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Autocorrelation and Multifractal Detrended Fluctuation Analyses Reveal Superdiffusive Mass Transport in Solvent-Filled Nanoporous Media

Fluorescence fluctuation spectroscopy experiments were conducted to better understand the complex mass transport dynamics of organic molecules in liquid-filled nanoporous media. Anodic aluminum oxide (AAO) membranes incorporating 10 and 20 nm diameter cylindrical pores were employed as model materials. Nile red (NR) dye was used as a fluorescent tracer. The dye was dissolved separately in ethanol and toluene at a concentration of 20 nM and used to fill the membrane nanopores. Confocal fluorescence microscopy was employed to capture photon intensity time series data reflecting apparent diffusion of the dye within the pores. Autocorrelation of these data revealed that NR diffusion within the membranes occurred over a broad range of time scales. The autocorrelation decays were fit to a model for one-dimensional diffusion incorporating both fast and slow components having apparent diffusion coefficients, D f and D s , differing by a factor of ∼100. The fast mechanism was attributed to hindered bulk-like diffusion in the central pore cavity, while slow diffusion likely involved absorption of the dye to the pore surfaces. Unfortunately, important evidence of diffusion anomalies is lost in the broad autocorrelation decays obtained. The method of multifractal detrended fluctuation analysis (MF-DFA) was applied to the same data as a means to overcome this limitation. MF-DFA revealed that time series acquired from within the nanopores were multifractal and exhibited evidence of anomalous superdiffusion, likely resulting from the participation of a desorption-mediated diffusion mechanism. Monte Carlo simulations of time series modeling desorption-mediated diffusion in cylindrical nanopores provided support for this assignment. Here, the new knowledge gained affords an improved understanding of hydrocarbon dynamics within nanoporous oil and gas shales.

Diffusion

Growth of fungi in NaCl-MgSO4 brines

Previous investigations have shown that common fungi of the Penicillium-Aspergillus group can be grown in a variety of brines or on moist salt crystals. This simulates salt flats as well as sizeable waterbodies stabilized as saturated brines such as Don Juan Pond (Antarctica), the Great Salt Lake of Utah, and the Dead Sea in the Jordan Valley. In general, salt media rich in KCl are favored over other alkali halides; the media become more selective as the salt concentration rises and nutrient requirements become more complex. In the present paper, it is shown that media which resemble the Dead Sea salt mix can, in fact, support the growth of selected fungal strains, even in the absence of reduced organic nutrients other than glucose. Such media may serve as models for localized microhabitats on Mars.

Siegel, S. M.

Developing Lanthanide-Nitrate Cluster Chemistry toward Rare Earth Separations

Nitrate-decorated hexamers with a [Ln 6 (μ 6 -O)(μ 3 –OH) 8 ] 8+ core have been reported for nearly every lanthanide ion and are used as precursors for the assembly of functional metal–organic frameworks. Yet, few studies have examined the correlation between the solution and solid-state species, and the formation of mixed-metal clusters. Toward this end, a series of homo- and heterometal lanthanide nitrate hexamers was prepared via pH adjustment of aqueous lanthanide nitrate solutions. Examination of the homometallic europium solutions using Small Angle X-ray Scattering and nESI-MS showed that lower order complexes dominate lanthanide speciation in nitrate media. Yet, powder X-ray diffraction data of the precipitated phase confirmed the formation of [Ln 6 (μ 6 -O)(μ 3 -OH) 8 (NO 3 ) 6 (H 2 O) 12 ]·2(NO 3 )·n(H 2 O), Ln 6 , for Ln = Eu and Tb. For heterometal systems, analysis of the solid-state product by ICP–MS showed the selective incorporation of the heavier rare earths into Ln 6 . Selectivity was quantified by calculating an average separation factor, which is defined as the ratio of recovery factors of both metals. Further examination of the luminescence behavior of mixed metal [Tb 6–x Eu x (μ 6 -O)(μ 3 -OH) 8 (NO 3 ) 6 (H 2 O) 12 ]·2(NO 3 )·n(H 2 O), with x = 1.1–3.6, showed that the relative intensities of the peaks at 489 nm (terbium, 5 D 4 → 7 F 6 ) and 690 nm (europium, 5 D 0 → 7 F 4 ) trend with the percent incorporation of europium and terbium into the cluster.

anions

Electroanalytical characterization of Np( VI )/Np( V ) redox in a pentadentate ligand environment and stabilization of [Np V O 2 ] + by hydrogen bonding

The redox chemistry of the actinyl cations (AnO 2 n+ ) heavily influences their reactivity and speciation in solution, but the redox properties of the actinyls in non-aqueous media have received far less attention than they deserve. Here, the non-aqueous electrochemistry of a chemically reversible Np(VI)/Np(V) redox manifold is reported in both protic (CH 3 OH) and aprotic (CH 3 CN) organic media. Using a neutral Np(VI) complex supported by a chelating and strongly donating pentadentate ligand that was fully characterized in prior work, a clean Np(VI)/Np(V) redox couple was found to be accessible under ambient conditions. Coupled electrochemical and spectroscopic studies, as well as simulations of cyclic voltammetry data, confirm the 1e− nature of this couple and establish it to be chemically reversible and nearly electrochemically reversible as well. Bulk electrolysis of a solution of the neutral Np(VI) complex facilitated isolation of the corresponding anionic and monomeric Np(V) species. Data from X-ray diffraction analysis as well as optical and vibrational spectroscopies provide strong evidence in support of metal-centered reduction and the Np(V) oxidation state, findings that are in accord with the measured reduction potentials. Distinctive hydrogen bonding interactions between the terminal (yl) oxo groups and water molecules appear to stabilize the isolated Np(V) species in the solid state, providing insight into the features that afford the uncommon chemically reversible redox encountered in this system.

Mikeska, Emily R.

Fostering a Guiding Multiscale Model for the Development of Advanced MgB 2 Hydrogen Storage Materials (Final Technical Report)

Project Goal and Objective. The demand for energy and for an upgraded energy infrastructure has steadily grown, as have the needs for energy independence and alternatives to our reliance on petroleum. Hydrogen is considered the most viable fuels for wide-scale implementation in the near future as it is less-polluting, non-toxic, and has more stored energy than petroleum. It is envisioned that hydrogen can eventually become the prime energy carrier, integrating the transportation, grid, and chemical sectors in a way that improves resiliency, diversifies feedstocks, and affords new economic opportunities. A key remaining challenge is the development materials with enhanced gravimetric and volumetric hydrogen storage capacities that offer a higher performance than compressed gas. These materials would eliminate the need for large-scale compression, thereby dramatically reducing the footprint and cost of gas storage. The high gravimetric and volumetric hydrogen capacities of complex hydrides has prompted an intensive investigation of the potential of this class of materials as hydrogen storage media over the past 25 years. Among the many complex hydrides that have been explored, magnesium borohydride, Mg(BH 4 ) 2 , has been found to possess the best combination of practical thermodynamic properties. These include a gravimetric H 2 density of 14.9 wt% H 2 and thermodynamics for the dehydrogenation of Mg(BH 4 ) 2 to MgB 2 (equation 1) (ΔH° = 39 kJ/mol H 2 , ΔS = 112 J/K mol H 2 ) which lie in the narrow window required Mg(BH 4 ) 2 $\Leftrightarrow$ MgB 2 + 4 H 2 (1) for reversibility under moderate pressure and temperature. However, overcoming the extremely slow kinetics of the reversible release of hydrogen by this material in the solid state is a daunting challenge. At temperatures greater than 400 °C, the borohydride releases up to 14 wt% hydrogen giving MgB 2 . We discovered that the direct re-hydrogenation of MgB 2 to Mg(BH 4 ) 2 can be accomplished under 950 bar H 2 at 400 °C. While this demonstrated that complete reversibility can be achieved, the conditions employed are far too extreme for commercial hydrogen storage applications. More recently, we found through US DOE funded research projects (EERE HyMARC and HySCOR), that hydrogen cycling, can be accomplish at much milder conditions upon modification of the borohydride or boride. Guided by these discoveries these discoveries, the objective of this research project was to obtain key information that will enable the development of a model of reversible hydrogenation of MgB 2 to Mg(BH 4 ) 2 . The ultimate goal of our efforts is to attain a model of this transformation that can be utilized to accelerate development further advanced materials. This project directly follows on discoveries that were made over the course of a US DOE, EERE HyMARC project that was focused on improvement of the hydrogen cycling kinetics of modified MgB 2 . We found that that mechanical milling with graphene results the desired, pronounced kinetic enhancement. The dramatic lowering of the conditions required for the hydrogenation of MgB 2 is a significant step towards overcoming its chemical inertness allowing its development as a practical onboard hydrogen storage material. However, the exact nature of the modification(s) of MgB 2 that is responsible for its activation towards hydrogenation is completely unknown. This situation is not unique, as efforts to develop hydrogen storage materials typically have a narrow focus rather than a comprehensive approach that takes atomic level bonding and structure; molecular dynamics; long range, nano- and mesoscale-structure and their interconnection all into account. The goal of this project was the development of a comprehensive, multi-scale computational model of reversible hydrogenation of MgB 2 to Mg(BH 4 ) 2 that can be utilized for development of higher performance versions of the modified material. Development of the model requires determination of: 1) the bulk, nano-scale, and meso-scale structural changes occurring at elevated pressure following mechano-chemical modification of MgB 2 ; 2) the reaction pathway of the reversible hydrogenation of MgB 2 to Mg(BH 4 ) 2 ; 3) the effect of elevated pressure and mechano-chemical modification on the chemical reaction pathways; 4) the interactions at solid-gas interfaces; and particle surfaces; and 5) the kinetics and thermodynamic parameters associated with each step of the hydrogenation reaction pathway. This investigation required advanced techniques as preliminary, standard XRD, 11 B NMR, and FTIR analysis showed no signs of material modification. In order to gain this level of understanding of modified MgB 2 , required the teaming of a diverse group of experts and state-of-the art experimental capabilities at the University of Hawaii at Manoa (UHM) and collaborating National Laboratories: Craig Jensen , Department of Chemistry (PI and Project Director), solid state, solution, and high pressure NMR spectroscopy; solid-state synthesis; and high pressure hydrogenation (collaboration with SNL); Godwin Severa , Hawaii Natural Energy Institute (co-PI) calorimetry; infrared and Raman spectroscopy (collaboration with NREL); Dera , high pressure X-ray diffraction including in situ experiments (collaboration with ANL); Hope Ishii , Hawaii Institute of Geophysics electron microscopy investigations (collaboration with LBNL); and Joe Brown , Mechanical Engineering , material electronic structure and electric field effects.

08 HYDROGEN

Electro-optical terrain reflectance modeling - A perspective

Electro-optical terrain reflectance modeling is one of the components required in the overall capability to simulate remote sensing measurement systems as an aid to the sensor or information processing designer. Given that sensor fields-of-view may vary from a few centimeters to several meters and that measurement devices may be placed at varying heights above the terrain surface, modeling of complex combinations of terrain classes or media with respect to both vertical and horizontal scales may be required. This paper addresses the issue of combining modeling approaches for different classes of materials in the optical regime and recommends a more formal approach to the radiative characterization of media properties as well as the calculation of the bidirectional reflectance distribution functions.

Smith, J. A.

The relationship between eddy-transport and second-order closure models for stratified media and for vortices

The question is considered of how complex a model should be used for the calculation of turbulent shear flows. At the present time there are models varying in complexity from very simple eddy-transport models to models in which all the equations for the nonzero second-order correlations are solved simultaneously with the equations for the mean variables. A discussion is presented of the relationship between these two models of turbulent shear flow. Two types of motion are discussed: first, turbulent shear flow in a stratified medium and, second, the motion in a turbulent line vortex. These two cases are instructive because in the first example eddy-transport methods have proven reasonably effective, whereas in the second, they have led to erroneous conclusions. It is not generally appreciated that the simplest form of eddy-transport theory can be derived from second-order closure models of turbulent flow by a suitably limiting process. This limiting process and the suitability of eddy-transport modeling for stratified media and line vortices are discussed.

Donaldson, C. D.

Environmental matrix and moisture influence soil microbial phenotypes in a simplified porous media incubation

Soil moisture and porosity regulate microbial metabolism by influencing factors, such as system chemistry, substrate availability, and soil connectivity. However, accurately representing the soil environment and establishing a tractable microbial community that limits confounding variables is difficult. Here, we use a reduced-complexity microbial consortium grown in a glass bead porous media amended with chitin to test the effects of moisture and a structural matrix on microbial phenotypes. Leveraging metagenomes, metatranscriptomes, metaproteomes, and metabolomes, we saw that our porous media system significantly altered microbial phenotypes compared with the liquid incubations, denoting the importance of incorporating pores and surfaces for understanding microbial phenotypes in soils. These phenotypic shifts were mainly driven by differences in expression of Streptomyces and Ensifer, which included a significant decrease in overall chitin degradation between porous media and liquid. Our findings suggest that the success of Ensifer in porous media is likely related to its ability to repurpose carbon via the glyoxylate shunt amidst a lack of chitin degradation byproducts while potentially using polyhydroxyalkanoate granules as a C source. We also identified traits expressed by Ensifer and others, including motility, stress resistance, and carbon conservation, that likely influence the metabolic profiles observed across treatments. Together, these results demonstrate that porous media incubations promote structure-induced microbial phenotypes and are likely a better proxy for soil conditions than liquid culture systems. Furthermore, they emphasize that microbial phenotypes encompass not only the multi-enzyme pathways involved in metabolism but also include the complex interactions with the environment and other community members.

54 ENVIRONMENTAL SCIENCES

Selective Reduction of Carbon Dioxide in Water Using [M(bpy2+)(CO)3(I)]2+ (M = Mn, Re) Electrocatalysts with Pendent Cations

Manganese(I) carbonyl complexes are promising electrocatalysts for CO2 reduction, yet their application in homogeneous aqueous media remains limited by poor solubility and selectivity. Here, we report water-soluble Mn(I) and Re(I) complexes fac-[M(bpy2+)(CO)3X]2+ (X = I or Cl), featuring bipyridine ligands functionalized with -Ph-CH2-(NMe3)+ cationic ammonium groups that integrate water solubility with secondary-sphere stabilization. In bicarbonate buffer at pH 6.8, the Mn catalyst is completely selective for CO production at a low overpotential (η = 0.3 V), operating by a protonation-first mechanism with observed rates of ~10 s−1. Pulse radiolysis reveals that the one-electron reduced Mn species undergoes dimerization in the absence of CO2 but uniquely reacts competitively with CO2 through an initial pre-equilibrium followed by fast formation of a dinuclear CO2-bridged species (ΔGo = −12.4 kcal mol−1). At a higher 0.6 V over-potential, a faster reduction-first pathway (~100 s−1) is available upon reduction of the metallo-carboxylic acid intermediate, Mn-CO2H2+; however, this regime is functionally limited by the formation of a resistive, noncatalytic film on the electrode surface. Comparison to the analo-gous water-soluble Re catalyst (kobs = 440 s−1, η = 0.6 V) highlights the distinct mechanistic ad-vantages of earth-abundant Mn in low-potential catalysis. These results demonstrate how cati-onic second-sphere design enables selective, homogeneous CO2 reduction in water while reveal-ing competing radical and electrode-mediated processes that govern catalytic performance.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH

Evaluating Np(v) disproportionation: effect of Np concentration

The role of Np(V) concentration as a potential chemical driver of Np(V) disproportionation was investigated by probing Np redox chemistry in two different acid media using visible-near-infrared absorbance spectroscopy. In situ spectroscopy of chemically and electrochemically manipulated Np oxidation states at molar concentrations of Np underscores the difficulty in stabilizing pure Np(V), even in dilute acid. A Np(VI) component coexisting with the majority Np(V) component was observed in both HNO 3 and HCl. Electrochemical tuning and subsequent spectroscopic analysis of the Np(VI/V) ratio revealed neptunyl self-complexation as a key mechanism occurring in both acid media. Chemical reduction of the Np(VI) component and stabilization of a minor Np(IV) component in HNO 3 were observed; however, spectral data indicated that these two oxidation states were not observed to coexist, and pure Np(V) was stabilized only briefly. These findings demonstrate that high Np concentrations significantly affect the redox chemistry of Np in acidic solutions. Finally, the occurrence of Np(V) disproportionation could not be definitely determined by spectral data, but other mechanisms such as self-complexation and radiolysis, which potentially compete with disproportionation, must be considered.

Gilson, Sara E. [Oak Ridge National Laboratory (OR

A Multiscale Approach to Simulate Non‐Isothermal Multiphase Flow in Deformable Porous Materials

Coupled thermal, hydraulic, and mechanical processes in porous materials play important roles in several energy and environmental technologies. The Darcy-Brinkman-Biot (DBB) framework has proven effective in modeling multiphase fluid flow in deformable porous solids across both pore and Darcy scales, including in systems where fractures coexist with a porous matrix. In this study, we extend the DBB framework, originally designed for isothermal conditions, to address non-isothermal problems by incorporating an energy conservation equation. The resulting solver, hybridBiotThermalInterFoam, enables simulations of coupled multiphase fluid flow, heat transfer, and solid deformation in hybrid-scale systems containing both solid-free regions and ductile porous domains. The new solver is validated through comparisons with analytical solutions and, also, against established heat transfer solvers chtMultiRegionFoam and compressibleInterFoam. Further, a series of 2D and 3D case studies, including two-phase heat transfer in solid-free, static, or deformable porous media, highlights the solver's capacity to simulate complex flow dynamics and heat transport in systems involving high mobility ratios, viscous fingering, and fracture propagation. Our results establish the feasibility of incorporating thermal effects in simulations of a wide variety of energy geotechnics and environmental applications, including enhanced hydrocarbon recovery, soil remediation, and enhanced geothermal energy systems.

04 OIL SHALES AND TAR SANDS

Multi-Ion Complexes and Competition from Bulky BArF – Anions for Chloride Binding in Ion Pairing Conditions

Cationic charges have long been used to enhance anion binding. Embedding charge introduces strong ion pairing for target anions but also for off-target ions, ultimately generating a mixture of multi-ion species that are hard to identify and quantify. While many sidestep this problem using polar solvents and weakly coordinating ions, these approaches exclude a substantial cross-section of conditions found in applications spanning recognition, assembly, separations, templation, and catalysis. To confront this complexity, we study the binding of an anion to a cationic receptor featuring low shape complementarity in a low-polarity solvent to maximize ionic interactions. We prepared the receptor as a salt of the weakly coordinating tetrakis­[3,5-bis­(trifluoromethyl)­phenyl]­borate (BArF – ) anion and studied the binding of small chloride (Cl – ) and medium-sized iodide (I – ) anions. Surprisingly, the use of the bulky BArF – anion does not suppress ion pairing interactions, with 65% of the receptor being paired at 0.5 mM in dichloromethane. We observe multi-ion receptor-Cl – complexes (2:1, 1:1, 1:2), reinforcing the complexity that emerges when working in low-polarity media. Here, we reveal the dependence of affinity on anion charge density and size and that bulky BArF – counteranions compete for chloride binding. These studies reveal the noninnocence of BArF – anions and strategies to quantify multi-ion species.

Ion pairing

Shallow Rate-Redox Potential Scaling in Aqueous Molecular Oxygen Reduction Electrocatalysis Across a Family of Iron Macrocycles

Rate-overpotential scaling relationships have been employed widely to understand trends in oxygen reduction reaction (ORR) electrocatalysis by dissolved metal macrocycles in organic electrolytes. Similar scaling relationships remain unknown for surface-adsorbed ORR electrocatalysts in the acidic aqueous environments germane to proton-exchange membrane (PEM) fuel cells. Herein, we examine ORR catalysis in aqueous perchloric acid media for a structurally diverse array of iron macrocycle complexes adsorbed on Vulcan carbon black. The macrocycles encompass Fe– N 4 , Fe–N 2 N' 2 and Fe–N x C 4-x motifs bearing pyrrolic, pyridinic, and N-heterocyclic carbene (NHC) moieties in the primary ligation sphere, giving rise to a 670 mV range in Fe(III/II) redox potentials, E Fe(III/II) . Experimental Tafel data in the micropolarization regime were extrapolated to the E Fe(III/II) to furnish estimated per-site-normalized current density (j per-site ) values that span ~4.6 orders of magnitude across the family of compounds. Despite the structural diversity of this family of compounds, extrapolated j per-site values correlate with the Fe(III/II) redox potentials in a roughly log-linear fashion with a shallow scaling factor of approximately 145 mV/decade. Further, these findings highlight that negative shifts in E Fe(III/II) lead to diminishing returns in catalytic rate promotion and suggest that changes to the primary ligating environment in a macrocycle are insufficient to break fundamental rate-potential scaling relationships in aqueous ORR catalysis. Together these studies motivate the further development of higher-potential iron complexes that employ motifs beyond the equatorial ligation plane to enhance ORR catalysis.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH

Systematic improvement of redox potential calculation of Fe(III)/Fe(II) complexes using a three-layer micro-solvation model

Electrochemical transformations of metal ions in aqueous media are challenging to model accurately due to the dynamic solvation structure surrounding ions at different charge states. Predictive modeling at the atomistic scale is essential for understanding these solvation architectures but is often computationally prohibitive. In this contribution, we present a simple, fast, and accurate three-layer micro-solvation model to evaluate the redox potential of metal ions in aqueous solutions. Our model, developed and validated for Fe 3+ /Fe 2+ redox potentials, combines the DFT-based geometry optimizations of the octahedral Fe complex with two layers of explicit water molecules to capture solute–solvent interactions and an implicit solvation model to account for bulk solvent effects. This approach yields accurate predictions for Fe 3+ /Fe 2+ redox potentials in water, achieving errors of 0.02 V with ωB97X-V, 0.01 V with ωB97X-D3, 0.04 V with ωB97M-V, and 0.02 V with B3LYP-D3 functionals. We further demonstrate the generality of our model by applying it to additional metal complexes, including the challenging Fe(CN) 6 3−/4− system, where our model successfully achieves close agreement with experimental values, with an error of 0.07 V and an average error of 0.21 V for all five systems. In summary, the presented simple solvation model has broad applicability and potential for enhancing computational efficiency in redox potential predictions across various chemical and industrial processes of metal ions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH

Probing the influence of ion-pairing on ligand-field excited-state dynamics

Exploration of the photophysical and photochemical properties of transition metal complexes has driven ground-breaking advancements in solar energy conversion technologies, including photoredox catalysis. While significant research has been devoted to understanding excited state properties of second- and third-row transition metal complexes, earth-abundant first-row metal complexes have received comparatively little attention in this context until very recently. In particular, the role of ion-pairing – which has been identified as a potentially significant factor for Ir(III)-based photosensitizers – has not been examined with regard to its influence on the ligand-field excited states that dominate much of first-row photophysics. A key challenge in studying ion-pair interactions lies in quantifying the extent and nature of ion-pairing, particularly in non-aqueous media where the vast majority of photophysical studies are performed. Cobalt(III) polypyridyl complexes provide an attractive platform to address such questions due to their demonstrated potential for applications in photoredox catalysis involving ligand-field excited states. In the present study, we prepared a cobalt(III) polypyridyl complex, [Co(4,4′-OMebpy) 3 ](BAr F 4 ) 3 (where 4,4′-OMebpy is 4,4′-dimethoxy-2,2′-bipyridine and BAr F 4 is tetrakis(3,5-bis(trifluoromethyl)-phenyl)borate) to probe ion-pairing in non-aqueous solutions. Specifically, analysis of data acquired from both variable-temperature diffusion ordered spectroscopy (DOSY) NMR and 1-D rotating-frame nuclear Overhauser effect (ROE) experiments allowed us to identify and differentiate between solvent-separated ion pairs in high-dielectric media and contact ion pairs in a low-dielectric solvent. Time-resolved absorption spectroscopy was then used to measure ground-state recovery dynamics under these varying conditions of ion-pairing, the results of which revealed an increase in excited-state lifetime for contact ion-pairs that we suggest arises from a reduction in outer-sphere reorganization energy relative to conditions which favored solvent-separated ion pairs. We believe this study demonstrates that one can leverage broadly available NMR-based methods to understand ion-pairing in non-aqueous solutions, which in turn can provide a microscopic picture of intermolecular interactions that can impact the photophysical properties of transition metal-based chromophores.

Ghosh, Atanu [Michigan State University, East Lans

Parametric study of stress-intensity factors in bonded composite stringer panels

Stress-intensity factors are determined for an infinite cracked orthotropic sheet adhesively bonded to an orthotropic stringer. Since the stringer is modeled as a semi-infinite sheet, the solution is most appropriate for a crack tip located near a stringer edge. Both adherends are treated as homogeneous, orthotropic media which are representative of many fiber-reinforced composite materials. The complex variable theory of elasticity was used to obtain a set of integral equations describing the problem. The integral equations are replaced by an equivalent sheet of algebraic equations, which are solved to obtain the shear stress distribution in the adhesive layer. From these adhesive stresses, the stress-intensity factors are found. A parametric study is conducted to determine the sensitivity of the system to material properties and specimen configuration. Unless the crack tip is very close to or under the stringer, the stress-intensity factor is approximately that of the unstiffened sheet. However, as the crack propagates beneath the stringer, the stress-intensity factor decreases significantly. Increasing the stringer stiffness or the adhesive stiffness also decreases the stress-intensity factor.

Bigelow, C. A.