Reza Vaziri

A Plane Strain Model for Process-Induced Deformation of Laminated Composite Structures

We present a plane strain finite element model for simulation of the development of process-induced deformation during autoclave processing of complex-shaped composite structures. A “cure-hardening, instantaneously linear elastic” constitutive model is employed to represent the mechanical behaviour of the composite matrix resin, and micromechanics models are used to determine composite ply mechanical properties and behaviour, including thermal expansion and cure-shrinkage. Structures with multiple composite and non-composite components can be simulated through the use of such strategies as adaptive time-stepping and incorporation of multiple composite plies into each finite element. The effect of process tooling can also be directly modelled through simulation of tool/part interfaces and post-processing tool removal. Integration of the residual deformation model with models for heat transfer and resin cure and resin flow permits analysis of all major identified sources of process-induced deformation during the autoclave process. Model application is demonstrated through prediction of process-induced deformation of a number of variations of a simple L-shaped laminate. The model is shown to provide accurate predictions of both spring-back angle and warped shape of the final part.

Application of a damage mechanics model for predicting the impact response of composite materials

Abstract A plane-stress continuum damage mechanics (CDM) based model for composite materials is implemented in the non-linear finite element code, LS-DYNA3D and its predictive capability is evaluated by carrying out a series of numerical simulations involving impact of laminated composite plates. The performance of the model relative to that of an existing model in LS-DYNA3D is assessed by comparing the computed results with instrumented impact test results. It is demonstrated that a CDM based approach offers a versatile tool for predicting damage progression in composite structures, however, the parameters used in such models are often non-physical and difficult to characterize.

A physically based continuum damage mechanics model for thin laminated composite structures

The present work focuses on the development, implementation, and verification of a plane-stress continuum damage mechanics (CDM) based model for composite materials. A physical treatment of damage growth based on the extensive body of experimental literature on the subject is combined with the mathematical rigour of a CDM description to form the foundation of the model. The model has been implemented in the commercial finite element code, LS-DYNA and the results of the application of the model to the prediction of impact damage growth and its effects on the impact force histories in carbon fibre reinforced plastic laminates are shown to be physically meaningful and accurate. Furthermore, it is demonstrated that the material characterization parameters can be extracted from the results of standard test methodologies for which a large body of published data already exists for many composite materials.

Finite element based prediction of process-induced deformation of autoclaved composite structures using 2D process analysis and 3D structural analysis

Dimensional control of composite components is critical for cost effective manufacturing of large composite aerospace structures. This paper presents an engineering approach to the prediction of process-induced deformations of three-dimensional (3D) autoclaved composite components. A 6-step method that uses a two-dimensional (2D) special purpose finite element (FE) based process simulation code and a standard 3D structural FE code is presented. The approach avoids the need to develop a full 3D process model, significantly reducing the computational effort yet retaining much of the detail required for accurate analysis. The methodology is presented together with numerical examples and two case studies demonstrating the validity, utility, and limitations of the approach.

A two‐dimensional flow model for the process simulation of complex shape composite laminates

A numerical flow-compaction model is developed and implemented in a finite element code to simulate the multiple physical phenomena involved during the autoclave processing of fibre-reinforced composite laminates. The model is based on the effective stress formulation coupled with a Darcian flow theory. A Galerkin approach is employed to discretize the weak form of the governing equations. The current formulation successfully describes the compaction behaviour of complex shape laminates caused by flow of the resin. A parametric study is performed to investigate the effect of the material properties on the compaction of angle-shaped composite laminates. It is found that the fibre bed shear modulus significantly affects the compaction behaviour in the corner sections of curved laminates while the resin viscosity and fibre bed permeability affect the compaction rate of the laminate. Copyright

Deformation and failure of blast-loaded square plates

Abstract Numerical results for clamped, thin square steel plates subjected to blast loading are presented. The numerical analysis is based on a finite element formulation, which includes the nonlinear effects of geometry and material as well as strain rate sensitivity. A phenomenological interactive failure criterion comprising bending, tension and transverse shear is proposed to predict the various modes of failure. A node release algorithm is developed to simulate the progression of plate rupture from the boundary. The analysis is continued in the post-failure phase to account for the free flight deformation of the torn plate. The predicted failure modes for a blast-loaded plate are presented and compared with previously published experimental data.

Analytical solution for low-velocity impact response of composite plates

An analytical model for the impact response of laminated composite plates is presented. The governing equations, which apply to small deflection elastic response of specially orthotropic laminates, include the combined effects of shear deformation, rotary inertia, and the nonlinear Hertzian contact law. For simply supported boundary conditions, a Fourier series solution is presented that, in contrast to previously published work, retains the frequencies associated with rotary inertia effects throughout the analysis. Errors that are incurred in the analysis of impact events, where the contact force history is obtained as part of the solution process, are investigated and guidelines to achieve converged solutions are recommended. For a benchmark impact problem, the present solution converges more rapidly than other analytical solutions available in the literature. Present analytical predictions are also found to agree well with the experimental results for composite fiber-reinforced plastic plates impacted by instrumented projectiles launched from both gas-gun and drop-weight test setups. The efficiency and robustness of the model in handling the complexities of the impact response of composite plates is further demonstrated by comparing the analytical predictions of contact force and fiber strain histories with those generated using detailed finite element analyses. The good agreement obtained instills confidence in using the model as a foundation for predictions of impact damage and response to penetrating impact events.

A Plasticity-Based Constitutive Model for Fibre-Reinforced Composite Laminates:

A continuum mechanics approach is adopted herein to develop a constitutive model for the nonlinear behaviour of laminated composites up to and including ultimate failure. The proposed model for single layers of fibre-reinforced composites (FRC) is derived within the framework of rate-independent theory of orthotropic plasticity. Both unidirectional and bidirectional (e.g., woven) FRC layers are modelled. The individual layer constitutive equations are superimposed using classical lamination theory to yield the global laminate response. The models accuracy is illustrated by comparing the results of numerical simulations with experimental data available in the literature.

Impact analysis of laminated composite plates and shells by super finite elements

Abstract A super finite element method that exhibits coarse-mesh accuracy is used to predict the transient response of laminated composite plates and cylindrical shells subjected to non-penetrating impact by projectiles. The governing equations are based on the classical theories of thin laminated plates and shells taking into account the von Karman kinematics assumptions for moderately large deflections. A non-linear Hertzian-type contact law accounting for curvatures of the colliding bodies is adopted to calculate the impact force . The theoretical basis of the present finite element model is verified by analysing impact-loaded laminated composite plate and shell structures that have previously been studied through analytical or other numerical procedures. The predictive capability of the present numerical approach is successfully demonstrated through comparisons between experimentally-measured and computed force-time histories for impact of carbon fibre-reinforced plastic (CFRP) plates. The current computational model offers a relatively simple and efficient means of predicting the structural impact response of laminated composite plates and shells.

Deformation and failure of blast-loaded stiffened plates

Numerical results for clamped, square stiffened steel plates subjected to blast loading are presented. The finite element formulation, which includes the effects of geometric and material nonlinearities as well as strain rate sensitivity, forms the basis for the numerical analysis. Failure is predicted using an interactive failure criterion comprising bending, tension and transverse shear. A node release algorithm is developed to simulate the progression of rupture. The analysis is continued in the post-failure phase to capture the free flight deformation of the torn plate. The predicted failure modes for a blast-loaded stiffened plate are presented and compared with previously published experimental data. Furthermore, the results of the numerical analysis are used to understand the experimentally observed localized tearing of stiffened plates.