Adhesive Energy Release Rate

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Adhesive energy release rate (Author: Prof. Dr. Michael Nase)

General

To characterize the peel behaviour of plastic or metal films, as well as metal-plastic composites, the T-peel test based on ASTM D 1876 “Standard Test Method for Peel Resistance of Adhesives (T-Peel Test)” and the fixed-arm peel test based on the ESIS TC4 standard proposal “Peel Testing of Flexible Laminates” are available.

The methods of linear-elastic fracture mechanics are used for the material-specific description of the peel process, which make it possible to derive parameters with a high information content, such as the energy release rate. Such parameters can then be advantageously used to evaluate the application behaviour of film systems.

Evaluation of the peel behaviour of sealed films using fracture mechanics parameters

The adhesive energy release rate G_aIc reflects only the amount of energy required to separate two sealed films (see: sealed seam) and is applicable to elastic-plastic material behaviour.

The adhesive energy release rate G_aIc is calculated according to Eq. (1).

$G_{aIc}={\frac {U_{a}}{WL}}={\frac {E_{G}-E_{d,P}-E_{d,S}}{WL}}$

(1)

with

Ua		direct adhesion energy
EG		total peel energy
Ed,P		deformation energy of the peel arm
Ed,S		deformation energy of the peeled seal seam
W		width of the seal seam
L		length of the sealed seam

The total peel energy E_G corresponds to the area under the peel force–fracture path diagram (also known as the peel curve; see Fig. 1). The deformation energy of the peel arms E_d,P is the energy absorbed by the peel test specimen in the run-up to the actual peel process. In the peel force–fracture path diagram, the start of the peel process is marked by a change in the rise of the peel curve at l_d,P, so that the deformation energy of the peel arm E_d,P corresponds to the area under the peel curve up to l_d,P. It is assumed that all deformations that occur after l_d,P as a result of the increase in force are absorbed by the peeled seal and no longer by the peel arm, since the peeled seal has a greater tendency to deform than the peel arm.

Fig. 1:

Representation of the ideal peel curve, i.e., without deformation of the seal seam (dotted curve) compared to the actual peel curve (continuous curve); ld,P – start of the peel process; lB – fracture path; lB,i – fracture path in the ideal peel test; Ed,P – deformation energy of the peel arms; Ed,S – deformation energy of the peeled seal seam and EG,i – ideal total peel energy with permitted deformation of the peel arm

The deformation energy of the peeled seal seam E_d,S is thus calculated by subtracting the ideal total peel energy E_G,i, i.e. the total peel energy in the presence of an ideal seal seam with infinite modulus of elasticity (dotted peel curve), from the total peel energy E_G according to Eq. (2). It is assumed that the peel arm can also absorb deformations in the presence of an ideal seal seam.

$E_{d,S}=E_{G}\,-\,E_{G,i}$

(2)

It is assumed that the deformation energy of the peeled seal seam E_d,S is not influenced by the deformation energy of the peel arms E_d,P, so that the two deformation processes, the deformation of the peel arms and the deformation of the seal seam, occur sequentially. The exact numerical value of the ideal total peel energy E_G,i cannot be calculated, but the deformation energy of the peeled seal E_d,S can be approximated using Eq. (3).

$E_{d,S}=E_{G}-E_{G,i}\approx (l_{B}-l_{B,i})F_{peel}$

(3)

with

lB		fracture path in the real peel test
lB,i		fracture path in the ideal peel test, i.e., without deformation of the peeled seal seam

The fracture path in the ideal peel test is calculated for the T-peel test according to Eq. (4) and for the fixed-arm peel test according to Eq. (5).

$l_{B,i}=l_{d,P}\,+\,2W$

(4)

mit

ld,P

start of the peeling process

$l_{B,i}=l_{d,P}\,+\,(W-W\cos \theta )$

(5)

with

$\theta$

peel angle

Application example for a PE-LD/iPB-1 peel system

The adhesive energy release rate in the low-density polyethylene peel system blended with isotactic polybutene-1 (abbreviation: PE-LD/iPB-1) is significantly influenced by the blend composition. As a result of the T-peel test, Fig. 2 shows the adhesive energy release rate as a function of the iPB-1 content. The adhesive energy release rate decreases exponentially with increasing iPB-1 content. This dependence is used as a basis for the targeted adjustment of the PE-LD/iPB-1 peel system using fracture mechanical values (see: fracture mechanical testing).

Fig. 2:

Influence of the mass content of iPB-1 on the adhesive energy release rate

See also

• Peel properties of peel systems
• Fixed-arm peel test
• T-peel test
• Peel behaviour – modelling

References

• Kinloch, A. J., Lau, C. C, Williams, J. G.: The Peeling of Flexible Laminates. Intern. J. of Fracture 66 (1994) 45–70 DOI: https://doi.org/10.1007/BF00012635
• Nase, M., Langer, B., Müller, C., Grellmann, W.: Bruchmechanische Kennwertermittlung im T-Peeltest und im Fixed-Arm Peeltest. In: Frenz, H., Grellmann, W. (Eds.): 26. Tagung Werkstoffprüfung „Herausforderung neuer Werkstoffe an die Forschung und Werkstoffprüfung“, Berlin (2008) Proceedings pp. 223–228, ISBN 978-3-00-026399-6 (see AMK-Library under A 10) Download als pdf
• Nase, M., Langer, B., Baumann, H. J., Grellmann, W.: Fracture Mechanics on Polyethylene/Polybutene-1 Peel Films. Polymer Testing 27 (2008) 1017–1025 DOI: https://doi.org/10.1016/j.polymertesting.2008.09.002
• Nase, M.: Charakterisierung von polymeren Peelsystemen durch Anwendung neuartiger Methoden der experimentellen Bruchmechanik. Habilitation, Otto-von Guericke-Universität Magdeburg, Shaker Publishing (2022) (ISBN 978-3-8440-8635-5; see AMK-Library under B 2-3), as pdf