Shear lag analysis of strength of dual phase steels

Abstract

Considering the similarities between structural distribution and deformation behaviour of martensite–ferrite dual phase steels with composite materials reinforced by short, discontinuous fibres, a new expression for the tensile strength of these steels was suggested using shear lag analysis, i.e.

<disp-formula><mml:math><mml:semantics><mml:mrow><mml:msub><mml:mi>σ</mml:mi><mml:mrow><mml:mtext>bDP</mml:mtext></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mfrac><mml:mn>1</mml:mn><mml:mi>K</mml:mi></mml:mfrac><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mfrac><mml:mi>β</mml:mi><mml:mrow><mml:mn>2</mml:mn><mml:msqrt><mml:mn>3</mml:mn></mml:msqrt></mml:mrow></mml:mfrac><mml:mo>+</mml:mo><mml:mn>0</mml:mn><mml:mo>⋅</mml:mo><mml:mn>65</mml:mn></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:msub><mml:mi>σ</mml:mi><mml:mrow><mml:mtext>bM</mml:mtext></mml:mrow></mml:msub><mml:msub><mml:mi>V</mml:mi><mml:mtext>M</mml:mtext></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>σ</mml:mi><mml:mrow><mml:mtext>bF</mml:mtext></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mn>1</mml:mn><mml:mo>−</mml:mo><mml:msub><mml:mi>V</mml:mi><mml:mtext>M</mml:mtext></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:annotation encoding='MathType-MTEF'></mml:annotation></mml:semantics></mml:math></disp-formula>

where σ_bDP, σ_bM, and σ_bF are the tensile strengths of the steel, the martensite, and the ferrite phases respectively, β is the aspect ratio of martensite islands, K is the strength ratio of martensite to ferrite σ_bM/σ_bF, V _M is the volume fraction of martensite, and (1 – V _M) is the volume fraction of ferrite. The experimentally measured strengths of a variety of dual phase steels are shown to be in good agreement with those calculated using this equation. Problems concerning the load transfer from ferrite to martensite and the degree of utilization of martensite strength are discussed.

Get full access to this article

View all access options for this article.

References

TAMURA

, TOMOTA

, YAMAOKA

, KANATANI

, OZAWA

, and AKAO

: Tetsu-to-Hagané (J. Iron Steel Inst. Jpn), 1973, 59, 454.

ARAKI

, TAKARA

, and NAKAOKA

: Trans. Iron Steel Inst. Jpn, 1977, 17, 710.

TOMOTA

, MORI

, KUROKI

, and TAMURA

: Mater. Sci. Eng., 1976, 24, 85.

RIOS

P. K.

, GUIMARAES

J. R. C.

, and CHAWLA

K. K.

: Ser. Metall., 1981, 15, 899.

DAVIES

R. G.

: Metall. Trans., 1978, 9A, 451.

KOO

J. Y.

, YOUNG

M. I.

, and THOMAS

: Metall. Trans., 1980, 11A, 852.

DAVIES

R. G.

: Metall. Trans., 1978, 9A, 671.

RAMOS

L. F.

, MATLOCK

D. K.

, and ICRAUGS

: Metall. Trans., 1979, 10A, 259.

BAILEY

and STEVENSON

: Metall. Trans., 1979, 10A, 47.

10.

BHADESHIA

H. K. D. H.

and EDMONDS

D. V.

: Met. Sci., 1980, 14, 41.

11.

OSTROM

: Metall. Trans., 1981, 12A, 355.

12.

KORZEKWA

D. A.

, LAWSON

R. D.

, MATLOCK

D. K.

, and KRAUSS

: Scr. Metall., 1980, 14, 1023.

13.

KELLY

: in ‘Strong solids’, 189; 1966, Oxford, Clarendon Press.

14.

MILEIKO

S. T.

: J. Mater. Sci., 1969, 4, 974.

15.

DAVIES

R. G.

: Metall. Trans., 1978, 9A, 41.

16.

DAVIES

R. G.

and MAGEE

C. L.

: J. Met., 1979, 31, 17.

17.

TAMURA

in Proc. 3rd Int. Conf. on ‘Strength of metals and alloys’, Vol. I, 611; 1977, Oxford, Pergamon.

18.

DAVIES

R. G.

: Metall. Trans., 1979, 10A, 1594.

19.

LEI

T. C.

and SHEN

H. P.

: Ada Metall. Sin. (China), 1982, 18, 75.

20.

LEI

T. C.

and cut

G. K.

: in ‘Mechanical behaviour of materials-IV’, (ed. Carlsson

and Ohlson

N.-G.

), 611; 1983, Oxford, Pergamon.

21.

TOMOTA

, KUROKI

, and TAMURA

: Tetsu-to-Hagané Iron Steel Inst. Jpn), 1975, 61, 107.

22.

SPEICH

G. R.

and MILLER

R. L.

: in ‘Structure and properties of dual-phase steels’, ( ed. Kot

R. A.

and Morris

J. W.

), 145; 1979, Warrendale, Pa, The Metallurgical Society, American Institute of Mining and Metallurgical Engineers.

23.

GARCIA

C. I.

and DeARDO

A. J.

: in ‘Structure and properties of dual-phase steels’, ( ed. Kot

R. A.

and Morris

J. W.

), 40; 1979, Warrendale, Pa, The Metallurgical Society, American Institute of Mining and Metallurgical Engineers.

24.

SZEWCZYK

A. F.

and GURLAND

: Metall. Trans., 1982, 13A, 821.

25.

GEIB

M. D.

, MATLOCK

D. K.

, and KRAUSS

: Metall. Trans., 1980, 11A, 1683.

26.

TANGRI

and YEGNESWARAN

A. H.

: in ‘Strength of metals and alloys’, ( ed. Gifkins

R. C.

), Vol. 1, 373; 1982, Oxford, Pergamon.

27.

BALLIGER

N. K.

and GLADMAN

: Met. Sci., 1969, 4, 974.

28.

WANG

D. Z.

: in ‘Mechanical behaviour of materials-IV’, ( ed. Carlsson

and Ohlson

N.-G.

), 1083; 1983, Oxford, Pergamon.

29.

RASHID

M. S.

: in ‘Formable HSLA and dual-phase steels’, ( ed. Davenport

A. T.

), 1; 1977, Warrendale, Pa, The Metallurgical Society, American Institute of Mining and Metallurgical Engineers.

30.

GERBASE

, EMBURY

J. D.

, and HOBBS

in ‘Structure and properties of dual-phase steels’, (ed. Kot

R. A.

and Morris

J. W.

), 118 1979, Warrendale, Pa, The Metallurgical Society, American Institute of Mining and Metallurgical Engineers.

31.

BAURAMANI

P. S.

, It. A. JAGO, and R. M. HOBBS: in ‘Strength of metals and alloys’, (ed. Gifkins

R. C.

), Vol. 1, 115; 1982, Oxford, Pergamon.

32.

ROSEN

B. W.

: in ‘Fiber composite materials’, 72; 1964, Metals Park, Ohio, American Society for Metals.

33.

GURLAND

: Scr. Metall., 1979, 13, 967.

34.

LEI

T. C.

, SHEN

H. P.

, and PAN

: Iron Steel (China), 1983, 18, 46.

35.

SHEN

H. P.

: Thesis for Master's degree, Harbin Institute of Technology, People's Republic of China, 1981.

36.

ICOO

J. Y.

and THOMAS

in ‘Formable HSLA and dual-phase steels’, (ed. Davenport

A. T.

), 40; 1977, Warrendale, Pa, The Metallurgical Society, American Institute of Mining and Metallurgical Engineers.

37.

YANG

D. Z.

, SUN

H. W.

, and LEI

T. C.

: Mater. Mech. Eng., 1982, 6, (6), 28.