Journal of Materials Science and Engineering A 5 (5-6) (2015) 209-220 doi: 10.17265/2161-6213/2015.5-6.004

Relationships between KIC and CVN at the Lower Shelf of the Transition Curve CVN-T

M. Habashi1* and M. Tvrdy2 1. Research advisor at C. N. R. S. France

2. C. P. I. T., Technical University of Ostrava, Czech Republic. Abstract: The objective of this work is to verify the validity of the Spink’s model at the lower shelf of the transition curve CVN-T. Knowing that in this field of temperatures, previous results have shown that CVN is se nsitive to the steel micro-structure of the steel, heat treatments and the existence of defects such as those caused by internal hydrogen. Mild steel, with and without internal hydrogen and a metastable austenitic 2404 alloyed steel transformed at − 196 °C to about 90% martensite are studied. Standard charpy specimens with different notch root radii varying from 0 to 1 mm are used to measure fracture toughness by applying j-integral and also to measure the impact energy CVN. For all, bending tests were performed and the tests temperature was − 196 °C. For mild steel without internal hydrogen, the changes in both fracture toughness and impact toughness as a function of notch acuity coincide perfectly and are, also, in good agreement with those obtained at the upper shelf by Ritchie et al in AISI 4340 steel in two different heat treatments. However; in the case of mild steel severely charged with internal hydrogen and containing more than 10 ppm H2, which promotes high density of defects in the grain boundaries, the two linear relations are not similar but for the two cases of zero notch radii are the same and equal to 0 mm. The bi-phases 2404 alloyed steel shows that the slopes and the critical notch root radii of the linear relations are also different. The strain induced martensite from the residual austenite γ during the fracture toughness measurements at − 196 °C, with low strain rate is assumed to be inhibited. Only the strain rate sensitivity is responsible for this difference. However; for all three cases studied at − 196 °C and for the results obtained at the upper shelf by Rithie et al, the effective notch root radii whether measured by fracture toughness or by impact energy tests are the same. The fracture type in mild steel free from internal hydrogen is by macro-cleavage, while in the presence of internal hydrogen, macro-cleavage and inter-granular feature, with large cracks are observed. After fracture toughness tests, the fracture surface of the aged martensite 2404 alloyed steel is by fine dimples “ductile-fragile” feature. The main conclusion is that by applying the Spink’s model described above, large dimension specimens satisfying the standard LFEM criterion (ASTM E23-01, 2001) are not necessary. Key words: Fracture toughness KA or KIC, impact energy CVN, Spink’s model, internal hydrogen, mild steel, aged martensite 2404 alloyed steel, fracture features, critical notch root radius ρ0.

1. Introduction

LEFM (Linear elastic fracture mechanisms) was the potential quality control to insure a fracture safe component. However, LEFM is limited for several reasons: The testing of a KIC specimen, the size requirements necessary to insure valid KIC test results which depends on the yield strength (σy) of the metal studied and the high capacity of the tensile machines able to realize these tests. Consequently, the need exists to correlate KIC data with test results obtained with less costly conventional mechanical property

*Corresponding author: Mahmoud Habashi. E-mail: mahmoud.habashi@orange.fr.

specimens. The most commonly used is CVN (Charpy-V) notch at the upper shelf of the transition curve CVN-T. Several results have shown in Refs. [1-5], the existence of different relationships between the mechanical toughness KIC measured either by the LEFM (Linear elastic fracture mechanisms) or by applying J-integral JIC = K2

IC (1-υ2)/E and the impact energy CVN. At the upper shelf, the most used correlation is that of Barsom-Rolfe: (K IC/σ y)2 = 5 (CVN/σ y − 0.05) [6]. The prediction of KIC is within 6 to 18% of the measured value. On the other hand, two analytical equations have been derived by a) Rithie, Francise and Server [7] and b) Rithie and Horn [8]

D DAVID PUBLISHING

Relationships between KIC and CVN at the Lower Shelf of the Transition Curve CVN-T

210

respectively. KA = 2.9 σy [exp (σf/σy − 1)1/2]1/2 ρ1/2 (1) KA = (3/2 σy Eσf)1/2 ρ1/2 (2)

where, KA is the apparent mechanical toughness, σf is the critical fracture stress, σy is the yield strength, E is the Young modulus and ρ is the notch root radius.

For these relations, it is considered that the material obeys the Von Mises yield criteria. It is difficult to justify failure results from the formation of micro-cracks at the crack root. Furthermore, Spink et al. [9] have shown that even in the post yield region the plain strain fracture toughness controls the mechanisms of fracture. They then assumed that Smith’s relationship [10] calculated for a state of anti-plane strain deformation may approximately be valid for plane strain state. Assuming that KA is the post yield region and equal to σf (πC)1/2 and relating it to the plane strain fracture toughness, the following model was thus established by Spink et al. [9] :

(KA/KIC) [1 + (ρ/C)1/2] = α (ρ/C)1/2 (3) where, the slope α = σU (πC)1/2/KIC = [1 + 1/(ρ0/C)1/2], C is the notch length and σU is the ultimate stress in bend which is difficult to estimate but we don’t need this value now. ρ0 could be deduced by the slope value.

2. Attempts at Unifying Relationships

2.1 At the Upper Shelf

2.1.1 (KIC/σy)2 = Φ (CVN/σy) In aged martensitic 2404 alloyed steel with different

sulphur content (0.012% to 0.045) N Mahloul [11] was showed that KIC or KC and CVN were sensitive to the austenitization temperature: 800, 1,050 and 1,200 °C for 2 h, generating grain sizes: 40, 70 and 125 µm respectively. Standard 12 mm thick SENT specimens thick, with fatigue precracked, were used to measure KIC or KC, while standard Charpy V-notch specimens were employed to measure impact energy using standard CVN specimens at room temperature. The strain rates respectively applied, were 3.3 × 10-4 m/s for mechanical toughness and 3.3 × 103 m/s for the impact energy tests. The results presented in Fig. 1 was showed the following empirical relationships:

(KC/σy)2 = α [(CVN)/σy]-β (4) where, α and β were constants depending on the grain size dγ and the sulphur content. [(CVN)/σy] is in m.

It is worth noticing that the relationships of Barsom and Rolf [6], Van der Sluys et al. [12] and Witt [13] are valid for high strength steels such as the reactor pressure vessel and the ultra-high aircraft steel, and for

Fig. 1 Relationships between (KIC/σy)2 or (KC/σy)2 and (CVN/σy) calculated from the data of Ref. [11].

2,0x10-4 3,0x10-4 4,0x10-4 5,0x10-4

0,000

0,002

0,004

0,006

0,008

0,010

0,012

0,014

2,0x10-4 3,0x10-4 4,0x10-4 5,0x10-4

0,000

0,002

0,004

0,006

0,008

0,010

0,012

0,014Barsom and Rolfe Relationship

B=2.5(KIC

/σy)2

Increasing S% from 0.012, 0.013, 0.021 to 0.045

Aged Martensitic 2404 Alloyed Steel " Upper Shelf"

Tγ癈 , d

γ 祄

Plane Stress State

Plane Strain State

800, 401050, 701200, 125

(KIC

/ σy)2

or (

K C/ σ

y)2, m

(CVN/σy), m

Journal of Materials Science and Engineering A 5 (5-6) (2015) 209-220 doi: 10.17265/2161-6213/2015.5-6.004

these obtained here at room temperature. The decrease in the value of the slope α found by Barsom and Rolfe ( ≈ 62 to 33) was explained by the relative lower yield strength in this study ( ≈ 850 MPa).

2.1.2 (KA/KIC)[1 + (ρ/C)2] = φ (ρ/C)2 Applying Spink’s model and plotting the variation

of (KA/KIC) against (ρ/C)1/2, the results issued from the literature [14-18] and obtained at the upper shelf of the transition curve KA-T, were showed that all the

relations were linear with slopes which increased as the yield strength σy or the ultimate stress σu going higher. Furthermore, the characteristic distance or the effective notch root radius ρ0 can be deduced from these slopes. Two types of curves were observed: Type I [14-16] is obtained when ρ0 ≈ 0 at (KA/KIC) = 1, Fig. 2a and type II [17, 18], for ρ0 > 0, Fig. 2b.

Fig. 2a shows that the slope increases as grain size decreases, keeping in mind that the yield strength σy is

(a)

(b)

Fig. 2 (a) Curve type I [14] and (b) curve type II, plotted from the data of Ref. [17].

0,0 0,2 0,4 0,6 0,8 1,00,0

0,5

1,0

1,5

2,0

2,5

3,0

3,5

4,00,0 0,2 0,4 0,6 0,8 1,0

0,0

0,5

1,0

1,5

2,0

2,5

3,0

3,5

4,0

Mild SteelT = -196°COATES (1967)

d', grain/mm 2

150 550 3050

(KA/K

Ic)[1

+ (

ρ/C

)1/2

]

(ρ/C)1/2

0,0 0,1 0,2 0,3 0,40,0

0,5

1,0

1,5

2,0

2,5

3,0

3,50,0 0,1 0,2 0,3 0,4

0,0

0,5

1,0

1,5

2,0

2,5

3,0

3,5

KIC

, MPa(m) 1/2

Slope α=1+1/(ρ0/C)1/2

(ρ0/C)1/2

AISI 4140 SteelRoom Temp.From Garça et al data(1982)

870°C+Q,σy=1333MPa 57.4

1200°C+Q,σy=1127MPa 71.8

870°C+350°C,σy=1327MPa 52.0

1200°C+350°C,σy=1140MPa 56.5

(KA/K

IC)[1

+ (ρ

/C)1

/2]

(ρ/C)1/2

Relationships between KIC and CVN at the Lower Shelf of the Transition Curve CVN-T

212

a linear function of 1/(d)1/2 following the Hall-Petch relationship. Fig. 2b points out that the yield strength of the AISI 4140 steel is high when austinitized temperature is low and especially when it is followed by a tempering heat treatments. When quenching from 870 °C and quenching from 870 °C followed by tempering, either at 200 or 350 °C, the paper [17] have shown that the crack is initiated by shear lips mechanism.

2.1.3 (KA/KIC) and [CVN)/(CVN)0]1/2 as a Function of (ρ/C)1/2

As it has been observed when KIC is improved, there is an unexplained reduction in Charpy impact energy. These contradictory results are due to important differences between fractures induced at a sharp root notch radius, ρ0 ≈ 0 (fracture mechanics) and at blunted notch with ρ > 0 (CVN). Furthermore, the strain rate in Charpy tests is several order of magnitude higher than that employed in KIC measurements. Thus, there is no physical reasons to compare KIC and CVN results. However, it is possible to compare the values of the two parameters if ρ is the same for the two types of tests. By applying Spink’s model as before, the following relationship was plotted from Ritchie [7] data relative to AISI 4340 steel, austenitized at 870 °C and austenitized at 1,200 °C, followed by tempering at 200 or 350 °C, the following relationship:

[(CVN)ρ>0/[(CVN)ρ=0]1/2 [1 + (ρ/C)1/2] =β (ρ/C)1/2 (5)

where, (CVN)ρ > 0 and (CVN)ρ ≈ 0 are the impact energies measured in Charpy specimens with machined notch root radii ρ > 0 and with fatigue pre-cracked with ρ ≈ 0 respectively, and β is the slope of the linear relations c) and d) and are presented in Fig. 3.

It is evident that there are similarities between the two Figs. For each notch root, the average values of (KA/KIC) are the same as [(CVN)/(CVN)0]1/2. Moreover, the values of ρ0 obtained either by mechanical toughness or by impact energy tests are the same.

2.2 KIC as a Function of CVN within the Transition Zone

The dynamic tear DT and the drop-weight tear DWT tests were developed to measure fracture energy and involve three-point bending tests using a notched bar which is considered as oversized Charpy specimen. The notched bar being much thicker and wider than the Charpy-V specimen, there is a much greater plastic constraint at the notch root. The transition temperature is thus shifted to significantly higher temperatures, especially for low and medium strength steels, since Charpy dynamic data are being compared with static fracture toughness values. This test methods should be considered valid only for materials that exhibit little or no strain-rate sensitivity. By conducting the test under both impact and slow - bending conditions, a fatigue pre-cracked Charpy specimen could be used to determine the strain-rate sensitivity of the studied material. Marandet and Sanz [5] have used a multi-step approach to predict a KIC-temperature curve for a set of medium-strength steels having various heat treatments. By taking KIC transition-temperatures (TK*IC) as the temperature at which toughness increases rapidly, they defined TK*IC as equal to 100 MPam1/2. Similarly they defined TK28 as the impact energy transition temperature at which Charpy V-notch energy is CVN = 28 J. They thus suggested, the following relationship:

TK*IC = 9 + 1.37 TK 28 (°C) (6) They also determined that by shifting the actual

KIC-temperature curves until TK*IC Coincided with TK28, a KIC-CVN correlation can be established as,

KIC = 19 (CVN)1/2 (MPa m1/2, j1/2) (7)

2.3 At the Lower Shelf or at − 196 °C

2.3.1 Materials and Experimental Procedures The materials used in this investigation are: I. An aged martensite 2404 alloyed steel (0.39% C,

24.09% Ni, 0.009% P, X% S). This alloy is the same as that studied at the upper shelf, Fig. 1, The 2404 alloyed steel is known as an metastable austenite

Relationships between KIC and CVN at the Lower Shelf of the Transition Curve CVN-T

213

(a)

(b)

Fig. 3 (a) (KA/KIC)[1+(ρ/C)1/2] against (ρ/C)1/2and (b) [(CVN)ρ>0/(CVN)ρ=0]1/2 against (ρ/C)1/2.

micro-structure after quenching it in water from 1050 °C/2 h, to room temperature. The martensite phase α' is obtained; either a) by plastic deformation (strain induced martensite) at temperatures lower than Md or b) by quenching the metastable austenite γ at − 196 °C, temperature lower than MS (martensite starting temperature) For Tγ equal to 800, 1050 and 1200 °C, MS is, respectively, − 44, − 39 and − 26 °C for dγ = 40, 70 and 125 µm. The martensitic phase α' formed is, thus, 90.2, 90.7 and 92% following the

relation: (α'%) = 95 + 0.11 MS [19]. The “aged martensite” is obtained after maintaining it, at room temperature, for several days. The micro-structure analysed by X-ray technique shows: 90% α' + 10% γ without plastic deformation. The micro-structure of this martensite is recognized by its Butterfly feature. Two types of test are achieved in order to study:

a) The effect of grain size and sulphur content (from 0.012% to 0.045) on the variation of (KIC/σy)2

or (KC/σy)2 as a function of (CVN/σy) In this case,

0,0 0,1 0,2 0,3 0,4 0,5 0,60

1

2

3

4

5

60,0 0,1 0,2 0,3 0,4 0,5 0,6

0

1

2

3

4

5

6

(ρ°/C)1/2

AISI 4340 SteelRoom Temp.RITCHIE (1976)

Heat

(870°C) (1200-870°C)

(KA/K

Ic)[1

+ (

ρ/C

)1/2

]

(ρ/C)1/2

0,0 0,1 0,2 0,3 0,4 0,5 0,60

1

2

3

4

5

60,0 0,1 0,2 0,3 0,4 0,5 0,6

0

1

2

3

4

5

6

(ρ0/C)1/2

AISI 4340 SteelRoom TempFrom RITCHIE 's data

Heat

(870°C) (1200-870°C)

[(CVN

)/(C

VN

) 0]1/2

[1+(

ρ/C

)1/2

]

(ρ/C)1/2

Relationships between KIC and CVN at the Lower Shelf of the Transition Curve CVN-T

214

12 mm thick SENT specimens with fatigue precracked are used to measure mechanical toughness and standard CVN specimens are used to measure impact energy;

b) The variation of (KA/KIC) and [CVN/(CVN)0]1/2

with (ρ/C)1/2 are also taken into account to verify Spink's model. For all conditions the test temperature is − 196 °C, for a given S% = 0.021 and P% = 0.009 and for Tγ = 1050 °C ( dγ = 70 µm),

II. Normalized mild steel with low carbon content (0.08% C, 1.52% Mn) and grain size d ≈ 70 µm. This homogeneous mild steel is studied without and intentionally with hydrogen charging. Hydrogen charging was performed in a molten salts bath at 300 °C, − 2 volts/Ag and for 2 h [20] (internal hydrogen). The hydrogen charged steel is immediately quenched in liquid nitrogen (− 196 °C) to avoid any escape of hydrogen atoms. The quantity of hydrogen thus introduced was more than 10 ppm H2 creating serious defects in grain boundaries, without hydrogen charging and for − 196 °C, Fig. 4 shows the appearance of twinning in the matrix (left side) and after introducing hydrogen with high density, the defects are concentrated in grain boundaries, (right side) For − 196 °C, the yield strength σy is about 60 MPa higher in the absence of the internal hydrogen than in its presence [20].

Charpy impact energies CVN and KA values were measured using standard sized [ASTM 23-01, 2001] Charpy-V specimens with root notch radius ρ varying between about 0 mm (fatigue pre-cracked notch) and 1mm. The notch root radii were precisely determined by

projecting them on a viewing screen at X 20. Pendulum type impact machine of hammer velocity 3.3 m·s-1 is used to measure CVN. KA or KIC values are determined by mean of a three-point bending device mounted on the tensile machine. The cross-head displacement was 1.67 × 10-5 m/s. The failure stress is defined as the maximum value of the elastic centre fibre stress σ with σ = 6 PS/4 BW2 with P the applied load, S the span, B the specimen thickness and W its width. Once the values of J are determined, for fatigue pre-cracked specimens, KIC or KC are calculated by the following relation:

KIC = [E JIC/(1- υ 2)]1/2 (8) with E is the elastic modulus at − 190 °C and equal to 2.034 × 106 MPa and υ is the poisson’s ratio, assumed to be 0.3.

3. Results and Discussion

3.1 (KIC/σy)2 = f(CVN/σy) for the Aged Martensitic 2404 Alloyed Steel at − 196 °C

Steels containing high Nickel content are well known not to or slightly exhibit transition temperatures. Doubt is raised if the aged martensitic 2404 alloyed steel tested at − 196 °C belongs to the lower shelf or to the transition zone. As in Fig. 1 obtained in aged martensitic 2404 alloyed steel at the upper shelf, Fig. 5 shows that the the relations between the two parameters; (KIC/σy)2 and (CVN/σy) are also linear with the constants α and β depending clearly on the grain size dγ. α and β are lowered with respect to those calculated at upper shelf. It is worth noticing that the levels of the measured impact energies are the same;

Fig. 4 Micro-structure of the mild steel at − 196 °C before and after hydrogen charging.

Fig. 5 (KIC/σ

at the upperyield strengroom tempetest temperaupper shelf. low temperafeature is “dtemperature shelf, the ruinter-granula

3.2 ApplicaMartensitic

The alloycontain 0.02there are linand the notenergy and tof the two rewith criticalare lower thathe strain rafive magnittoughness tetransformatimartensite p

Relationshi

σy)2 or (KC/σy)

r and at − 19gth level is lerature, whileature is − 196

However; Kature. Fig. 6aductile-fragile

is achieved aupture featurear.

ation of Sp2404 Alloyed

yed steel is a21% S and 0.0near relationstch root radithe notch rooelations are nl radii: 38 anan the grain ste used to metudes higherests. It is sugion of the resphase α' at −

(KIC

/σy) 2

or (

K C/σ

y) 2, m

ips between

2 against (CVN

96 °C. Moreolower than te the ductility6 °C than tha

KIC or KC levea and b showe” with fine dat − 196 °C we is a mixture

pink's Moded Steel

austinititized 009% P. Fig.s between frus and also

ot radius. Hownot similar; arnd 45 µm ressize dγ = 70 µeasure impacr than that uggested that tidual austeni− 196 °C is

0,00,000

0,002

0,004

0,006

0,008

0,010

0,012

0,014

0,0

B=

Barsom Rela

ICy

Cy

KIC and CVN

N/σy).

over; the avethat measurey is higher wat obtained atels are reduce

w that the rupdimples whenwhile at the upe of cleavage

el to the A

at 1,050 °C . 7 points outacture toughbetween im

wever; the slore 8.3 againstspectively, wµm. Knowingct energy is abused in fracthe kinetic ofite γ (10%) toslowed dow

002 0,00

002 0,00

Aged Marte Uppe

2.5(KIC

/σy)2

m and Rolfeationship(*)

N at the Lowe

rage d at

when t the ed at pture n test pper and

Aged

and that

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opes t 7.7

which that bout

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Fig.Allothe

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003 0,00

003 0,00

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(CVN/σy),

r Shelf of the

ibited (highe

. 6 (a) Fractuoyed Steel; (b)Martensitic 24

ly the strain rher slope, conius with resppact energy.

004 0,00

004 0,00

ed Steelelf

m

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(a)

(b) ure feature atfracture featu

404 Alloyed Ste

rate effect is nsequently to pect to that

05 0,000

05 0,000

0

0

0

0

0

0

0

0

* Upper shelf--Lower shelf

Tγ癈 , dγ 祄

800, 40* 1050, 70* 1200, 125* 800, 40-- 1050, 70-- 1200, 125--

Curve CVN-T

nd lower yie

t − 196 °C of ure at Room Teel.

favoured [21a lower criticobtained in

06

06

0,000

0,002

0,004

0,006

0,008

0,010

0,012

0,014

215

eld strength).

f 90% α' 2404emperature of

1], leading tocal notch root

the case of

5

.

4 f

o t f

Relationships between KIC and CVN at the Lower Shelf of the Transition Curve CVN-T

216

3.3 Application of Spink' Model to the Mild Steel

Fig. 7 Fracture toughness and impact energy ratios against notch root radius.

Fig. 8 presents the variation of (KA/KIC) [1 + (ρ/C)1/2] and [(CVN)/(CVN)0]1/2[1 + (ρ/C)1/2] as a function of (ρ/C)1/2 for mild steel without hydrogen charging (Fig. 8a) and with the presence of the internal hydrogen (Fig. 8b).

The transition temperature (CVN-T) of the carbon steels is also known to increases as the carbon content is higher. For the mild steel studied (0/08% C), transition temperature is about − 70 °C and the change in the CVN-T curve from upper shelf to lower shelf is abrupt. The results obtained at − 196 °C in mild steel without internal hydrogen show that there is a good agreement with the values of (KA/KIC) and [CVN/(CVN)0]1/2 for a given (ρ/C)1/2 ratios: The same slopes and ρ0 values are also observed, Fig. 8a. Moreover; the similarities between our results obtained at − 196 °C and those shown in Fig. 3 obtained in AISI 4340 steel at the upper shelf are evident, Fig. 9. The behaviour of the two steels belongs to the curve type II. On the other hand; in the presence of internal hydrogen, the slope of [(CVN/(CVN)0]1/2 as a function of (ρ/C)1/2 is higher than that measured in the case of the (KA/KIC) as a function of (ρ/C)1/2. Moreover: ρ0 = 0 for the two parameters (see curves type I) Fassina et al. [22] have shown, in X 65 (0.11 C%)

steel in the range of temperatures − 60 to − 100 °C with and without prior hydrogen charging that impact energy, using standard Charpy V-notch specimens [(ρ/C)1/2 = 0.316], was not affected by the presence of internal hydrogen, while in the presence of hydrogen, the fracture toughness J, measured in CT specimens, with fatigue pre-cracked notch was drastically reduced in the range: room temperature to − 80 °C; the transition zone. The authors assumed that micro-cracks were developed at the fatigue crack tip. The possibility of hydrogen atoms-dislocations interaction assisted by the slow strain rate performed in this range of these temperatures is to be considered. In our case, not only grains boundaries are embrittled by hydrogen atoms, but also, the development of micro-cracks at the notch tip are implied for this behavior. It is worth noticing that at − 190 °C, hydrogen atoms-dislocations interaction is inhibited. The slopes are lower for the two parameters than those observed in the absence of internal hydrogen, Fig. 8 and could suggest that the yield strength σy is lowered. Results obtained by tensile tests at − 196 °C in α iron with or without hydrogen charged with the same method and charging conditions [20] showed that the yield strength of uncharged steel was higher by about 60 MPa and the maximum plastic

0,0 0,1 0,2 0,3 0,4 0,5 0,6 0,70

1

2

3

4

5

6

70,0 0,1 0,2 0,3 0,4 0,5 0,6 0,7

0

1

2

3

4

5

6

7

(ρ0/C)1/2

2404 Martensitic Alloy T = -196°C

[CVN

/(CVN

) 0]1/2

[1+(

ρ/C

)1/2

]

(KA/K

IC)

[CVN/(CVN)0)]1/2

(KA/K

IC) 2

[1+

(ρ/C

)1/2

]

(ρ/C)1/2

Relationships between KIC and CVN at the Lower Shelf of the Transition Curve CVN-T

217

deformation is about 10%, slightly higher in the presence of internal hydrogen [23].

(a)

(b)

Fig. 8 Fracture toughness and impact energy ratios against (a) (ρ/C)1/2 for mild steel without hydrogen charging and (b) (ρ/C)1/2 for mild steel without internal hydrogen.

The rupture feature for mild steel without internal hydrogen at − 196 °C is by macro-cleavage, while in the presence of internal hydrogen, it is by macro-cleavage, containing large cracks in grain boundaries. This type of rupture could be predicted by Fig. 8. Inter-granular large cracks are promoted by the high hydrogen concentration trapped in grain

boundaries. Finally, plotting all the values of the measured

critical radii ρ0 measured, either by fracture toughness tests or for those measured by impact energy, Fig. 10. The results show that they are about the same, generally lower or equal to the grain size and independently of the type of test and the material,

0,0 0,2 0,4 0,6 0,80

1

2

3

4

50,0 0,2 0,4 0,6 0,8

0

1

2

3

4

5

Mild SteelT= -196°C

[(CV

N)/(

CV

N) 0)]1

/2 [1

+(ρ/

C)1

/2]

(KA/K

IC)[1+(ρ/C)1/2]

[(CVN)/(CVN)0]1/2 [1+(ρ/C)1/2]

(KA/K

IC)[1

+(ρ/

C)1

/2]

(ρ/C)1/2

0,0 0,2 0,4 0,6 0,80,0

0,5

1,0

1,5

2,0

2,5

3,0

3,5

4,00,0 0,2 0,4 0,6 0,8

0,0

0,5

1,0

1,5

2,0

2,5

3,0

3,5

4,0

Mild Steel with internal hydrogen T= -196°C

[(CV

N)/(

CVN

) 0]1/2

[1+(

ρ/C

)1/2

]

(KA/K

IC)[1+(ρ/C)1/2]

[(CVN)/(CVN)0]1/2[1+(ρ/C)1/2]

(KA/K

IC)[1

+(ρ/

C)1

/2]

(ρ/C)1/2

Relationships between KIC and CVN at the Lower Shelf of the Transition Curve CVN-T

218

whether at the upper or at the lower shelf [24] of the transition curve.

Fig. 9 Average values of (KA/KIC) against [CVN/(CVN)0]1/2 for different steel at room temperature and − 196 °C.

Fig. 10 Similarities of ρ0 between the fracture toughness and the impact energy tests.

4. Conclusions

This study is devoted to find emperical relationships between mechanical toughness and impact energy at the upper and the lower shelf of the transition curve and to verify also the Spink’s model

at low temperature, i.e. at − 196 °C, in aged martensite 2404 Alloyed Steel and in mild steel with and without prior severe hydrogen charging. The results obtained suggest the following conclusions:

At room temperature and at − 196 °C and for the aged martensitic 2404 Alloyed Steel which does not

1 2 3 4 5 61

2

3

4

5

61 2 3 4 5 6

1

2

3

4

5

6

(KA/K

IC)=[CVN/'CVN)

0]1/2

4340 Steel, 870°C+Q, Room Temp. 4340 Steel, 1200°C+870°C, Room Temp. Mild Steel at -196°C 2404 Alloyed Steel at -196°C Mild Steel+H

2 at -196°C

____

_(K

A/KIC

)

_________ [CVN/(CVN)

0]1/2

0 20 40 60 80 100 120 140

0

20

40

60

80

100

120

140

160

180

2000 20 40 60 80 100 120 140

0

20

40

60

80

100

120

140

160

180

200AI

SI 4

340

Stee

l (12

00-8

00°C

)

Mild

Ste

el

Aged

α' 2

404

Allo

yed

Stee

l

AIS

I 434

0 S

teel

(870

°C)

Mild

Ste

el (H

2)

ρ 0 from

(KA/K

IC),

µmm

ρ0 from [(CVN)/(CVN)

0]1/2, µmm

Relationships between KIC and CVN at the Lower Shelf of the Transition Curve CVN-T

219

exhibit transition temperature, empirical relationships between (KIC/σy)2 or (KC/σy)2 and (CVN/σy) are found and are similar to those found in literature and could be expressed as: (KIC/σy)2 or (KC/σy)2 = α (CVN/σy) + β, where α and β are dependent on: sulphur content, test temperature and grain size:

Applying Spink’s model avoids the need of high specimen dimensions to measure KIC. Only small specimen dimensions, such as Charpy specimen with different notch root radii varying from 0 (fatigue pre-cracked) to 1 mm are required,

There are similarities between the values (KA/ KIC) and the corresponding [(CVN)/(CVN)0]1/2 for specimens with the same notch root radius, suggesting that the steel micro-structure is homogeneous. Otherwise, excessive defect density in grain boundaries provoked by hydrogen introduction or in the case of the strain rate sensitivity material, such as the bi-phases aged martensite 2404 Alloyed Steel, the correlation between the two parameters are possible but the similarities are not observed,

Generally, the fracture type is by macro or micro-cleavage feature and is observed when the similarities exist between the two parameters. When fine dimples or a mixture of cleavage with inter-granular rupture are observed, the similarities are not established,

The critical notch root radii measured either by fracture toughness or by impact energy tests have almost the same values, and lower than the grain size, in the upper and lower shelf of the transition curves.

The few results obtained in this study do not allow the establishment of a definitive relationship between mechanical toughness and impact energy in the lower shelf of the transition curves. More results are thus available in steels or other materials having homogeneous microstructures.

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[19] Kozelkova, I. 1996. “Transformation Martensitique par

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220

Trempe et Induite par Deformation Plastique dans les Alliages Fe-Ni-C.” PhD, Ecole Centrale Paris

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