curve quantifies the spread of the data points around the regression curve. As the quality of the model increases, the standard error approaches to zero. The correlation coefficient “r”, is defined as: r=

St − S r St

Eq. 13

Where St standard deviation is expressed as: St =

y=

Sr =

n po int s

∑ (y − y )

Eq. 14

∑y

Eq. 15

i =1

n po int s

1 n po int s n po int s

∑(y i =1

2

i

i

32

i =1

i

− f ( xi )) 2

Eq.16

Stress (Ksi)

Strain-Stress Curve Compression Test (c-1 07/14/05)

-0.05

80 75 70 65 60 55 50 45 40 35 30 25 20 15 10 5 0 -5 0.00

0.05

0.10

0.15

0.20

0.25

0.30

Strain (% ) Front

Back

Regression

Fig. 1.6 Strain-stress Best-fit curve by regression analysis

33

0.35

0.40

Using the parameters obtained by the regression analysis the stress strain relationship can be expressed in the form:

σ

⎛ σ ⎞ + 0.002⎜ ε= ⎟ 29,000 ⎝ 46.02 ⎠

The results are shown graphically in Fig. 1.7.

34

7

Eq. 17

Stress (Ksi)

Strain-Stress Curve Compression Test (c-1 07/14/05)

-0.05

80 75 70 65 60 55 50 45 40 35 30 25 20 15 10 5 0 -5 0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

Strain (% ) Front

Back

Osgood

Regression

Fig. 1.7 Strain-stress Best-fit Ramberg-Osgood curve

35

0.40

Step 2: Determine Fy by the offset method

The graphic offset method stated in ASTM A –370-03 “Standard test methods and definitions for mechanical testing of steel products”, described previously on page 22, is followed to determine the yield strength Fy. The procedure performed to determine the yield strength for a offset of 0.2%, is shown on Fig. 1.8 where the yield strength Fy hence obtained is: Fy = 46.05 ksi

36

Stress (Ksi)

Strain-Stress Curve Compression Test (c-1 07/14/05)

-0.05

80 75 70 65 60 55 50 45 40 35 30 25 20 15 10 5 0 -5 0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

Strain (%) Front

Back

Osgood

Regression

Fig. 1.8 Compression test – strain-stress curve Determination of Eo, and Fy

37

0.40

CHAPTER 2 AXIALLY COMPRESSED STAINLESS STEEL MEMBERS 2.1 Introduction

This chapter summarizes available design guidelines related to axially compressed stainless steel members. These guidelines include the American Society of Civil Engineers (ASCE 2002) “Specification for the design of cold-formed stainless steel structural members,” the Australian/New Zealand Standard (Aust/NZS 2001) “Coldformed stainless steel structures” and the European Code (Eurocode 3 1996) “Design of steel structures part 1.4: Supplementary rules for stainless steel.”

2.2 Cold formed stainless steel design

One of the earliest studies concerning design guidelines of axially compressed cold-formed stainless steel members was conducted by Johnson & Winter (1966) who investigated the structural behavior of 304 annealed stainless steel columns and beams. Two types of columns were tested. One type was composed of two channels placed back-to-back to form an I section; the other was fabricated from identical channels placed together to form a box section. In both types, the two halves were joined by means of structural adhesive cured at room temperature. A total of 11 I-section and 4 box section column specimens were tested. The columns cross-sections and properties are shown in Fig. 2.1 and Table 2.1. The columns were designed so that the primary limit state was over-all column buckling. The columns were tested between knife-edges to simulate pin-ended boundary conditions.

38

Table 2.1 Section properties, Johnson & Winter (1966)

I- sections Box sections

Iy, in4 0.0202 0.0337

Area, in² 0.364 0.361

ry, in 0.235 0.306

Fig. 2.1 Section dimensions, Johnson & Winter (1966)

The critical stresses corresponding to the experimentally attained critical loads are given in Table 2.2. These experimental buckling stresses were computed from the equation:

σ cr =

Pcr π 2 Et = A ⎛ l ⎞2 ⎜ ⎟ ⎝r⎠

Eq. 18

Where σcr = Critical stress; Pcr = Critical load; A = area; Et = Tangent modulus corresponding to σcr; l = length of the pin-ended column; and r = radius of gyration about axis of buckling. The computations were carried out in two ways, the first of which Et was estimated as the tangent of the stress-strain curve of a flat coupon cut from the material before any cold rolled or formed process. In the second way, Et was estimated as the tangent modulus of the stress-strain curve of a stub-column test.

39

Table 2.2 Critical column stress vs. slenderness, Johnson & Winter (1966)

σcr experimental ksi

Column number

l/r

PC-7 8 9 10 14 12 13 15 16 5 6

28.03 36.84 45.74 54.44 59.68 70.69 79.88 99.96 130.03 158.19 177.03

47.68 42.85 37.05 33.35 29.65 26.45 23.68 18.06 13.60 9.66 8.14

PC-103 104 105 106

37.25 55.66 72.37 81.62

46.55 36.25 29.13 28.26

Tangent modulus formula Flat material Stub Column

σcr predicted

σcr predicted σcr

(a) I- Sections 39.0 35.6 32.5 29.7 28.3 25.4 23.4 19.3 14.2 10.5 8.7 Average – 3.7 (b) Box Sections 35.4 29.4 25.0 23.0 Average -18.9

σcr predicted

σcr predicted σcr

-18.2 -16.9 -12.3 -10.9 -4.6 -4.0 -1.2 +6.9 +4.4 +8.7 +6.9

47.0 41.2 36.5 32.2 30.0 26.0 23.5 18.2 13.0 9.5 8.1 -1.6

-1.4 -3.9 -1.5 -3.4 +1.2 -1.7 -0.8 +0.8 -4.4 -1.7 -0.5

-24.0 -18.9 -14.2 -18.6

41.1 31.6 25.6 22.8 -14.0

-11.7 -12.8 -12.1 -19.3

The predicted critical stresses when the stub column tangent modulus was used correlates well with the experimental results, because it better reflects the influence of the strain hardening effect due to the cold-formed process. The results obtained are plotted in Fig 2.2 together with the curve known as the Column Research Council (CRC) column curve, which is the basis for column design equations in the design specifications for ordinary carbon steel, with a yield stress of 34.5 ksi and an initial modulus of 29,500 ksi.

40

The “CRC Column Strength Curve,” named after the acronym of the former name of the Structural Stability Research Council (i.e., Column Research Council), is a formula based on the tangent- modulus theory. The CRC-Column strength Curve is given by:

σ cr σy

⎧ λ2 ⎪⎪1 − 4 =⎨ ⎪1 ⎪⎩ λ2

for λ ≤ 2

Eq. 19 for λ ≥ 2

Where:

λ=

KL 1 σ y r π E

Eq. 20

As shown in Fig 2.2, this parabolic curve was found to be inapplicable to stainless steel throughout the entire range shown. This is because the low proportional limit and the general shape of the stress-strain curve of annealed stainless steel differ substantially from the stress-strain curve of mild carbon steel.

41

Critical Column Stress Vrs Slenderness Ratio Type 304 stainless steel annealed 60

50

Effective Flat

40

CRC Curve

σcr, ksi

I Box

30

20

10

0 0

100

200

300

l/r

Fig. 2.2 Critical Column stress vs. slenderness radio Johnson & Winter (1966)

Rasmussen & Rondal, (1997), described a design procedure for estimating the flexural buckling load of stainless steel columns. In their approach, the stress-strain curve was modeled according to the Ramberg-Osgood equation, defined in terms of the initial modulus (E0), the 0.2% proof stress (σ0.2) and the parameter n. Then using the Perry-type curve, outlined on the Eurocode 3 (1996), the basic strength curve was evaluated, expressing the imperfection parameters in terms of E0, σ0.2 and n. The results obtained with the application of the Eurocode 3 are compared with the iterative approach

42

described in the ASCE Load and Resistance Factor Design (LRFD), “Specification for the Design of cold formed stainless steel structural members,” (2002), which uses a tangent modulus approach for the evaluation of flexural buckling load in columns. In their paper Rasmussen & Rondal (1997a, 1997b) proposed the following procedure to evaluated the nondimensional strength for flexural buckling (χ).

χ=

φ=

1

Eq. 21

φ + φ 2 − λ2

(

1 1 + η + λ2 2

)

Eq. 22

Where the imperfection parameter

η = α [(λ − λ ) β − λ0 ]

Eq. 23

1

was expressed in terms of the parameters e=σ0.2/E0 and n as follows:

α ( n, e ) =

1.5 (e

0.6

+ 0.03)[n

( 0.0048 e − o .55 +1.4 )

+ 13]

+

0.002 e 0.6

6 × 10 −6 0.36 exp(− n) n + + + 0.004) tanh( 180 e 0.45 + 0.007 e1.4 e − 0.01n) ≥ 0.2 λ0 (n, e) = 0.82( e + 0.0004 2 0.6 ⎫ ⎧ ⎡ ⎤ ⎛ ⎞ ⎪ ⎢⎜ ⎟ ⎥ ⎪ e n − 5.5 ⎪ ⎢⎜ ⎟ ⎥ ⎪⎬ λ1 (n, e) = 0.8 ⎨1 − 6e − 0.0054 ⎟ ⎥ ⎪ e + 0.0018 ⎪ ⎢⎜ ⎜n+ ⎟ ⎢ e + 0.0015 ⎠ ⎥⎦ ⎪ ⎪ ⎣⎝ ⎭ ⎩

β ( n, e ) =

Eq. 24 Eq. 25 Eq. 26

Eq.27

The slenderness reduction factor (χ) and the normalized slenderness (λ) are defined as

43

χ=

σu σ 0.2

Eq. 28

σ 0.2 σE

λ=

Eq. 29

0

σE = 0

π 2 E0

(L r )

Eq. 30

Where σu, L and r are the ultimate stress, effective length, and radius of gyration, respectively. The authors stated that equations 24 to 27 have been shown to be accurate within the ranges e ∈ [0.001.0.008] and n ∈ [3, ∞ ], which covers the structural stainless steel alloys used in practice. In the ASCE specification, the nondimensional column strength χ is defined as

χ=

π 2E t ⎛ L⎞ ⎜ 2 ⎟σ 0.2 ⎝r ⎠

≤1 Eq. 31

(Et) = Tangent Modulus (χ) = Non-dimensional column strength The results obtained using the explicit design approach described in Eqs. 21 to 30 were compared with those obtained on specimens tested within other investigation made by Johnson and Winter (1966) from austenitic (AISI) 304 annealed and skin-passed coldformed sheets, Rasmussen & Hancock (1993) austenitic 304 L and Hyttinen (1994) austenitic 304 and ferritic 409, both were cold-formed from annealed flat sheets. In all tests, local buckling did not occur prior to the ultimate load. The Ramberg-Osgood parameters were obtained from stub column tests and thus included the effect of residual stresses.

44

Table 2.3 shows the Ramberg-Osgood parameters of the most common structural alloy, as obtained from the ASCE specification (2002) as well as the corresponding values of λ, β, λo and λ1

Table 2.3 Mechanical properties, Johnson & Winter (1996)

Property Annealed 193,100 E0 (MPa) 193.1 σ0.2 (MPa) 4.1 n 1.56 α 0.27 β 0.55 λ0 0.21 λ1

ALLOY AND HARDENESS 409 201, 301, 304, 316 1/16 hard ¼ hard ½ hard 193,100 186,200 186,200 186,200 282.5 344.8 448.2 206.9 4.1 4.58 4.22 9.7 1.45 1.29 1.27 0.74 0.22 0.16 0.16 0.18 0.61 0.64 0.67 0.52 0.29 0.37 0.39 0.20

430,439 186,200 275.8 6.25 1.07 0.14 0.59 0.34

Rasmussen & Rondal (1997) also proposed that the column strength φPn be determined using: Pn = χσ 0.2 Ae

Eq.32

φ = 0.90 Ae = Effective area; and χ determined as shown above The comparison of results obtained using the proposed expression and ASCELRFD strength curves for Annealed AISI 304 alloy is shown in Fig 2.3.

45

Proposed Curve Rasmussen (1997) ASCE-LRFD

1.6 1.4 1.2 1

Euler (Eo)

χ 0.8

Eo = 200GPa σ0.2 = 400 MPa n =5

0.6

Eo = 193 GPa σ0.2 = 193 MPa n = 4.1

0.4 0.2 0 0

0.5

1

λ

1.5

2

2.5

Fig. 2.3 Critical column stress vs. slenderness, Rasmussen & Rondal (1997)

Bezkorovainy et al. (2003), presented a generalized strength formulation for metal plates made of alloys with nonlinear stress strain curves. The formulation was based on a generalized Winter-curve featuring two material dependent parameters. Analytical expressions were derived for these parameters so that they can be determined for given material properties expressed in terms of the Ramberg-Osgood parameters (E0, σ0.2, n). Thus, the generalized formulation allowed the plate strength equation to be determined for a given alloy, requiring only the Ramberg-Osgood parameters. The strength curves obtained using the generalized formulation were shown to correlate well with finite element results (Bezkorovainy et al. 200ko3). The strength equations were developed for uniformly compressed plates simply supported along all four edges. The validity ranges for the material properties are 3