Thomas E. Lacy

Numerical modeling of impact-damaged sandwich composites subjected to compression-after-impact loading

Semi-empirical numerical models are developed for predicting the residual strength of impact-damaged sandwich composites comprised of woven fabric carbon epoxy facesheets and Nomex honeycomb cores subjected to compression-after-impact loading. Results from non-destructive inspection and destructive sectioning of damaged sandwich panels are used to establish initial conditions for damage (residual facesheet indentation, core crush dimensions, etc.) in the numerical analyses. Honeycomb core crush test results are used to establish the non-linear constitutive behavior for the Nomex core. The influence of facesheet property degradation on the strain redistribution in damaged sandwich panels is examined. Facesheet strains from material and geometric non-linear finite element analyses correlate relatively well with experimentally determined values. Moreover, numerical predictions of residual strength are consistent with experimental observations. Similar calculations may prove useful in the development of a damage tolerance plan for sandwich composites that accounts for relevant details of damage morphology and provide conservative estimates of residual strength.

Gradient concepts for evolution of damage

Abstract While low-order measures of damage have sufficed to describe the stiffness of bodies with distributed voids or cracks, such as the void volume fraction or the crack density tensor of Vakulenko, A.A., Kachanov, M., 1971. [Inz. AN SSSR., Mekhanika Tverdogo Tela (Mech. Solids) 6 (4), 159], addressing the growth of distributed defects demands a more comprehensive description of the details of defect configuration and size distribution. Moreover, interaction of defects over multiple length scales necessitates a methodology to sort out the change of internal structure associated with these scales. To extend the internal state variable approach to evolution, we introduce the notion of multiple scales at which first and second nearest-neighbor effects of nonlocal character are significant, similar to homogenization theory. Further, we introduce the concept of a cutoff radius for nonlocal action associated with a representative volume element (RVE), which exhibits statistical homogeneity of the evolution, and flux of damage gradients averaged over multiple subvolumes. In this way, we enable a local description at length scales below the RVE. The mean mesoscale gradient is introduced to reflect systematic differences in size distribution and position of damage entities in the evolution process. When such a RVE cannot be defined, the evolution is inherently statistically inhomogeneous at all scales of reasonable dimension, and the concept of macroscale gradients of internal variables is the only recourse besides micromechanics. Based on a series of finite element calculations involving evolution of 2D cracks in brittle elastica arranged in random periodic arrays, we examine the evolution of the mean mesoscale gradients and note some preliminary implications for the utility of such an approach.

Classical micromechanics modeling of nanocomposites with carbon nanofibers and interphase

A micromechanics parametric study was performed to investigate the effect of carbon nanofiber morphology (i.e. hollow vs. solid cross-section), nanofiber waviness, and both nanofiber–resin interphase properties and dimensions on bulk nanocomposite elastic moduli. Mori–Tanaka and self-consistent models were developed for composites containing heterogeneities with multilayered coatings. For a given nanofiber axial force–displacement relationship, the elastic modulus for hollow nanofibers can significantly exceed that for solid nanofibers resulting in notable differences in bulk nanocomposite properties. In addition, the development of a nanofiber–resin interphase had a notable effect on the bulk elastic moduli. Consistent with results from the literature, small degrees of nanofiber waviness resulted in a significant decrease in effective composite properties.

On Representation of Damage Evolution in Continuum Damage Mechanics

The effect of damage patterning on elastic moduli and damage evolution in ideal brittle cracked solids is examined. Key limitations associated with typical continuum damage mechanics approaches are addressed. Critical shortcomings arising from the use of spatially-averaged damage descriptors in the evaluation of effective moduli and thermodynamic forces are investigated using numerical simulations of evolving two-dimensional crack systems. Fundamental elements of a higher-order continuum description of damage based on distribution functions are discussed, which directly include damage interaction effects.

Effect of Temperature on the Shear-Thickening Behavior of Fumed Silica Suspensions

Shear-thickening fluids (STFs) can be subjected to a significant temperature variation in many applications. Polymeric or oligomeric fluids are commonly used as suspending media for STFs. Because the viscosities of polymeric fluids are strongly temperature-dependent, large temperature changes can profoundly affect the shear-thickening responses. Here, the effect of temperature on the shear-thickening behavior of four low-molecular-weight polymeric glycols/fumed silica suspensions is reported. The dispersed-phase volume fraction, its surface chemistry, and the chemical compositions of the suspending media were varied. These factors influence the viscosity and the interactions between the suspended particles and the suspending media. Fumed silica particles with two different silanol-group surface densities were suspended in the polymeric glycols, where these silanol surface groups formed hydrogen bonds with the suspending medias glycols and internal oxygen atoms. Steady-shear experiments were performed over a temperature range spanning approximately 100 °C. The critical shear rate for the onset of shear thickening decreased with decreasing temperature. The critical shear rates were inversely proportional to the viscosity of the pure suspending media over these same temperature ranges. The response of STFs to varying both the temperature and shear rate investigated here will help to design application-specific STFs. Mitigation of a hypervelocity (6.81 km/s) impact on an aluminum facesheet sandwich composite filled with one of these STFs was demonstrated.

Dynamic mechanical analysis and optimization of vapor-grown carbon nanofiber/vinyl ester nanocomposites using design of experiments

A design of experiments approach demonstrated how four formulation and processing factors (i.e., nanofiber type, use of dispersing agent, mixing method, and nanofiber weight fraction) affected the dynamic mechanical properties of carbon nanofiber/vinyl ester nanocomposites. Only <0.50 parts of nanofiber per hundred parts resin produced a 20% increase in the storage modulus vs. that of the neat cured resin. Statistical response surface models predicted nanocomposite storage and loss moduli as a function of the four factors and their interactions. Nanofiber type and weight fraction were the key interacting factors influencing the mean storage modulus. Nanofiber weight fraction, mixing method, and dispersing agent had coupled effects on the mean loss modulus. Employing this methodology, optimized nanocomposite properties can be predicted as a function of nanocomposite formulation and processing.

Effective property estimates for composites containing multiple nanoheterogeneities: Part II nanofibers and voids

The Effective Continuum Micromechanics Analysis Code was used to predict effective elastic moduli of vinyl ester composites containing a combination of solid/hollow carbon nanofibers with varying degrees of fiber waviness, voids, and traditional E-glass fibers. The predicted effective elastic moduli for nanofiber-reinforced composites matched well with experimental results from the literature. In addition, single- and multiple-step homogenization procedures were both used to determine effective properties for hybrid composites containing reinforcements of disparate sizes (i.e., nanofibers combined with traditional E-glass fibers). This work aims to facilitate the development of engineered multiscale materials design by providing insight into relationships between nanomaterial physical characteristics, interactions, and structure across disparate spatial scales that lead to improved macroscale performance.

Effective property estimates for composites containing multiple nanoheterogeneities: Part I Nanospheres, nanoplatelets, and voids

Effective Continuum Micromechanics Analysis Code (EC-MAC) was developed to predict effective properties of composites containing multiple distinct nanoheterogeneities (fibers, spheres, platelets, voids, etc.) each with an arbitrary number of coating layers based upon either the modified Mori–Tanaka method or the self-consistent method. The influence of solid and hollow nanoreinforcement geometries and distinct elastic properties was addressed for solid silica nanosphere/epoxy, hollow glass nanosphere/polyester, and α-zirconium phosphate nanoplatelet/epoxy composites, along with the influence of spherical voids. The notion of “effective volume fraction” was introduced to denote the fraction of nanoreinforcements that contribute to overall composite properties through their good dispersion. The predicted nanocomposite effective elastic moduli obtained using the Effective Continuum Micromechanics Analysis Code matched well with experimental results from the literature.

Determination of carbon nanofiber morphology in vinyl ester nanocomposites

Key aspects of nanofiber morphology in vapor-grown carbon nanofiber (VGCNF)/vinyl ester nanocomposites were characterized using transmission electron microscopy (TEM) images. Three-parameter Weibull probability density functions were generated to describe the statistical variation in nanofiber outer diameters, wall thicknesses, relative wall thicknesses, visible aspect ratios, and visible waviness ratios. Based upon a linear regression of experimental data, the relative nanofiber wall thicknesses were reasonably constant over a range of nanofiber radii. Such information could be used to establish more realistic nanofiber moduli and strengths obtained from nanofiber tensile tests, as well as to develop physically motivated computational models for predicting nanocomposite behavior. While the nanofiber aspect ratios and fiber waviness measurements were restricted to the visible portions of nanofibers lying in the plane of the TEM images, such data can be used to predict bounds on the effective nanocomposite elastic properties. This study represents one of the first attempts to experimentally characterize the distribution of VGCNF features in real thermoset nanocomposites.

Numerical Estimates of the Compressive Strength of Impact-damaged Sandwich Composites

Improved numerical models have been developed for predicting the compressive strength of impact-damaged sandwich composites comprised of woven-fabric graphite-epoxy facesheets and Nomex honeycomb cores. The proposed methodology contains three key elements: (1) the use of nondestructive inspection estimates of damage, (2) the incorporation of nonlinear through-the-thickness core-crush constitutive response to account for core failure, and importantly (3) the simulation of progressive loss of facesheet structural integrity based upon userspecified ply failure criteria. The finite element predictions of residual strength for panels impacted with relatively blunt objects correlate well with the experimental observations; this is in contrast to a number of estimates from literature that tend to overestimate the strength. The proposed approach may potentially facilitate sandwich design by providing insight into the relationships between material configuration and damage that lead to improved damage tolerance characteristics.