The Debonding and Fracture of Si Particles during theFatigue of a Cast Al-Si Alloy

KEN GALL, NANCY YANG, MARK HORSTEMEYER, DAVID L. McDOWELL, andJINGHONG FAN

Constant-amplitude high-cycle fatigue tests (smax 5 133 MPa, smax/sy 5 0.55, and R 5 0.1) wereconducted on cylindrical samples machined from a cast A356-T6 aluminum plate: The fracture surfaceof the sample with the smallest fatigue-crack nucleating defect was examined using a scanning electronmicroscope (SEM). For low crack-tip driving forces (fatigue-crack growth rates of da/dN , 1 31027 m/cycle), we discovered that a small semicircular surface fatigue crack propagated primarilythrough the Al-1 pct Si dendrite cells. The silicon particles in the eutectic remained intact and servedas barriers at low fatigue-crack propagation rates. When the semicircular fatigue crack inevitablycrossed the three-dimensional Al-Si eutectic network, it propagated primarily along the interfacebetween the silicon particles and the Al-1 pct Si matrix. Furthermore, nearly all of the silicon particleswere progressively debonded by the fatigue cracks propagating at low rates, with the exception ofelongated particles with a major axis perpendicular to the crack plane, which were fractured. As thefatigue crack grew with a high crack-tip driving force (fatigue-crack growth rates of da/dN . 1 31026 m/cycle), silicon particles ahead of the crack tip were fractured, and the crack subsequentlypropagated through the weakest distribution of prefractured particles in the Al-Si eutectic. Only smallrounded silicon particles were observed to debond while the fatigue crack grew at high rates. Usingfracture-surface markings and fracture mechanics, a macroscopic measure of the maximum criticaldriving force between particle debonding vs fracture during fatigue-crack growth was calculated tobe approximately Ktr

max ' 6.0 MPa!m for the present cast A356 alloy.

I. INTRODUCTION predicting the fatigue life of cast Al-Si alloys that containeither significant or negligible porosity levels.THE outstanding mechanical, physical, and casting prop-

In the automotive industry, one technologically importanterties of Al-Si alloys make them attractive for use in cheaperAl-Si casting alloy is A356. The microstructure of A356and lighter engineering components. However, to success-consists of primary Al-1 pct Si dendrites and a eutectic withfully utilize cast Al-Si alloys in long-life components, it issilicon particles (12 pct volume fraction) embedded in annecessary to thoroughly understand their resistance toAl-1 pct Si matrix. Other trace elements such as strontium,fatigue. Numerous studies have shown that when large-scaleiron, and magnesium are added to improve the silicon parti-casting porosity is present in cast Al-Si alloys, the largestcle morphology, to prevent die soldering, and to promotepores dictate the fatigue life of the material.[1–13] Moreover,precipitation hardening, respectively. In the absence of inter-in cast materials with a maximum pore size À100 mm, themetallic particles and large-scale porosity, the fracture andfatigue life of a specimen can be estimated by integrating adebonding of irregular-shaped silicon particles controls theParis law crack-growth-rate equation. Ting and Lawrence[4]

ductility of A356 alloys.[15] When intermetallics are presentconcluded that the crack-nucleation life from large poresencompasses a negligible fraction of the fatigue life of cast in the material, they are expected to further limit the macro-Al-Si alloys. However, continual advances in casting tech- scopic ductility of the material.[16] Under monotonic loading,nology are driving the maximum pore size well below 100 the debonding and fracture of second-phase particles causesmm in typical Al-Si castings.[6,12,14] Furthermore, the highly the nucleation of voids in the surrounding Al-1 pct Si matrixevolved design of industrial castings permits the control of material. In modeling the failure of cast Al-Si alloys sub-porosity in regions that will experience large stresses during jected to monotonic loading, it is not critical to distinguishservice. In parallel with these materials-processing develop- between particle debonding or fracture, as will be rational-ments, we need to further understand the micromechanisms ized subsequently. Near-cracked and debonded particles,of fatigue-crack growth in cast Al-Si alloys. Understanding subsequent void growth, and coalescence mechanisms willlocal fatigue-crack growth mechanisms will facilitate the overshadow any initial differences in local stress fields fordevelopment of micromechanical fatigue models capable of a debonded vs cracked particle, because of the large-scale

yielding occurring in the material. Consequently, monotonicconstitutive relationships with coupled damage evolution

KEN GALL, Assistant Professor, is with the Department of Mechanical usually treat a fractured and debonded particle as the sameEngineering, University of Colorado, Boulder, CO 80309. NANCY YANGentity, i.e., a damaged particle. Constitutive models basedand MARK HORSTEMEYER, Technical Staff, are with the Materials and

Engineering Sciences Center, Sandia National Laboratories, Livermore, on a single-particle damage parameter have proven success-CA 94550. DAVID L. McDOWELL, Professor, and JINGHONG FAN, ful in reproducing the monotonic stress-strain response ofResearch Scientist, are with the GWW School of Mechanical Engineering,

cast Al-Si alloys at all strain levels.[17]Georgia Institute of Technology, Atlanta, GA 30332.

Manuscript submitted April 1, 1999. Under cyclic loading conditions, the difference between

METALLURGICAL AND MATERIALS TRANSACTIONS A U.S. GOVERNMENT WORK VOLUME 30A, DECEMBER 1999—3079NOT PROTECTED BY U.S. COPYRIGHT

the debonding and fracture of silicon particles is more perti- Small specimens were used to increase the chance that atleast a few specimen gage sections would be free of large-nent to fatigue-life modeling efforts. If the silicon particles

remain intact and fatigue cracks are forced to propagate scale casting porosity, which would act as a crack nucleationsite. A specimen without large-scale casting porosity wouldgradually along the particle-matrix interface, the crack may

experience significant growth retardation.[18] Crack-growth allow the study of fatigue-crack growth mechanisms forcrack sizes smaller than typical casting pores. Room-temper-retardation occurs because the effective crack length is

increased as the crack grows around a network of particles ature constant-amplitude fatigue tests were conducted witha maximum stress amplitude of 133 MPa, a frequency of 5within a ductile matrix. In addition, a meandering crack path

forces the crack tip to propagate under unfavorable local Hz, and loading conditions of R 5 0.1. The voltage (poten-tial) drop was measured across the entire specimen gagemixed-mode loading conditions rather than under a favorable

mode I driving force. Conversely, if the particles prematurely length in the dog-bone-shaped tensile bars. Although thepotential-drop method is traditionally used to measurefracture before the fatigue-crack tip reaches them, the

cleaved particles provide a weak material path for the propa- fatigue-crack growth rates, in this experimental set-up it wasused to monitor the relative size of the most dominant fatiguegating crack tip.[18] Differences in the crack-tip shielding

mechanism and respective growth rate will have a dramatic crack. When the potential drop reached an arbitrary criticalvalue (the same for all specimens), the test was stopped,influence on the fatigue life of cast Al-Si alloys, particularly

at small crack sizes. Consequently, in order to more accu- and the specimen was carefully broken to reveal the fatiguedfracture surfaces. The fracture surfaces of the sample wererately model fatigue-crack growth in cast Al-Si alloys, we

need to understand the conditions that promote particle frac- studied with a scanning electron microscope (SEM).ture vs debonding during fatigue.

Previous fatigue-crack growth studies[3,14,19] have qualita- III. FRACTURE-SURFACE OBSERVATIONStively shown that silicon particles in cast Al-Si alloys have

The undeformed microstructure of the present cast A356a tendency to debond or fracture, depending on the crack-alloy is presented in Figure 1. Figure 1(a) is an SEM imagetip driving force. However, such investigations have notof undeformed A356, where the Al-1 pct Si was deeplyoutlined the microstructural and external conditions that pro-etched with a sodium hydroxide solution to reveal the three-mote particle debonding vs cracking during fatigue-crackdimensional shape and distribution of the silicon particles.growth. Furthermore, many previous studies on cast Al-SiThe etchant only attacks the Al-1 pct Si material and leavesalloys have considered fatigue cracks growing from largethe Si particles intact. Figure 1(b) is an optical image of amicrostructural defects such as casting porosity[3,4] or thosepolished arbitrary cross section of the same undeformedin compact-tension specimens with large initial crackA356 cast aluminum alloy. In Figure 1(a) the dark matrixsizes.[19] Such studies do not provide insight into the earlyis aluminum with 1 pct silicon in solution (Al-1 pct Si), andstages of fatigue-crack propagation, when the overall crackthe bright particles sitting on top of the matrix are pure-size is on the order of several dendrite cells. The purposesilicon inclusions. Conversely, in Figure 1(b) the brightof the present work is to quantitatively analyze the transitionmatrix is Al-1 pct Si and the dark-gray areas are pure silicondriving force between crack growth along the particle-matrixparticles. The large cell-shaped Al-1 pct Si regions in bothinterface vs across a fractured particle. The foundation ofimages are Al-1 pct Si primary dendrite cells, and the net-the analysis is based on fracture-surface observations of thework containing the silicon particles is an Al-Si eutecticconditions that promote particle fracture vs debonding overphase. Silicon particles of various sizes and shapes are founda varying range of crack lengths and crack-tip driving forces.in the A356 alloy eutectic regions (Figure 1). However,due to the strontium modification and long solutionizing

II. EXPERIMENTAL TECHNIQUES treatment (16 hours at 810 K), the silicon particles are notinterconnected in a subdendrite structure even when deepThe nominal composition of the A356 aluminum alloy is

7 pct Si, 0.4 pct Mg, 0.01 pct Fe, 0.01 pct Cu, 0.01 pct Mn, etching is carried out. The Al-Si eutectic network has athree-dimensional character due to the dendritic nature of the0.01 pct Sr, 0.01 pct Ti, 0.01 pct Zn, and the balance Al.

To produce A356 cast plates, an A356.2 ingot was melted solidification front. Consequently, regardless of the preferredmaterial path of fatigue-crack propagation, a fatigue crackin an induction furnace. The melt was grain refined with

titanium-boron, modified with strontium, and degassed using must cross Al-1 pct Si dendrites and Al-Si eutectic regions.However, the material path chosen by the fatigue cracka rotary degasser. The castings were poured between 950

and 977 K and then were fully cooled over a 16-hour period. depends on the relative crack-tip driving force, as demon-strated by the following observations.The A356 aluminum plates were cast in rectangular molds

with interior dimensions of 25 3 14 3 5 cm. Iron chills A summary of the fatigue tests on the cast A356 aluminumspecimens is presented in Table I. As shown in Table I, thewere employed on the top, bottom, and end of the casting

mold to simulate a permanent mold casting. A no-bake silica combined characteristics and overall size (fracture-surfacearea) has a dramatic influence on the number of cyclessand was used to create the sides of the plate, the riser, and

the down sprue. A ceramic foam filter was used between required to create a crack of significant size (,1 mm) inthe specimen. In general, the larger the area projected onthe down sprue and the riser. The plates were removed from

the mold and then heat treated to a T6 aging treatment the fracture surface, the smaller the fatigue life of the sample.However, it is also evident that distributed porosity with an(solution heat treated at 810 K for 16 hours, quenched in

hot water at 344 K, and then aged for 4 hours at 518 K). equivalent total fracture-surface area is less detrimental tothe fatigue performance than is that of a single large poreNumerous smooth cylindrical-(dog-bone-) shaped fatigue

specimens were machined from the cast plate, with a gage (compare the fatigue performance in samples 5 and 10). Inorder to study the mechanisms of fatigue-crack growth overlength of 15 mm and a gage section diameter of 3 mm.

3080—VOLUME 30A, DECEMBER 1999 METALLURGICAL AND MATERIALS TRANSACTIONS A

Fig. 2—SEM image of the overall fatigue fracture surface on sample 11.

as indicated in Figure 2. The black curve in Figure 2 corres-ponds to the approximate position of the crack front alongwhich the fracture surface demonstrates a noticeable changein the surface roughness. The semicircular shape of the crackfront is consistent with other observations of fatigue cracksgrowing in a solid circular cylinder.[20] In a previous studyon cast A356 aluminum,[16] it has been demonstrated thatthe increase in the surface roughness corresponds to a changein the fatigue-crack growth path at the microstructural level.At low stress intensity ranges, the fatigue cracks grow pri-marily through the Al-1 pct Si dendrites, while, at highranges, the cracks grow through the Al-Si eutectic regionsand iron intermetallics, if present. In the aforementionedstudy,[16] this transition point was marked by a drasticincrease in the area fraction of damaged iron intermetallicson the fracture surface. The present study will demonstratethat the transition from fatigue-crack growth primarilythrough the Al-1 pct Si dendrites to growth primarily throughthe Al-Si eutectic is also accompanied by a change of the

Fig. 1—Arbitrary (a) etched and (b) polished cross sections of the unde- debonding and fracture characteristics of the Si particles.formed cast A356-T6 aluminum used for fatigue testing. A higher-magnification image of the fatigue-crack nucle-

ation site is shown in Figure 3. A pair of aluminum andmagnesium oxides at the specimen surface serves as thefatigue-crack nucleation site in specimen 11. The effectivea wide range of crack sizes, the specimen with the smallest

nucleation site (specimen 11) was selected for further metal- nucleation site is outlined with a black curve in Figure 3.As indicated in Figure 2, several representative locationslographic examination. Figure 2 is an SEM image of the

overall fracture surface of specimen 11. The fatigue-crack were chosen on the fracture surface to elucidate the localfatigue-crack growth mechanisms as influenced by siliconnucleation site is located at the bottom of the fracture surface,

Table I. Constant Amplitude Fatigue Test Results on Five Specimens Machined from an A356 Casting*

Nucleation Site Area onTest Number of Applied Crack Nucleation Specimen Fracture

Identification Cycles Site Characteristics Surface

5 9,369 casting pore with major axis (900 mm) along specimen surface 0.225 mm2

14 49,420 two near-surface casting pores 200 mm apart from each other 0.118 mm2

8 142,755 two near-surface casting pores 300 mm apart from each other 0.060 mm2

10 157,569 distributed casting porosity near specimen surface. total , 0.225 mm2

11 331,629 oxides near specimen surface (Figure 3). 0.012 mm2

*The specimens were cycled until the voltage drop across the specimen gage section reached a critical value. The critical value wasarbitrarily chosen but was the same for all tests.

METALLURGICAL AND MATERIALS TRANSACTIONS A VOLUME 30A, DECEMBER 1999—3081

fatigue crack evaded elongated particles with a major axisperpendicular to the crack plane, or (2) the fatigue crackfractured such particles even at low crack-tip driving forces.Since there were a few fractured particles on the fracturesurface within 100 mm of the nucleation site, and significantcrack-tip meandering was not evidenced near the debondedparticles, the latter explanation is more plausible.

As shown in Figure 5(a), silicon particle debonding isstill the dominant particle failure mechanism 300 mm awayfrom the crack nucleation site (location 2 in Figure 2). Simi-lar to location 1 near the nucleation site, fine fatigue striationssurround the debonded particles (Figure 5(b)). However, theoverall tolerance for the fracture of elongated particles witha major axis parallel to the crack plane decreases as thecrack size increases (due to the constant-amplitude test con-ditions, the maximum crack-tip driving force also increases).In other words, the number density of fractured silicon parti-cles on the fracture surface is larger at a greater distancefrom the nucleation site. For example, in the upper-right-hand corner of Figure 5(a), several silicon particles are frac-Fig. 3—SEM image of the fatigue crack nucleation site.tured rather than debonded. The increase in the number offractured particles is partially due to a local difference inthe crack-tip driving force, i.e., the striations in the upper-

particle fracture and debonding. Images from locations 1, right-hand corner are coarser than the striations near the2, and 3 are presented in Figures 4, 5, and 6, respectively. center of the image. Small differences in the local crack-tipFigures 4(a) through (c) are a series of SEM images of a driving force and growth rates are inevitable due to thefatigued region at a distance of 100 mm from the crack three-dimensional nature of the crack fronts and the spatialnucleation site (location 1 in Figure 2). Although the crack distribution of microstructural features in a heterogeneouspassed primarily through the Al-1 pct Si dendrite cells very material. Nevertheless, when the fatigue crack passedclose to the nucleation site, the three-dimensional nature of through the eutectic near location 2, it primarily propagatedthe dendrite cell structure evidently forced the crack to pass along the silicon particle and Al-1 pct Si matrix interface.through some Al-Si eutectic regions. When the fatigue crack Generally speaking, while the fatigue-crack tip was withinencountered silicon particles within the eutectic, the small the black boundary line in Figure 2, the crack progressedcrack primarily propagated along the interface between the

along the interface between the silicon particles and the Al-silicon particles and the Al-1 pct Si matrix (Figure 4(a)).1 pct Si matrix when eutectic regions were encountered.Crack growth along the interface between the two phasesHowever, in an overall sense, the fatigue crack avoided theis asserted due to the extremely smooth and rounded surfaceeutectic regions when it was within the boundary line. Theof the exposed silicon particles at extremely high magnifica-dominant fatigue crack primarily grew straight through thetions (Figure 4(c)). In addition, the smooth character of theAl-1 pct Si dendrite cells, as evidenced by the large planardebonded particles on the fracture surface is consistent withsections of Al-1 pct Si on the fracture surface. Furthermore,the particle morphology in the sample where the Al-1 pctwithin the boundary line, fatigue striations were oftenSi was completely etched away (Figure 1(a)). On the otherobserved on the surfaces of cavities that once containedhand, the apparently smooth Al-1 pct Si matrix materialsilicon particles (Figure 5(b)). These fatigue striations indi-(Figure 4(b)) shows evidence of fatigue-crack growth stria-cate that debonding occurred gradually as a fatigue cracktions at higher magnifications (Figure 4(c)). The striationsgrew up to and around a silicon particle. Therefore, it canare extremely fine (less than 0.1 mm), indicating that thebe asserted that the silicon particles retard the growth of thefatigue-crack growth rate in the vicinity of the debondedfatigue cracks at low crack-tip driving forces, since theparticles is very low (da/dN , 1 3 1027 m/cycle). Lowcracks generally avoid the particles and must grow aroundgrowth rates for a fatigue crack indicate that the crack-tipthe particles when they are encountered. If the particles weredriving force, i.e., the stress intensity range, is also relativelydebonding a significant distance away from the crack tip,small. It should be noted that the striation spacing was diffi-then the debonded Al-Si eutectic regions would provide acult to estimate due to the fine scale of the markings. How-weak material path for the fatigue cracks rather than aever, striation spacing is certainly less than 0.1 mm.deflective one. Subsequently, the fatigue crack would beThe shapes of the debonded silicon particles on the frac-expected to propagate preferentially through the damagedture surface in Figure 4 provide insight into the operanteutectic region. However, the crack did not grow preferen-fatigue mechanisms. Numerous elongated silicon particlestially through the Al-Si eutectic at low crack-tip drivingwere found on the fracture surface near the fatigue-crackforces within the boundary line.nucleation site. The extended (major) axis of the debonded

Observations past the boundary line in Figure 2 (locationelongated particles was always parallel to the fracture-sur-3) show a significant change in the fatigue-crack growthface plane. Debonded elongated particles with a major axismechanisms (Figure 6). The overall area fraction of Al-Siprotruding out of the fracture surface were not observed.

These observations indicate one of two mechanisms: (1) the eutectic (including damaged Si particles) on the fracture

3082—VOLUME 30A, DECEMBER 1999 METALLURGICAL AND MATERIALS TRANSACTIONS A

Fig. 4—(a) through (c) SEM images of particle debonding 100 mm from the crack nucleation site (location 1).

surface increases dramatically past this boundary line. On the fatigue crack propagates with an increased driving forceand growth rate (da/dN , 1 3 1026 m/cycle), nearly all ofthe microscale, the fatigue-crack striations are coarser (about

1 mm) and the morphology of damaged silicon particles on the silicon particles in the crack path are fractured (Figure6(a)). Although both round and large irregular-shaped parti-the fracture surface changes. Comparing Figures 4(b), 5(b),

and 6(b), it is obvious that the striations just past the bound- cles (in the plane of the fracture surface) are cracked pastthe transition boundary, the abnormal number of irregular-ary line are much coarser than within the boundary. The

increase in the spacing of the fatigue striations is consistent shaped particles indicates that a biased crack path isfollowed.with an increase in the local crack-tip driving force. When

METALLURGICAL AND MATERIALS TRANSACTIONS A VOLUME 30A, DECEMBER 1999—3083

Fig. 5—(a) through (c) SEM images of particle debonding 300 mm from the crack nucleation site (location 2).

The fact that a fatigue crack growing with a large crack- order for the crack to consistently locate fractured particlesduring growth, such particles must experience fracturetip driving force is biased toward growth through irregular-

shaped silicon particles is consistent with observations dur- before the crack tip reaches them. Fractured particles mayalso act as nucleation sites for microcracks, which increasesing monotonic material failure.[15] The irregular-shaped par-

ticles readily fracture, since the local stress concentrations the local driving force for the coalescence of fractured parti-cle regions and the dominant crack. In other words, the crackare higher than those in rounded particles. Furthermore, in

3084—VOLUME 30A, DECEMBER 1999 METALLURGICAL AND MATERIALS TRANSACTIONS A

Fig. 6—SEM images of particle fracture 800 mm from the crack nucleation site (location 3).

will only meander, as evidenced by the rougher fatigue- IV. DISCUSSIONfracture surface, if there is a weak path for the fatigue crack

We assert that the silicon particles have an explicit influ-to propagate through. The mechanism of local materialence, i.e., not quantifiable by “overall” material properties,weakening through silicon particle fracture at high fatigue-on the mechanisms of fatigue-crack growth when the fatiguecrack-tip driving forces is in contrast to the shielding mecha-crack is small or has a low crack-tip driving force. Thenism offered by intact silicon particles at low crack-tip driv-

ing forces. present observations on cast aluminum alloys are consistent

METALLURGICAL AND MATERIALS TRANSACTIONS A VOLUME 30A, DECEMBER 1999—3085

with previous findings on wrought alloy systems. During schematically illustrates the dominant fatigue-crack growthstage I fatigue-crack growth, microstructure plays an explicit mechanisms operating, depending on the relative intensityrole on the fatigue-crack growth behavior for many classes of the maximum crack-tip driving force. Figure 7 summa-of wrought engineering alloys.[22–27] Furthermore, micro- rizes the mechanisms of fatigue-crack growth through thestructure has an extremely dominant influence on cracks Al-Si eutectic regions, not the Al-1 pct Si dendrites. Atgrowing in the stage I regime, which are very small with low crack-tip driving forces, fatigue cracks will propagaterespect to pertinent microstructural features (microstructur- primarily along the interface between the silicon particlesally small cracks[22–27]). As the fatigue-crack length and and the Al-1 pct Si matrix. Only elongated particles withcorresponding crack-tip driving force increases, cracks are the major axis perpendicular to the primary crack planecharacterized as growing in the stage II, or Paris law, regime. will be fractured. Furthermore, the particles are graduallyDuring stage II growth, the microstructure still affects debonded as the fatigue cracks grow around the particles.fatigue-crack growth, but the microstructural effect is accu- At high crack-tip driving forces, silicon particles fracturerately represented by overall material properties. The explicit ahead of the crack tip, and the crack subsequently propagatesinfluence of the microstructure at smaller crack sizes and through the damaged regions (Figure 7). Although somecrack-tip driving forces is governed by the statistical nature smaller particles may debond during this stage of fatigue-of microstructural features in engineering alloys. The process crack growth, particle fracture is the dominant failurezones of the small cracks simply cannot sample a statistically mechanism.significant portion of the local microstructural features to Essentially, we maintain that the transition between parti-represent a continuum. Consequently, average properties do cle debonding vs particle fracture is controlled by the extentnot accurately represent the fatigue-crack growth process of the crack-tip process zone. A small fatigue crack with afor such cracks, and information on the influence of micro- low crack-tip driving force (small process zone) only sam-structural features is necessary to accurately predict fatigue- ples a small volume fraction of a silicon particle, includingcrack growth. With this in mind, the present discussion the particle matrix interface in-line with the crack tip. Offocuses on mechanisms pertinent to stage I fatigue-crack possible particle failure modes, local debonding is the mostgrowth and the transition to stage II growth (fatigue-crack probable, since the small process zone at the crack tip cannotgrowth rates near and below da/dN , 1 3 1027 m/cycle). produce the elastic strain energy required to fracture the

The SEM images of the fracture surface on the fatigued entire silicon particle. Conversely, for particle orientationssamples indicate two distinctly different growth mechanisms where the major axis is perpendicular to the crack plane,through the silicon particle–rich Al-Si eutectic. Figure 7 the resistance to debonding is relatively high, since a large

area of the interface is parallel to the maximum principalstress field for a fatigue crack growing under mode 1 loadingcondition.[21] In addition, numerical simulations show thatthe resistance to silicon-particle fracture decreases whenthe major axis of a particle is parallel to a principal stressdirection.[28] The counterbalancing effects of shape on frac-ture and debonding mechanisms promote the fracture ofsilicon particles with a major axis perpendicular to the crackplane, even for a small crack-tip process zone. When thefatigue crack become large enough, the crack-tip processzone engulfs many particles and is capable of fracturingparticles, since the elastic strain energy released by the parti-cle fracture is smaller than the energy supplied by the cracktip. Although the silicon particles may not contain initialprecracks per se, many of them have discontinuous shapesand local sharp corners. In single-crystal silicon deformed atroom temperature, such sharp notches lead to failure stressessignificantly lower than those in a pristine particle, as pre-dicted by modified fracture-toughness criteria.[29]

Due to the three-dimensional nature of fatigue crackscoupled with the heterogeneity of this A356 aluminum alloy,the crack growth mechanisms are never uniform along theperiphery of a crack front. However, at the macroscale, arelatively abrupt transition between the two different growthmechanisms is observed. This transition point is accompa-nied by a dramatic increase in the surface roughness of thefracture surface, as marked by a black line in Figure 2. Giventhe two growth mechanisms outlined in Figure 7, an increasein the fracture-surface roughness is expected as the fatiguecracks begin to follow paths dictated by the fracture ofsilicon particles in the Al-Si eutectic. Traditionally, the localcrack-tip driving force during fatigue is estimated using anFig. 7—Schematic of the fatigue crack process through the silicon particle–

rich eutectic regions at low and high crack tip driving forces. effective stress intensity range (DKeff ). In the present study,

3086—VOLUME 30A, DECEMBER 1999 METALLURGICAL AND MATERIALS TRANSACTIONS A

the maximum stress intensity value (Kmax) will be calculated MPa!m. Even with a significantly large crack-tip drivingforce, the extremely small fatigue crack cannot sample aand used as the parameter governing the transition between

growth patterns in the Al-Si eutectic. The Kmax and DKeff statistically significant number of silicon particles. Conse-quently, the transition value determined here cannot be usedparameters both have potential advantages for analyzing the

transition behavior. In general, DKeff may better characterize strictly to quantify the growth behavior of extremely smallfatigue cracks. However, the present observations do helpthe fatigue-crack driving force; however, Kmax may better

characterize the propensity for the silicon particles to crack to qualitatively understand the growth of microstructurallysmall fatigue cracks, as will be discussed in closing.during fatigue. Consequently, Kmax will be used to quantify

the transition point between growth through the silicon parti- In the absence of large-scale porosity, very small fatiguecracks will nucleate from microporosity or damaged siliconcles vs around them.

Using numerical fracture-mechanics solutions, we esti- particles in the eutectic.[12,14] Immediately after nucleation,such cracks are considered microstructurally small. Undermated the value of the maximum applied stress intensity

factor at the transition crack size between the two growth typical high-cycle fatigue loading conditions, the maximumcrack-tip driving force for microstructurally small cracks ismechanisms (the black boundary line in Figure 2). Such an

analysis provides an average critical value for crack growth well below the transition value of 6.0 MPa!m. Thus, duringits propagation life, the microstructurally small cracks arethrough the silicon particles vs crack growth along the inter-

face between the silicon particles and the Al-1 pct Si matrix. unable to fracture silicon particles, and they are forced togrow along the particle-matrix interface. Consequently, dur-The general solution for the maximum crack-tip driving

force during fatigue is ing growth along the particle-matrix interface, the siliconparticles should act as barriers to the growth of microstruc-

Kmax 5 f(g)smax!pa [1] turally short cracks. Experimental observations have shownthat microstructurally small cracks experience a severewhere f(g) is a function of the specimen geometry and load-decrease in growth rates as the cracks approach the siliconing configuration, smax is the maximum applied stress duringparticles.[12] Finally, it will be mentioned that the fatiguethe fatigue test, and a is the crack length. For a round cylindermechanisms and quantitative calculations in the presentwith a circular edge crack subjected to axial loading, thestudy were only validated for an Al-Si alloy with a modifiednumerical solution for f(g) is given as[30]

silicon particle morphology. Al-Si alloys with a coarseunmodified silicon particle morphology demonstratef(g) 5 0.67 2 1.24

ad

1 28.0 1ad2

2

2 162.4 1ad2

3

[2]extremely high crack growth rates at large stress ratios.[31]

The extremely high crack growth rates in unmodified alloysmakes them impractical for engineering applications.1 472.2 1a

d24

2 629.6 1ad2

5

1 326.1 1ad2

6

Moreover, we note that the article only presented imagesfrom the fracture surface of one fatigued sample. Numerous

where a is the maximum crack length into the specimen, samples were examined in the SEM, and the general trendsand d is the diameter of the cylindrical specimen. The values described are absolutely consistent with the theories pre-for the crack front marked in Figure 2 are a 5 0.75 mm, sented here. The maximum transition stress intensity valued 5 3 mm, and smax 5 133 MPa. From Eq. [2], the geometry calculated here is similar for other fatigued samples fromfactor is calculated as f(g) 5 0.88. Using the previous num- the same material batch (for example, Reference 16). How-bers, the maximum stress intensity factor at the transition ever, we do concede that the transition value will dependpoint is calculated as on the cast material considered. The cast A356 employed

in the present study contained a very low volume fractionKtrmax 5 5.69 ' 6.0 MPa!m [3]

of porosity and well-spherodized Si particles. Cast Al-SiThe value of Ktr

max ' 6.0 MPa!m is slightly lower than pre- alloys may contain coarser Si eutectic particles and signifi-vious calculations for the same cast material, which gave a cant casting porosity, depending on the casting procedure.transition value of Ktr

max ' 7.0 MPa!m.[16] The calculation The point of transition between the fracture and debondingin the previous study relied on the increase in the area of coarser Si particles in a cast Al-Si alloy is not consideredfraction of iron intermetallics on the fracture surface to esti- here and may be a topic of future research, if necessary.mate the transition point between growth through the Al-1pct Si dendrite cells vs growth through the Al-Si eutectic

V. CONCLUSIONSregions. The difference between the two values is an indica-tion of the error involved in choosing the crack-front position From SEM examination of the fracture surface of ausing two different criteria (Figure 2). fatigued specimen machined from a cast A356 aluminum

As a first-order approximation, we conclude that all plate, the following conclusions are drawn.fatigue cracks propagating with a maximum applied stressintensity lower than 6.0 MPa!m avoid eutectic regions and 1. At a maximum crack-tip driving force less than Ktr

max '6.0 MPa!m, a fatigue crack propagates at a low rateprimarily debond particles when the eutectic regions are

inevitably encountered. Fatigue cracks propagating with a (da/dN , 1 3 1027 m/cycle), primarily through the Al-1 pct Si dendrite cells. Above a maximum driving forcemaximum applied stress intensity above 6.0 MPa!m will

travel primarily through eutectic regions via fractured silicon of 6.0 MPa!m, a fatigue crack propagates at a higherrate (da/dN . 1 3 1026 m/cycle), preferentially throughparticles. It should be noted that if the crack size is on the

order of the mean silicon particle spacing, then a fatigue the Al-Si eutectic regions. On the microscale, the transi-tion point between dominant fatigue-crack growthcrack may debond silicon particles even if it is propagating

with a maximum applied stress intensity above 6.0 through the Al-1 pct Si dendrites and crack growth

METALLURGICAL AND MATERIALS TRANSACTIONS A VOLUME 30A, DECEMBER 1999—3087

Struct., 1990, vol. 13, pp. 213-27.through the Al-Si eutectic corresponds to a change in the4. J.C. Ting and F.V. Lawrence: Fat. Fract. Eng. Mater. Struct., 1993,debonding and fracture characteristics of silicon particles

vol. 16, pp. 631-47.in the eutectic regions. 5. S.E. Stanzl-Tschegg, H.R. Mayer, E.K. Tschegg, and A. Beste: Int. J.

2. Below a maximum driving force of 6.0 MPa!m and for Fat., 1993, vol. 15, pp. 311-16.6. S. Gungor and L. Edwards: Fat. Fract. Eng. Mater. Struct., 1993, vol.a small crack with a length much smaller than the mean

16, pp. 391-403.silicon particle spacing, the silicon particles remain intact7. B. Skallerud, T. Iveland, and G. Harkegard: Eng. Fract. Mech., 1993,and act as barriers to fatigue-crack propagation. The vol. 44, 857-74.

fatigue cracks propagating at low rates are forced to move 8. C.M. Sonsino and J. Ziese: Int. J. Fat., 1993, vol. 15, pp. 75-84.9. R.B. Gundlach, B. Ross, A. Hetke, S. Valtierra, and J.F. Mojica: AFSalong the interface between the silicon particles and the

Trans., 1994, vol. 102, pp. 205-23.Al-1 pct Si matrix, gradually debonding the silicon10. J.F. Major: AFS Trans., 1994, vol. 102, pp. 901-06.particles.11. A.A. Dabayeh, R.X. Xu, B.P. Du, and T.H. Topper: Int. J. Fat., 1996,

3. At low fatigue-crack propagation rates, all silicon parti- vol. 18, pp. 95-104.cles are debonded except elongated particles with a major 12. K. Shiozawa, Y. Tohda, and S.-M. Sun: Fat. Fract. Eng. Mater. Struct.,

1997, vol. 20, pp. 237-47.axis parallel to the primary crack plane. The growing13. A.A. Dabayeh, A.J. Berube, and T.H. Topper: Int. J. Fat., 1998, vol.fatigue crack fractures particles with a major axis perpen-

20, pp. 517-30.dicular to the fatigue crack growth plane. 14. A. Plumtree and S. Schafer: in The Mechanical Behavior of Short4. Above a maximum crack-tip driving force of Fatigue Cracks, K.J. Miller and E.R. de los Rios, eds., Suffolk, United

Kingdom, 1986, pp. 215-27.6.0 MPa!m, and for a sufficiently long crack relative to15. M.D. Dighe and A.M. Gokhale: Scripta Metal., 1997, vol. 37, pp.the mean particle spacing, the silicon particles are frac-

1435-40.tured ahead of the crack tip, and they create weakened16. K. Gall, N. Yang, M.F. Horstemeyer, D.L. McDowell, and J.H. Fan:

material paths for the fatigue cracks to propagate through. Fat. Fract. Eng. Mater. Struct., in press.During this stage of growth, the crack primarily follows 17. M.F. Horstemeyer and A.M. Gokhale: Int. J. Solid Struct., 1999, vol.

36, pp. 5030-55.large silicon particles with an irregular shape on the frac-18. D. Broek: in Fracture 1969, P.L. Pratt, ed., Chapman and Hall, London,ture surface plane.

p. 734.19. F.T. Lee, J.F. Major, and F.H. Samuel: Fat. Fract. Eng. Mater. Struct.,

1995, vol. 18, pp. 385-96.20. T.L. Mackay and B.J. Alperin: Eng. Fract. Mech., 1995, vol. 21, pp.

ACKNOWLEDGMENTS 391-97.21. R.C. McClung and H. Sehitoglu: Eng. Fract. Mech., 1989, vol. 33,

This work has been sponsored by the United States pp. 237-71.Department of Energy, Sandia National Laboratories, under 22. S. Pearson: Eng. Fract. Mech., 1975, vol. 7, pp. 235-47.

23. J. Lankford: Fat. Fract. Eng. Mater. Struct., 1982, vol. 5, pp. 233-48.Contract No. DE-AC04-94AL85000. This work was per-24. J. Lankford: Fat. Fract. Eng. Mater. Struct., 1985, vol. 8, pp. 161-75.formed under the leadership of Dick Osborne and Don Pen-25. K. Tanaka: Fracture Mechanics: Perspectives and Directions, 20th

rod for the USCAR Lightweight Metals Group. We thank Symp., ASTM STP 1020, R.P. Wei and R.P. Gangloff, eds., ASTM,Gerry Shulke for providing the material and Westmoreland Philadelphia, PA, 1989, pp. 151-83.

26. S. Suresh: Fatigue of Materials, Cambridge University Press, Cam-Mechanical Testing and Research for conducting thebridge, United Kingdom, 1991.fatigue tests.

27. R.C. McClung, K.S. Chan, S.J. Hudak, and D.L. Davidson: ASMHandbook, ASM, Materials Park, OH, 1996, vol. 19, pp. 153-58.

28. K. Gall, M.F. Horstemeyer, D.L. McDowell, and J.H. Fan: Mech.REFERENCES Mater., in press.

29. M.L. Dunn, W. Suwoto, S. Cunningham, and C.W. May: Int. J. Fract.,1. P.C. Inguanti: 17th SAMPE Conf., Oct. 22–24, 1985, pp. 61-72. 1997, vol. 84, pp. 367-81.

30. A.F. Liu: Structural Integrity of Fasteners, ASTM STP 1236, ASTM,2. C.C. Wigant and R.I. Stephens: Fatigue and Fracture Toughness ofA356-T6 Cast Aluminum Alloy-SAE SP 760, SAE, Warrendale, PA, Philadelphia, PA, 1995, pp. 124-40.

31. F.T. Lee, J.F. Major, and F.H. Samuel: Metall. Mater. Trans. A, 1995,1987, pp. 1-100.3. M.J. Couper, A.E. Neeson, and J.R. Griffiths: Fat. Fract. Eng. Mater. vol. 26A, pp. 1553-70.

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