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Fatigue Crack Initiation and Propagation of Binder-Treated Powder Metallurgy Steels S.J. POLASIK, J.J. WILLIAMS, and N. CHAWLA Many of the targeted applications for powder-metallurgy materials, particularly in the automotive industry, undergo cyclic loading. It is, therefore, essential to examine the fatigue mechanisms in these materials. The mechanisms of fatigue-crack initiation and propagation in ferrous powder-metallurgy components have been investigated. The fatigue mechanisms are controlled primarily by the inherent porosity present in these materials. Since most, if not all, fatigue cracks initiate and propagate at the specimen surface, surface replication was used to determine the role of surface porosity in relation to fatigue behavior. Surface replication provides detailed information on both initiation sites and on the propagation path of fatigue cracks. The effect of microstructural features such as pore size and pore shape, as well as the heterogeneous microstructure on crack deflection, was examined and is discussed. Fracture surfaces were examined to elucidate a mechanistic understanding of fatigue processes in these materials.

I. INTRODUCTION

SINTERED powder-metallurgy components are increasingly replacing wrought alloys in many applications, due to their high performance, low cost, and ability to be processed to near-net shapes. The main thrust toward higher performance in powdermetallurgy alloys has been achieved by introducing alloying additions such as Mo, Mn, Cu, and Ni. While alloying additions increase the strength of the Fe alloy, in elemental form they may oxidize or diffuse inhomogeneously into the surrounding Fe particles. Introduction of the alloying additions during melting atomization to form prealloyed Fe particles is effective, but significantly decreases the compressibility of the powders. In conventional powder-metallurgy processing, “diffusion-alloyed” powders have typically been used. This process involves bonding iron and alloying particles through an intermediate annealing step which allows partial diffusion and sintering of the particles to take place, prior to pressing and sintering. Binder treatment of the powder mixture prior to pressing and sintering is a new and effective technique to increase the compressibility of prealloyed powders, eliminating the diffusion-alloying step, while still minimizing segregation.[1–5] In the binder-treated process, a polymeric binder mechanically bonds the alloying additions to the larger iron particles (Figure 1). The enhancement in compressibility of the powder mixture is accompanied by a smaller path for diffusion during sintering, which results in enhanced densification of the sintered product. Burnout of the binder is accomplished either by a debinding step (at an intermediate temperature below the sintering temperature) or by heating at a relatively slow rate until the sintering temperature is reached. Other advantages of binder processing include faster and more consistent flow into the die cavity and an increased green strength, which results S.J. POLASIK, Undergraduate Research Assistant, J.J. WILLIAMS, Postdoctoral Research Fellow, and N. CHAWLA, Assistant Professor, are with the Department of Chemical and Materials Engineering, Arizona State University, Tempe, AZ 85287-6006. Manuscript submitted May 10, 2001. METALLURGICAL AND MATERIALS TRANSACTIONS A

from enhanced bonding of particles. Additionally, there is a reduction of fine-particle dusting, resulting in more efficient use of alloy powders. Sintered ferrous materials are typically characterized by a porous and heterogeneous microstructure which develops from incomplete diffusion of alloying elements during sintering. Due to the incomplete diffusion of alloying elements, multiple phases are formed. The detrimental effect of porosity on the mechanical properties of powder-metallurgy components is fairly well known.[4–10] Under monotonic tensile loading, porosity reduces the effective load-bearing crosssectional area and acts as a stress-concentration site for damage, decreasing both strength and ductility.[7] One may characterize the porosity in these materials as either interconnected or isolated in nature. Isolated porosity results in more homogeneous deformation, while interconnected porosity causes an increase in the localization of strain at relatively smaller sintered regions between particles. Thus, for a given amount of porosity, interconnected porosity is more effective in reducing macroscopic ductility.[7,9] Porosity also significantly affects fatigue performance, although the role of porosity in fatigue is somewhat different than that in tension. In many investigations,[4–6,8–10] crack initiation occurred at pores or pore clusters located at or near the surface of the specimen. Holmes and Queeney[8] proposed that the relatively high stress concentration at pores, particularly surface pores, is responsible for localized slip leading to crack initiation. In general, an angular pore creates a higher stress concentration and stress-intensity factor than a round pore.[10] Christian and German[9] showed that total porosity, pore size, pore shape, and pore separation are important factors that control the fatigue behavior of powder-metallurgy materials. Pores have also been proposed to act as linkage sites for crack propagation through interpore ligaments.[4,5,10] In this study, we have examined the fatigue behavior of a binder-treated Fe-0.85Mo-Cu-Ni alloy. Comparisons are made with the fatigue resistance of diffusion-alloyed materials of similar composition. Recent limited data indicate that binder-treated materials have similar tensile and fatigue VOLUME 33A, JANUARY 2002—73

Fig. 1—SEM micrograph of alloying additions bonded to iron particles by the binder.

properties to those of diffusion-alloyed materials.[4,5] A thorough examination of crack initiation and propagation in these materials, particularly the behavior of short fatigue cracks, was conducted. Short cracks range in size from a fraction of a millimeter to several millimeters and have been shown to propagate at much faster rates than long fatigue cracks under the same driving force.[11] Additionally, short cracks propagate at stress intensities well below the longcrack stress-intensity factor, (⌬Kth). It will be shown that short fatigue cracks are important in causing fatigue damage and failure in these materials. By using surface replication, a detailed and in-situ understanding of fatigue-crack initiation and propagation processes in these materials was obtained. Since the preferred initiation site for fatigue cracks is frequently the specimen surface, surface replication is an ideal means to study crack initiation and growth of short cracks. The heterogeneous nature of the microstructure in these materials results in significant crack deflection, which has also been modeled to adequately characterize the effective stress intensity for fatigue-crack growth. II. MATERIALS AND EXPERIMENTAL PROCEDURE Powder mixtures of an Fe-0.85Mo prealloy, 1.5 pct Cu, 1.75 pct Ni, and 0.6 pct graphite were binder treated using a proprietary process developed by Hoeganaes Corp.[1,2,3] All powders were pressed into rectangular blanks to a green density of 7.0 g/cm3 and sintered at 1120 ⬚C for 30 minutes in a 90 pct N2-10 pct H2 reducing atmosphere. The assintered microstructure of the powder-metallurgy alloys was examined by etching with a 2 pct Nital solution. Digital image-analysis techniques were used to determine the pore morphology (pore size and shape distribution). In order to characterize the pore structure, both the pore size and shape distribution were determined from optical micrographs of cross-sections of the samples. The pore size was estimated by measuring the pore area, while pore shape was characterized using a shape-form factor (F ): 4␲A F⫽ 2 P

[1]

where A is the measured pore area and P is the measured 74—VOLUME 33A, JANUARY 2002

pore perimeter. For the shape-form factor, a value of “1” denotes a perfectly round pore, and values that approach zero denote increasingly irregular pores. Uniform-diameter cylindrical specimens for tensile and axial fatigue were machined from the sintered rectangular blanks. The specimens had a diameter of 5 mm and a gage length of 15 mm.[12] All testing was conducted on a servohydraulic frame. Tensile tests were conducted in strain control at a constant strain rate of 10⫺3/s, while fatigue testing was conducted in load control, with an R-ratio (␴min/␴max) of ⫺1 and a frequency of 40 Hz (40 cycles per second). Fatigue specimens were hand polished, using diamond paste, to a 1 ␮m finish. Surface replication was conducted by interrupting the fatigue test and placing the sample under a relatively small tensile load (⬃0.25 ␴max) to avoid closure of any fatigue cracks during the replicating procedure. The entire gage section was then bathed with acetone and subsequently covered with cellulose acetate tape. After the solvent (acetone) evaporated and the replicating tape dried, the replicas were flattened onto double-stick tape and placed between two microscope slides. Using an optical microscope, digital micrographs were taken of the entire replicated surface at various fatigue cycles. The largest crack present on the last replica prior to failure was identified on prior replicas until the point of crack initiation. The resolution of the surface replicas allowed identification of cracks greater than about 15 ␮m. Details of the surface-replication technique may be obtained elsewhere.[13,14] III. RESULTS AND DISCUSSION A. Microstructure During sintering, multiple phases are formed due to localized variations in composition. The microstructure of the Fe0.85Mo-1.5Cu-1.75Ni-0.6 graphite alloy, in the as-sintered condition, is shown in Figure 2. The residual porosity from sintering may be characterized as either primary or secondary (Figure 2(a)). Primary porosity consists of larger pores which result from geometric packing of the particles or from binder burnout. Secondary porosity is typically smaller in nature and may be attributed to residual porosity from liquidphase formation and diffusion of alloying additions, such as copper. A heterogeneous microstructure consisting of martensite, nickel-rich ferrite, and divorced pearlite (termed “divorced” since it is not lamellar, as in conventional pearlite) was observed, as shown in Figure 2(b), and nickel-rich regions surrounding pores were also observed (Figure 2(c)). Results of the pore-size and shape analyses are shown in Figure 3. The pore-size and shape analyses show that the microstructure consists of pores with sizes below 300 ␮m2 and relatively irregular shapes (shape factors are between 0.4 and 0.7). The largest fraction of pores has an area of about 75 ␮m2. The irregularity of the pores suggests a greater amount of local stress concentration and, subsequently, a larger amount of potential fatigue-crack initiation sites than in a similar material with perfectly spherical porosity. B. Tensile Behavior The tensile stress-strain behavior of the Fe-0.85Mo1.5Cu-1.75Ni-0.6 graphite alloy is shown in Figure 4. Table I summarizes the tensile properties of this alloy. Porosity METALLURGICAL AND MATERIALS TRANSACTIONS A

(a) (a)

(b) (b) Fig. 3—Distributions in (a) pore size and (b) pore shape in powder-metallurgy alloy.

(c) Fig. 2—Microstructure of powder-metallurgy material tested in as-sintered condition: (a) primary and secondary porosity, (b) heterogeneous nature of the microstructure, and (c) nickel-rich areas from incomplete sintering of Ni.

METALLURGICAL AND MATERIALS TRANSACTIONS A

Fig. 4—Tensile stress-strain behavior of the binder-treated alloy.

clearly decreases the elastic modulus over that of wroughtalloy steel. Macroscopic ductility due to strain localization of the sintered neck regions is also significantly lower than VOLUME 33A, JANUARY 2002—75

Table I. Tensile Properties of Fe-0.85Mo Binder-Treated Alloy

Elastic Modulus (GPa) 121

Proportional Limit Stress (MPa)

0.2 Pct Offset Yield Stress (MPa)

Ultimate Tensile Strength (MPa)

Strain-toFailure (Pct)

233

526

774

1.83

that of most fully dense wrought alloys. The locally hard phases shown in Figure 2 may also contribute to a higher work-hardening rate and lower ductility than that exhibited in wrought materials. The tensile strength of these materials has also been shown to increase with Mo content.[5] An increase in fraction of carbides with increasing Mo content may account for this behavior. It is important to note that the onset of microplasticity, given by the proportional-limit stress (taken here as the point at which the stress deviates 1 pct from linearity) or the stress at which the stress-strain curve begins to deviate from linearity, takes place at a stress much lower than the 0.2 pct offset yield stress. The microplasticity can be attributed to the localized stress concentrations and yielding that takes place in sintered necks between very closely spaced pores.[15] Fractographic examination of tensile surfaces indicated localized microvoid growth and coalescence at sintered necks (Figure 5(a)). Regions where particle contact was not present, and, thus, sintering did not take place, were also apparent. Cleavage fracture, in what are thought to be pearlitic colonies, was also observed. It should be noted that damage was more predominant in the form of localized ductile rupture of sintered necks. Given the lower strength and localized higher ductility of these necks, it is plausible that it is the dominant mode of damage during tensile deformation.

(a)

C. Fatigue Behavior The stress vs cycles behavior of the Fe-Mo steel is shown in Figure 6 (fatigue run-out was taken as 107 cycles). The results of the present investigation are compared to the results of Chawla et al.,[5] who studied an Fe-Mo alloy with 0.5 pct Mo (using similar specimen dimensions and surfacepreparation techniques to this study). A distinct increase in fatigue strength with increasing Mo content is observed, which, as in the case of tensile behavior, may be attributed to a higher fraction of carbides. Quantification of stress-strain behavior can shed some insight into the fatigue mechanisms in these alloys, particularly relating to cyclic hardening or cyclic softening. The width of the stress-strain hysteresis loop at zero stress was used to determine the cyclic plastic strain amplitude, and the slope of the loop, i.e., the secant modulus, was used to estimate fatigue damage. In this analysis, a useful parameter to quantify the evolution of damage is the damage parameter[16] (DE), defined as DE ⫽ 1 ⫺

E Eo

[2]

where E is the secant modulus at any given number of cycles 76—VOLUME 33A, JANUARY 2002

(b) Fig. 5—SEM micrographs of tensile fracture: (a) ductile rupture in localized sinter bonds and (b) cleavage in large pearlitic grains.

and Eo is the elastic modulus of the as-sintered material. Figure 7(a) shows the evolution of the damage parameter for specimens in the low-cycle fatigue (LCF) and high-cycle fatigue (HCF) regime. The number of cycles to the onset of crack initiation of the LCF specimen, from surface-replication measurements, is denoted by Ni . The onset of crack initiation correlates fairly well with the point at which DE shows a noticeable increase. As expected, the extent of damage was much lower in the HCF regime. The plastic-strain amplitude seems to be much more sensitive to cyclic hardening and cyclic softening (Figure 7(b)) than the damage parameter. In the LCF regime, the plasticstrain amplitude decreases relatively early in the fatigue life, indicating cyclic hardening, followed by a gradual increase, i.e., cyclic softening, until failure takes place. Cyclic softening correlates well with the onset of crack initiation and an increase in damage. Lindstead and Karlsson[17] conducted METALLURGICAL AND MATERIALS TRANSACTIONS A

Fig. 6—Comparison of binder-treated alloys with 0.5 pct Mo[5] and 0.85 pct Mo. An increase in Mo results in an increase in fatigue life.

(a)

(b) Fig. 7—(a) Damage parameter and (b) plastic strain data from stress-strain hysteresis measurements during fatigue. The specimens tested in the HCF regime (210 MPa) exhibit cyclic hardening and gradual cyclic softening, while specimens tested in the LCF regime (300 MPa) remain relatively unchanged. Ni, the number of cycles to crack initiation determined from surface replication, for the LCF specimen is indicated. METALLURGICAL AND MATERIALS TRANSACTIONS A

Fig. 8—Ratio of cycles to initiation to cycles to failure. Note that in the LCF regime a significant fraction of life is spent in crack propagation, while in the HCF regime, most of the fatigue life is spent in crack initiation.

strain-controlled LCF fatigue tests on powder-metallurgy stainless steels and observed that, for a given strain, the peak stress in compression was higher than that in tension. This was attributed to the inability of pores to transfer load in tension, while in compression, collapse of the pores takes place, and a higher degree of load transfer to the sintered regions can take place. The early onset of cyclic hardening was attributed to the high stress concentrations and, thus, high localized plasticity. The localized stresses cannot be relieved easily because of the surrounding interconnected porosity, which causes the cyclic hardening. At lower strain amplitudes, the size of the plastic zone is sufficiently small to cause a gradual increase in the hardening process. In the HCF regime, both the damage parameter and plastic-strain amplitude remained relatively unchanged since, in this regime, a large fraction of the total strain is elastic in nature. As mentioned previously, one of the most important controlling factors in the fatigue resistance of powder-metallurgy materials is porosity. Fatigue cracks tend to initiate near pores or pore clusters because of the higher localized stress intensity associated with these defects. On the other hand, microstructural heterogeneities surrounding the pores, such as the locally stronger Ni-rich areas shown in Figure 2(c), may contribute to a decrease in the stress intensity at the pores and increase the number of cycles to fatigue-crack initiation. Typically, cracks initiate at pores located at or near the surface of the specimen, because the stress intensity is higher there than at a pore in the interior.[6] The number of cycles required for crack initiation (Ni) was determined from surface replication, and the fraction of the life of the specimen spent initiating a crack (Ni/Nf) was plotted as a function of cycles to failure (Nf) in Figure 8. This approach provides a quantitative estimate of the fraction of fatigue life spent in initiation and propagation. From this relationship, it can be seen that in the LCF regime, cracks initiate very early (15 pct) and the majority of the fatigue life is spent in crack propagation, while in HCF, about 80 pct of the fatigue life is spent initiating the crack. Interestingly, the same relationship between Ni/Nf and Nf has been observed in other systems where fatigue-crack initiation takes place at exogeneous surface defects.[18–21] One can rationalize this VOLUME 33A, JANUARY 2002—77

Fig. 9—Fatigue crack propagation in Fe-Mo alloy. Note the fatigue crack gradually linking between pores and following a torturous path, presumably d ue to localized microstructural inhomogeneities (arrows indicate loading axis).

behavior by an incubation concept to describe the fatiguecrack initiation process in these materials. At intermediate to low stresses, crack initiation did not occur immediately upon cycling. Rather, a period of cyclic loading, i.e., an incubation period, was required to create a localized deformation that resulted in cracking initiation at a pore or cluster of pores. The number of cycles required to initiate the fatigue crack appears to be a function of the maximum applied stress, with lower stresses requiring longer incubation times for a given pore size and shape. This is to be expected, because the contribution to the total strain amplitude is primarily elastic in nature. Defect size and shape also play a role, as larger and more irregular defects are more susceptible to crack initiation for a given applied stress and will naturally lead to lower fatigue strength. After a fatigue crack has initiated at surface or subsurface pores, it tends to propagate and grow through the interpore ligaments, using pores as linkage sites. The evolution of fatigue-crack growth, from surface-replication measurements, is shown in Figure 9. While other investigators have postulated crack linkage as a possible mechanism,[22,23] surface replication allows in-situ monitoring of the crack initiation and growth process and confirms the linkage of smaller cracks to form a final crack that causes failure of the material. Fatigue fractography provided additional insight into fatigue damage. A scanning electron microscope micrograph of a fatigue-crack initiation site is shown in Figure 10(a). The intermittent nature of fatigue-crack growth during each cycle can be observed through the existence of localized fatigue striations in various fractured sinter bonds (Figure 10(b)). Striations in conventional steels and alloys are relatively homogeneous and of a single orientation. The formation of striations has been attributed to plastic strains at the crack tip, which cause localized slip on planes of maximum shear.[24] The crack front undergoes repetitive blunting and sharpening during propagation during cyclic loading. Unlike 78—VOLUME 33A, JANUARY 2002

(a)

(b) Fig. 10—(a) Fatigue crack initiating pore on specimen surface and (b) fracture surface after fatigue showing fatigue striations and localized ductile rupture. METALLURGICAL AND MATERIALS TRANSACTIONS A

striations in wrought materials, however, the striations in porous sintered materials seem to be highly localized. This may be due to the multiple sites of favorable orientation and size, with respect to the loading axis, that undergo blunting and sharpening and give the step-like appearance of the striations. Similar localized fatigue striations were also observed by Rodzinak and Slesar.[25] Ductile rupture is also present on the fatigue fracture surface, as seen in Figure 10(b). The ductile failure regions are highly localized in sinter bonds and seem to develop from microvoid nucleation and coalescence. The localized necking and microvoid growth, while present in the crackinitiation stage, are predominately found in the later stages of fatigue. Small spherical inclusions, which likely contributed to microvoid formation, were found at the bottom of some microvoids (Figure 10(b)). The composition of the inclusions was identified as MnS, although Fe oxides were also found. This is consistent with other authors’ observations of precipitates and oxides at the periphery of the Fe particles and at previous particle boundaries.[6] Cleavage fracture was also observed on the fracture surface. Since this type of failure was seen in the tensile tests and, therefore, in fast fracture, cleavage failure may be associated with the fracture-surface region corresponding to the final, fast crack propagation leading to failure. Generally, when this cleavage fracture occurred, it was found to be in large pearlitic grains, similar to what is shown in Figure 5(b).

(a)

D. Fatigue-Crack Growth Rate and Modeling of Crack Deflection The fatigue-crack growth rate of short cracks was calculated from a surface-replication measurement of fatigue cracks. We use the approach developed by Raju and Newman[26] for a surface crack in a cylinder (c) to calculate the stress intensity (K): ⌬K ⫽ F⌬␴

冪␲ Qa

Fig. 11—da/dN vs stress intensity ranges (⌬K ) as calculated using Raju and Newman analysis[26] for (a) LCF and (b) HCF.

[3]

where a is the crack depth, Q is the shape factor for an ellipse (defined as 1 ⫹ 1.464(a/c)1.65 for a/c ⱕ 1), ⌬␴ is the tensile component of the fatigue stress, and F is a boundary correction-size factor which accounts for crack size, crack shape, and the ratio of the crack size to specimen diameter. Note that only the tensile component of the fatigue-stress range is used to compute ⌬K, since the crack growth can be attributed primarily to the tensile component of the fatigue stress. Raju and Newman[26] calculated the values for F using the finite-element method. The value for the a/c ratio used for the calculations in this study was determined from the fracture surface and was measured to be about 0.58. This agrees well with the work of Lindstedt et al.,[10] who measured an a/c ratio of about 0.67 in a powder-metallurgy stainless steel. Figure 11 shows the crack growth rate vs stress-intensity factor in the LCF and HCF regimes. The stress intensity for propagation of the short crack is significantly lower than the Kth value obtained from long-crack fatigue growth of these materials. This reinforces the importance of quantifying short-fatigue-crack nucleation and growth in these materials. The value for the crack length (2c) was taken as the horizontal projection of the crack (the length of the crack METALLURGICAL AND MATERIALS TRANSACTIONS A

(b)

was taken to be perpendicular to the loading axis). The influence of crack deflection on the stress-intensity factor in the crack was also calculated and is discussed later in this section. The da/dN data in Figure 10 show that while several cracks initiate and link together, some fatigue cracks show a deceleration in crack growth rate, followed by arrest. Conversely, some cracks are arrested, but, after a dormant period, continue to grow. Crack arrest or deceleration may be attributed to microstructural barriers such as grain boundaries, locally hard regions (such as Ni-rich regions), interaction with other cracks, or even porosity. Short-crack growth also seems to be dependent on fatigue stress, with higher crack growth rates at higher stresses, for nominally similar stress-intensity ranges. In addition, many of these cracks measured through surface replication are small cracks, and the plastic zone is of comparable size to the crack size, requiring higher stresses for propagation. Crack deflection may also take place due to microstructural barriers in the material. Nickel-rich regions have been proposed as possible microstructural obstacles for crack growth.[27,28] Since crack deflection is significant in these materials, it is important to address the effect of deflection on the overall VOLUME 33A, JANUARY 2002—79

Fig. 12—Crack deflection profile used in the model proposed by Suresh.[29,30]

stress intensity of the fatigue crack. We use the model developed by Suresh[29,30] to introduce an approximate measure of deflection in the crack growth rate. The model assumes a deflected crack profile, shown in Figure 12. The crack travels a length of S in mode I, then deflects at an angle of ␪ over a length of D. The deflection segment D ⫹ S is repeated, assuming that a given segment is much smaller than the total length of the crack and that the degree of deflection in two adjoining segments takes place in opposite directions. The contribution from deflection is estimated by the average angle and by D/(D ⫹ S), taken over the entire crack profile. The stress-intensity range of the deflected portion of the crack is ⌬kdef, while that of the straight segment is ⌬KI . The effective driving force in the total segment (⌬KI) is given by the weighted average of the effective stressintensity factor across the deflected length D and that across the straight length S: ⌬KI ⫽

D⌬kdef ⫹ S⌬KI D⫹S

(a)

[4]

where ⌬kdef ⬇ ⌬KI ((cos3 (␪ /2))2 ⫹ (sin (␪ /2) cos2 (␪ /2)2)1/2. Simplifying Eq. [5], we can obtain an expression for ⌬KI in terms of ⌬KI:

⌬KI ⬇ ⌬KI

冢

Dcos2

␪ ⫹S 2

冢冣

D⫹S

(b)

冣

[5]

In a straight crack, the effective stress intensity (⌬keff) is equal to the applied stress intensity (⌬KI,app). In order to propagate a deflected crack at the same rate as the straight crack, ⌬keff ⫽ ⌬KI, so ⌬KI,app may be written as

⌬KI,app ⬇ ⌬keff

冢

Dcos2

␪ ⫹S 2

冢冣

D⫹S

⫺1

冣

[6]

Measurements of S, D, and ␪ were taken from digital optical micrographs of the surface replica just prior to failure. Figure 13 shows the effective stress-intensity increase required to propagate a deflected crack at the same crack growth rate as a straight crack of equal length (measured experimentally from surface replication). For large interpore spacings, the heterogeneous microstructure in these materials seems to effectively decrease the crack propagation rate. However, with a higher porosity content and smaller interpore spacing, the microstructural effects on deflection and subsequent crack propagation will most likely be outweighed by the porosity contribution to crack deflection. The stress and strain concentration around pores, for instance, will most likely influence the crack path more than microstructural features within an interpore ligament. Cracks propagate for 80—VOLUME 33A, JANUARY 2002

Fig. 13—da/dN curves illustrating the higher stress intensity required to propagate a crack at a given growth rate when deflection occurs for (a) LCF and (b) HCF.

a longer fraction of the total life in LCF (in which cracks initiate at approximately 10 pct) than in HCF (in which initiation occurs at around 70 pct of the life span), making the crack-deflection model most useful in crack growth in the LCF regime. IV. CONCLUSIONS The following conclusions can be made concerning the fatigue behavior of binder-treated Fe-0.85Mo-1.5Cu1.75Ni-0.6 graphite alloys. 1. The microstructure of the alloy consisted of a heterogeneous microstructure with areas of divorced pearlite, martensite, and nickel-rich ferrite. Two types of porosity were characterized: (1) primary porosity, due to particle packing and binder burnout, and (2) secondary porosity formed due to the copper particles forming a liquid phase and diffusing into Fe particles during sintering. 2. An increase in Mo content increases the fatigue resistance of the alloy, presumably due to an increase in the fraction of carbides. METALLURGICAL AND MATERIALS TRANSACTIONS A

3. During fatigue, an initial period of cyclic hardening was followed by a period of gradual cyclic softening. This behavior was most pronounced in the LCF regime. Additionally, the incubation period required for crack initiation correlated very well with the onset of cyclic softening. 4. The fraction of the life required to initiate a fatigue crack, Ni/Nf , increased with a decrease in fatigue-stress amplitude. Thus, crack initiation occurred early in the life of LCF specimens, and a majority of the fatigue life was spent in the crack-propagation mechanism. In contrast, since crack initiation occupied a much higher fraction of fatigue life in the HCF regime, defect size has a higher impact on the fatigue life, so pore size was the more dominant factor in this regime. 5. Short fatigue cracks initiated at surface pores or pore clusters and propagated at faster rates and lower stress intensities than long fatigue cracks. Linkage of these small fatigue cracks to form the final critical-size crack caused failure, which was characterized by in-situ surface replication. Localized microstructural obstacles resulted in significantly torturous fatigue growth. 6. Application of a crack-deflection model provided a quantitative estimate to the role of crack deflection. It was demonstrated that the effective stress intensity at the crack tip of a deflected crack must be increased significantly to achieve similar crack growth rates to those observed for a straight crack of equal length. ACKNOWLEDGMENTS The authors gratefully acknowledge Dr. K.S. Narasimhan, Hoeganaes Corp., for supplying the materials and for the financial support for this work. REFERENCES 1. N. Chawla, G. Fillari, and K.S. Narasimhan: in Powder Materials: Current Research and Industrial Practices, F.D.S. Marquis, ed., TMS, Warrendale, PA, 1999, p. 247. 2. F.J. Semel: Advances in Powder Metallurgy and Particulate Materials, Metal Powder Industries Federation, Princeton, NJ, 1989, p. 9. 3. S.H. Luk and J.A. Hamill, Jr.: Advances in Powder Metallurgy and Particulate Materials, Metal Powder Industries Federation, Princeton, NJ, 1993, p. 153.

METALLURGICAL AND MATERIALS TRANSACTIONS A

4. N. Chawla, S. Polasik, K.S. Narasimhan, M. Koopman, and K.K. Chawla: Int. J. Powder Metal., 2001, vol. 37, pp. 49-57. 5. N. Chawla, T.F. Murphy, K.S. Narasimhan, M. Koopman, and K.K. Chawla: Mater. Sci. Eng. A, 2001, vol. A308, pp. 180-88. 6. A. Hadrboletz and B. Weiss: Int. Mater. Rev., 1997, vol. 42, pp. 1-44. 7. H. Danninger, D. Spoljaric, and B. Weiss: Int. J. Powder Metall., 1997, vol. 33, pp. 43-53. 8. J. Holmes and R.A. Queeney: Powder Metall., 1985, vol. 28, pp. 231-35. 9. K.D. Christian and R.M. German: Int. J. Powder Metall., 1995, vol. 31, pp. 51-61. 10. U. Lindstedt, B., Karlsson, and R. Masini: Int. J. Powder Metall., 1997, vol. 33, pp. 49-61. 11. S. Suresh: Fatigue of Materials, 2nd ed., Cambridge University Press, Cambridge, United Kingdom, 1998, p. 541. 12. N. Chawla, C. Andres, J.W. Jones, and J.E. Allison: Metall. Mater. Trans. A, 1998, vol. 29A, pp. 2843-54. 13. M.H. Swain: Small Crack Test Methods, ASTM STP 1149, ASTM, Philadelphia, PA, 1992, pp. 34-56. 14. M. Caton, J.W. Jones, J.M. Boileau, and J.E. Allison: Metall. Mater. Trans. A, 1999, vol. 30A, pp. 3055-68. 15. J.A. Lund: Int. J. Powder Metall. Powder Technol., 1984, vol. 20, pp. 141-48. 16. Z.R. Xu, K.K. Chawla, A. Wolfenden, A. Neuman, G.M. Liggett, and N. Chawla: Mater. Sci. Eng., 1995, vol. 203A, pp. 75-80. 17. U. Lindstedt and B. Karlsson: Advances in Powder Metallurgy & Particulate Materials, compiled by T.M. Cadle and K.S. Narasimhan, MPIF, Princeton, NJ, 1996, vol. 5, pp. 17-35. 18. K.V. Sudhakar: Int. J. Fatigue, 2000, vol. 22, pp. 729-34. 19. D.A. Lukasak and D.A. Koss: Composites, 1993, vol. 24, p. 262. 20. N. Chawla, L.C. Davis, C. Andres, J.E. Allison, and J.W. Jones: Metall. Mater. Trans. A., 2000, vol. 31A, pp. 951-57. 21. S.M. McGuire and M.E. Fine: Metall. Mater. Trans. A, 1996, vol. 27A, pp. 1267-71. 22. H. Drar and A. Bergmark: Fatigue Fract. Eng. Mater. Struct., 1997, vol. 20, pp. 1319-30. 23. H. Drar, Mater. Characterization, 2000, vol. 45, pp. 211-20. 24. C. Laird: Fatigue Crack Propagation, Special Technical Publication 415, ASTM, Philadelphia, PA, pp. 131-68. 25. D. Rodzinak and M. Slesar: Powder Metall. Int., 1980, vol. 12, pp. 127-30. 26. I.S. Raju and J.C. Newman: Fracture Mechanics, ASTM STP 905, J.H. Underwood, R. Chait, C.W. Smith, D.P. Wilhem, W.A. Andrews, and J.C. Newman, eds. ASTM, Philadelphia, PA, 1986, pp. 789-805. 27. S. Carabajar, C. Verdu, A. Hamel, and R. Fougeres: Mater. Sci. Eng., 1998, vol. A257, pp. 225-34. 28. T.M. Cimino, A.H. Graham, and T.F. Murphy: Advances in Powder Metallurgy and Particulate Materials, Metal Powder Industries Federation, Princeton, NJ, 1998. 29. S. Suresh: Metall. Trans. A, 1983, vol. 14A, pp. 2375-85. 30. S. Suresh: Metall. Trans. A, 1985, vol. 16A, p. 249.

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