Todd O. Williams

A general theory for laminated plates with delaminations

Abstract An approximate analytical model for the behavior of a laminated composite plate in the presence of delaminations and other local effects is presented. The model is based on a generalized displacement formulation implemented at the layer level. The governing equations for a layer are obtained using the principle of virtual work. These governing equations for a layer are used in conjunction with the explicit satisfaction of both the interfacial traction continuity and the interfacial displacement jump conditions between layers to develop the governing equations for a laminated composite plate, including delaminations. The fundamental unknowns in the theory are the dis-placements in the layers and the interfacial tractions. The theory is sufficiently general that any constitutive model for the interfacial fracture (i.e. delamination) as well as for the layer behavior can be incorporated in a consistent fashion into the theory. The interfacial displacement jumps are expressed in an internally consistent fashion in terms of the fundamental unknown interfacial tractions. The current theory imposes no restrictions on the size, location, distribution, or direction of growth of the delaminations. Therefore, the theory can predict the initiation and growth of delaminations at any location as well as interactive effects between delaminations at different locations within the laminate. Paganos exact solution for the cylindrical bending of a laminated plate has been modified to include the effects of delamination. An interface model, which expressed the displacement jump as a linear function of the surface tractions, was implemented into this modification of the exact solution. This extension was used to validate the approximate plate theory. The correlation between the approximate approach and the exact solution is seen to be excellent. The approximate plate theory is seen to give very accurate predictions for the interfacial tractions in a direct and consistent fashion, i.e. without the need to use integration of the pointwise equilibrium equations. This allows the interfacial displacement jumps in the presence of delaminations to be modeled accurately. It is seen that these displacement jumps have a significant effect on both the macroscopic and microscopic behavior of a laminated plate.

A generalized multilength scale nonlinear composite plate theory with delamination

Abstract A new type of plate theory for the nonlinear analysis of laminated plates in the presence of delaminations and other history-dependent effects is presented. The formulation is based on a generalized two length scale displacement field obtained from a superposition of global and local displacement effects. The functional forms of global and local displacement fields are arbitrary. The theoretical framework introduces a unique coupling between the length scales and represents a novel two length scale or local-global approach to plate analysis. Appropriate specialization of the displacement field can be used to reduce the theory to any currently available, variationally derived, displacement based (discrete layer, smeared, or zig-zag) plate theory. The theory incorporates delamination and/or nonlinear elastic or inelastic interfacial behavior in a unified fashion through the use of interfacial constitutive (cohesive) relations. Arbitrary interfacial constitutive relations can be incorporated into the theory without the need for reformulation of the governing equations. The theory is sufficiently general that any material constitutive model can be implemented within the theoretical framework. The theory accounts for geometric nonlinearities to allow for the analysis of buckling behavior. The theory represents a comprehensive framework for developing any order and type of displacement based plate theory in the presence of delamination, buckling, and/or nonlinear material behavior as well as the interactions between these effects. The linear form of the theory is validated by comparison with exact solutions for the behavior of perfectly bonded and delaminated laminates in cylindrical bending. The theory shows excellent correlation with the exact solutions for both the inplane and out-of-plane effects and the displacement jumps due to delamination. The theory can accurately predict the through-the-thickness distributions of the transverse stresses without the need to integrate the pointwise equilibrium equations. The use of a low order of the general theory, i.e. use of both global and local displacement fields, reduces the computational expense compared to a purely discrete layer approach to the analysis of laminated plates without loss of accuracy. The increased efficiency, compared to a solely discrete layer theory, is due to the coupling introduced in the theory between the global and local displacement fields.

Efficiency and accuracy considerations in a unified plate theory with delamination

Abstract The accuracy and efficiency of a new type of plate theory within the context of the cylindrical bending problem is examined. The theoretical framework of the theory employs a generalized two-length scale displacement field obtained from a superposition of arbitrary orders/forms of global- and local-displacement effects. The current work particularly concentrates on the impact of different combinations of the global- and local-displacement effects on the theorys ability to accurately and efficiently predict the local fields for cross-ply plates. The theory is shown to accurately predict both the displacement and stress fields as well as the displacement jumps due to delaminations. Consideration of the trends in the predictions obtained using different combinations of global- and local-fields indicates that accurate solutions are obtained in a computationally efficient manner by using relatively low orders of global- and local-fields. Furthermore, the results imply that the theory can be directly used to examine convergence of a solution simply by changing the orders of the global, local, or both global- and local-displacement effects.

A dynamic model for laminated plates with delaminations

Abstract A generalized theory for laminated plates, including delamination, is developed. The laminate model is based on a generalized displacement formulation implemented at the layer level. The equations of motion for a layer, which are explicitly coupled with both the interfacial traction continuity and the interfacial displacement jump conditions between layers, are used to develop the governing equations for a laminated composite plate. The delamination behavior can be modeled using any general constitutive fracture law. The interfacial displacement jumps are expressed in an internally consistent fashion in terms of the fundamental unknown interfacial tractions. The current theory imposes no restrictions on the size, location, distribution, or direction of growth of the delaminations. Therefore, the theory can predict the initiation and growth of delaminations at any location as well as interactive effects between delaminations at different locations within the laminate. The proposed theory is used to consider the dynamic response of laminated plates in cylindrical bending. First it is shown that the dynamic implementation agrees well with the exact predictions of a plate under static loading conditions. Static, cylindrical bending is considered to validate the numerical implementation. Next, different dynamic loading cases are considered. First, the required level of discretization through the thickness of the laminate necessary to accurately capture the wave propagation characteristics for monotonic tensile loading transverse to the plate is determined. Next, the influence of the delamination on the free vibration behavior of a plate is considered. It is shown that the presence of delaminations can result in significant deviations from the perfectly bonded free vibration behavior. Finally, the plate is subjected to dynamic loading conditions that demonstrate the influence of internal wave interactions on the overall behavior of the plate.

Buckling of composite plates by global–local plate theory

Abstract The bifurcation buckling problem of laminated composite plates is formulated within the framework of a multilength scale plate theory. This theory is a combination of single-layer and layer-wise theories. It is generated by representing the displacement as the sum of global and local effects that introduce a coupling between the two length scales. Comparisons between the presently predicted buckling loads of homogeneous and orthotropic laminated plates and the exact solutions show a very good correlation. Furthermore, the theory accurately predicts the buckling load of symmetric cross-ply plates as compared with the results of a layer-wise approach. This accuracy is achieved with reduced computation expense. The global–local plate theory is general enough to incorporate delamination effects. As a result of the inclusion of these effects, the buckling loads of plates with imperfect interlaminar bonding are predicted.

A Coupled Approach to Developing Damage Prognosis Solutions

Funding for the Los Alamos Damage Prognosis Initiative is being provided by the Department of Energy through Laboratory Directed Research Development. In addition to the authors, the Damage Prognosis research team includes Los Alamos staff members Matt Bement, Irene Beyerlein, Norm Hunter, Cheng Liu, Brett Nadler, and Jeni Wait. Los Alamos graduate research assistants Tim Fasel, Jan Goethals and Trevor Tippetts, and. Professor Dan Inman and graduate student David Allen at Virginia Tech.

A coupled micro–macromechanical analysis of hygrothermoelastic composites

Abstract A micro–macromechanical procedure is developed to establish the response of multiphase composites whose constituents behave, in general, as hygrothermoelastic materials. The response of the single phase is governed by the fully coupled theory of heat, moisture and deformation, and the micromechanical theory provides the hygrothermoelastic behavior of the composite. Results are presented to illustrate the effects of coupling between temperature, moisture and stress, and the interaction between the phases on the overall temporal and spatial response of a composite slab.

Coupling Grain Scale and Bulk Mechanical Response for PBXs Using Numerical Simulations of Real Microstructures

PBXs are complex composites geometrically (irregularly shaped grains vary greatly in size), and constitutively (grains are anisotropic, twin and fracture). Heterogeneity at the grain scale results in localized damage and the creation of hot spots. To develop accurate, quantitative and predictive models it is imperative to develop a sound physical understanding of the grain scale material response. Numerical simulation is a useful tool to further model development. Here an inherent advantage of a particle method in discretizing geometrically complex materials is exploited to import three‐dimensional material configurations from x‐ray microtomography data, i.e. “real” microstructures. Numerical simulations determine representative volume element size and generate statistics on grain scale strain heterogeneity. These statistics calibrate the Stochastic Transformation Field Analysis bulk constitutive model.

A FULLY COUPLED THERMO-MECHANICAL MICROMECHANICS MODEL

The development for a micromechanical model with full thermomechanical coupling, which is based on the combined effects of the mechanical and energy equations, is presented. The model is based on a combined approximate kinematic and thermal analysis of a repeating unit cell in a triply periodic array of inclusions. The unit cell is considered to consist of different subregions that can be composed of any desired material. The behavior of the material within the different subregions can be modeled using elastic, plastic, viscoelastic, viscoplastic, or damage constitutive models. The analysis satisfies the equations of motion and the energy equation for the different subregions of the unit cell in an average sense. The interfacial continuity conditions for the velocities, stresses, temperature, and thermal fluxes between the different subregions are also satisfied in an average sense. Arbitrary heat source terms are included in the energy equation to allow for the analysis of reactive materials. The resulti...

A Computational Framework for Multiscale Analysis of Laminated Composite Plates

Advanced structural applications are requiring ever increasing levels of performance at both the structure and material point scales. Increasingly laminated composite materials are being applied as the material/structural combination of choice to achieve viable realizations of these advanced concepts.