shell mold cracking and its prediction during the casting ... · alloy (hereafter called ac4c...

© Toyota Central R&D Labs., Inc. 2011

R&D Review of Toyota CRDL, Vol.42 No.4 (2011) 55-65 55

Research ReportShell Mold Cracking and Its Prediction during the Casting of AC4CAluminum Alloy

Shuxin Dong, Yasushi Iwata, Hiroshi Hohjo, Hiroaki Iwahori, Takashi Yamashita and Haruyoshi HiranoReport received on Oct. 12, 2011

The mechanism of shell mold cracking and its prediction during the casting of analuminum alloy were elucidated. A cylindrical shell mold made of silica sand will fracture easily when filledwith an aluminum alloy melt. The cracking mechanism is as follows. The inner surface of the shell moldundergoes a sudden temperature rise caused by contact with the melt, and attempts to expand. This thermalexpansion is restrained by the rest of the mold, which is still at a lower temperature. Consequently,compressive stress develops near the inner surface, and tensile stress develops near the outer surface, causingthe shell mold to fracture once the tensile stress exceeds the tensile strength of the shell mold. If a portionof a cylindrical shell mold is cut to reduce its thickness, a higher tensile stress act on the outer surface ofthis thinner region, and a crack will form more quickly after the mold is filled with an aluminum alloy melt.The relation of fracture stress and effective volume based on Weibull's statistical method, which is utilizedfor evaluating the strength of brittle materials, was obtained from the statistical properties of the tensilestrength of the shell mold material. The criterion for shell mold cracking, enabling us to predict the shellmold cracking, can be described by the relation of fracture stress and effective volume.

Shell Mold, Crack, Fracture Stress, Effective Volume, Prediction, Veining Defect,Casting, Aluminum, Alloy, Weibull’s Statistical Method

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1. Introduction

Components with intricate cavities, such as thecylinder heads of automobiles, can be cast as a singlepiece, without requiring assembly. In this casting, coremolds made of shell molds or organic self-hardeningsand are used in conjunction with a main mold to formcomplex cavities. However, if a crack occurs in thecore mold during casting, the resulting cylinder headmay be defective because of burrs or fins formed bythe solidification of melt penetrating the crack. Suchburrs or fins, commonly referred to as veining defects,are difficult to detect and remove. Therefore, it isimportant to choose an appropriate casting design andconditions that can avoid such defects in foundryproduction.

Generally encountered in sand mold castings alongwith metal penetration, pinholes, and blowholes,veining defects often occur in sand molds that containorganic binders. Campbell(1) proposed that veiningdefects originate from the thermal expansion of sandmolds because of heating by the melt, but it remainedunclear how much thermal expansion can occur beforesand mold cracking occurs and when these cracks willappear during casting. Makiguchi(2) suggested that

veining defects occur when the binder, grain size,filling state of the sand, or pouring temperature of meltare inappropriate, and that cracking is also influencedby the shape and dimension of the casting. Oda(3)

argued that the thermal expansion coefficient of thesand has little to do with veining defects. Severalmethods of preventing veining defects have beenreported. One of these is the addition of substances thatreact with the sand to form a glassy material.(4) Anotheris the mixing of boric acid or other substances with thesand to improve the deformability of the surface layerof the sand mold at elevated temperatures,(5) or addingFe2O3 to the sand.(6,7) Coatings that can seal cracks onthe surface of the sand mold by softening at elevatedtemperatures are commercially available. However, theabove methods and products for the prevention ofveining defects are mainly intended for cast iron or caststeel, and the complete prevention of veining defectsremains a significant challenge.

In the past few decades, simulation technology forfoundry engineering has made remarkable progress.The prediction of casting quality and die design arebeing conducted flourishingly based on numericalanalysis of mold filling and solidification in variousfoundries.(8,9) Nevertheless, simulation techniques for

R&D Review of Toyota CRDL, Vol.42 No.4 (2011) 55-65

sand molds and cores, such as the prediction of veiningdefects, will remain under development until themechanical models of sand molds and the crackingmechanism of the mold surface can be adequatelyunderstood.

In the present research, the thermo-mechanicalbehavior of shell molds heated by the melt duringcasting was investigated as it relates to mold surfacecracking. A criterion for cracking is proposed, andpredictions based on this criterion were investigated inthe actual foundry production of cylinder headcastings.

2. Experimental Method

2. 1 Casting Experiments

The cup-shaped experimental shell mold shown inFig. 1 was formed with an inside diameter of 60 mm,a height of 120 mm, and a thickness of 10 mm. Theshell mold was formed in a steel mold using resin-coated sand (RCS) that was prepared by mixing JIS100silica sand (99.8% SiO2) with 1.5 mass% phenolicresin followed by curing at 300°C. The mold crackingwas examined after pouring a JIS-AC4C aluminumalloy (hereafter called AC4C alloy) melt at 700°C intothe cup-shaped experimental mold with a filling timeof about 3 seconds. The effect of mold wall thicknesson cracking was investigated by vertically grinding apart of the mold wall to various thicknesses. Toinvestigate the effect of the pouring method oncracking, the following pouring experiments were alsocarried out.1) Pouring to the inner or outer side of the mold only,

so that only the inner or outer side contacted themelt.

2) Pouring to the inner and outer sides of the moldsimultaneously, so that both sides contacted the meltat the same time.

3) Pouring to the inner and outer sides of the mold witha time lag, so that the inner side contacted the meltprior to the outer side, or vice versa.

The mold used for these experiments was a 40-mm-high cylindrical mold cut from the upper part of thecup-shaped mold shown in Fig. 1. The filling time was1 second for both the inner side and outer side of themold.

The strain generated in the cup-shaped mold duringpouring was measured by installing strain gaugesaround the circumference of the outer surface of themold at a height of 60 mm above the bottom. To avoidthe dissipation of the strain gauge adhesive into thegrain interstitials of the mold, a high-viscosity adhesivewas used. A high-temperature strain gauge, ZFLA-3(Tokyo Sokki Kenkyujo Co., Ltd.) was used in theabove measurements. The occurrence and propagationof the cracks were recorded by a high-speed camerawith a recording speed of 1 × 105 fps.

2. 2 Thermal Stress Analysis of the Sand Mold

Coupled thermo-mechanical analysis of the moldwas carried out with the commercial structural analysiscode MSC MARC in two or three dimensions,depending on the purposes. To examine therelationship between stress and mold cracking duringpouring, a two-dimensional thermo-mechanicalanalysis was conducted using a ring-shaped model torepresent a horizontal cross section of the mold. It wasnecessary to calculate the temperature variation in themold with a high accuracy in order to correctlydetermine the stress distribution. Besides measuringthe thermal properties of the mold, the heat transfercoefficient at the interface between the melt and themold surface was determined by the following method.A cup-shaped mold was made for temperaturemeasurement. This mold had ∅0.1 mm chromel-alumelthermocouples embedded at three positions along thethickness direction of the mold wall, with an intervalof approximately 2.5 mm and at a height of 60 mmfrom the bottom of the mold. The correct positioningof the thermocouples was confirmed by X-raytransmission photography before pouring and thetemperatures of the three points were measured duringpouring. In the present study, the melt-mold interfaceheat transfer coefficient during the first 30 seconds was

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Fig. 1 Experimental cylindrical shell mold.

57R&D Review of Toyota CRDL, Vol.42 No.4 (2011) 55-65

considered significant because all of the observed moldcracks occurred within 30 seconds of melt pouring.The heat transfer coefficient was calculated to be0.05 cal·cm–2·°C–1·s–1 by an inverse method, in whichthe heat transfer coefficient giving the nearestcalculated temperatures to the measured results waschosen as the correct heat transfer coefficient. In theabove thermal calculations of the heat transfercoefficient, a two-dimensional analysis was adopted.The time at which the melt surface within the moldarrived at the position of the embedded thermocouplesduring pouring was taken as the starting time of theanalysis. The heat transfer coefficient of the mold-airinterface was taken as 0.0008 cal·cm–2·°C –1·s–1.

A three-dimensional analysis taking into account thefilling process of the melt was also carried out tocalculate the temperature and stress distributions in thecup-shaped mold. To describe the gradual heatingprocess of the mold correctly during the 3 seconds ofmelt filling, the 120 mm height of the mold cavity wasdivided equally into 24 sections. Each ring-shapedsection had a height of 5 mm and a heat transferboundary condition with a heat transfer coefficient of0.05 cal·cm–2·°C–1·s–1. An environmental temperatureof 700°C was applied section-by-section with a timelag of 0.125 seconds along the inner surface of thering-shaped mold, starting from the bottom andarriving at the top 3 seconds later. The object of theabove thermo-mechanical analysis was taken as themold only and the radiation heat transfer of the meltsurface in the mold was ignored.

Analysis of the 40-mm-high cylinder-shaped moldwas performed using a two-dimensional modelconsisting of the mold and melt but ignoring the fillingtime of 1 second.

The thermal and mechanical properties of the moldare shown in Table 1. The mechanical properties wereacquired by tensile and compressive tests usingdumbbell-shaped planar specimens (5.5 mm inthickness, 25 mm in width, 75 mm in gauge length,and a transition radius of 30 mm) and columnarspecimens (20 mm in diameter, 40 mm in length)respectively. The specimens were made from the samesand and cured under the same conditions as the molds.

The mechanical properties of the mold at elevatedtemperatures were estimated through extrapolating theroom temperature properties according to thetemperature dependence of the three-point bendingstrength, which was measured by a series of bendingtests from room temperature to 400°C. The stress-strain curves at room temperature were measured usinga video camera strain gauge. The thermal conductivity,specific heat, density, and thermal expansioncoefficient of the mold were measured by box probemethod, vacuum bottle method, bulk density method,and JACT M-2 test method (Japan Association ofCasting Technology), respectively.

The stress-strain behavior of the mold was assumedto be as illustrated in Fig. 2 for the thermo-mechanicalanalysis. The modulus and compressive yield stress ofthe mold were taken as the measured values given inTable 1. As was described in section 3.5, the tensilestrength of the mold varied considerably with changesin effective volume, and so the stress-strainrelationship under tension was assumed to be that ofan ideal elastic material.


Density (kg ·m–3) 1.55 × 103

Thermal conductivity (W·m–1 ·°C–1) 0.70

Specific heat (J·kg–1 · –1) 1.13×103

Linear thermal expansion coefficient (°C–1) 1.16 ×10–5

Tensile strength, σt (MPa) 3.15

Compressive strength, σc (MPa) 10.44

Modulus of elasticity, E (GPa) 3.72

Poisson's ratio ( - ) 0.20

Table 1 Thermal and mechanical properties of the shellmold used for thermal and mechanicalsimulations.

σc

ε

σ

E

εc

Fig. 2 Stress-strain model of the shell mold used formechanical simulation.

heated inner area was constrained by the outer area,resulting in a compressive stress at the inner side anda tensile stress at the outer side of the mold wall. Withtime, the area of the heated inner side increased, andthe area of the outer side decreased. The tensile stressat the outer side increased to match the compressivestress in the cross section. Cracking should occur whenthe tensile stress at the outer side exceeds the tensilestrength of the mold. As shown in Fig. 4, the tensilestress reached the tensile strength (ranging from 2.16to 3.87 MPa, averaging 3.15 MPa) 8 seconds after thestart of pouring. In experiments, cracking occurred 8to 12 seconds after the start of pouring. The crackingtime calculations included some errors, because theabove thermo-mechanical simulation was conductedusing a two-dimensional model, and there weremeasurement errors in the determination of the moldproperties, and the unevenness of the sand fillingduring preparing the mold. Nevertheless, the calculatedcracking time agreed well with the measured value. Aset of three representative strain curves measured usinga cup-shaped mold with strain gauges installed at threecircumferential positions around the outer surface isshown in Fig. 5. When the inner surface was heated bythe melt, the tensile strains at the three positions aroundthe outer surface of the mold began to increase. A crackoccurred at a strain of about 500μ approximately 10seconds after starting to pour. The strains at all threepositions dropped simultaneously when the crackoccurred. As shown in Fig. 5, the calculated andmeasured strains showed the same increasingtendency, although the measured values were lowerthan the calculated values. The fluctuation ofapproximately 100μ between the strains measured atthe three positions may have resulted from unevenness

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3. Experimental Results and Discussion

3. 1 Cracking and Thermal Stress of the

Experimental Mold

Figure 3 shows an example of cracking after pouringan AC4C alloy melt into the cup-shaped mold ofFig. 1. A crack began to propagate in the verticaldirection of the mold wall accompanied by a sound,and the melt in the mold flowed out through the crackabout 8 to 12 seconds after the start of pouring.

The calculated temperature and stress distributionsin the mold wall along the thickness direction aftercontacting the melt are illustrated in Fig. 4. The innersurface of the mold underwent a rapid temperature riseupon contacting the melt, but the interior of the moldwall changed temperature much more slowly due tothe low thermal conductivity of the sand. The outersurface of the mold, which was 10 mm away from theinner surface, showed almost no temperature changein the 10 seconds after pouring. The thermal stressdistribution arising from the above temperaturechanges in the mold caused a tensile stress at the outerside and a compressive stress at the inner side of themold wall in contact with the melt. The tensile stressat the outer side increased rapidly after pouring,because of thermal expansion of the silica sand of themold, which had a linear thermal expansion coefficientof 1.16 × 10–5°C–1. The inner side of the mold wallexpanded rapidly upon contact with the melt, while theouter side of the mold wall did not undergo thermalexpansion because of the low thermal conductivity ofthe mold. Therefore, the thermal expansion of the

Fig. 3 A crack in the cylindrical shell mold.

0 2 4 6 8 100

600

400

2001s3s5s10s

Tem

pera

ture

, °C

Distance from the inner surface of the mold, mm

0 2 4 6 8 10-8

4

2

-2

1s3s

5s10s

Stre

ss, M

Pa 0

-4

-6

Tensile strength of the shell mold

2.16

3.87

Fig. 4 Temperature and stress distributions along thethickness direction in the cross section of thecylindrical mold (two-dimensional analysis).

of the gauge adhesive, non-uniform filling of the sand,or other structural irregularities.

3. 2 The Effect of Pouring Method on Thermal

Stress and Cracking

As discussed in the previous section, a crackappeared on the surface of the mold because thethermal stress exceeded the tensile strength of themold. The relationship between thermal stress andcracking was further investigated by employing severaldifferent pouring methods. In the first method, anAC4C alloy melt was poured onto only the inner orouter surface of the ring-shaped mold described insection 2.1. In the second method, an AC4C alloy meltwas poured onto both the inner and the outer surfacessimultaneously. In the third method, an AC4C alloymelt was first poured onto one surface, and then ontothe other before any cracking, with a surface-to-surfacetime lag of 6 seconds. When using the first pouringmethod, a crack would occur at the side opposite fromthe pouring; that is, if the melt was poured onto theinner surface, the outer surface would crack, and viceversa. When using the second and the third methods,no cracks were observed. The temperature and stressdistributions along the thickness direction of the moldwall, calculated using a two-dimensional model of thethird filling method, are illustrated in Fig. 6. Althougha tensile stress existed at the outer surface of the moldwall 5 seconds after melt filling of the inside of themold, the stress changed to a compressive stress at 6.5

seconds once the melt had been poured onto theoutside of the ring-shaped mold. The region undercompressive stress continued to spread towards thecenter of the mold wall with time. The tensile stress ofthe central part in the thickness direction of the moldwall entered the tensile strength range at some time,but no crack was observed. Immediately upon pouringthe melt by the second method, in which AC4C waspoured onto the inner and outer surfaces of the moldat the same time, compressive stresses appeared at boththe inner and outer surfaces, while tensile stressdeveloped in the interior of the mold wall. The aboveexperimental and simulation results suggest that crackswill occur if the tensile stress at mold surface exceedsthe tensile strength, and that no crack will appear if thestresses at the surfaces are compressive, even if thetensile stresses within the mold wall exceed the tensilestrength of the mold.

3. 3 Crack Origins

Stress distributions in a cup-shaped mold with a partof the wall vertically ground to a thickness of 5 mmare shown in Fig. 7. The mold shown in Fig. 7(a) wasfully filled, while the mold shown in (b) was partlyfilled to a position 20 mm from the top edge of themold. In Fig. 7(a), the highest stress acted on the lowerarea of the outer surface of the mold 2.8 seconds afterthe beginning of filling, but the point of the higheststress then migrated to the upper edge of the mold overthe next few seconds as the filling continued. A crackappeared in the mold 5 to 6 seconds after the beginning

59



Fig. 5 Comparison of measured and calculated strains inthe outer surface 60 mm above the bottom of thecylindrical shell mold from the start of pouring(three-dimensional analysis).

0 2 4 6 8 100

600

400

200

1s

3s5s

6.5s

Tem

pera

ture

,

Stre

ss, M

Pa

8s

Distance from the inner surface of the mold, mm

0 2 4 6 8 10-8

4

2

-2 1s3s 5s

6.5s

0

-4

-68s

2.163.87

Tensile strength of the shell mold

Fig. 6 Temperature and stress distributions along thethickness direction in the cross section of the ring-shaped shell mold contacting the melt at bothsurfaces, but with a time lag of 6 seconds (two-dimensional analysis).

of filling. The cracking time differed from that shownin Fig. 4, for reasons that will be discussed in thefollowing section (3.4). Using a high-speed camera,the crack was observed to initiate at the upper edge andthen propagate toward the bottom of the mold. InFig. 7(b), the highest stress acted on the lower area ofthe mold, and the position of highest stress moved verylittle during the filling process. Under these fillingconditions, the initial crack occurred approximately 15seconds after the beginning of filling, and the crackwas clearly observed to propagate toward the upperpart of the mold. That is to say, for condition (a), theupper and lower parts of the mold developedcomparatively high stresses, and the stress at the upperpart exceeded the tensile strength of the mold at thetime the crack occurred. For condition (b), the peakstress occurred only in the lower part of the moldthroughout the filling process, and the stress in thisarea greatly exceeded the tensile strength of the moldwhen the crack initiated.

3. 4 The Effect of Mold Shape on Cracking Stress

In a mold with a thinly ground region 5 mm thick,as shown in Fig. 7(a), a crack occurred 5 to 6 secondsafter the beginning of melt filling. To investigate theeffect of the thinly ground region on cracking, regionson several different molds were ground to thicknesses

60



varying from 10 mm (not ground) to 3 mm, andpouring experiments were carried out. In all cases,cracks occurred in the thinly ground region. Thesecracks appeared approximately 7 seconds, 5.5 seconds,and 4 seconds after the beginning of melt filling forground thicknesses of 8 mm, 5 mm, and 3 mm,respectively. The cracks appeared sooner in morethinly ground parts.

The strains generated in the surfaces of molds beforecracking were measured, as shown in Fig. 8 for thinlyground parts of different thickness. For the ungroundmold, the strain was about 500μ at all the threemeasured points when the crack occurred. However,with decreasing thickness of the thinly ground parts,the strain in the thinly ground region became higherand the strain in the other regions became lower whenthe crack occurred. When the ground region wasthinner than 5 mm, the strain in the ground region roserapidly with decreasing thickness, and the strain for athickness of 3 mm reached 3000μ. The mean tensilestrength of the mold was determined to be 3.15 MPaby N = 10 tensile tests, as shown in Table 1. The tensilestrength ranged from 2.16 MPa to 3.87 MPa, and thecorresponding facture strain ranged from 580μ to1040μ. That is to say, the strain of 3000μ measured ina mold with a thickness of 3 mm in the thinly groundregion reached three times the fracture strain of themold. In the above experiments, it was observed thatin the unground mold with an even wall thickness of10 mm, the strain was distributed evenly around the

Fig. 8 Measured strains of cylindrical shell molds withthinly ground regions of different thicknesses at thetime of cracking of the outer surface of the thinlyground region 60 mm above the bottom of the mold.

Fig. 7 Stress distributions within cylindrical shell molds(a) fully filled with the melt, and (b) only partiallyfilled with the melt (100-fold amplifieddeformation, three-dimensional analysis).

mold circumference. Therefore, cracks should occur ifthe stress corresponding to the strain in the moldexceeds the tensile strength. For the experimentalmold, some irregularity in the sand filling during moldpreparation is likely, and any cracking should occur atthe weakest point of the mold. When a portion of themold wall was thinly ground, a comparatively largestrain was generated in the thinly ground region. Thisstrain increased rapidly with decreasing thickness ofthe ground region, and led to earlier cracking duringmelt filling. However, the reason that the strain atcracking increased with decreasing thickness of theground region remained unexplained.

The temperature distributions and deformationconfigurations of the cross sections of cup-shapedmolds with and without thinly ground wall regions atcracking are illustrated in Fig. 9. For the ungroundmold (which had a uniform wall thickness of 10 mm),the cross section remained circular but was enlarged.For molds with ground regions ranging from 10 mmto 3 mm thick, the thinly ground portion deformedsignificantly from the initial circular shape to a shapewith a larger curvature. This curvature increased withdecreasing thicknesses of the thinly ground region.When the ground region was thinner than 5 mm, theincrease in curvature became especially marked.Owing to the lower thickness, the thinly ground parthad a bending moment that resulted in a stress gradientin the thickness direction during melt filling. Thisstress gradient became larger with decreasing thicknessof the ground region. It is possible that it was merelythis stress gradient that caused the fracture stress(strain) of the mold to be much higher than the tensilestrength obtained by tensile tests. That is to say, as isgenerally observed for brittle materials, the bending

strength is higher than the tensile strength for a givenspecimen size.

3. 5 Criterion for Mold Cracking

For a mold that is exposed to an even distribution oftensile stress, such as in the case of the unground cup-shaped mold, the tensile strength of the mold can beconsidered to be the criterion for mold cracking. Thatis, if the tensile stress in the mold exceeds the tensilestrength, then cracks will occur. However, as wasobserved in the above experiments, if there is a largebending moment or a severe stress gradient in a sectionof the mold, then the cracking stress will increase.Thus, the tensile strength obtained from a tensile testcan not be used as the criterion for cracking. Therefore,the criterion for cracking under a severe stress gradientwas examined using the effective volume method,(10)

which is based on Weibull statistics and is used toevaluate the strength of brittle materials. The effectivevolume (VE) is a parameter based on the assumptionthat the larger the volume under comparatively highstress in a body, the higher the probability of thatvolume containing relatively large defects that arecapable of originating cracks. The effective volume isdescribed by Eq. 1.

VE = ∫V(σ/σmax)m dV, · · · · · · · · · · · · · · · · · · (1)

where σ is the stress in the specimen, σmax is themaximum stress in the specimen, m is the Weibullparameter, and V is the total volume of the specimen.

The relationship between the mean fracture stress μand the effective volume VE of a brittle material can beexpressed as:

lnμ = −(1/m)ln VE + c,· · · · · · · · · · · · · · · · ·(2)

where c is a constant.Furthermore, for a given fracture probability F, the

fracture stress can be obtained from the above meanfracture stress using Eq. 3.

σF = μ/Sp, · · · · · · · · · · · · · · · · · · · · · · · · · (3)

where Sp is a safety coefficient that can be calculatedusing Eq. 4.

Sp = Γ((m + 1)/m)/(ln(1/(1 − F)))1/m, · · · · · · · (4)

61



Fig. 9 Cross-sectional shapes of shell molds with thinlyground regions of different thicknesses after meltfilling (100-fold amplified deformation, two-dimensional analysis).

where Γ(x) is the Gamma function.If the Weibull parameter m and the constant c are

known, the relationship between the fracture stress fora given fracture probability and the effective volumecan be obtained by substituting Eqs. 2 and 4 intoEq. 3. The Weibull parameter m and the constant cwere calculated from the tensile test results as follows.

First, a Weilbull plot of the tensile test results wasdrawn as shown in Fig. 10. The median rank methodwas adopted to calculate the fracture probability,because of the small tensile test number of 10. TheWeibull parameter was calculated to be 6.04 from thetangent of the Weibull plot shown in Fig. 10. ThisWeibull parameter is between 5 and 20,(11) which is thetypical range for general ceramics, although it is at theside of a comparatively larger fluctuation.

If only the gauge length region of the tensilespecimen is taken into account when calculating theeffective volume of the tensile test, the effectivevolume simply equals the volume of the gauge lengthregion because the stress is the same everywhere inthat region, i.e., σ = σmax in Eq. 1. However, in theactual tensile tests, some of the specimens did notfracture in the gauge length region but in the nearbytransition region. Therefore, the integration range ofEq. 1 was extended from the gauge length region toinclude the transition regions, and the effective volumeof the tensile specimen was calculated as VE = 1.26 ×10–5 m3 (12.6 cm3). Here, it should be noted that thecross section of the transition region was larger thanthat of the gauge length region, so the stress in thetransition region was lower than that of the gaugelength region.

By substituting m = 6.04, VE = 1.26 × 10–5 m3 (12.6 cm3),

and the mean tensile strength μ = 3.15 MPa into Eq. 2,the constant c was obtained as c = 4.72.

The relationships between σF and VE, correspondingto fracture probabilities of F = 1%, 10%, 50%, and95% were obtained by substituting Eqs. 2 and 4 intoEq. 3. These relationships between σF and VE areillustrated in Fig. 11, in which the fracture stressincreased with decreasing effective volume. Thebending strengths measured by three-point bendingtests of specimens with different effective volumes arealso plotted in Fig. 11 (solid circles) and showed goodagreement with the fracture stresses calculated fromthe tensile test strengths.

The maximum principal stresses and the effectivevolumes at cracking were calculated for the cup-shaped molds with thinly ground regions that wereused for the experiments shown in Fig. 8. The resultsfor each mold are plotted in Fig. 11 (solid squares). Themaximum principal stresses at mold cracking werelocated in the region of fracture probabilities of 50–95%. Therefore, the fracture stress-effective volumerelationship corresponding to the fracture probabilityof 50% was assumed as the criterion for shell moldcracking.

3. 6 Predicting the Cracking of a Jacket Mold for

Aluminum Alloy Cylinder Heads

To accurately predict the occurrence of cracks, it isfirst necessary to understand the detailed process bywhich a mold contacts the melt during casting. Thiswas accomplished by melt filling simulation followedby the calculation of thermal stresses in the mold basedon the heat transport between the mold and the melt.

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Ordered fracture stress, σσ/MPa

Cum

ulat

ive

frac

ture

pro

babi

lity,

F/%

1

20

1.5 2.0 2.5 3.0 4.5

60809099

40

10

5

2

3.5 4.0

m = 6.04

1

Fig. 10 Weibull plot of the fracture stresses obtained fromtensile tests of the shell mold material.

Effective volume, VE /cm3

Stre

ss, σ

F/M

Pa

0

4

0.01 0.1 1 10 100

8

10

12

14

1%10%

50%95%

Curves of differentfracture probability

6

2

Cracking stress of the mold3-point bending strength

Tensile strength

Shell mold core of the cylinder head

Maximum stress of the shellmold core of the cylinder head

Fig. 11 Relationship between the fracture stress and theeffective volume of the shell mold.

Figure 12 shows the measured strains (N = 3) in ajacket mold when it was heated by the melt as itssurface rose from the lower side to the upper side ofthe mold vertical section. Compressive strains weremeasured when the surface of melt rose from t1 to t2.The strains began to change towards tension once thesurface of the melt passed t2, and the tensile straincontinuously increased as the melt surface rose. Whenthe melt surface arrived at the position of the installedstrain gauges, the strain suddenly dropped toward thecompressive side, and the strain gauges were damageddue to contact with the hot melt. The strain of the mold,calculated on the basis of a melt filling simulationusing the foundry CAE software TOPCAST, is alsoshown in Fig. 12. The calculated strain showed asimilar tendency to that of the measured strains. Thedistribution of the maximum principal stress in a partof the mold (the portion of one cylinder of the fourcylinder head) is shown in Fig. 13, which shows thetime at which the surface of the melt had passed t2 andalmost arrived at the position of the strain gauge shownin Fig. 12. The maximum value of the maximumprincipal stress was approximately 1 MPa, which wasmuch lower than the tensile strength of the mold, andwas located at a position with a fracture probabilitylower than 0.01%, according to Fig. 11. Therefore, therisk of cracking is extremely low under the presentcasting conditions.

4. Conclusions

The cracking of shell molds during the casting ofJIS-AC4C aluminum alloy was investigated, with afocus on the thermal stress in the mold arising frommelt heating. The following conclusions were obtained.

1. The temperature of the inner side of the cup-shapedmold increased due to heating by the aluminummelt. The thermal expansion of the inner sidecorresponding to this temperature increase wasrestrained by the outer side of the mold thatremained at a lower temperature, resulting incompressive and tensile stresses in the inner andouter sides of the mold, respectively. The tensilestress in the outer side of the mold can rise to a highlevel in a short time. If this tensile stress exceeds thetensile strength of the mold, cracking will occur.

2. Even if tensile stress occurs in the outer side of amold, if that side is heated by the melt before thestress exceeds the tensile strength, the tensile stresswill decrease rapidly, and no cracking will occur.

3. For a cup-shaped mold with a thinly ground region,cracks occurred in the thinly ground part, and thecracking time decreased with decreasing thicknessof the thinly ground part.

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300

200

t3Average peak value of measured strains

Stra

in, μ

100

measuredcalculated

0

t1t2

-100

0

Time100

Fig. 12 Comparison of the measured and calculated strains of a jacket shell moldof a cylinder head during melt filling.

Fig. 13 Stress distribution in a jacket shell mold of acylinder head during melt filling at t3 in Fig. 12.

4. In a mold with a thinly ground part, the maximumtensile stress occurred in the thin region, and cracksoccurred in this region. The cracking stress (strain)increased with decreasing thickness of the thinlyground part.

5. The cracking criterion for shell molds can bedescribed by the effective volume method, which isused to assess the strength of brittle materials and isbased on Weibull statistics. Whether cracks willoccur can be predicted by comparing the tensilestresses in the surfaces of molds with the fracturestress (strength) of the same effective volume, whichcan be obtained from a graph of the fracture stress-effective volume relationship based on tensile orbending tests.

6. The proposed cracking criterion in the presentresearch was successfully applied to predict thecracking of water jacket molds in the casting ofautomotive cylinder heads.

Acknowledgements

The authors are grateful to the people of SANEISILICA Ltd., Japan for their help in the measurementof shell mold properties.

References

(1) Campbell, J., CASTINGS (1991), 98, Butterworth-Heinemann Ltd.

(2) Makiguchi, T., IMONO (in Japanese), Vol.62 (1990),p.566.

(3) Oota, H., Sakaguchi, Y., Kuniyoshi, K. and Murata, H., Report of JFS Meeting (in Japanese),

Vol.152 (1979), p.48.(4) Morey, R. E., Trans. AFS, Vol.54 (1949), p.129.(5) Katashima, S., Tashima, S. and Mikawa,Y., Report of

AFS Meeting, Vol.113 (1988), p.91.(6) Nakano, T., Muto, K. and Tanabe, H., IMONO (in Japanese), Vol.50 (1978), p.36.(7) Yajima, M. and Hase, H., IMONO (in Japanese),

Vol.55 (1983), p.765.(8) Onaka, I., Journal of Japan Foundry Engineering

Society (in Japanese), Vol.78 (2006), p.602.(9) Otsuka, Y., Journal of Japan Foundry Engineering

Society (in Japanese), Vol.78 (2006), p.609.(10) The Ceramic Society of Japan, The Mechanical

Properties of Ceramics (in Japanese), (1979), p.22.(11) Davidge, R. W., (Translated by Suzuki, H. and Iseki, T.), The Strength and Fracture of Ceramics (in Japanese), (1982), p.147, Kyoritsu Shuppann.

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Figs. 1-13 and Table 1Reprinted from Materials Transactions, Vol.51, No.8(2010), pp.1420-1427, Dong, S., Iwata, Y., Hohjo, H.,Iwahori, H., Yamashita, T. and Hirano, H., Shell MoldCracking and Its Prediction during Casting of AC4CAluminum Alloy, © 2010 JFES, with permission fromJapan Foundary Engineering Society.

Shuxin Dong

Research Fields: - Metallic Materials- Modeling of Casting and SolidificationProcesses

Academic Degree: Dr. Eng.Academic Societies:

- The Japan Institute of Metals- Japan Foundry Engineering Society- The Surface Finishing Society of Japan

Awards: - The Tsutsumi Award of Japan Foundry EngineeringSociety, Tokai, 2005

- The Best Paper Award of Japan Foundry EngineeringSociety, 2010

Yasushi Iwata

Research Field: - Modeling of Casting and SolidificationProcesses

Academic Degree: Dr. Eng.Academic Society:

- Japan Foundry Engineering SocietyAwards:

- The Onoda Award of Japan Die Casting Association,1989

- The Kobayashi Award of Japan Foundry EngineeringSociety, 1989

- The Tsutsumi Award of Japan Foundry EngineeringSociety, Tokai, 1999

- The Best Paper Award of Japan Foundry EngineeringSociety, 2001 and 2010

Hiroshi Hohjo

Research Fields: - Material Strength- Fracture Mechanics


- The Society of Materials Science, Japan- The Japan Society of Mechanical Engineers

Award: - JSMS Award for Technical Developments, 2007

65



Hiroaki Iwahori

Research Field: - Casting Technology and Materials


- Japan Foundry Engineering Society- The Japan Institute of Light Metals- The Japan Institute of Metals

Awards: - The Sokeizai Industrial Technology Award, 1991- The Best Technical Paper Award of the 62th World Foundry Congress, 1996

- The Iidaka Award of Japan Foundry EngineeringSociety, 2009

- The Technological Development Award of JapanFoundry Engineering Society, 2010

- The Best Paper Award of Japan Foundry EngineeringSociety, 2001 and 2010

Takashi Yamashita*

Research Field: - CAE of Casting Processes

Academic Society: - Japan Foundry Engineering Society

Awards: - The Technological Development Award of JapanFoundry Engineering Society, 2009

- The Encouragement Award of Japan FoundryEngineering Society, Tokai, 2011

Haruyoshi Hirano*

Research Fields: - Foundry Engineering- Quality Engineering- Production Management

Academic Societies: - Japan Foundry Engineering Society- The Japan Society for Quality Control

Awards: - The Toyota Award of Japan Foundry EngineeringSociety, 1998

- The Technological Development Award of JapanFoundry Society, Inc., 1999

- The Nagai Technological Development Award ofthe Nagai Foundation for Science and Technology,2004

- The Technological Development Award of JapanFoundry Engineering Society, 2010

- The Distinguished Contribution Award of JapanFoundry Engineering Society, 2011

*Toyota Industries Corporation

shell mold cracking and its prediction during the casting ... · alloy (hereafter called ac4c...

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