Browsing by Author "Mukherjee, Bikramjit"
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- Debonding of confined elastomeric layer using cohesive zone modelMukherjee, Bikramjit; Dillard, David A.; Moore, Robert Bowen; Batra, Romesh C. (Elsevier, 2016-04-01)Wavy or undulatory debonding is often observed when a confined/sandwiched elastomeric layer is pulled off from a stiff adherend. Here we analyze this debonding phenomenon using a cohesive zone model (CZM). Using stability analysis of linear equations governing plane strain quasi-static deformations of an elastomer, we find (i) a non-dimensional number relating the elastomer layer thickness, h, the long term Young's modulus, E∞, of the interlayer material, the peak traction, Tc, in the CZM bilinear tractionseparation (TS) relation, and the fracture energy, Gc, of the interface between the adherend and the elastomer layer, and (ii) the critical value of this number that provides a necessary condition for undulations to occur during debonding. For the elastomer modeled as a linear viscoelastic material with the shear modulus given by a Prony series and a rate-independent bilinear TS relation in the CZM, the stability analysis predicts that a necessary condition for a wavy solution is that Tc2h=GcE∞ exceed 4:15. This is supported by numerically solving governing equations by the finite element method (FEM). Lastly, we use the FEM to study three-dimensional deformations of the peeling (induced by an edge displacement) of a flexible plate from a thin elastomeric layer perfectly bonded to a rigid substrate. These simulations predict progressive debonding with a fingerlike front for sufficiently confined interlayers when the TS parameters satisfy a constraint similar to that found from the stability analysis of the plane strain problem.
- Edge Debonding in Peeling of a Thin Flexible Plate From an Elastomer Layer: A Cohesive Zone Model AnalysisMukherjee, Bikramjit; Batra, Romesh C.; Dillard, David A. (2016-11-07)A cohesive zone modeling (CZM) approach with a bilinear traction-separation relation is used to study the peeling of a thin overhanging plate from the edge of an incompressible elastomeric layer bonded firmly to a stationary rigid base. The deformations are approximated as plane strain and the materials are assumed to be linearly elastic, homogeneous, and isotropic. Furthermore, governing equations for the elastomer deformations are simplified using the lubrication theory approximations, and those of the plate with the Kirchhoff–Love theory. It is found that the peeling is governed by a single nondimensional number defined in terms of the interfacial strength, the interface fracture energy, the plate bending rigidity, the elastomer shear modulus, and the elastomeric layer thickness. An increase in this nondimensional number monotonically increases the CZ size ahead of the debond tip, and the pull-off force transitions from a fracture energy to strength dominated regime. This finding is supported by the results of the boundary value problem numerically studied using the finite element method. Results reported herein could guide elastomeric adhesive design for load capacity and may help ascertain test configurations for extracting the strength and the fracture energy of an interface from test data.
- Effect of confinement and interfacial adhesion on peeling of a flexible plate from an elastomeric layerMukherjee, Bikramjit; Batra, Romesh C.; Dillard, David A. (2016-09)The finite element method and a cohesive zone model are used to analyze plane strain interfacial debonding of an elastomeric layer from an overhanging deformable plate when it is peeled off by applying a normal displacement at the edge of the overhang. The commercial software, ABAQUS, is employed in this work that is focused on understanding the collective role of the following two non-dimensional parameters: (i) the confinement parameter, α, defined in terms of the flexural rigidity of the plate, and the modulus and the thickness of the interlayer, and (ii) the adhesion parameter, φ, defined in terms of the cohesive zone parameters and the modulus to thickness ratio of the interlayer. The interfacial adhesion is characterized by a bilinear traction-separation (TS) relation. Numerical experiments reveal that when α is greater than αc , damage initiates at an interior point on the interface and at the interface corner on the traction-free edge irrespective of the value of φ. However, φ must be greater than φc for the debonding to become wavy/undulatory. The critical value, φc , of the adhesion parameter agrees with the necessary condition found in our previous work on debonding of an elastomeric layer from a rigid block when it is uniformly pulled outward. For α < αc , damage/debonding initiates only from the interface corner, and no wavy debonding ensues. The peak peeling force prior to the initiation of an internal debond is found to be a monotonically increasing function of φ/ α, suggesting its potential use as a design variable and as a guide for determining the TS parameters. Results of a few additional numerical experiments in which the elastomeric layer can debond from both adherends provide insights into designing a demolding process for a sandwiched elastomeric layer.
- Interfacial debonding from a sandwiched elastomer layerMukherjee, Bikramjit (Virginia Tech, 2016-06-25)The problem of a thin elastomeric layer confined between two stiff adherends arises in numerous applications such as microelectronics, bio-inspired adhesion and the manufacture of soft biomedical products. A common requirement is that the debonding of the elastomeric layer from the adherends be controlled to avoid undesirable failure modes. This level of control may necessitate understanding the collective role of the interfacial adhesion, material properties, part geometries, and loading conditions on the debonding. Analytical and numerical approaches using the finite element method and a cohesive zone model (CZM) for the interfacial debonding are used in this dissertation to delineate the role of the afore-mentioned parameters on the initiation and propagation of debonding for both rigid and non-rigid adherends. Extensively studied in the dissertation is the debonding of a semi-infinite relatively stiffer adherend from an elastomer layer with its other surface firmly bonded to a rigid base. The adherend is pulled upwards by applying normal displacements either on its entire unbonded surface or on the edge of its part overhanging from the elastomer layer. The adherend and the elastomeric layer materials are assumed to be linear elastic, homogeneous and isotropic and the elastomer is assumed to be incompressible. Viscoelasticity of the elastomer is considered in the first part of the work. Plane strain deformations of the system with a bilinear traction-separation (TS) relation in the CZM are analyzed. Two non-dimensional numbers, one related to the layer confinement and the other to the interfacial TS parameters, are found to determine if debonding initiates at interior points in addition to at corner points on the adherend/elastomer interface, and if adhesion-induced instability is exhibited. This work is extended to axisymmetric problems in which debonding can take place at both interfaces. Motivated by an industrial demolding problem, numerical experiments are conducted to derive insights into preferential debonding at one of the two interfaces, including for curved adherends. Results reported herein should help engineers design an elastomer layer sandwiched between two adherends for achieving desired failure characteristics.
- Reflections on the 150th Anniversary of Winkler’s Foundation and its Profound Influence on the Field of AdhesionDillard, David A.; Mukherjee, Bikramjit; Batra, Romesh C. (2017-02-27)This year, 2017, marks the 150th anniversary of Emil Winkler’s seminal publication of the beam on elastic foundation (BoEF) solution [1] published in 1867 while a professor at the University of Prague. With wide-ranging interests in analysis of civil engineering structures, he initially proposed the BoEF model for the rather obvious application to sleepers and rails supported by the earth upon which they rest [2]. The essence of the model lies in the simple but profound assumption that the restoring force of an elastic foundation is linearly proportional to the deflection. The important resulting mechanics of materials solution has been applied to a wide range of engineering applications, including a plethora of discrete and continuous loading and boundary conditions, extensions to plates and pontoon bridges, nonlinear behavior, and even the analysis of deflections and stresses in pressurized cylindrical tanks, where the effective restoring force is not supplied by a separate medium but rather by the hoop stresses developed due to stretching of the curved walls.