## Abstract

In pursuit of research to create a synthetic tissue scaffold by a micropunching process, material properties of polycaprolactone (PCL) in liquid nitrogen were determined experimentally and used for finite element modeling of cryogenic micropunching process. Specimens were prepared using injection molding and tested under compression to determine the stress–strain relationship of PCL below its glass transition temperature. Cryogenic conditions were maintained by keeping the PCL specimens submerged in liquid nitrogen throughout the loading cycle. Specimens of two different aspect ratios were used for testing. Yield strength, strength coefficient, and strain hardening exponent were determined for different specimen aspect ratios and extrapolated for the case with zero diameter to length ratio. Material properties were also determined at room temperature and compared against results available in the literature. Results demonstrate that PCL behaves in a brittle manner at cryogenic temperatures with more than ten times increase in Young's modulus from its value at room temperature. The results were used to predict punching forces for the design of microscale hole punching dies and for validation of a microscale hole punching model that was created with a commercially available finite element software package, deform 3D. The three parameters, yield strength, strength coefficient, and strain hardening exponent, used in Ludwik's equation to model flow stress of PCL in deform 3D were determined to be 94.8 MPa, 210 MPa, and 0.54, respectively. The predicted peak punching force from finite element simulations matched with experimentally determined punching force results.

## 1 Introduction

Development of tissues and organs from synthetic and natural scaffolds has been a persistent goal of research in the field of tissue engineering. The need for such research is pressing given that on average 20 people die every day as they wait for an organ transplant according to a recent study by the U.S. Department of Health and Human Services [1]. A synthetic 3D engineered micro-architecture that is suitable for a cell scaffold is of interest to many researchers. A well-designed synthetic scaffold has microfluidic channels that mimic natural tissue vascularity [2]. Solid freeform fabrication methods (additive manufacturing) like 3D printing, stereolithography, fused deposition modeling, and phase-change jet printing can be used to fabricate engineered porous microstructures. However, many of these methods require an internal support structure, which needs to be dissolved at the end of the fabrication process using organic solvents. Organic solvents are also used to convert raw stock polymer pellets into materials suitable for scaffolds. Residuals from these solvents can be potentially toxic to the seeded cells [3]. In addition, these methods are primarily intended for low volume patient-specific implants, rather than for high volume industrialized manufacturing, where the demands for production efficiency are much greater than contemporary approaches.

A relatively new approach to fabricating synthetic 3D tissue scaffolds with engineered microporosity is multilayer stacking of 2D porous polymeric membranes [4]. This is an attractive alternative to freeform methods due to the potential for high throughput manufacturing without the use of solvents. One method of rapidly creating 2D membranes with a multitude of holes for cell seeding is a micropunching process. In pursuit of modeling the forces involved in this new micropunching process, material properties of biodegradable and biocompatible polymers must be known below the glass transition point, which invokes clean hole punching under shear conditions.

Polycaprolactone (PCL) is an Food and Drug Administration-approved biocompatible and biodegradable material that is commonly used in the development of tissue scaffolds [5]. However, the practice of making scaffolds from PCL has not progressed from low-volume prototyping for research purposes into the realm of high-volume manufacturing, such as an automated punching process. A pilot study conducted by the authors on micropunching PCL demonstrates that microscale holes cannot be reliably punched when the material is at room temperature. The fracture strain of PCL at room temperature is too high to facilitate shearing within a typical die set clearance zone. Rather, PCL exhibits hyperplastic behavior, stretching excessively to form a bag-like structure around the punch, Fig. 1(a), or if shearing does occur it is only a partial tear, resulting in a tentacle of PCL that prevents full separation of the punched-out material.

Following unsuccessful micropunching of PCL at room temperature, a new manufacturing process, named by the authors as “cryogenic micropunching,” was developed as a part of current research [6–8]. To improve the punching (shearing) characteristics of PCL, liquid nitrogen is used to cool the material below its glass transition temperature, which is approximately −60 °C [9]. Cooling invokes a brittle material response as the polymer chains are prevented from stretching and gliding past one another during the high deformation punching process resulting in a clean hole as shown in Fig. 1(b). Development of such a manufacturing process requires knowledge of material properties of PCL under cryogenic conditions. The existing literature contains several articles that investigate material properties of PCL at room temperature [10–13]. However, there is a gap in the literature when it comes to the determination of PCL material properties at cryogenic temperatures. Hence, the motivation for the research presented here is to contribute to the literature material properties of PCL under cryogenic conditions.

The dissemination of this research on PCL material properties is relevant and contemporary as new methods are being investigated to scale engineered tissues from bench validation to commercial availability. From the authors' perspective, stacking successive layers of 2D porous films, which lend themselves well to highly automated manufacturing processes, may be an economical approach to producing multilayer tissue scaffolds. The guiding theme is to produce a scaffold that has two types of porosity: (i) holes of sufficient size and shape to act as home sites for cell seeding and growth, and (ii) holes and channels that form microvascularity when the 2D layers are stacked into a 3D construct.

Both circular and noncircular holes can be punched with silicon dies, which can be fabricated using conventional microfabrication methods, such as deep reactive ion etching [14]. Since silicon is relatively brittle, an estimate of the punching force is vital for the punch and die design. An estimation of punching forces requires knowledge of material properties of the PCL membrane during microscale punching at cryogenic temperatures.

## 2 Materials and Methods

Uniaxial compression testing was performed to obtain the true stress–strain behavior of PCL. The detailed procedure for uniaxial compression testing of polymers is given by Jerabek et al. for polypropylene [15], which closely follows the procedure given by ASTM for compression testing of plastics [16]. The compressive stress–strain relationship was used in the finite element simulation of the micropunching process to predict peak punching force. It is assumed that for PCL under cryogenic conditions, the stress–strain relationship in tension is same as the stress–strain relationship in compression for the purpose of finite element simulation discussed in this paper.

### 2.1 Sample Preparation.

Polycaprolactone pellets, with an average diameter of 3 mm, were purchased from Sigma Aldrich (Part No. 440744, Saint Louis, MO). According to the manufacturer, the molecular weight of the polymer varies from 70,000 to 90,000, with a polydispersity index of 2. The average pellet density is noted as 1.145 g/mL at room temperature, with less than 1% water impurity.

Following ASTM Standard D695-10 (compressive properties of rigid plastics) sample specimens were prepared by injection molding. For this research, a custom injection mold was designed to fabricate the PCL specimens. Since PCL is a thermoplastic, it regains its bulk material properties after the molded component is cooled. A sectional view of the injection mold is shown in Fig. 2. The injection mold assembly consists of several components: hot plate, bottom plate, specimen die, top plate, T-bolt, and 1-in. hex head screw. A thermocouple was connected to the top plate to monitor temperature, which was assumed to be close to the temperature of the molten PCL as they were in direct contact.

To create an injection molded PCL specimen, the bottom plate, specimen die, top plate, and the T-bolt were first rigidly fixed together. Then, the T bolt was partially filled with PCL pellets. The bolt was closed from the top by hand tightening the 1-in. hex head screw. Afterward, the completed assembly was placed on a hot plate, Fig. 2. Once the thermocouple temperature indicated that the assembly has reached 160 °C, it was quickly moved from the hot plate to a vise, where the bottom plate was fixed. Finally, the 1-in. hex head screw was tightened using a spanner wrench until molten PCL was observed in the relief groves, indicating successful filling of the specimen die cavity. After molding the specimen, the assembly was left to cool to room temperature, after which the unfinished specimen was removed from the die. The specimen was then trimmed and cut into smaller lengths, which were close to the final desired length required for compression testing. The rough-cut specimen was fixed in a holder to maintain the ends perpendicular to the cylindrical axis while it was hand-sanded and polished to its final length. By this method, samples with two different aspect ratios were fabricated. Throughout this paper, aspect ratio refers to the ratio of specimen length to specimen diameter.

Compression testing of PCL was conducted at two temperatures: (1) room temperature, and (2) below the glass transition temperature with the specimen fully immersed in a bath of liquid nitrogen. The room temperature tests were carried out on specimens of a fixed aspect ratio. The goal of the room temperature tests is to validate the setup and procedure by comparing the results to information available in the literature. The compression tests of PCL in liquid nitrogen were carried out for two different aspect ratios.

### 2.2 Experimental Setup.

A Universal Tensile Test machine (Instron - Series 3360, Norwood, MA) was used for the compression test of PCL. A custom-designed fixture was fabricated to accommodate liquid nitrogen for tests where the sample was below the glass transition temperature. The same fixture was used for tests at room temperature with the liquid nitrogen reservoir left empty. A force sensor of 10 kN capacity was used for all tests. Figure 3 shows the cross-sectional view of the fixture.

The ASTM standard for compression testing of rigid plastics recommends using a ball-aligned compression tool for most plastics [16]. However, this may not be necessary for plastics with a low modulus (below 3500 MPa). The elastic modulus of PCL at room temperature is expected to be very low, i.e., of the order of a few hundred MPa, but below the glass transition temperature, the modulus is expected to increase significantly, which may exceed the upper limit for not using a ball-aligned compression tool. Therefore, to keep the tests consistent with respect to ASTM recommendations, a custom ball-aligned compression tool was fabricated and used for all tests, including the tests at room temperature, Fig. 3.

The base plate, compression plunger, and force sensor adaptor were constructed from steel. As the modulus and strength of steel are orders of magnitude greater than those of PCL, fixture compliance is assumed to have a negligible effect on results. The liquid nitrogen reservoir was made from polypropylene, which acts like a thermal insulator and reduces direct contact area between the base plate and the liquid nitrogen. The hardened ceramic ball serves two purposes: (1) it helps to align the compression tool, and (2) it thermally insulates the force sensor adaptor from the compression plunger, which was in direct contact with liquid nitrogen. The base plate was rigidly fixed to the base of the tensile test machine. The liquid nitrogen reservoir was press fit with the base plate. Vacuum grease was applied between the base plate and the reservoir to avoid any liquid nitrogen leakage. The compression plunger, ceramic ball, and force sensor adaptor were put together with some vacuum grease on the ceramic ball. The vacuum grease helps to keep all three parts together without using a rigid fastener. The force sensor adaptor was rigidly fixed with the force sensor, which in turn was fixed to the moving head of the tensile test machine.

### 2.3 Procedure.

The polished PCL specimens were numbered, and their diameters and lengths were measured using a micrometer. The dimensions were measured at three locations on each specimen and the average values of length and diameter were used for calculation of the aspect ratio. The variation in measurement of diameter and length of each specimen was determined to be negligible. Two sets of specimens were prepared with approximate aspect ratios of 1.0 and 1.5. Each set had five specimens in it. The first set of specimens had both diameter and length approximately equal to 8 mm. The second set had an approximate diameter of 8 mm and length of 12 mm. The variation in length across different specimens of the same set was below 1 mm and the variation in diameter across specimens was negligible. The dimensions used in calculation of stress and strain were measured with a precision of 0.01 mm.

After taking size measurements, the specimen was placed at the center of the base plate on a circular post. The head of the tensile test machine, along with the compression tool, was then moved manually to bring the surface of the compression plunger close to the top surface of the specimen without making contact. The load indicator and the displacement indicator on the software graphical user interface were balanced at this point so that both sensors read zero. After that, the test program ran and completed the compression test automatically with limited user engagement. The compression program used in the tests has three phases:

Constant speed with displacement control

Constant preload of 10 N with force control (liquid nitrogen added in this phase)

Constant speed with displacement control

During phase I of the compression test, the crosshead moves freely with constant speed (1.0 mm/min) before touching the specimen's top surface. At the end of phase I, after touching the top surface of the specimen, the program senses the compressive load and when it becomes 10 N, it switches to phase II where the load is maintained at 10 N for 300 s. During initial trials, it was observed that the crosshead movement almost stops after about 150–200 s of adding liquid nitrogen to the reservoir. Therefore, the 300 s dwell time is included in the program to accommodate adding liquid nitrogen to the reservoir and to allow time for the temperature of the specimen and surrounding materials to be saturated. During this time, some boiling of liquid nitrogen occurs, but the reservoir is replenished by hand pouring until an equilibrium temperature is reached. Upon contact with liquid nitrogen, the PCL specimen immediately cools and shrinks in both the radial and axial (length) directions. The force sensor detects the reduction in sample length due to a decrease in the compressive load. This causes the program to reengage movement of the crosshead to maintain 10 N of preload. This keeps the specimen situated in place during boiling of the liquid nitrogen and also the recorded value of head movement during phase II helps correct for any error occurring from the changes in specimen dimensions due to cooling.

For the compression tests at room temperature, the dwell time in phase II was not utilized. At the end of the 300 s, the program automatically switches to phase III. Phase III is the actual compression phase where the machine's crosshead moves with a constant speed until it reaches an end criterion. There were two end criteria set for all specimens: either the displacement reached 4.0 mm or the compressive load reached 10 kN, which was the maximum capacity of the load sensor.

ASTM D695-10 [16] recommends a crosshead speed between 1.0 mm/min and 1.6 mm/min during compression tests for recommended specimen length of 50 mm. This results in a strain rate of approximately 0.02 min^{−1}. However, since specimens with different aspect ratios (different lengths) were used in this study, the crosshead speed was adjusted to maintain the ASTM recommended strain rate of 0.02 min^{−1}. After meeting one of the end test criteria, the compression test is automatically stopped, and the data are recorded for postprocessing and further analysis.

### 2.4 Calculation of Compressive True Stress and True Strain.

Engineering stress–strain is plotted and analyzed for calculating Young's modulus, yield strength, and strain at yield.

Figure 4 shows a typical stress–strain curve for a rigid plastic. The toe region, indicated by line segment *ad*, does not provide useful material property information; rather it is an artifact caused by slack, misalignment, or seating of the specimen. Therefore, Young's modulus is obtained by calculating the slope of the linear zone, line segment *de*. The error due to the toe region is corrected by creating a hypothetical zero at point *b*, which is obtained by extending the linear region *de* and intersecting it with the strain axis. All strain and yield offset values are measured from the new corrected zero at point *b*. Figure 4 also shows an offset strain at point *c* for obtaining the yield strength. A 0.2% offset strain is used to calculate the yield strength in this study. Any deformation beyond the yield point is considered a combination of elastic and plastic deformation.

*f*. In this study, the plastic deformation zone is explicitly determined by isolating it from the total stress–strain curve. First, the true stress and true strain values are obtained from the engineering stress and strain values. The following two equations from ASTM E646-07 are used to calculate true stress and true strain (subscript

*t*) from engineering stress and engineering strain (subscript

*e*) [17]:

The true yield stress $\sigma t,Y$ and true yield strain $\epsilon t,Y$ values corresponding to the engineering yield strength and engineering yield strain for each specimen are obtained. All data points beyond the yield point are then translated to the origin by subtracting $\sigma t,Y$ from the true stress values and $\epsilon t,Y$ from the true strain values. The translated values of true stress and true strain values are then processed to fit a strain hardening model.

For compression tests at room temperature, only the engineering stress–engineering strain curve was plotted as these data were only used for validation of the fixture and not for finite element modeling of the cryogenic micropunching process. For tests below the glass transition temperature of PCL, the true stress–true strain curves were obtained for two different aspect ratios (1.0 and 1.5) and then, extrapolated for a reciprocal of aspect ratio, i.e., $D/L$ ratio of zero to obtain the effective theoretical true stress–true strain curve to be used in finite element modeling [15].

### 2.5 Finite Element Modeling of Micropunching Process.

deform v10.2.1 (Scientific Forming Technology Corporation, Columbus, OH) was used to develop a finite element model for the cryogenic micropunching process of PCL. In the actual micropunching experiment, the female die base was approximately 25 mm by 25 mm square and the strip of PCL film was approximately 12 mm wide by 125 mm long. However, in the FE model, a 1 mm by 1 mm section of the female die and workpiece was considered to avoid unnecessarily high number of elements during meshing. The male die was a cylinder with a 200 *μ*m diameter and a 400 *μ*m length. Due to orders of magnitude difference in moduli of steel dies and the PCL workpiece, the dies were assumed to be perfectly rigid. Due to symmetry in geometry of the micropunching model for circular holes, a quarter model was used to reduce computational time as shown in Fig. 5.

Due to high deformation nature of the micropunching process, adaptive remeshing was used with tetrahedron elements for the finite element simulation. Besides adaptive remeshing, element deletion was used based on normalized Cockroft and Lantham damage model with critical damage coefficient of 0.5 to model fracture in the workpiece. The deleted elements lose all load-bearing capacity upon deletion triggering redistribution of the load among the other elements. Several convergence tests were carried out to obtain the optimal values of smallest element size, solution increment step size, work piece dimensions, and boundary conditions. The smallest element size considered for the 70 *μ*m film thickness was set to be 4.0 *μ*m. However, after meshing, the measured smallest element side length was 2.8 *μ*m. The solution increment step (incremental movement of the punch into the workpiece) was set at 0.10 *μ*m, which is approximately 20 times smaller than the smallest element size. This exceeds the requirement that the solution increment step be at least 10 times smaller than element size as recommended in the deform 3D user manual to avoid large deformation of the elements, which can result in numerical instability.

The workpiece dimensions were optimized to have a minimum number of elements without losing accuracy. The high deformation zone lies within the die clearance region. A pilot study indicated that small variations in the workpiece dimensions did not have a significant effect on the calculated peak punching force. Similarly, to mimic the experimental conditions, tension boundary conditions were applied to the workpiece and compared to simulations with fixed boundary conditions (two sides fixed and two sides free). There was no significant difference in the calculated maximum punching force when considering the various workpiece boundary conditions. Hence, fixed boundary conditions were used to minimize complexity and to reduce computational time.

## 3 Results

Engineering stress and engineering strain, resulting from compression tests of five PCL samples of aspect ratio 1.5 at room temperature, are plotted in Fig. 6. Note that the toe region of the stress–strain curve is not corrected as raw data are shown in Fig. 6. The zero of the strain axis needs to be corrected for calculation of the yield strength as recommended by ASTM D695-10. Similar steps are followed for all specimens to calculate Young's modulus, yield strength, and yield strain. The results for material properties of PCL determined at room temperature are summarized in Table 1. For compressive testing of specimens below the glass transition temperature, i.e., in boiling liquid nitrogen, an additional step of correction is added to take into account shrinkage of specimens due to cooling.

The yield strength was obtained by following the steps recommended by ASTM D695-10. The procedure for calculating the strength coefficient and the strain hardening exponent is given in ASTM E646-07. First, the plastic deformation region beyond the yield point was isolated for each specimen. Then, the data were processed through a curve fitting tool using a nonlinear least square method to obtain the applicable power law. For all the specimens tested in this study, the *R*-square values obtained for the appropriateness of the fit ranged from 0.8617 to 0.9896. Finally, the parameters were obtained for each specimen and their average values were calculated. Results for material properties of PCL below its glass transition temperature, i.e., in liquid nitrogen for aspect ratios 1.0 and 1.5, are summarized in Table 2. Plots of engineering stress–strain and flow stress for PCL in liquid nitrogen, for an aspect ratio of *L/D* equal to 1.0, are given in Figs. 7 and 8, respectively.

For large deformation finite element simulations in deform 3D, only three parameters are needed for the material model while using Ludwik's equation for flow stress: (1) yield strength, (2) strength coefficient, and (3) strain hardening exponent. As shown herein, these parameters are obtained experimentally for two aspect ratios. However, to use these parameters in a simulation, the effective theoretical values must be obtained by extrapolating the reciprocal of aspect ratio (*D/L*) to zero, i.e., a specimen of infinite length and a finite diameter. The extrapolated values of yield strength, strength coefficient, and the strain hardening exponent, for use in the FE simulation, are approximately 94.8 MPa, 210 MPa, and 0.54, respectively. Similarly, the extrapolated value of Young's modulus is 4160 MPa. The experimentally determined flow stress for reciprocal aspect ratios (*D/L*) of 1.0 and 2/3, and the extrapolated value for *D/L* equal to zero, are plotted in Fig. 9.

Finite element simulation was performed for micropunching 200 *μ*m holes in 70 μm polycaprolactone film with an approximate die clearance of 17.1%. The peak punching force obtained from the simulation was 5.74 N.

## 4 Discussion

The material properties of PCL at room temperature are obtained in order to validate the fixture and the test procedure. Young's modulus obtained experimentally is 323.3 ± 5.1 MPa, which compares well with what was obtained by Eshraghi and Das [13], i.e., 317.1 ± 3.9 MPa. Also, the experimentally obtained Young's modulus matches well with what is reported by other researchers [10–12]. Similarly, the compressive Yield strength reported by Eshraghi et al. is 10.3 ± 0.2 MPa [13], which is close to the experimentally obtained yield strength of 9.2 ± 0.7 MPa. The yield strain obtained by Eshraghi et al. is 0.037 ± 0.002, which also matches closely with the experimentally obtained yield strain of 0.031 ± 0.002. These comparisons validate the fixture and the procedure used to obtain compressive material properties at room temperature.

Jerabek et al. have used linear extrapolation of parameter values obtained from specimens of different aspect ratios to estimate effective value of the parameters at *D/L *=* *0 [15]. In the current research, specimens with two different aspect ratios are used, which is sufficient for linear extrapolation of the parameters. Using specimens with more aspect ratios will result in more accurate estimation of the parameters and reduced variance. Note that caution should be used when extrapolating parameters with significant variance. In the current research, out of the three parameters needed for large deformation simulations in deform 3D, experimentally obtained yield strength and strength coefficient have significant variances, with the coefficient of variation changing with aspect ratio. Although there is no direct association between variance and aspect ratio, it is a conservative approach to extrapolate variances in these parameters for a reciprocal aspect ratio *D/L* equal to zero. Consequently, this method creates an upper bound and a lower bound for the effective flow stress curve.

The FE simulation on deform can be run with mean, upper bound, and lower bound values of the flow stress and results can be compared to see which one best represents the actual material properties. It can be seen from Table 2 that the variance of yield strength and the strain hardening exponent are decreasing as *D/L* is reduced from 1.0 to 2/3. Therefore, upon linear extrapolation of the upper bound and the lower bound values of these parameters, they will converge before reaching *D*/*L* equal to zero, which may result in negative variances and therefore can be neglected. However, the variance of the strength coefficient diverges as the reciprocal aspect ratio is reduced. Therefore, this parameter will have a finite upper bound and a lower bound when extrapolated to *D/L* equal to zero as shown in Fig. 10. Upon using the extrapolated strength coefficient, its upper bound and lower bound values are found to be 250 MPa and 170 MPa, respectively. The flow stress is plotted for all three values of the strength coefficient in Fig. 11.

Peak punching force results of micropunching FE simulations using PCL properties from current research match with the experimentally obtained punching force results. From the experiments, the peak punching force for micropunching 200 *μ*m holes in 70 *μ*m thick polycaprolactone film with an approximate die clearance of 17.1% was determined to be 5.3 ± 0.36 N for a sample size of 41. From finite element simulation, the peak punching force for the same case was determined to be 4.95 N, 5.74 N, and 6.22 N using the lower bound, mean, and upper bound of flow stress curves, respectively, from Fig. 11.

## 5 Conclusion

In this paper, experimental methods were presented to determine material properties of polycaprolactone under cryogenic conditions. Samples with two different aspect ratios were tested under compression in boiling liquid nitrogen. Material properties of PCL under compression were also obtained at room temperature and compared with data available in the literature. The most important results are:

PCL material properties at room temperature matched closely with data available in the literature for Young's modulus, yield strength, and yield strain, thus validating the experimental set up and procedure.

All parameters were obtained experimentally to calculate flow stress of PCL in liquid nitrogen using Ludwik's equation:

Yield strength: 94.8 MPa

Strength coefficient: 210 MPa

Strain hardening exponent: 0.54

Peak punching force obtained from experiments matches with the predicted force from finite element simulations using the experimentally determined cryogenic material properties of polycaprolactone.

## Funding Data

School of Engineering at Tufts University (No. 04-2103634, Funder ID: 10.13039/100008090).

## Nomenclature

- $D$ =
specimen diameter at room temperature

- $DLN$ =
specimen diameter in liquid nitrogen

- $F$ =
applied force

- $K$ =
strength coefficient

- $L$ =
specimen length at room temperature

- $LLN$ =
specimen length in liquid nitrogen

- $n$ =
strain hardening exponent

- $Y$ =
yield strength

- $\alpha $ =
coefficient of thermal expansion

- $\Delta L$ =
change in specimen length

- $\Delta T$ =
change in temperature

- $\epsilon e$ =
engineering strain

- $\epsilon p$ =
plastic strain

- $\epsilon t$ =
true strain

- $\epsilon t,Y$ =
true yield strain

- $\sigma e$ =
engineering stress

- $\sigma f$ =
flow stress

- $\sigma t$ =
true stress

- $\sigma t,Y$ =
true yield stress