Journal of Aerospace Engineering

An experimental and analytical program is carried out to explore key behaviors in the loading and unloading behavior of polymers. Specifically, the effects of strain rate and hydrostatic stresses on the nonlinear portions of the deformation response are examined. Tension, compression, and shear load only and load/unload tests are conducted on a representative polymer across a range of strain rates, and key features of the experimental results are identified. To conduct a preliminary exploration of how the key features of the deformation response could be simulated analytically, a previously developed set of constitutive equations, which were developed to analyze the strain rate dependent, nonlinear deformation of polymers including the effects of hydrostatic stresses, were modified in order to approximate key features of the nonlinear unloading behavior observed in the polymer. The constitutive relations are based on state variable constitutive equations originally developed for metals. The nonlinear unloading observed in the experiments is approximated by reducing the unloading modulus of the material as the effective inelastic strain is increased. The effects of the hydrostatic stress state on the unloading modulus are also simulated analytically. To examine the revised formulation, the loading and load/unload responses of the representative polymer in tension, compression, and shear are examined at several strain rates. Results computed using the developed constitutive equations were found to correlate reasonably well with the experimental data.

A modified Hashin failure model is developed to characterize different failure modes related to high-velocity impact of composite laminates. Hashin’s compressive fiber failure mode has been extended to consider the shear stress effect. Several micromechanics-based degradation rules are developed and applied to the stress and material property calculations according to different failure modes after the corresponding failure criterion is satisfied. This model has been implemented into a recently developed micromechanics model. Computational results show that this model is able to address shear failure, delamination, and tearing failure observed in the high-velocity impact of composite laminates.

A previously developed constitutive model has been modified in order to incorporate the rate dependence of elastic modulus of the polymer matrix constituent into the nonlinear, strain-rate-dependent deformation analysis of polymer matrix composites. To compute the inelastic strains in the polymer matrix, state-variable-based viscoplastic equations originally developed for metals are modified in order to account for the effects of hydrostatic stresses, which are significant in polymers. The polymer constitutive equations are implemented within the strength of a material-based micromechanics method in order to predict the nonlinear, strain-rate-dependent deformation of the polymer matrix composite. The polymer and the composite models are implemented into a commercially available explicit finite-element code, LS-DYNA, as user defined materials (UMATs). The deformation behaviors of several representative polymers and two polymer matrix composites of various fiber configurations are simulated in LS-DYNA with the UMATs for a wide range of strain rates, and the numerical results agree well with the experimental data. UMAT is applied for simulations of braiding/weaving composites using the modified through-thickness integration points method.

A simplified methodology has been developed for modeling two-dimensional triaxially braided composite plates impacted by a soft projectile using an explicit nonlinear finite-element analysis code LS-DYNA. The fiber preform architecture is modeled using shell elements by incorporating the fiber preform architecture at the level of integration points. The soft projectile was modeled by an equation of state. An arbitrary Lagrangian–Eulerian formulation is used to resolve numerical problems caused by large deformation of the projectile. The computed results indicate that this numerical model is able to simulate a triaxially braided composite undergoing a ballistic impact effectively and accurately, including the deformation and failure with a reasonable level of computational efficiency.

The next generation aircraft engines are designed to be lighter and stronger than engines currently in use by using carbon fiber composites. In order to certify these engines, ballistic impact tests and computational analyses must be completed, which will simulate a “blade out” event in a catastrophic engine failure In order to computationally simulate the engine failure, properties of the carbon fiber and resin matrix must be known. When conducting computer simulations using a micromechanics approach, experimental tensile, compressive, and shear data are needed for constitutive modeling of the resin matrix material. The material properties of an Epon E862 epoxy resin will be investigated because it is a commercial $176°\mathrm{C}$ $(350°\mathrm{F})$ cure resin currently being used in these aircraft engines. These properties will be measured using optical measurement techniques. The epoxy specimens will be tested in tension, compression and torsional loadings under various strain rates ranging from ${10}^{-5}\text{to}{10}^{-1}{\mathrm{s}}^{-1}$ and temperatures ranging from room temperature to $80°\mathrm{C}$ . To test the specimens at high temperatures, a specialized clear temperature chamber was used. The results show that the test procedure developed can accurately and quickly categorize the material response characteristics of an epoxy resin. In addition, the results display clear strain rate and temperature dependencies in the material response.

This paper presents a numerical study of the failure response of an aircraft engine containment panel obliquely impacted by a titanium turbine fragment. A three-branch Bao-Wierzbicki fracture criterion is first calibrated for the target material (2219-T851 aluminum alloy) by performing tensile tests on round bars and upsetting tests on short cylinders. With this fracture model, the finite-element simulation of the impact test successfully captures the formation of an indentation/gouging channel on the proximal surface of the panel and the growth of a crack on the distal surface. An extensive parametric study is conducted on the effect of fracture criteria, mesh size, projectile pitch angles, and finite-element codes. Deficiencies of the Johnson-Cook and the constant critical strain fracture model are identified. It is found that the numerically predicted residual thickness and mass loss of the panel are sensitive to the magnitude of the pitch angle of the projectile. A large difference in calculated energy dissipation between ABAQUS and LS-DYNA is observed.

The traditional methods for analyzing deformation in structures attempt to solve the partial differential equations of the classical theory of continuum mechanics. Yet these equations, because they require the partial derivatives of displacement to be known throughout the region modeled, are in some ways unsuitable for the modeling of discontinuities caused by damage, in which these derivatives fail to exist. As a means of avoiding this limitation, the peridynamic model of solid mechanics has been developed for applications involving discontinuities. The objective of this method is to treat crack and fracture as just another type of deformation, rather than as pathology that requires special mathematical treatment. The peridynamic theory is based on integral equations so there is no problem in applying the equations across discontinuities. The peridynamic method has been applied successfully to damage and failure analysis in composites. It predicts in detail the delamination and matrix damage process in composite laminates due to low velocity impact, and the simulation results of damage area correlates very well with the experimental data.