Fracture of hot formed ledeburitic chromium steels

Pergamon

Engineering Fracture Mechanics Vol. 58, No. 4, pp. 311-325, 1997

PII: S0013-7944(97)00118-5

© 1997 Elsevier Science Ltd. All rights reserved Printed in Great Britain 0013-7944/97 $17.00 + 0.00

FRACTURE OF HOT FORMED LEDEBURITIC CHROMIUM STEELS H. BERNS and C. BROECKMANNt Lehrstuhl Werkstofftechnik, Ruhr-Universit/it Bochum, Germany D. WEICHERT Institut fiir allgemeine Mechanik, RWTH Aachen, Germany Abstract--Due to the hot forming procedure the overall mechanical properties of ledeburitic chromium steels become anisotropic. As shown by experiments the fracture toughness Kic of these steels depends on the hardness of the metal matrix and the orientation of the load with respect to the axis of hot forming. The degree of crack deflection, expressed by the width of the crack path, was found to be the governing quantity for differences in the resistance against crack propagation. The Kit-tests were modelled by the finite element method using an orthotropic elasto-plastic material law. While the behaviour of the hardened and low tempered specimens could be well predicted by this model, differences between simulation and experiment in the case of a ductile state indicate the occurrence of additional effects acting on a microscopical scale. © 1997 Elsevier Science Ltd Keywords---fracture toughness, J-integral, anisotropy, two-phase material, ledeburitic chromium steel, finite element method.

1. I N T R O D U C T I O N LEDEBURITIC CHROMIUM steels are commonly used as tool materials for cold work applications. In order to generate high resistance against abrasive wear they consist of coarse ceramic hard phases (HP) embedded in a metal matrix (MM). Due to the high volume fractions of those brittle particles and the high hardness of the composite, the resistance against crack propagation, expressed by the fracture toughness Kxc, is very poor. The influence of volume fraction, size and shape of the hard phases on the fracture toughness is well known [1]. Conventionally produced tool steels are cast and afterwards hot formed. In the as-cast state metal cells are surrounded by a eutectic network [Fig. l(a)]. The overall mechanical properties are isotropic. After hot forming with an area reduction of 2 = 10 the net-like structure is transformed to a bandlike microstructure[2], as can be seen in Fig. l(b). Then the mechanical properties become anisotropic. The objective is to describe the influence of this anisotropy on the fracture toughness.

2. E X P E R I M E N T A L INVESTIGATIONS Steel AISI-SAE D3 was tested as an example of the group of ledeburitic tool steels. The chemical composition is given in Table 1. The steel was tested in the hot worked condition (rods of square cross-section 50 x 50 mm2). In order to compare the fracture behaviour of the bandlike microstructure with that of a net-like microstructure some samples were taken of a cast ingot (diameter 120 mm). The volume fraction of eutectic M 7 C 3 carbides is flip = 16%. The average size of the hard phases in the hot worked material expressed by the diameter of a circle equal in area to the particle is 2s = 5.11 pm, and the average distance between two carbide bands dcB = 130 #m. In order to investigate the influence of the matrix ductility on the fracture behaviour, the material was tested in three states of heat treatment. Index "wg" resembles the state "soft annealed" as delivered (Twg = 800°C). For the two other states the steel was austenized at TA=950°C for 30 min under an argon atmosphere and quenched in oil. After subsequent tempering (30 min) the hardness curve (Fig. 2) was measured. For further tests tempering temperatures of TT = 380°C (index "380") and TT = 600°C (index "600") were chosen. fAuthor to whom all correspondence should be addressed. 311

312

H. BERNS

et al.

Fig. 1. T h e m a c r o h a r d n e s s o f the three states are listed in T a b l e 2. T h e specimen t a k i n g o f the h o t w o r k e d m a t e r i a l is described b y a c o o r d i n a t e system a c c o r d i n g to A S T M E399-74 [3] as s h o w n in Fig. 3. The fracture toughness o f the m e t a l m a t r i x was d e t e r m i n e d with specimens m a d e o f m a terials which are a s s u m e d to c h a r a c t e r i z e the m e c h a n i c a l b e h a v i o u r o f the m a t r i x in D 3 steel. F o r the soft a n n e a l e d c o n d i t i o n a m a t e r i a l was c h o s e n whose c h e m i c a l c o m p o s i t i o n is equal to t h a t o f the m a t r i x in D3 steel. It is k n o w n t h a t r e t a i n e d austenite influences the fracture t o u g h ness o f h a r d e n e d tool steel [4]. Thus, in the h a r d e n e d a n d t e m p e r e d c o n d i t i o n a m a t e r i a l with

Table 1. Chemical composition of D3 steel (in wt%)

D3 hot worked D3 cast Matrix (wg) Matrix (380, 600)

Fe

Cr

Mo

Mn

V

C

Base Base Base

12.0 11.5 5.3

--1.1

0.3 0.3 0.2

--0.2

2.1 2.0 1.0

Base

0.4

--

2.0

0.1

0.9

Fracture of ledeburitic chromium steels

900

o -i-

¢/) ¢/)

•

hot~orked

313

.

800 700

¢600 ¢-

2 to

500,

E

400] 300J"

i

0

'

I

I

I

I

200

400

600

800

TT

[*c]

Fig. 2.

equal volume fraction of retained austenite was chosen to characterize the matrix behaviour. The composition and macro hardness of those two matrix materials are given in Tables 1 and 2, respectively. In the hardened and tempered states fracture toughness was determined using the standard Kit-test [3]. The specimen's geometry and loading condition is given in Fig. 4. All measured Ki-values fulfil the condition d> --

2 . 5 ( KIc ,~2, I~Rp0.01 ]

(1)

where Rp0.01 denotes the yield stress at 0.01% plastic strain and d is the thickness of the specimen. Thus, they can be treated as valid Kl:values. In contrast to this the soft annealed specimens do not fulfill eq. (1). Therefore J-integral tests were carried out. A one-specimen method was used [5]. Precracked specimens with a crack length ratio of a/w ,,~ 0.6 (Fig. 4) were loaded in a three-point bending device. The displacement u of the upper point was measured and plotted against the force F [Fig. 5(b)]. An ultrasonic signal, transmitted into the specimen perpendicular to the crack area was also measured [Fig. 5(a)]. The ultrasonic method was used in order to Table 2. Hardness, fracture toughness KIc and width of crack path p of D3 steel in different states of heat treatment State of heat treatment wg

600

380

Specimen L-T T-S T-L Net Matrix L-T T-S T-L Net Matrix L-T T-S T-L Net Matrix

Hardness HV 30 250 305 215 460 460 510 396 648 678 543

K,c (MPam °-5) (Kit-test)

Kit (MPam °.5) (Jlc-test)

-----28.40 28.01 25.59 28.3 -21.67 24.79 22.21 25.8 27.1

49.89 31.61 46.08 28.8 73.4 30.69 28.94 26.51 -49.84 24.53 25.24 19.40 ---

p (# m) 151 104 72 110 64 84 64 121 40 56 51 116

314

H. BERNS et al.

Fig. 3.

monitor the first onset of crack propagation which usually occurs in the centre of the specimen. A typical curve US = US(F) shows three regions. Region I corresponds to the separation of the crack surfaces during loading, region II to crack opening and region III to crack propagation. The transition from region II to region III was used to define the critical load for crack propagation Ft. With this force the J-integral was calculated by[6] r/Upo~

(2)

J - a(w - a)'

where the potential energy Upot is obtained by integrating the F - u curve [see Fig. 5(b)]. The factor q takes into account specimen's geometry. Under the assumption that deformation takes place in a zone restricted to the ligament of the crack, the geometry factor of a bending specimen is set to q = 2.0. This assumption is justified in the case of a long crack and a large span. Usually three-point bending specimens with a/w >10.6 and s/w ~ 4 are used. For transverse specimens made of the material under investigation this span/width ratio was too large. Thus, a specimen with reduced s/w was used. Finite element calculations showed that a factor r/ = 2.0 appears to be valid in this case, too. For all specimens tested, the geometry condition [7]

7thick

36,4 45 -I Fig. 4.

Fracture of ledeburitic chromium steels

I_l

II

_ t_

315

1II

Upot=fF du }

w

Fc

Fc

F

F

(hi

(ol Fig. 5.

d > 25

2JIc

(3)

Rp0.01 q- R r n '

leads to valid Jlc-values. In order to express the fracture toughness in terms of a critical stress intensity factor these data were transformed using K1c =

JIc,

tc = 3 - 4v,

# - 2(1 + v)"

(4)

Here, # is the shear modulus and v is Poisson's ratio. The results of the tests are listed in Table 2. The function Kic = KI~(TT) is plotted in Fig. 6 for all materials tested. Generally, in two-phase materials the crack path is not a straight line. The running crack is more or less deflected (Fig. 7). These local changes of the crack direction can be expressed by the width of the crack path p. After the tests were carried out p was determined using a light optical microscope. Starting from the fatigue crack tip the amplitude of roughness of the crack path was measured in a longitudinal section over a length of 400 pm. The average results are listed in Table 2 and plotted in Fig. 8. 80-

28

70-

~" 26

matrix= ~-

60-

o,

E

50-

• net

matrix

je

T-S A

24

]~" ~''~ 22"

• L-T

201~ - - . 0 o

. ~ - L - T T-L

i"1 40. _o

T-S net

30 20 300

i

I

I

i

I

400

500

600

700

800

T T C°C] Fig. 6.

316

H. BERNS et

al.

Fig. 7. 3. NUMERICAL SIMULATIONS The finite element method (FEM) was used to compute the stress intensity factors" The FEM-program CRACKAN, used for these calculations, is based on a code published in ref. [8]. Structures can be modelled under the assumption of plane stress or plane strain. A geometrically linear and physically non-linear theory is used. Differences in the elastic behaviour of the three specimen takings, caused by the uniaxial orientation of carbide bands, are considered by using Hooke's law for orthogonal anisotropy. Plasticity is modelled by J'2 flow theory and Hill's yield criterion [9]. Different deformation behaviour with respect to three orthogonal directions is taken into account by weight factors F, G, H, L, M and AT.. 2f(a) = F . (0-22 - 0-33)2 -{- G. (0"33 - o-11)2 --}-H-(o-11 - 0"22)2 Jr- 2L. a223+ 2 M . o-32]+ 2N. a22

160 140 f 120

/

/.L-T

fatigue crack tip v~

_

_ _ - - - - - - - - - - - v ~

net

T-S

=,--,.=

E loo o.

80

6O

~

~ T-L

40 I

300

400

i

I

I

500

I

600 T T [°C] Fig. 8.

i

I

700

~

I

800

i

(5)

Fracture of ledeburitic chromium steels

317

With this definition the following yield criterion is assumed:

cb(a,k) = f(a, k) -

1

~= 0

(6)

k is a material parameter and depends on the hardening parameter ~:, which in case of isotropic strain hardening is the effective plastic strain ~. The coefficients F, G, H, L, M and N depend on the yield stress in uniaxial tension/compression (asl, as2, as3) and torsion (Zs12, ~s23, ~s31): 1 2F

1

a~s2-{- 2

1

2 '

O's3

O'sl

1

1

1

0"2

O'sI

0"s2

2G=--+

2

1

2H=azls +

2'

1

1

tTs2

O's3

2

z ,

1 2L =

2 , Ts23

1

2M=

2 '

"Cs31

2N=--.

1

T212

(7)

For plane problems the number of parameters is reduced. Under the assumption of isotropic strain hardening the material behaviour can be described by the initial values F0, Go, Ho, No and the uniaxial stress-strain curve for the first orthotropic axis. It may be assumed that in a transverse section the in-plane mechanical behaviour of a hot worked material is isotropic. Thus, different properties only exist in the longitudinal (L) and transverse (T) directions. Equation (7) reduces to 2Fo-

2

1

2 O'sT

2' O'sL

1

1

O'sL

TsLT

2G0 = --5"-' 2N0 = 2T---' 1

2H0 = ST-'

(8)

(TsL

where trsL and O'sT denote the uniaxial yield stress in the L- and T-direction, respectively. "CsLT is the uniaxial yield stress under torsion. After the stress and the displacement fields were calculated the stress intensity factors KI and Kit, corresponding to fracture mode I and II, were determined using three different procedures: computing the J-vector, the integrals Jl and Jn by the separation method and the energy release rate G by the modified virtual crack closure method (MVCCI). Small-scale yielding was assumed and therefore in all cases the stress intensity factor was obtained by eq. (4) and the identity J = G. Although only macroscopic mode I conditions were considered the program was developed to simulate mixed mode situations. With this extension the crack deflection which only can occur under mixed mode could be investigated on a microscopic scale[5]. According to Budiansky and Rice[10] the J-vector is defined as a line integral developed on an integration path surrounding the crack tip.

Ji=fF( wni-(rjkO"ujnk~ds'O/xi

(9)

w is the strain energy density, n; the outward normal vector, a 0. the stress tensor and ui the displacement. The integral is computed numerically over a path through the gaussian integration points of the elements. The integrant is calculated for each Gauss point lying on this path. The relation between the vector components Ji and the J-integrals J1 and Jn is given by[11] J1 = Jl + JII, J2 = - 2 JV/~J~t.

(10)

One of the assumptions for the proof of path independence are traction-free crack surfaces. This condition is not fulfilled under mode II loading. Thus, path independence is only given for

H. BERNS et al.

318

v ( r = x ÷6Q,O= l t , o * B n )

I~

~1--

-t--

-I

Fig. 9.

the Jl-component. The separation method developed by Ishikawa e t al. [12] leads to path-independent integral expressions even in the mode II case. The stress and displacement fields are decomposed into symmetrical (index S) and asymmetrical (index AS) parts: 1

1

0"11S = ~(0"11 p "-~ O'llp,),

GIIAS = ~(O'11 p -- O'1 lp,),

1

1

a22S = ~ (G22p "4- a22p'),

a22As = ~

(a22e -

a22e'),

1

1

0"12S = ~(Ul2p -- O'12p,),

1

(11)

O-12AS = ~(Ol2p ..1¢-O-12p,),

1

Ulp'),

u]s = ~(Ulp + U~p,),

/'/IAS "~- ~ (/'/Ip --

1 U2S = ~(U2p -- U2p'),

U2AS ~-~ ~(U2p + U2p').

I

(12)

-y//////

II

II

w:20 I

~

II II t I

/ •

a=8 U r-

_A.

N

/~//I //I

v

I ) ~\\N I I ~\\ I

il II II

Fig. 10.

t

•

Fracture of ledeburitic chromium steels

319

Assuming the origin of the coordinate system in the crack tip, p is the material point under consideration with coordinates (xl, x2) and p' is a corresponding point with coordinates (xl, -x2). J~ is calculated with the symmetrical parts of stress and displacements according to aui ,

Ji = fr (wdx2 - ti-~xl os),

(13)

while Jn is determined using the asymmetrical parts of stress and displacement. The integration is carried out the same way as described before. A third method implemented to the program is the modified virtual crack closure integral, as introduced by Theilig et al. [13]. The energy release rate G is defined as the change of total potential energy U caused by a virtual crack extension 6a. Under linear elastic conditions the energy for crack opening is the same as for crack closure. With Fig. 9 the energy release rate is calculated by GI

----

2 fx=e,a 1 ~ ayy(r = x, 0 = 0, a ) . v(r = ha - x, 0 = zc, a + f a ) d x ,

lira - - l

6a 0 (~a J_v=0

Gn = ~c,__,0 lim ~aa 2 j.~= f x =°~ " l~ a x y ( r = x, 0 = O, a) . u(r --- 6a - x, 0 = n, a + 6 a ) d x ,

(14)

where r and 0 are polar coordinates originating in the crack tip, aij is the stress tensor and u and v are the displacement components in the x- and y-directions, respectively. The three ways to determine the stress intensity factors were tested in a first numerical example assuming isotropic material behaviour. A plate with an edge crack was loaded by a displacement of u = 0.02828 mm. The angle a was changed between 0 and 90 ° (Fig. 10). Young's modulus was assumed to be E = 220,000 MPa and Poisson's ratio was v = 0.3. Figure 11 shows the calculated stress intensity factors using the identity

Ji : Gi,

K i : ~8----~l Ji,

(15)

where i is replaced by the fracture mode I or II and # and x are calculated according to eq. (4).

K t , K ~t in MPam °'5

30

20

eparation) Kii (separation)

\

10-

"

/

~

K i (vector)

',,

_

0 0

15

30

45 Fig. 11.

60

75

90

ot

320

H. BERNS et al.

1

u

F 2

zxAA

777777777

w:15

Fig. 12.

It is evident that the differences in Kt, computed by the three methods, vanish for the whole range of ~, while the KII factors of the separation method differ from those obtained by the MVCCI method. Moreover, KII depends on the discretization in the latter case. Therefore in the following only the separation method was used. The three point bending tests were simulated using the model shown in Fig. 12. Due to symmetry only one half of the specimen was modelled. The model was loaded by the experimentally determined force Fc (see Fig. 5). In all calculations a state of plane strain was assumed. The material was modelled assuming elastically and plastically orthotropic behaviour. The material parameters are given in Table 3. The properties corresponding to the longitudinal axis are denoted by L, those of the two transverse axis by T. The initial yield stress under uniaxial torsion is determined by ZsLT = (trsL + troT)~2. The uniaxial stress-strain curve of the first orthotropic axis is assumed to obey the following hardening law: tr = as

( sT

for

tr > as,

(16)

where as is the uniaxial initial yield stress and es is the corresponding strain. The hardening Table 3. Material parameters used in the numerical model. E = Young's modulus, v = Poisson's ratio, asj = initial uniaxial yield stress, n = hardening exponent, asj corresponds to a~L and CrsT defined in eq. (8), where j is replaced by L for the L-orientation and by T for the transverse orientation. In the net-like microstructure and in the matrix material trsj does not depend on the orientation State of heat treatment 380

600

wg

Orientation

E (MPa)

v

asj (MPa)

n

L T Net Matrix L T Net Matrix L T Net Matrix

220000 215000 223000 210000 220000 215000 223000 210000

0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3

1460 1380 1430 1210 1073 1071 875 900 311 343 240 435

0.450 0.450 0.519 0.448 0.305 0.305 0.433 0.382 0.220 0.220 0.441 0.200

220000

215000 223000 210000

Fracture of ledeburiticchromium steels 60 orientationT-L

orientationL-T expedment~

4O

321

~'®40 a.

I

numericalm

==~/

30.

numericalmodel

~ experiment

o~

20.

%

400

'

SO0

"

6 0 0'

"

7 0 '0

'

8 0 '0

TT [ ' C ]

TT ~C] 80-

matrix

net

50,

~

7060-

40.

expedment~,--~

E

~. 3o.

expedmen~

50-

~o~ ~ .

30-

numericalmodel

10-

20-

10-

0

3OO

,,-

.

40o i

"'

•

~ ,

.

60o J

•

xT [°c]

?oo i

,

8~o

o

~o

400

•

i

•

5oo eoo " J

•

i

TT [°C]

760 " 8~o

Fig. 13. exponent is given in Table 3. An isotropic model was used to simulate the pure matrix as well as D3 steel in the as-cast condition. Using the separation method, J~ was computed according to eq. (13). The results of the simulation are shown in Fig. 13. The calculated fracture toughness K~c and the experimental values are plotted over the tempering temperature. In order to compare computations under the assumption of plane stress with those assuming plane strain, Fig. 14 shows the stress intensity factor of an annealed T-S-specimen in dependence of the acting force.

K~in MPam °'5

60

•

wg

ne strain)~ ~ (planeWsgress)/ / ~

50 40

•

/

600

.

(plane strain)

30 20 10 1000

2000

3000

Fig. 14.

4000

F in N

322

H. BERNS et al.

4. DISCUSSION The experiments show that the fracture toughness of D3 steel generally increases with the ductility of the metal matrix, expressed by the tempering temperature (6). This effect is well known [14] and was even observed in high-speed steels[15]. In a highly tempered condition the size of the plastic zone at the onset of crack propagation is bigger than that in a low tempered state. Due to dissipation in the plastic zone the amount of energy available for crack propagation decreases. As can also be seen in 6, the specimen orientation additionally influences the fracture toughness. While in the hardened and low tempered state D3 steel in the as-cast condition has the highest fracture toughness, the L-T orientation shows the highest Kit-values in the annealed state. The sensitivity of the fracture toughness to the direction of loading is known from other band-like microstructures, particular in aluminium-SiC composites [16], in high-speed steels [17] and in austenitic steels with non-metallic inclusions [18]. This effect can be explained by the crack deflection, as seen in 7, where the roughness of the crack path is plotted against the tempering temperature. Obviously, a high crack deflection corresponds to a high fracture toughness and vice versa. A deflecting crack leads to a local increase in crack surface. Thus, a higher energy is required for crack propagation. The positive effect of crack deflection and crack branching on the toughness was also observed in other materials such as ceramics or MMCs[15, 16]. Let us now look on the influence of the coarse hardphases on the fracture toughness in detail. At high macro hardness (i.e. state "380") the differences in crack resistance between the matrix and the composite are essentially smaller compared to the ductile state. This effect is caused by the brittle behaviour and the low fracture toughness of the matrix in the hardened and low tempered condition. The presence of carbides decreases the fracture toughness of the matrix up to 20%. It is important to notice that the netlike microstructure shows the highest K~c value of all carbide distributions under consideration. The reason for this is the tendency of the crack to follow carbide-rich regions (see Fig. 7). Therefore, a high crack deflection is obtained (Fig. 8) which is only influenced by the size of the eutectic network. In the T-L orientation a running crack might follow a carbide band. The width of the crack path is restricted to jumps between adjacent carbide bands, but most of the crack surface is produced by cleavage of carbides in one band. Thus, the lowest fracture toughness is measured for this orientation. Although the net-like distribution of hard phases appears to be the optimum with respect to fracture toughness, it should be mentioned that this distribution supports crack initiation in smooth specimens at lower load levels than in the case of a band-like microstructure. This means that the bending strength in the as-cast state is rather poor. In the ductile condition (i.e. state "wg") the loss of fracture toughness due to the hard phases is more distinct. For example, a net-like distribution of eutectic carbides reduces the fracture toughness of the matrix up to 60%. In this particular case Kic does not depend on the matrix ductility. The crack follows the brittle carbide network without running through the matrix. Thus, independent of the heat treatment fracture toughness is only determined by the cell size of the microstructure. The crack resistance of the band-like microstructure depends on the ratio of crack propagation in the matrix to crack propagation in the carbide bands. Dependent on the specimen taking fracture toughness of the hot worked material lies between that of the pure matrix and that of the hard phase network. Crack deflection is a minor important factor as can be seen by comparing Fig. 6 with Fig. 7. The three-point bending tests were numerically modelled using the FE-method. The macroscopic model presented here takes into account the anisotropy of material properties caused by the inhomogeneous microstructure and the stress limitation in the plastic zone. It disregards local effects such as particle cracking or decohesion. As discussed earlier, generally this local damage influences macroscopical crack propagation. Thus, good agreement between model and experiment could only be expected in those cases where local damage is restricted to a very small zone ahead of the crack tip. Assuming that the size of this damage zone depends on the size of the plastic zone leads to the conclusion that good agreement should only be achieved in the hardened and low tempered state. Moreover, in the pure matrix material no damage of the

Fracture of ledeburiticchromiumsteels

323

described kind is expected. Indeed, in those cases the experimental results could be modelled quite well (see Fig. 13). In D3-steel in the soft annealed condition the size of the damage zone cannot be neglected. For all specimens in this ductile state fracture toughness was determined using the J-integral concept. J is proportional to the potential energy Upot [eq. (2)]. If damage occurs ahead of the crack tip the compliance of the specimen increases. Let us compare in a theoretical experiment two specimens equal in crack length, one undamaged and one with a damage zone ahead of the crack tip. The potential energy at a given force would be higher in the damaged specimen. Therefore, the experimental determined J increases with the size of the damage zone. J can be interpreted as energy flux to the crack tip during a differential crack growth. In the case of local damage J is the sum of the energy flux towards all discontinuities within the area of interest. In the numerical model the main crack is the only discontinuity and thus, J describes only the

Fig. 15.

324

H. BERNSet al.

energy flux towards this crack tip. If damage occurs before macroscopical crack growth the experimentally determined J-integral is therefore expected to be higher than the computed J. This idea is supported by the results plotted in Fig. 13, examining the graphs for the net-like microstructure and the L-T orientation of the band-like microstructure. The T-L-orientation shows good agreement between experiment and model in the whole hardness range. The reason is that in this orientation no local damage develops ahead of the crack tip before the onset of macroscopical crack propagation, even in the soft annealed state. As soon as carbide fracture occurs unstable crack propagation starts along the carbide bands. This effect was proved by experiment. Figure 14 shows the change in the stress intensity factor KI by increasing the force. As long as the deformation field is linearly elastic, this function is a straight line as predicted by linear elastic fracture mechanics. Plastic deformation in front of the crack tip leads to a progressive deviation from this straight line. The increase of the slope of this curve is higher under the assumption of plane stress as compared to plane strain. In other words, a crack under plane strain conditions requires a higher crack length ratio a/w for a given KI as a crack under plane stress conditions. In fracture mechanical specimens the behaviour of the bulk can be well described by plane strain, while the specimen's surface is characterized by plane stress. Thus, assuming the specimen to be constructed out of several layers without any mechanical interactions in between leads to an arched form of the crack front. This shape was indeed found by experimentation (Fig. 15). The difference between the states of plane stress and plane strain might be expressed in terms of triaxiality (, where ( is defined as the ratio of hydrostatic mean stress ah and effective von Mises stress aeq. Under plane strain conditions ( is much higher as in the case of plane stress. As found elsewhere [20] the most important mechanism for crack p~opagation is the local degree of triaxility. These results are supported by the current investigations. As mentioned before the curved crack front depends on the degree of plastic deformation, which was also proved by experiment: in contrast to the soft annealed state the hardened and low tempered specimens did not show the arched shape of the crack front. New results show that microcracking in front of the main crack due to carbide cleavage begins at the surface of the specimen [21]. Thus, one can conclude that in the case of hardened material macrocrack propagation is mainly governed by microcrack initiation, while in the soft state this kind of local damage also occurs, but is less dangerous. In the latter case propagation of the macrocrack is governed by crack propagation in the matrix, which depends on the local degree of triaxiality.

5. CONCLUSIONS The experimental determined fracture toughness of D3 steel depends on the hardness of the metal matrix, on the distribution of eutectic carbides and in case of hot worked material on the orientation of the specimen with respect to the rolling direction. In the hardened and low tempered state fracture toughness is mainly determined by the width of the crack path. High deflection of the crack path causes high fracture toughness. The crack deflection of the net-like microstructure (i.e. the as-cast condition) corresponds to the mesh size of the eutectic network, and therefore depends only on the cooling conditions. Fracture toughness might be increased by increasing the cell size. In the soft annealed state the fracture toughness depends on the part of crack propagation through the metal matrix. Thus, the netlike microstructure shows the lowest Kit-values while the L-T orientation is the optimum. The three-point bending tests were numerically modelled taking into account the anisotropy in elastic and plastic material behaviour. A good agreement between experiment and model was achieved in the hardened and low tempered conditions. The differences between numerical and experimental determined J-integral could be used as an indicator for the occurrence of local damage ahead of the main crack tip before onset of macroscopical crack propagation. Acknowledgements--The authors would like to thank the European Union (EU) which sponsored the research activities

under contract numberBRE2.CT92.0150.

Fracture of ledeburitic chromium steels

325

REFERENCES 1. Berns, H., Fischer, A. and H~insch, W., EinfiuB der Carbidorientierung auf Bruchz~ihigkeit und abrasiven VerschleiBwiderstand ledeburitischer Kaltarbeitsst~ihle. HTM, 1990, 45(4), 217-222. 2. Kiintscher, W. and Werner, K., Technische Arbeitsst(ihle, Vol. 3. VEB-Verlag Technik, Auflage, Berlin, 1966. 3. ASTM E 399-74, Standard test method E 399-74 for plane-strain toughness of metallic materials. In 1976 Annual Book of A S T M Standards. ASTM, Philadelphia, PA, 1976. 4. Berns, H., Restaustenit in ledeburitischen Chromst~ihlen und seine Umwandlung durch Kaltumformen, Tiefktihlen und Anlassen. HTM, 1974, 29(4), 236-247. 5. Broeckmann, C., Bruch karbidreicher St~hle--Experiment und FEM-Simulation unter Beriicksichtigung des Gefiiges. Dissertation Ruhr-Universit~it Bochum, s.a. Fortschr.-Ber. VDI, Reihe 18, no. 169, Diisseldorf. 6. Schwalbe, K. H., Bruehmechanik metallischer Werkstoffe. Carl Hanser, Miinchen, 1980. 7. Clarke, G. A., Andrews, W. R., Begley, J. A., Donald, J. K., Embley, G. T., Landes, J. D., McCabe, D. E. and Underwood, J. H., A procedure for the determination of ductile fracture toughness values using J-integral techniques. Journal of Testing and Evaluation, 1979, 7, 49. 8. Owen, D. R. J. and Fawkes, A. J. F., Engineering Fracture Mechanics: Numerical Methods and Applications. Pineridge, Swansea, 1983. 9. Hill, R., The Mathematical Theory of Plasticity. Oxford University Press, New York, 1971. 10. Budiansky, B. and Rice, J. R., Conservation laws and energy-release rates. Journal of Applied Mechanics, 1973, 3, 201-203. 11. Raju, I. S. and Sbivakumar, K. N., An equivalent domain integral for analysis of two-dimensional mixed mode problems. In Proceedings of the 30th AIAA Meeting, 3-5 April, 1989, paper AIAA, pp. 89-1299. 12. Ishikawa, H., Kitagawa, H. and Okamura, H., J integral of a mixed mode crack and its application. ICM3, 1979, 3, 447-455. 13. Theilig, H., Wiebe, P. and Buchholz, F. G., Computational simulation of non-coplanar crack growth and experimental verification for a specimen under combined bending and shear loading. In Proceedings of the 9th European Conference on Fracture (ECFg). Varna, Bulgarien, 1992, pp. 789-794. 14. Hiinsch, W., Geffige und Bruchz~ihigkeit ledeburitischer ChromstS.hle--Messung und Finite-Elemente-Nachbildung. Dissertation Ruhr-Universit~it Bochum, s.a. Fortschr-Ber. VDI, Reihe 18, no. 81, Diisseldorf. 1990. 15. Olsson, L. R. and Fischmeister, H. F., Fracture toughness of powder metallurgy and conventionally produced highspeed steels. Powder Metallurgy, 1978, 1, 13-28. 16. Kasteele van de, J. C. W. and Broek, D., The failure of large second phase particles in a cracking aluminium alloy. Engineering Fracture Mechanics, 1977, 9, 625-635. 17. Fischmeister, H. F. and Olsson, L. R., Fracture toughness and rupture strength of high speed steels. In Proceedings of the International ConJerence on Cutting Tool Material. ASM-CIRP, Cincinnati, OH, 1980, ASM, Metals Park, OH, 1981, pp. 111-131. 18. Maekawa, I., Tanabe, Y. and Lee, J. H., The influence of non-metallic inclusion on the fracture behaviors of 25Mn5Cr-lNi austenitic steel. Engineering Fracture Mechanics, 1987, 28, 577 587. 19. Berns, H., Broeckmann, C. and Weichert, D., Fracture mechanisms in particle reinforced metal matrix composites. In Proceedings of the International Conference on Failure Analysis and Prevention, 23-26 June, 1995, Beijing. 20. Shan, G., Kolednik, O. and Fischer, F. D., A numerical study on the crack growth behaviours of a low and a highstrength steel. International Journal of Fracture, 1996, 78, 335 346. 21. Broeckmann, C., Fracture of tool steel on a microscopical scale. In Proceedings of the 4th International Conference on Tooling, 11. Bochum, 1996, pp. 491-499.

(Received 11 November 1996, in final form 10 July 1997, accepted 5 August 1997)