Anthony M. Waas

Compressive failure of composites, part I: Testing and micromechanical theories

Abstract When structures made of composite materials are designed to be used in load bearing applications, a primary consideration is the evaluation of their load carrying capacity in compression. To this end, a vast number of research investigations, whose main objective is linked to ascertaining the compressive strength of a composite structure has been carried out and/or is currently being performed. Apart from its practical significance, the complexity associated with the task of predicting compression strength is the main reason for the overt attention this problem is receiving. One such difficulty has been associated with testing. When laboratory tests are carried out to determine compression strength, structural instabilities dictated by the geometry of the structure may interfere with material strength dictated by the mechanical properties of the constituents and their alignment and geometry (needed to describe the microstructure of the material). In addition stress concentrations may occur at undesirable locations. In Part I, issues pertaining to compression testing and micromechanical failure theories are reviewed.

Compressive failure of composites, part II: Experimental studies

Abstract In Part I of this two part sequence, issues related to compression testing of composites and micromechanical failure models were reviewed. The present paper (Part II) is written with a focus on understanding experimental studies that have been carried out to illuminate those micromechanical influences that affect compression strength. The use of model composites to study compression failure is discussed. The advantages and disadvantages of the many different experimental techniques to measure fiber strengths are presented. Many suggestions for future investigations are given.

Compressive response and failure of braided textile composites: Part 1—experiments

Abstract Experimental results obtained by examining the planar biaxial compression/tension response of carbon 2D triaxial braided composites (2DTBC) are reported in this paper. These experiments were motivated by a need to examine the failure of 2DTBC in a state of stress that would be similar to what is experienced by the walls of a tubular member under compressive crush loads. Results obtained from a series of biaxial tests that were conducted with different proportional displacement loading ratio combinations of compression and tension are reported. In all cases, the dominant failure mechanism under such a stress state is the buckling of the bias and axial tows within the composite. Full field surface displacement data is acquired concurrently during all biaxial and some uniaxial tests using the technique of digital speckle photography. Digital images of the specimen surface that is illuminated with a He–Ne laser are acquired at discrete time intervals during the loading history using a high-resolution digital camera. These images are stored and analyzed to obtain the incremental inplane surface displacement field, Δu(x,y) and Δv(x,y). From these, the incremental inplane surface strains Δex, Δey and Δγxy are obtained by numerical differentiation. The present paper, which is the first in a two part series, is devoted to the biaxial experimental results pertaining to 2DTBC failure.

Numerical Implementation of a Multiple-ISV Thermodynamically-Based Work Potential Theory for Modeling Progressive Damage and Failure in Fiber-Reinforced Laminates

A thermodynamically-based work potential theory for modeling progressive damage and failure in fiber-reinforced laminates is presented. The current, multiple-internal state variable (ISV) formulation, referred to as enhanced Schapery theory, utilizes separate ISVs for modeling the effects of damage and failure. Damage is considered to be the effect of any structural changes in a material that manifest as pre-peak non-linearity in the stress versus strain response. Conversely, failure is taken to be the effect of the evolution of any mechanisms that results in post-peak strain softening, resulting in a negative tangent stiffness. It is assumed that matrix microdamage is the dominant damage mechanism in continuous fiber-reinforced polymer matrix laminates, and its evolution is controlled with a single ISV. Three additional ISVs are introduced to account for failure due to mode I transverse cracking, mode II transverse cracking, and mode I axial failure. Typically, failure evolution (i.e., post-peak strain softening characterized through a negative tangent stiffness) results in pathologically mesh dependent solutions within a finite element (FE) framework. Therefore, consistent characteristic lengths are introduced into the formulation to govern the evolution of the three failure ISVs. Using the stationarity of the total work potential with respect to each ISV, a set of thermodynamically consistent evolution equations for the ISVs are derived. The theory is implemented in association with the commercial FE software, Abaqus. Objectivity of total energy dissipated during the failure process, with regards to refinements in the FE mesh, is demonstrated. The model is also verified against experimental results from two laminated, T800/3900-2 panels containing a central notch and different fiber-orientation stacking sequences. Global load versus displacement, global load versus local strain gage data, and macroscopic failure paths obtained from the models are compared against the experimental results.

Characterization of carbon nanotubes produced by arc discharge: Effect of the background pressure

Single walled carbon nanotubes (SWNT) produced by the anodic arc discharge over a range of constant background pressures of helium (100–1000 Torr) were examined under a high-resolution transmission electron microscope, and a Raman spectrometer. It was found that the average SWNT diameter is about 2 nm and fairly independent of the background pressure. Analysis of the relative purity of SWNTs samples suggests that highest SWNT relative concentration can be obtained at background pressure of about 200–300 Torr. Measured anode ablation rate increases linearly with background pressure. The model of the anodic arc discharge was developed. It was found that the predicted anode ablation rate agrees well with experiment suggesting that electron temperature in the anodic arc is about 0.5 eV.

Convective Heat Transfer in Open-Cell Metal Foams

Convective heat transfer in aluminum metal foam sandwich panels is investigated with potential applications to actively cooled thermal protection systems in hypersonic and reentry vehicles. The size eects of the metal foam core are experimentally investigated and the eects of foam thickness on convective transfer are established. Four metal foam specimens are utilized with a relative density of 0.08 and pore density of 20 ppi in a range of thickness from 6.4 mm to 25.4 mm in increments of approximately 6 mm. An exact-shapefunction nite element model is developed that envisions the foam as randomly oriented cylinders in cross o w with an axially varying coolant temperature eld. Our experimental results indicate that larger foam thicknesses produce increased heat transfer levels in metal foams. Initial FE simulations using a fully developed, turbulent velocity prole show the potential of this numerical tool to model convective heat transfer in metal foams. Metal foam sandwich panels have been proposed as alternative multi-functional materials for structural thermal protection systems in hypersonic and re-entry vehicles 1 . 2 This type of construction oers numerous advantages over other actively cooled concepts because of the unique properties of metal foams. These materials, when brazed between metallic face sheets, are readily suited to allow coolant passage without the addition of alien components that may compromise structural performance. Moreover, the mechanical properties can be varied to suit dieren t structural needs by varying the foam relative density. From a heat transfer point of view, these materials have been shown to be exceptional heat exchangers primarily due to the increased surface area available for heat transfer between the solid and uid phases. The thermo-mechanical response of metal foam sandwich panels has been recently studied and characterized. 2 In particular, it has been shown that using air as coolant at sucien tly high velocities, the strain due to buckling of these structures under thermo-mechanical loads can be virtually eliminated. The implementation of these materials in thermal protection systems, however, requires that a proper heat transfer model exists that allows the coupling between the thermo-mechanical and heat transfer problems to be properly analyzed. In other words, it is necessary to understand how dieren t foam properties such as relative density, pore density, and foam thickness will aect the heat loads that this type of structural component can remove. Heat transfer in metal foams has been a subject of active research in recent years. Lu et al. 3 developed an analytical model envisioning the foam as an array of mutually perpendicular cylinders subjected to cross-o w. In this study, a closed-form expression for the convective coecien t of a foam-lled channel with constant wall temperatures was presented based on foam geometry and material and uid properties. These authors reported that the simplifying assumptions used in their analysis were likely to lead to an over-prediction of the actual heat transfer level. This model has been partially validated by Bastawros and Evans 4 who performed forced convection experiments on aluminum foams adhered to silicon substrate face sheets. These authors reported that the predictions of Lu et al. 3 regarding the dependence of the convective coecien t on coolant velocity and strut diameter were qualitatively consistent with their observations, but that the foam thickness eects were not adequately modeled. In particular, they reported that the heat dissipation rate

The inplane elastic properties of circular cell and elliptical cell honeycombs

SummaryThe inplane elastic properties of perfectly circular and elliptic cell honeycombs are derived through an analytical method and validated numerically. In the case of perfectly circular cell hexagonally packed honeycomb, the inplane elastic properties are shown to be isotropic. However, a departure from circularity of the cells leading to cell ellipticity results in the inplane properties becoming orthotropic. The orthotropic elastic constants are also derived analytically and validated numerically.

Thermal buckling of metal foam sandwich panels for convective thermal protection systems

Sandwich panels with metal foam cores are studied with application to actively cooled thermal protection systems. To evaluate these panels under thermal loading, a novel experimental technique and load frame, which provide a prominent improvement in the simultaneous preservation of thermal and mechanical boundary conditions during thermomechanical structural testing, are introduced and validated. With this technique, the response of metal foam sandwich panels (MFSPs) to thermally induced in-plane equibiaxial loading is investigated, and the elastoplastic pre- and postbuckling response of MFSPs is measured and analyzed. The in-plane response of the panels is quantified with strain-gauge measurements, and the out-of-plane response across the surface of the panel is captured via shadow moire interferometry. These measurements provide direct visualization and quantification of the initial buckled mode shapes, as well as the evolution of the elastoplastic postbuckled mode shapes from initial buckling into the postbuckling regime. This experimental investigation is the first of its kind, complementing the largely theoretical and numerical body of information on the thermomechanical response of sandwich panels.

Size Effects in Metal Foam Cores for Sandwich Structures

The shear response of aluminum foam, including size effects, is measured and quantified for a closed-cell aluminum foam. The shear stiffness is shown to depend linearly on density, whereas the strength exhibits a power law dependence. The linear response is shown to be independent of strain rate up to rates of 0.17/s, whereas the strength and energy absorption increase with increasing strain rate. The density dependence of the stiffness is reproduced analytically based on the composite cylinders model. Optical techniques are used to measure the strain field of the experimental specimens throughout the loading program. By evaluation of concentric subregions of the sample, a sample size of 18 mean cell diameters is determined to be the dimension below which the uncertainty in the predicted shear modulus of an aluminum foam sample increases significantly. This length scale threshold is replicated in a periodic finite element structure with randomly distributed imperfections. I. Introduction M ETAL foams represent an attractive alternative for sandwich structure cores for multiple reasons. First, with metal foam cores, the adhesive substrate of a sandwich structure may be eliminated with in-production integral bonding to metallic face sheets, stiffening the sandwich and broadening its range of operating environments. Second, metal foams exhibit a compressive stress‐strain response that is ideal for energy absorption and impact alleviation with a long, constant stress, plastic strain plateau. 1 Third, an opencell metal foam offers an opportunity to eliminate the catastrophic nature of water or cryogenic gas permeation that has crippled the long-term use of sandwich constructions with honeycomb cores. 2 Fourth, an open-cell construction also allows for active cooling of the sandwich structure, elevating its range of acceptable operating temperatures. For integration into sandwich structures, the shear behavior of metal foam must be understood. Some disparate results regarding shear behavior currently exist in the literature. One study found a linear relationship between shear strength and density, 3 whereas a cubic lattice model subjected to shear loading predicted a nonlinear power law dependence. 4 Another investigation offers only a few data points for shear stiffness and strength of melt-foamed aluminum. 5 Furthermore, these experiments involved thin specimens, with no account for size effects. The present paper offers the full shear response curves for a broad range of density. The density dependence of stiffness and strength are found experimentally with the former being reproduced analytically. The strain rate dependence of the shear response is also considered. The effect of specimen size, relative to the mean cell size, is analyzed experimentally with a unique approach involving digital image correlation. The observed behavior is reproduced with a finite element model. These analyses identify a threshold in the ratio of specimen size to cell size, below which the shear response of a given sample is associated with a significant amount of uncertainty.

Abiotic tooth enamel

Tooth enamel comprises parallel microscale and nanoscale ceramic columns or prisms interlaced with a soft protein matrix. This structural motif is unusually consistent across all species from all geological eras. Such invariability—especially when juxtaposed with the diversity of other tissues—suggests the existence of a functional basis. Here we performed ex vivo replication of enamel-inspired columnar nanocomposites by sequential growth of zinc oxide nanowire carpets followed by layer-by-layer deposition of a polymeric matrix around these. We show that the mechanical properties of these nanocomposites, including hardness, are comparable to those of enamel despite the nanocomposites having a smaller hard-phase content. Our abiotic enamels have viscoelastic figures of merit (VFOM) and weight-adjusted VFOM that are similar to, or higher than, those of natural tooth enamels—we achieve values that exceed the traditional materials limits of 0.6 and 0.8, respectively. VFOM values describe resistance to vibrational damage, and our columnar composites demonstrate that light-weight materials of unusually high resistance to structural damage from shocks, environmental vibrations and oscillatory stress can be made using biomimetic design. The previously inaccessible combinations of high stiffness, damping and light weight that we achieve in these layer-by-layer composites are attributed to efficient energy dissipation in the interfacial portion of the organic phase. The in vivo contribution of this interfacial portion to macroscale deformations along the tooth’s normal is maximized when the architecture is columnar, suggesting an evolutionary advantage of the columnar motif in the enamel of living species. We expect our findings to apply to all columnar composites and to lead to the development of high-performance load-bearing materials.