Performing Microscope-Mounted Y-Shaped Cutting Tests

Summary

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.

Abstract

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.

Introduction

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 tip^2,3. One method to approach such descriptions is through in situ visualization of the crack tip during failure^4,5. 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 G_cut (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, f_pre, and the angle between the legs and the cutting axis, θ. The cutting force, f_cut, 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 approaches^12,13,14 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).

Protocol

1. Adjustment and manufacturing of modifiable and consumable parts

1. Use a laser cutter or 3D printer to manufacture disposable ABS or acrylic tabs that fit within the width of the sample legs, B1 and B2 (7.5 mm x 7.5 mm for a 1.5 cm x 7 cm x 3 mm sample) (Figure 1B and Figure 2D). Two tabs are needed for each test, one for each leg.
2. Razor blade clip
   NOTE: The exact dimensions of the required razor blade clip depend on the depth of the razor blade used.
   1. Modify the CAD design (see Table of Materials) file Blade clip.SLDPRT (Supplemental Coding File 1) by changing the width of the clip base such that the distance from the tip of the selected razor blade to the back of the clip is 30.35 mm (Figure 1D). This adjustment keeps the tip of the blade directly under the pivot point (Figure 1E) of the angle adjustment mechanism (Figure 1A and Figure 2A) used to adjust the angle between the legs.
      NOTE: The apparatus can hold blades with a depth of 8-20 mm.
   2. Using fine settings, 3D-print the razor blade clip (Figure 1D). Due to 3D printing errors, the razor blade clip dovetail may not fit as printed. To fix this, use sandpaper or a fine file to remove material from the back of the razor blade clip until it can be inserted and removed from its slot on the blade clip mount by hand but is still tight during the cutting.
3. Modify the sample holder dimensions (Figure 1C) using the CAD design file Sample holder.SLDPRT (Supplemental Coding File 2) to fit the opening of the specific microscope stage (Figure 2B). To ensure the apparatus can use its full range of motion, it is important that the inner cavity of the holder stays as large as possible.
4. Load cell holder
   NOTE: Bending type load cells come in many geometries. The location upon which to mount the load sensor (the inner slide, Figure 1E) will require adjustment depending on the load cell selected.
   1. Adjust the following dimensions on the inner slide (Figure 1E) to accommodate the specific load cell: 1) the location of the mounting holes (currently two M3 holes with a 6 mm center-to-center distance); 2) the distance between the load cell beam and the inner slide plane, depending on the maximum deflection of the load cell beam (currently at 3 mm); and 3) the height and width to accommodate load cell geometry (currently 35 mm and 12.1 mm, respectively).
      NOTE: The load cell length range that can be used without interfering with the vertical adjust system (Figure 1E and Figure 2A) is 10-63 mm. If the load cell size is out of this range, an alternative is to remove the height adjust system or redesign/lengthen the pulley arms (Figure 1A).
5. Redesign, using the appropriate CAD files, the mounting platform and frame arms (Figure 1A) to fit the specific microscope/microscope stage used. Specifically, the frame arms (frame arm.SLDPRT, Supplemental Coding File 3) may need to be modified to facilitate attachment. The height of the pulley arms (Figure 1A) (pulley arm.SLDPRT, Supplemental Coding File 4, and pulley arm_Mirror.SLDPRT, Supplemental Coding File 5) may also need to be modified depending on the heights of the plane of the microscope mounting holes and the top plane of the microscope's XY stage.

2. Mechanical assembly

1. Once all the microscope, load-cell, razor blade, and sample components have been appropriately modified, manufacture all the components and construct the apparatus (Figure 2A). The components include 3D-printed, laser-cut, and commercial off-the-shelf parts. A detailed list of parts is given in the Table of Materials. Computer assembly drawings of all the parts and apparatus assembly are available in Supplemental Coding Files 1-17.
2. To mount the load cell, first attach the blade clip mount to the load cell (Figure 1E). Attach this assembly to the inner slide of the vertical adjust system (Figure 1E and Figure 2A). Attach the combined system of the blade clip mount, load cell, and inner slide of the vertical adjust system into the outer slide of the vertical adjust system (Figure 1E) that is mounted to the bottom of the angle adjustment mechanism (Figure 1A and Figure 2A).
   ​NOTE: Micro load cells are fragile. Use caution when handling the load cell to minimize any forces applied to it outside of testing, especially forces in the direction of load measurement.

3. Electrical assembly

1. Set up the load cell and data acquisition system. Build an amplification circuit following the schematic (Figure 1F, Amplification circuit schematic.SchDoc [Supplemental Coding File 18], and Amplification circuit PCB.PcbDoc [Supplemental Coding File 19]). Connect the output signal directly to a data acquisition system with a 0-5 V input range. Connect the elements of the circuit according to Figure 1G.
2. Calibrate the load cell by placing a weight of known quantity on the deflection beam and recording the voltage output in the calibration code (calibrate_ni_daq.mlapp, Supplemental Coding File 20). Repeat this process at least 5x for different weights of known quantity.
3. Calculate the load cell calibration constant by fitting the known weight versus voltage data to a line. Input this calibration value into the data collection code (collect_data.mlapp, Supplemental Coding File 21).
   ​NOTE: The approach to data acquisition will depend on the type of load cell selected. In this study, a deflection load cell with a maximum rated capacity of 0.5 N, 0.05% rated output (R.O.) maximum repeatability, and 0.03% R.O. hysteresis was used. The ~10 mV output signal is amplified to enable the use of a commercial data acquisition (DAQ) system (−5 to 5 V input range, 16-bit resolution). As a result, a force resolution finer than 1 mN was obtained while collecting data at a rate of 20 Hz after applying a rolling median filter.

4. Apparatus mounting

1. After the apparatus has been constructed and the load cell and data acquisition system have been set up, replace the original, stage-mounted slide holder with the custom sample holder.
2. Attach the assembly to the microscope. Use mounting holes on the top surface of the microscope if available.
3. Set the angle of the cut by loosening the angle adjust thumb screw and then moving the linear slide (Figure 1A). Set the angle after measuring it with a protractor (Figure 2A) and tighten the angle adjust thumb screw. The angle between a leg and the sample midplane, θ, can be adjusted from 8°-45° (Figure 1B).
4. Set up two vertical pulleys behind the apparatus.

5. Sample preparation

1. Sample dimensions: Prepare a thin rectangular sample (e.g., 1.5 cm x 7 cm x 3 mm) of PDMS (see Table of Materials) by either cutting it from a larger sheet or using a mold of the correct dimensions. The dimensions may vary, but a width of 1.5 cm or less for a sample with a thickness of 3 mm or less is recommended to start.
2. Cutting the legs: Using a razor blade, cut the sample 3 cm lengthwise along the centerline to create the Y-shaped sample (Figure 1B). This length may vary, but the legs should be long enough to accommodate the tabs yet short enough to leave uncut sample for measurement.
3. Strain measurement marking: Using a marker or ink, place two marks, centered and separated by approximately 1 cm, on each of the thin legs (Figure 2D) and the body of the sample (six in total) to enable the measurement of the applied stretch in each of the three sample legs under load.
4. Attaching the tabs: Use adhesive-like cyanoacrylate glue to attach a 3D-printed or laser-cut tab (step 1.1) to the end of each leg (Figure 1B and Figure 2D).
5. Prepare the tension Line: Measure and cut two lengths of thin fishing line. Approximately 30 cm of line is needed for internal routing through the mechanism; add more as needed to route the line to the external set of pulleys (step 4.4). Attach 5 g weighing plates to the end of the lines passing through the external pulleys and tie the other end to the tab on each leg.

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.

1. Clamp the base of the sample using the sample holder thumb screw (Figure 1C).
2. Route the line for each leg through each side of the pulley system (Figure 1A and Figure 2A). Take a picture of the sample from the top while the sample is under negligible weight by holding a camera against the underside of the angle adjustment mechanism. Make sure the camera is parallel to the sample plane to minimize perspective effects.
3. Add the desired preload weight of 75 g to both ends of the fishing line near the external pulleys. Increase this quantity to 150 g or decrease it to 50 g to change the tearing contribution if desired for this example material and geometry. Take a second picture of the sample after the weight is added, again making sure that the camera is parallel to the sample plane.
   NOTE: The example weights provided here apply specifically to the PDMS sample used in this study.
4. Align the fishing line from the lowest pulley with the Z plane of the sample legs using the Z component of the three-way micro-adjustment stage (Figure 1A). Approximately position the anticipated blade tip close to the objective's field of view (Figure 2B).

7. Blade mounting

1. Place the razor blade into its corresponding blade clip (step 1.2) and secure the blade in place with a set screw. Seat the blade firmly into the blade clip (Figure 1D and Figure 2C) to ensure that it is square. Slide this clipped razor blade into the blade clip mount attached to the load cell (Figure 1E).
   ​NOTE: The blade should always be placed after the sample is mounted. If the blade is in place before the sample, it presents a safety risk to the user.

8. Apparatus alignment

1. Select the 2.5x microscope objective, or as high as 20x if closer images are desired.
2. Use the transmitted light setting, augmenting the light behind the sample if needed.
3. With the blade in place, focus the microscope on the bottom of it, using the blade's vertical adjust system if necessary to bring the tip to the appropriate working distance for the objective (Figure 1E and Figure 2A). Carefully align the razor blade within the microscope's field of view using only the X and Y directions of the three-way micro-adjustment stage (Figure 1A).
4. Next, focus the microscope on the sample. Align the crack tip with the razor blade (Figure 2B) by translating the microscope XY stage (Figure 1A) to ensure that the midplane of the sample aligns with the midplane of the angle adjustment mechanism.

9. Testing

1. Open the code used for the load cell data collection (collect_data.mlapp, Supplemental Coding File 21).
2. Start recording the load cell data by clicking the Start Recording button.
3. Translate the sample through the razor blade for 1 cm or more at a constant velocity using microscope stage control. Simultaneously gather images using the microscope's imaging interface.
4. When the microscope XY stage stops (Figure 1A), click the Stop Recording button to stop recording data and automatically save a *.txt file of the load and time response.

Results

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, f_pre, and the angle between the legs and the cutting axis, θ. The following data are also required: the cutting force, f_cut, and the average leg strain,

Discussion

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-prin...

Materials

Name	Company	Catalog Number	Comments
Buy Parts
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
Make Parts
Angle adjustment system- arm	3D Printing		solidworks: arms_arm_single.SLDPRT QTY: 2 Setting: Fast/0.2 mm layer height
Angle adjustment system- arms stationary	3D Printing		solidworks: arms_stationary.SLDPRT QTY: 1 Setting: Fast/0.2 mm layer height
Angle adjustment system- link	3D Printing		solidworks: arms_arm_link.SLDPRT QTY: 2 Setting: Fast/0.2 mm layer height
Angle adjustment system- slider	3D Printing		solidworks: arms_slider.SLDPRT QTY: 1 Setting: Fast/0.2 mm layer height
Angle adjustment system- spacer	3D Printing		solidworks: arms_front_spacer.SLDPRT QTY: 1 Setting: Fast/0.2 mm layer height
Clip- Blade clip	3D Printing		solidworks: Blade clip.SLDPRT QTY: 1 Setting: Fine/0.1 mm layer height
Clip- Blade clip mount	3D Printing		solidworks: Blade clip mount.SLDPRT QTY: 1 Setting: Fine/0.1 mm layer height
Frame arm	3D Printing		solidworks: frame arm.SLDPRT QTY: 2 Setting: Fast/0.2 mm layer height
Mounting platform	Laser Cut Acrylic		solidworks: mounting platform.SLDPRT QTY: 1
Pulley arm (left)	3D Printing		solidworks: pulley arm_Mirror.SLDPRT QTY: 1 Setting: Fast/0.2 mm layer height
Pulley arm (right)	3D Printing		solidworks: pulley arm.SLDPRT QTY: 1 Setting: Fast/0.2 mm layer height
Sample holder and tab- Clamp	3D Printing		solidworks: Clamp.SLDPRT QTY: 1 Setting: Fast/0.2 mm layer height
Sample holder and tab- Sample holder	3D Printing		solidworks: Sample holder.SLDPRT QTY: 1 Setting: Fast/0.2 mm layer height
Sample holder and tab- Tab	3D Printing		solidworks: Tab.SLDPRT QTY: 2 per test Setting: Fine/0.1 mm layer height, no brim
Vertical adjust system- Inner slide	3D Printing		solidworks: Inner slide.SLDPRT QTY: 1 Setting: Fast/0.2 mm layer height
Vertical adjust system- Outer slide	3D Printing		solidworks: Outer slide.SLDPRT QTY: 1 Setting: Fast/0.2 mm layer height