On the influence of microstructure on crack propagation mechanisms and fracture toughness of metallic materials

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M~~honier, 1977. vol. 9, pp. 793-332.

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ON THE INFLUENCE OF MICROSTRUCTURE ON CRACK PROPAGATION MECHANISMS AND FRACTURE TOUGHNESS OF METALLIC MATERIALS KARL-HEINZ SCHWALBE German Aerospace Research Establishment (DFVLR), 5000 KMn 90. Gennany Abntmct-A survey is given on the effect of microstructure on crack propagation mechanisms and fracture toughness. The intluence of inclusions and of the material’s matrix are treated separately. An attempt was made to correlate some simple, but typical microstructures with corresponding crack propagation mechanisms and to establish a qualitative sequence of these microstructures with respect to their effect on I&. Because of the lack of suthcient experimental evidence this attempt is necessarily incomplete. Finally, some K,.-calculations are compared with measured values.

NOTATION cross section before test Ar cross section at fracture d particle distance, dimple dieter d* qicrostructuraf element size d, thickness of grain boundary. (I in Ti-alloys A0

D grainsize D' grain size for oV =a., D. a grain size DE D E F Gr. I$ K KC Ko T u W

B-size thickness of precipitate free zone Young’s modulus force critical strain energy release rate stress intensity rate of stress intensity plane strain fracture toughness candidate value for KC temperature volume fraction plastic deformation work

Greek symbols 8,

6, c e, c; et 4 e, c, lr A k Y po Q (~a or (rT u, av TV 0 O* $3

crack

tip opening displacement crack tip advance displacement strain u&xiai true fracture strain true fracture strain of plane strain tensile specimens fracture strainat crack tip uniformehgation strain crack tip strain strain in y-direction u,.fE mean free path between primary(I particles in Ti-alloys shear modufus Poisson’s number effective root radiusof a crack stress cleavage stress true fracturestress tensile stren@h stress in y-direction yield strength oul2 length of plastic zone 0 at fracture length of zone of intense plastic deformations

1. INTRODUCTION of a material, especially plastic deformation and fracture, are determined by its microstructure. Therefore, the treatment of these properties by continuum

THE MECHANICALproperties

795

7%

KARL-HEINZSCHWALBE

mechanics has limitations. It is obvious that mechanical considerations must incorporate the microstructure of the material, i.e. microstructure mechanics are necessary for the understanding of the mechanical behavior of materials. Basing on dislocation theory, considerations of that kind have been applied successfully on the plastic behavior of metals. But because of greater complexity, a microstructure mechanics theory of fracture is still lacking. It is even not yet possible to establish an empirical system of the effect of microstructure on crack propagation and fracture since the presently .available experimental evidence is still too fragmentary. Two reasons may be responsible for that: (a) Microstructures of metallic materials exhibit such a variety that a great number of parameters have to be varied. (b) It is not always possible to describe the microstructure accurately. The knowledge of the influence of microstructure on crack propagation properties gains increasing interest since it can support the solution of some interesting problems: (a) Systematic development of tougher alloys. (b) The inverse relationship between strength and toughness of a specific material. (c) A material heat treated by different procedures resulting in identical strength levels can exhibit quite different toughness values. (d) Different materials with different strengths can be equally tough and vice versa. (e) The design of physical models for the calculation of crack propagation requires detailed information about the mechanical behavior of the elements of the material’s microstructure in the stress and strain field of a crack. In spite of the limitations mentioned above, it may be useful to give a tentative survey on empirical results concerning the effect of microstructure on crack propagation properties. Only crack propagation under static load will be considered. The preparation of the present paper has been stimulated by the excellent compilations of G. T. Hahn and co-workers. 2. MICROSTRUCTURR In the following, those elements of the microstructure of a metallic material[l] appearing essential for crack propagation and for which experimental results with respect to their influence on toughness are available will be briefly introduced. In the simplest case a metallic material consists of a single crystal of a pure metal with a specific orientation. However, technical materials are usually polycrystalline, Fig. l(a). In alloys the alloying elements can be in solid solution. The material consists then still of a single phase. In other cases the alloying elements form a second phase #l (or several phases), which is distributed in the first phase a (Fig. l(b)) or exists along with the latter in the form of Fig. l(c). Both phases can be pure metals, solid solutions, or compounds with nonmetals (for example 0, N, C, S, P) or with metals (intermetallic compounds). The boundaries between crystals of the same kind are designated grain boundaries; those between different phases are designated phase boundaries[2]. In Fig. l(a) there are only grain boundaries aa, in Fig. l(b) aa grain boundaries and a/3 phase boundaries, in Fig. l(c) aa and /3/I grain boundaries and a/3 phase boundaries. Fiiy, a phase can occur along the boundaries of the a phase as discrete particles (Fig. l(d)) or as a continuous three dimensional network (Fig. l(e)). In technical materials each type sketched in Fig. l(b)-(e) can occur along with one or several other types, with two or more phases. The configuration of Fig. l(b) occurs often as a dispersion or precipitation of small, hard particles in the soft a-phase often designated as “matrix”. For a given volume fraction, u, of the second phase the mean particle distance, d, can be calculated [3] as d=Dj/($)(l-s) if the particle diameter, D, is known. Finally, in Fig. 2 two examples of anisotropic microstructure are shown[l].

197

Crack propagationmechanismsand fracturetoughnessof metallic materials

a)

b)

b)

dl (b) e) Fig. 1. Fig. 2. Fii. 1. Some types of microst~ciures of metallic materials,partly accordin to Hombogen[l]. (a) Si@e phase, polycrystallinemetallicmaterial.(b) two phase material,/3 in a. (c) two phase mate& fl and (I with approximatelyequal volume content (d) sewnd phase particlesalong the grainbowlaries of the firstphase. (e) continuousnetwork of the second phase alon the grainboundariesof the first phase. Fii. 2. Aligned particlesof a second phase.

3. CRACK PROPAGATION BY CLEAVAGE Many structural materials, namely non-alloyed and low alloy steels exhiiit a characteristic transition behavior which manifests itself as a rapid decrease of toughness with decreasing temperature. The transition is related with a changeover from the ductile dimple mechanism to crack propagation by cleavage. Several investigations[47] have demonstrated that the yield strength, au, and the cleavage fracture stress, SI, are the major material properties controlling plane strain fracture toughness, when crack propagation occurs by cleavage. With decreasing difference between both quantities the fracture toughness decreases, since small plastic deformations and hence low applied loads are needed to raise the local stresses near the crack tip from the yield strength level to the cleavage fracture stress level. In this context the grain size is an important microstructural element since the difference between CT~and ucr decreases with increasing grain size, D[8], Fig. 3. The figure suggests that also the strain hardening behavior of the material should be of importance. The grain size, D’, above which (rCl= au decreases with decreasing temperature. At D + D’ yield strength and cleavage fracture stress converge and macroscopic plastic deformations cease. Hence, grain refinement should result in an increase of fracture toughness. Application of these considerations on the transition temperature predicts, that large difference between UY and (~~1,low strain hardening exponent and fine grain result in a low transition temperature. Experimental data[7,9,101 show, that grain refinement indeed shifts the transition temperature to lower values but that below the transition temperature (where the difference between UY and uCIis small or even zero) grain size has no large effect on KC.

( f-Jl)-l/Z

D-n

Fig. 3. Influenceof 8rain size on oy and CT=,, Tetelmanand McEvily[8].

798

KARL-HEINZ SCHWALBE

According to a compilation of Rosenfield, Hahn, and Embury [ 1l] the cleavage fracture stress of steels is mainly dependent on the ferrite grain size and can be approximated by ucr = 343 + 103D-“2 (MN/m3

(2)

when D is inserted in mm. The actual values scatter about this relation. This scatter is mainly due to difIerent carbide morphologies [ll, 121.Pearlite grains and grain boundary cementite act as effective obstacles for dislocation motion. Hence, dislocation pile-ups cause large local tensile stresses and correspondingly low applied fracture stresses, ~~1.Spherodization, therefore, increases the cleavage fracture stress and should increase IL, too. Apart from cleavage fracture by dislocation motion cracks formed in carbides or other precipitates can spread into the surrounding ferrite grain [ 131.In addition, twinning can cause cleavage fracture, too [8]. Systematic investigations[9, M-161 have shown that the effect of grain size on K,= is comparable to that of the loading rate, K. Increasing the inclusion concentration, u, has probably the same effect as increasing D and K [ 171. This is schematically illustrated in Fig. 4. Figure 4(a) shows a load/crack opening diagram as usually recorded during fracture toughness tests, and Fig. 4(b) shows the temperature dependence of K,=.The numbers of the sketches of the crack propagation mechanism in Fig. 4(c) correspond to the numbered points in Fig. 4(a, b). At low temperatures (high K, large D) and correspondingly low toughness, fracture occurs within the linear portion of the F-COD-diagram, point 1. Crack tip deformation is very limited, and cleavage fracture is initiated immediately at the crack tip [18]. Increasing temperature allows more plastic crack tip deformation and hence increased crack tip blunting, point 2. At the begimiing of the sharply rising portion of the &-T-curve the plastic deformation now possible is sufficient for dimple formation at the crack tip before the conditions for complete cleavage fracture are fulfilled, point 3. At even higher temperatures (smaller grain size, lower K, lower u) an increasing amount of ductile crack propagation prior to cleavage initiation is possible, point 4. Finally, the value of IL is determined entirely by the ductile rupture process instead of cleavage initiation. The surface of final fracture can be of pure cleavage type or of mixed cleavage dimple type[181 but only the crack propagation mechanisms close to the crack tip (at most 2% crack length increase) determine the value of Kr,. The levels of the lower shelf portions of the curves in Fig. 4(b) don’t differ very much from each other, they may even coincide since there is no large effect of grain size, loading rate and inclusion content on Kr, [7,9,15-181.

cl al

b) TV/

F

’

3 f

f 2

T. K,,

/

Fig. 4. Schematicalrepresentationof the influenceof grainsize, loadingrate and inclusioncontenton crack propagationmechanismand fracturetoughness.

4. DUCTILE CRACK PROPAGATION 4.1 Injbence of inclusions This chapter deals with the influence of the material purity, i.e. of inclusions, on KIC,whereas in the following chapter the influence of the matrix will be discussed. This classification is insofar

199

Crack propagationmechanismsand fracturetoughness of metallic materials

arbitrary as the matrix itself can contain precipitates, i.e. particles of another phase. But it was chosen since it is often used and since inclusions are caused by impurities, which often don’t contribute to the material’s strength. This is the situation of the configuration shown in Fig. l(b). The significance of inclusions for ductile crack propagation and hence for fracture toughness can be discussed by means of Fig. 5, which shows the well-known dimple formation mechanism. At low stress intensities the crack tip is blunted. Both crack faces are displaced at the crack tip by the amount S, (crack tip opening displacement). Constancy of volume of the plastically deformed material and the state of plane strain require negative strains in the x-direction ( = direction of crack propagation) [ 191and hence a crack tip advance displacement, 8,. Due to the large plastic strainS occurring in the plastic zone inclusions in front of the crack fracture and thereby cause the formation of voids. Alternatively void formation can be initiated by decohesion along the particle-matrix interface. Which mechanism is operative depends on the properties of particles, matrix and interface [20]. The voids grow with increasing stress intensity and finally coalesce with the crack tip. In this &ant crack tip blunting ceases. Hence the crack tip radius should be roughly equal to half the dimple diameter [21]. Since the dimple size corresponds to the average distance, d, between inclusions the relation St = d

(3)

is to be expected. Some observations [22] are in accordance with that. The denser the inclusions are, the smaller is the crack tip opening displacement at the instance of first void coalescence with the crack tip. If one assumes that this event bears a relation to the onset of instability under plane strain conditions one should expect an increase of KI, with increasing d. This assumption is based upon the consideration that unstable fracture occurs when crack propagation has taken place along the minimum distance necessary for the development of the crack propagation mechanism. In case of the dimple mechanism this minimun distance equals the inclusion distance. Indeed, it can be shown that fracture toughness increases with increasing material purity, i.e. with increasing inclusion distance. Systematic variation of inclusion content[23-251 yields K,, - v

-(Us).

-(l/S)

(4)

An example is given in Fig. 6 for aluminum alloys.

6txl

fatigue crack

5

-

static crack

Fii 5. Ductile crack propagationby dimple formation.

0.05 Fii.6. Fracturetoughnessof

0.1

0.5 v. %

1

?

some aluminumalloys versus volumefractionof inclusions,0, data fmmr%V 0, data from[25].

800

KARLHEINZ SCHWALBE

In Fii. 7 similarresults obtained on steels are plotted. The diagramshows also the well-known inverse relationship between toughness and strength. The embrittling effect of sulfur is due to dimple formation at sulfides. At low sulfur levels small dimples were observed, which are probably due to cementite particles. A quantitative relationship between KC and d is shown in Fig. 8[26]: (5) 1001

I

I

I

I

I

I

goSULFUR LEVEL 0 0.006% o 0.016 % l 0.025 % 0 O.OL9 %

80-

70N 7 ;

60-

3 Y 50-

40 -

900

800 700

TEMPERING

I

I

200

600

LOO

TEMPERATURE

I

1F I

I

220 240 260 TENSILE STRENGTH

Pi 7. Illnuenceof sulfur level on frachue tougbcss

(

I

I

280 ksi 1

300

of 0.45 C-Ni-C-MO

steels, Bikle et al. [U].

QO-

BOE 70‘E $

60-

&OLO__ Testing

IO0

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I

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I

I

I

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I

2

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6

8

IO

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IL

16

16

(I?-$1 Pii 8. K,c for a

temperature 0 T 200°C o T LOO°C o T 500°C

a.

20

MNmex2

dtic 0.45 C-Ni-Cr-Mo-V steel as a functionof inclusionspacingand yield streagth, Priest[261.

Crack propagationmechanismsand fracturetoughnessof metallic materials

801

where a* = 290 ksi. For a given strength, Kr, is proportional to v/(d). This is in accordance with eqn (3). Not only the volume fraction of inclusions is essential but also kind, size and distribution of the particles. Commercial alloys contain often inclusions with difIerent properties which behave ditferently during the fracture process. The aluminum alloys (2014-T& 2024-T851, 2124T851, 7075-T7351,7079-T651) investigated by Low et al.[25] contain two main types of inclusions with different composition, size and distribution. The 8rst type has dimensions > 2~ and various compositions. It contains from the impurity elements mostly Fe and Si. In ordinary tensile specimens the particles of the 2000 alloys begin to fracture at 0.25% plastic strain; at 5-6% plastic strain one half of the particles are broken. In the 7000-alloys the inclusions are more fracture resistant; the first particles fracture above 1% plastic strain, and at 6% plastic strain only 30% of the particles are broken. It has been observed that the plastic strain necessary to fracture an inclusion increases with decreasing inclusion size. Whereas the particle size determines the onset of void formation the distance between the particles controls void growth. The void forming particles have center to center distances between 7 and 12~. The diameters of the resulting dimples are between 7 and 10~. Void coalescence occurs in a late stage of the fracture process. The matrix between neighbouring voids ruptures by formation of small dimples which can be related to the second inclusion type. The size of this inclusion type is about O.lp, the center to center spacing amounts to 0.2-O&~, depending on the respective alloy. The particles contain the impurity elements Fe, Cr and Si. The good coincidence between dimple size and particle spacing described above, however, cannot be generalized. Burghard [27l has shown that in other aluminum alloys the dimples can be considerably larger than the particle spacing. From that follows that only a certain fraction of the inclusions present in the material contributes to the fracture process. Particle size reduction without changing the volume fraction causes an increase of Kr, in spite of the reduced particle spacing[28]. Evidently, the better resistance of smaller particles overrides the detrimental effect of reducing the particle spacing. Numerous investigations[21,29-341 have shown that fracture toughness can depend considerably on crack orientation. Toughness and ductility are reduced in the transverse, and particularly in the short transverse direction. This effect can be attributed to an alignment of inclusions during mechanical processing (configurations of microstructure in Fig. 2). It is interesting to see how second phase particles influence the material properties determined in a tensile test. The ductility decreases with increasing content of a dispersed second phase[35-371, Fig. 9(a). This is also the case, when the second phase consists only of voids[3]. For a given volume fraction the ductility is the higher the tougher the second phase particles are and the better they are bonded to the matrix[38]. In addition, their shape is an important parameter. Figure 10 demonstrates how the ductility of the steels investigated by Gladman et al. [373depends on size and type of the second phase particles. Sulphides are more detrimental to ductility than carbides, plate sized particles are more detrimental than equiaxed ones. The mechanism of Fig. 5 suggests that there should be any relation between toughness and ductility. Therefore the findings mentioned above are expected to yield some information about fracture toughness behavior: fracture toughness should exhibit the trend shown in Fig. 10. The other material properties exhibit different behavior. Edelson and Baldwin[3] found for powder metallurgically produced copper with several types and contents of dispersed particles a decrease of the true fracture stress (Fig. 9(b)) and of the strain hardening exponent with increasing volume fraction. The yield stress increases with increasing D in those systems where the dispersed particles are well bonded to the matrix. Yield stress and tensile strength of nickel increase with increasing volume fraction of A1203 particles (Cremens and Grant[35]). The unalloyed steels investigated by Liu and Gurland[36] with spheroidal cementite exhibited an inverse relationship between tensile strength and u. 4.2 Influence of the matrix The influence of the matrix on fracture toughness is evident from the plots in Figs. 7 and 8 since at given volume fractions of inclusions tensile strength and yield stress are matrix properties. But, as will be shown below, strength is not the only parameter by which the matrix affects fracture toughness.

KARL-HEINZSCHWALBE I.5 0

0 x 0 0 0

COPPER-IRON-MOLY COPPER HOLES COPPER CHROMIUM COPPER ALUMINA COPPER IRON COPPER MOLYBDENUM

0 COPPER m COPPER

1.0

ALUMINA SILICA

GB + z i 5

0.5

2

0.2

0.1 ” (a)

-0

O.OL

0.08

0.16

0.12

0.20

0.2k

0;6

” 0.4 FI.

9. JSect of dispersedphasesontruefracturestrain(a), and truefracturestress (b), of copper;Edelson and Baldwia[3].

4.2.1 Steels. The physical mechanism by which the matrix strength affects fracture toughness has been investigated by Psioda and Low[39] for a maraging steel. The decrease of KC with increasing strength is accompanied by a decrease of dimple size. When strength is increased the normal stresses, u,, in the plastic zone increase according to[40]

(6) Thus, smaller particles (which withstand higher stresses than larger ones) can contribute to dimple formation, and the average effective inclusion spacing and hence the dimple size decrease. The material behaves as if it had more inclusions. A similar observation was made by the present author [41] who found that the decrease of IL of a maraging steel is correlated with decreasing

Crack propagation mechanisms and fracture toughness of metallic materials

0

I 5

I IO

-

803

IO -0

v, %

Fig. 10. Effect of second phase particles on ductility; Gladman et al. 1371.

dimple size and increasing yield strength when the test temperature is lowered. These findings suggest that K,= decreases with increasing yield strength irrespective of the reason of the increase of uY: low temperature, high deformation rate, or heat treatment, provided the latter causes no qualitative changes of those elements of the microstructure contributing signiftcantly to crack propagation. In that case the crack propagation mechanism is expected to be altered. Increasing strength by tempering has also another effect: because of the increasing normal stresses in the plastic zone and because of the increasing size of the precipitates which strengthen the matrix the precipitates can be incorporated in the crack propagation mechanism. Roesch and Henry [42] observed that in a maraging steel dimples can occur at inclusions and precipitates (see also [39]). The precipitates must exceed a critical size of about 200 A. The critical size decreases with decreasing test temperature which is in accordance with the observations concerning the behavior of inclusions mentioned above. From these observations the conclusion may be drawn, that void nucleation at hard particles is normal stress controlled while coalescence is a deformation process and hence strain controlled. According to Pellissier[31] the high fracture toughness values of maraging steels are the consequence of fine, homogeneously distributed particles of intermetallic compounds while alloyed martensitic steels of similar strength with higher carbon content contain carbides being detrimental to toughness. Maraging steels can be embrittled by slowly cooling in the temperature range lOOO-750°Cafter heating to temperatures above llOO“C,Beachem and Pelloux[431. During this heat treatment titanium carbonitrides form at austenite grain boundaries and provide a path for preferred crack propagation, Fig. 11(a). Evidently, this heat treatment may produce also weak martensite lath boundaries since a considerable proportion of crack propagation can take place along these boundaries, Fig. 11(b). Also in other cases grain and phase boundary precipitates (situation of Fig. l(d) and (e)) are reported to have an embrittlling effect. Wei[44] traces the low toughness values of steel AISI 4340 (Fig. 12) at low tempering temperatures to a carbide film at martensite lath and microtwin boundaries. This interpretation is supported by observations of Liu[45,46] on steel HP 9445. At equal strength, the bainitic condition of this material is superior to the tempered martensitic condition since the carbides are homogenuously distributed and crack propagation occurs by ductile dimple formation whereas the fracture surface of tempered martensite shows only limited plastic deformation. In the as-quenched condition the fracture toughness of steel AISI 4340 and other, similar steels is determined by precipitation at the prior austenite grain boundaries (Parker and Zackay 1471).Increasing the austenitizing temperature from 870 to 1200°Cresults in an increase of the fracture toughness of 4340 from 63.5 to 91.5 MNmm3’* . This effect is attributed to a decrease of grain boundary energy during grain growth which in turn delays precipitation along the grain boundaries. El% VOL. 9 NO. CD

KABLHEINZ SCHWALBE

IOOG 1 Gy

0

u)o

WO

800

1000

Steel A B 0 0 0

l

1200

Tempering Temperature , F Fig. 12. Tensile strength and fracture toughness of steel AlSI 4340as a function of tempering temperature; Wei(441.

When no precipitates are present at the grain boundaries, as it was the case for the low-alloy steel investigated by Robinson and Tuck[48], it is beneficial to toughness to care for a small austenite grain size since coarse austenite grains cause large ferrite and carbide plates while fine austenite grains cause a fine equiaxed structure which exhibits more ductile crack propagation than the coarse structure. Another example of improving toughness by microstructure refinement has been demonstrated by Zackay [49]. Conventional austenitizing and quenching treatment of steel AISI 4130 produces blocky martensite and ferrite, Fig. 13(a). Austenitizing at 1200°Cand quenching in ice brine inhibits ferrite formation and the resulting martensite consists of thin, wide plates, Fig. 13(b). Fracture toughness is improved by this treatment, Fig. 14. Even better results are obtained after additional liquid nitrogen refrigeration (IBQLN). Retained austenite is a microstructure element being advantageous to the fracture toughness of quenched and tempered steels, as reported by several authors [49-521. An example is given in Fig. 15 where the fracture toughness of AISI 4340 steel is plotted versus tempering temperature, Zackay[49]. The heat treatment: austenitizing at 12WC/quench at 87OWoil quench at room temperature provides a lOO-2OOAthick austenite film surrounding the martensite plates (this corresponds to the configuration shown in Fig. l(e)). In addition, the high austenitizing temperature avoids carbide precipitation along prior austenite grain boundaries as already mentioned above. The austenite film is deformed plastically during martensite formation and is thereby stabilized, Lai[53]. Compared with the conventional heat treatment: austenitizing at 87O”C/oil quench K,, increases considerably. Between 200 and 350°C embrittlement occurs, which is related to crack propagation along prior austenite grain boundaries, whereas at all other temperatures dimple formation is observed. This behavior is attributed to segregation of impurities at the austenite grain boundaries[491. The positive effect of retained austenite on toughness can be explained by arrest of cracks originated in martensite in the ductile austenite[50]. According to Antolovich et al. [52] the fracture energy, G,,, of steels with structures consisting of two phases with different properties can be regarded as the sum of the fracture energies, GI,., and G,,,,, of each phase:

G,,= G,,,, * VI+ G&l - u,)

(7)

Fig. 11.Crack propagation in a mamging steel. (a) along a prior austenitc grain boundary, (b) along marte laths; Schwalbc[41].

805

03 Fig. 13. Microstructureof steel AISI 4130; courtesyZackay[49]. (a) austenitizedat 870°C and oil quenched. (b) austenitizedat 1200°Cand ice-brine quenched.

806

Fig. 17. Crack propagation mechanisms in commercial and pure 7075, Liitjering and Gysler[59]. (a) and (b) 7075 (24h, KKPC), K,= = 41 MNm-‘@. (c) and (d) X-7075 (24h, MOT), crack propagation along grain boundaries and slip planes, KIc = 54 MNm-” (d) enlargement of slip plane fracture). (c) and (f) X-7075 (48 hr, 180°C);grain boundary fracture, K,, = 42 MNm-“‘(f) dimples on a grain boundary). Courtesy Ltitjering and Gysler.

807

Fig. 26. Crack propagation in Ti-1lhio along slip planes and grain boundaries, aged at 3WC, 60 hr; courtesy Gysler, Mtjering and Gerold[741.

Fig. 27. Void formation due to (a) slip plane/slip plane interaction in Ti-1lMo, (b) slip plane/grain boundary interaction in Ti-14Mo: courtesy Gysler, Liitjering and Gerold[741.

808

Crack propagationmechanismsand fracturetoughness of metallic materials I20

100

I

I

I

I

I

I

I

Ll30- A, 30°C n I200 IBOLN A 870 OIL v 1100 IBOLN Q 070 IBQLN

-

LOL

AS QUENCHED

100

200

TEMPERING

TEMPERATURE

go9

_

_

LOO

300 (OC 1

Fig. 14. Fracturetoughness of steel AISI 4130 as a function of temperingtemperature;zackay [491.

T 1200-870 870 OIL

OIL

l

AS QUENCHED

100

200

TEMPERING

TEMPERATURE

300

LOO

I OC I

Fig. IS. Fracturetoughness of steel AISI 4340 as a function of temper@ttemperature;Zackay[49].

where u1is the volume fraction of phase 1. Hence, the plane strain fracture toughness is given by KID=

J($

(Gw * ul+ G,c,d - ~1))

>

03)

Rack and Kalish[54] investigating an 18 Ni (350) maraging steel found no toughness improvement after producing a film of reverted austenite by overaging. The beneficial effect of the austenite tilm is balanced by embrittlement of the martensite since overaging results in 200-400 A large precipitates (see Fig. 9(a) in[M]) which serve as void nucleators as already mentioned above. People often try to correlate fracture toughness with other material properties, like yield strength, fracture strain, etc. These attempts can only be successful if these other properties are influenced by the test conditions and by the microstructure in such a way that they are unambiguously related to fracture toughness, i.e. that unambiguous relationships between KJCand the other properties exist. In Fig. 16 several mechanical properties of an alloy steel are plotted versus tempering temperature[SS]. The KrCcurve has a characteristic maximum/minimum shape. The reason for this behavior is not clear yet. Unlike the embrittlement of AISI 4340 steel at 3OOT

KARL-HEINZ SCHWALBE

810

L

0 KI, l

15’

GY

1600

0 6

no

valid //

120 -

K,, b

i - 1500 lT

N 7 E

0.6-

1100

0.5-

1300

f 4 Y 90 O.L- I200

03-

1100

0.06 -

j ODL o02-

I 100

I 200 TEMPERING

I LOO

I 300

TEMPERATURE,

I 500

I 600

700

OC

(b)

Fig. 16. Some propertiesof an alloy steel (0.3X, 0.27Si, 0.63h4n,1.30, 3.3Ni, 0.47Mo)as a function of temperingtemperature;Schwalbe ~IUJBacktisch[SS].(a) fracturetoughness, IL,, yield strength,uv, and logarithmicfracturestrainl,; (b) uniformelongationstrain,e,, strainhardeningexponent, n, dimplesize, d, and microstructural element size, d*. The quantitiesuv, e,, e,, and n have been determinedwith plane strain tensile specimens.

(Fig. 15) the embrittlement of the steel shown in Fig. 16 is not correlated with crack propagation along prior austenite grain boundaries. Crack propagation takes place by dimple formation in the entire temperature range between 100 and 600°C. Dimple size d, microstructural size parameter d*, and true fracture strain, 9, exhibit a similar, but less pronounced shape, whereas the behavior of uniform elongation strain, strain hardening exponent (as defined in[S6]) and yield strength deviates partly considerably. Plots of IL vs each of these quantities fail to yield unambiguous relationships. It is therefore unlikely that it will generally be possible to relate fracture toughness to one other material property, even if in many cases such relationships (IL vs uy, 6. . .) do exist. Relationships of this kind can only be valid within narrow limits. Rather, combinations of material properties like’that shown in Fig. 8 may represent useful correlation parameters. Indeed, theoretical calculations of K,, (see Section 6.2) show that K,, is a function of a number of

Crack

propagation mechanisms andfracturetoughnessof metallic materials

811

properties. One interesti& feature of Fig. 16 is the good coincidence between dimple size and microstructural size parameter. From that the conclusion can be drawn that one dimple is form’ed in one microstructural element. The microstructural elements are martensite plates at low tempering temperatures and ferrite zones between carbide stringers at high tempering temperatures. An interesting group of high-toughness steels is formed by the TRIP (transformation induced plasticity) steels which are austenitic at room temperature by suitable alloying. During plastic deformation the austenite transforms partially to martensite. Two thirds to three fourths of the crack propagation resistance are due to this mechanism, Antolovich and Singh[57]. The phase transformation has an interesting additional effect: the increase in volume due to phase transformation compensates a large portion of the triaxial stresses at the crack tip. This effect causes slow decrease of toughness with thickness[47]. 4.2.2 Aluminum alloys. Liitjering[58] and Liitjering and Gysler[59] have demonstrated that the deformation and fracture mechanisms of 7075 can be significantly changed when the impurity elements Fe, Si and Cr are removed. The alloy is then almost free from both large and small inclusions and fracture toughness increases from 41 to 54 MNm-” in the underaged condition. The improvement by removing the inclusions is accompanied by the following effect. In the commercial alloy the small Cr-rich particles suppress the tendency of age-hardened alloys with coherent precipitates for inhomogeneous slip. Without the presence of these particles, cutting of the coherent precipitates by dislocations and hence slip concentration on relatively few slip bands consisting of soft material takes place. Crack propagation takes place by slip plane and grain boundary decohesion. This slip concentration is avoided by overaging the alloy, but now plastic deformation concentrates on the precipitate-free soft zones at the grain boundaries. Consequently, crack propagation is almost entirely intergranular but with formation of small dimples at q-precipitates which reduce the & value to 42 MN m-3’*. Figure 17 shows micrographs of the mechanisms described above. Since ductility measured in a tensile test and fracture toughness often show the same trends it may be expected that according to the following findings grain size plays an important role [60]. In either case of slip concentration in soft zones-at grain boundaries and at slip planes-the tensile ductility exhibits a l/D dependence[581. Therefore, K,, should increase with decreasing grain size. Plane stress fracture toughness data of Thompson and Zinkham[61] are indeed in accordance with this assumption, Fig. 18. In case of intergranular fracture the grain size dependence can be explained by the increase of the volume fraction of the precipitate free zones with decreasing grain size whereby the local strains in the soft zones decrease. In case of slip plane decohesion the grain size controls the number of dislocations and hence the degree of weakening of the slip planes. 160

FINE. ELONGATED, RECRYSTALLIZED

120 N ‘E

100

f . 80 x”

MODERATE SIZE. LOW

GRAIN ASPECT

60 LARGE

0

1.6

3.2

1.8 SPECIMEN

64

8.0 9.6 THICKNESS.

EQUIAXED

Il.2 mm

12.8

Fig. 18. Effect of thicknesson K. of overaged7000 seriesalloys with various grain sizes; Thompsonand ZinkhamI611.

812

KARL-HEINZ SCHWALBE

The results obtained by Kirman[62] by notched tear tests on 7075, Fig. 19, may also be indicative for the behavior of IL,. Overaging leads to an increasing amount of grain boundary fracture due to increasing size of q-particles at the grain boundaries, Fig. 19(a). A reduction of toughness is the consequence, Fig. 19(b). Comparison of both diagrams in Fig. 19 shows that the critical particle size for onset of grain boundary fracture depends on the aging temperature and covers a range between 200 and 600 A. The data listed in Table 1 indicates that the critical particle size increases with decreasing yield stress. The same finding was already mentioned in the preceding section for maraging steels. Table 1. Critical grain boundary particle size and yield stress of 7075, data from Kiian[62]

Asine

Critical

temperature (“c)

particle size (A)

Yield stress

120

-200

150 I77

=400 -600

= 515 -447 -412

WN/m2)

i= ; IOOOz BOOd 5 600mo

LOO$ g 200y d

o+

I AGING

w z

TIME.

IO hr

100

(a) 900 -

sooOVERAGING, INCREASING AMOUNT OF GRAINBOUNDARY FRACTURE

700 -

*. z 2 600m -I + soo-

_

i g LOOB z 3000 5 2 2008 !z IOO-

5 300 0.

NUMBERS AT SIDE OF POINTS REFER TO AGING TIME IN HOURS

350

100

GO G,.

500

200

550

600

MN/m2

W Fig. 19. (a) Average. grain boundary particle size of 7075 after aging at diierent temperatures, (b) unit propagation energy of 7075 for various aging times at 120’. 150”and 177°C;Kiian[62].

Crack propagation mechanisms and fracture toughness of metallic materials

813

It is interesting to note that the strain hardening exponent shows the same variation with aging time as the unit propagation energy, Fig. 20 (Ostermann[631). The strain hardening behavior of a material influences crack propagation by affecting the ease of void coalescence: the lower the strain hardening, the easier the material between two neighbouring voids collapses. 4.2.3 Tilanium alloys.Because of the dithcult reproducibility of the microstructure of titanium alloys and the resulting large scatter of mechanical properties-especially toughness-a great number of investigations about the influence of microstructure on fracture toughness has already been carried out [64-771.The problem of reproducibility can be illustrated by the results reported in[70] and [75]. In the same bar of Ti6A14V the microstructures: equiaxed, equiaxed+ Widmannstatten and Widmannstatten were found with KQ values between 41 and 78 MN m-” (the symbol Ko is used since not all ASTM requirements were fulfilled). The material was in the mill annealed condition. In the investigations described below equiaxed and Widmannstatten structures were obtained by quenching and aging resulting in primary a and aged /3. Greenfield and Margolin[69] derived empirically a relation between fracture toughness and microstructural parameters. Unfortunately their fracture toughness measurements did not meet entirely the conditions for valid K,, determination. Therefore, their results are expressed in terms of KQ rather than K,,. For equiaxed microstructure of Ti5.25A15.5V0.9FeOXu the authors obtained KQ = 46 + 43010,

(9)

vrith KQ in MN rnm3’*and De (j3 grain size) in p. Hence, the grain size of the /3 phase is the toughness controlling microstructural parameter. Strength, however, depends also on the (r grain size and the mean free path between the primary a particles. The Widmannstatten structure exhibits a similar relationship, but now the soft Q!film at the fl grain boundaries gives an additional contribution to KQ (configuration Fig. l(e)): K0 = 46 + 430/D8 + 1l(D, - 2.6) in MN m+‘*

(10)

where D, denotes the thickness of grain boundary a in k. The thickness of the a film must exceed 2.6~ to contribute significantly to toughness. At D, = 5.5~ the K, increase due to the a film takes a saturation value of about 26 MN me3’*. Similar investigations of Rogers [72] on various alloys did not confirm the relations described above. Rather, for equiaxed grains Rogers obtained in MNmm3’*

(11)

where A denotes the mean free path between primary Q particles in Jo and a the mean aspect ratio of primary a particles. For the Widmannstatten microstructure Rogers did not succeed in finding a correlation between fracture toughness and microstructural parameters. The discrepancy between the results of both investigations may be partly due to different microstructures since the comparison of the respective micrographs show different microstructural patterns in spite of equal disignations “equiaxed” and “Widmannstatten” (see Figs. 2 and 3 in[69] and Figs. 1 and 2 in[72]).

0

100

Fii. 20. Strain hardening exponent

vs

200

300 Gy. MNlm’

yield strength of 7075,0,

LOO

500

600

underaged; 0, overaged; Ostemann[63].

814

KARL-HEINZ SCHWALBE

Also Crossley and Lewis1641could not confirm eqn (IO) for equiaxed Ti6A14V. Their data fit the relation

KI, = 46 + 88lI.X.in MN rnm3”.

(121

The crack propagation mechanism in Widmannstatten and equiaxed (Y+/I structures is characterized by dimple formation. In both kinds of structure the crack propagates along the (r - /3 interfaces [69]. Greenfield and Margolin [69] explain the positive effect of the a film at the $I grain boundaries by the high toughness of the a phase. When the film exceeds a certain thickness KQ cannot increase further since the crack does not propagate in the interior of the (Yphase but along the a - fl interface. When the LYfilm is too thin, it cannot deform independently from the surrounding /3 phase. So its contribution to fracture toughness vanishes. In Widmannstatten structures Rogers [72] observed transcrystalline crack propagation. The crack deviates frequently from its macroscopic propagation direction. Therefore, the true fracture surface and hence the work necessary for crack propagation increase. Figure 21 shows a plot of the dimple size observed on fracture surfaces of Ti6A14V [75] as a function of the grain size. The plot contains equiaxed, Widmannstatten and mixed structures. In fine-grained structures a dimple is formed in each grain, coarser structures tend to develop more dimples per grain (see also d and d* in Fig. 16(b)). In contrast to the findings cited above, fracture toughness measured in this investigation tends to increase with grain size, Fig. 22. In this diagram

6 12 0 10 D. CI Fig. 21. Dimple size vs grain size, TiAl6V4, Gaida, Munz and Schwalbe[‘lS]. 2

90

I

I

I

Ko O Ko l

80,

#I 8

70*

2

‘E

60-

s so-

:

y”

lQ

.

J LO

0 0

0

0

30-

20’

I

I 2

L

6

I 0

10

12

Fig. 22. KQ and S@CSS intensity, I&, at onSet of crack propagation vs grain size for Ti6A14V;Gdda, Mung and Bchwalbe[75].

815

Crack propagationmechanismsand fracture toughnessof metallic materials

two characteristic K-values +re plotted, namely K,, that is the stress intensity at the onset of crack propagation, and K,, that is the stress intensity at 2% crack growth. It can be concluded that the onset of crack propagation is relatively insensitive with respect to grain size whereas crack growth (because of its definition I& is a measure for crack growth) does exhibit an increase with increasing grain size although a large scatter is present. The same result is obtained when K. and KQ are plotted versus the uniaxial fracture strain, Fig. 23. Ductility is a better correlation parameter since this quantity is influenced by the microstructure in a similar manner as K,=. The discrepancies between the toughness/grain size relations of the aforementioned investigations may be attributed to different yield stress/grain size trends. Greenfield and Margolin[69] held the yield stress constant for the entire investigation; for one of his alloys Rogers [72] obtained increasing (ro.2with decreasing D; Galda, Munz and Schwalbe [75] found uo.z tending to decrease with increasing D. These results show again that correlations between K,, and another, single material property can be valid only within narrow limits. In the investigations being now described solution and aging temperature were varied in order to obtain various microstructures. According to Curtis and Spurr [66] aging after quenching from increasing temperature results in the following microstructures: large a plates in /3 matrix a particles in /3 matrix fl particles in (Ymatrix

TQ

I

Increasing the solution temperature increases the amount of metastable transformation products, Fig. 24. In this graph yield stress and fracture toughness are plotted, too. The authors[66] conclude, that the amount of transformation product is more important for the mechanical behavior than its morphology and that precipitation of a and j3 particles is approximately equivalent with respect to mechanical properties. With increasing aging temperature and time the precipitates coarsen and become less numerous whilst the yield stress decreases and K,, increases. In contrast to these results are the findings of Feeney and Blackbum[68] who investigated the beta alloy Ti-1 1.SMo-6Zr-4SSn. With increasing aging temperature and aging time precipitates of the brittle w phase grow in size. This is accompanied by an increase of yield stress and decrease of fracture toughness, Fig. 25. When the o particles are larger than 1008, fracture toughness is no longer affected by the size of w precipitates. The decrease of Krc with

0.L

I

I

I

0.5

0.6

07

E‘

=I”1

l-4

Fig.23.& andstressintensityK,,.at onset of crack propagationvs ductility for Ti6A14V; and Schwabe[75].

&Ida, Mung

816

KARL-HEINZ SCHWALBE

p TRANSUS

9ooL

900 SOLUTION

J

-1

1050

950 1000 TEMPERATURE, OC

Fk.

24. Effect of solution temperature on tensile and fracture properties of Ti6A14V (aged 680% 4 hr, air cooled after solution treatment) and on amount of metastable quench product; Curtis and SpurrM.

A TENSILE YIELD STRESS 0 COMPRESSIVE YIELD STRESS

,200

A KI, a)

- 100

, I

-80

“E z‘ I IOOO-

- 60 ‘E

G-

-a

s 5

800-

Y

. 0

- 20 600

1

0 1000

0.1 1600’-

A TENSILE

AGING

TIME.

YIELD

STRESS

hr

100 80 N 60 TE

b) LO

I Y

i

20

? loo00 AGING

TIME,

hr

Fii. 25. Effect of u phase precipitation on yield stress and fracturetou&ess of Ti-I lJMo-Ur4.5Sn. (a) aging temperature = 2900~; (IY)aging temperature = 370”~; 100 and WA indicates the size of the (I) particles Feeney and Blackbume[681.

increasing o size is accompanied by a change of the crack propagation mechanism (Gysler, Liitjering and Gerold[74]). Precipitation of coherent o particles causes inhomogeneous slip distribution. The crack propagates along grain boundaries or slip planes, depending on the aging conditions, Fig. 26. On both kinds of fracture surfaces fine dimples can be observed. These dimples are the result of slip plane/slip plane or slip plane/grain boundary interactions, Fig. 27. The dimple distance coincides with the distance between slip planes and not with the distance between precipitates or inclusions, Fig. 28. In this case the soft zones are detrimental to toughness.

817

Crack propagation mechanisms and fracture toughness of metallic materials

#’

/

‘f

I

I

I

2

2.

I

6 PARTICLE

* HOMOGENOUS INHOMOGENOUS

I

-

IO 50 SPACING. 1

SLIP SLIP

l

Fig. 28. Dimple distance vs particle distance for some age hardening alloys; LGtjering[78].

In the quenched condition slip distribution is homogeneous and dimple formation occurs primarily at large inclusions. Figure 29 gives a survey on fracture toughness data of Ti6A14V, Crossley and Lewis [64]. An inverse relationship between KI, and uo.2 with a large scatter can be recognised. The Widmannstatten and aged martensite structures are superior to the equiaxed structures. The fine equiaxed condition exhibits two very different KICvalues. Comparison of the micrographs shown in[64] demonstrates that the higher KIC value can be related to some grains with Widmannstatten pattern. In contrast to findings cited above the coarse equiaxed structure seems to be superior to the fine equiaxed structure. The micrographs, however, show, that the coarse microstructure contains many grains with Widmannstatten structure. This indicates that it is difficult to describe accurately the microstructure of an (Y+ /3 titanium alloy. If the grain size of the conditions tested in[641 is determined by counting each lamella as a grain the plot in Fig. 30 is obtained. For aged structures the grain size has been determined according to Fig. 31. The correlation is to some degree better than in Fig. 29, but again it is obvious that a correlation between KIC and a single other material parameter is not successful. Finally, some problems arising with fracture toughness testing of titanium are to be mentioned. It has been shown[75,79] that titanium exhibits steeply rising R-curves, even in plane strain. Thus, KIC determined by the ASTM secant method depends significantly on

ll0l

FINE FINE

IOO-

0

x

COARSE COARSE

x

802 0

V

70-

x

A

f Y

-

T x

_

ANNEALED p TRANSFORMED

EOUIAXED. EOUIAXED,

MARTENSITIC,

.

VW E

ANNEALED p TRANSFORMED

WIOMANSTATTEN. WIDMANSTATTEN.

O

90 -

EDUIAXEO EDUIAXEO.

ANNEALED p TRANSFORMED

AGED

’ I

60T

‘!

A

so-

LO30 700

I

800

1

900

I

Km0

I

I

1100 I200 67. MNlm2

Fii. 29. Fracture toughness of Ti-6AMV

I

1300

I

IL00

1

1500

vs yield stnss: Crossley and Lewis[t%J.

1

1600

I

818

KARL-HEINZ SCHWALBE 100

I

I

a a

go-

80 N

‘:

E 70I i

v

v

lV A

v

fl

60-

Y A 50-

A A

A

v

.

LO30

I

I

5

IO 0. P

Fig. 30. Fracture toughness data of Fig. 29 vs grain size.

tronsfqrned

p

p

Fig. 31. Grain size determination for aged /J structures.

specimen size, i.e. Krcincreases with increasing specimen size. Hence, Krcvalues can only be compared when they are obtained on equally sized specimens. Looking at the inlluence of heat treatment on fracture toughness one should be careful if the heat treatment involves rapid cooling. Because of the low heat conductivity of titanium the thickness of the cross section can affect the microstructure. In addition, it is to be expected that there are ditIerent properties near the specimen surface and in the interior of the specimen. 5. SUMMARY AND CONCLUSIONS The following discussion willbe carriedout by means of Fig. 32. In metallic materials a great variety of crack propagation mechanisms is observed. Under certain circumstances low and medium strength steels like some other ductile materials, lose their ductility and fracture by low energy cleavage (Fig. 32(a)). This ductile/brittle transition is caused by low temperature, high deformation rate, and triaxial stress state. Microstructural features affecting the transition and the crack propagation properties below the transition are the grain size of the cleaving phase (i.e. ferrite for steels) and the morphology of a precipitated hard phase (carbides in steels). Both parameters influence the effectiveness of dislocation pile-ups which cause the ferrite cleavage. While fracture toughness seems to be,rather insensitive to grain size well below the transition temperature it is strongly affected by grain size in the transition range (see Fig. 4). Concerning carbide morphology, only some information on cleavage stress is available which in turn affects K,.Systematic investigations about the influence of microstructure on fracture toughness when cleavage is the dominating mechanism are still lacking. The formation of dimples is the typical process for ductile crack propagation. The prototype and best established dimple mechanism is a consequence of the presence of hard particles (inclusions or precipitates) in a ductile environment. Brittle fracture of a particle or decohesion at the matrix/particle interface lead to the formation of voids and consequently of dimples. Other, less known void and dimple formation mechanisms are due to slip plane/slip plane or slip

Crack propagation mechanisms and fracture toughness of metallic materials

dl

12)

(11

&

/-

/

9

s)

h)

Fii. 32. Crack propagation mechanisms(a) cleavage crack propagation.(b) dimple fracturedue to coarse particles.(c) dimple fracturedue to fine particles.(d) dimple fracturedue to coarse and 6ne particles.(e) intercrystallinecrack propagationdue to grainboundaryprecipitates.(f) intercrystallmecrack propagation due to a hard phase grain boundary t%n. (9) crack propagationmechanisms when a soft phase grain boundaryfilm is present.(II)crack propagationby slip planehlip plane interaction.(3 crack propagationby slip plane/grainboundaryinteraction.(i) crack propagationsolely by plastic blunting.

plane/grain or phase boundary interactions. In technically pure alloys large inclusions are often responsible for crack propagation since they fracture after small deformations (Fig. 32(b)). They provide the crack path with the lowest energy. Fracture toughness increases with decreasing particle size, with increasing particle spacing, and with the homogeneity of the particle distribution. For a given volume fraction of particles IL can be increased by particle refinement in spite of reduction of particle spacing (Fig. 32(c)). The former effect is more effective than the latter one.

KARL-HEINZ SCHWALBE

820

If inclusions are removed by suitable manufacturing procedures such that they do not contribute markedly to crack propagation their role can be taken by precipitates, i.e. voids are now initiated at precipitates but at higher K levels than at inclusions (Fig. 32(c)) since they are usually smaller and tougher than inclusions. Fig. 32(d) illustrates the case when two kinds of particles contribute to crack propagation. Three cases of crack propagation with dimple formation at particles can be distinguished: (a) Only large particles are active: low toughness. (b) Only small particles are active: high toughness. (c) Both types of particles are active: even lower toughness than for (a) is to be expected since the small particles reduce the ductility of the material between the large particles. Hard, brittle particles should be diitributed as homogeneously as possible since inhomogeneous distribution causes locally small particle spacings and hence a weak crack path. Examples are the inclusion arrangements by processing and grain boundary precipitates (Fig. 32(e)). In case of grain boundary precipitates increasing the grain size will be beneficial to toughness when grain growth leads to reduced grain boundary precipitation. An extreme case is given by film-like precipitation at grain or phase boundaries providing a continuous low energy crack path and consequently leading to low fracture toughness. Segregation of impurities can have the same result. Two alternative crack propagation mechanisms may be possible (Fig. 32(f)). Either a normal stress controlled brittle failure of the film or a matrix/film decohesion by void initiation due to dislocation pile-ups. The latter mechanism may be expected to exhibit higher toughness than the former one. The effect of soft phases or zones on fracture toughness is the result of two competing events. Slip concentration causes large local strains and hence low bulk ductility and tends to decrease toughness. This effect can be overcompensated by very high ductility of the soft zones. Hence, depending on the ductility and on the degree of slip concentration (the latter being dependent on the volume fraction of the soft zones) soft zones can either be detrimental or beneficial to toughness. Examples for a beneficial effect are titanium alloys with an a phase film in the Widmannstatten microstructure and retained austenite in martensitic steels. The harder phase representing the bulk of the material provides high strength whereas the softer phase serves as an energy absorber during crack propagation. The question arises how the soft phase contributes to the high toughness values observed. Two possible mechanisms are shown in Fig. 32(g). In version (1) the soft phase acts as a crack stopper whenever it is crossed by a crack. In version (2) the crack propagates along the soft phase film. Which mechanism actually operates depends on the ease with which slip in either phase creates voids. An idea about the energy dissipation during crack growth may be given by the following simple estimation. For simplicity, the crack opening Mode III is considered since for this case a simple solution for the plastic deformation work W has been derived by McClintock and Irwin[80]: (13) where T,, = uY/2, o = length of the plastic zone, and cc = shear modulus. Because of the diRerent yield stresses of both phases two plastic zones have to be distinguished (Fig. 33). When u designates the volume fraction of the soft phase the contribution of the hard phase to the plastic work at a given stress intensity is given by

w,=&u-0)

%I

)%2

Z&y%

h&Nb&

plastically mater,a,

(14)

deformed

Fii. 33. Plastic zones for a two phase material.

Crack propagation mechanisms and fracture toughness of metallic materials

821

and the contribution of the soft phase is

Taking AISI steel 4340 with retained austenite as an example[49] the yield stress for the hard phase (martensite) is approx. 200 ksi. The yield strength for the retained austenite can only be estimated; it may be 40 ksi. For 10% retained austenite the total plastic work is given by 0.9 0.1 4. lo, + 1600 = C(2.25 - lo-‘+ 6.25 - lo-‘). W = W, + Wz = C --

(16)

This result indicates that in spite of its small amount the soft phase contributes about three times more to the plastic work than the hard phase does. Although this estimation is confined to a stationary crack it may also give an impression for the behavior of a propagating crack. A special kind of crack propagation without the contribution of a second phase occurs when plastic deformation is inhomogeneous, i.e. when it is concentrated on a few slip planes. Slip plane/slip plane and slip plane/grain boundary interactions are the void forming mechanisms (Fig. 32(h, i)). Finally, Fig. 32(j) shows the crack propagation mechanism to be expected when no void forming mechanisms are active. Crack propagation then occurs by pure plastic blunting. It may now be interesting to speculate how fracture toughness is affected by the mechanisms described above, i.e. is it possible to predict an improvement or a deterioration of K,, if one specific crack propagation mechanism is replaced by another specific mechanism. This question implicates another problem: if it is possible to predict the effect of specific crack propagation mechanisms on fracture toughness then one should know by which treatment the material’s microstructure can be affected such that a desired mechanism will be operative or an undesired mechanism will be suppressed. The extremes of fracture toughness can be easily derived as follows: Since cleavage is the crack propagation mechanism with the lowest energy dissipation the mechanism drawn in Fig. 32(a) represents lowest fracture toughness. Looking at ductile crack propagation, the formation of voids ahead of the crack-by whichever mechanism-leads to internal necking and hence to.a reduction of the resistance against crack propagation. Consequently, Fig. 32(j) should represent maximum toughness. Since the effectiveness of void formation depends on several parameters of the microstructure the following assumptions are made: (a) A material is considered which consists of a matrix of fixed properties and which contains a fixed amount v of a hard second phase. (b) It is possible to arrange the second phase according to the sketches shown in Fig. 32, i.e. it is possible to produce coarse and fine particles and to precipitate the second phase in the grain as well as at the grain boundary. Then the sequence of the mechanisms-arranged for increasing K,,-will be f

I,

fae,b, c.

Adding a further phase of hard particles (Fig. 32(d)) will result in

firf2, e,4 b, c. (c) The amount of the second phase can be changed. (d) The hard phase can be removed and a soft phase can be added. The soft phase can also be a precipitate free zone or a slip band with dissolved precipitates.

822

KARL-HEINZSCHWALBE

Thus, the following scheme results: grain

I

occasionally

/Q h, i ,--------

CJ-

%c

I

0

-1 l-L \ \ 47 e f2 f1 a

particle epacing

1

particle size

1

I

I volume

size

- 4 - -

content

_-----------L_-.__

4

The scheme reads as follows: KIc increases when the kind of crack propagation mechanism changes as indicated. For a given mechanism K,, is affected by particle size (and particle spacing, both quantities are related to one another when II = const., see eqn (l)), by the volume content of the hard phase and by grain size. The arrows indicate in which direction K,, is shifted when the respective parameters have increasing values. This scheme is designed for simple situations and it may not represent an exact sequence. But it may be indicative for the trend of K,,. Summarizing, it can be concluded that fracture toughness and the crack propagation mechanism depend on the properties of the phases in the material, on volume content, size, shape and distribution of the phases, on the properties of the grain and phase boundaries and probably on the differences of the phase properties. Thus, returning to the statements made in the introduction it comes clear why it is so difficult to establish a system which gives comprehensive information about the influence of microstructure on toughness: the parameters are so numerous that only relatively simple cases can be treated.

6. QUANTITATIVE CONSIDEEATIONS Numerous attempts have already been made to calculate K,, from properties which can be obtained more easily and more economically than K,, by simple tests, like tensile tests etc. Several problems arise when trying to calculate any crack propagation process: (a) The stress and strain distribution in the plastic zone must be known. For crack opening mode I no closed form solutions exist. (b) The proper fracture criterion has to be chosen. (a) For normal stress controlled processes like cleavage the local stresses must equal a critical normal stress. Plastic rupture processes are strain controlled. Thus, the local strains must exceed a critical strain. (/3) Some doubts exist about the proper choice of the critical strain. Sometimes the uniform elongation strain (instability strain) is favoured; in other cases the true fracture strain is considered to be the critical strain. (y) The sharp crack approach in fracture mechanics predicts infinite stresses and strains at the crack tip. On the other hand, the blunt crack treatment predicts constant values of stresses and strains at the crack tip, but different distributions for different loads (for zero strain hardening). Both theoretical concepts lead to the conclusion that the critical value for stress or strain has to be reached or exceeded over a certain distance or volume. A reasonable assumption is to set the critical distance equal to the smallest fracture unit: for ductile crack propagation this is the dimple size ( = process zone size of KralIt[81]), for cleavage the grain size may be the controlling parameter. (8) It can be assumed that the critical stress is independent of the stress state. But the critical strain depends strongly on the stress state. Unfortunately the stress state varies near the crack tip (Fig. 34). So, the critical strain varies along the process zone. This complicates the situation very much. (4) Once it is established for which stress state the critical strain has to be determined appropriate specimen design and test procedure must be developed. The plane strain tensile specimen[21,82,83] and the hydraulic bulge test[W offer two alternative possibilities. (c) Calculation of K,= is based upon the assumption that instability, i.e. fracture+ccurs when the fracture criterion is satisfied. The fracture criterion implicates a fixed amount of crack

Crack propagationmechanisms and frachm

toUghnCSs Of meticmatCrids

823

critica; strain

FGg.34. Normal stresacs and fracturestrain near crack tip.

propagation, i.e. crack propagation over the process zone. A specimen failing under this condition will exhibit a linear load-displacementrecord. However, if IL must be determined by the ASTM secant method a 2% crack length in&ease will have occurred. Since the R-curve can rise also under plane strain conditions l75,85,8a] the stress intensities at the onset of crack propagation and at 2% crack length increase can be quite different. Consequently, calculated and measured & values are not always comparable. 6.1 Crack propagation by cleavage The empirical formulae by Hahn and Rosenfield[4] & = 0.55(&l- aY) in MNrn-=

(17)

and by Hahn, Hoagland and Rosenfield[6]

where cr&signifiesthe’cleavagestress (both cr and ucl are to be inserted in ksi), indicate that cr and ucl are the major variables.The yield stress depends on temperature, deformation rate, grain size, alloying and heat treatment whereas ucr is mainly influenced by the ferrite grain size. A theoretical model of Wilshaw, Rau and Tetelman[87] (see also[88]) states that fracture occurs when a, exceeds a&over the process zone size. Using the stress distribution according to the slip line theory for 6nite notch radii the authors obtain Kr, =

2.89uv[exp(U&U - 1)- 110”- t&0).

(19)

The parameter po is the effective root radius of the crack. It is a measure of the extent of the process zone. For low carbon steels po=3D, 0~87~

(20)

where D = grain size. For D > 87~ pi = 300~. A simple approximation is based upon the assumption that a smooth tensile specimen fractures after a microcrack has been formed[lO]. As grain size plays an important role in cleavage the size of the microcrack should be coupled to the grain size; its diameter 21 may be a . D. In other words, a smooth tensile specimen represents an internally cracked specimen the fracture stress of which equals ud. If ud would be * uy, KI, conditions would be present and for a penny-shaped crack[lB] one could set (21) However, cleavage of a smooth specimen occurs at the onset of general yield. Thus, eqn (21) doesn’t represent small scale yielding conditions. Assuming that eqn (21) can be converted to small scale yielding by a constant factor, p,

EFM VOL. 9 NO. 4-E

~lH3lNZ

824

!XXiWALBE

Comparison with some experimental results obtained on the carbon steel Ck45[101yields

To account for aa > crv at increasing temperature the arbitrary correction factor cr&r~ was introduced. Hence, the fracture toughness

Using QCcalculated by eqn (2) IG, was calculated by eqns (1%19,241for several steels listed in[lOJand plotted in Fi. 35 vs the exigent results to compare the aeeuracy of the ~~erent equations. For the limited data available eqn (24) yields best coincidence with measured L values. Crack tip blunting. According to the two stage process shown in Pi. 5 plastic blunting represents the fvst stage of ductile.crack prop~tion. The eraek tip advance displ~ment, &, is equal to half the crack tip opening displacement if one considers the crack tip prothe to be sernic~c~~:

60

E k

P fj $30

30

0.

60

KS, exp. MN rn*‘* a)

0

30

60

K:; exp. MN rri3’* d) Fii. 35. Measured and caledatcd fntctsrt tougbm& datafro@& 10,91; (a) talcby cqn (17). (b) Calby cqn (18). (c) c&x&ion by eqn (19). (d) akuhtion by eqa (24.

Crack pmpagatbn mechanismsand fracturetoughness of

metallicmaterials

where the plane strain relation for 8, K2 8l ==Q.S~

W)

was used [90]. Another expression for 6, [91] yields lower values. It has been derived for strain hardening materials:

where n is the strain hardening exponent when the strain hardening curve is given by

1 ”

m

(r=cr,$ [

In Table 2 some measured values of 6, and 8, are listed and compared with eqns (25-27). The calculations have been carried out with K = Kr,. When dimple formation is due to coarse inclusions (0.45C-Ni-Cr-Mo steel and AlZnMgCu0.5) the data suggest 8, = d

but when dimples are formed at fine particles (X2NiCoMo 18 8 5) St >d

as already discussed earlier. Equation (26) seems to be a reasonable approximation for the crack tip opening displacement while the relations for & exhibit appreciable deviations from measured values. Onset of voidfornation. The onset of void formation ahead of the crack can be estimated by the assumption that an inclusion must enter into the zone fI of intense plastic deformations (Rice and Johnson[19]). Setting Q=d

m

n = 1.98#

(30)

where

yields the stress intensity K* at the onset of void formation K* = ~(Emd)

0.45C-Ni-Cr-MO 0.008s 0.025s X2 NiC!&h 188 5 T=2YC T=-l%V AyaD&.5

(31)

[22]

[lo]

1211

71.44 55.80

6.1 4.4

10” 5.

8.8 5.3

J. .I.

90.7 41.2

5.2 3.3

10.4 6.3

12.8 2.8

4.85 1.15

6.46 1.42

2s

18

11

14

1.6

7

1450 1472

0.06 0.06

2.24 0.46

1854 2276

0.1 0.013

1.4

397

0.11

KARL-HEINZ SCHWALBE

826

Some experimentalresults[92]are in accordance with this model. But it is to be expected that this model works only when voids form at coarse inclusions as they fracture at low strains, i.e. they fail when they are reached by the edge of the plastic zone 0. Smallparticles, however, can resist relatively high deformations, i.e. they fail somewhere in the interior of the plastic zone, Fig. 36. This may also be true for void formation mechanisms without participation of hard particles. Instubili~y. From the various Krc calculations (see for instance the compilation of Sengupta[M]) some equations will now be discussed which refer to microstructural parameters and which can be verified by means of some experimental results. The simplest way to assume a strain distribution ahead of a crack is to consider the elastic solutions to be valid. This can be supported by strain measurements of Liu et al. [93,94] who found a l/v(x) dependence of cY.However, their nearest distance to the crack tip was approx. 0.3 mm whereas the fracture process occurs at much smaller distances. The elastic strain distribution was used by I&&[811 who introduced the “process zone size” as a material parameter which is equal to the inclusion spacing. Instability is assumed to occur when the uniform elongation strain o at the instability of a tensile specimen which is equal to the strain hardening exponent, n, is reached at the distance, d, ahead of the crack tip: Kk = EnV(2vd) = EErd(2wd).

(32)

The elastic stress distribution was also assumed by SenguptaM (see alsoI%]) who calculated the plastic work required for crack propagation and obtained G,, = S *

P*w:($ 1)

(33)

where S = shape factor characterizing the plastic zone, p* = Neuber’s micro-support effect constant (which may be set equal to d). The fracture strain cf at the crack tip cad be calculated from the fracture strain measured in hydraulic bulge tests considering the stress states in both cases rf = 0.279- em (strain hardening exponent II = 1).

(34)

where em is the hydraulic bulge ductility. Because of the lack of data for eP and p* the predictions of eqn (33) cannot be compared with experimental results. Another approximation of the strain distribution can be made if it is assumedP71 that the strain distribution in ‘amode I plastic zone is simii to the shear strain distribution of Mode III derived by Rice[95]:

[I

1/1+n

6 =er

-lncreosq

6,nZd

(35)

;

Lood --

6;; d

bl b,>d Fig. 36.

6;ad

Void fommtion at bard particks in front of tbe crack tip (a) coarse part&s. (b) i& part&s.

Crackppg&ion

mechanismsand fracturetoughnessof metallicmatcriats

827

where ly is av/E and (36) the plain strain plastic zone size. Application of Krafft’s model yields [21] Kk =+‘$-J(dlr(l+n)[~‘+“).

(37)

Objections may be raised against calculation models using instability strains since it could be shown[83,84] that fracture toughness is related to fracture strain. Hence, an alternative formulation of eqn (37) is (38) where rf designates the fracture strain at the crack tip. Furthermore, the argument that the average strain over the distance x = d has to equal the fracture strain leads to[lO]

&=a

l-2v

dr(l+n)[$&-]I+“).

(39)

For elastic-ideally plastic behavior the strain distribution in analogy to the Mode III solution would be

4y =

‘p.

W)

Setting the work done along the x-axis in the region d IX 5 o equal to GI, Osbom and Embury [98] obtained G,c = UT u g(x) dx Id where

(TT

(41)

designates the tensile strength. From the condition c=cr

at

x=d

(42)

one obtains with eqn (40) o=zd

(43)

and the fracture toughness[98]

So ‘far, models with assumed stress and strain distributions were considered. Rice and Johnson1191 gave a numerical solution for the strain distribution at a blunt crack in a rigid-ideally plastic body. Their strain distribution can be approximated by ,=~-0.23=!$$-0.23, Y

(45)

828

KARL-HEINZSCHWALBE

With eY= et at x = d the fracture toughness is given by [ lo] K,, = t/(4.55(~) + 0.23)Eavd).

WI

Basing on Fig. 36(a) a simple expression for IL is given by the condition 8, J d,

(47)

KIc = ~(2Em-d).

(48

hence,

This expression is expected to be applicable only when dimples are nucleated at coarse particles. A semi-empirical expression for IL was derived by Hahn and Rosenfield[99] who used a linear strain distribution in the plastic zone. With this assumption and the average strain -

v=G

8,

(49)

the crack tip strain 6 J 2<.

(50)

At the instant of fracture, 4 = af. With eqn (26) KIC= V(2EuYgo9

(51)

where w* denotes the length of the plastic zone at fracture. For a number of materials w* has been calculated by eqn (51) with known IL values. The authors found o* +J25.4. lo-“(n’+ 0.0005) (a.

(52)

K,c = 5d(2Eauef(n2 + 0.0005) * 10-3) (MNm-3n).

(53)

Hence,

This relation is considered here although it contains no microstructural parameters since it is (together with K&t’s equation) the best known KI= relation. The authors assume that +,

(54)

with ef = uniaxial fracture strain. Hombogen[60] applied the Hahn and RosenGeld model on precipitation hardened alloys which fracture along the precipitate free zones (PFZ) at the grain boundaries. Taking the local properties of these zones uy ,, x1, and E# and considering Pf =

exg

(55)

with D* = thickness of the PFZ Hombogen obtained KI, = 5+&r:

+ 0.0005). E; %)

= k . D-l”.

(56)

The same considerations can be made with the other calculation models described above. Equation (56) is applicable when UY1* UY and n I 4 n. Because of the lack of data for the local properties eqn (56) cannot be verified. On principle, however, the D-‘” dependence is in accordance with experimental data[61] (see Fig. 18). In Table 3 measured and calculated K,, values are listed along with the material properties

s

I?$

tt, setequal to a.

Tt=4O(PC &=5OlPC G=6lxPc lt%) Q

z:z

;: :;gg AlzeMgcuO.5 Orimt.T-S M&x-3R steel T,=lWt!

;:

OXUS 0.049s x2 NiioMo 188 5 T=ZSY:

s

om

0.016

Steel

0.45C-Ni-Cr-MO

I29 1551

HOI

WI

1569 1570 1413 1329 1265 1143

1884 1840 1589 1419 1366 1214

481

E 2214 2347

1883

1632 1633 1633 1621

E 2036 2139 1923

3012

2933 z 3o!m 31%

_

0.757 0.855 0.839 0.808 0.765 0.901

0.993 0.915 0.803 0.795

0.965

0.65 0.51 0.59 0.54

0.50 0.54 0.55 0.49 0.52 0.58

0.159

0.432 0.416 0.280 0.250

0.530

102 89.6 98.6 123 128

77.8

E 40 2.02

37.7 40 24.15 27.6

c5 2.65

z

34.2 37.2 25 21.7 26 30 61 2.84

107.3 120.8 88.3 %o w.2 105 39 1.4 29.15 30.9 19.5

1.9 2.4 1.6

0.162 0.147 0.118 0.104 0.124 0.119

0.053 0.05 0.037 0.041 0.034 0.053

16

58.2

31

37.4

2%

29.6 29

35.7

40 33 32.3 22.8 8.0

75.6 74.2

91.3

149.6 127 122 90.7 73.1

18

51.4 4x4

46.25 43.55 39.55

0.6512 0.11

765 72 65

&I 45.0

71.41 60.83 55.79 46.82 72.4 56.5 45.8 65.9 72s

6.1 5.4 4.4 3.7 90.52 84.94 71.18 64.8 47.12

0.06 0.06 0‘06

0.1 5.2 0.093 4.6 0.097 4.2 0.077 0.013 :::

t

s 41.5 48 2.1

39 46 35.5

18

2 46.5 34.5 30.5

3: 27

39

t: 28 1.6

45.5 52 40.5 39

29.5

:; 65 xi.5 52.5

: 46

61

468 439s 340 2755 328 3163 199 3

52

293 253.5 265 179.5 56.3

ii5 RX? 110.5

35.3 39.5 30.5 30.5 31.5 34.5 35 1.93

31.3

56.7 54.7 53.5 51.5 50

60.5 57 51.7 47.7

830

KARL-HEINZ

SCHWALBE

necessary for calculation. All fracture strains were determined according to c;=hl-

1 l-Z&I

(57)

where RA is the reduction of area; ri was determined.on plane strain tensile specimens. For the calculations e) = c;

W-9

was assumed. When ci was not available, the assumption of Hahn and RosenGeld[99] in eqn (54) was used, although it is only a rough estimation. uf was determined as load at fracture of a smooth tensile specimen divided by the cross sectional area at fracture. To compare the prediction accuracy of the equations two dif?erent errors were calculated, namely: an average relative error (59) and an average factor

or

i.e. the factor, by which prediction deviates from measurement, where N denotes the number of data pairs. Both kinds of errors yield ditferent sequences of the accuracy of prediction. Of course, the data listed in Table 3 is too liited to allow general judgements of the calculation models. However, compared with the prediction of fatigue crack propagation rates all the models yield relatively good results since prediction of fatigue crack propagation within a factor of 2 . . .3 (without data fit) can be considered as an excellent result. Within the range of materials considered in Table 3 eqns (38) and (46) exhibit closest coincidence with experimental results. REFERENCES [f] E. Hornbogen,System&&e Betrach~ der Gef@e von Metallen.2. MeMkde 64,867 (1973). [2] E. Horn-n, Wcrktrofe. Spri&er-Verlag,Berlin (1973). [3] B. I. Edelson and W. M. Baldwin,Jr.,‘Ibe effect of second phasesonthemechanicalpropertiesof alloys. Trans.ASM 55, 230 (1%2). [4] G. T. Hahnend A. R. Rosentield,Experimentaldetermbmtionof plastic constraintaheadof a sharpcrack underplane strainco&ions. Tmns. ASM 5). 909 (1966). [5] T. R. Wdshaw, C. A. Rau end A. S. Tetelman,A generalmodel to predii the elastic-pi8sticstress distributionand fractures&e& of notched bar8in plane strainbendin&JJngngFractwr Me& 1,191(1968). [6] G. T. Hahn,R. G. Hoaglandend A. R, Rosenlkld,The varia&mof K, with temperatureand logdingrate. Met.Trans.2, 537 (1971). [71 S. Enshe and A. S. Tetelman,The effect of microstructureon the fracturetoughnesdof low-alloy steels. Reporl Grant Nr. DAHCO4-69-CdoB,University of California(1974). [8] A. S. Tetelmanand A. J. McEvily, Jr., Fmctvn of StructumlMaterials.Wiley, New York (1%7). [9] W.-B. Kretzs&ma~, Ph.D. Thesis, RWTHAachen (1974). [lo] K.-H. Schwa&e, in preparation. 11I] A. R. Rosen&Id, 0. T. Hahn and J. D. Embury,Practureof steels containingpeerlite. Met. ‘Itons. 3, 2797 (1972). [12] L. R. Hettche end A. R. Cax, Fractureresirtadceof low-carbonalloy Irons.Met. Trans.3,2327 (1972). [13] I. L. &ford, The deformationand frac@reof two-phase nubriab. Md. Reo. 12,49 (1%7). [14] A. K. S&oemakerend S. T. Rolfe, Staticand dynamiclow-temperatureK,=behaviorof steels. 1. Bas. Engng,(TRIM. ASME) 512 (1%9). (151A. K. Schoemakerand S. T. Rolfe, The static end dynamic low-temperaturecrack toughnessperformanceof seven stNctural steels. Engng FmcturrMe&. 2, 319 (1971).

Crack propagation mechanisms and fracture tou&t~ss of metallic materials

831

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