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 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'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° leg angle, 75 g preload) and found to fall within the error of previous measurements taken with a vertical setup (132.9 J/m2 ± 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.
Nonlinear continuum mechanics has provided a critical lens through which to understand the concentration of energy that leads to failure in soft solids1. However, the accurate prediction of this failure also requires descriptions of the microstructural characteristics that contribute to new surface creation at the crack tip2,3. One method to approach such descriptions is through in situ visualization of the crack tip during failure4,5. However, crack blunting in typical far-field fracture tests makes the acquisition of in situ data challenging by spreading out the highly deformed material, potentially outside the microscope's field of view6. Y-shaped cutting offers a unique alternative for microstructural visualization because it concentrates the region of large deformation at the tip of a blade7. Furthermore, previous work from our group demonstrates that this unique experimental approach can provide insight into the differences in failure response between far-field tearing and contact-mediated loading conditions7.
The Y-shaped cutting method used in the apparatus presented here was first described decades ago as a cutting method for natural rubber8. The method consists of a fixed blade push-cutting through a preloaded Y-shaped test piece. At the intersection of the "Y" is the crack tip, which is created prior to testing by splitting a portion of a rectangular piece into two equal "legs" (Figure 1B and Figure 2D). The primary advantages of this cutting method include the reduction of frictional contributions to the measured cutting energy, the variable blade geometry (i.e., constraint of the crack tip geometry), the control of the failure rate (via the sample displacement rate), and the separate tuning of the cutting, C, and tearing, T, energy contributions to the total energy Gcut (i.e., altering the failure energy in excess of a cutting threshold)8. The latter contributions are expressed in a simple, closed-form expression for the cutting energy9
Eqn (1)
which uses experimentally selected parameters, including sample thickness, t, average leg strain, , preload force, fpre, and the angle between the legs and the cutting axis, θ. The cutting force, fcut, is measured with the apparatus as detailed in Zhang et al.9. Notably, the apparatus presented here includes a new, simple, and accurate mechanism for tuning the leg angle, θ, and ensuring the sample is centered. While both features are critical for a microscope-mounted setup, the mechanism may benefit future vertical implementations of the Y-shaped cutting test as well by increasing the ease of use.
Progress in determining the appropriate failure criteria for soft solids has been ongoing since the early success of sample-independent fracture geometries introduced by Rivlin and Thomas10. Critical energy release rates10, cohesive zone laws11, and various forms of stress- or energy-at-a-distance approaches12,13,14 have been used. Recently, Zhang and Hutchens leveraged the latter approach, demonstrating that Y-shaped cutting with sufficiently small radius blades could yield threshold failure conditions for soft fracture7: a threshold failure energy and a threshold length scale for failure that ranges from tens to hundreds of nanometers in homogeneous, highly-elastic polydimethylsiloxane (PDMS). These results were combined with continuum modeling and scaling theory to develop a relationship between cutting and tearing in these materials, thus demonstrating the utility of Y-shaped cutting for providing insights into all modes of soft failure. However, the behavior of many material classes, including dissipative and composite materials, remains unexplored. It is anticipated that many of these will exhibit microstructure-governed effects at length scales above the wavelength of visible light. Therefore, an apparatus was designed in this study that allows for the close visual characterization of these effects during Y-shaped cutting for the first time (e.g., in composites, including soft tissues, or of dissipative processes, anticipated on the micrometer to millimeter length scales15).
1. Adjustment and manufacturing of modifiable and consumable parts
2. Mechanical assembly
3. Electrical assembly
4. Apparatus mounting
5. Sample preparation
6. Sample mounting
NOTE: Take caution during this step to ensure that the sample does not touch the microscope objective to avoid damaging it. It may help to adjust the objective and microscope stage to create as much space as possible for sample mounting.
7. Blade mounting
8. Apparatus alignment
9. Testing
The parameters used during step 4 and step 6 and the data gathered during step 6 and step 9 combine to yield the cutting energy of the sample. According to Eqn. 1, the determination of the cutting energy requires the following parameters: sample thickness, t, preload force, fpre, and the angle between the legs and the cutting axis, θ. The following data are also required: the cutting force, fcut, and the average leg strain, . The former comes from force-time data gathered via the computer code. The force-time data from a typical test (Figure 3A) illustrate a high initial force, as is typically required for cut initiation, followed by a constant force, indicating steady state cutting. The cutting force, fcut, is the maximum value of the force within this steady state regime9. The average strain in the legs, , is given by
Eqn (2)
where images of the pre- and post-loaded sample prior to cutting (step 6.2 and step 6.3) are used as an optical strain gage to measure λB1, λB2, and λA. Finally, these values are combined to calculate the cutting energy using Eqn. 1.
For the representative results reported here: an ultrasharp blade (129 nm radius), a 32° leg angle, and a 75 g preload ( = 1.04), we measured a cutting energy of 132.96 J/m2 for PDMS. This value aligns well with the previously obtained cutting energy under these conditions of 132.9 J/m2 ± 3.4 J/m2, thus validating the mechanical portion of the test setup demonstrated here9. If desired, the force-time data can be converted approximately to force-displacement data using the microscope stage motion protocol (e.g., constant velocity).
The viability of the setup for simultaneously gathering microscope images is illustrated in Figure 3B. These images are gathered using a 2.5x objective 1) from the start of the test, 2) past the cut initiation, and 3) throughout the steady state in a speckle-patterned PDMS sample mixed at the manufacturer's ratio of 10:1. We maintained focus throughout the test and demonstrated one-to-one correspondence between the mechanical and optical data. We note that the quality and magnification of the microscope images obtained will depend on the system/objective/stage /program combination used.
Figure 1: CAD images of the microscope-mounted Y-shaped cutting device. (A) The full cutting apparatus mounted above an inverted microscope with an automated XY stage. Not shown are the vertical pulleys behind the system from which dead weights are hung to create preload forces, fpre, on the sample. (B) The sample consists of a single leg, "A", from which two equal legs are cut, "B1" and "B2", to create a "Y" shape with leg angle θ. (C) The sample holder holds the sample in place within a slot in the microscope stage. (D) The top view of the customizable blade clips shows how their redesign accommodates blades of different heights while maintaining the 30.35 mm spacing that aligns the top with the pivot point of the angle adjustment mechanism. (E) A close-up side view of the vertical adjust system, load cell, and blade clip mounting parts. (F) The signal from the load cell is mediated by an amplification circuit used to convert the load cell output (0-10 mV) to the 0-5 V range of the data acquisition system. (G) This circuit is implemented by connecting it to the power supply, load cell, and data acquisition system using a printed circuit board. Please click here to view a larger version of this figure.
Figure 2: Photographs of the microscope-mounted Y-shaped cutting device. (A) A photograph of the operational Y-shaped cutting device with false-colored regions added to indicate the key design features. (B) A forward view of the device illustrating the approximate alignment of the load cell and sample midplane and indicating the region to be cut that falls within the microscope objective's field of view. (Blade and blade clip not mounted.) (C) Examples of mounted blades and clips with an equal overall height of 30.35 mm. (D) A PDMS Y-shaped sample prior to mounting, with the tabs and fishing line attached. Fiducial markers have been added to the legs "B1" and "B2" to measure the average stretch upon preload application. Please click here to view a larger version of this figure.
Figure 3: Representative in situ cutting results. (A) A force-time curve for PDMS (10:1) using an ultrasharp blade (129 nm radius), 32° leg angle, and 75 g preload ( = 1.04). The elastic loading, cut initiation, steady state cutting, and unloading regions of the curve are labeled. (B) Red circles that correspond to the images obtained by the microscope are shown. A yellow circle has been added to facilitate observation of the speckle-pattern motion. Scale bar = 1 mm. Time stamps, in seconds, are included in the upper left-hand corner of each image. Please click here to view a larger version of this figure.
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The horizontal, Y-shaped cutting apparatus reported here enables in situ imaging capabilities along with improved ease-of-use for this failure technique. The apparatus includes a modular/portable design for quick mounting/unmounting from a microscope and continuous, pre-aligned leg angle adjustment. All the CAD files, required materials, and procedures have been included to facilitate the implementation of this method. In many instances (blade holders, sample holder, load-cell mount, mounting frame), the 3D-printed parts can be easily modified for a given material/blade or specific load cell/microscope. However, the following tips apply to all the parameters and usages of this apparatus.
The weight used to hold each leg in tension is critical to a successful measurement. A sufficiently low weight ensures that the test does not fail immediately (it can be helpful to apply weight slowly and incrementally). However, loading the legs with too little force will result in sample buckling, leading the sample to fold under or in front of the blade instead of or while being cut. An “apparent” cutting force may be measured under these conditions, but it will not be the cutting force of the material.
The sample legs must be of an appropriate length for the sample holder and desired travel. Legs that are too long will run into the pulley system before a long enough cut has been made. The legs must be long enough to accommodate the tabs. For the sample holder geometry reported here, a 7 cm total sample length with 3 cm legs provides a good starting point. The load cell should be calibrated before each use. Abrupt movement of the apparatus can cause the load cell to become uncalibrated or even damaged.
The key modifications fall into two categories: accommodation of available equipment/components and material/imaging requirements. In terms of the first category, the apparatus mounting frame may be adjusted for implementation on different microscopes. The load-cell mount, the vertical adjust, or the arms supporting the first set of pulleys may all be modified to accommodate load cells of different lengths. The blade clips may require adjustment depending on the blade depth, as detailed in step 2.2 of the protocol. In terms of the second category, the sample holder may be modified to adapt to the objective working distance or sample environment limitations. For example, in the case of testing hydrated materials, a Petri dish or slide may be incorporated beneath the sample to protect the microscope and maintain hydration.
As with vertical Y-shaped cutting, this approach applies primarily to soft, reasonably robust solids. Stiff materials prefer to twist rather than bend outward and maintain a planar sample when a Y-inducing load is applied16. When samples are extremely brittle, low leg angles are required to achieve a sufficiently low tearing contribution (Eqn. 1), at which point friction can become a problem. Hydrated samples, typically possessing very low friction, may be the exception for tests at such low leg angles. From experience, leg angles >35° generally avoid frictional effects in relatively “sticky” silicone7,9. Changes in the sample geometry, environment, or blade angle may overcome many of these barriers, in time. Limitations in the cutting speed and control will vary with the automated XY microscope stage used. Specifically, some stage/software combinations provide only a few standard options for constant velocity. At higher cutting speeds, image acquisition may be insufficient to avoid blurring. All such limitations are dependent on the microscope and stage manufacturers but may be overcome by applying this apparatus to a custom microscope.
Y-shaped cutting facilitates the determination of the threshold failure properties of soft solids and provides insight into the fundamental failure responses of these materials under highly controlled conditions. With the modification provided by the apparatus detailed here, these mechanical measurements can now be combined with existing optical characterization techniques such as, but not limited to, the following: mechanophore activation5, second harmonic generation (SHG)17, and digital image correlation18. This combination is expected to yield new, quantifiable observations of the intimate relationship between microstructure and stress concentration in soft failure.
The authors have nothing to disclose.
We would like to thank Dr. James Phillips, Dr. Amy Wagoner-Johnson, Alexandra Spitzer, and Amir Ostadi for their advice on this work. Funding came from the start-up grant provided by the Department of Mechanical Science and Engineering at the University of Illinois Urbana-Champaign. M. Guerena, J. C. Peng, M. Schmid, and C. Walsh all received senior design credit for their work on this project.
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1" OD Pulley | McMaster Carr | 3434T75 | Pulley for Wire Rope (Larger) |
100 g Micro Load Cell | RobotShop | RB-Phi-203 | |
1K Resistor | Digi-Key | CMF1.00KFGCT-ND | 1 kOhms ±1% 1 W Through Hole Resistor Axial Flame Retardant Coating, Moisture Resistant, Safety Metal Film |
1M Resistor | Digi-Key | RNF14FAD1M00 | 1 MOhms ±1% 0.25 W, 1/4 W Through Hole Resistor Axial Flame Retardant Coating, Safety Metal Film |
3/8" OD Pulley | McMaster Carr | 3434T31 | Pulley for Wire Rope |
4" Clear Protractor with Easy Read Markings | S&S Worldwide | LR3023 | |
Breadboard | ECEB | N/A | |
IC OPAMP ZERO-DRIFT 2 CIRC 8DIP | Digi-Key | LTC1051CN8#PBF-ND | |
M2 x 0.4 mm Nut | McMaster Carr | 90592A075 | Steel Hex Nut |
M2 x 0.4 mm x 25 mm | McMaster Carr | 91292A032 | 18-8 Stainless Steel Socket Head Screw |
M2 x 0.4 mm x 8 mm | McMaster Carr | 91292A832 | 18-8 Stainless Steel Socket Head Screw |
M3 x 0.5 mm x 15 mm | McMaster Carr | 91290A572 | Black-Oxide Alloy Steel Socket Head Screw |
M3 x 0.5 mm x 16 mm | McMaster Carr | 91294A134 | Black-Oxide Alloy Steel Hex Drive Flat Head Screw |
M3 x 0.5 mm, 4 mm High | McMaster Carr | 90576A102 | Medium-Strength Steel Nylon-Insert Locknut |
M4 x 0.7 mm Nut | McMaster Carr | 90592A090 | Steel Hex Nut |
M4 x 0.7 mm x 15 mm | McMaster Carr | 91290A306 | Black-Oxide Alloy Steel Socket Head Screw |
M4 x 0.7 mm x 16 mm | McMaster Carr | 91294A194 | Black-Oxide Alloy Steel Hex Drive Flat Head Screw |
M4 x 0.7 mm x 18 mm | McMaster Carr | 91290A164 | Black-Oxide Alloy Steel Socket Head Screw |
M4 x 0.7 mm x 20 mm | McMaster Carr | 91290A168 | Black-Oxide Alloy Steel Socket Head Screw |
M4 x 0.7 mm x 20 mm | McMaster Carr | 92581A270 | Stell Raised Knurled-Head Thumb Screw |
M4 x 0.7 mm x 30 mm | McMaster Carr | 91290A172 | Black-Oxide Alloy Steel Socket Head Screw |
M4 x 0.7 mm x 50 mm | McMaster Carr | 91290A193 | Black-Oxide Alloy Steel Socket Head Screw |
M4 x 0.7 mm, 5 mm High | McMaster Carr | 94645A101 | High-Strength Steel Nylon-Insert Locknut |
M5 x 0.8 mm Nut | McMaster Carr | 90592A095 | Steel Hex Nut |
M5 x 0.8 mm x 16 mm | McMaster Carr | 91310A123 | High-Strength Class 10.9 Steel Hex Head Screw |
M5 x 0.8 mm x 35 mm | McMaster Carr | 91290A195 | Black-Oxide Alloy Steel Socket Head Screw |
M5 x 0.8 mm, 13 mm Head Diameter | McMaster Carr | 96445A360 | Flanged Knurled-Head Thumb Nut |
M5 x 0.8 mm, 5 mm High | McMaster Carr | 90576A104 | Medium-Strength Steel Nylon-Insert Locknut |
Solidworks | Dassault Systemes | CAD software | |
Wiring Kit | ECEB | N/A | |
XYZ Axis Manual Precision Linear Stage 60 mm x 60 mm Trimming Bearing Tuning Platform Sliding Table | OpticsFocus | N/A | |
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Angle adjustment system- arm | 3D Printing | solidworks: arms_arm_single.SLDPRT QTY: 2 Setting: Fast/0.2 mm layer height |
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Angle adjustment system- arms stationary | 3D Printing | solidworks: arms_stationary.SLDPRT QTY: 1 Setting: Fast/0.2 mm layer height |
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Angle adjustment system- link | 3D Printing | solidworks: arms_arm_link.SLDPRT QTY: 2 Setting: Fast/0.2 mm layer height |
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Angle adjustment system- slider | 3D Printing | solidworks: arms_slider.SLDPRT QTY: 1 Setting: Fast/0.2 mm layer height |
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Angle adjustment system- spacer | 3D Printing | solidworks: arms_front_spacer.SLDPRT QTY: 1 Setting: Fast/0.2 mm layer height |
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Clip- Blade clip | 3D Printing | solidworks: Blade clip.SLDPRT QTY: 1 Setting: Fine/0.1 mm layer height |
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Clip- Blade clip mount | 3D Printing | solidworks: Blade clip mount.SLDPRT QTY: 1 Setting: Fine/0.1 mm layer height |
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Frame arm | 3D Printing | solidworks: frame arm.SLDPRT QTY: 2 Setting: Fast/0.2 mm layer height |
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Mounting platform | Laser Cut Acrylic | solidworks: mounting platform.SLDPRT QTY: 1 |
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Pulley arm (left) | 3D Printing | solidworks: pulley arm_Mirror.SLDPRT QTY: 1 Setting: Fast/0.2 mm layer height |
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Pulley arm (right) | 3D Printing | solidworks: pulley arm.SLDPRT QTY: 1 Setting: Fast/0.2 mm layer height |
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Sample holder and tab- Clamp | 3D Printing | solidworks: Clamp.SLDPRT QTY: 1 Setting: Fast/0.2 mm layer height |
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Sample holder and tab- Sample holder | 3D Printing | solidworks: Sample holder.SLDPRT QTY: 1 Setting: Fast/0.2 mm layer height |
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Sample holder and tab- Tab | 3D Printing | solidworks: Tab.SLDPRT QTY: 2 per test Setting: Fine/0.1 mm layer height, no brim |
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Vertical adjust system- Inner slide | 3D Printing | solidworks: Inner slide.SLDPRT QTY: 1 Setting: Fast/0.2 mm layer height |
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Vertical adjust system- Outer slide | 3D Printing | solidworks: Outer slide.SLDPRT QTY: 1 Setting: Fast/0.2 mm layer height |