The assumption of a perfect bond means that the finite element analysis takes no account of the adhesion properties of the interface. There is no obvious method for predicting interface strength, as often the input data needed requires knowledge of the interface strength, or the failure stress/strain of the adhesive. However, there are methods of accounting for adhesion in an FE analysis, by modelling adhesive failure. This section highlights some of the options available. There are two main approaches for modelling the failure of an adhesive interface. One approach is to model the growth of a crack (fracture mechanics energy-based approach) and the other is to model adhesive debonding (stress- or strain-based approach).
The fracture mechanics approach assumes that a sharp crack exists within the material and failure occurs through propagation of this crack. A debonded area or delamination can be classified as a crack. This approach does not predict the crack initiation stress or energy. Advancing the crack front when the local strain-energy release-rate rises to its critical value can simulate crack propagation. In ABAQUS , potential crack surfaces are modelled using contact surface definitions. Surfaces may be partially bonded initially, but may debond during crack propagation.
The three debonding criteria are:
· Crack opening displacement
· Critical stress criterion at a critical distance ahead of the crack tip
· Crack length as a function of time.
After debonding, the interface behaviour reverts to standard contact, including any frictional effects. Alternatively, virtual crack growth method may be used to model crack propagation. Cracks are introduced into the mesh by renumbering nodes of adjacent elements. The virtual crack growth method for assessing strain-energy release-rate is based on the concept that the energy released in growing the crack is equal to the energy which would be required to close the crack. Forces and displacements at the crack tip are obtained from finite element simulations and the energy can be calculated.
Interface elements located along the debonding interface can be used to predict crack growth. In this method, a softened decohesion material model is provided with traction/relative displacement relationships that are constructed so that the enclosed area is equated to the critical fracture energy. Initial flaws are not required with initiation being governed by a strength criterion. Two material properties are required for interface elements: Gc , the total energy from experiments and St , the assumed interfacial material strength.
Another method of analysing failure of an interface is using a cohesive zone model in which cohesive elements are incorporated between element edges, thus extending conventional finite element analysis in a way that allows independent specification of interfacial fracture and bulk constitutive behaviour. The cohesive elements describe the deformation and failure of the interface between two bulk finite elements by specifying the tractions that resist relative motion.
An alternative debonding method can be employed using the debond option in which an amplitude-time function is used to give the relative magnitude of force to be transmitted between the surfaces at time t0 + ti (t0 being the time when debonding begins). When the fracture criterion is met at a node, the force at that node is ramped down according to the debonding data. The force at the node must have a value of 1.0 at zero time and must end with a magnitude of zero at the final time (i.e. node debonded).
ABAQUS/Explicit also offers two damage models; a shear failure model driven by plastic yielding; a tensile failure model driven by tensile loading. These failure models provide simple failure criteria that are designed to allow stable removal of elements from the mesh as a result of tearing, ripping or tensile spalling of the structure. Each model provides several failure choices including the removal of elements from the mesh.
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2. Shen, C.H. and Springer, G.S., “Moisture Absorption and Desorption of Composite Materials”, Journal of Composite Materials”, Volume 10, pp 2-20, 1976.
3. Crank, J., “The Mathematics of Diffusion”, Clarendon Press, 1956.
4. Hinopoulos, G. and Broughton, W.R., “An Improved Modelling Approach of Mositure Absorption in Adhesive Joints Using the Finite Element Method”, NPL Report CMMT(A) 204, 1999.
5. Hinopoulos, G. and Broughton, W.R., “Evaluation of the T-Peel Joint Using the Finite Element Method”, NPL Report CMMT(A) 207, 1999.
6. ABAQUS/CAE Users Manual Version 6.5, HKS Inc., USA, 2004.