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Title:
NON-CONTACT METHOD OF CHARACTERIZING ISOSTATIC STRENGTH OF CELLULAR CERAMIC ARTICLES
Document Type and Number:
WIPO Patent Application WO/2017/123919
Kind Code:
A1
Abstract:
A non-contact method of characterizing the isostatic strength of a ceramic member or article includes capturing a digital image of the ceramic article, and then forming a two-dimensional representation of the ceramic article and the web therein based on the captured digital image. The method also includes performing finite-element analysis on the two-dimensional representation of the ceramic article using a select amount of simulated isostatic pressure to determine a maximum stress value within the two-dimensional representation of the web. The method further includes using the maximum stress value to characterize the isostatic strength of the ceramic article.

Inventors:
NICKERSON, Seth Thomas (10923 Hidden Meadow Trl, Corning, New York, 14830, US)
WORTHEY, David John (15 Autumn View Way, Pine City, New York, 14871, US)
Application Number:
US2017/013400
Publication Date:
July 20, 2017
Filing Date:
January 13, 2017
Export Citation:
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Assignee:
CORNING INCORPORATED (1 Riverfront Plaza, Corning, New York, 14831, US)
International Classes:
G06F17/50; B23B3/12; G06K9/36; G06K9/62
Foreign References:
US20130212051A12013-08-15
US20130212151A12013-08-15
Other References:
LANGER S A ET AL: "OOF: an image-based finite-element analysis of material microstructures", COMPUTING IN SCIENCE AND ENGINEERING, IEEE SERVICE CENTER, LOS ALAMITOS, CA, US, vol. 3, no. 3, 1 May 2001 (2001-05-01), pages 15 - 23, XP002561466, ISSN: 1521-9615
S.T. GULATI ET AL.: "Isostatic strength of extruded cordierite ceramic substrates", SAE 2004 WORLD CONGRESS AND EXHIBITION, SAE TECHNICAL PAPER 2004-01-1135, 8 March 2004 (2004-03-08)
Attorney, Agent or Firm:
HOMA, Joseph M (Corning Incorporated, Intellectual Property DepartmentSP-Ti-03-0, Corning New York, 14831, US)
Download PDF:
Claims:
What is claimed is:

1. A non-contact method for characterizing an isostatic strength SC of a ceramic article having a web defined by walls that in turn define an array of cells, comprising:

a) capturing a digital image of the web;

b) forming a two-dimensional (2D) representation of the ceramic article, comprising the web therein, based on the captured digital image;

c) simulating a select amount of isostatic pressure Piso applied to the 2D

representation to determine a maximum stress value OC-MAX within the 2D representation of the web; and

d) using the maximum stress value OC-MAX to determine the isostatic strength SC of the ceramic article.

2. The non-contact method according to claim 1, wherein act b) comprises representing the web using rectangular beam elements.

3. The non-contact method according to claim 2, wherein act c) comprises performing a finite-element analysis.

4. The non-contact method according to claim 1, wherein act d) comprises:

defining a stress concentration factor oF = OC-MAX/PISO; and

determining the calculated stress SC via the relationship 1/OF = aSC - β, wherein a and β are constants determined by a best-fit to said relationship but using measured values of isostatic strength SM made on test ceramic articles.

5. The non-contact method according to claim 1, further comprising after act d):

comparing the isostatic strength SC to a threshold value STH-

6. A non-contact method for characterizing an isostatic strength SC of a ceramic article having a web defined by walls that in turn define an array of cells, comprising:

a) capturing a digital image of the web;

b) forming a two-dimensional (2D) representation of the ceramic article, comprising the web therein, based on the captured digital image;

c) performing a finite-element analysis on the 2D representation of the ceramic article using a select amount of simulated isostatic pressure Piso to determine a maximum stress value OC-MAX within the 2D representation of the web; and

d) using the maximum stress value OC-MAX to determine the isostatic strength SC of the ceramic article.

7. The non-contact method according to claim 6, wherein forming the 2D

representation of the ceramic article of act b) comprises representing the web using 2D rectangular beam elements.

8. The non-contact method according to claim 6, further comprising, between act a) and act b), processing the captured digital image to form a processed image using at least one of a filtering operation, a dynamic threshold operation, an island-removal operation, a smoothing operation, and a hole- filling operation, and then using the processed image to perform acts b) through d).

9. The non-contact method according to claim 6, wherein act d) comprises:

defining a stress concentration factor OF = OC-MAX/PISO; and

determining the calculated stress SC via the relationship l/oF = aSC - β, wherein a and β are constants determined by a best-fit to said relationship but using measured values of isostatic strength SM made on test ceramic articles.

10. The non-contact method according to claim 6, wherein act a) comprises either directly capturing a two-dimensional digital image with a two-dimensional image sensor or capturing a series of one-dimensional images with a linear image sensor.

11. The non-contact method according to claim 6, further comprising after act d):

comparing the isostatic strength SC to a threshold value STH-

12. The non-contact method according to claim 11, comprising basing the threshold value STH on a use of the ceramic article.

13. A non-contact method of characterizing an isostatic strength SC of a ceramic article having a web that comprises walls that define an array of cells, comprising:

a) capturing a digital image of the ceramic article and the web therein;

b) processing the digital image to form a processed image;

c) generating from the processed image a two-dimensional (2D) representation of the ceramic article using rectangular beam elements to represent the web;

d) determining a maximum stress value oC-MAxwithin the web by simulating the application of a select amount of isostatic pressure Piso to the 2D representation of the ceramic article; and

e) using the maximum stress value OC-MAX to determine the isostatic strength SC of the ceramic article.

14. The non-contact method according to claim 13, wherein processing the digital image comprises performing at least one of a filtering operation, a dynamic threshold operation, an island-removal operation, a smoothing operation, and a hole- filling operation.

15. The non-contact method according to claim 13, wherein act d) comprises performing a finite-element analysis.

16. The non-contact method according to claim 13, wherein act d) comprises:

defining a stress concentration factor oF = OC-MAX/PISO; and

determining the calculated stress SC via the relationship 1/OF = aSC - β, wherein a and β are constants determined by a best-fit to said relationship but using measured values of isostatic strength SM made on test ceramic articles.

17. The non-contact method according to claim 13, wherein act a) comprises either directly ca pturing a two-dimensional digital image with a two-dimensional image sensor or capturing a series of one-dimensional images with a linear image sensor.

18. The non-contact method according to claim 13, further comprising after act e): comparing the isostatic strength SC to a threshold value STH-

19. The non-contact method according to claim 18, comprising basing the th reshold va lue STH on a use of the ceramic article.

20. The non-contact method according to claim 19, wherein the use is can ning of the ceramic a rticle.

Description:
NON-CONTACT METHOD OF CHARACTERIZING ISOSTATIC

STRENGTH OF CELLULAR CERAMIC ARTICLES

CROSS-REFERENCE TO RELATED APPLICATIONS

[0001] This application claims the benefit of priority of U.S. Provisiona l Application Seria l No. 62/279,397 filed on Janua ry 15, 2016, the content of which is relied upon and incorporated herein by reference in its entirety.

FIELD

[0002] The present disclosure relates to cellular ceramic articles, and in particu lar relates to a method of characterizing the isostatic strength of ceramic articles such as extruded cellu lar ceramic articles.

[0003] The entire disclosure of any publication or patent document mentioned herein is incorporated by reference, including Pre-Grant Published Patent Application No.

US 2013/0212151, and the article by S . Gulati et al, "Isostatic strength of extruded cordierite ceramic substrates," SAE 2004 World Congress and Exhibition, SAE Technical Paper 2004-01-1135, 2004, doi:10.4271/2004-01-1135; pu blished March 08, 2004.

BACKGROUND

[0004] Cellula r ceramic articles are used as particulate filters and catalytic converters in internal combustion engines. The cells can be densely arranged to provide a relatively la rge surface area for catalytic material to react with the exhaust gases that pass through the cells. The walls can have a relatively thin cross-sectionai dimension to provide a

substantially large open frontal area, thereby reducing back pressure within the entire exhaust system. The cellular ceramic article requires sufficient mechanical and thermal integrity to withstand norma l automotive impact and thermal requirements.

[0005] in particu lar, a ceramic article made for use as a vehicular filter or catalytic converter must have sufficient mechanica l strength to survive being disposed in a metal housing during a process referred to as "canning." One measure of mecha nica l strength of a ceramic a rticle is its isostatic strength. The isostatic strength of a ceramic article can be measured by subjecting the ceramic article to increasing amounts of an isostatic force or pressure to the point of structural failure. However, such a measurement results in damage to or destruction of the ceramic article and so is not a preferred method for characterizing isostatic strength, especially in a manufacturing environment. Such direct measurements of isostatic strength are also very time consuming and can slow down production.

SUMMARY

[0006] An aspect of the disclosure is a non-contact method for characterizing an isostatic strength SC of a ceramic article having a web defined by walls that in turn define an array of cells. The method comprises: a) capturing a digital image of the web; b) forming a two- dimensional (2D) representation of the ceramic article, comprising the web therein, based on the captured digital image; c) simulating a select amount of isostatic pressure P| S o applied to the 2D representation to determine a maximum stress value OC-MAX within the 2D representation of the web; and d) using the maximum stress value O C -MAX to determine the isostatic strength SC of the ceramic article.

[0007] Another aspect of the disclosure is the method described above, wherein act b) comprises representing the web using rectangular beam elements.

[0008] Another aspect of the disclosure is the method described above, wherein act c) comprises performing a finite-element analysis.

[0009] Another aspect of the disclosure is the method described above, wherein act d) comprises: defining a stress concentration factor o F = O C -MAX/PISO; and determining the calculated stress SC via the relationship 1/OF = aSC - β, wherein a and β are constants determined by a best-fit to said relationship but using measured values of isostatic strength SM made on test ceramic articles.

[0010] Another aspect of the disclosure is the method described above, further comprising after act d): comparing the isostatic strength SC to a threshold value S T H-

[0011] Another aspect of the disclosure is a non-contact method for characterizing an isostatic strength SC of a ceramic article having a web defined by walls that in turn define an array of cells. The method comprises a) capturing a digital image of the web; b) forming a 2D representation of the ceramic article, comprising the web therein, based on the captured digital image; c) performing a finite-element analysis on the 2D representation of the ceramic article using a select amount of simulated isostatic pressure Piso to determine a maximum stress value O C -MAX within the 2D representation of the web; and d) using the maximum stress value OC-MAX to determine the isostatic strength SC of the ceramic article.

[0012] Another aspect of the disclosure is the method described above, wherein forming the 2D representation of the ceramic article of act b) comprises representing the web using 2D rectangular beam elements.

[0013] Another aspect of the disclosure is the method described above, further comprising, between act a) and act b), processing the captured digital image to form a processed image using at least one of a filtering operation, a dynamic threshold operation, an island-removal operation, a smoothing operation, and a hole- filling operation, and then using the processed image to perform acts b) through d).

[0014] Another aspect of the disclosure is the method described above, wherein act d) comprises: defining a stress concentration factor o F = O C -MAX/PISO; and determining the calculated stress SC via the relationship 1/OF = aSC - β, wherein a and β are constants determined by a best-fit to said relationship but using measured values of isostatic strength SM made on test ceramic articles.

[0015] Another aspect of the disclosure is the method described above, wherein act a) comprises either directly capturing a two-dimensional digital image with a two-dimensional image sensor or capturing a series of one-dimensional images with a linear image sensor.

[0016] Another aspect of the disclosure is the method described above, further comprising after act d): comparing the isostatic strength SC to a threshold value S T H-

[0017] Another aspect of the disclosure is the method described above, comprising basing the threshold value STH on an anticipated use of the ceramic article.

[0018] Another aspect of the disclosure is a non-contact method of characterizing an isostatic strength SC of a ceramic article having a web that comprises walls that define an array of cells. The method comprises: a) capturing a digital image of the ceramic article and the web therein; b) processing the digital image to form a processed image; c) generating from the processed image a 2D representation of the ceramic article using rectangular beam elements to represent the web; d) determining a maximum stress value OC-MAX within the web by simulating the application of a select amount of isostatic pressure Piso to the 2D representation of the ceramic article; and e) using the maximum stress value OC-MAX to determine the isostatic strength SC of the ceramic article.

[0019] Another aspect of the disclosure is the method described above, wherein processing the digital image comprises performing at least one of a filtering operation, a dynamic threshold operation, an island-removal operation, a smoothing operation, and a hole- filling operation.

[0020] Another aspect of the disclosure is the method described above, wherein act d) comprises performing a finite-element analysis.

[0021] Another aspect of the disclosure is the method described above, wherein act d) comprises: defining a stress concentration factor OF = OC-MAX/PISO; and determining the calculated stress SC via the relationship l/o F = aSC - β, wherein a and β are constants determined by a best-fit to said relationship but using measured values of isostatic strength SM made on test ceramic articles.

[0022] Another aspect of the disclosure is the method described above, wherein act a) comprises either directly capturing a two-dimensional digital image with a two-dimensional image sensor or capturing a series of one-dimensional images with a linear image sensor.

[0023] Another aspect of the disclosure is the method described above, further comprising after act e): comparing the isostatic strength SC to a threshold value STH-

[0024] Another aspect of the disclosure is the method described above, comprising basing the threshold value S T H on an anticipated use of the ceramic article.

[0025] Another aspect of the disclosure is the method described above, wherein the anticipated use is canning of the ceramic article.

[0026] Additional features and advantages are set forth in the Detailed Description that follows, and in part will be readily apparent to those skilled in the art from the description or recognized by practicing the embodiments as described in the written description and claims hereof, as well as the a ppended drawings. It is to be understood that both the foregoing general description and the following Detailed Description are merely exemplary, and are intended to provide an overview or framework to understand the nature and character of the claims.

BRIEF DESCRIPTION OF THE DRAWINGS

[0027] The accom panying d rawings are included to provide a fu rther understanding, and are incorporated in a nd constitute a part of this specification. The d rawings illustrate one or more embodiment(s), and together with the Detailed Description serve to explain principles and operation of the va rious embodiments. As such, the disclosure will become more fully understood from the following Detailed Description, taken in conjunction with the accom panying Figures, in which:

[0028] FIG. 1 is a side view of an example cellula r ceramic article such as an extruded cellu lar ceramic article;

[0029] FIG. 2 is a close-up front-on view of the example cellular ceramic a rticle of FIG. 1;

[0030] FIGS. 3A through 3D are close-up views of example webs of cel lu lar ceramic articles, il lustrating th ree different types of structural defects in the web that can reduce the isostatic strength of the ceramic a rticle;

[0031] FIG. 4A is a schematic diagram that shows a digital camera arranged adjacent the front end of the ce llular ceramic article , which resides on a conveyor;

[0032] FIG. 4B is similar to FIG. 4A and illustrates an example wherein the digital camera comprises a linea r sensor;

[0033] FIG. 5A is a representation of an example portion of an original or "raw" captured image;

[0034] FIG. 5B is a representation of an example of a processed image formed from the raw captured image of FIG. 4B; [0035] FIG. 6A is similar to FIG. 5B and shows an example of the skeleton that runs down the center of the web and that is used to determine the thickness of the web at various positions along the web walls;

[0036] FIG. 6B is a close-up view showing how the thickness of the web wall is determined based on the skeleton;

[0037] FIG. 7A is similar to FIG. 6A and shows a two-dimensional representation of a cellular ceramic article wherein the web is represented by rectangular beam elements that vary in size with the thickness of the web walls;

[0038] FIG. 7B is similar to FIG. 6B and shows a close-up view of some example rectangular beam elements that define a portion of a web wa ll of FIG. 7A;

[0039] FIG. 8 shows a n example 2D representation of the ceramic article, with the large arrows showing the isostatic pressure P| S o being a pplied inwardly at the outer surface, according to the simulation; and

[0040] FIG. 9 is plot of 1/OF versus the measured isostatic strength SM (bars) for the data obtained from modeling and then testing eleven test ceramic articles of the same type, with the plot including a best-fit line having a n R 2 value of 0.9.

DETAILED DESCRIPTION

[0041] Reference is now made in detail to various embodiments of the disclosure, examples of which are illustrated in the accompanying drawings. Whenever possible, the same or like reference num bers and symbols are used throughout the drawings to refer to the same or like parts. The drawings are not necessarily to scale, and one skil led in the art will recognize where the drawings have been simplified to illustrate the key aspects of the disclosure.

[0042] The claims as set forth below a re incorporated into and constitute part of this Detailed Description.

[0043] Cartesian coordinates are shown in some of the Figures for the sake of reference and are not intended to be limiting as to direction or orientation. [0044] FIG. 1 is a side view of an example cellula r ceramic article ("ceramic article") 10. FIG. 2 is a close-up, front-on view of the example ceramic a rticle 10 of FIG. 1. The ceramic article 10 comprises a central axis Al, a front end 12, a back end 14, and an outer surface 16. Ceramic article comprises a web 18 defined by walls 30 that in tu rn define cells 20. The cells 20 can have shapes other than square, such as triangular, hexagonal, etc., depending on the type of extrusion die used to form ceramic article 10. An outer wall or skin 40 defines an outer shape of the ceramic article 10 as well as outer surface 16. The close-u p inset of FIG. 2 illustrates an example portion of perfectly formed web 18 with perfectly formed walls 30 that define perfect cells 20.

[0045] FIGS. 3A through 3D a re close-up views of example webs 18 illustrating three different types of structu ral defects that can reduce the isostatic strength of ceramic article 10. FIG. 3A shows deformed "wavy" walls 30 that form distorted cells 20. FIG. 3B shows some walls having missing portions that represent wall defects 30D, which includes one wal l that is essentially entirely missing. FIG. 3C shows an example of a local deformation in the walls 30 that result in a highly localized group of defective or deformed cel ls 20D. FIG. 3D shows "wavy" walls 30 located adjacent the outer wall or skin 40.

[0046] Given that the walls 30 of web 18 serve in large measure to define the isostatic strength of ceramic article 10, it is expected that wall/cell defects can reduce the isostatic strength. Yet, to date there has not been very good correlation between the type and location of wall/cel l defects and isostatic strength. This has made it very difficu lt to use the characterization and location of wall/cel l defects to obtain a reasonable estimate of the isostatic strength.

Characterization method

[0047] An example method for cha racterizing isostatic strength disclosed herein comprises four main steps or acts: 1) image capture, 2) defining a 2D representation of the ceramic a rticle, 3) calculating the maximum stress in the web, and 4) calculating the isostatic strength.

[0048] A fifth step of comparing the ca lculated isostatic strength to a threshold value can also be included in the method. [0049] Each of the above main steps can comprise one or more sub-steps, operations, acts, etc. as described below.

[0050] Step 1 - Image capture

[0051] The first step of the method involves capturing an image of the ceramic a rticle 10 and the web 18 therein. FIG. 4A is a schematic diagram that shows a digital camera 120 operably arranged adjacent the front end 12 of ceramic article 10. The ceramic article 10 is supported by a conveyor 130 that conveys the ceramic article past a digital camera 120. The digital camera 120 comprises an image sensor 122 having pixels 124. The digital camera 120 is shown operably (e.g., electrically) connected to a computer 140 that has a display 142. The digital camera 120 is configured to captu re a ( raw) digital image 150R of at least a portion of web 18 at the front end 12 of the cera mic article.

[0052] In an example illustrated in FIG. 4B, the image sensor 122 is a linear image sensor defined by a line of pixels 124 shown in the close-up inset as running in the y-direction. The linear image sensor 122 is used to capture a line image of the front end 12 of the ceramic article 10 as the ceramic article is conveyed past digital camera 120. In an example, the linear image sensor 122 is used as a line scanner and is arranged immediately adjacent to the front end 12 of ceramic a rticle 10 to capture a scanned digital image.

[0053] In an example, computer 140 is used to stitch together line-scan images of web 18 to form the la rger 2D raw captured image 150R. I n an example, the raw captured image 150R comprises the entire front end 12 of ceramic a rticle 10 so that it includes the entire web 18. FIGS. 4A and 4B show the raw captured image 150R being displayed on display 142 of computer 140. Captu ring an image of one end (e.g., front end 12) of the ceramic a rticle 10 is usually sufficient to perform the method disclosed herein since the ceramic a rticle is formed by extrusion and a ny defects tend be extrusion-related defects that are substantially consistent along the axial dimension of the ceramic article.

[0054] The captured raw image 150R has associated therewith a first resolution defined by the relationship between the pixel size and the size of the ca ptured image. In an example, digital camera 120 is configured such that each pixel 124 of image sensor 122 represents a 5 micron x 5 micron region of web 18. Different optical resolutions can be used to change this pixel-to-region relationship. The optical resolution ca n be selected depending on the characteristics of the ceramic articles 10 being measured, e.g., different cell densities. A range of diameters of ceramic articles 10 can be from 4 inches to 14 inches. The cross-sectional shapes can also vary, e.g., rou nd or oval. The ca ptured raw image 150R at 5 microns per pixel level can thus range in size from 20,000 x 20,000 pixels for a 4 inch part to 70,000 x 70,000 pixels for a 14 inch part. An example of a portion of a captured raw image is shown in FIG. 5A.

[0055] Once the captured raw image 150R of the front end 12 of ceramic article 10 is obtained, it can be processed using on ore more processing steps to form a processed image 150P, an example of which is shown in FIG. 5B. In an example, the processed image 150P has a second resolution that is equal to or less than the first resolution of the captured raw image 150R. Strictly speaking, the image processing step is optional within the main image capture step, but the cha racterization method disclosed herein benefits from including it, as explained below.

[0056] In an example, the image processing step comprises applying a mean filter to the captured image with an appropriate kernel size. The kernel size is chosen so the mean filter result represents the variation in illumination across the pa rt. I n an example, the kernel size is large enough so that the filtered image does not show the individual cells but is small enough so the filtered image shows variations in overall lighting in the image. In an example, the kernel size covers between 8 to 16 cells, or even 10 to 12 cells.

[0057] Next, a dynamic threshold operation is performed on the original (raw) captured image 150R. This operation finds all pixel values that are brighter than the corresponding pixel value in the mea n filtered image by a certain amount. I n an example, a threshold value of N grey levels is used. This selects all pixel values that are at least N grey levels brighter than the value of the corresponding pixel in the mean filtered image as possibly belonging to the ceramic article. Pixels having values that are darker than this intensity threshold va lue are considered to be backgrou nd pixels that do not represent web 18 or skin 40.

[0058] Next, any isolated regions or "islands" of connected bright pixels that are smaller than some fixed size a re removed. This "island removal" process is carried out to reduce noise since the small unconnected bright regions in the processed image 150P can be considered as not actua lly pa rt of ceramic article 10. This can be done for islands having some minimum threshold size, e.g., less than 100 pixels.

[0059] Next, a morphologica l smoothing operation is performed by first closing any small dark regions in the ceramic article that a re less than a certain size, and then performing a morphological opening to return the outline of ceramic article image to the original size. In an example, a morphologica l smoothing radius of approximately 3 pixels is convenient.

[0060] Next, any small holes represented by small dark areas in the image that do not meet the dynamic threshold limit are filled. For example, holes smaller than 400 pixels in size are filled. In an example where cells 20 are a pproximately 160 x 160 pixels (25,600 pixels in area), holes that are 1.5% the size of a normal cell can be filled. This operation is referred to herein as "hole filling."

[0061] All of the bright pixels that remain in the processed image 150P are considered to be part of the ceramic a rticle 10. FIG. 5A is a representation of an example portion of an original (raw) captured image 150R while FIG. 5B represents an example of the

corresponding processed captured image 150P.

[0062] Thus, in an example, the image processing step comprises at least one of a filtering operation, a dynamic threshold operation, an isla nd-removal operation, a smoothing operation, and a hole- filling operation.

[0063] The raw ca ptured image 150R and the processed image 150P each defines a two- dimensional representation of the web 18. The filtering, th reshold, fil ling and smoothing operations result in the reduced second resolution for the processed image 150P as compared to the initial captured image 150R. The reduced resolution simplifies the subsequent methods steps or acts and ma intaining sufficient information to obtain an accurate cha racterization of the isostatic strength of the ceramic a rticle 10 being characterized. For example, the captu red raw image 150R typica lly includes noise that can adversely affect the isostatic strength characterization. The processed image 150P is processed in a manner that reduces noise as com pared to the captured raw image 150R and therefore can be effectively employed to achieve a more accurate characterization of the isostatic strength.

[0064] Step 2 - Defining a 2D representation of the ceramic article

[0065] Once the image capture step is completed, the resulting image (either the captured image 150R or the processed image 150P) is used to define a two-dimensional (2D) representation ("2D representation") 10R of the ceramic article 10) suitable for use in carrying out numerical simu lations or modeling (see FIG. 7A, introduced and discussed below). I n the discussion below, it is assumed for the sake of illustration that the processed image 150P is used to define the 2D representation 10R.

[0066] In an example, the 2D representation 10R is generated by representing the wa lls 30 of web 18 and the outer wal l or skin 40 in the processed image 150P as a series of 2D beam elements BE. In an example, the 2D beam elements BE are rectangular. With reference to FIG. 6A, this is accomplished by first finding a skeleton 200 of web 18 a nd outer wall or skin 40 in the processed image 150P. The skeleton 200 is a series of single-pixel lines that fol low the medial axis of the web 18 and skin 40.

[0067] With reference now to FIG. 6B, the next step involves calculating the distance d from each pixel along the skeleton 200 to the closest background (da rk) pixel. This distance d represents half of the thickness of wall 30 at each point along the skeleton 200. Twice this distance is the al l or web thickness TH at the given point of the measu rement. FIG. 6B shows the measurement of distance d for one point a long the skeleton 200 on a vertica l wal l 30.

[0068] The next step involves generating series of the beam elements BE that

approximate the size, shape and location of each wall 30 in web 18. In an example, beam elements BE have a rectangular shape and are generated by following the path of the skeleton 200 a long a given wall 30 (see FIG. 7B, introduced and discussed below). A given beam element BE has a width equal to the thickness TH of the wall 30 at the given location. A new beam element BE is generated any time the direction of the skeleton 200 deviates from a straight line by more than a certain number of pixels, or the wall thickness TH changes by more tha n a certain number of pixels. [0069] FIG. 7A is similar to FIG. 6A and represents an example 2D representation 10R of ceramic a rticle 10. The 2D representation 10R comprises web 18R, wal ls 30R and cells 20R. The differences between FIGS. 6A and 7A a re subtle, but a close inspection shows that FIG. 7A has more squared-off edges between the light portion that defines the wal ls 30R of web 18R and the black background portion of the image that define cells 20R. FIG. 7B is a close- up view of portion of web 18R and shows a num ber of example beam elements BE as identified by the dashed-line boxes. The beam elements BE in FIG. 7B are shown slightly smaller than their actual size so that they can be readily seen.

[0070] In an example, direction changes in skeleton 200 or thickness changes in wal l 30R that are greater than some number of pixels (e.g., 1 to 3 pixels) are tracked and used to define new beam elements BE. The smaller the change threshold used to define new beam elements BE, the more accurately the actual geometry of ceramic article 10 is captured by the 2D representation 10R. Using a larger change threshold reduces accuracy, but also reduces the number of generated beam elements BE, thus decreasing the computation time needed to calculate the stresses as described below.

[0071] The beam elements BE are defined for the various walls 30R to make up web 18R. In an example, standa rd computer techniques can be used to define the beam elements BE and link them together to form web 18R. This can be done using computer 140 and standard computer techniques, such as by using ANSYS files, which su pport reading the rectangular beam data from ASCII coded files. The ANSYS files describe individua l rectangular beam elements of the ceramic article 10 and how these beam elements are linked together to form web 1R8 as well as skin 40R (see FIG. 8, introduced and discussed below).

[0072] In an example, computer 140 comprises instructions embodiment in a non- transient computer-reada ble medium that wa lks the list of generated beam elements BE to define web 18R of the 2D representation 10R of ceramic article 10.

[0073] Step 3 - Calculating the maximum stress in the web

[0074] Standard numerical techniques are then used to model (simulate) the 2D mechanical response of the 2D representation 10R of the ceramic article to a select (simulated) isostatic pressure Piso- FIG. 8 shows an example 2D representation 10R of ceramic a rticle 10 7 with arrows AR showing the isostatic pressure P| S o being applied inward ly at the outer surface 16R of skin 40R according to the simulation. In a n example, the select amount of isostatic pressure PISO being applied fa lls within a range of reasonable isostatic pressures that a ceramic article 10 typically might experience in the field, e.g., from close to zero up to its design isostatic strength.

[0075] This modeling or simulation of the 2D mechanical response can be accomplished using for example finite-element analysis, with the mechanica l response being measured in terms of stress at various locations (e.g., beam elements BE) in web 18R. I n a n example, the output of the finite-element analysis comprises linearized calculated stress values Oc for each rectangula r beam element RB. The results can be stored in computer 140, e.g., as an ASCII file. The maximum value of the calcu lated stress is denoted oc-MAx and is easily determined form the list of ca lculated stress values o c .

[0076] In an example, the maximum calculated stress value O C -MAX is used to define a stress concentration factor OF. The stress concentration factor OF is defined by the ratio of the maximum calculated stress value O C -MAX to the applied isostatic pressure P| S o, e.g., OF = OC-MAX /Piso- The stress concentration factor OF is unitless since the ca lculated stress va lues a nd the isostatic pressure P| S o have the same units, e.g., PSI or bars. I n an example, the stress concentration factor OF fa lls mostly within the range between about 5 and about 80, with lower and higher extremes possible.

[0077] Step 4 - Calculating the isostatic strength

[0078] The next step involves calculating the isostatic strength SC. This is accomplished in one example by using an equation (relationship) that relates the stress concentration factor o F to the calculated isostatic strength SC.

[0079] An example equation can be expressed as:

Here, a and β are constants determined by a best-fit to EQ. 1 using actua l measurements of isostatic strength SM on test ceramic a rticles in place of SC. The test ceramic a rticles a re also modeled using the method described above to obtain corresponding values of OF SO that enough data with different values for the measured isostatic strength SM can be obtained to perform a reasona ble curve fit. The test ceramic articles need to be

substantially the same (and prefera bly formed in an identical ma nner as possible) as the ceramic a rticles whose isostatic strength is to be characterized using the non-contact methods disclosed herein in order to achieve the best results.

[0080] Example

[0081] In one example, measurements of isostatic strength SM were performed on test ceramic a rticles formed from cordierite having square cells with a density of 200 cells per inch and a web wall thickness TH of 0.008 inch. The test ceramic articles had a variety of web and cel l defects, comprising sheared cel ls, distorted cells and missing cell walls and thus had a ra nge of measured isostatic strengths SM. The measurements of isostatic strength SM were carried out using a conventional apparatus. The modeling to obtain the stress concentration factor o F was carried out per the above steps for each of the test ceramic articles. The beam elements BE used were rectangular.

[0082] FIG. 9 is plot of 1/OF versus measured isostatic strength SM (bars) for the data obtained from modeling and measurements performed on the above-described test ceramic articles. The solid black circles represent test cera mic articles that had sheared cells 20 while the white-filled circles represent test ceramic articles that had cut webs 18 (i.e., cuts in walls 30).

[0083] A best-fit calculation to the data in FIG. 9 was performed based on EQ. 2 below and is represented by the dashed straight in in FIG. 9:

[0084] The best-fit ca lculation was carried out using standard spreadsheet software and yielded values for the curve-fitting constants a and β of a = 0.0041 and β = 0.0054, with an R 2 value of 0.9, indicating good correlation between the stress concentration factor o F a nd the measured isostatic strength SM. These values of a and β can be used in EQ. 1 for non- contact characterizing the isostatic strength for like ceramic articles as described above. [0085] The curve-fitting approach to establish a relationship between the stress concentration factor o F and the isostatic strength can be carried out for any type of ceramic articles 10 7 particularly extruded ceramic articles, irrespective of the composition, cell design (hexagonal, triangular, square, octasqua re, asymmetric, etc.) and web/cell geometry (e.g., cell sizes and densities, wall thicknesses, etc.).

[0086] In characterizing the isostatic strength, only the maximum value of the stress OC-MAX is required. Thus, an embodiment of the method comprises using only the maximum stress va lue OC-MA to cha racterize the isostatic strength SC of the ceramic a rticle.

[0087] Step 6 - Comparing the calculated isostatic strength to a threshold value.

[0088] Once the calculated isostatic strength SC is obtained, it can be compa red to a threshold value S T H- The threshold value S T H can be defined by a use for the ceramic article 10, a nd the demands such use will place on the pa rticu lar ceramic article. For example, the threshold value S T H can be defined by or required by a canning process and whether the ceramic a rticle can survive the process. Not all canning processes have the same isostatic strength requirements, so that the threshold value S-m can vary between different can ning processes. For example, some ca nning processes might have an isostatic strength threshold va lue STH = 10 bars, while others can have an isostatic strength threshold value S T H = 30 bars or 50 bars or greater. A benefit of having a non-contact characterization of the isostatic strength is that ceramic a rticles can be grouped by their cha racterized isostatic strength and then used for applications where the threshold va lue requirement can be met without damaging or destroying the ceramic articles.

[0089] The non-contact method of characterizing the isostatic strength of ceramic articles as disclosed herein has the advantage that it is based on a single parameter - namely, the maximum value of the calculated stress O C - MAX (or the stress concentration factor, which is based only on the maximum stress value OC- MAX)- The method does not require an examination or characterization of the many different types of possible cell or web defects, such as sheared cel ls, distorted cells, missing webs, thinned webs, etc., and does not require determining the location(s) of such defects. [0090] Without wishing being bound by theory, it is conjectured that a single location of sufficiently high stress within the web 18 of a ceramic article 10 can compromise the structural integrity of the entire ceramic article and lead to a substantial reduction in the isostatic strength, e.g., to be below a desired threshold value S T H- For example, when an isostatic force or pressure is applied to the outer surface 16 of ceramic article 10 that comprises a cell or web defect, the force is communicated through web 18 and to a highest- stress location, which may not identically correspond to a web or cell defect. The force can cause failure of one or more walls 30 within the web 18 at or near the high stress location. This wall failure causes the applied force to be immediately redistributed to the surrounding walls 30 of the nearest web 18. The added force can then lead to failure of one or more of the surrounding walls, thereby causing the applied force to be redistributed once again to the adjacent surrounding walls 30. This failure process can end up cascading through substantial portions of web 18, leading to the structural failure of the ceramic article.

[0091] In an example, the non-contact method disclosed herein is used in the production of ceramic articles and can be performed at any step along the manufacturing process where an image of the web can be obtained. In one example, the non-contact method is performed on newly extruded wet logs, while in another example the non-contact method is performed on dried logs, while in yet another example the non-contact method is performed on dried and fired logs. In an example, the non-contact method is performed in less than 1 minute, thereby providing a relatively quick characterization of the isostatic strength as compared to direct contact-based methods. Thus, in this regard, the term "ceramic article" as used herein is intended to also include "ceramic-forming article" such as greenware or unfinished ware, such as newly extruded wet logs, or dried logs or green logs, or fired logs, or newly extruded wet cellular structured bodies, or dried cellular structured bodies, and the like.

[0092] it will be apparent to those skilled in the art that various modifications to the preferred embodiments of the disclosure as described herein can be made without departing from the spirit or scope of the disclosure as defined in the appended claims. Thus, the disclosure covers the modifications and variations provided they come within the scope of the appended claims and the equivalents thereto.