A Note on Transients in Rate-dependent Adhesion of Gelatin

Abstract The transient behavior of rate-dependent adhesion in poro-viscoelastic contact is more complex than crack propagation in Mode I opening due to time-dependent material behavior, crack acceleration from nonlinear kinematics, and variation in contact radius. This study revisits our previous experiment, where a spherical glass probe is unloaded on flat gelatin, and investigates crack velocity ( $$V_\text {c}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>V</mml:mi> <mml:mtext>c</mml:mtext> </mml:msub> </mml:math> ) and energy release rate (ERR). For a given unloading rate, $$V_\text {c}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>V</mml:mi> <mml:mtext>c</mml:mtext> </mml:msub> </mml:math> increases monotonically by one order of magnitude, and the wide range of unloading rates ensures that $$V_\text {c}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>V</mml:mi> <mml:mtext>c</mml:mtext> </mml:msub> </mml:math> spans 3–4 orders of magnitude. ERR remains almost unchanged at 2–3 times the thermodynamic work of adhesion at slow rates. At fast rates, ERR initially increases to 4–8, then decreases until full separation. We hypothesize that the decreasing ERR trend is due to finite-size effects: the hysteretic energy dissipation zone grows with crack acceleration, while the material volume decreases during peeling. To explain these trends and the finite-size effect, we adapt de Gennes’ viscoelastic crack propagation model, modifying it to account for crack acceleration and the reduction in contact radius. Under the given time scales (peeling time and viscoelastic relaxation time) and length scales (crack tip radius and initial contact radius), we simulate the evolution of ERR as peeling proceeds and compare the results with experimental data. The model’s results show good qualitative agreement with the experiments. Finally, we discuss the model’s limitations, assumptions, and directions for future research.