The authors acknowledge the help from Michael Pluchinsky with the high-speed photography work

Use adequate personal protective equipment e.g. safety glasses, gloves etc. for performing any tasks referred to in this manuscript. The starting material used here whether, for the measurement of bending strength, collision, aspect ratio or bulk crushing is always extrudates obtained from laboratory studies or pilot equipment studies or are commercial materials. Catalyst extrudate strength depends on pretreatment conditions hence it is important for the user to select the appropriate treatments. The outcome of the measurements allows to decide which materials to use in further studies at least from a strength perspective.
1. Bending Strength
<ol>
	<li>Bending Strength Sample Preparation
	<ol>
		<li>Riffle the extrudate sample of interest to a representative size of 25 particles minimum. Use a spinning riffler or riffle-type sample divider. 
		Note: Catalyst strength is dependent on the thermal pretreatment, hence the sample requires certain choices to be made by the user concerning pretreatments.</li>
		<li>Perform one of the following two typical pretreatments but their conditions may be changed depending on the need of the user.
		<ol>
			<li>Calcine the sample at 538 &#176;C for 1 h.
			<ol>
				<li>Place a minimum of 25 riffled catalyst extrudates in a porcelain dish or heat resistant beaker.</li>
				<li>Place the dish with the catalyst into a refractory-type muffle oven at 538 &#176;C for 1 h.</li>
				<li>After calcination, place the hot sample into a desiccator and allow it to cool to ambient conditions.</li>
			</ol>
			</li>
			<li>Dry the sample at 121 &#176;C for 2 h minimum.
			<ol>
				<li>Place a minimum of 25 riffled catalyst extrudates in a porcelain dish or heat resistant beaker.</li>
				<li>Place the dish with catalyst in a drying oven, set for 121 &#176;C for a minimum of 2 h.</li>
				<li>Remove the hot sample from the drying oven and place it into a desiccator and allow it to cool to ambient conditions</li>
			</ol>
			</li>
		</ol>
		</li>
	</ol>
	</li>
	<li>Bending Strength Instrumentation Set-up 
	Note: The error bar for the modulus of rupture is +/- 10%. Calibrate the equipment daily according to the procedure set forth by the manufacturer. Choose the method that correctly matches the shape of the sample, as the calculation of MOR depends on the shape factor.
	<ol>
		<li>Start the bending test frame and allow the system to warm up for at least 20 min before using. Then open the required software.</li>
		<li>Attach the 10 N (10 Newton force) load cell per manufacturer instructions.</li>
		<li>Select an anvil speed of 0.2 mm/sec with a 5-mm support span. 
		Note: It was observed that for this rate of speed, the catalyst is not in a strain rate sensitive region and the rupture force is reproducible.</li>
		<li>Select &#39;Modulus of Rupture (MOR)&#39; and &#39;Maximum Force&#39; in the Results tab.</li>
		<li>Ensure the crosshead on the MOR frame is in the &#34;Zero&#34; position by firmly pressing the &#34;Return&#34; button on the frame console. The position of the crosshead and anvil may be changed if necessary to accommodate extrudates of different diameter.</li>
	</ol>
	</li>
	<li>Bending Strength Measurement
	<ol>
		<li>Take the catalyst extrudate sample from the desiccator and place it in an inverted 5-6 cm diameter filter with N2 blowing upwards through it to create a blanket of dry gas.</li>
		<li>Use tweezers to take an extrudate specimen from the filter tray and place it across the support beams. Minimize the time of extrudate specimen placement and measurement to minimize moisture pick-up.</li>
		<li>Center the catalyst extrudate specimen as best as possible left to right and front to back on the support beams</li>
		<li>Click the &#34;Start&#34; icon on the right toolbar. 
		Note: During this step, the extrudate is being bent beyond the breaking point and hence the test is destructive in that sense.</li>
		<li>Ensure crosshead stops and returns to the starting position upon experiencing a 40% drop in load force. 
		Note: This usually occurs upon extrudate breakage.</li>
		<li>Select the &#34;Next&#34; icon on the right toolbar to continue to the next extrudate.</li>
		<li>Hit &#34;back&#34; to view the data point on the graph and on the results table.</li>
		<li>Select &#39;Finish Sample&#39; after measuring the 25th extrudate specimen. 
		Note: The software generates the report with the strength properties</li>
	</ol>
	</li>
</ol>
2. Collision Test
Note: The feed rate with which catalyst is fed to the drop tube is kept low so that individual catalyst extrudates collide essentially with an empty surface at the bottom of the drop tube without hindering each other
<ol>
	<li>Collision Equipment Preparation
	<ol>
		<li>Assemble the drop tube (0.15 m diameter and 1.83 m long plastic tube) with the recovery plate (316 SS) at the bottom. Set the feeder discharge at the correct height of choice (here 1.83m) centered over the drop tube. Alter the drop heights to vary the severity of the collision.</li>
		<li>Set resonate frequency of vibratory feeder to 250 Hz with power off.</li>
		<li>Position local ventilation over the feed hopper.</li>
	</ol>
	</li>
	<li>Collision Sample Preparation
	<ol>
		<li>Riffle the catalyst sample of interest to a representative size of 50 particles minimum. Use a spinning riffler or riffle-type sample divider.</li>
		<li>Gently sieve the prepared sample in order to avoid small particles with a length to diameter ratio less than or equal to 1.</li>
		<li>Measure the initial aspect ratio of the sample by using protocol section 3.</li>
	</ol>
	</li>
	<li>Collision Catalyst Drop Procedure
	<ol>
		<li>Manually transfer the entire sample into the feed hopper.</li>
		<li>Ensure the feeder chute outlet is centered over the drop tube.</li>
		<li>Turn on the toggle switch to power the feeder and set to &#39;Start.&#39;</li>
		<li>Allow all particles to fall freely into the drop tube and impinge on the bottom plate.</li>
		<li>Turn off the power to the feeder once all particles have been fed and dropped.</li>
		<li>Transfer all the particles from the recovery plate and gently remove the fines from the sample by sieving to remove dust and chips.</li>
		<li>Measure the aspect ratio of the sample using protocol section 3 to complete the first drop measurement designated 1X.</li>
		<li>Using the sample of step 2.3.7, repeat steps 2.3.1 to 2.3.6 and measure the aspect ratio using protocol section 3 to complete the second drop measurement designated 2X.</li>
		<li>Repeat the above steps to complete up to 5X and 10X drop measurements. 
		Note: One can elect to skip the intermediate aspect ratio measurements since the aspect ratio only changes little after multiple drops.</li>
	</ol>
	</li>
</ol>
3. Catalyst Aspect Ratio
<ol>
	<li>Aspect Ratio Sample Preparation
	<ol>
		<li>Riffle the catalyst sample of interest to a representative size of 50 to 250 particles. Use a spinning riffler or riffle-type sample divider to obtain a representative sample.</li>
		<li>Sieve the prepared sample to avoid small particles with an L/D less than or equal to 1 where L stands for the length of an extrudate while D stands for the diameter of an extrudate.</li>
	</ol>
	</li>
	<li>Aspect Ratio Software and Set-up
	<ol>
		<li>Open the software and select the &#34;SCAN&#34; toolbar button at the top of the screen.</li>
		<li>Wipe the glass with a microfiber cloth to remove any dust. Place a clean transparency sheet on the scanner.</li>
		<li>Sprinkle the extrudates on top of the transparency and avoid particles from touching each other. Place the particles within a rectangular area measuring maximum 10 cm by 20 cm.</li>
		<li>Randomly distribute the extrudates across the area to be scanned. Use a pair of tweezers to slide particles away from each other or to place them in more open areas.</li>
		<li>Close the scanner lid.</li>
		<li>Select the shape of the particle</li>
		<li>Enable the message function in the software setting, for touching particles (highlighted in red on the screen), particles that are overlapping (or brushing) the edge of the scan area and these are automatically removed, any particles with excessive curvature, any particles that are too small (e.g. dust specks), and any particles that are touching each other.</li>
		<li>Click on the &#34;Scan&#34; toolbar button. 
		Note: The scanner will start to scan the particles. It will take between 2-3 min. The tabulated results and optically scanned image are displayed on the screen.</li>
	</ol>
	</li>
	<li>Aspect Ratio Analysis
	<ol>
		<li>Examine the scanned results and ensure that all legit particles are included in the scan. 
		Note: Legit particles have and L/D &#62; 1, rest in a natural position for the scan and do not touch other extrudates.</li>
		<li>Review each particle suspected of touching a neighboring particle as the computation algorithm is not perfect.</li>
		<li>Eliminate particles that rest improperly due to crowding (touching or lying on top of each other) with eliminated with the software. Alternatively, adjust the particle&#39;s position with tweezers and the entire sample can be re-scanned.</li>
		<li>Save the results and record the following information: average diameter, average length, and the particle number.</li>
	</ol>
	</li>
</ol>
4. Bulk Crush testing
<ol>
	<li>Bulk Crush Sample Preparation
	<ol>
		<li>The catalyst extrudate sample of interest should be riffled so as to obtain a suitable representative of the total amount.</li>
		<li>Heat-treat the catalyst sample at 538 &#176;C for minimum 1 h in a muffle oven or similar and place it hot in a desiccator and allow it to cool to ambient conditions.</li>
	</ol>
	</li>
	<li>Bulk Crush Procedure
	<ol>
		<li>Tare the catalyst sample container (cup) and fill it to overflowing with the catalyst so that there is an excess catalyst in the container.</li>
		<li>Carefully level the cup with a metal straight edge without over-packing the bed.</li>
		<li>Reweigh the container with a leveled catalyst to obtain the weight of the sample.</li>
		<li>Carefully place the sample in the load block and piston assembly. Place the load block on top of the sample without crushing the catalyst.</li>
		<li>Place the ball bearing in the center of the load block and adjust the lock arm to the proper height evenly over the ball bearing using a small carpenter&#39;s level. Lock the arm in place.</li>
		<li>Check that the pressure regulator is set at the pressure specified by the user to be applied to the catalyst sample. 
		Note: Typically, it is in the 5-1,000 kPa range and it is normally found by trial and error for the particular application.</li>
		<li>Check that the load control valve and pressure valve are open and then close the bleed valve. 
		Note: The load block will rise to its set pressure.</li>
		<li>Wait for 60 s for the sample to equilibrate.</li>
		<li>Release the pressure by opening the bleed valve and closing the pressure valve. Watch the load block coming back to its original position.</li>
		<li>Unlock the adjustable lock arm and take the bearing ball and load block out carefully.</li>
		<li>Measure and record the indentation of the sample after the crush test.</li>
		<li>Sieve out the fines. Record the fines collected and measure the aspect ratio of the sample according to protocol section 3.</li>
	</ol>
	</li>
</ol>

<ol><li>Le Page, J. F. <a target="_blank" href="http://scholar.google.com/scholar?hl=en&safe=off&q=author%3aLe+Page%2C+JF+%22Applied+Heterogeneous+Catalysis%22">Applied Heterogeneous Catalysis</a>. , Institut Français du Pétrole publications, Éditions Technip. Paris. (1987).</li>
<li>Woodcock, C. R., Mason, J. S. <a target="_blank" href="http://scholar.google.com/scholar?hl=en&safe=off&q=author%3aWoodcock%2C+CR+%22Bulk+Solids+Handling%3A+An+Introduction+to+the+Practice+and+Technology%22">Bulk Solids Handling: An Introduction to the Practice and Technology</a>. , Chapman & Hall. New York. (1987).</li>
<li>Bertolacini, R. J. <a target="_blank" href="https://pubs.acs.org/doi/abs/10.1021/bk-1989-0411.ch034">Mechanical and Physical Testing of Catalysts.</a> ACS Symposium series. , Washington D.C. 380-383 (1989).</li>
<li>Wu, D. F., Zhou, J. C., Li, Y. D. <a target="_blank" href="https://www-sciencedirect-com.remotexs.ntu.edu.sg/science/article/pii/S0263876206730039">Distribution of the mechanical strength of solid catalysts.</a> Chem Eng Res Des. 84 (12), 1152-1157 (2006).</li>
<li>Li, Y., Wu, D., Chang, L., Shi, Y., Wu, D., Fang, Z. <a target="_blank" href="https://pubs.acs.org/doi/abs/10.1021/ie980360j?journalCode=iecred">A model for bulk crushing strength of spherical catalysts.</a> Ind Eng Chem Res. 38, 1911-1916 (1999).</li>
<li>Li, Y., et al. <a target="_blank" href="https://www-sciencedirect-com.remotexs.ntu.edu.sg/science/article/pii/S003259100000231X">Measurement and statistics of single pellet mechanical strength of differently shaped catalysts.</a> Powder Technol. 113, 176-184 (2000).</li>
<li>Staub, D., Meille, S., Le Corre, V., Chevalier, J., Rouleau, L. <a target="_blank" href="https://ogst.ifpenergiesnouvelles.fr/articles/ogst/abs/2015/03/ogst130158/ogst130158.html">Revisiting the side crushing test using the three-point bending test for the strength measurement of catalyst supports.</a> Oil Gas Sci Technol. 70, 475-486 (2015).</li>
<li>Bridgwater, J. Chapter 3, Particle Breakage due to Bulk Shear. <a target="_blank" href="https://www-elsevier-com.remotexs.ntu.edu.sg/books/book-series/handbook-of-powder-technology">Handbook of Powder Technology, 1st ed</a>. 12, Elsevier B. V. (2007).</li>
<li>Heinrich, S. Multiscale Strategy to Describe Breakage and Attrition Behavior of Agglomerates. Frontiers in Particle Science & Technology Conference, Houston, TX. , Available from: 
 <a target="_blank" href="www.aiche.org/conferences/frontiers-particle-science-and-technology">www.aiche.org/conferences/frontiers-particle-science-and-technology</a> (2016).</li>
<li>Wassgren, C. Discrete Element Method Modeling of Particle Attrition. Frontiers in Particle Science & Technology Conference, Houston, TX. , Available from: 
 <a target="_blank" href="www.aiche.org/conferences/frontiers-particle-science-and-technology">www.aiche.org/conferences/frontiers-particle-science-and-technology</a> (2016).</li>
<li>Potyondy, D. Bonded-Particle Modeling of Fracture and Flow. Frontiers in Particle Science & Technology Conference, Houston, TX, 2016. , Available from: 
 <a target="_blank" href="www.aiche.org/conferences/frontiers-particle-science-and-technology">www.aiche.org/conferences/frontiers-particle-science-and-technology</a> (2016).</li>
<li>Potapov, A. Approaches for Accurate Modeling of Particle Attrition in DEM Simulations. Frontiers in Particle Science & Technology Conference, Houston, TX, 2016. , Available from: 
 <a target="_blank" href="www.aiche.org/conferences/frontiers-particle-science-and-technology">www.aiche.org/conferences/frontiers-particle-science-and-technology</a> (2016).</li>
<li>Carson, J. Particle Attrition: The Bane of many Industrial Plants - Problems, Solutions and Red Flags. Frontiers in Particle Science & Technology Conference, Houston, TX, 2016. , Available from: 
 <a target="_blank" href="www.aiche.org/conferences/frontiers-particle-science-and-technology">www.aiche.org/conferences/frontiers-particle-science-and-technology</a> (2016).</li>
<li>Farsi, A., Xiang, J., Latham, J. P., Carlsson, M., Stitt, E. H., Marigo, M. <a target="_blank" href="https://www.researchgate.net/publication/320085255_Does_shape_matter_FEMDEM_estimations_of_strength_and_post_failure_behaviour_of_catalyst_supports">Does Shape Matter? FEMDEM Estimations of Strength and Post Failure Behaviour of Catalyst Supports.</a> 5th International Conference on Particle-Based methods. , Hannover, Germany. (2017).</li>
<li>Beeckman, J. W. L., Fassbender, N. A., Datz, T. E. <a target="_blank" href="http://onlinelibrary.wiley.com/doi/10.1002/aic.15231/full">Length to Diameter Ratio of Extrudates in Catalyst Technology, I. Modeling Catalyst Breakage by Impulsive Forces.</a> AIChE J. 62, 639-647 (2016).</li>
<li>Beeckman, J. W. L., Fassbender, N. A., Datz, T. E. <a target="_blank" href="http://onlinelibrary.wiley.com/doi/10.1002/aic.15231/full">Length to Diameter Ratio of Extrudates in Catalyst Technology, II. Bending strength versus Impulsive Forces.</a> AIChE J. 62, 2658-2669 (2016).</li>
<li>ASTM D7084-04, Standard Test Method for Determination of Bulk Crush Strength of Catalysts and Catalyst Carriers. , ASTM International. Conshohocken, PA. Available from: 
 <a target="_blank" href="www.astm.org">www.astm.org</a> (2004).</li>
<li>Beeckman, J. W. L., Cunningham, M., Fassbender, N. A., Datz, T. E. <a target="_blank" href="http://onlinelibrary.wiley.com/doi/10.1002/ceat.201600550/full">Length-to-Diameter Ratio of Extrudates in Catalyst Technology: III. Catalyst Breakage in a Fixed Bed.</a> Chem. Eng. Technol. , 1844-1851 (2017).</li>
</ol>

The authors have nothing to disclose.

Breakage by Impulsive Forces due to Collision: 
The reduction in extrudate aspect ratio due to collision against a surface can be measured in a laboratory drop test. In this test, the extrudates are released from a chute, fall and accelerate due to gravity and also experience drag with ambient air.
The method outlined above is so far only available in the literature as described in Beeckman15,16. Until recently, the high degree of tediousness to make manual measurements by caliper for a large number of extrudates is likely a contributing factor for this. The exposure time to ambient air and hence humidity should be minimized during and between measurements. If necessary, the protocol for the drop test may need to be performed with a N2 purge or a dry-air purge into the cylinder. One may also choose to let the catalyst equilibrate in ambient air overnight prior to taking any measurements to make moisture pick-up less of an issue. The protocol and method here employed has the benefit that it quickly yields the aspect ratio for over 100-300 extrudates and hence it takes most of the variability that can be observed with small samples out of contention.
It is important that extrudates with a length to diameter ratio less than unity be removed from the sample since the shape recognition software could assign length and diameter of such catalyst pieces erroneously. Hence it is also important to minimize and better yet to eliminate the number of such short extrudates. Therefore, it is recommended to work with extrudates that have a sufficiently large aspect ratio at the beginning of the test and to limit the impact severity of the test.
For future work and from a fundamental perspective, it would be very interesting to study the collision of single extrudates as a function of their length, as a function of the drop height, as a function of the impact angle and as a function of angular momentum to mention just a few variables. Upon breakage, it will be interesting to determine the location of the rupture surface(s) along the length of the original extrudate. This methodology may also be applicable to materials that are not extruded but that are rather obtained by pressing or for spherical pellets and hence may have applications for the pharmaceutical industry and the food industry.
Breakage due to stress in a fixed bed 
The method outlined above is so far only available in the literature as described in Beeckman18. For the bulk crush strength, it is important to follow the standard operating protocol as outlined in ASTM D7084-0417 for reason of repeatability.
The exposure time to ambient air and hence humidity should be minimized during and between measurements. If necessary, the protocol may need to be performed in a glove box for the application of the bulk crush strength.
As in the case of collision, this methodology may also find applicability to materials that are not extruded but rather obtained by pressing into pellet form or for spherical pellets obtained via dripping or granulation.

Catalyst manufacturing is the backbone that supports the petrochemical industry and related industries. Commercial catalysts, see Le Page1, are typically extruded according to recipes that are well guarded trade secrets or have patented methods of manufacture. Typical catalyst sizes range from 1 mm to about 5 mm in diameter and come in a variety of shapes like a cylinder, a trilobe or a quadrulobe together also with a variety of their hollow counterparts. While the diameter and the cross section of extruded catalysts are often very well controlled, the length of individual extrudates have a more Gaussian like distribution and the individual lengths typically range from about equal to one diameter to several diameters. An exception is extruded catalysts of sufficiently large diameter, that allows them to be cut as they exit the die face, and these have a much tighter length distribution. The length distribution of the smaller 1 mm to 3 mm diameter extruded catalysts that are typical for the petrochemical industry are normally obtained by natural breakage or forced breakage depending on their intrinsic strength.
Le Page1, Woodcock2, Bertolacini3, Wu4 and Li5&#160;show typical catalyst properties and the intricacies of the strength measurements. Typical strength measurements in the literature and in commercial settings comprise of the average crush strength of single extrudates and of the bulk crush strength. Both strength properties are in use to judge whether a catalyst has adequate strength to survive the loading and use in processes. Often also an attrition test is added to judge the catalyst attrition resistance in the process. Though a very large database exists in commercial plants on catalyst strength and use, that information is rarely accessible in the open literature. Also, many of the catalyst recipes are ad hoc and have been established after much trial and error. The modeling of this aspect of catalyst manufacturing is still challenging to say the least.
Applied here is the flexural strength of the catalyst obtained from a measurement of the Euler-Bernoulli modulus of rupture which is typically obtained in a three-point bending test. Li6 and Staub7 comment on the flexural strength of catalysts but their work is done on fairly large diameter extrudates and no direct application is given to model catalyst breakage. The flexural strength is rarely measured and reported in the literature for typical commercial catalyst sizes. Further, the flexural strength is often not applied for guidance in catalyst manufacturing
Measuring and modeling the breakage of catalysts either during its manufacture or during its use in the process is difficult. Often the catalyst extrudate length to diameter ratio is modeled based on empirical methods that relate it to strength via power laws, however, this in many instances still has a strong ad hoc component. Bridgwater8 provides a comprehensive overview of particle breakage due to shear but the length to diameter ratio of the extrudates are outside of the commercial range of extrudates discussed in this paper. Discrete element methods (DEM) and finite element methods (FEM) are now also used to investigate breakage of granules and these methods approach the problem at a fundamental level. Reference is given to Heinrich9, Wassgren10, Potyondy11, Potapov12, Carson13, and Farsi14 for details on this approach. The methods and techniques employed herein attempt to help improve modeling catalyst breakage due to collision via Newton&#39;s second law to determine the impact force and balancing this with the strength expressed by the Euler-Bernoulli modulus of rupture. For breakage by load stress in a fixed bed, a balance of load force and bed flexural strength is applied, and this allows to predict the aspect ratio of the bed as a function of the load. Very important are the measurement methods themselves that must be applied under well controlled conditions and this aspect is here in this paper detailed comprehensively. For instance, it is well known that the catalyst strength is strongly influenced by the heat treatment that is applied and also by the conditions of use when the catalyst can pick up moisture. Higher heat treatment temperatures typically strengthen the catalyst while high moisture pick-up typically weakens it. It is, therefore, important that the strength is measured on a catalyst that has seen the appropriate heat treatment and that moisture is controlled where it is necessary in order to make it representative for the use of the catalyst either during its manufacture or during its use in the process. Little is found in the literature that specifically measures and models the length to diameter ratio of catalyst extrudates that are typical for the petrochemical industry. Recently, Beeckman15,16 has used the bending strength of the catalyst to predict natural breakage and forced breakage of catalysts due to the collision. Here specific attention is given to the catalyst aspect ratio (L/D) which is defined as the arithmetic mean of the length to diameter ratios of the individual catalyst extrudates in a representative sample. The experimental methods described herein are relatively simple and allow to fundamentally study and compare experimental measurements with theoretical treatments.
The modulus of rupture (MOR) of the catalyst is a measure of its bending strength. Leonhard Euler and Daniel Bernoulli developed the first theoretically sound approach to elastic behavior and strength at rupture back in the 1750&#39;s. Figure 1 shows a schematic of the bending test and the rupture force Fr. For the specific case of a cylindrical extrudate, the modulus of rupture can be calculated from:
<img alt="Equation 1" src="/files/ftp_upload/57163/57163eq1.jpg" />&#160; &#160;(1)
Where &#963; is called the modulus of rupture and has dimensions of stress (Pa). D stands for the diameter of the extrudate while w is the distance between the two support points. The variable s is the shape factor and equals 8/&#960; for a cylinder. For a comprehensive explanation of the forces and stresses at hand during the experiment as well as how to deal with different cross-sectional shapes reference is given to Beeckman16. Specifically, &#963; is the tensile stress at rupture directed perpendicularly to the cross section of the extrudate and located at the extreme fiber in the middle between the two support points.
For collision of an extrudate with a surface, Beeckman15&#160;shows that two asymptotes exist with respect to the extrudate aspect ratio. The first asymptote called &#934;&#8734; is reached upon many repeated impacts. This asymptotic behavior is easily understood since, after breakage upon collision, shorter catalysts have less momentum and therefore experience less force upon impact. At the same time, shorter catalysts also require more force to break from a perspective of torque and hence the catalyst is expected to reach an asymptotic aspect ratio &#934;&#8734;&#160;upon many impacts. The second asymptote called &#934;&#945;&#160;is reached after a single impact when extrudates are dropped that are sufficiently long. Long extrudates have proportionally more momentum and break upon the first impact in several places along their length and the aspect ratio post collision reaches the second asymptote designated &#934;&#945;. Both asymptotes can be found by regression of collision data that measure the aspect ratio as a function of the number of repeated impacts from:
<img alt="Equation 2" src="/files/ftp_upload/57163/57163eq2.jpg" />&#160; &#160;(2)
Where&#160;&#934;0 is the initial aspect ratio and&#160;&#934;j is the aspect ratio after j drops. Both the parameters&#160;&#934;&#8734; and&#160;&#934;&#945; have a physical-mechanical meaning that is related to the severity of the impact and the strength of the catalyst. The severity of the impact can be varied by varying the drop height though for large drop heights the catalyst approaches terminal velocity and hence the severity will level out.
Particle length and particle diameter are important properties of the catalyst during its manufacture and use. The size and the shape of catalyst particles are also determining factors in their packing characteristics and influence the pressure drop across the catalyst bed. In earlier days, these properties were often measured by hand and this is a very tedious procedure. Now, these properties can be readily obtained by first optically scanning a large sample of catalyst extrudates. Then, imaging software is used to determine individual particle sizes. This allows a large number of particles to be analyzed quickly and accurately, see Beeckman15. These systems are tuned to effectively recognize and measure particles with a diameter in the range of 0.8 to 4.0 mm and with lengths that can be several diameters long. This method uses a &#34;top down&#34; view of the catalyst and hence yields an &#34;optical&#34; diameter. For certain shapes, care must be exerted when comparing the optical diameter with diameter values determined manually with calipers.
The bulk crush strength test for catalysts and catalyst carriers, ASTM D7084-0417 used herein is an accepted standard test method.The catalyst is loaded in a cylindrical cell and pressure (stress) is applied typically in the 5-1,000 kPa range and is allowed to equilibrate. After each pressure point, the catalyst is unloaded. The catalyst fines are screened out from the catalyst sample and weighed while the bulk of the catalyst sample is riffled to obtain a representative sample to accurately measure the aspect ratio. While the standard bulk crush strength test procedure focusses on the amount of fines that is created in order to gauge catalyst strength, this manuscript focusses on the reduction of the aspect ratio after breakage as a function of the load, see also Beeckman18.

<table><tbody><tr><td>Modulus of rupture (MOR)</td><td>INSTRON</td><td>MODEL 5942 SINGLE COLUMN TABLE TOP</td><td></td></tr><tr><td>Modulus of rupture (MOR)</td><td>INSTRON</td><td>10 NEWTON LOAD CELL</td><td></td></tr><tr><td>Modulus of rupture (MOR)</td><td>INSTRON</td><td>50 NEWTON LOAD CELL</td><td></td></tr><tr><td>Modulus of rupture (MOR)</td><td>INSTRON</td><td>BLEUHILL 3 SOFTWARE</td><td></td></tr><tr><td>Filter</td><td>VWR</td><td>BUCHNER FILTER</td><td></td></tr><tr><td>Aspect ratio (avg L/D)</td><td>EPSON</td><td>PERFECTION V700 PHOTO INSTRUMENT</td><td></td></tr><tr><td>Software</td><td>CASCADE DATA SYSTEMS</td><td>ALIAS 3-4 SOFTWARE</td><td></td></tr><tr><td>Riffling</td><td>HUMBOLDT MFG. Co</td><td>SPINNING RIFFLER</td><td></td></tr><tr><td>Riffling</td><td>HUMBOLDT MFG. Co</td><td>RIFFLE -TYPE SAMPLE DIVIDER</td><td></td></tr><tr><td>Sieve screen</td><td>VWR</td><td>US MESH SIEVE SCREEN, # 16</td><td></td></tr></tbody></table>

predicting catalyst extrudate breakage based on the modulus of rupture

The mechanical strength of extruded catalysts and their natural or forced breakage by either collision against a surface or by a compressive load in a fixed bed are important phenomena in catalyst technology. The mechanical strength of the catalyst is measured here by its bending strength or flexural strength. This technique is relatively new from the perspective of applying it to commercial catalysts of typical sizes used in the industry. Catalyst breakage by collision against a surface is measured after a fall of the extrudates through the ambient air in a vertical pipe. Quantifying the impact force is done theoretically by applying Newton's second law. Measurement of catalyst breakage due to stress in a fixed bed is done following the standard procedure of the bulk crush strength test. Novel here is the focus on measuring the reduction in the length to diameter ratio of the extrudates as a function of the stress.

Breakage by Collision: 
To give the reader an idea of the complexity of an impact of an extrudate onto a surface, it was thought to be beneficial to supply a few snapshot pictures at the highest frame speed we had available at the time (10,000 frames/s). Figure 2 shows such high-speed photography and captures the breakage of individual extrudates as they impact a polycarbonate surface. This surface has the added advantage that it shows the approach of the extrudate prior to impact by reflectance off the surface and allows to clearly define the instance of contact. The duration of the breakage by impact appears to be less than 10-4 s while the full impact history shows to be very complex. The forces experienced by the extrudate as a function of time during the collision are very spiked and irregular. The average deceleration defined as the impact speed over the contact time is only a rough estimate of what happens. When multiplied by the mass of the extrudate it is again only a rough estimate of the force.
The asymptotic aspect ratio &#934;&#8734;&#160;has been determined on 25 different kinds of catalysts and their properties are given in Beeckman16. The model parameter&#160;&#934;&#8734; for each catalyst has been obtained by non-linear regression using Eq. (2) shown in the introduction.
Figure 3&#160;shows the reduction in the aspect ratio of a typical fresh catalyst of the same catalyst batch dropped repeatedly from different heights. This sequence clearly shows the line-out towards the asymptotic aspect ratio,&#160;&#934;&#8734; for different drop heights i.e. different severities. Beeckman16 shows that the difference in aspect ratio for large drop heights becomes smaller and smaller due to the drag by ambient air during the fall which slows the acceleration of the extrudates and finally reaches the terminal velocity for large drop heights. It was also shown that the extrudates follow a second order break law which explains the shape of the trend curve of the aspect ratio with the number of consecutive drops. Figure 4 shows the aspect ratio of the same catalyst as in figure 3 but now starting with very long select catalyst strands after a single impact (each data-point is generated from a single extrudate). The solid symbols represent averages of the aspect ratio for each group of sizes. This shows the presence of the second asymptote&#160;&#934;&#945;&#160;and also an appreciation for the error bar that is involved when the length to diameter ratio is obtained from a very limited number of extrudates.
The impulsive force that acts on the extrudate during the collision can be found by applying Newton&#39;s second law. It is shown that at the asymptotic aspect ratio &#934;&#8734;, equating the rupture force to the impulsive force leads to the following correlation:
<img alt="Equation 3" src="/files/ftp_upload/57163/57163eq3.jpg" />&#160; &#160;(3)
With the normalized dimensionless group given by:
<img alt="Equation 4" src="/files/ftp_upload/57163/57163eq4.jpg" />&#160; &#160;(4)
Where &#963;, &#936;, p, D and g are respectively the catalyst modulus of rupture, the catalyst shape factor, the catalyst density, the catalyst diameter and the gravitational acceleration. The normalized dimensionless severity of the impact S&#8734; can be expressed as:
<img alt="Equation 5" src="/files/ftp_upload/57163/57163eq5.jpg" />&#160; &#160;(5)
Where is v the impact velocity, &#916;t is the duration of the collision and C is a collision interaction factor. It is further shown that for a total of 25 catalysts of different size, shape and chemical make-up that were tested in the drop test that in first approximation, the group <img alt="Equation 5b" src="/files/ftp_upload/57163/57163eq5b.jpg" /> is essentially a constant.
Breakage by stress in a fixed bed: 
Five catalysts shown in Table 1 are investigated with the bulk crush test for various pressures. Below a certain pressure, here called the critical pressure, no essential change occurs in the catalyst aspect ratio of the bed. Once the pressure increases above this critical value, the catalyst extrudate starts to break down and the aspect ratio in the bed adjusts naturally until the flexural strength of the bed is again able to withstand the applied stress. An example of the comparison of the experimental results and the predicted results are shown in Figure 5. Predicted values are shown as the solid curve and is obtained by beginning from the starting aspect ratio&#160;&#934;0 of the catalyst extrudates and remaining at that value until the critical pressure Pc is reached. Thereafter, the value of the aspect ratio diminishes with the negative one third power of the load pressure.
The methodology to find the maximum allowable load for a bed to withstand catalyst breakage utilizes a balance of the load force to the strength of the catalyst bed at rupture.
Beeckman18 shows that the aspect ratio of the catalyst in balance with the load force can be described by:
<img alt="Equation 6" src="/files/ftp_upload/57163/57163eq6.jpg" />&#160; &#160;(6)
Wherein&#160;&#934; is the extrudate aspect ratio while Ber is a dimensionless group given by:
<img alt="Equation 7" src="/files/ftp_upload/57163/57163eq7.jpg" />&#160; &#160;(7)
Where &#963;, is the modulus of rupture, s is the same extrudate shape factor as for collision, and P is the stress. The value for&#160;&#936; is determined by the bed packing and by the bed particle to particle force interactions and the authors give a theoretical value of 61/6 or about 1.35 for &#936;.
To summarize, if a bed of extrudates is loaded in the bulk crush strength test and a stress P is applied, then the extrudates will break throughout the entire bed under the applied stress P to an average value given by Eq. (6). Hence a bed with a starting aspect ratio&#160;&#934;0 has a critical pressure Pc it can withstand given by:
<img alt="Equation 8" src="/files/ftp_upload/57163/57163eq8.jpg" />&#160; &#160;(8)
<table fo:keep-together.within-page="1">
	<tbody>
		<tr>
			<td>Catalyst</td>
			<td>Shape</td>
			<td>D, diameter</td>
			<td>&#934;0 , initial aspect ratio</td>
			<td>s, shape factor</td>
			<td>&#961;, density</td>
			<td>&#963; MOR</td>
			<td>Pc, critical stress&#160;</td>
		</tr>
		<tr>
			<td></td>
			<td></td>
			<td>m</td>
			<td>(-)</td>
			<td>(-)</td>
			<td>kgm-3</td>
			<td>MPa</td>
			<td>kPa</td>
		</tr>
		<tr>
			<td>A</td>
			<td>QUADRULOBE</td>
			<td>1.43E-03</td>
			<td>3.18</td>
			<td>2.20</td>
			<td>1250</td>
			<td>0.81</td>
			<td>27.9</td>
		</tr>
		<tr>
			<td>B</td>
			<td>CYLINDER</td>
			<td>9.50E-04</td>
			<td>5.92</td>
			<td>2.55</td>
			<td>750</td>
			<td>1.38</td>
			<td>6.4</td>
		</tr>
		<tr>
			<td>C</td>
			<td>CYLINDER</td>
			<td>8.30E-04</td>
			<td>7.48</td>
			<td>2.55</td>
			<td>1870</td>
			<td>2.83</td>
			<td>6.5</td>
		</tr>
		<tr>
			<td>D</td>
			<td>TRILOBE</td>
			<td>2.89E-03</td>
			<td>2.28</td>
			<td>2.28</td>
			<td>970</td>
			<td>0.76</td>
			<td>69.3</td>
		</tr>
		<tr>
			<td>E</td>
			<td>CYLINDER</td>
			<td>1.55E-03</td>
			<td>3.54</td>
			<td>2.55</td>
			<td>NA</td>
			<td>1.37</td>
			<td>39.7</td>
		</tr>
	</tbody>
</table>
Table 1:&#160;Catalysts and their properties employed in the bulk crushing study. Table 1 shows catalyst properties and derived stress properties that allow to calculate the reduction in aspect ratio during compression in the bulk crush strength measurement. Adapted from Beeckman et al. 201718
<img alt="Figure 1" class="xfigimg" src="/files/ftp_upload/57163/57163fig1.jpg" /> 
Figure 1: Three-Point Bending of a Catalyst Extrudate by an External Force F. Schematic representation of the catalyst and the position of the force applied in the middle of the two support points for the determination of the modulus of rupture. The amount of bending is highly exaggerated. According to elasticity theory, the axial stress is compressive at the top of the extrudate and the axial stress is tensile at the bottom of the extrudate. Hence there is an axis with zero stress and this is called the centroid. When the tensile stress at the bottom reaches the tensile strength of the material or modulus of rupture, the extrudate breaks at the extreme fiber located at the very bottom and propagates very fast to complete extrudate failure. Adapted from Beeckman et al. 2016 16. <a href="/files/ftp_upload/57163/57163fig1large.jpg" target="_blank">Please click here to view a larger version of this figure.</a>
<img alt="Figure 2" class="xfigimg" src="/files/ftp_upload/57163/57163fig2.jpg" /> 
Figure 2: Impact of Extrudates on an Empty Polycarbonate Surface. High speed photography showing a sequence of two catalyst extrudate impingements against a polycarbonate surface. Shots are 0.1 ms apart from each other. Adapted from Beeckman et al. 2016 16. <a href="/files/ftp_upload/57163/57163fig2large.jpg" target="_blank">Please click here to view a larger version of this figure.</a>
<img alt="Figure 3" class="xfigimg" src="/files/ftp_upload/57163/57163fig3.jpg" /> 
Figure 3: The aspect ratio as a function of the drop height and the number of impacts. Aspect ratio as a function of the drop height or severity and the number of impacts. For high drop heights, the asymptotic aspect ratio changes only little since the extrudates reach their terminal velocity. Adapted from Beeckman et al. 2016 15. <a href="/files/ftp_upload/57163/57163fig3large.jpg" target="_blank">Please click here to view a larger version of this figure.</a>
<img alt="Figure 4" class="xfigimg" src="/files/ftp_upload/57163/57163fig4.jpg" /> 
Figure 4: Aspect ratio after 1 drop of catalyst A with a large initial aspect ratio. Aspect ratio after a single drop of extrudates that have a large aspect ratio prior to the drop. For such long extrudates, the second asymptote becomes plainly visible even in the presence of substantial experimental error due to the limited number of extrudates used. Adapted from Beeckman et al. 2016 15. <a href="/files/ftp_upload/57163/57163fig4large.jpg" target="_blank">Please click here to view a larger version of this figure.</a>
<img alt="Figure 5" class="xfigimg" src="/files/ftp_upload/57163/57163fig5.jpg" /> 
Figure 5: Catalyst Aspect ratio versus load stress for catalyst A. Reduction of the aspect ratio as a function of the applied load stress in the bulk crush strength measurement according to method ASTM D7084-04. The aspect ratio remains constant until the critical pressure is reached whereafter the catalyst breaks to smaller and smaller values as the pressure increases. Each data-point is a separate measurement with fresh catalyst from the beginning. Adapted from Beeckman et al. 201718 <a href="/files/ftp_upload/57163/57163fig5large.jpg" target="_blank">Please click here to view a larger version of this figure.</a>

Watch this Scientific Journal Video about Predicting Catalyst Extrudate Breakage Based on the Modulus of Rupture at JoVE.com

Predicting Catalyst Extrudate Breakage Based on the Modulus of Rupture

Here we present a protocol to measure the modulus of rupture of an extruded catalyst and the breakage of said catalyst extrudates by collision against a surface or by compression in a fixed bed.

The mechanical strength of extruded catalysts and their natural or forced breakage by either collision against a surface or by a compressive load in a ...

predicting-catalyst-extrudate-breakage-based-on-the-modulus-of-rupture

Nanyang Technological University

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Unit 1

Principal Stresses under a Given Loading

SCIENTISTS IN ACTION

8.3K Views.  ExxonMobil Research and Engineering Company. Hier presenteren we een protocol voor het meten van de absolute waarde van de breuk van een geëxtrudeerde katalysator en de breuk van bovengenoemde katalysator extrudates door botsing tegen een oppervlak of compressie in een vast bed.

Video: Predicting Catalyst Extrudate Breakage Based on the Modulus of Rupture

Synthesis of Programmable Main-chain Liquid-crystalline Elastomers Using a Two-stage Thiol-acrylate Reaction

This study presents a novel two-stage thiol-acrylate Michael addition-photopolymerization (TAMAP) reaction to prepare main-chain liquid-crystalline elastomers (LCEs) with facile control over network structure and programming of an aligned monodomain. Tailored LCE networks were synthesized using routine mixing of commercially available starting materials and pouring monomer solutions into molds to cure. An initial polydomain LCE network is formed via a self-limiting thiol-acrylate Michael-addition reaction. Strain-to-failure and glass transition behavior were investigated as a function of crosslinking monomer, pentaerythritol tetrakis(3-mercaptopropionate) (PETMP). An example non-stoichiometric system of 15 mol% PETMP thiol groups and an excess of 15 mol% acrylate groups was used to demonstrate the robust nature of the material. The LCE formed an aligned and transparent monodomain when stretched, with a maximum failure strain over 600%. Stretched LCE samples were able to demonstrate both stress-driven thermal actuation when held under a constant bias stress or the shape-memory effect when stretched and unloaded. A permanently programmed monodomain was achieved via a second-stage photopolymerization reaction of the excess acrylate groups when the sample was in the stretched state. LCE samples were photo-cured and programmed at 100%, 200%, 300%, and 400% strain, with all samples demonstrating over 90% shape fixity when unloaded. The magnitude of total stress-free actuation increased from 35% to 115% with increased programming strain. Overall, the two-stage TAMAP methodology is presented as a powerful tool to prepare main-chain LCE systems and explore structure-property-performance relationships in these fascinating stimuli-sensitive materials.

A novel methodology is presented to synthesize and program main-chain liquid-crystalline elastomers using commercially available starting monomers. A wide range of thermomechanical properties was tailored by adjusting the amount of crosslinker, while the actuation performance was dependent on the amount of applied strain during programming.

This study presents a novel two-stage thiol-acrylate Michael addition-photopolymerization (TAMAP) reaction to prepare main-chain liquid-crystalline ...

Chemistry

Environmentally-controlled Microtensile Testing of Mechanically-adaptive Polymer Nanocomposites for ex vivo Characterization

Implantable microdevices are gaining significant attention for several biomedical applications1-4. Such devices have been made from a range of materials, each offering its own advantages and shortcomings5,6. Most prominently, due to the microscale device dimensions, a high modulus is required to facilitate implantation into living tissue. Conversely, the stiffness of the device should match the surrounding tissue to minimize induced local strain7-9. Therefore, we recently developed a new class of bio-inspired materials to meet these requirements by responding to environmental stimuli with a change in mechanical properties10-14. Specifically, our poly(vinyl acetate)-based nanocomposite (PVAc-NC) displays a reduction in stiffness when exposed to water and elevated temperatures (e.g. body temperature). Unfortunately, few methods exist to quantify the stiffness of materials in vivo15, and mechanical testing outside of the physiological environment often requires large samples inappropriate for implantation. Further, stimuli-responsive materials may quickly recover their initial stiffness after explantation. Therefore, we have developed a method by which the mechanical properties of implanted microsamples can be measured ex vivo, with simulated physiological conditions maintained using moisture and temperature control13,16,17. 
To this end, a custom microtensile tester was designed to accommodate microscale samples13,17 with widely-varying Young's moduli (range of 10 MPa to 5 GPa). As our interests are in the application of PVAc-NC as a biologically-adaptable neural probe substrate, a tool capable of mechanical characterization of samples at the microscale was necessary. This tool was adapted to provide humidity and temperature control, which minimized sample drying and cooling17. As a result, the mechanical characteristics of the explanted sample closely reflect those of the sample just prior to explantation.
The overall goal of this method is to quantitatively assess the in vivo mechanical properties, specifically the Young's modulus, of stimuli-responsive, mechanically-adaptive polymer-based materials. This is accomplished by first establishing the environmental conditions that will minimize a change in sample mechanical properties after explantation without contributing to a reduction in stiffness independent of that resulting from implantation. Samples are then prepared for implantation, handling, and testing (Figure 1A). Each sample is implanted into the cerebral cortex of rats, which is represented here as an explanted rat brain, for a specified duration (Figure 1B). At this point, the sample is explanted and immediately loaded into the microtensile tester, and then subjected to tensile testing (Figure 1C). Subsequent data analysis provides insight into the mechanical behavior of these innovative materials in the environment of the cerebral cortex.

Environmentally-controlled Microtensile Testing of Mechanically-adaptive Polymer Nanocomposites for ex vivo Characterization

A method is discussed by which the in vivo mechanical behavior of stimuli-responsive materials is monitored as a function of time. Samples are tested ex vivo using a microtensile tester with environmental controls to simulate the physiological environment. This work further promotes understanding the in vivo behavior of our material.

Implantable microdevices are gaining significant attention for several biomedical applications1-4. Such devices have been made from a range of materials, ...

Bioengineering

Challenges in Rheological Characterization of Highly Concentrated Suspensions &#8212; A Case Study for Screen-printing Silver Pastes

A comprehensive rheological characterization of highly concentrated suspensions or pastes is mandatory for a targeted product development meeting the manifold requirements during processing and application of such complex fluids. In this investigation, measuring protocols for a conclusive assessment of different process relevant rheological parameters have been evaluated. This includes the determination of yield stress, viscosity, wall slip velocity, structural recovery after large deformation and elongation at break as well as tensile force during filament stretching.
The importance of concomitant video recordings during parallel-plate rotational rheometry for a significant determination of rheological quantities is demonstrated. The deformation profile and flow field at the sample edge can be determined using appropriate markers. Thus, measurement parameter settings and plate roughness values can be identified for which yield stress and viscosity measurements are possible. Slip velocity can be measured directly and measuring conditions at which plug flow, shear banding or sample spillover occur can be identified clearly. 
Video recordings further confirm that the change in shear moduli observed during three stage oscillatory shear tests with small deformation amplitude in stage I and III but large oscillation amplitude in stage II can be directly attributed to structural break down and recovery. For the pastes investigated here, the degree of irreversible, shear-induced structural change increases with increasing deformation amplitude in stage II until a saturation is reached at deformations corresponding to the crossover of G' and G'', but the irreversible damage is independent of the duration of large amplitude shear. 
A capillary breakup elongational rheometer and a tensile tester have been used to characterize deformation and breakup behavior of highly filled pastes in uniaxial elongation. Significant differences were observed in all experiments described above for two commercial screen-printing silver pastes used for front side metallization of Si-solar cells.

A protocol for a robust and application relevant rheological characterization of highly concentrated suspensions is presented. Silver pastes used for screen-printing application in solar cell production are employed as model systems.

A comprehensive rheological characterization of highly concentrated suspensions or pastes is mandatory for a targeted product development meeting the ...

Disentangling High Strength Copolymer Aramid Fibers to Enable the Determination of Their Mechanical Properties

Traditionally, soft body armor has been made from poly(p-phenylene terephthalamide) (PPTA) and ultra-high molecular weight polyethylene. However, to diversify the fiber choices in the United States body armor market, copolymer fibers based on the combination of 5-amino-2-(p-aminophenyl) benzimidazole (PBIA) and the more conventional PPTA were introduced. Little is known regarding the long-term stability of these fibers, but as condensation polymers, they are expected to have potential sensitivity to moisture and humidity. Therefore, characterizing the strength of the materials and understanding their vulnerability to environmental conditions is important for evaluating their use lifetime in safety applications. Ballistic resistance and other critical structural properties of these fibers are predicated on their strength. To accurately determine the strength of the individual fibers, it is necessary to disentangle them from the yarn without introducing any damage. Three aramid-based copolymer fibers were selected for the study. The fibers were washed with acetone followed by methanol to remove an organic coating that held the individual fibers in each yarn bundle together. This coating makes it difficult to separate single fibers from the yarn bundle for mechanical testing without damaging the fibers and affecting their strength. After washing, fourier transform infrared (FTIR) spectroscopy was performed on both washed and unwashed samples and the results were compared. This experiment has shown that there are no significant variations in the spectra of poly(p-phenylene-benzimidazole-terephthalamide-co-p-phenylene terephthalamide) (PBIA-co-PPTA1) and PBIA-co-PPTA3 after washing, and only a small variation in intensity for PBIA. This indicates that the acetone and methanol rinses are not adversely affecting the fibers and causing chemical degradation. Additionally, single fiber tensile testing was performed on the washed fibers to characterize their initial tensile strength and strain to failure, and compare those to other reported values. Iterative procedural development was necessary to find a successful method for performing tensile testing on these fibers.

The primary goal of the study is to develop a protocol to prepare consistent specimens for accurate mechanical testing of high strength copolymer aramid fibers, by removing a coating and disentangling the individual fiber strands without introducing significant chemical or physical degradation.

Traditionally, soft body armor has been made from poly(p-phenylene terephthalamide) (PPTA) and ultra-high molecular weight polyethylene. However, to ...

Determination of the Mechanical Properties of Flexible Connectors for Use in Insulated Concrete Wall Panels

This document contains recommendations for performing a non-standard, double-shear test suitable for both continuous and discrete insulated concrete sandwich wall panels (ICSWPs). Such a standardized test does not exist, but several iterations of this and similar tests have been performed in the literature to varying degrees of success. Further, the tests in the literature are rarely-if ever-described in detail or discussed at length with respect to the testing, data analysis, or safety procedures. A test specimen configuration is recommended herein, and variations are discussed. Important mechanical properties are identified from the load versus displacement data, and their extraction is detailed. The use of test data for design, such as for determining the stiffness of the connectors, is briefly demonstrated to show how ICSWP deflection and cracking behavior may be calculated. The strength behavior of panels may be determined using the full load versus displacement curve or only the maximum connector strength. Shortcomings and unknowns are acknowledged, and significant future work is delineated.

We propose a testing protocol that can be combined with widely available analytical methods to assess the mechanical properties of shear connectors for use in the design of insulated concrete wall panels to predict full-scale insulated panel behavior.

This document contains recommendations for performing a non-standard, double-shear test suitable for both continuous and discrete insulated concrete ...

Mechanoluminescent Visualization of Crack Propagation for Joint Evaluation

In this study, methods for the mechanoluminescent (ML) visualization of crack propagation and mechanical behavior to evaluate adhesive joints are demonstrated and explained. The first step involved sample preparation; an air spray was used to apply ML paint to the surface of the adhesive joint specimens. The performance of the ML sensor was described to examine the measurement conditions. The results of ML sensing during a double cantilever beam (DCB) test and a lap-shear (LS) test are demonstrated as these are the most frequently and widely used methods for evaluating adhesives. Originally, it was difficult to directly quantify the crack tip and strain/stress distribution and concentration because the crack tip was too small, and the effects of the strain could not be observed. The mechanoluminescence, crack propagation, and mechanical behavior during mechanical testing can be visualized via the ML pattern during the adhesive evaluation. This allows for the recognition of the precise position of the crack tips and other mechanical behaviors related to structural failure.

In this study, a protocol is presented that describes the use of mechanoluminescent (ML) visualization for monitoring crack propagation and mechanical behavior during adhesive joint evaluation testing.

In this study, methods for the mechanoluminescent (ML) visualization of crack propagation and mechanical behavior to evaluate adhesive joints are ...

Performing Microscope-Mounted Y-Shaped Cutting Tests

Y-shaped cutting has recently been shown to be a promising method by which to understand the threshold length scale and failure energy of a material, as well as its failure response in the presence of excess deformation energy. The experimental apparatus used in these studies was vertically oriented and required cumbersome steps to adjust the angle between the Y-shaped legs. The vertical orientation prohibits visualization in standard optical microscopes. This protocol presents a Y-shaped cutting apparatus that mounts horizontally over an existing inverted microscope stage, can be adjusted in three dimensions (X-Y-Z) to fall within the objective&#39;s field of view, and allows easy modification of the angle between the legs. The latter two features are new for this experimental technique. The presented apparatus measures the cutting force within 1 mN accuracy. When testing polydimethylsiloxane (PDMS), the reference material for this technique, a cutting energy of 132.96 J/m2 was measured (32&#176; leg angle, 75 g preload) and found to fall within the error of previous measurements taken with a vertical setup (132.9 J/m2 &#177; 3.4 J/m2). The approach applies to soft synthetic materials, tissues, or bio-membranes and may provide new insights into their behavior during failure. The list of parts, CAD files, and detailed instructions in this work provide a roadmap for the easy implementation of this powerful technique.

Y-shaped cutting measures fracture-relevant length scales and energies in soft materials. Previous apparatuses were designed for benchtop measurements. This protocol describes the fabrication and use of an apparatus that orients the setup horizontally and provides the fine positioning capabilities necessary for in situ viewing, plus failure quantification, via an optical microscope.

Y-shaped cutting has recently been shown to be a promising method by which to understand the threshold length scale and failure energy of a material, as ...

High Throughput Traction Force Microscopy Using PDMS Reveals Dose-Dependent Effects of Transforming Growth Factor-&#946; on the Epithelial-to-Mesenchymal Transition

Cellular contractility is essential in diverse aspects of biology, driving processes that range from motility and division, to tissue contraction and mechanical stability, and represents a core element of multi-cellular animal life. In adherent cells, acto-myosin contraction is seen in traction forces that cells exert on their substrate. Dysregulation of cellular contractility appears in a myriad of pathologies, making contractility a promising target in diverse diagnostic approaches using biophysics as a metric. Moreover, novel therapeutic strategies can be based on correcting the apparent malfunction of cell contractility. These applications,&#160;however, require direct quantification of these forces.
We have developed silicone elastomer-based traction force microscopy (TFM) in a parallelized multi-well format. Our use of a silicone rubber, specifically polydimethylsiloxane (PDMS), rather than the commonly employed hydrogel polyacrylamide (PAA) enables us to make robust and inert substrates with indefinite shelf-lives requiring no specialized storage conditions. Unlike pillar-PDMS based approaches that have a modulus in the GPa range, the PDMS used here is very compliant, ranging from approximately 0.4 kPa to 100 kPa. We create a high-throughput platform for TFM by partitioning these large monolithic substrates spatially into biochemically independent wells, creating a multi-well platform for traction force screening that is compatible with existing multi-well systems.
In this manuscript, we use this multi-well traction force system to examine the Epithelial to Mesenchymal Transition (EMT); we induce EMT in NMuMG cells by exposing them to TGF-&#946;, and to quantify the biophysical changes during EMT. We measure the contractility as a function of concentration and duration of TGF-&#946; exposure. Our findings here demonstrate the utility of parallelized TFM in the context of disease biophysics.

We present a high throughput traction force assay fabricated with silicone rubber (PDMS). This novel assay is suitable for studying physical changes in cell contractility during various biological and biomedical processes and diseases. We demonstrate this method's utility by measuring a TGF-&#946; dependent increase in contractility during the epithelial-to-mesenchymal transition.

Cellular contractility is essential in diverse aspects of biology, driving processes that range from motility and division, to tissue contraction and ...

Fibroblast Derived Human Engineered Connective Tissue for Screening Applications

Fibroblasts are phenotypically highly dynamic cells, which quickly transdifferentiate into myofibroblasts in response to biochemical and biomechanical stimuli. The current understanding of fibrotic processes, including cardiac fibrosis, remains poor, which hampers the development of new anti-fibrotic therapies. Controllable and reliable human model systems are crucial for a better understanding of fibrosis pathology. This is a highly reproducible and scalable protocol to generate engineered connective tissues (ECT) in a 48-well casting plate to facilitate studies of fibroblasts and the pathophysiology of fibrotic tissue in a 3-dimensional (3D) environment. ECT are generated around the poles with tunable stiffness, allowing for studies under a defined biomechanical load. Under the defined loading conditions, phenotypic adaptations controlled by cell-matrix interactions can be studied. Parallel testing is feasible in the 48-well format with the opportunity for the time-course analysis of multiple parameters, such as tissue compaction and contraction against the load. From these parameters, biomechanical properties such as tissue stiffness and elasticity can be studied.

Presented here is a protocol to generate engineered connective tissues for a parallel culture of 48 tissues in a multi-well plate with double poles, suitable for mechanistic studies, disease modeling, and screening applications. The protocol is compatible with fibroblasts from different organs and species and is exemplified here with human primary cardiac fibroblasts.

Fibroblasts are phenotypically highly dynamic cells, which quickly transdifferentiate into myofibroblasts in response to biochemical and biomechanical ...

A Method to Study the Correlation Between Local Collagen Structure and Mechanical Properties of Atherosclerotic Plaque Fibrous Tissue

The rupture of atherosclerotic plaques in coronary and carotid arteries is the primary cause of fatal cardiovascular events. However, the rupture mechanics of the heterogeneous, highly collagenous plaque tissue, and how this is related to the tissue's fibrous structure, are not known yet. Existing pipelines to study plaque mechanics are limited to obtaining only gross mechanical characteristics of the plaque tissue, based on the assumption of structural homogeneity of the tissue. However, fibrous plaque tissue is structurally heterogeneous, arguably mainly due to local variation in the collagen fiber architecture.
The mechano-imaging pipeline described here has been developed to study the heterogeneous structural and mechanical plaque properties. In this pipeline, the tissue's local collagen architecture is characterized using multiphoton microscopy (MPM) with second-harmonic generation (SHG), and the tissue's failure behavior is characterized under uniaxial tensile testing conditions using digital image correlation (DIC) analysis. This experimental pipeline enables correlation of the local predominant angle and dispersion of collagen fiber orientation, the rupture behavior, and the strain fingerprints of the fibrous plaque tissue. The obtained knowledge is key to better understand, predict, and prevent atherosclerotic plaque rupture events.

We have developed a mechano-imaging pipeline to study the heterogeneous structural and mechanical atherosclerotic plaque properties. This pipeline enables correlation of the local predominant angle and dispersion of collagen fiber orientation, the rupture behavior, and the strain fingerprints of the fibrous plaque tissue.

Predicting Catalyst Extrudate Breakage Based on the Modulus of Rupture

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