Predicting Durability - Durability Digital Twin

1. Predicting durability
Thermomechanical simulation helps optimize a catalytic
converter assembly for durability and performance.
By Sandeep Muju, Robert L. Sager, Jr., and Benny J. Snider
T
HE CAT A LYTIC CONVERTER ID
an automobile changes the
most harmful by-products
of gasoline combustion-carbon
monoxide, nitrogen oxides, and
unburned hydrocarbons-into less
harmful substances: water, carbon
dioxide, and nitrogen. The popu-
lar three-way catalysts typically
employ the noble metals platinum,
rhodium, and palladium to induce
reactions that make these conver-
sions. Since the reactions are het-
erogeneous, the noble metals must
be exposed to the exhaust gas on a
ceramic or metallic substrate. This
substrate is housed within a metal-
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o 100 200 300 400 500 600 700 BOO
Temperature (degrees C)
lic can with a vermiculite or Ine-
Figure 1. Relative expansion of the intumescent mat as a function of temperature.
tallic packaging mat to hold the substrate in place.
The catalytic converter is vulnerable to mechanical fail-
ure in many ways-from excess deformation of the can,
failure of the can's weld, substrate fracture during can-
ning, meltdown of the substrate, or from the mat's loss of
holding pressure, failure, erosion, or sintering. The mat
serves several functions: It provides frictional forces to
hold the substrate, absorbs vibrational shock, gives ther-
Sandeep Mllju was a senior analytical engineer at
Tenneco Automotive in Grass Lake, Mich., when the
work reported here was done. He is now an engineer
specialist at AlliedSignal Engines in Phoenix.
Robert L. Sager, Jr. is an aftermarket project engineer,
and Benny J. Snider is original-equipment program
manager at Tenneco Automotive.
64 M A R C H 1999 M EC H AN I CA L ENG I NEE RI NG
mal insulation, and seals exhaust gas leaks from non-
monolith sections, those surfaces of the substrate in
contact with the mat.
The predomjnant factor in the erosion of mats made
from vermiculite is believed to be the impingement
of pulsating high-temperature exhaust gases. A combi-
nation of cyclic thermal expansion of the n1.etallic can
and vibratio nal loading accelerates mat degradation,
culminating in loss of emissions conversion or substrate
failure. A careful examinati on of a typical, freshly
manufac tured vermiculite mat reveals high H ertzian-
type mat defor mation under the inward ribs. Excess
pressures under these ribs during canning may lead
to substrate cracking or m icrofractures in the m at,
which under gas impingement may lead to accelerated
mat erosion.
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2. O ther researchers have already m odeled the room-
temperature canning process; they treated the mat
material using soft contac t elem ents follow ing the
room - temperature loading-displacement relation. T hey
did not address the high-temperature case. The present
study also has been fo cused on thermomech ani cal
modeling of the venniculite mat's swelling and its effect
on durability, using the Abaqus nonlinear finite element
analysis code from Hibbit, Karlsson & Sorensen Inc.
of Paw tu cket, R.I. , to study th e case ofa clam-shell
converter package with ceramic package and vermi-
culite-ceramic mat. In addition to the room-tempera-
ture canning process, the high- temperature hysteretic
ratcheting expansion and the instantaneous and relaxed
constitutive characteristics of the mat was modeled.
(CTE) reveals a highly nonlinear dependence on temper-
ature. T he axjal CTE was found to be negative for tem-
peratures up to 600°C.
The n"lat material combines ceramic fibers (alumina sili-
cate) and vermiculite material. T he vermiculite is a mica-
ceous hydrated m agnesium aluminum-silicate mineral
which, when heated, loses som e of its water, causing the
layers to expand by 10 to 20 times in thickness. The intu-
mescent behavior of the m at tested, model XPE-3100
from the Unifrax C orp. of Niagara Falls, N.Y, is shown in
Figure 1. At first, the mat tends to contract, until the first
high-temperature thermal cycle reaches about 300°C, at
which point the mat rapidly expands by about 50 percent,
a level reached at about 550°C. Typically, the mat starts to
sinter at about 750°C, after which point it loses its load-
Hill's hyperfoam con-
stitutive model was used
for the continuum mat
elements. Small sliding
frictional contact mod-
eling w as used for the
contacting can, mat, and
substrate surfaces. T = 500·C lO 700°C
mal
Th e cell geometr y
within a typical ceramic
D
D
-
Ceramic Subslrule
Venniculile Mal
Can
700"c
T = 525't lO 700"C
mm
T =525"
C
ClIlI
substrate is either square
or triangular. Cell geo-
m etry affects pressure
drop, heat transfer char-
acteristics, and the ther-
momechanical integrity
o f the substrate . The
cells typically run as long
Figure 2. Maximum temperature distribution across the cross section.
channels along the length of the substrate. At a continuum
level, the geometric cell structure of the substrate lends it-
self to being treated as a homogeneous orthotropic medi-
um. But from the standpoint of strength, a mesoscopic
analysis is needed, where the continuum stress state is trans-
formed to a local microscopic stress state in individual cell
walls and vice versa. (M esoscopic quantities are larger than
microscopic and sm aller than macroscopic, and are not
visible to the naked eye.)
CONTINUUM DAMAGE MECHANICS
T he subject of continuum damage m echanics has been
researched quite actively in the past few years. The issues
that still must be resolved are related to establishing a
suitable criterion for application of micromechanical
modeling versus continuum modeling and examining
the process so as to allow a smooth transition from con-
tinuum to micromechanical modeJing. Due to practical
difficulties with measuring the mesoscopic quantities of
interest, the strength characteristics of these substrates
typically have been described in terms of macroscopic
quantities such as crush strength, modulus of rupture,
and isostatic strength.
The homogenized transversely isotropic moduli of the
substrate reveal an inverse temperature dependence. The
transversely isotropic coeffi cient of thermal expansion
bearing abilities. Between 550° and 750°C, the mat ex-
pansion is relatively constant. After the mat cools down
(and assuming that sintering did not take place), its con-
traction does not follow the heat- up cycle expansion
curve. A net residual expansion of about 30 percent re-
mains in the mat at room temperature. D epending on the
chemical composition of the mat material, subsequent
thermal cycles produce varied degrees of sinlliar inelastic
expansion response to temperature cycles.
From the standpoint of a m echanical constitutive rela-
tion, the typical compressive load displacem ent curve
reveals a nonlinear elastic ch aracteristic. Further, be-
cause of the viscoelastic nature of the mat, the instanta-
neous load displacement curve typically shows ;1 stiffer
response than the steady-state response. Because of the
relatively high compressibiJity of the mat material, the
hyperfoam formulation based on Hill's strain energy po-
tential is taken as the appropriate constitutive model.
In this analysis the canning is treated as a quasi-static
process. T he instantaneous load displacem ent data are
used to simulate the instantaneous stresses and deforma-
tions in the assembly. After canning, the catalytic con-
verter assembly is typically shipped to another location
for assembly into the exhaust system. Since there is am-
ple time for the mat to reach a steady state before the ex-
haust system is assembled, it is possible to disregard the
ME C H AN I C AL ENG I NEE R I N G MAR C H 1999 65
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3. temporal effect of the mat re ponse from instantaneous
carming to steady state. Therefore, the steady-state load
displacement relation for the mat is taken as the load dis-
placement relation for the high-temperature analysis.
The can, which is made of 409 stainless steel, is treat-
ed as elastoplastic with isotropic hardening. The com-
plete stress-strain curves under elevated ten'lperature
conditions were not avail able. Therefore, th e roo m
temperature curve was scaled according to the effect of
temperature on yield.
THERMOMECHANICAL SIMULATION
A quarter-symmetry model was analyzed with appro-
priate boundary conditions. The model has over 4,800
continuum elements, with about half as quadrilateral,
reduced-integration, hourglass-control (S4R and S3R )
3-D sheU elements for the can, and the rest 3-D hexa-
hedral elements (C308 and C306) for the mat and sub-
strate. Care was exercised in minimizing the number of
triangular and prism elements. The contact between the
shell and the mat, and between the mat and the sub-
strate, was modeled using a smalJ sliding contact formu-
lation with a Coulomb friction model. Since the mat
material undergoes relatively large strains and the can
also undergoes large strains and displacements, this ther-
momechanical analysis is of the large-deformation type.
The maximum temperature profile of the cross section
is shown in Figure 2. The temperature profile along the
length of the converter is assumed to be constant.
Because of the viscoelastic nature of the vermiculite
mat, the stiffer "instantaneous" pressure response relax-
es to a steady-state " relaxed" pressure response. Both
the instantaneous canning and the relaxed can analysis
Proposed Design
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2.33c-02
Figure 3. Pressure contour for mat compression at instantaneous canning.
are studied. Since th e instantaneous mat response is
stiffer, it should lead to the worst-case canning stresses
for the ce rami c substrate. The relaxed can analysis
forms th e initial condition for the high- temperature
thermal excursion analysis.
The vermiculite mat of 5- mm original thickness wa
modeled using three-dimensional continuum elements.
Within Abaqus, the shrink parameter of contact interfer-
ence was used to simulate the canning process design
compression of the mat. A Coulomb friction model was
66 MARC H 1999 MEC HAN IC AL EN G INEERING
used with a coefficient of friction f.l=0.25 between the
mat and the can and f.l=0.4 between the ceramic sub-
strate and the mat. The can displacements matched weU
with experimental data.
The investigators found that the contours for displace-
ment, stress components, and plastic strains did not sig-
nificantly change shape as the simulation continues fi'om
instantaneous canning (point 1 on Figure 1) to the end
of cool-down (point 5 on Figure 1). The peak pressures
in the vermiculite mat during instantaneous calming are
almost double those at relaxed steady state. There is plas-
tic deformation of about 0.1 percent equivalent plastic
strain on the flange edge of the can-that is, the canning
pressures are high enough to permanently deform the
can. From the stresses in the ceramic substrate it can be
seen that the peak instantaneous stresses at instantaneous
canning are almost double those at the steady state.
Therefore, for the substrate and mat canning fa ilure
issues, the instantaneous canning forces are critical.
Since these equivalent stresses and pressures are contin-
uum va riabl es, for an acc urate fractu re assess ment
a mi cromechanical model would be required. Some
unit cell-based models have been developed for this
purpose, but because of the nonperiodic surface and
edge effects, more generalized multiaxial failure crite-
ria are needed.
The first-cycle inelastic thermal expansion character-
istic of the mat material is incorpo rated in the high-
temperature analysis. The thermal expansion properties
of the mat are determined from the heat-up and cool-
down curves of Figure 1. The instantaneous and relaxed
hyperfoam material constants are derived from the load
displacement curves. The temperature-dependent stress-
strain curve fo r th e
elastoplastic can is based
on th e te mp eratu re
sca ling of the room -
temperature stress-strain
curve, according to the
effec t o f tempe rature
on the yield strength.
Th e homogenized or-
thotrop ic non lin ea r
thermoelastic properties
were used to model the
ceramic substrate.
Th e relaxe d stea dy
state (point 2 in Figure
1) of the assembly forms
the initial condition for the heat-up cycle. The expan-
sion characteristics of the heat-up cycle are used (points
3 and 4 on Figure 1). Point 4 is taken as the initial con-
dition for the cool-down cycle from point 4 to point 5.
The appropriate expansion parameters are taken from
this part of the expansion curve. Based on this proce-
dure, any number of thermal cycles may be modeled. It
was found that although the finite element capability for
cyclic plasticity and thermal cycling simulation exists, the
cyclic material property data is more difficult to obtain.
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4. Therefore, much effort is required to obtain appropriate
cyclic material data so that cyclic simulations with a large
number of thermomechanical cycles yield physically
meaningful re ults.
Since the shape of the contours does not change signif-
icantly during the simulation, the location of the peak
values of the Von Mises stress in the ceramic substrate is
the same as in the contour plot of Figure 3. As expected,
due to the negative expansion of the
mat until point 3 of Figure 1, the
pressure in the mat is reduced. This
brings up a concern with respect to
a field cycle in which the tempera-
ture never exceeds point 3 and thus
lack of holding pressure may lead to
accelerated mat erosion. Typically,
this condition is difficult to design
for. But based on th e simulation
procedure developed here, it is now
possible to quantify this scenario.
After point 3, the mat goes
through a sharp increase in expan-
sion characteristic, which starts ap-
plying increasing pressures on the
can and substrate, thus raising the
stresses and strains in both can and
substrate. At the end of the heat-
up cycle (point 4), th e ca n ha s
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,nanufacturing (the welding process and ca n-closing
force profile), geometry (the substrate shape and size,
mat thickness, can and rib shape and size), and material
properties (coated substrate strength, mat basis weight,
and can metal properties).
An unfavorable concentration of variabilities at one
extrelne may lea d to a " loose" assembl y, or at the
other extreme to an excessively stressed assembly. It
2 3 4 5 6
Simulation step (see Figure 1 on page 64)
peak equivalent plastic strains on
the order of 8 percent. Th e sub-
Figure 4. History of peak pressure in the mat through one thermal cycle.
strate stresses also increase significantly and are double
those observed during th e instantaneous ca nning at
room tem.perature.
Further, at the end of the cool-down cycle (point 5) a
residual equivalent plastic strain on the order of 1 percent
remains in the can. This strain may significantly reduce
the can's thermomechanical fatigue life.
For example, Figure 4 shows the peak mat pressure
through one thermal cycle. Other relevant quantities,
such as peak can displacement history, peak substrate
stress history, and peak can stress and strain histories, are
also obtained from the analysis. Due to limitations of the
experimental techniques, these thermomechanical quan-
tities at high temperature typically are not known. This
thermomechanical method provides a way to analyze the
complete thermomechanical behavior of catalytic con-
verter assemblies. This method models the entire life
cycle of the converter assembly from the manufacturing
canning process (point 1 in Figure 1) to the thermal
cycled state (point 5 in Figure 1). This unique ability to
model the entire life cycle of the converter assembly sig-
nificantly improves the ability to optimize the converter
assembly for durability and performance for the life cycle
of the converter assembly.
VARIABILITY ISSUES
Since all of these analyses are deterministic, they are usu-
ally perform.ed for the nominal (design) geom etric
dimensions. But, variability is inevitable. It can arise in
has been shown that a ±8 percent variability in mat
basis weight may produce as much as ±30 percent vari-
ability in the mat pressure versus strain co nstitutive
behavior. Therefore, for converter durability the mat
property variations are an important factor to be con-
troll ed, especially since th e resistance of th e mat to
hot-gas erosion is highly sensitive to the mat pressures.
Typically, th e variability in metallic properties and
shape of the can is relatively small.
A statistical analysis of each of the variables would lead
to some form ofprobability distribution function for each
variable. Based on the probability distribution functions
for the size of the substrate, mat, and can, a cumulative
distribution for lower and upper bound on the assembly
dimensions could be determined. Based on these lower
and upper bounds, a deterministic thermomechanical
stress analysis may be conducted for the two bounds, or
up to the desired levels of reliability limits. The stress and
strain distributions obtained at these bounds may then be .
overlaid with the material strength/ deformation bounds,
providing the statistical data for probability of converter
assembly parameters exceeding the allowed bounds based
on material strength variations. Doing so will lay the
fo'undations for a reliability-based durability design and
analysis methodology. _
This arlicle is adapledJrolll a lee/lllical paper (97-WA I OE- /5) prese/lted
01 Ihe /997 ASME IlItematiollal Mechallical Ellgilleerillg COII<~ress & Exposi-
lioll ill Oallt,s.
ME C HANI AL ENG I NE ER I NG MAR C H 1999 67
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