Fatigue failure criterion based on plastic strain energy density applied to welds

Int J Fatigue 13 No 3 (1991) pp 223-226

Fatigue failure criterion based on plastic strain energy density applied to welds J e r z y Dziubifiski

An experimental verification of a method of calculating the plastic strain hysteresis energy density, applied for welds in joints made of low-alloy steels and for flash welds in joints made of pearlitic steels, has been carried out. This energy criterion has been used to describe the fatigue lifetime of welds and flash welds, and also to describe the parameters of the fatigue crack growth rate for these materials. The results of calculations have been compared with the author's own as well as other authors' experimental data. Key words: hysteresis; fatigue lifetime; welds

Notation b ¢

C da/dN E K' g~=

r/t Nf

R fatigue strength exponent fatigue ductility exponent the Paris law constant crack growth rate Young's modulus cyclic strength coefficient critical stress intensity factor the Paris law exponent cyclic hardening exponent number of cycles to failure

AK AK~

A~p

A~

Orm

The fatigue of metals can be described by using a stress amplitude, a strain amplitude I or by a combination of stress amplitude and strain amplitude through a cyclic strain curve. 2 During the fatigue of metals hysteresis loops have been observed, which arise from plastic strains in which energy dissipation occurs. Strain hysteresis is then the principal cause of the fatigue of metals and is often assumed as a failure parameter. 3 The hysteresis energy is almost constant for strain control tests. 4 The plastic strain energy for materials which satisfy Masing's principle can be determined by means of the expression :,,s \ l + n ' ] AGrA%

(1)

Taking into account the expressions for the strain and stress amplitude: Act = 2Gr~(2Nf) b

AEp =

2~(2Nr) c

(2)

the expression (1) is given as follows: AWp - 4 ( 1 - n ' ) cr~e;(2Nf)~+ c l+n'

stress ratio size of the failure zone stress intensity range critical stress intensity factor under specific loading conditions (when R=0, AK~=KIc) plastic strain energy density plastic strain amplitude stress amplitude fatigue ductility coefficient fatigue strength coefficient mean stress

(3)

In order to determine the fatigue crack growth rate, one may use the local strain and stress analysis and bring the crack growth rate and the mechanical and cyclic properties of the materials into the relationship. One of the solutions of this problem assumes as the failure criterion the product of the stress amplitude Acr and the plastic strain amplitude A~p, which is proportional to the density of the dissipated energy in a material. This energy density is obtained from a hysteresis loop. 6 According to this solution, the crack growth rate is influenced by the value of the product Ao.A~v and by the size of the failure zone 8". The size of this zone can be determined as follows: 6 B* -

(4) 4(l+n')cr;e[~rE

where ARc is the critical stress intensity factor range under specific conditions of loading; when R=0 it can be assumed that AK~ = K~c. However, in accordance with Ref. 6, the Paris law constant and the exponent can be obtained from the following expressions: C = 28* [ 4 ( 1 + n ' ) ( ~ - O'm)e~rES"*] l/(b+c)

(5)

m = -2/(c+b)

(6)

0142-1123/91/030223-04 © 1991 Butterworth-Heinemann Ltd Int J Fatigue May 1991

223

Results and discussion

I. Low-alloy steel 2, MMA weld 3 SAweld 4. ES weld(Table I ) Experiment Calculation

d

It is the aim of this paper to verify experimentally a method of calculating the plastic strain energy density, applied for welds in joints made of low-alloy steels and for flash welds in joints made of pearlitic steels. This energy criterion has been used to describe the fatigue lifetime of welds and also to describe the parameters of the fatigue crack growth rate for these materials. The materials tested and their mechanical and cyclic properties have been gathered together in Table 1. The results of the calculations of the hysteresis energy according to expression (3) have been compared with experimental data7 and are presented in Fig. 1. The results of the calculations of the parameters of the crack growth rate have been presented in Figs 2 and 3 together with the experimental results, s-it The fatigue failure criterion, based on the plastic strain energy density, has been verified experimentally in the case of many structural materials, for instance, for ferritic-martensitic steelsJ 2 There are no verifications of this kind, however, for

4 ~'-~ I i %

102

~{{'~~ E v

i

i

I

I

I0

I

i

IiiJ

I

102

i

i

2Nf

i

i IIii

i

i

i

I

i i i

103

104

Fig. 1 Hysteresis energy density plotted against number of

cycles to failure

Table 1. Cyclic and mechanical properties of welds and base metals Item*

Tested material

~ (MPa)

e~

Kt

b

n'

Kic (MPa k/m)

(MPa)

1

Low alloy steel: 0.18% C, 1.5% Mn, 0.6% Si

1033

0.396

-0.0980

-0.5559

915.4

0.1478

100

2

Weld made by means of basic covered electrodes (MMA): 19 layers, 0.12% C, 1.5% Mn, 0.6% Si

1033

0.107

-0.0980

-0.5153

1036.1

0.1481

125

3

Weld made by means of submerged arc (SA) method highmanganese-content wire with a manganese-free superbasic flux: 12 layers, 0.12% C, 1.5% Mn, 0.6% Si

1033

0.226

-0.0980

-0.5371

971.6

0.1340

95

4 •

Weld made by means of the electroslag method (ES), high-manganesecontent wire with neutral flux: 1 layer, 0.12% C, 1.5% Mn, 0.6% Si

1033

0.663

-0.0980

-0.6251

925.4

0.1533

47

5

Pearlitic steel after rolling: 0.7% C, 1.1% Mn, 0.3% Si Pearlitic steel after rolling and heat treatment: 0.7% C, 1.1% Mn, 0.3% Si Flash weld in joint made of pearlitic steel after heat treatment

2142

0.313

-0.0802

-0.4878

1730.0

0.1890

44

3194

0.5366

-0.0755

-0.4950

1562.0

0.1239

67

1960

0.0995

-0.0772

-0.4787

1775.1

0.1712

67

6

7

*Items 1-4 according to Ref. 7, items 5-7 author's own data

224

Int J Fatigue May 1991

01

(D

(O

..t

-<

a~ t(1)

t.. "11

l0 -8

10

10-7 __

I

- -

---

-....

--

/

t

Scofferbond

I

&K (MPo

ESweld (colc.)

SA weld

Low-alloy steel IVlMAweld

I

I

I

I

I

I iO 2

Fig. 2 Crack growth rate plotted against stress intensity range. The scatterband for weld metals is according to Refs. 8, 10 (experiment)

E

A O

10"6~ --

10-5

i

,o

io -7

o

I. Rails after rolling

-

a

~

AK (MPa./'~)

3. Scottert~nd for rails

2. Railsafter rolling and heat treatment

102

*O

b

E

A O

io -s

10-7

,o

io-6

10-5

If

I ~K(.Po~)

5. Scofferbond for flesh weld

4. Flash welds in rail joints after heat treatment

I

I

I

I

I I

'°2

Fig. 3 Crack growth rate plotted against stress intensity range. The bold full curves s h o w the experimental results and the full curves s h o w the theoretical results. The scatterbands are taken from (a) Ref. 11 and (b) Ref. 9

a

E

10-6

IO-5

welds or flash welds in joints made of low-alloy steels and pearlitic steels, respectively. The results of calculations of the lifetime Nf of welds made by means of covered electrodes (MMA), the submerged arc (SA) method and the electroslag (ES) method (Fig. 1) are presented in this paper. They agree well with the results of experimental t e s t s / T h e results of calculations of the crack growth rate parameters of these welds agree with the experimental data, s'*° as well (Fig. 2), the results of calculations being grouped near the upper limit of the scatterband of the experimental tests. The results presented of the calculations of the crack growth rate parameters for rails made of pearlitic steels lie within the scatterband of experimental tests for rails H (Fig. 3). The results of calculations for the flash welds of rails agree with the experimental data, *° as well (Fig. 3).

3.

Kujawski, D. 'Low-cycle fatigue life in terms of energy dissipation', Mach Dyn Prob 1 1 (1984) pp 127-138

4.

Ellyin, F. and Kujawski, D. 'Plastic strain energy in fatigue failure' J Pressure Vessel Technol, Trans ASME 106 (1984) pp 342-347

5.

Lefebvre, D. and Ellyin, F. 'Cyclic response and inelastic strain energy in low cyclic fatigue' Int J Fatigue 6 (1984) pp 5-15

6.

Kujawski, D. and Ellyin F. 'A fatigue crack growth model with load ratio effects' Eng Fract Mech 28 4 (1987) pp 367-378 Dziubifiski, J. et al 'A welded joint microstructure effect on low cycle fatigue' Proc of Second Int Conf on Low Cycle Fatigue and Elasto-Plastic Behaviour of Materials, Munich, Germany, September 1987 (Elsevier, London, 1987) pp 455-460

7.

8.

Dziubi~ski, J. and Adamie¢, P. 'Effect of microstructure on the fatigue crack propagation and failure of welds' Proc of the 7th Coll. on Mechanical Fatigue of Metals, Miskolc, Hungary, 1983 (Publications of the Technical University for Heavy Industry, Miskolc, Series C, Machinery 39 (1983) pp 9-20)

Conclusions The fatigue failure criterion based on the plastic strain energy density has been verified experimentally for many structural materials, but not for welds. In addition, the results presented in this paper confirm the assumed criterion for welds. Based on this criterion one can determine the lifetime of welds and flash welds as well as the crack growth rate parameters. The results of calculations agree with the experimental data.

9.

Dziubihski, J. and Szymanski, A. 'Abbrennstumphschweissen von Schienen und mechanische Eigenschaften der Verbindungen' Schweissen Schneiden 42 1 (1990) pp 22-25

10.

Maddox, S.J. 'Fatigue crack propagation in weld metal and HAZ' Met Const Brit Welding J 2 (1970) pp 185-289

References

11.

Feddersen, C. E. and Broek, D. Fatigue Crack Propagation in Rail Steels, ASTM STP 644 (American Society for Testing and Materials, 1978)

12.

Mediratta, S. R. et al 'On the estimation of the cyclic plastic strain energy of dual-phase steels' Int J Fatigue 10 1 (1988) pp 13-19

1. 2.

226

Koca~da, $. Fatigue Cracks of Metals (WNT, Warsaw, 1985) in Polish Laird, C. 'The fatigue limit of metals' Mater Sci Eng 22 (1976) pp 231-236

Int J F a t i g u e M a y 1991