Michelle S. Hoo Fatt

Ballistic impact of GLARE fiber-metal laminates

Abstract Analytical solutions to predict the ballistic limit and energy absorption of fully clamped GLARE panels subjected to ballistic impact by a blunt cylinder were derived. The analytical solutions were based on test results from NASA Glenn. The ballistic limit was found through an iterative process such that the initial kinetic energy of the projectile would equal the total energy dissipated by panel deformation, delamination/debonding and fracture. The transient deformation of the panel as shear waves propagate from the point of impact was obtained from an equivalent mass–spring system, whereby the inertia and stiffness depend on the shear wave speed and time. Predictions of the ballistic limit from the resulting non-linear differential equation were within 13% of the test data. The deformation energy due to bending and membrane accounted for most of the total energy absorbed (84–92%), with the thinner panels absorbing a higher percentage of deformation energy than the thicker panels. Energy dissipated in delamination represented 2–9% of the total absorbed energy, with the thinner panels absorbing a lower percentage of delamination energy than the thicker panels. About 7% of the total energy was attributed to tensile fracture energy of the glass/epoxy and aluminum.

Dynamic models for low-velocity impact damage of composite sandwich panels – Part A: Deformation

Abstract Equivalent single and multi degree-of-freedom systems are used to predict the low-velocity impact response of rigidly supported, two-sided clamped, simply supported and four-sided clamped composite sandwich panels. The composite sandwich panels have orthotropic facesheets and are symmetric. Analytical solutions for the transient deformation response of the sandwich panels are presented in this paper, and analytical predictions of impact damage initiation are given in a companion paper. Equivalent masses are derived by assuming velocity distributions and calculating average kinetic energies (KEs) in terms of the amplitude of the top facesheet indentation and the global panel deflection. Equivalent spring and dashpot resistances are derived from the static load–indentation response and adjusted with dynamic material properties of the facesheet and core. Analytical predictions of the impact force compare well with experimental values from three independent studies.

Dynamic models for low-velocity impact damage of composite sandwich panels : Part B : Damage initiation

Equivalent single and multi degree-of-freedom systems are used to predict low-velocity impact damage of composite sandwich panels by rigid projectiles. The composite sandwich panels are symmetric and consist of orthotropic laminate facesheets and a core with constant crushing resistance. The transient deformation response of the sandwich panels subjected to impact were predicted in a previous paper, and analytical solutions for the impact force and velocity at damage initiation in sandwich panels are presented in this second paper. Several damage initiation modes are considered, including tensile and shear fracture of the top facesheet, core shear failure, and tensile failure of back facesheet. The impact failure modes are similar to static indentation failure modes, but inertial resistance and high strain rate material properties of the facesheets and core influence impact damage loads. Predicted damage initiation loads and impact velocities compare well with experimental results.

Localized damage response of composite sandwich plates

Abstract The objective of this article is to derive closed-form solutions for the deformation and fracture responses of a composite sandwich plate subjected to static indentation of a hemispherical-nose indenter. The composite sandwich is modeled as an infinite, orthotropic, elastic plate resting on a rigid-plastic foundation. The facesheet deflection is several times the laminate thickness so that bending moments may be neglected and only membrane forces are considered in the facesheet. The rigid-plastic foundation force is given by the honeycomb crushing resistance. The deformation of the facesheet is found by using the principle of minimum potential energy. The elastic strain energy resulting from the membrane forces in the facesheet, the plastic work dissipated in crushing the honeycomb, and the external work are evaluated using an appropriate shape function for the facesheet deflection. The relations between the indentation load and the transverse deflection and length of deformation are obtained by minimization of the total potential energy. Minimization of the total potential energy has to be done numerically because of an implicit expression for the contact radius between the hemispherical-nose indenter and the facesheet of the honeycomb. An approximate solution for the load–indentation response is derived by assuming an average value of the contact radius. For the particular composite sandwich plates and indenters considered, the difference between the numerical and approximate solutions is about 3%. Furthermore, the approximate predictions are within 15% of the experimental results. Conservative estimates of the failure loads which cause cracking of the facesheet are predicted using the Maximum Stress and Tsai–Hill Criteria. The equations derived by the above failure criteria yield important design considerations for composite sandwich plates. It was observed that the failure load increases with the square of the ply thickness and indenter radius and is inversely proportional to the crushing resistance of honeycomb.

Perforation of Composite Plates and Sandwich Panels under Quasi-static and Projectile Loading

Analytical solutions for the deformation, penetration, and perforation of composite plates and sandwich panels subjected to quasi-static punch indentation and projectile impact are derived. Discrete spring-mass models are used to calculate the impact response of the composite plates and sandwich panels. Equivalent load resistance functions are obtained from the quasi-static analysis and adjusted for high strain rate. A generalized solution methodology for projectile impact of composite plates and sandwich panels are then proposed based on three key factors: (i) the contact load duration, (ii) the through-thickness transit time, and (iii) the lateral transit time. A two-dimensional wave propagation model is used to determine the ballistic limits of E-glass/polyester panels and GLARE fiber-metal laminates, and predicted values are found to be within 20 and 13% of the experimental results, respectively. A quasi-static impact model is used to predict the ballistic limit for E-glass/epoxy-aluminum honeycomb sandwich impacted by hemispherical nose projectile and the predicted values are within 11% of test results.

Analytical Modeling of Composite Sandwich Panels under Blast Loads

Analytical solutions were derived for the transient response and damage initiation of a foam-core composite sandwich panel subjected to blast loading. The panel response was modeled in two consecutive phases: (1) a through-thickness wave propagation phase leading to permanent core crushing deformations and (2) a transverse shear wave propagation phase resulting in global panel deflections. The predicted transient deformation of a sandwich panel consisting of E-glass vinyl ester facesheets and H100 PVC foam core compared well with ABAQUS predictions. Analytical predictions of the critical impulse for damage initiation in several foam sandwich panels also compared well with ABAQUS predictions.

Elastic-plastic collapse of non-uniform cylindrical shells subjected to uniform external pressure

The objective of this paper is to derive analytical solutions for the elastic buckling and plastic collapse pressures of a cylindrical shell with reduced thickness over part of its circumference. The section of reduced thickness is used to represent a corroded region in a pipe. The proposed solutions are extensions of Timoshenkos solutions for the elastic-plastic collapse of a linear elastic, perfectly plastic cylindrical shell subjected to uniform external pressure. A modified interaction formula for the fully plastic membrane forces and bending moments in the non-uniform cylinder has been proposed for plastic collapse. A parametric study shows that the elastic buckling pressure decreases smoothly with corrosion angle when the corrosion depth is less than 0.5t. When the corrosion depth is greater than 0.5t, the elastic buckling strength first decreases very rapidly with corrosion angle. Furthermore, the elastic buckling pressure decreases uniformly with corrosion depth when the corrosion angles are greater than 30°, while the elastic buckling strength decreases more rapidly at higher corrosion depths when corrosion angles are less than 30°. Another parametric study on a steel pipe shows that the initial and fully plastic yield pressures both decrease monotonically with corrosion depth for a given corrosion angle and imperfection.

Perforation of Sandwich Panels with Honeycomb Cores by Hemispherical Nose Projectiles

Analytical models for the static and low-velocity perforation of composite sandwich panel with woven E-glass/epoxy prepreg facesheets and aluminum honeycomb core are developed. The analytical models are based on a set of experimental results. A three-stage perforation process involving consecutive failures of top facesheet, core, and bottom facesheet is proposed. The analytical predictions of static failure loads and deformation are within 10 and 8% of the test data, respectively. The predicted ballistic limit is within 10% of the test data, while the total energy dissipated at the ballistic limit is within 18% of the test results.

Propagating buckles in corroded pipelines

Abstract Rigid–plastic solutions for the steady-state, quasi-static buckle propagation pressure in corroded pipelines are derived and compared to finite element predictions (ABAQUS). The corroded pipeline is modeled as an infinitely long, cylindrical shell with a section of reduced thickness that is used to describe the corrosion. A five plastic hinge mechanism is used to describe plastic collapse of the corroded pipeline. Closed-form expressions are given for the buckle propagation pressure as a function of the amount of corrosion in an X77 steel pipeline. Buckles that propagate down the pipeline are caused by either global or snap-through buckling, depending on the amount of corrosion. Global buckling occurs when the angular extent of the corrosion is greater than 90°. When the angular extent is less than 90° and the corrosion is severe, snap-through buckling takes place. The buckle propagation pressure and the corresponding collapse modes also compare well to finite element predictions.

Pressure pulse response of composite sandwich panels with plastic core damping

An analytical technique is presented for obtaining the large amplitude, damped response of a foam-core composite sandwich panel subjected to uniform pressure pulse loading. The predicted panel response was in agreement with finite element analysis, and it was used to examine the blast resistance of panels with various foam cores. Although blast resistance generally increased with the increasing core density, panels with the densest cores exhibited no energy absorption before panel failure. The panel with the PVC H200 foam also sustained higher failure pressure per unit areal weight density than the denser panels with Klegecell R300 and HCP100 foams.