This article discusses that thermomechanical simulation helps optimize a catalytic converter assembly for durability and performance. A careful examination of a typical, freshly manufactured vermiculite m at reveals high Hertzian-type mat deformation under the inward ribs. Excess pressures under these ribs during canning may lead to substrate cracking or microfractures in the mat, which under gas impingement may lead to accelerated mat erosion. The present study also has been focused on thermomechanical modeling of the vermiculite mat's swelling and its effect on durability, using the Abaqus nonlinear finite element analysis code from Hibbit, Karlsson & Sorensen Inc., Pawtucket, RI, to study the case of a clam-shell converter package with ceramic package and vermiculite-ceramic mat. Because of the viscoelastic nature of the mat, the instantaneous load displacement curve typically shows a stiffer response than the steady-state response. Because of the relatively high compressibility of the mat material, the hyperfoam formulation based on Hill's strain energy potential is taken as the appropriate constitutive model.
The Catalytic 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 popular three-way catalysts typically employ the noble metals platinum, rhodium, and palladium to induce reactions that make these conversions. Since the reactions are heterogeneous, the noble metals must be exposed to the exhaust gas on a ceramic or metallic substrate. This substrate is housed within a metallic can with a vermiculite or metallic packaging mat to hold the substrate in place.
The catalytic converter is vulnerable to mechanical failure in many ways-from excess deformation of the can, failure of the can 's weld, substrate fracture during canning, 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 thermal insulation, and seals exhaust gas leaks from nonmonolith sections, those surfaces of the substrate in contact with the mat.
The predominant factor in the erosion of mats made from vermiculite is believed to be the impingement of pulsating high-temperature exhaust gases. A combination of cyclic thermal expansion of the metallic can and vibrational loading accelerates mat degradation, culminating in loss of emissions conversion or substrate failure. A careful examination of a typical, freshly manufactured vermiculite mat reveals high Hertziantype mat deformation under the inward ribs. Excess pressures under these ribs during canning may lead to substrate cracking or microfractures in the mat, which under gas impingement may lead to accelerated mat erosion.
Other researchers have already modeled the roomtemperature canning process; they treated the mat material using soft contact elements following the room-temperature loading-displacement relation. They did not address the high-temperature case. The present study also has been focused on thermomechanical 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 Pawtucket, R.I., to study the case of a clam-shell converter package with ceramic package and vermiculite-ceramic mat. In addition to the room-temperature canning process, the high-temperature hysteretic ratcheting expansion and the instantaneous and relaxed constitutive characteristics of the mat was modeled.
Hill's hyperfoam constitutive model was used for the continuum mat elements. Small sliding frictional contact modeling was used for the contacting can, mat, and substrate surfaces.
The cell geometry within a typical ceramic substrate is either square or triangular. Cell geometry affects pressure drop, heat transfer characteristics, and the thermomechanical integrity of the substrate. The cells typically run as long channels along the length of the substrate. At a continuum level, the geometric cell structure of the substrate lends itself to being treated as a homogeneous orthotropic medium. But from the standpoint of strength, a mesoscopic analysis is needed, where the continuum stress state is transformed to a local microscopic stress state in individual cell walls and vice versa. (Mesoscopic quantities are larger than microscopic and smaller than macroscopic, and are not visible to the naked eye.)
Continuum Damage Mechanics
The subject of continuum damage mechanics 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 continuum to micromechanical modeling. 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 coefficient of thermal expansion (CTE) reveals a highly nonlinear dependence on temperature. The axial CTE was found to be negative for temperatures up to 600°C.
The mat material combines ceramic fibers (alumina silicate) and vermiculite material. The vermiculite is a micaceous hydrated magnesium aluminum-silicate mineral which, when heated, loses some of its water, causing the layers to expand by 10 to 20 times in thickness. The intumescent behavior of the mat tested, model XPE-3100 from the Unifrax Corp. of Niagra 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- bearing abilities. Between 550° and 750°C, the mat expansion is relatively constant. After the mat cools down (and assuming that sintering did not take place), its contraction does not follow the heat- up cycle expansion curve. A net residual expansion of about 30 percent remains in the mat at room temperature. Depending on the chemical composition of the mat material, subsequent thermal cycles produce varied degrees of similar inelastic expansion response to temperature cycles.
From the standpoint of a mechanical constitutive relation, the typical compressive load displacement curve reveals a nonlinear elastic characteristic. Further, because of the viscoelastic nature of the mat, the instantaneous load displacement curve typically shows a stiffer response than the steady-state response. Because of the relatively high compressibility of the mat material, the hyperfoam formulation based on Hill's strain energy potential is taken as the appropriate constitutive model.
In this analysis the canning is treated as a quasi-static process. The instantaneous load displacement data are used to simulate the instantaneous stresses and deformations in the assembly. After canning, the catalytic converter assembly is typically shipped to another location for assembly into the exhaust system. Since there is ample time for the mat to reach a steady state before the exhaust system is assembled, it is possible to disregard the temporal effect of the mat response from instantaneous canning to steady state. Therefore, the steady-state load displacement relation for the mat is taken as the load displacement relation for the high-temperature analysis.
The can, which is made of 409 stainless steel, is treated as elastoplastic with isotropic hardening. The complete stress-strain curves under elevated temperature conditions were not available. Therefore, the room temperature curve was scaled according to the effect of temperature on yield.
A quarter-symmetry model was analyzed with appropriate boundary conditions. The model has over 4,800 continuum elements, with about half as quadrilateral, reduced- integration, hourglass- control (S4R and S3R) 3-D shell elements for the can, and the rest 3-D hexahedral elements (C308 and C306) for the mat and substrate. 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 substrate, was modeled using a small sliding contact formulation with a Coulomb friction model. Since the mat material undergoes relatively large strains and the can also undergoes large strains and displacements, this thermomechanical 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 vermiculitemat, the stiffer "instantaneous" pressure response relaxes to a steady-state "relaxed" pressure response. Both the instantaneous canning and the relaxed can analysis are studied. Since the in stantaneous mat response is stiffer, it should lead to the worst-case canning stresses for the ceramic substrate. The relaxed can analysis forms the initial condition for the high-temperature thermal excursion analysis.
The vermiculite mat of 5-mm original thickness was modeled using three-dimensional continuum elements. Within Abaqus, the shrink parameter of contact interference was used to simulate the canning process design compression of the mat. A Coulomb friction model was used with a coefficient of friction μ=0.25 between the mat and the can and μ=0.4 between the ceramic substrate and the mat. The can displacements matched well with experimental data.
The investigators found that the contours for displacement, stress components, and plastic strains did not significantly change shape as the simulation continues from 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 plastic 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 failure issues, the instantaneous canning forces are critical. Since these equivalent stresses and pressures are continuum variables, for an accurate fracture assessment a micromechanical 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 criteria are needed.
The first-cycle inelastic thermal expansion characteristic of the mat material is incorporated in the high temperature analysis. The thermal expansion properties of the mat are determined from the heat-up and cooldown curves of Figure 1. The instantaneous and relaxed hyperfoam material constants are derived from the load displacement curves. The temperature-dependent stress strain curve for the elastoplastic can is based on the temperature scaling of the room temperature stress-strain curve, according to the effect of temperature on the yield strength. The homogenized orthotropic non linear thermoelastic properties were used to model the ceramic substrate.
The relaxed steady state (point 2 in Figure 1) of the assembly forms the initial condition for the heat-up cycle. The expansion characteristics of the heat-up cycle are used (points 3 and 4 on Figure 1). Point 4 is taken as the initial condition 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 procedure, 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. 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 results.
Since the shape of the contours does not change significantly 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 temperature 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 the simulation procedure developed here, it is now possible to quantify this scenario.
After point 3, the mat goes through a sharp increase in expansion characteristic, which starts applying increasing pressures on the can and substrate, thus raising the stresses and strains in both can and substrate. At the end of the heatup cycle (point 4), the can has peak equivalent plastic strains on the order of 8 percent. The substrate stresses also increase significantly and are double those observed during the instantaneous canning at room temperature.
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 quantities at high temperature typically are not known. This thermomechanical method provides a way to analyze the complete thermomechanical behavior of catalytic converter 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 significantly improves the ability to optimize the converter assembly for durability and performance for the life cycle of the converter assembly.
Since all of these analyses are deterministic, they are usually performed for the nominal (design) geometric dimensions. But, variability is inevitable. It can arise in manufacturing (the welding process and can-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 extreme may lead to a "loose" assembly, or at the other extreme to an excessively stressed assembly. It has been shown that a ±8 percent variability in mat basis weight may produce as much as ±30 percent variability in the mat pressure versus strain constitutive behavior. Therefore, for converter durability the mat property variations are an important factor to be controlled, especially since the resistance of the mat to hot-gas erosion is highly sensitive to the mat pressures. Typically, the 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 of probability 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 mate rial strength variations. Doing so will lay the foundations for a reliability- based durability design and analysis methodology.