Chapter IV: Process Zone Smoothing of Heterogeneous Effects in Tape Peeling 64
4.3 Simulation
state, E-F. The rapidly decreasing load from C-D indicates that the brittle case is affected by the step down in film thickness, it is likely that the rapid crack propa- gation that follows the pinning results in slack in the system that must be removed, obscuring this phenomenon.
4.3 Simulation
Figure 4.7: Peeling of a PET/epoxy tape from an acrylic substrate with a step down heterogeneity; a. Schematic of the tape; b. Peel force versus tape displacement. A-F show images of the peel front (marked with an arrow) corresponding to the loads in b.
Figure 4.8: Geometry of the tape and simulation parameters for modeling the heterogeneous adhesive tape peeling from a rigid substrate.
Figure 4.9: Traction separation laws and associated parameters used in ABAQUS simulations.
ness and the size of the cohesive zone affect the peak and valley loads in peeling heterogeneous tapes.
Results
Figures 4.10 and 4.11 show representative results of the tape peeling simulations.
These simulations are for an adhesive energy, Gc = 25 N/m and δf = 0.1. Peel force and the cohesive zone size are plotted as a function of time (applied vertical displacement). The peel force reaches a steady state value in the homogeneous section of the tape as it approaches the heterogeneity at A in Fig. 4.10. The load begins to rise and the size of the cohesive zone increases as the crack front reaches the heterogeneity at B-C. The load peaks at C, and the cohesive zone has penetrated well into the heterogeneous region of the tape. The load begins to decrease and as the crack front passes through the heterogeneity at D the stress is more evenly distributed through the deadhered portion of the tape. The load decreases rapidly as the front reaches the other side of the heterogeneity at E-F and the load is once again
concentrated in the uniform thinner portion of the tape. The size of the cohesive zone returns to its original value. The tape reaches the same steady state value at F as in the beginning at A as the peel angle returns to 90 degrees.
Figure 4.11 shows additional detail of the variation of the cohesive zone size with peel force. The size of the cohesive zone takes two constant values during crack propagation associated with the thickness of the tape above the crack front. The size of the cohesive zone does not begin to increase until after the peel force has reached roughly half of its peak value. The peak load coincides with the maximum size of the cohesive zone.
The beginning of the cohesive zone size increase varies with the size of the cohesive zone. Figure 4.12a-d show selected load and cohesive zone size results forδf = 0.05.
The beginning of the cohesive zone size increase is marked with a dashed vertical line. In the simulations, as the crack approaches the heterogeneity it is pinned and the load begins to increase while the cohesive zone stays the same size or reduces slightly. At some load prior to the peak, the cohesive zone size begins to increase which coincides with the beginning of peel front penetration into the heterogeneous region. The location of this increase relative to the peak load varies with adhesive strength,G. In order to quantify this variation, the increase load is normalized by calculating the ratio of the load at the onset of increasing cohesive zone size to peak load:
Pinc−Phom
Ppeak −Phom
, (4.3)
where Pinc is the peel force when the cohesive zone size begins to increase, Ppeak
is the peak peel force, and Phom is the homogeneous peel force. Figure 4.12e plots onset of the increase in cohesive zone size versus the size of the cohesive zone in the initial homogeneous region. There is a correlation between the size of the initial cohesive zone and the onset of peel front penetration into the heterogeneous region;
as the cohesive zone size increases, the peel front penetrates into the heterogeneous region at a proportionally lower load relative to the peak load. However, Fig.
4.12f plots onset of the increase in cohesive zone size versus the normalized peak force and does not demonstrate nearly as clear of a correlation between the two quantities. For individual values of adhesion strength, G, higher peak loads occur with later penetration into the heterogeneous region. However, the onset of the increase in cohesive zone size depends on the adhesion strength as well, and lower values of adhesion strength correspond with earlier onsets of penetration into the heterogeneous region.
Figure 4.10: Normalized peel force and cohesive zone size are plotted as a function of time. Contour of plots of von Mises stress are plotted at various stages of the peeling process (A-F). Parametric values, G=25 N/m,δf = 0.1.
Figure 4.11: Normalized peel force and cohesive zone size are plotted as functions of time forG=25 N/m; a-c: δf = 0.025, 0.05, 0.10.
Figure 4.13 shows the normalized peak loads (PPpeak
hom) versus normalized cohesive zone size and Fig. 4.14 shows the normalized valley loads (PPvalley
hom ) versus normalized cohesive zone size for all simulations. The cohesive zone size is normalized against λcalculated for the simulations according to Eq.4.1. Fig. 4.13 indicates that smaller normalized cohesive zone sizes are related to higher peak loads. Fig. 4.14 shows that smaller normalized cohesive zone size is related to lower normalized minimum (valley) loads.