Thermomechanical simulation was used to optimize a catalytic converter assembly for durability. The simulation modeled the intumescent mat material that holds the substrate in place within the metal can. It found that the mat expands significantly at high temperatures, applying pressure to the substrate. The instantaneous pressures during assembly were highest and most critical for substrate failure. The simulation analyzed the assembly through one full thermal cycle and found stresses and strains increased in the can and substrate during heating due to mat expansion. Peak mat pressures and substrate stresses doubled from assembly to high temperature operation.
EFFECT OF SCANDIUM ON THE SOFTENING BEHAVIOUR OF DIFFERENT DEGREE OF COLD ROL...msejjournal
The softening behavior of different cold rolled Al-6Mg alloys containing scandium 0.2 wt% and 0.6 wt% have been investigated by means of microscopy, hardness and electrical conductivity measurements. It is found that the scandium added alloys attend the higher hardness at every state of cold rolling at higher
annealed temperature due to the precipitation of scandium aluminides. Electrical resistivity of the scandium added alloys show higher than base alloy due to grain refining. It is seen from the microstructure that scandium refine the grain structure and inhibit recrystallization.
EFFECT OF SCANDIUM ON THE SOFTENING BEHAVIOUR OF DIFFERENT DEGREE OF COLD ROL...msejjournal
The softening behavior of different cold rolled Al-6Mg alloys containing scandium 0.2 wt% and 0.6 wt% have been investigated by means of microscopy, hardness and electrical conductivity measurements. It is found that the scandium added alloys attend the higher hardness at every state of cold rolling at higher
annealed temperature due to the precipitation of scandium aluminides. Electrical resistivity of the scandium added alloys show higher than base alloy due to grain refining. It is seen from the microstructure that scandium refine the grain structure and inhibit recrystallization.
Dispersion Hardening:
Hard particles:
Mixed with matrix powder
Consolidated
Processed by powder metallurgy techniques
Second phase – Very little solubility (Even at elevated temp.)
No coherency
So thermally Stable at very high temp.
Resists :
Grain growth
Over aging
Recrystallization
Mobility of dislocation
Different from particle Metallic Composites (Volume Fraction is 3 to 4% max.) (Does not affect stiffness)
Examples : Al2O3 in Al or Cu, ThO2 in Ni
Strengthening Mechanisms of Metals and alloysDEVINDA MAHASEN
In this presentation, I have explained 4 types of strengthening processes of metals.
Grain-size reduction
Solid-solution alloying
Strain hardening (work hardening or cold working)
Annealing of deformed metals
Stress-Strain Curves for Metals, Ceramics and PolymersLuís Rita
Homework II - Biomaterials Science
We are interested about studying and comparing stress-strain curves of metals, ceramics and polymers. Primarily, differences are due to their different chemical bonding properties.
IST - 4th Year - 2nd Semester - Biomedical Engineering.
Magnetic nde characterization of tempered 2.25 cr 1mo steelAPOORVKRISHNA1
A descriptive presentation on heat treatment analysis of Tempered 2.25Cr-1Mo steel ,commonly known as P22 steel. The presentation includes history of the material, objective and work-plan with procedures adopted to carry out the project.
An overview of the major materials used in aeronautical and automotive structures will be given in this section. The mechanical and physical properties of the materials will be highlighted, with an emphasis placed on the stiffness versus density and strength versus density of various materials.
About: «Experiments in 1992 in Finland seemed to show that the Earth's gravity could be shielded with a superconductor configured in a certain manner. This experiment, by Eugene Podkletnov, at Finland's Tampere University of Technology, apparently created a reduction in the weight of objects placed above a levitating, rotating superconducting disk...»
Quote: "The second generation of flying machines will reflect gravity waves and will be small, light, and fast, like UFOs. I have achieved impulse reflection; now the task is to make it work continuously." - Podkletnov, Breaking the Law of Gravity (1998)
REVIEW ON ANALYSIS OF CREEP IN AN ISOTROPIC UNIFORM COMPOSITE CYLINDERijiert bestjournal
The steady state creep in Al- SiCP composite cylinder subjected to internal pressure was investigated. The creep
behavior of the material was described by threshold stress based creep law by assuming a stress exponent of 5.
The effect of size and content of the reinforcement (SiCP), and operating temperature on the stresses and strain
rates in the composite cylinder were investigated. The stresses in the cylinder did not have significant variation
with varying size and content of the reinforcement, and operating temperature. However, the tangential as well
as radial strain rates in the cylinder could be reduced to a significant extent by decreasing size of SiCP,
increasing the content of SiCP and decreasing operating temperature.
Dispersion Hardening:
Hard particles:
Mixed with matrix powder
Consolidated
Processed by powder metallurgy techniques
Second phase – Very little solubility (Even at elevated temp.)
No coherency
So thermally Stable at very high temp.
Resists :
Grain growth
Over aging
Recrystallization
Mobility of dislocation
Different from particle Metallic Composites (Volume Fraction is 3 to 4% max.) (Does not affect stiffness)
Examples : Al2O3 in Al or Cu, ThO2 in Ni
Strengthening Mechanisms of Metals and alloysDEVINDA MAHASEN
In this presentation, I have explained 4 types of strengthening processes of metals.
Grain-size reduction
Solid-solution alloying
Strain hardening (work hardening or cold working)
Annealing of deformed metals
Stress-Strain Curves for Metals, Ceramics and PolymersLuís Rita
Homework II - Biomaterials Science
We are interested about studying and comparing stress-strain curves of metals, ceramics and polymers. Primarily, differences are due to their different chemical bonding properties.
IST - 4th Year - 2nd Semester - Biomedical Engineering.
Magnetic nde characterization of tempered 2.25 cr 1mo steelAPOORVKRISHNA1
A descriptive presentation on heat treatment analysis of Tempered 2.25Cr-1Mo steel ,commonly known as P22 steel. The presentation includes history of the material, objective and work-plan with procedures adopted to carry out the project.
An overview of the major materials used in aeronautical and automotive structures will be given in this section. The mechanical and physical properties of the materials will be highlighted, with an emphasis placed on the stiffness versus density and strength versus density of various materials.
About: «Experiments in 1992 in Finland seemed to show that the Earth's gravity could be shielded with a superconductor configured in a certain manner. This experiment, by Eugene Podkletnov, at Finland's Tampere University of Technology, apparently created a reduction in the weight of objects placed above a levitating, rotating superconducting disk...»
Quote: "The second generation of flying machines will reflect gravity waves and will be small, light, and fast, like UFOs. I have achieved impulse reflection; now the task is to make it work continuously." - Podkletnov, Breaking the Law of Gravity (1998)
REVIEW ON ANALYSIS OF CREEP IN AN ISOTROPIC UNIFORM COMPOSITE CYLINDERijiert bestjournal
The steady state creep in Al- SiCP composite cylinder subjected to internal pressure was investigated. The creep
behavior of the material was described by threshold stress based creep law by assuming a stress exponent of 5.
The effect of size and content of the reinforcement (SiCP), and operating temperature on the stresses and strain
rates in the composite cylinder were investigated. The stresses in the cylinder did not have significant variation
with varying size and content of the reinforcement, and operating temperature. However, the tangential as well
as radial strain rates in the cylinder could be reduced to a significant extent by decreasing size of SiCP,
increasing the content of SiCP and decreasing operating temperature.
Fundamentals, synthesis and applications of Al2O3-ZrO2 compositesTANDRA MOHANTA
When the word “Ceramic” comes to our mind, we usually associate them with plates, saucers, cups and mugs. But, the word “Ceramic” encompasses more than just the word “plates” or “saucers”. Indeed, ceramic materials are hard and inherently brittle, but this is just the tip of the iceberg. They have multifarious properties and have acquired a status of high technical importance in the field of scientific research. Ceramics are the soul of the modern day’s structural applications owing to their high mechanical and thermal stability under different challenging conditions. They exhibit remarkable properties such as high hardness, high wear resistance, high corrosion resistance, high elastic modulus, high melting point and the ability to retain high strength at elevated temperatures. Alumina (Al2O3) is one such remarkable ceramic material known for its unique optical, mechanical and electrical properties. But the brittle nature of Al2O3 limits its use in certain engineering applications. Therefore, the strength of Al2O3 and Al2O3- based ceramics can be enhanced by tailoring the microstructural design through the application of strategic techniques that may involve secondary phase particle inclusion (such as Zirconia, ZrO2)
Role of αc–relaxation in high-temperature polymer deformation.
Proceedings of the American Society for Composites 2009-Twenty-Fourth Technical ConferenceWith the Canadian Association for Composite Structures and Materials (Joint Canadian-American International Conference), September 15-17, Newark, DE
In recent years, the application of high-power semiconductor lasers has been expanding, and they are more and more widely used in industry and medical treatment. The thermal characteristics of lasers seriously restrict their reliability and service life. In order to improve the reliability and prolong the service life of the device,high power semiconductor laser bars with different solders, different thickness of solders and different thickness of WCu heat sink packages were simulated by COMSOL Multiphysics, and the "Smile" values of laser bars under different packaging conditions were measured. The results show that the maximum thermal stress of in solder or AuSn solder occurs at the interface between WCu secondary heat sink and Cu heat sink; the thermal stress of laser chips packaged with the same thickness of In solder and AuSn solder is 3.57 GPa and 3.83 GPa respectively,and the peak spectra are 800.5 and 798 nm, respectively.; reducing the thickness of solder is beneficial to reducing the thermal stress and temperature in the laser chips,but the solder is not. If the thickness is too thin,it may lead to weak welding of the laser core or uneven distribution of solder,and voids in the solder layer,so the selection of solder thickness should be considered as a whole. With the increase of the thickness of WCu secondary heat sink, the thermal stress of the laser chip decreases,but the temperature of the core rises,and the optimal thickness of tungsten-copper secondary heat sink is 380 um. This paper provides a basis for optimizing the packaging of high power semiconductor lasers and has guiding significance for practical production.
Neural Aerospace Manufacturing – a highly networked ecosystem that is connected, intelligent, resilient, automated, adaptive, personalized, and cognitive
Ac 9 academic research - san jose state university _ scorecard _ institution...Sandeep (Sandy) Muju
AASHE STARS Gold Report
The Sustainability Tracking, Assessment & Rating System™ (STARS®) is a transparent, self-reporting framework for colleges and universities to measure their sustainability performance
In this presentation, we have discussed a very important feature of BMW X5 cars… the Comfort Access. Things that can significantly limit its functionality. And things that you can try to restore the functionality of such a convenient feature of your vehicle.
Why Is Your BMW X3 Hood Not Responding To Release CommandsDart Auto
Experiencing difficulty opening your BMW X3's hood? This guide explores potential issues like mechanical obstruction, hood release mechanism failure, electrical problems, and emergency release malfunctions. Troubleshooting tips include basic checks, clearing obstructions, applying pressure, and using the emergency release.
Comprehensive program for Agricultural Finance, the Automotive Sector, and Empowerment . We will define the full scope and provide a detailed two-week plan for identifying strategic partners in each area within Limpopo, including target areas.:
1. Agricultural : Supporting Primary and Secondary Agriculture
• Scope: Provide support solutions to enhance agricultural productivity and sustainability.
• Target Areas: Polokwane, Tzaneen, Thohoyandou, Makhado, and Giyani.
2. Automotive Sector: Partnerships with Mechanics and Panel Beater Shops
• Scope: Develop collaborations with automotive service providers to improve service quality and business operations.
• Target Areas: Polokwane, Lephalale, Mokopane, Phalaborwa, and Bela-Bela.
3. Empowerment : Focusing on Women Empowerment
• Scope: Provide business support support and training to women-owned businesses, promoting economic inclusion.
• Target Areas: Polokwane, Thohoyandou, Musina, Burgersfort, and Louis Trichardt.
We will also prioritize Industrial Economic Zone areas and their priorities.
Sign up on https://profilesmes.online/welcome/
To be eligible:
1. You must have a registered business and operate in Limpopo
2. Generate revenue
3. Sectors : Agriculture ( primary and secondary) and Automative
Women and Youth are encouraged to apply even if you don't fall in those sectors.
5 Warning Signs Your BMW's Intelligent Battery Sensor Needs AttentionBertini's German Motors
IBS monitors and manages your BMW’s battery performance. If it malfunctions, you will have to deal with an array of electrical issues in your vehicle. Recognize warning signs like dimming headlights, frequent battery replacements, and electrical malfunctions to address potential IBS issues promptly.
Symptoms like intermittent starting and key recognition errors signal potential problems with your Mercedes’ EIS. Use diagnostic steps like error code checks and spare key tests. Professional diagnosis and solutions like EIS replacement ensure safe driving. Consult a qualified technician for accurate diagnosis and repair.
What Exactly Is The Common Rail Direct Injection System & How Does It WorkMotor Cars International
Learn about Common Rail Direct Injection (CRDi) - the revolutionary technology that has made diesel engines more efficient. Explore its workings, advantages like enhanced fuel efficiency and increased power output, along with drawbacks such as complexity and higher initial cost. Compare CRDi with traditional diesel engines and discover why it's the preferred choice for modern engines.
Things to remember while upgrading the brakes of your carjennifermiller8137
Upgrading the brakes of your car? Keep these things in mind before doing so. Additionally, start using an OBD 2 GPS tracker so that you never miss a vehicle maintenance appointment. On top of this, a car GPS tracker will also let you master good driving habits that will let you increase the operational life of your car’s brakes.
"Trans Failsafe Prog" on your BMW X5 indicates potential transmission issues requiring immediate action. This safety feature activates in response to abnormalities like low fluid levels, leaks, faulty sensors, electrical or mechanical failures, and overheating.
What Does the Active Steering Malfunction Warning Mean for Your BMWTanner Motors
Discover the reasons why your BMW’s Active Steering malfunction warning might come on. From electrical glitches to mechanical failures and software anomalies, addressing these promptly with professional inspection and maintenance ensures continued safety and performance on the road, maintaining the integrity of your driving experience.
What Does the PARKTRONIC Inoperative, See Owner's Manual Message Mean for You...Autohaus Service and Sales
Learn what "PARKTRONIC Inoperative, See Owner's Manual" means for your Mercedes-Benz. This message indicates a malfunction in the parking assistance system, potentially due to sensor issues or electrical faults. Prompt attention is crucial to ensure safety and functionality. Follow steps outlined for diagnosis and repair in the owner's manual.
Core technology of Hyundai Motor Group's EV platform 'E-GMP'Hyundai Motor Group
What’s the force behind Hyundai Motor Group's EV performance and quality?
Maximized driving performance and quick charging time through high-density battery pack and fast charging technology and applicable to various vehicle types!
Discover more about Hyundai Motor Group’s EV platform ‘E-GMP’!
𝘼𝙣𝙩𝙞𝙦𝙪𝙚 𝙋𝙡𝙖𝙨𝙩𝙞𝙘 𝙏𝙧𝙖𝙙𝙚𝙧𝙨 𝙞𝙨 𝙫𝙚𝙧𝙮 𝙛𝙖𝙢𝙤𝙪𝙨 𝙛𝙤𝙧 𝙢𝙖𝙣𝙪𝙛𝙖𝙘𝙩𝙪𝙧𝙞𝙣𝙜 𝙩𝙝𝙚𝙞𝙧 𝙥𝙧𝙤𝙙𝙪𝙘𝙩𝙨. 𝙒𝙚 𝙝𝙖𝙫𝙚 𝙖𝙡𝙡 𝙩𝙝𝙚 𝙥𝙡𝙖𝙨𝙩𝙞𝙘 𝙜𝙧𝙖𝙣𝙪𝙡𝙚𝙨 𝙪𝙨𝙚𝙙 𝙞𝙣 𝙖𝙪𝙩𝙤𝙢𝙤𝙩𝙞𝙫𝙚 𝙖𝙣𝙙 𝙖𝙪𝙩𝙤 𝙥𝙖𝙧𝙩𝙨 𝙖𝙣𝙙 𝙖𝙡𝙡 𝙩𝙝𝙚 𝙛𝙖𝙢𝙤𝙪𝙨 𝙘𝙤𝙢𝙥𝙖𝙣𝙞𝙚𝙨 𝙗𝙪𝙮 𝙩𝙝𝙚 𝙜𝙧𝙖𝙣𝙪𝙡𝙚𝙨 𝙛𝙧𝙤𝙢 𝙪𝙨.
Over the 10 years, we have gained a strong foothold in the market due to our range's high quality, competitive prices, and time-lined delivery schedules.
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-
1.6 ,-----------------------------------------------------,
c1.4
o
'(jj
c
co
0.
~ 1.2
ID
.~
co
ID
a: 1.0
2
- 3
•
- 4
•
O.B L..----1._--'-_'-----1._...1...----''----'-_-'-------L_--'-_'-----1._...1...----'_--'----'
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.
Downloaded From: https://memagazineselect.asmedigitalcollection.asme.org on 01/07/2019 Terms of Use: http://www.asme.org/about-asme/terms-of-use
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
Downloaded From: https://memagazineselect.asmedigitalcollection.asme.org on 01/07/2019 Terms of Use: http://www.asme.org/about-asme/terms-of-use
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
> 1.43e+00
-c 1.4Se+OO
< 1.30.+00
« l.1Sc+OO
« 1.05e+OO
-< 9.1ge-Ol
« 7.9Ie-OI
< 6.63.·01
... 5.35e-Ol
< 4.07.·01
< 2.79.·01
« 1.51c-OI
« 2.33e-02
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
ro
Cl.
3
~2
~
:::J
en
en
Q)
0.
'iii
E
o
o
,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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