Variable-amplitude fatigue of a dual-phase sheet steel subjected to prestrain

Variable-amplitude fatigue of a dual-phase sheet steel subjected to prestrain A. Gustavsson

and A. Melander

Swedish lnsritute for Metals Research, Drottning Stockholm, Sweden (Received

12 January

1994; revised

30 March

Kristinas vsg 48, S-l 14 28

1994)

work concerns variable-amplitude strain-controlled fatigue of a dual-phase sheet steel (RM = 444 MPa and RPO,*= 266 MPa). The material was tested in the as-received condition as well as after ageing and prestraining by 10% uniaxially in the direction of fatigue loading. Four variableamplitude strain sequences were considered with different types of overstrain cycles interspersed each tenth cycle. The experimental investigation indicated a sequence effect and a weak positive influence on the fatigue life of the prestrain operation. During constant-amplitude testing at fatigue lives higher than about lo5 cycles the prestrained material exhibited a mean stress and the as-received material did not. However, under variable-amplitude testing these mean stresses were found to vanish owing to the overstrain cycles. Several different life-prediction methods based on linear damage accumulation were applied to the variable-amplitude sequences used. The methods took due account of the

The present

experimentally determined mean stresses and turned out to predict the fatigue lives properly. (Keywords: variable amplitude;

dual-phase

sheet steel; life prediction)

Cold-rolled dual-phase sheet steels are well suited as components of automotive bodies owing to their good press-forming properties as well as the monotonic strength increments caused by work-hardening during sheet forming and ageing obtained during the bakehardening treatment after painting of the panels. These beneficial contributions to the monotonic strength are documented in the literature1-6. Experimental efforts have also been put into investigating the fatigue properties of dual-phase sheet steels after prestrain and ageing. Fatigue testing under load control at a stress ratio of R, = ~min/U~ax= 0 have shown fatigue strength increments of up to 50% of the monotonic strength increment due to prestrain and ageing7-9. However, load-controlled fatigue testslo have revealed a weaker influence of prestrain and ageing at R, = -1 as compared with R, = 0. Furthermore, fully reversed strain-controlled testing of moderately prestrained (2-5%) and aged materials resulted in small changes in the fatigue strength as compared with the base materia15~6~8,9,11.At higher degrees of prestrain (up to 30%) it has been found that the strain amplitude at fatigue lives of about lo4 cycles can increase by up to 20% as compared with materials not prestrained l*. The stress amplitude may increase by as much as 50% under the same conditions. In the latter work it was noticed that mean stresses occurred during fatigue testing of prestrained sheet material. It was also argued that these mean stresses could influence the fatigue properties and, in particular, the question was raised as to how variable-amplitude loading as experienced in most real-life components would affect the persistence of the mean stresses and 0142-1123/94/070503-07 @ 1994 Butterworth-Heiuemann

Ltd

what the effect would be on the fatigue strength’*. The present paper picks up this problem by means of an experimental investigation of variable-amplitude strain-controlled fatigue testing of a cold-rolled dualphase sheet steel. Four different repetitive variableamplitude strain cycle sequences were applied to smooth specimens of the material in the as-received condition, after 10% prestrain and in the prestrained and aged condition. The investigation was concentrated at fatigue lives at about 100000 cycles. MATERIAL AND FATIGUE PROCEDURE

TESTING

Material and specimen preparation A cold-rolled dual-phase sheet steel with a gauge thickness of 1.2 mm was studied. The chemical composition of the material is given in Table 1. The microstructure was ferritic-martensitic with 2% martensite and a ferrite grain size of 8 pm as determined by the intercept method. The ultimate tensile strength of the as-received material was RM = 444 MPa, the 0.2% proof stress RPo.2= 266 MPa and the elongation to fracture 6 = 0.44.

Table 1

Chemical composition of the tested dual-phase sheet steel (wt%) C

Si

0.069 0.01

Mn

P

S

N

Cr

0.19

0.08

0.012 0.003 0.03

Ni

Cu

0.010 0.03

Fatigue, 1994, Vol 16, October

Al 0.044

503

Variab/e-amp/itude fatigue of a dual-phase sheet stee/: A. Gustavsson and A. Me/ander Prestraining of the material was conducted before milling the test specimens. Uniaxial tensile prestrain was carried out on macro specimens with a gauge section of 350 mm x 115 mm and with the rolling direction along the specimen axis. From this section, five specimens were milled parallel to the axis of prestrain. The effective strain achieved was 10%. The ultimate tensile strength of the prestrained material w a s R M -- 467 MPa and the 0.2% proof stress Rpo.2 = 442 MPa. Ageing, corresponding to the baking operation during paint curing in the automotive industry, was carried out on the prestrained samples at 190 °C for 15 min after the specimens had been milled after prestraining. Ageing resulted in an ultimate tensile strength of RM = 492 MPa and a 0.2% proof stress of Reo2 = 467 MPa. All specimens were stored in a refrigerator ( - 2 0 °C) to prevent natural ageing before testing.

Fatigue testing The fatigue test specimens used display a 6 mm long by 3.7 mm wide test section of the sheet with the original rolled surface left intact 5,6'1m2. The fully reversed strain levels were controlled by mounting an extensometer over the test section as seen in Figure 1. The distance between the extensometer edges was 6 mm and the range was +--4% strain. The tests were carried out at a strain rate of 0.02 s -1. The fatigue life was defined as the number of strain cycles to 25% load drop as compared with the load obtained at half the fatigue life where conditions are stable. The four variable-amplitude strain sequences applied in addition to constant-amplitude loading are displayed in Figure 2 together with their labels, as used throughout this paper. Each strain sequence consisted of blocks of 10 cycles, which were continuously repeated. Within each block the first cycle was an overstrain cycle followed by nine baseline cycles. The strain amplitude of the baseline cycles was ~B,a = 0.0016 and in the overstrain cycles the maximum and minimum strain was 50% higher, i.e. 0.0024. In spectrum P10 of Figure 2 the strain reversals recorded during testing have been hatched, which indicates that the overstrain reversal and three baseline reversals were recorded within each block. For these recordings, both stresses and strains were stored for the entire loop. A similar acquisition scheme was used for the other strain sequences in this investigation.

PIO NIO PNIO

- i ~ - EOS,mm¢

........ £B,mJn 80$,mia Figure 2 Utilized strain sequences and labels. Hatched areas indicate recorded strain reversals

10 ¢

•

,

. . . . . .

i

.

.

.

.

.

.

.

.

i

. . . . . . . .

i

. . . . . . .

.. 10 .3

10 .4 10 3

105

10 4

108

107

Number of cycles to failure, N,

Figure 3 Strain-life curves for fully reversed and constant-straincontrolled testing of as-received material (solid curves) and prestrained material (dashed curves) F A T I G U E TEST RESULTS

Fully reversed constant-strain-amplitude testing Figure 3 displays the strain-life curves for the asreceived material (labelled Ref.mtrl) and the 10% prestrained material. For clarity, fatigue life curves have been fitted to experimental data 13. The analytical form of these curves is ea = ~- (Nf)b + e;(N~)C

(i)

where it is assumed that the total strain amplitude ~. can be partitioned into an elastic part ~¢~,. (the first term) and a plastic part %1,~ (the second term). The parameters in Equation (1) were found by linear regression of these two parts to the experimental data and are displayed in Table 2.

llOmm R12

i Table 2 Parameters of Equation (1) as obtained by regression to experimental data together with tensile data

6 ram.

Rollingdirection

L15.0mm

RM

I

!

Rvo.2

~r'f

Pretreatment

(MPa) (MPa) (MPa)

Reference 10% prestrain

444 467

b

gf

c

Extensometer Figure 1 Sketch of the application of the extensometer over the 6 mm test section. The extensometer edges are fixed to the specimen by rubber bands around the specimen

504

Fatigue, 1994, Vol 16, O c t o b e r

266 442

390 798

-0.0432 0.0489 -0.369 -0.0956 1.585 -0.704

Variable-amplitude fatigue of a dual-phase sheet steel: A. Gustavsson and A. Melander As seen in Figure 3, the strain-life curves of the two material states intersect at a fatigue life of about N~ ~ 60000 cycles. Above this point the reference material is superior to the prestrained material and below the reverse holds true. During constant-amplitude testing of the prestrained material a mean stress was observed. Figure 4 displays this observation in terms of the stress ratio R~ = trm~,/ (rm~x versus the number of cycles, N. The square symbols indicate the behaviour of the material tested in the as-received condition, and it can be seen that the stress ratio remains virtually equal to - 1 throughout the test: that is, the mean stress is zero. In contrast, testing at the same strain amplitude (E~ -- 0.0016) of the prestrained material produced a considerable tensile mean stress, which decreased slightly during testing (triangles in Figure 4). At a stage close to rupture the stress ratio equalled -0.75, which corresponds to a mean stress of about 30 MPa for the prestrained material. It is interesting to note in this case that the stress amplitude was observed to stabilize, although the mean stress did not. However, when testing the prestrained material at a higher strain amplitude, ~ -- 0.0024, the mean stress as obtained initially during testing almost vanished until half the fatigue life was reached (inverted triangles in Figure

4). Variable-amplitude testing An overview of the fatigue lives for the different pretreatments (as-received, 10% prestrain, and 10% prestrain plus ageing) and the different repetitive strain amplitude sequences is given in Table 3. For each combination of pretreatment and strain amplitude sequence, six specimens were tested until the condition of failure was reached at an applied baseline strain amplitude of 0.0016. Table 3 also shows the recorded stress amplitudes (ra and stress ratios R,, as obtained at about half the fatigue life for the overstrain cycles (OS) and the baseline cycles (BS). Table 4 compares the different fatigue lives of Table 3 in a cross-tabular way. The test conditions given in the left column are the as-received material under constant-amplitude strain ( A R CA), the material prestrained by 10% a n d tested under constant-amplitude strain (10% CA), and the as-received material

0

........

,

........

,

........

,

........

,

........

-0.5 v

v

tl V v

V

~

-1 o

-1.5

Rel. mtrl.~-0.0016 10% prestrain, ~==0.0016

v

v

10% prestrain, ~ - 0 . 0 0 2 4 °

~0'

. . . . . . . .

I

102

. . . . . . . .

I

103

,

i

i

.....

J

i

104

|

i

illlll

i

10 s

i

.....

10 e

Number of cycles, N Figure 4 The development of stress ratio during fatigue testing at fully reversed constant-strain-amplitude loading

under spectrum P10 ( A R P10). The percentages given in the table indicate the change relative to these three conditions when the conditions in the top row are applied. For instance, we can notice that the reduction in mean fatigue life of the prestrained material is 13% compared with the as-received material when testing at a strain amplitude of 0.0016. Under strain amplitude sequence P10 the reduction in life of the as-received material was 36% compared with the conditions under constant-amplitude loading. The same comparison for the prestrained material indicated a 17% decrease of the fatigue life. This means that the fatigue loading of sequence P10 yielded 12% higher fatigue life for the prestrained material compared with the as-received material. Hence the ranking of the two pretreatment states has changed order compared with testing under constant-strainamplitude loading. Furthermore, adding ageing to prestraining only increased the fatigue life by 3% under sequence P10. For the material subjected to 10% prestrain, four different strain amplitude sequences were applied at a baseline strain amplitude of 0.0016. Compared with constant-strain-amplitude testing a negative strain reversal applied every tenth cycle (sequence N10) reduced the mean fatigue life by as much as 34%, which was twice the reduction following positive strain reversals in sequence P10 as discussed above. Application of sequence PN10 produced the same mean fatigue life reduction as spectrum N10. However, when the order in the overstrain cycle in PN10 was reversed from positive-to-negative strain reversal to negative-to-positive strain reversal (sequence NP10), a further reduction of the mean fatigue life of 14% was noted. In other words, application of spectrum NP10 reduces the mean fatigue life by 44% compared with constant-strain-amplitude testing at this particular level of applied strain amplitude. It is also interesting to look into the cyclic stress-strain behaviour as observed during testing with variable-amplitude sequences. In particular, for the prestrained material it is of interest to investigate the behaviour of the mean stress observed at constantstrain-amplitude testing. Figure 5 shows the development of the stress amplitude with the number of cycles when testing the prestrained material under sequences PN10 and NP10. For these sequences the stable stress amplitudes in the overstrain cycles were about equal: about 260 MPa (cf. Table 3), after initial softening. This was 3% higher than obtained at constant-strainamplitude testing at the same level. However, for the baseline cycles both sequences showed a lower stress amplitude than the constant-strain-amplitude testing did. The reduction was about 4%. As regards the variation of the stress ratio R,, with the number of cycles N, for sequences PN10 and NP10, Figure 6 shows that this stress ratio for the overstrain cycles falls above the stress ratio as obtained at constantamplitude straining (about 4%) whereas for the baseline cycles it falls below the constant strain curve. However, it is difficult to separate the baseline data and the overstrain data in Figure 6 as their stress ratios are similar (cf. Table 3). In the case of sequence P10 (Figure 7), the stress ratio of the overstrain cycles (-0.79) is close to that obtained at constant-amplitude testing at ea = 0.0016, Fatigue, 1994, Vol 16, October

505

Variable-amplitude fatigue of a dual-phase sheet steel: A. Gustavsson and A. Melander Table 3 Summary of recorded quantities as extracted from hysteresis loops at about half the fatigue life. The mean fatigue lives were in all cases computed from six tests and defined at 25% load drop from the load recorded at about half the fatigue life

Pretreatment

Spectrum

Mean fatigue life, Type of cycle in N7 x 103 spectrum

e~ (%)

R,

cr~ (MPa)

R~

As-received

CA P10

160 103

0.16 0.20 0.16

- 1.00 -0.67 - 1.00

205 230 216

-0.99 -0.93 - 1.02

CA CA P10

36 139 115

N10

91

PN10

91

NP10

78

0.24 0.16 0.20 0.16 0.20 0.16 0.24 0.16 0.24 0.16

- 1.00 1.00 -0.67 - 1.00 -1.5 -1.00 - 1.00 - 1.00 - 1.00 -1.00

253 231 246 222 252 223 260 216 264 222

-0.90 -0.75 -0.79 -0.93 -0.90 -0.72 -0.93 -0.87 -0.93 -0.91

10% prestrain

-

-

OS B -

-

-

-

OS B OS B OS B OS B

Table 4 Selected cross-correlations (%) of mean fatigue lives under various variable-amplitude loading sequences

0

. . . . . . . .

i

. . . . . . . .

i

. . . . . . . .

i

. . . . . . . .

i

AR CA 10% CA AR P10

10% CA

AR P10

10% P10

10% N10

-13 --

-36 --

. -34

-

-

. . -17 12

-

-

-

10% PN10

10% NP10

-34

-44

-

-

-

-

~ ea=0.16%

-0.5

.

.~ ~ co

-1

I

, Q

~,

PN10

v

NP10

--

........ ,

........ ,

........ ,

........ ,

Overstrain cycles \

300

10%

-2

........

i

Gonst. = ......

amp= i

........

102

101

i

........

.......

i

104

103

prestrain

i

10 s

108

Number of cycles, N

X x x

Figure 6 Stress ratio R . = (rmi./a~. ~ as function of the number of cycles. Sequences PN10 and NP10 were applied to the prestrained material. Observe that the baseline and overstrain cycles are nested in this case and therefore not clearly separable.

tl.

200

z

-

-1.5

400

. . . . . . . .

prestrain

10%

Baseline cycles ~ z~ PN10 v

NP10

. . . . . . . .

i

. . . . . . . .

i

. . . . . . . .

|

. . . . . . . .

........

100101

i

102

........

i

103

.

.

.

.

.

.

.

.

i

.......

104

,~1

105

. . . . . . .

......

-0.5

I06

o . . . . .

Figure 5 Cyclic stress amplitude as function of the number of cycles. Sequences PN10 and NP10 were applied to the prestrained material

w h e r e a s t h e stress r a t i o f o r t h e b a s e l i n e cycles is l o w e r ( - 0 . 9 3 ) . F h e r e v e r s e s e e m s to b e t r u e , h o w e v e r , f o r s p e c t r u m N 1 0 (Figure 8). I n this c a s e t h e b a s e l i n e stress r a t i o a n d c o n s t a n t - a m p l i t u d e - t e s t i n g stress r a t i o were practically equal: -0.72 and -0.75, respectively. F o r t h e o v e r s t r a i n c y c l e t h e stress r a t i o at h a l f f a t i g u e life was - 0 . 9 6 . Figure 9 d i s p l a y s a s e l e c t i o n o f s t r e s s - s t r a i n l o o p s o b t a i n e d at d i f f e r e n t n u m b e r s o f cycles f o r b o t h b a s e l i n e cycles ( t o p ) a n d o v e r s t r a i n cycles ( b o t t o m ) o f p r e s t r a i n e d s a m p l e s . It c a n b e s e e n t h a t t h e g r a d u a l s o f t e n i n g d u r i n g t h e f a t i g u e life, f o r b o t h o v e r s t r a i n cycles a n d b a s e l i n e cycles, was d u e to r e l a x a t i o n o f t h e m a x i m u m stress w h i l e t h e m i n i m u m stress r e m a i n e d v i r t u a l l y c o n s t a n t . T h e s a m e b e h a v i o u r was also f o u n d

F a t i g u e , 1994, V o l 16, O c t o b e r

o

~

~_

~_~_ g~

_~ o

~ ~

~

5

Baselinecycles ~

Number of cycles, N

506

i

10% prestrain

Const. amp.

O3

Overstrain cycles

-

:

[]

.,

~

-1.5 o

P10

-=

Const.

. . . . . . . .

-2

01

ampL

i

102

. . . . . . . .

i

. . . . . . . .

103

t

. . . . . . . .

104

t

10 s

. . . . . . .

108

Number of cycles, N Figure 7 Stress ratio R~, vs the number of fatigue cycles. Sequence P10 and prestrained material f o r t h e s y m m e t r i c a l s e q u e n c e s P N 1 0 a n d N P 1 0 as w e l l as f o r c o n s t a n t - a m p l i t u d e l o a d i n g a p p l i e d to t h e prestrained material. FATIGUE

LIFE PREDICTIONS

Four different methods were used to predict the fatigue life f o r t h e o v e r l o a d s e q u e n c e s b y u s i n g t h e f a t i g u e

Variable-amplitude fatigue of a dual-phase sheet steel: A. Gustavsson and A. Melander

. . . . . . . .

i

........

|

. . . . . . . .

i

. . . . . . . .

!

prestrain

10%

-0.5

%

~

0

•

•

•

•

~

Baseline

was applied to calculate the damage. This method utilizes the product of strain amplitude Caand maximum stress Crmax to correct for the mean stress effect. In terms of the parameters of Equation (1) this method reads

. . . . . . . .

cycles

oo

6

Overstrain

cycles ~

o

o o

-1

u~ o~ ¢D

r 2

oo~oo

~aO'max-

-1.5

o --

N10 Const.

01

ampl.

10s

10 2

104

10s

06

Number of cycles, N Figure 8 Stressratio R~ vs the number of fatigue cycles. Sequence

N10 and prestrained material

500

PIO 10% PRESTRAIN

NIO 10% PRESTRAIN Baseline cycles

Baseline cycles

¢3

b

-500 500

.Cycles 58 12 8O8 111 208

.cycles 58

6t~

91 208

/ /

Oversfrnin cycles

Overstrain cycles

t:l

Q_

b

3.005

E

0.005-0.005

Cycles 51 6 1.01 91 201

E

0~05

life data from constant-amplitude strain tests (Figure 3). In all cases the traditional hypothesis of linear damage accumulation (Palmgren-Miner rule) was used 14 to calculate the damage of each strain excursion. When the sum of damage equalled unity the number of cycles for fatigue failure was assumed to be reached. In the first instance, Equation (1) was used without any further corrections than applying the strain amplitudes of the overstrain and baseline cycles respectively in order to calculate the damage. Next, the correction for the mean stress in Equation (1) due to Morrow 15 was applied, which reads Ea-

E

~"fJ + Ef(Nf)c

~l--2b

''f

+

eft crf, N f b + c

(3)

where the experimentally determined maximum stresses at half fatigue life were inserted together with the nominally applied strain amplitude. In the life predictions of the prestrained material according to Equation (1), the material parameters were correctly taken from the constant-amplitude loading of the prestrained material. However, when coming to predictions according to Equations (2) and (3), where we account for the mean stress, it would be erroneous to apply the coefficients of these equations directly for the prestrained material. The reason, albeit an empirical one, is that during constant-amplitude straining of the prestrained material the observed mean stress did not relax, and therefore the strain-life curve could be biased because of a mean stress effect. Instead, we also used for the prestrained material the coefficients of the as-received materials when performing the life estimates according to Equations (2) and (3), thus accounting for the mean stress effect. Finally, the mean stress correction of Topper and Sander 17 was used. They put strain-life curves together for different levels of prestrain by defining an 'equivalent completely reversed strain amplitude' ~*, given by ,

Figure 9 Selected stress-strain loops for sequences P10 and N10 applied to the prestrained material. Note the relaxation of the maximum stress

I t __ O'm ( ~ J ~b

E

t~m

(4)

Ea = ~a -{- E -

.Cycles 51 12801 111201

-500

(O'f )

where a is a fitting parameter. In the present work a was found by comparing the constant-strain-amplitude data at ~* = Ca = 0.0016 for the reference material with constant-strain-amplitude data for the prestrained material at the same fatigue life. A value of a = 0.97 was found to correlate the data. Table 5 and Figure 10 summarize the life predictions described above. Fatigue life predictions according to Equation (1) yield an overestimate for the reference material under strain sequence P10 and an underestimate of between 24 and 40% for the various strain sequences for the prestrained samples. The predictions according to Equation (1) can be seen to be outside the scatterbands of the experimental results in all cases

(Figure 10). Allowing for the mean stress in Morrow's equation (Equation (2)), the predictability is unchanged for the Table 5

Predictions of fatigue lives according to Equations (1)-(4) divided by the experimentally determined mean life. In all cases the hypothesis of linear damage accumulation has been used

Method

(2)

lnsertirig the applied strain amplitudes together with the measured mean stresses at half the fatigue life in this equation yielded the damage in this case. In the third case the method due to Smith et al. 16

Equation Equation Equation Equation

(1) (2) (3) (4)

Reference material P10

10% prestrained material P10

1.33 1.32 1.40 1.23

0.60 0.76 1.08 1 . 1 8 0.91 0.90 0.89 0.85

N10

PN10

NP10

Mean

0.61 0.82 0.85 0.96

0.71 0.97 0.96 1.01

0.80 1.07 1.00 0.99

Fatigue, 1994, Vol 16, October

507

Variable-amplitude fatigue of a dual-phase sheet steel: A. Gustavsson and A. Melander 200 10% prestrain

Ref.rntrl.

% 10P

z- 15o

Q

10N

10PN

10NP

10P

100

o

"6 e~

E

50

Z

[]

Exp. [ ] s," [ ] s= ~

Ii

Morroweq, ~

Smith-Watson-Topper

Figure 10 Comparisonof experimentallydeterminedfatigue lives for different strain sequences and different material pretreatment with the various life-predictionmethods discussed

reference material. This is to be expected, as the mean stress during strain sequence P10 was small for the reference material (Table 3). In the case of the prestrained material the constant-amplitude data of the reference material were used, and Morrow's mean stress correction resulted in good (within 18%) predictions for the fatigue life. Utilizing the constantamplitude data of the prestrained material for the same method resulted in worse estimates of the fatigue life: between 32 and 46% underestimates. The Smith et al. relation with correction for mean stress (Equation (3)), produced results similar to Morrow's method. Once again, utilizing constantamplitude data for the prestrained material instead of the reference material resulted in underestimates of between 8 and 28%. Both life predictions based on mean stress corrections according to Equations (2) and (3) described the experimental fatigue lives qualitatively, with the longest life for strain sequence P10, the shortest for NP10, and the other following in between (Figure 10). Also, the method of Topper and Sandor (Equation (4)), produced good correlation with experimental data. The prediction fell within 11% for the prestrained material and in all tested cases the predictions fell virtually within the scatterbands of the experimental data. DISCUSSION At strain amplitudes producing fatigue lives longer than about 100000 cycles, the elastic strain amplitude dominates the total strain amplitude and we could therefore expect an increasing fatigue strength with increasing monotonic strength TM. However, at an applied constant strain amplitude of 0.16% it was found in the present work that the effect of 10% prestrain, which increases the ultimate tensile strength by 5%, reduces the fatigue life slightly as compared with the as-received material. Similar results were found for material subjected to various types and degrees of prestrain, resulting in up to 30% increase 508

Fatigue, 1994, Vol 16, October

in the monotonic strength but a very small effect on the fatigue life at lives in the order of 106 cycles 12. A plausible reason for this effect could be the appearance of tensile mean stresses, which arise in the prestrained material during fatigue testing in this life regime, and are known to be detrimental to the fatigue life. However, the present results for constant-strain-amplitude loading of 0.24% of the prestrained material revealed a virtually complete relaxation of the mean stress. In this case we found an increase of the fatigue life by a factor of 2.6 as compared with the as-received material, which could be attributed to the strengthening effect of the prestrained material being effective during fatigue cycling in the absence of a mean stress. With this background it can be suspected that the strain-life curve for the prestrained material in Figure 3 is somewhat biased at longer lives owing to the mean stress, and this is the rationale behind using the curve for the as-received material when making life predictions for the overload sequences in combination with mean stress corrections (Equations (2) and (3)). Also, the life prediction carried out above for the prestrained material supports this idea. Using constantstrain-amplitude data for the prestrained material in the predictions yielded underestimates of the fatigue lives. These conservative predictions were improved by utilizing constant-amplitude data for the reference material, which were believed to be closer to constantamplitude data for the prestrained material with zero mean stress, as can be inferred from the discussion above. It is also interesting to notice in this context that the life prediction due to Morrow (Equation (2)) for the prestrained material subjected to straining sequence N10 resulted in an overestimate of 18%. In sequence N10, the absence of tensile overstrains resulted in non-relaxing tensile mean stresses; in the other sequences with tensile overstrains the mean stress virtually vanished. Consequently, it can be concluded that Morrow's method does not fully account for the presence of the mean stress in the baseline cycles, whereas the method according to Smith et al. (Equation (3)) handles this better (Table 5). This is in agreement with the previously reported tendency of the Smith et al. method to overpredict fatigue lives ~9. CONCLUSIONS Both constant-amplitude and variable-amplitude fatigue testing under strain control has been carried out for a cold-rolled dual-phase sheet steel. The material was tested as-received, after 10% prestrain and after 10% prestrain plus ageing. Different fatigue life prediction methods, which allowed for the mean stress effect, were applied to predict the fatigue lives for variable-amplitude sequences. The following conclusions can be drawn. 1. At fully reversed constant-strain-amplitude loading at a strain amplitude of 0.16%, a reduction of 13% of the fatigue life for the prestrained material as compared with the as-received material was noticed. The reduction in fatigue life could be attributed to a non-relaxing mean stress of 33 MPa at half the fatigue life in the prestrained material. At a strain amplitude of 0.24% the mean stress in the

Variable-amplitude fatigue of a dual-phase sheet steel: A. Gustavsson and A. Melander prestrained material was found to relax and the resulting fatigue life exceeded that of the as-received material by a factor of 2.6. 2. Tensile overstrains of 50% seem to be necessary for relaxation of the mean stress in baseline cycles in the variable-amplitude sequences applied to the prestrained material. Only for compressive overstrains did the mean stress remain. 3. For the strain sequence with a tensile overstrain only (P10), the influence of ageing was found to be negligible. 4. Life prediction taking account of the mean stress was found to be satisfactory although, for the asreceived material, overpredictions by 30% were noted and, in general, small underpredictions were noted for the prestrained material. In the life predictions for the prestrained material the utilization of strain-life data for the as-received material was found to be best and was explained in terms of a bias of the strain-life curve for the prestrained material following from the non-relaxing mean stresses. In particular, the life-prediction models due to Smith et al. 16 and Topper and Sandor 17 were successful.

9 10

11 12 13 14 15 16 17 18 19

Shinozaki,M., Kato, T., Irie, T. and Takahashi, I. 'Fatigue of automotive high strength steel sheets and their welded joints', SAE Technical Paper 830052, 1983 Bergengren,Y., Gustavsson, A.I. and Melander, A. 'The effect of ageing and prestraining at different load ratios on the fatigue properties of a high strength dual phase sheet steel', Swedish Institute for Metals Research, Report IM2684, 1990 Fredriksson,K., Melander, A. and Hedman, M. Int. J. Fatigue 1988, 10, 139 Gustavsson,A. and Melander, A. 'Fatigue of a largely prestrained dual-phase sheet steel', 1993 (to be published) Morrow, J. 'Cyclic Plastic Strain Energy and Fatigue of Metals', ASTM STP 378, American Society for Testing and Materials, 1964, pp. 45-87 Fuchs,H.O. and Stephens, R.I. 'Metal Fatigue in Engineering', John Wiley and Sons, 1980 Morrow,J.D. Fatigue Design Handbook, Section 3.2, Society of Automotive Engineers, 1968 Smith, K.N., Watson, P. and Topper, T.H.J. Materials 1970, JMSAL 5, 767 Topper,T.H. and Sandor, B.I. 'Effects of Mean Stress and Prestrain on Fatigue-Damage Summation', ASTM STP 462, American Societyfor Testing and Materials, 1970,pp. 93-104 Landgraf,R.W. In 'Achievement of Fatigue Resistance in Metals and Alloys', ASTM STP 467, American Society for Testing and Materials, 1970, pp. 3-36 Nowack,H., Hanschmann, D., Foth, J. Liitjering, G. and Jacoby, G. 'Prediction Capability and Improvements of the Numerical Notch Analysis for Fatigue Loaded Aircraft and Automotive Component', ASTM STP 770, American Society for Testing and Materials, 1982, pp. 269-295

ACKNOWLEDGEMENTS This work was financed by the National Swedish Board for Technical Development ( N U T E K ) under contract no. 89-02059P and was part of the E U R E K A project no. 137, 'New steels with high static, dynamic and fatigue strength for automotive applications'. The material was delivered by SSAB (Swedish Steel Corporation).

NOMENCLATURE b, c

E RM

REFERENCES 1 2 3

4 5

6 7 8

Davies,R.G. In 'Fundamentals of Dual-Phase Steels' (Ed. R.A. Kot and B.L. Bramfit), AIME, New York, 1981, pp. 265-279 Tanaka,R., Nishida, M., Hashiguchi, K. and Kato, T. In 'Fundamentals of Dual-Phase Steels' (Ed. R.A. Kot and B.L. Bramfit), AIME, New York, 1981, pp. 221-241 Osawa, K., Shimomura, T., Kinoshita, M., Matsudo, K. and Iwase, K. 'Development of high strength cold rolled steel sheets for automotive use by continuous annealing', SAE Technical Paper No. 830359, 1983, pp. 109-121 Wilson,D.V. Scand. J. Met. 1984, 13, 359 Fredriksson,K., and Melander, A. 'Influenceof Prestraining and Aging on the Fatigue Properties of a Dual Phase Sheet Steel', Proc. Int. Conf. Fracture (ICF7), Houston, USA, K. Salama, K, Ravi-Chandar, D.M.R. Taplin and P. Rama Rao (eds), Pergamon Press, Voi. 4, 1989, pp. 2491-2499 Fredriksson, K., Melander, A. and Hedman, M. Scand. J. Met. 1989, 18, 155 Sperle,J.-O. Int. J. Fatigue 1985, 7, 79 Nagae,M., Katoh, A., Kagawa, H., Kurihara, M., Iwasaki, T. and Inagahi, H. J. Iron Steel Inst. 1982, 9, 304

Rpo.2 R e = ~min/~max R t r = O'min/Ormax

ea

~*a EB,a fiB,max ~ ~B,min

~, o,~ EOS,max, E'OS,min o-~ orm O'ma x

Fatigue strength and ductility exponents Young's modulus Number of cycles to failure Ultimate tensile strength 0.2% proof stress Strain ratio Stress ratio Fitting parameter for e* Elongation Strain amplitude Equivalent completely reversed strain amplitude Strain amplitude of baseline cycles Maximum and minimum strain level of baseline cycles Fatigue strength and ductility coefficients Maximum and minimum strain level of overstrain cycles Stress amplitude Mean stress Maximum stress

Fatigue, 1994, Vol 16, October 509