Engineering Failure Analysis 9 (2002) 63±76

www.elsevier.com/locate/engfailanal

Thermal cracking in disc brakes

Thomas J. Mackin *,1, Steven C. Noe, K.J. Ball, B.C. Bedell, D.P. Bim-Merle,
M.C. Bingaman, D.M. Bomleny, G.J. Chemlir, D.B. Clayton, H.A. Evans,
R. Gau, J.L. Hart, J.S. Karney, B.P. Kiple, R.C. Kaluga, P. Kung, A.K. Law,
D. Lim, R.C. Merema, B.M. Miller, T.R. Miller, T.J. Nielson, T.M. O'Shea,
M.T. Olson, H.A. Padilla, B.W. Penner, C. Penny, R.P. Peterson,
V.C. Polidoro, A. Raghu, B.R. Resor, B.J. Robinson, D. Schambach,
B.D. Snyder, E. Tom, R.R. Tschantz, B.M. Walker, K.E. Wasielewski,
T.R. Webb, S.A. Wise, R.S. Yang, R.S. Zimmerman
Department of Mechanical and Industrial Engineering, The University of Illinois at Urbana-Champaign,
1206 West Green Street, Urbana, IL 61802, USA

Received 29 August 2000; accepted 23 September 2000

Abstract
Disc brakes are exposed to large thermal stresses during routine braking and extraordinary thermal stresses during
hard braking. High-g decelerations typical of passenger vehicles are known to generate temperatures as high as 900 C
in a fraction of a second. These large temperature excursions have two possible outcomes: thermal shock that generates
surface cracks; and/or large amounts of plastic deformation in the brake rotor. In the absence of thermal shock, a
relatively small number of high-g braking cycles are found to generate macroscopic cracks running through the rotor
thickness and along the radius of the disc brake. The analysis herein shows that rotor failure is a consequence of low
cycle thermo-mechanical fatigue. An analysis of the vehicle dynamics was used to ®nd a heat ¯ux equation related to
braking forces. The heat ¯ux equation was then used in a ®nite element analysis to determine the temperature pro®le in
the brake. Once the brake temperature was obtained, a simpli®ed shrink ®t analysis was used to estimate the stresses
that arise during hard braking. This approach shows that plastic deformation occurs due to the large thermal strains
associated with high-g braking. The calculated strain amplitude was then used in a Con Manson law to predict the
number of high-g braking cycles to failure. Good agreement was obtained between reported braking cycles to failure
and the proposed theoretical approach # 2002 Elsevier Science Ltd. All rights reserved.
Keywords: Thermal fatigue; Heat cracks; Brake failures; Thermal stress; Fatigue

* Corresponding author. Tel.: +1-217-244-1016; fax: +1-217-333-1942.

E-mail address: t- machi@vivc.edu (T.J. Mackin).
1
This paper was equal part of a group project assigned by Professor T.J. Mackin to a senior level class on Failure Analysis.

1350-6307/02/$ - see front matter # 2002 Elsevier Science Ltd. All rights reserved.
PII: S1350-6307(00)00037-6
64 T.J. Mackin et al. / Engineering Failure Analysis 9 (2002) 63±76

1. Introduction

Thermal cracking is commonly observed in disc brake rotors following high-g braking events [1,2]. The
cracks fall into two broad categories: a series of heat cracks that partially penetrate the surface of the discs
[2]; and thru-cracks that completely pass through the disc wall. Though it is well known that thermal
cracks do arise from hard braking [1], there is no formal treatment of the problem of thru-cracks. This
paper presents a failure analysis of thermal cracking in disc brake rotors. The analysis was motivated by
thermal cracking in the front disc brakes in a heavy duty Ford F-250 pickup truck (Fig. 1). The front
brakes failed while the truck was hauling a trailer ®lled with cattle. Failure occurred after several stops, and
was indicated by an audible `ping' and a pronounced ticking sound during subsequent braking.
Disc brakes are fabricated from grey cast iron with the typical geometry shown in Fig. 2. Grey cast iron
is chosen for its relatively high thermal conductivity, high thermal di€usivity and low cost. The brake rotor
consists of a hat, or hub, which is connected to the wheel and axle, and an inboard and outboard braking
surface. The outboard braking surface is attached directly to the hat, while the inboard braking surface is
attached to the outboard unit by a series of cooling vanes. A small groove is machined around the per-
iphery of the hat-rotor attachment site to relieve the stress concentration associated with the change in
section. It is important to note that the inboard disc is not directly attached to the hat; its only attachment
to the hat is through the cooling vanes. The inboard and outboard rotors are squeezed by the brake pads
during braking. The subsequent frictional work arrests the rotation of the wheel and generates a sub-
stantial amount of heat. Braking events last on the order of seconds, generating frictional heating in the
rotors while leaving the hat very near room temperature. Thermal cracking is not common in passenger
vehicles but it is relatively common in trucks and emergency vehicles; the very sorts of vehicles that are
exposed to extreme conditions. It is important to note that those conditions are not considered abusive,
rather they simply expose the limitations of braking technology. Though the present article was motivated
by failure of disc brakes on a truck, the following sections present a general treatment of the problem that
is applicable to any vehicle.

Fig. 1. Picture of a failed front brake rotor from a Ford F-250 Pickup truck. Cracks are seen to run radially from the hat to the
exterior of the disc.
 T.J. Mackin et al. / Engineering Failure Analysis 9 (2002) 63±76 65

Fig. 2. Schematic of a typical passenger car brake rotor with dimensions used in the present analysis.

2. Vehicle dynamics

Braking must, necessarily, remove the kinetic energy of a moving vehicle in a timely and repeatable
fashion. In order to estimate the temperatures that arise during braking, it is necessary to calculate the
forces acting on the brake rotors. A typical vehicle schematic is shown in Fig. 3, from which a moment
balance about the center of gravity provides the following:

hG 
b
x2 †cos † hG sin † K1 V 2 V
g
Fz1 ˆ mg 1a†
l ‡
x1 ‡
x2

Fig. 3. Typical vehicle schematic with relevant dimensions.

66 T.J. Mackin et al. / Engineering Failure Analysis 9 (2002) 63±76

hG 
a ‡
x2 †cos † hG sin † K2 V 2 V
g
Fz2 ˆ mg 1b†
l ‡
x1 ‡
x2

where:

  S 
K1 ˆ C x hG lCMy ‡ b
x2 †Cz 2a†
2mg

  S 
K2 ˆ C x hG lCMy ‡ a ‡
x1 †Cz 2b†
2mg

K1 and K2 are drag coecients available in Genta [3], and all other symbols are as identi®ed in Fig. 3.
Eqs. (1) can be further simpli®ed by assuming that braking occurs on a perfectly ¯at surface ( =0).
Furthermore, the
x terms measure the distances by which the tire normal forces shift from center. Since
these
x values are small compared with all other vehicle dimensions, these terms are dropped from Eqs.
(1) and (2). The drag coecients were found to amount to less than 1% of the load on each tire and were
also ignored. As a result, Eqs. (1) reduce to the following simpli®ed form:
!
mg hG 
Fz1 ˆ b V 3a†
l g

!
mg hG 
Fz2 ˆ b V 3b†
l g

Eqs. (3) show that the load distribution on the tires depends upon the distance of each tire from the
center of gravity, and the acceleration of the vehicle. During deceleration, the load shifts to the front tires
so that a large fraction of the work-of-braking is done by the front brakes. Most cars are out®tted with a
proportioning valve that meters the hydraulic force applied to the front and rear brakes, reducing the
deceleration of the vehicle and generating a 60/40 front/rear load distribution on the tires. A 60/40 load-
ratio was used for the subsequent braking analysis. A free-body diagram of a front tire±rotor system,
(Fig. 4), is used to derive the following equations of equilibrium:
X
Fy ˆ N W ˆ may ˆ 0 4a†

X
Fx ˆ Faxel 2Frotor ‡ Ftire ˆ max 4b†

X
M0 ˆ rrotor 2Frotor † ‡ rtire Ftire † ˆ Irotor 4c†

Since 60% of the braking load is borne by the front brakes, that amount of kinetic energy into a single
disc is given by [4,5]:
 T.J. Mackin et al. / Engineering Failure Analysis 9 (2002) 63±76 67

Fig. 4. Free body diagram of an automotive wheel.

1
0:3
M20 ˆdissipated ˆ Pdissipated t†dt ˆ 2Frotor †vrotor t†dt 5†
2

The power dissipated by each rotor face is equal to the instantaneous heat ¯ux into the rotor face. Such a
relationship can be used to predict the magnitude of the temperature excursions seen in the rotors. The
energy balance equation can be used to this end, utilizing the following kinematic relationships for con-
stant acceleration:

vinitial;vehicle 9
Vvehicle ˆ t† ˆ vinitial;vehicle at a ˆ >
=   
tstop rrotor vinitial;vehicle
v t† ˆ vinitial;vehicle 6†
Vvehicle t†
ˆ ! t† ˆ
vrotor > rotor
; rtire tstop
rtire rrotor

Frotor is constant with respect to time, and vrotor(t) varies only linearly with time so the energy balance
equation becomes:

tstop    
1 rrotor 1 v0 2
0:3
Mv20 ˆ 2Frotor † vrotor t†dt ˆ 2Frotor † v0 tstop tstop 7†
2 0 rtire 2 tstop

Industry representatives have stated that a typical hard braking event is one that takes a vehicle from 45
m/s to a dead stop in 6 s. Experiments on a simulation rig have shown that 300 cycles of such braking are
sucient to generate thermal cracks in a brake rotor. The rotor force for a typical vehicle is calculated
using the vehicle data contained in Table 1, resulting in:
68 T.J. Mackin et al. / Engineering Failure Analysis 9 (2002) 63±76

Table 1
Vehicle data

Vehicle mass, M 1500 kg

Initial velocity, V0 45 m/s
Time to stop, tstop 6s
E€ective rotor radius, rrotor 0.10 m
Tire radius, rtire 0.38 m

1
30%†

Mv20
Frotor  2    8†
rrotor 1 v0 2
2

v0
tstop t
rtire 2 tstop stop

The instantaneous heat ¯ux into the rotor face is directly calculated using the following:
  

rrotor v0
Qin t† ˆ Frotor †vrotor t† ˆ 6412N† v0 t 9†
rtire tstop

 w
Qin t† ˆ 75;938W 12;656 t
s

Finally, the total rotor force applied to both the inboard and outboard rotors can be used to calculate
the caliper clamping force required to stop the vehicle. The magnitude of the clamping force is found using
Coulombic friction, where  is about 0.4:

Frotor
Fcaliper ˆ  16;000N 10†
pad

This force generates a clamping stress in the brake rotor while the rotor force generates a shear stress.
Brake pads typically cover a 60 swath along the rotor. In the present case this results in a contact area of
A=53 cm2. Using this area and the forces calculated Eqs. (8) and (10), the rotor stresses that arise from the
mechanics of braking are given by:

3 ˆ 2 MPa

 ˆ 1:2 MPa 11†

2.1. Material properties

The automotive industry typically utilizes ¯ake cast irons in braking applications [6±8]. Hardness tests
were conducted on the rotor depicted in Fig. 1 to determine the exact iron alloy. Three measurements each
were made on the hat region, the outboard rotor and the inboard rotor. Several trends emerged: ®rst, the
hardest material is found on the inboard rotor (97 HRB), followed by the outboard rotor (94 HRB), and,
®nally, the hat (88 HRB). A statistical comparison of these data shows that each region has hardness that
 T.J. Mackin et al. / Engineering Failure Analysis 9 (2002) 63±76 69

is signi®cantly di€erent from each other region. These hardness di€erences are expected to arise from the
di€erential cooling rates associated with the casting process and are not thought to arise from the thermal
transients associated with braking. The measured Rockwell-B hardness values correspond to Brinell hard-
ness in the range of 170±220 HB, placing the UTS on the order of 400 MPa [6]. A comparison with handbook
data on cast irons identi®es the present alloy as a GG25 cast iron [6]. The key material properties for this
alloy are listed in Table 2.
A sample section was cut from the brake rotor for micro-structural evaluation (Fig. 5). The sample was
cut from the outside toward the inside using an oil-cooled band saw. Signi®cant residual tensile stresses
were noted during sample machining: the ®rst cut resulted in a partial fracture through a 1cm wide section of
the brake when the saw was within that distance of the inner radius. The fracture was accompanied by an
audible `ping' and the saw cut was seen to open by several millimeters (Fig. 5). The wider cut in Fig. 5 shows
the initial slice through the rotor. The second cut reveals the actual width made by the saw, while the opening
of the initial cut includes displacement associated with the relief of residual tensile hoop stresses. The sample
section was polished and etched using a 5% nital solution, and the microstructure was examined at several
points on the brake sample, denoted as locations 1, 2, and 3 in Fig. 5. The microstructures con®rm that the
brake material is a ¯ake graphite (Fig. 6). In addition to graphite ¯akes, the low magni®cation images of
Fig. 6 also show spherical inclusions consistent with slag contamination during casting. These inclusions
are not intended to be present and will have a detrimental e€ect on the thermal performance of the brake.
The measured di€erences in hardness with location on the brake correspond with the microstructures
shown in Fig. 6, where the higher hardness regions exhibit ®ne pearlite.

3. Estimated braking temperatures

A ®nite element analysis was conducted to obtain an estimate of the temperature distribution in the brake
rotor. Radial symmetry was assumed, and a one-degree section of the rotor was chosen as a representative
volume and meshed into roughly 50 elements. A stepped heat ¯ux was applied to the brake surface in contact
with the pad. The surface adjacent to the hub and the cross-sectional surfaces were insulated due to radial
symmetry. Convection was applied to the other surfaces in a stepped manner, with the ®lm convection coef-
®cient decreasing from 30 W/m2 K at each successive time step to simulate the decrease in angular velocity of
the rotor over the braking cycle. The initial temperature of the rotor was set to 300 K. A transient analysis
was performed over an interval of 6 s, in half-second time steps using the heat ¯ux formula given by Eq.
(9b). The resulting curve was integrated over each 1/2 second interval and each of those values was divided
by the area of the brake pad for input into a heat ¯ux table (J/m2). A plot of the temperature pro®le
through the width of the outboard rotor after 2.5 s of braking is shown in Fig. 7.

4. Estimating the lifetime of the brake disc

Braking causes rapid heating of rotor surface that can lead to thermal shock in the skin of the brake [2].
That problem can be treated using the method of stress suppression [9] to calculate the stresses in the skin

Table 2
Parameters for estimating fatigue lifetime

Material Brinnel hardness  y (MPa) E (GPa)  f0 b "f0 c

GG25 #4 174 215 90 241 0.115 0.008 0.360

70 T.J. Mackin et al. / Engineering Failure Analysis 9 (2002) 63±76

Fig. 5. Views of the Ford F-250 disc brake: (a) cross-section of the brake; (b) close-up of a fracture that occurred while machining the
sample section; (c) comparison of the ®rst and second cuts used to remove the cross-section shows considerable stress relief during
machining.

of the disc. In addition to that problem, braking leads to rapid heating of the rotor with little or no change
in the temperature of the hat. As such, the hat constrains the outboard braking surface. The following
treatment ignores thermal shock in the rotor skin and concentrates on the thermal stress generated between
the rotors and the hat. We approximate the stresses in the disc brake assembly by assuming that the hat
remains at room temperature and constrains the thermal displacement of the outboard rotor. Furthermore,
the hat was modeled as a solid rather than an open-walled cylinder. The constraint o€ered by the hat is
akin to an internal pressure on the annulus of the outboard rotor and generates considerable constraint
stresses in the outboard rotor. As a ®rst approximation we ignore the e€ect of the inboard rotor and its
vane attachments to the outboard side. Though this represents a considerable simpli®cation, the results
obtained are in good agreement with experience and experiment.
 T.J. Mackin et al. / Engineering Failure Analysis 9 (2002) 63±76 71

Fig. 6. Micrographs at several locations along the sample cross-section show the ¯ake graphite structure along with carbide nodules:
(a) center of hub; (b) center of outboard brake surface; (c) center of inboard brake surface.

The constraint of the hub prevents the free expansion of the rotor and is modeled as a two-element
shrink ®t (Fig. 8). In the absence of constraint, the outboard rotor would freely expand by an amount:

b ˆ b
T 12†

However, this thermal expansion is constrained by the hat so that the total de¯ection is shared between
an elastic outward displacement of the hat and an inward de¯ection of the rotor. Following [10], the
inward de¯ection of an internally pressurized body (in this case the rotor) is given by:
   2  
P a ‡ b2

b ˆ b ‡ 13†
E a2 b2

where the symbols are de®ned in Fig. 8. Likewise, the outward de¯ection of the hat, would be given by:

P

c ˆ
c
1 † 14†
E

The sum of these de¯ections must be equal to the free thermal de¯ection of the rotor, as follows:

Tb ˆ
c ‡
b 15†

At the interface of the hat and rotor, c=b, so that:

72 T.J. Mackin et al. / Engineering Failure Analysis 9 (2002) 63±76

Fig. 7. Computed temperature pro®le through the thickness of the outboard rotor.

 2  
P P a ‡ b2

T
b ˆ
b
1 † ‡ b ‡  16†
E E a2 b2

which is re-arranged to provide the constraint pressure:

   1
a2 ‡ b2
P ˆ
TE ‡ 1 17†
a2 b2

To arrive at an approximation for the constraint pressure generated by the hat, we utilize the average
temperature through the thickness of the rotor at time t=2.5 s (Fig. 7). The average increase in rotor
temperature is roughly 220 C, generating a constraint pressure of approximately 100 MPa. This constraint
pressure generates stresses in the hoop and radial directions according to:


Pb2 a2 ‡ r2
1 ˆ 2 2 18†
r a b2 †

Pb2 a2 r2
2 ˆ 2 2 19†
r a b2 †
 T.J. Mackin et al. / Engineering Failure Analysis 9 (2002) 63±76 73

Fig. 8. Schematic of the brake rotor illustrating the overall view of the brake (upper), the internal pressure on the disc (bottom left),
and the external restraining pressure from the hat (bottom right) generated by thermal stresses.

where  1 is the hoop stress, and  2 is the radial stress.

Plots of these stresses as well as the equivalent von Mises stress are shown in Fig. 9. Fig. 9 reveals that
the mean equivalent stress is roughly 180 MPa. Recall that the GG25 cast iron alloy has a yield strength of
215 MPa and elastic modulus of 90 GPa. A close look at Fig. 9 shows that the braking temperatures gen-
erate thermal stresses that clearly exceed the yield strength adjacent to the hub and extending about 1 cm
outward from the hub. Furthermore, the rotor yields in compression upon braking, while a residual tensile
hoop stress sets in upon cooling. This cycling between compression and tension, in phase with the temperature
of the brakes, is the thermo-mechanical mechanism responsible for failure. Accounting for the constraint
a€orded by the cooling ®ns makes the matter worse because the ®ns would further restrict the thermal defor-
mation of the rotor. The braking stresses shown in Eqs. (11) would also increase the equivalent stress and
74 T.J. Mackin et al. / Engineering Failure Analysis 9 (2002) 63±76

Fig. 9. Plot of the radial, hoop, and equivalent stresses in the brake rotor resulting from the shrink-®t model.

further drive plastic deformation during braking. One could use the method of stress suppression to include the
thru-thickness thermal gradient as well. This, again, would increase the equivalent stress and hasten the demise
of the disc.
In order to estimate of the fatigue lifetime of the rotor, we utilize the Con±Manson law, where:

"a ˆ f0 Nbf ‡ "0f Ncf 20†

The empirical constants are identi®ed as:

"a is the applied strain amplitude,

 f0 is the stress amplitude coecient,
"f0 is the strain amplitude coecient,
Nf is the number of cycles to failure.

The applied strain amplitude is estimated by calculating the elastic strain associated with the average
equivalent rotor stress of 180 MPa, giving "a =0.2%. The fatigue lifetime is found by plotting Eq. (20)
over a broad range of strain amplitudes, (Fig. 10), using the fatigue constants for a GG25 cast iron alloy,
shown in Table 2. As shown in Fig. 10, the fatigue lifetime associated with "a =0.2% is approximately 333
cycles to failure. Remarkably, experiments at Ford Motor Company have found that failure under the
speci®ed braking conditions occurs at roughly 300 braking cycles.
 T.J. Mackin et al. / Engineering Failure Analysis 9 (2002) 63±76 75

Fig. 10. Plot of the Con±Manson law for a GG25 cast iron alloy. An applied strain amplitude of 0.2% provides an estimated life of
333 cycles.

5. Conclusions

Thermal cracking in disc brake rotors is a low cycle thermo-mechanical fatigue problem. The frictional
work of braking rapidly heats the rotors while having no e€ect on the hat region. This di€erence in tem-
peratures sets up compressive thermal stresses in the rotor during braking that reverse sign upon cooling.
Thermo-mechanical stresses were calculated using a simple shrink-®t analysis wherein the hat was modeled
as constraining the free thermal expansion of the rotor. These stresses were found to exceed the yield
strength in the rotor over considerable distances from the hub and were very near the yield strength over
most of the rotor. Following cool down a tensile residual stress, at or very near the yield strength, is set
into the rotor. Subsequent braking cycles the rotor through an applied stress range that has an amplitude
near that of the yield strength of the rotor, leading to a design problem of low cycle fatigue. Such high
stress/strain amplitudes are modeled using the Con±Manson law. In the present study, the strain ampli-
tude is simply calculated using the elastic strain associated with an average thermo-mechanical stress
amplitude. This approach shows that thermal cracking can be expected in a relatively small number of
high-g braking cycles.
There are three ways to eliminate thermal cracking in brake rotors: (1) increase the yield and fatigue
strength of the rotor material; (2) decrease the braking temperatures; and/or (3) re-design the hub±rotor
unit to eliminate constraint stresses. New brake materials have been identi®ed that can operate at sub-
stantially higher temperatures [2]. However, this leads to a need for heat shielding around the brakes, the
use of higher temperature bearing materials and a radical re-design of the entire brake assembly. Advanced
76 T.J. Mackin et al. / Engineering Failure Analysis 9 (2002) 63±76

designs that incorporate cooling into the brakes are also dicult to achieve and add considerable cost to
the brake unit [11]. The simplest approach is to eliminate the constraint brought about by the rotor±hub
assembly [11]. The challenge of a new mechanical design that relieves the thermal constraint is left as an
open invitation to the reader.

References

[1] Gunther, B, Klingelhoe€er, H. A systematic study for fatigue life prediction of grey cast iron disc brakes. In: Fatigue 2000.
p. 397±405.
[2] Jimbo, Y, Mibe, T, Akiyama, K, Matsui, H, Yoshida, M, Ozawa, A. Development of high thermal conductivity cast iron for
brake disc rotors. SAE Technical Paper #900002, 1990.
[3] Genta G. Motor vehicle dynamics: modeling and simulation. River Edge (NJ): World Scienti®c, 1997.
[4] Newcombe TP. Temperatures reached in disc brakes. J Mechanical Engineering Science 1960;2(3).
[5] Noyes, RN, Vickers, PT. Prediction of surface temperatures in passenger car disc brakes. SAE Technical Paper # 690457, 1969.
[6] Walton, CF, Editor. Iron castings handbook. Iron Castings Society, Inc., 1981.
[7] Nayar A. The metals data book. New York: McGraw-Hill, 1997.
[8] Anon. Metals handbook, vols. 1 and 10. 10th ed. ASM International, 1990.
[9] Timoshenko S. Strength of materials, part II. Krieger Publishing, 1983.
[10] Timoshenko SP, Goodier, JN. Theory of elasticity. McGraw-Hill, 1970.
[11] Metzler H. The brake rotor Ð friction partner of brake linings. SAE Technical Paper # 900847, 1990.