21st European Conference on Fracture, ECF21, 20-24 June 2016, Catania, Italy

An investigation of cutting resistance in stretched polymer films

T. M. Millara, Y. Patela, H. Wangb, L. Changb, D. S. Balinta, J. G. Williamsa,b

aDepartment of Mechanical Engineering, Imperial College London, London, SW7 2AZ

bAero, Mechanical and Mechatronics Eng Department, University of Sydney, Australia

Abstract

An investigation is made into the fracture properties of polymer films and laminates under cutting by a sharp tool and lateral tension under pure shear conditions. The method involves use of a sharp razor blade applied to the crack tip of polymer films which are also stretched orthogonal to the direction of the blade. The reaction force is measured as the cutting tool cuts the material and the force from applying a lateral strain is measured. The analysis and tests assume quasi-static conditions. The method is applied to a polyester film and three polyester laminates.

Steady-state cutting forces are observed from cutting tests and loads at crack initiation are observed from lateral stretching tests. With fracture mechanics analysis the energy contributions from cutting and tearing are used to determine apparent fracture properties from the experimental results. It is observed that the cutting and tearing tests yield similar fracture toughness properties for the three tested polyester laminates, despite the different crack tip geometry at the point of crack growth. However, significantly larger fracture toughness values are measured from tearing tests versus cutting tests for the tested polyester film.

© 2016 The Authors. Published by Elsevier B.V.

Peer-review under responsibility of the Scientific Committee of ECF21.

Keywords: cutting; polymer; film; fracture.

Introduction

The use of cutting tests can be an effective alternative for when standard fracture toughness tests cannot be used. A common way to measure fracture toughness of polymers is by critical or testing, which have established standards. However, it can be difficult to determine toughness using the traditional methods such as when polymers have high toughness, low modulus, low yield stress or when the material is difficult to shape. Other common problems are stable crack growth prior to instability or crack tip blunting, which are a nature of the fracture process. A popular approach has been the use of J-integral testing which was initially developed for metals (ASTM E1820-08). This method has also been applied to polymers (ASTM D6068-96) and has been favoured for testing low density polyethylenes by Hashemi and Williams (1986). One alternative fracture toughness testing method is to use cutting or machining tests. Patel et al. (2009) have explored machining tests to determine fracture toughness in tough polymers. For rubber, experimental work on stretched natural rubber vulcanizate sheet has been used to determine fracture toughness properties by Lake and Yeoh (1978). These involved use of a razor blade applied to a pre-cracked rubber sheet loaded laterally.

This method of cutting with a sharp tool with lateral stretching is investigated for selected polymer films with thickness between 15 µm and 70µm. The investigation hopes to explore the value of such a method to determine fracture toughness properties for polymer films and to understand the criteria for fracture initiation.

Nomenclature

Cutter force

Width

Length

Thickness

Young’s modulus

Energy associated with cutting

Strain energy release rate

Apparent fracture toughness

Stress intensity factor

Energy associated with tearing

Strain energy density

Stress

Experimental method

Cutting by a sharp razor blade is applied directly to the crack tip of a specimen of thickness , unstrained width and length under pure shear conditions. The specimen is held at a fixed width by two clamps while the razor blade is moved at a constant rate vertically towards a pre-made crack tip in the specimen. The reaction force on the blade is measured using a piezo-electric load cell. The experimental setup is shown schematically in Fig 1. The razor blade material is stainless steel with a tip radius of 2 µm. The cutting rates used are such that quasi-static conditions can be assumed.

Fig. 1. Schematic diagram of cutting stretched polymer film by a razor blade.

Constant rate cutting

Figure 2 shows an example force-displacement trace obtained from a typical constant rate cutting test. The figure shows a transient peak when the blade initially contacts the specimen. But a steady-state cutting force is soon reached as the cutting process continues. An average force is calculated from the steady-state region of the trace and the cutting process continues until the end of the specimen is reached.

Fig. 2. Typical load trace from cutting of stretched polymer film showing the steady-state cutting region and point of first contact.

Tearing

A lateral stretching test is also conducted to determine the tearing energy required to cause fracture under absence of any cutting. The specimen is strained under pure shear conditions until the material begins to fracture at a pre-made crack tip orthogonal to the direction of applied strain. A camera attached to the testing rig is used to monitor the crack tip region to determine when fracture initiates. At fracture initiation the reaction force is noted which is used to calculate the tearing energy. A typical trace from the experiment is shown in Fig 3. The figure shows the force increasing as the material is loaded laterally until a maximum load is reached. The load then falls as a crack propagates through the material.

Fig. 3. Typical load trace from stretching polymer film showing the maximum obtained force.

Analysis

Analysis on the cutting of stretched rubber sheet containing a pre-crack by a sharp blade has been done by Lake and Yeoh (1978). The tests use a pure shear specimen which is loaded laterally before a cutting implement is applied at the crack tip. The available energy for fracture is a combination of energy associated with the application of the cutting implement and the lateral load. The total applied energy, , available for fracture per unit area of increased fracture surface can be given by,

(1)

The tearing energy, , is due to lateral loading of the specimen and is an energy term associated with the blade cutting force. For pure shear specimens the tearing energy and energy associated with the blade cutting force are,

(2)

(3)

The force on the cutter is and is the unstrained thickness of the specimen. is the strain energy density and is the unstrained width of the specimen. The tearing energy can be calculated using,

(4)

The bulk stress is and is the material Young’s modulus.

The results for unfilled natural rubber vulcanizate are shown in Fig 4 from the experiments by Lake and Yeoh. The results show a linear region for low values where is constant. But after a critical the total energy required to cause fracture increases dramatically with increased crack blunting.

Fig. 4. Experimental results from Lake and Yeoh (1978) for cutting of stretched rubber. Pure shear shown as •, other symbols are for different test geometries.

Experimental results

The following sections show results obtained using a similar method of cutting and tearing but for selected polymer films. The following four polymers were tested: polyester film (3M 9757) and three polyester laminates (3M 9730, 9733 and 9736). The results are summarised in Table 1.

Table 1. Results from cutting and tearing tests on selected polymer films and laminates.

Material	t (mm)	E (GPa)	G from cutting (kJ/m2)	G from tearing (kJ/m2)
3M 9757	0.015	4.0	3.5 ± 0.2	6.0 ± 0.5
3M 9730	0.070	1.1	2.4 ± 0.2	2.3 ± 0.3
3M 9733	0.050	1.4	1.8 ± 0.2	2.1 ± 0.2
3M 9736	0.040	1.6	3.8 ± 0.2	3.6 ± 0.3

Results for polyester film 9757

The first set of experimental data is for polyester film of thickness 0.015 mm. Film strips with a gauge length of 130 mm and a width of 10 mm were tested at a speed of 0.16 mm/s. The measured elastic modulus was 4.0 GPa and the yield stress was 70 MPa.

Figure 5 (a) shows the load trace for the case of cutting with no lateral force and Figure 5 (b) from tearing with no contribution from a cutting implement. For the cutting tests specimen sizes with of 25 mm and of 152 mm were used. The steady-state cutting force was measured to be 0.053 N at a rate of 1.6 mm/s. For the tearing tests specimen sizes with of 25 mm, of 140 mm and initial crack length of 15 mm were used. The load at fracture from tearing was measured to be 82 N. For the case of only cutting, the calculated was 3.5 kJ/m2. For the case of only tearing, the calculated was 6.0 kJ/m2.

Fig. 5. (a) Load trace from cutting polyester film (9757) without lateral tension; (b) Load trace from tearing without cutting.

Results for polyester laminate 9730

The same method was applied to a polyester laminate (3M 9730) with thickness 0.070 mm. Film strips with a gauge length of 120 mm and a width of 20 mm were tested at a speed of 0.16 mm/s. The measured elastic modulus was 1.1 GPa and the yield stress was 18 MPa.

Figure 6 (a) shows the load trace for the case of cutting with no lateral force and Figure 6 (b) from tearing with no contribution from a cutting implement. For the cutting tests specimen sizes with of 23 mm and of 140 mm were used. The steady-state cutting force was measured to be 0.167 N determined at a rate of 1.6 mm/s. For the tearing tests specimen sizes with of 25 mm, of 140 mm and initial crack length of 15 mm were used. The load at fracture from tearing was measured to be 106 N. For the case of only cutting, the calculated was 2.4 kJ/m2. For the case of only tearing, the calculated was 2.3 kJ/m2.

Fig. 6. (a) Load trace from cutting polyester film (9730) without lateral tension; (b) Load trace from tearing without cutting.

Results for polyester laminate 9733

The same method was applied to a polyester laminate (3M 9733) with thickness 0.050 mm. The measured elastic modulus was 1.38 GPa and the yield stress was 24 MPa.

Figure 7 (a) shows the load trace for the case of cutting with no lateral force and Figure 7 (b) from tearing with no contribution from a cutting implement. For the cutting tests specimen sizes with of 23 mm and of 140 mm were used. The steady-state cutting force was measured to be 0.092 N determined at a rate of 1.6 mm/s. For the tearing tests specimen sizes with of 25 mm, of 140 mm and initial crack length of 15 mm were used. The load at fracture from tearing was measured to be 86 N. For the case of only cutting, the calculated was 1.8 kJ/m2. For the case of only tearing, the calculated was 2.1 kJ/m2.

Fig. 7. (a) Load trace from cutting polyester film (9733) without lateral tension; (b) Load trace from tearing without cutting.

Results for polyester laminate 9736

The same method was applied to a polyester laminate (3M 9736) with thickness 0.040 mm. Film strips with a gauge length of 111 mm and a width of 20 mm were tested at a speed of 0.16 mm/s. The measured elastic modulus was 1.61 GPa and the yield stress was 32 MPa.

Figure 8 (a) shows the load trace for the case of cutting with no lateral force and Figure 8 (b) from tearing with no contribution from a cutting implement. For the cutting tests specimen sizes with of 23 mm and of 140 mm. The steady-state cutting force was measured to be 0.167 N determined at a rate of 1.6 mm/s. For the tearing tests specimen sizes with of 25 mm, of 140 mm and initial crack length of 15 mm. The load at fracture from tearing was measured to be 85 N. For the case of only cutting, the calculated was 3.8 kJ/m2. For the case of only tearing, the calculated was 3.6 kJ/m2.

Fig. 8. (a) Load trace from cutting polyester film (9736) without lateral tension; (b) Load trace from tearing without cutting.

Conclusion

The fracture toughness properties of a polyester film and three polyester laminates have been investigated using both cutting and tearing tests. It has been shown that both test methods measure similar fracture toughness properties for the three polyester laminates. This is unlike existing experimental results that have been published for stretched rubber sheets. However, significantly greater fracture toughness values were measured for the polyester film from tearing tests versus cutting tests.

Acknowledgements

The authors acknowledge financial support from EPSRC.

References

Hashemi, S., Williams, J. G., 1986. A fracture toughness study on low density and linear low density polyethylenes. Polymer, 27(September 1985), 384–392.

Patel, Y., Blackman, B. R. K., Williams, J. G., 2009. Determining fracture toughness from cutting tests on polymers. Engineering Fracture Mechanics, 76(18), 2711-2730.

Lake, G. J., Yeoh, O. H., 1978. Measurement of rubber cutting resistance in the absence of friction. International Journal of Fracture, 14(5), 509-526.

* Corresponding author. Tel.: +44-203-608-2662.

E-mail address: tino.millar@imperial.ac.uk