Fatigue crack propagation mechanisms in a thermally aged duplex stainless steel

Materials Science and Engineering, A 183 ( 1994) 91-101

91

Fatigue crack propagation mechanisms in a thermally aged duplex stainless steel T. J. M a r r o w

Department of Materials, University of Oxford, Parks Road, Oxford OX1 3PH (UK) J. E . K i n g

Department of Materials Science and Metallurgy, University of Cambridge, Pembroke Street, Cambridge, CB2 3QZ (UK) (Received August 3, 1993)

Abstract Zeron 100 duplex stainless steel is susceptible to embrittlement following ageing at temperatures between 350 °C and 450 °C. The embrittlement is associated with cleavage of the age-hardened ferrite phase, initiated by deformation twinning. This can result in order of magnitude increases in the fatigue crack propagation rate. The effects of ageing on the mechanisms of fatigue crack propagation in Zero 100 are investigated, and a quantitative model is developed, accounting for the effects of hardness, temperature, stress level and microstructure on the fatigue crack growth rate.

1. Introduction

High alloy ferritic stainless steels, and duplex stainless steels containing ferrite, are susceptible to age hardening and embrittlement when exposed to temperatures between 250°C and 1000°C [1-10]. The embrittlement can result either simply from an increase in strength or from the development of a number of deleterious brittle phases as the ferrite decomposes [2]. The degree of embrittlement depends on the nature and the extent of the phases developed, and hence on the temperature and time of exposure. Embrittlement occurs within two temperature regimes: via nucleation and growth of phases such as carbides and Laves phases between around 600 °C and 1000 °C, and via decomposition to iron- and chromium-rich regions below about 500 °C. The higher temperature embrittlement can be a problem in large castings and weldments, and may be avoided by rapid cooling through the critical regime. The lower temperature form, classically termed "475 °C embrittlement" is, however, of considerable importance to the potential long-term operation (20-30 years) of duplex stainless steel in applications experiencing temperatures between 250 °C and 325 °C. Such applications include reactor cooling water systems [9] and linepipe in deep oil and gas fields [11]. Pre-heating of large 0921-5093/94/$7.00 SSDI 0921-5093(93)09443-M

complex weldments, which may be subject to temperatures of 400 °C for several days, may also result in agehardening. 475 °C embrittlement occurs in the absence of any optically resolvable change in microstructure [6]. Embrittlement develops most rapidly at around 475 °C, and may be removed by a resolution heat treatment between 500 °C and 600 °C [5, 7]. The decomposition responsible for 475 °C embrittlement [12] may occur by diffusion-controlled spinodal decomposition [6, 9, 13] or nucleation and growth of precipitates [3, 4, 6, 13], depending on ferrite composition, temperature and time [2-6, 13-18]. High alloy duplex stainless steels, such as Zeron 100, decompose via spinodal decomposition below 450 °C [19]. Decomposition of duplex and ferritic stainless steels, by either mechanism, has been reported to increase strength and hardness, with a commensurate decrease in ductility and toughness [1-10, 13, 20]. The magnitude of the effect depends on alloy composition, temperature and time of exposure, and on the mechanism of decomposition via a direct effect of the decomposition products on dislocation mobility [2, 6, 15]. Embrittlement results from the effect of increased flow stress on potential fracture mechanisms. Thus the transition from ductile to brittle modes of fracture is very sensitive to ageing, and is the most frequently © 1994 - Elsevier Sequoia. All rights reserved

92

T.J. Marrow,J. E. King / Fatiguecrackpropagation mechanisms

measured parameter [2, 9, 10]. However, until recently [21], there has been little systematic application of fracture mechanisms to 475 °C embrittlement. Determining the more rapid effects on the mechanical properties of thermal decomposition at higher temperatures (350-450 °C), allows the prediction of properties developed over longer periods at lower temperatures given an activation energy for the process, provided that the embrittling mechanism is unchanged over the temperature range studied [9, 10]. Activation energies reported in the literature for spinodal decomposition are generally close to that for Cr diffusion in iron-based alloys ( - 2 3 0 kJ mo1-1) [2, 5, 9, 10, 12], though significantly lower values ( - 150 kJ mol- l) have been reported [2, 9]. These low values may arise from changes in the fracture mode and decomposition mode with ageing. For example, the onset of austenite cleavage in low alloy duplex stainless steel [9], or a change from spinodal decomposition to nucleation and growth, the latter having a stronger embrittling effect [2]. Applying fracture mechanics to the influence of ageing and identifying the controlling factors might enable embrittlement to be characterized as a function of ageing time and temperature. Such an approach would assist in the prediction of end-of-life resistance to fracture and fatigue. This paper considers the effects of age-hardening on the fracture and fatigue resistance of Zeron 100 duplex stainless steel. A semi-empirical model is presented, identifying a critical microstructure-controlled parameter which may be used to predict fatigue crack propagation rates.

2. Experimental details and results

2.1. Effect of ageing in mechanical properties Zeron 100 duplex stainless steel (supplied by Weir Materials Services Ltd., Park Works, Manchester, M 10 6BA, UK) was aged as 12.5 mm plate (Fig. 1) at A E A Technology, Harwell* between 350 °C and 450 °C for 100, 500, 1000 and 5000 h. The plate was air cooled on removal from the furnace. The Zeron 100 alloy composition is given in Table 1. Typical tensile mechanical properties, including hardness, of asreceived and aged Zeron 100 are given in Table 2. Full data and test procedures are published in detail in ref. 22. The tensile specimens were oriented parallel to the L axis, and impact specimens were oriented with the crack plane normal to the L axis, propagating in the T direction (L-T orientation)(Fig. 1). *AEA Technology, Harwell, Fracture and Materials Evaluation Department (FAME), Didcot, Oxfordshire, OX11 0RA, UK.

Ageing increased the strength and hardness via agehardening of the ferrite phase, with no significant effect on the austenite, as shown by the microhardness data (Table 2). Ageing also decreased the tensile elongation. Frequent audible clicks during tensile tests above approximately 30% of the yield stress were detected in the materials aged for periods greater than 100 h. The frequency of clicking was greatest around yield. Standard Charpy "V" notch impact tests on Zeron 100 aged at 350 °C, 400 °C and 450 °C were performed at - 4 4 °C. In unaged material, the "upper shelf" of the impact transition curve extended down to approximately - 4 4 °C [22], at which temperature the transition region commenced. Tests at this temperature were therefore particularly sensitive to embrittlement. Impact energy at - 4 4 °C showed a smooth decrease with increasing hardness, independent of ageing temperature (Fig. 2). Transgranular cleavage of the ferrite matrix was observed on the fracture surfaces of aged material from impact and tensile specimens. The extent of cleavage increased with increasing hardness. In etched sections of tensile specimens deformation twinning and associated microcracking were seen (Fig. 3). The density of twinning increased with increasing plastic strain and hardness.

2.2. The effect of ageing on fatigue crack propagation 2.2.1. The effect of ageing time Constant load amplitude fatigue crack growth tests were performed at 20 Hz at a load ratio, R Pmin/Pmax, of 0.5 in air at room temperature (22 °C) using materials aged at 400 °C for 100, 500, 1000 and 5000 h. L-T orientation specimens were used. The results are shown in Fig. 4(a), compared with data for the as-received material. At low AK (AK=stress intensity factor range), crack growth rates were close to those for the as-received material. Above some critical stress intensity factor range, A Kx, the crack growth rate was greater than in the as-received material. The degree of enhancement of growth rate increased with increasing ageing time, although the crack growth rates in material aged for 1000 h and 5000 h were similar. A K T tended to decrease with increasing hardness. Estimated values of A K v are given in Table 3. A K at specimen fracture decreased with increasing hardness, though again the values at 1000 h and 5000 h were similar. =

2.2.2. The effect of ageing on fatigue failure mode Scanning electron microscopy (SEM) showed that a fraction of the ferrite matrix failed by cleavage, identical in appearance to the cleavage failure observed in the tensile and impact specimens (Fig. 5(a)). The extent

T. J. Marrow, J. E. King / Fatiguecrack propagation mechanisms

93

TABLE 1. Zeron 100 composition (wt.%) Cr

Ni

Mo

Mn

Cu

Si

S

P

C

N

W

Fe

24.4

6.83

3.70

0.770

0.626

0.175

0.002

0.025

0.024

0.213

0.625

bal.

A series of fractographs was taken for each test at several AK values, each sampling an area of approximately 200/~m × 300/~m. The area fraction of ferrite cleavage facets (ferrite cleavage fraction) was measured using a SeeScan microcomputer-controlled image analyser. The mean ferrite cleavage fraction was determined as a function of AK for each ageing condition (Fig. 6(a)). There was a strong trend of increasing ferrite cleavage fraction with increasing ageing time up to 1000 h at 400 °C. 5000 h at 400 °C produced similar results to 1000 h. The maximum mean ferrite cleavage fraction was around 45%, close to the volume fraction of ferrite in the microstructure, which was determined by image analysis of the polished and etched microstructure.

\

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-L

1 0 0 ~tm -

2.2.3. The effect of R-ratio Fatigue crack growth tests were performed at 20 Hz in air at room temperature at an R-ratio of 0.1, on asreceived material and material aged from 5000 h at 400 °C. The results are shown in Fig. 4(b). The fatigue crack growth rate increased above the crack growth rate in the as-received material at a critical AKT, which was close to that observed at R--0.5 (approximately 16 MPa ml/2). Above around A K = 26 MPa m 1/2 the growth rate exponent decreased to a similar value to that in the as-received material. The ferrite cleavage fraction increased with increasing AK, independent of R-ratio, saturating at around 45% for A K > 2 8 MPa m '/2 (Fig. 6(b)).

Fig. 1. Zeron 100 microstructure, hot-rolled. The crack propagation plane (L) and crack propagation direction (T) were used in all fracture and fatigue tests.

of cleavage, i.e. the observed area fraction of cleaving ferrite grains, and the fracture surface roughness, increased with increasing AK, increasing ageing time and increasing crack growth rate. The remaining ferrite failed by ductile striated fatigue. Etch pits were produced on cleavage facets by electrolytic etching with 10% oxalic acid. These were found to be orthogonally sided and approximately square. The cleavage facets were rough, showing river lines, angular steps and cleavage tongues (Fig. 5(b)). In all conditions austenite failed by ductile striated fatigue, forming ligaments when by-passed by cleavage in the ferrite. Fatigue cracks initiated from the austenite/ferrite grain boundaries, growing towards the centre of the ligament, which then failed by ductile shear (Fig. 5(c)).

2.2.4. The effect of test temperature Tests were performed at temperatures of 153 °C and 305 °C with material aged for 1000 h at 400 °C at R = 0.5 Hz and 0.1 Hz. Increasing the test temperature increased fatigue crack growth rates by a factor of 5-6 at 153 °C and by 10-12 at 305 °C over those observed

TABLE 2. Mechanical properties of as-received and aged Zeron 100 Ageing time at 400 °C (h)

Yield stress (0.2% strain) (MPa)

Ultimate tensile stress (MPa)

Failure strain (%)

Vickers hardness (30 kg load)

Ferrite hardness (25 g load)

Austenite hardness (25 g load)

0 100 500 1000 5000

624+5 812 + 1 921 956 + 2 988 + 1

835+ 1 1039 + 2 1146 t 139 + 26 1203 + 1

46.1+5 43.5 + 0.4 36.7 37.2_+ 0.8 33.4_+ 1.6

255+5 320_+ 9 340 + 8 352 + 12 362 + 10

452+41 ---604 + 73

298 _+10

304_+ 13

T.J. Marrow, J. E. King

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20 30 40 50 Stress Intensity Range : AK (MPa~/m) Fig. 4. Fatigue crack propagation rates as a function of stress intensity factor range (AK) in Zeron 100 aged at 400 °C: (a) for up to 5000 h, tested at room temperature (22 °C), 153 °C and 305 °C at R = 0.5 (see legend), (b) for 5000 h, tested at room temperature at R = 0.1.

T. J. Marrow, J. E. King

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Fatigue crack propagation mechanisms

TABLE 3. The effect of ageing time at 400 °C on AKcrit, the critical stress intensity range for ferrite cleavage at room temperature, compared with observed and predicted values of AKT, the transition between regimes A and B Ageing time at 400 °C (h)

AKcrit (MPa m 1/2)

AK T (observed) (MPa m 1/2)

AK v (calculated) (MPa m 1/2)

100 500 1000 5000

14.5 12.8 10 10.45

2 0 t o 31 19 14 15

30 23 14.5 16

95

[1 100 hoursIat 400"C I: 22 "C l o 500 hours at 400"C : 22'C 60 -/~. 1000hours at 400'C : 22"C v 5000 hours at 400"C : 22"C • 1000hours at 400"C : 153"C • 1000hours at 400"C : 305"C

~40 O '~,

20

10 . . . .

50

1'5 . . . . 2'0 . . . . 2'5 . . . . 3'0' Stress Intensity Range : (MPa~/m)

• R=0.5 [] R--0.1 .... FerriteContentof Zeron 100

,_,40

g .g ~3o U 20

10 Fig. 5. Fatigue fracture surfaces of Zeron 100: (a) aged for 1000 h, tested at 22 °C ( A K = 18 MPa m 1/2, R =0.5), showing ferrite cleavage, (b) aged for 1000 h and tested at 22 °C (R = 0.5), showing cleavage tongues, steps and river lines on a ferrite cleavage facet, and (c) an austenite ligament, isolated within a ferrite cleavage facet, which failed by ductile fatigue from the ferrite/austenite grain boundary (aged 5000 h, tested at 22 °C, R = 0.5).

1'0 . . . . 2'0 . . . . 3'0 . . . . 4'0' Stress Intensity Range : AK (MPa~/m) Fig. 6. The variation of ferrite cleavage fraction (%) with stress intensity range (AK) for Zeron 100 aged at 400 °C: (a) for up to 5000 h, tested at room temperature, 153 °C and 305 °C at R = 0 . 5 and (b) for 5000 h, tested at room temperature and at R =0.1.

96

T.J. Marrow, J. E. King / Fatiguecrack propagation mechanisms

ferrite cleavage fraction increased with increasing AK (Fig. 6(a)), and at 305 °C was comparable with that at 22 °C at the same AK value, but was significantly higher than 153 °C.

2.3. Summary Zeron 100 duplex stainless steel is susceptible to 475 °C embrittlement. Ageing for up to 5000 h at 400 °C causes a significant increase in strength and hardness. This is associated with a reduction in tensile elongation and impact resistance as a consequence of transgranular cleavage of the ferrite matrix. Cleavage is accompanied by deformation twinning, which is favoured by increasing ferrite hardness and plastic strain. Fatigue crack growth rates in duplex stainless steels are increased by ageing at 400 °C for times between 100 h and 5000 h. The increase in crack growth rate is associated with cleavage of the ferrite matrix. The extent of cleavage is independent of Rratio and generally increases with increasing ageing time, appearing to saturate for ageing times over 1000 h. Increasing the test temperature to 153 °C and 305 °C causes a marked increase in fatigue crack growth rates. However, the extent of cleavage first decreases and then increases with increasing temperature. Fatigue crack growth rates at low AK in the absence of significant cleavage are independent of ageing condition. 3. Discussion

3.1. The effect of ageing on fracture behaviour The impact energy at - 4 4 °C decreases smoothly with increasing hardness for ageing between 350 °C and 450 °C (Fig. 2), indicating a strong correlation between the flow stress dependence of cleavage in the ferrite and the impact resistance. Ferritic Fe-Cr-Ni alloys (20-30 wt.% Cr, 1-10 wt.% Ni) can deform by combined slip and mechanical twinning at and above room temperature. Ageing increases the tendency for and frequency of twin formation [7, 8, 18]. Similar behaviour has been observed in the ferritic matrix of duplex stainless steels [20, 23, 24]. Deformation twinning can also be induced by ageing in high chromium ferritic alloys ( - 2 9 wt.% Cr) which contain no Ni and do not normally twin at room temperature [1]. Dislocation mobility is reduced and slip planarity increased by ageing-induced decomposition, favouring twinning. Aged and embrittled high alloy ferritic stainless steels fail by transgranular cleavage on {001} [7], also demonstrated here by the etch pit symmetry, which is similar in appearance to low temperature fracture. Although twinning is not necessary for embrittlement [6], twin interactions with grain boundaries [25] and with other twins [25, 26] can initiate cleavage. The

incidence of twinning, evidenced by clicking sounds in tensile tests and cleavage tongues on fracture surfaces (Fig. 6) is promoted by the age-hardening. In the absence of any sign of cleavage facet initiation at inclusions or precipitates, it seems probable that the cleavage is twin-initiated. 3.2. The effect of ageing on fatigue crack propagation The fatigue crack growth behaviour of aged Zeron 100 at room temperature can be divided into three regimes, shown schematically in Fig. 7. At low stress intensity ranges, i.e. AK less than AKT, crack growth rates are similar to those observed for non-aged material (regime A). Regime B is the transition to a high crack growth rate regime, C, with increasing AK, where the increase in growth rate over the as-received condition is associated with brittle cleavage of the ferrite matrix. The extent of ferrite cleavage varies with the stress intensity range in regime B, saturating at the onset of regime C. The fatigue crack growth rate in all regimes is dependent on the R-ratio, while AK T and the extent of ferrite cleavage are insensitive to the Rratio. Regime C is only clearly demonstrated in the test at R--0.1 (Fig. 4(b)). The remaining tests, at R = 0.5, show only regimes A and B, failing catastrophically at high maximum stress intensity values (Km~) before entering regime C (Fig. 4(a)). The crack growth rate in regime A is unaffected by ageing. The effect of R-ratio in regime A is considered elsewhere [22]. The transgranular cleavage facets are fractographically similar to the twin-associated cleavage observed Cleavage/ Satu~

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No Clea~

Aged / / _ . No

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Log Stress Intensity Range Fig. 7. Classification of the regimes of fatigue crack propagation behaviour observed in age-hardened Zeron 100: regime A--ductile fatigue, regime B--ferrite cleavage fraction increasing with AK, regime C--ferrite cleavage fraction saturated. The observed transition from regime A to regime B occurs at AK=AKT (AKT>AK~rit, where AKcrit is the critical stress intensity factor range for ferrite cleavage).

T. J. Marrow, J. E. King

/

Fatigue crack propagation mechanisms

in tensile and impact specimens, suggesting that the sub-critical ferrite cleavage during fatigue occurs in the same way. The duplex microstructure contains approximately 55% austenite by volume, hence even when all the ferrite matrix cleaves the austenite prevents failure from becoming unstable until much higher stress intensities. This restraining action by austenite allows sub-critical ferrite cleavage and its effect on fatigue crack propagation to be modelled as a function of ageing.

3.3. A model for sub-critical cleavage during fatigue Cleavage can be thought of as a two-stage mechanism, controlled by the more difficult of the two processes: initiation or propagation. Twin-associated cleavage can occur by the formation of cleavage initiation sites at favourable twin-twin or twin-grain boundary intersections, from which cleavage propagates either immediately (initiation-controlled) or on further loading when some critical local tensile stress is reached (propagation-controlled). Twinning occurs on the attainment of a critical resolved shear stress [25, 27], and twin-associated cleavage has been observed to be either initiation-controlled or propagationcontrolled, depending on whether the tensile stress criterion for propagation is satisfied with or subsequent to the shear stress criterion for twinning [28, 29]. The following discussion describes the development of a model for fatigue crack propagation in agehardened duplex stainless steel, based on the experimental observations and assumptions summarized below. The model is first outlined before considering the mathematical basis.

3.3.1. Experimental observations (1) The extent of cleavage is a function of AK, and not Kmax,and is insensitive to R-ratio (Fig. 6(b)). This is in marked contrast to other reports of sub-critical cleavage during fatigue [30-32]. (2) When cleavage occurs, accelerated growth rates are observed above a transition, AK, termed AKv, which decreased with increasing ferrite hardness (Fig. 4(a)). (3) Cleavage occurs on, or close to [001}.

97

(3) Cleavage occurs above a critical AK value, which the cleavage criterion is first satisfied. AKcrit is closely related to, but not the same as, the measured parameter AK T. (4) At a given R-ratio and temperature, the fatigue crack growth rate in regime B is determined by the extent of ferrite cleavage. It is proposed that ferrite cleavage in regime B forms a semi-cohesive or bridging zone ahead of the crack tip (Fig. 8). The extent of cleavage in the semi-cohesive zone increases through regime B with increasing AK, independent of R-ratio, saturating at the onset of regime C. In regime C, the crack growth rate depends solely on the rate of failure of ductile bridging ligaments within the semi-cohesive zone. The ligaments fail by high strain, low cycle fatigue with crack extension by successive blunting and sharpening of the local crack tip, indicated by the clearly defined and rounded appearance of the striations (Fig. 5(c)). The rate of ligament failure is therefore controlled by the crack opening displacement range, ACOD, and thus AK 2. The increased crack growth rate in regimes B and C consequently arises from the increased plastic strain in the ligaments due to the reduced load-bearing area of the semi-cohesive zone giving increased crack opening, rather than by crack extension directly from ferrite cleavage. Decreasing the ferrite content would decrease the crack growth rate in regime C by decreasing the ligament strain. This is equivalent to the variation of ferrite cleavage fraction with AK in regime B, with austenite and non-cleaving ferrite both forming ligaments. The crack growth rate in regime B is therefore controlled by the interaction of ferrite cleavage and ligament failure. The ferrite cleavage fraction shows a stronger dependence on AK than the ductile ligament fatigue mechanisms. Hence, as a reasonable approximation, it may be assumed that in regime B, at constant R-ratio, the crack growth rate is controlled by the extent of ferrite cleavage alone. This will be seen to be strictly

AKcrit , at

Semi-cohesive zone

3.3.2. Assumptions (1) Ferrite cleavage is initiated via deformation twin-twin or twin-grain boundary interactions. (2) Cleavage is propagation-controlled, and occurs on the attainment of a cleavage criterion, comprising a critical tensile stress acting over a critical distance, which depends on the local fracture stress and the availability of twin-induced cleavage initiation sites

[33].

Reversed Plasuc Lone

Fig. 8. The semi-cohesivezone, formed by ferrite cleavageahead of the fatigue crack tip, controlled by cleavage initiation in the reversed plastic zone.

98

T.J. Marrow,J. E. King / Fatiguecrackpropagation mechanisms

appropriate only at high cleavage fractions but is useful in understanding the effects of R-ratio and temperature. The strong effect of R-ratio on the overall crack growth rate in regimes B and C, where the extent of cleavage is insensitive to R-ratio, is commensurate with the effect of R-ratio on ACOD [22, 34]. Roughnessinduced crack closure is insufficient to explain the observed effect. The increase in crack growth rates between 22 °C and 305 °C for material aged at 400 °C for 1000 h (Fig. 4(a)), where the ferrite cleavage fractions are similar (Fig. 6(a)), arises from the effect of temperature on the rate of ligament failure. Increasing temperature decreases the flow stress and increases the rate of fatigue crack propagation by A COD-controlled crack tip blunting irrespective of the ferrite cleavage fraction. Similarly, the fatigue crack growth rate at 153 °C is high despite the lower ferrite cleavage fraction. The change in ferrite cleavage fraction with temperature can be understood by considering the effect of temperature on the incidence of deformation twinning. Twinning in non-aged, nickel-containing, ferritic and duplex stainless steels has been observed in two temperature regimes: below 150 °C, and between approximately 200 °C and 550 °C [8, 18]. Below 150 °C, twinning increases with decreasing temperature as the critical resolved shear stress for dislocation glide increases. Twinning tends to cease at around 150 °C in non-aged materials, although age hardening increases the temperature limit for twinning. Twinning has been observed in aged ferritic stainless steel at 150 °C [8]. Increasing temperature to 153 °C in aged Zeron 100 decreases the tendency for deformation twinning, thereby reducing the extent of twin-associated ferrite cleavage, as observed (Fig. 6(a)). The higher temperature twinning regime in non-aged alloys (200-550 °C) [18] has been shown not to arise from age-hardening and may be due to dynamic strain ageing [8]. The low cyclic frequency (0.1 Hz) and high temperature in the test at 305 °C, increase the tendency for twinning and hence ferrite cleavage, as seen in Fig. 6(a).

3.4. The relationship between sub-critical ferrite cleavage and fatigue crack propagation The experimental results show that the extent of cleavage is controlled by AK, not by gma x (Fig. 6(b)). For a macroscopic crack under mode I fatigue loading, the dominant stresses in the reversed plastic zone act normal to the crack plane. The tensile stress normal to an {001} plane inclined at some angle to the macroscopic crack plane is therefore smaller than the tensile stress acting normal to an {001} plane which is parallel to the macroscopic crack plane. The inclined plane effectively sees a lower AK than the parallel plane, and therefore cleaves at a higher applied AK, given a

AK-controlled cleavage criterion. Defining Agcrit as the cleavage criterion for {001} planes parallel to the macroscopic mode I crack, it is reasonable to conclude that the ferrite cleavage fraction is some function ot AK/AKcrir From assumption (4), it then follows that the fatigue crack growth rate is also a function of A K / AKcrit, where Agcrit depends on the ageing condition. Figure 9 shows the variation of ferrite cleavage with AK/AKcrit for material aged at 400 °C for up to 5000 h, tested at R = 0.1 and 0.5 at room temperature. The agreement between data for different ageing conditions is good and should be contrasted with the plot vs. A K in Fig. 6(a). Values of AKcrit were determined from crack growth rate data as follows. AKcrit was obtained for each ageing condition from the ratio of the fatigue crack growth rates at R =0.5 at high ferrite cleavage fractions, relative to an assumed value of AKc,it = 10 MPa m 1/2 for material aged for 1000 h. Values of AKcnt are given in Table 3. The agreement between the data confirms the assumed correlation between ferrite cleavage and crack growth rate.

50

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2~ 2o

R=0.5 R=0.5 R=0.5 R=0.5 R=0.1 Ferrite Model

: 100 hours : 5 0 0 hours : 1 0 0 0 hours : 5000 hours : 5000 hours C o n t e n t in Z e r o n 10( Prediction

10

0 i

....

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AK/AKcrit Fig. 9. The variation of ferrite cleavage fraction (%) with AK/AKcrit, where AKcrit is the critical stress intensity factor range for ferrite cleavage,for Zeron 100 aged at 400 °C for up to 5000 h, tested at room temperature at R-ratios of 0.5 and 0.1 (see legend). The prediction by the geometric model is also shown (see text).

T. J. Marrow,J. E. King / Fatiguecrackpropagation mechanisms The variation of ferrite cleavage fraction may be approximated by eqn. (1) [35], by calculating the stresses resolved normal to an inclined cleavage plane and using the AKcrit cleavage criterion. From the cubic symmetry, the principal mode I stress always lies within 54°44 ' of an {001} cleavage plane normal, thus the cleavage fraction saturates as A K increases.

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X = 1 for # > 5 4 ° 4 4 '

(5)

The predicted variation of ferrite cleavage fraction is shown in Fig. 9 and agrees well with the experimental data. The ferrite cleavage fraction may therefore be predicted as a function of AK, given AKcrit. Hence from assumption (4), the fatigue crack growth rate can be calculated given a relationship between ferrite cleavage fraction and crack growth rate. This empirical relationship was determined from the data at R = 0.5 and 22 °C, for material aged for 1000 h. The predicted fatigue crack growth curves for the other aged conditions are shown in Fig. 10(a). These were determined using (a) the AKcrit values in Table 3, (b) ferrite cleavage fractions calculated from eqn. (1) and (c) the empirical relationship between cleavage fraction and crack growth rate described above. The transition between regimes A and B at AKT, is assumed to occur when the predicted regime B cleavage-controlled crack growth rate exceeds the regime A ductile fatigue crack growth rate. Predicted AKT values are compared with measured values in Table 3. The agreement is good. The effect of bridging ligament fatigue on overall crack growth rate is seen in the effect of both temperature and R-ratio. The model can be extended to predict the effect of R-ratio by considering the A COD control of ligament failure rate.

A COD o c gmax 2 -- Kmin 2

(6)

therefore,

ACODoc(1 ( I _+RR) )AK2

(7)

,

lb

,

i

. . . .

i

. . . .

i ....

i,.

20 30 40 50 Stress Intensity Range : AK (MPa~/m) , *

R=0.1

: as-received

•

- -

.

,

- ,

....

,

.

R=0.5

: as-received

o

R=0.I

:aged

"

•

R=0.5

: aged

"

Predicted

Crack

•

Growth

Rate

10-3

.

f

_~

/ /:

:

"~

fat

°

Z

/• / ' f

°

~ 10-4

r~

d t 10-5

10

2'0 3'0 . . . . 4'0''' 5'0 Stress Intensity Range : AK (MPa',]m) Fig. 10. Fatigue crack propagation rates as a function of stress intensity factor range (AK) compared with crack growth rates determined by the semi-empirical model (see text) in Zeron 100 aged at 400 °C: (a) for up to 5000 h, tested at 22 °C and R = 0.5 and (b) for 5000 h, tested at 22 °C and R = 0.1.

100

T.J. Marrow, J. E. King / Fatiguecrack propagation mechanisms

The crack growth rate (da/dN) in regime B for tests at R = 0.1 is given by, x

d-N (n=0.1)= ~

'

(8)

(R=0.5) ACOD(n=o.5)

The prediction for material aged for 5000 h is shown in Fig. 10(b). A similar approach might be taken to predicting the effect of temperature. The agreement between experimental and predicted fatigue crack growth rates is very good at high crack growth rates and high cleavage fractions due to the selfconsistency of the model. AKT was higher than mgcrit in all cases, implying that a critical cleavage fraction is required before the presence of the semi-cohesive zone influences the fatigue crack growth rate. The semiempirical model demonstrates that fatigue crack propagation rates may be predicted with reasonable accuracy as a function of AK and R-ratio, given the material characterizing parameter Agcrit. Similar behaviour has been reported in a 22 wt.% Cr, 5.5 wt.% Ni, 3 wt.% Mo duplex stainless steel aged at 475 °C for up to 100 h. The Vickers hardness increased from 245 to 325, and enhanced crack growth rates were observed at R = 0.1 for AK values above approximately 25 MPa m 1/2 [36]. No enhancement was seen when the same material was tested at R=0.7. However, crack growth rates at AK values above 30 MPa m 1/2 were not determined at R = 0.7 since the high Kmaxlevel led to fracture at low AK. This behaviour is consistent with the AK-controlled cleavage criterion with Agcrit at around 20-25 MPa m 1/2. 3.5. The stress intensity range criterion for ferrite cleavage Previous research [30-32] has shown that subcritical cleavage in ferritic structural steels is controlled by Kraal. The experimental results and analysis presented here indicate a AK~it cleavage criterion is operative in aged duplex stainless steel. For propagation-controlled cleavage, AKcrit is considered to represent the condition where the stress distribution in the reversed plastic zone satisfies a cleavage criterion of critical stress acting over a critical distance [33]. The increase in ferrite strength on ageing would suggest, for a Kmax-Controiled cleavage process, a weak dependence of critical K on flow stress. A Kcrit shows a marked dependence on ageing condition, furthermore cyclic softening has been observed in aged duplex stainless steel [36], hence a simple flow stress criterion is insufficient. The form of the critical parameter, AKcrit , implies that cleavage is controlled by a critical distance related to the extent of intense, i.e. reverse, plasticity ahead of the crack. The density of deformation twinning in a

25 wt.% Cr, 5 wt.% Ni, 1 wt.% Mo ferritic stainless steel was found to saturate within a few cycles at a level independent of plastic strain range [37]. An increased level of ageing could increase the saturation twin density. Assuming cleavage propagates from twininitiated microcracks in the reverse plastic zone, then increasing the twin density increases the density of potential cleavage initiation sites, thus reducing the critical distance component of the cleavage propagation criterion. Such an effect could account for the large changes in A Kent.

4. Summaryand conclusions Thermal ageing of Zeron 100 duplex stainless steel for between 1 0 0 h and 5 0 0 0 h at temperatures between 350 °C and 450 °C increases the hardness and decreases the tensile strength and impact resistance. Ageing at 400 °C for up to 5000 h significantly increases the fatigue crack propagation rate at room temperature. This results from hardening and embrittlement of the ferrite matrix, which fails by transgranular cleavage, associated with deformation twinning. The onset and extent of ferrite cleavage during fatigue crack propagation is insensitive to R-ratio and is characterized by a critical stress intensity factor range AKcnt, which varies with temperature and ageing condition. A model for the fatigue crack propagation mechanism has been proposed which explains the observed effects of ageing. Semi-empirical models are then developed to predict the variation of ferrite cleavage and the fatigue crack growth rate as a function of A K, A Kcri~and R-ratio at room temperature. The model predicts a very strong effect of ferrite volume fraction. Weld and heat-affected zone microstructures with large grain sizes, high alloy content and high ferrite contents are therefore likely to be particularly sensitive to age-hardening-assisted fatigue crack propagation.

Acknowledgments Thanks are due to Professor C. J. Humphreys for providing laboratory facilities at Cambridge University, to A E A Technology (Harweil), British Gas and the Fellowship of Engineering for financial support, and to Dr. C. A. Hippsley for helpful discussions.

References 1 G. Aggen, H. E. Deverell and T. J. Nichol, Micon '78: Optimization of processing, properties and service performance

T. J. Marrow, J. E. King

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/

Fatigue crack propagation mechanisms

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