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DOE OSTI2025

Competition between roughness and strength for scale-dependent surfaces

Rocks famously have scale-dependent strength, yet the actual dependence is notoriously hard to measure or incorporate into any theoretical framework. Natural rough surfaces present an opportunity to solve the problem. Surfaces sliding in shear evolve as protrusions collide. These asperities can deform or break, thus creating a new surface shape. In particular, natural surfaces have roughness at all scales as well as scale-dependent strength. Based on a scaling analysis, we have previously suggested that the scale-dependent aspect ratio of steady-state surfaces should be proportional to the scale-dependent shear strain at yield. If true, scale-dependent strength could easily be inferred from natural surfaces. Thus, moving beyond the scaling argument to a rigorous treatment of scale-dependent strength for multiscale rough surfaces in shear is important. However, analytic frameworks for analyzing multiscale problems are challenging, as conventional continuum mechanics typically involves a single value for a material property across scales. Here, in this work, we build on the formalism of Persson (2001) that presents a method to compute contact area for rough surfaces with a prescribed topographic spectrum using a stochastic differential equation. The Persson formalism allows for plastic yield under normal loading of otherwise elastic materials and leaves open the possibility of scale-dependent yield stress. In this study, we pursue this route to develop a theory and numerical results for the yielding of a rough, elastoplastic surface with scale-dependent yield stress. Here, we examine surfaces for which the power spectrum of the topography 𝐶 and yield stress 𝑌 follow power laws as a function of scale 𝜆, such that 𝐶∼𝜆 −𝑚 and 𝑌∼𝜆 −𝑛 , respectively. In this formal treatment of the problem, we focus on surfaces in contact and the resulting yield and do not impose shear. Numerical solutions show that the deviation from the elastic scaling solution is bounded as expected by the prior 1D heuristic scaling argument that anticipates the Hurst exponent as 1−𝑛. We also show that the plasticity is expected to erode the contacts if 𝑚 is lower than 𝑛−3, which corresponds to a Hurst exponent lower than 1−𝑛/2. This result is rigorously sound for 2D, i.e., realistic surfaces, and quantitatively different than the prior scaling argument. The theory now permits a correspondingly quantitative approach to interpreting natural surfaces.

elasticity↗

NASA NTRS1985

Stability and vibration of isotropic, orthotropic and laminated plates according to a higher-order shear deformation theory

A higher-order shear deformation theory is used to demonstrate the natural frequencies and buckling loads of elastic plates. The theory accounts for parabolic distribution of the transverse shear strains through the thickness of the plate and rotary inertia. Exact solutions of simply supported plates are obtained and the results are compared with the exact solutions of three-dimensional elasticity theory, the first-order shear deformation theory, and the classical plate theory. The present theory predicts the frequencies and buckling loads more accurately when compared to the first-order and classical plate theories.

Reddy, J. N.↗

NASA NTRS1986

A refined shear deformation theory for the analysis of laminated plates

A refined, third-order plate theory that accounts for the transverse shear strains is presented, the Navier solutions are derived for certain simply supported cross-ply and antisymmetric angle-ply laminates, and finite-element models are developed for general laminates. The new theory does not require the shear correction factors of the first-order theory (i.e., the Reissner-Mindlin plate theory) because the transverse shear stresses are represented parabolically in the present theory. A mixed finite-element model that uses independent approximations of the generalized displacements and generalized moments, and a displacement model that uses only the generalized displacements as degrees of freedom are developed. The displacement model requires C sup 1-continuity of the transverse deflection across the inter-element boundaries, whereas the mixed model requires a C sup 0-element. Also, the mixed model does not require continuous approximations (between elements) of the bending moments. Numerical results are presented to show the accuracy of the present theory in predicting the transverse stresses. Numerical results are also presented for the nonlinear bending of plates, and the results compare well with the experimental results available in the literature.

Reddy, J. N.↗

NASA NTRS1983

Damping mechanisms in fiber reinforced laminates

Low strain damping in fiber reinforced composite materials is due to material loss factors in both fibers and matrix materials. The high modulus of the fibers makes up for the low damping factor. Strains high enough to cause transverse layer cracking in laminates with organic matrix materials causes a large permanent increase in the damping factor. This increase is not due to the transverse cracks but rather to short microcracks in the high shear strain regions. Other damping mechanisms at high strains are also discussed.

Plunkett, R.↗

NASA NTRS2000

Satellite-Derived Dynamics of Southern Ocean Sea Ice

Antarctic ERS-2, RADARSAT Synthetic Aperture Radar and ERS-1/2 Scatterometer images were analyzed with SMMI radiometer image time-series data to investigate seasonal variability in satellite-tracked sea-ice dynamics in the Southern Ocean during 1992. Supporting field data were acquired during 'in-situ' experiments including the winter 1992 Ice Station Weddell and Winter Weddell Gyre studies. A variety of surface measurements were made during these experiments including Argos-buoy deployment and GPS drift measurements. These are used in conjunction with International Program for Antarctic Buoys drift trajectories for ice-motion tracking validation. Comparisons between gridded Special Sensor Microwave Imager (SSMI) ice-motion vectors and European Center for Medium Range Weather Forecasts/National Centers for Environmental Prediction (ECMWF/NCEP) analyses indicate that large-scale drift is forced predominantly by the long-term mean, large-scale synoptic pressure field. Only sub-daily SAR sea-ice tracking can capture high-frequency fluctuations, driven by polar lows or tidal forcing. In these cases, sea-ice drift can respond rapidly to changes in forcing on semi-diurnal time scales depending on the location with respect to the coastline. Seasonality of ice drift, particularly in the Weddell and Ross Seas, is linked to ice extent and compactness, and internal ice stresses transmitted through the pack ice from the coast. Three-monthly seasonal climatologies are presented of austral winter of ice drift in the Southern Ocean. The large Weddell and Ross Sea gyres are clearly resolved along with key seasonal and spatial attributes of their cyclonic circulation. Regional time series of ice dynamics parameters are used to illustrate correlations with meteorological forcing. Persistent divergence such as that occurring in the Ronne-Filchner polynya system results in large fractions of new ice. Similarly, convergence zones produce large fractions of deformed ice and characterize the dynamics of regions where perennial ice is observed. High shear strains also help delineate the axis of the Antarctic divergence in many places in the ice cover. In these regions, the separation between the coastal 'east wind drift'and ACC-dominated drift regimes is characterized by zonally extended regions of intense shear.

Drinkwater, Mark R.↗

NASA NTRS1978

A biaxial method for inplane shear testing

A biaxial method for performing inplane shear tests of materials using a shear frame is described. Aluminum plate and sandwich specimens were used to characterize the uniformity of shear strain imparted by the biaxial method of loading as opposed to the uniaxial method. The inplane stiffening effect of aluminum honeycomb core was determined. Test results for (+ or - 45) graphite-epoxy laminate are presented. Some theoretical considerations of subjecting an anisotropic material to a uniform shear deformation are discussed.

Bush, H. G.↗

NASA NTRS2002

Automation Tools for Finite Element Analysis of Adhesively Bonded Joints

This article presents two new automation creation tools that obtain stresses and strains (Shear and peel) in adhesively bonded joints. For a given adhesively bonded joint Finite Element model, in which the adhesive is characterised using springs, these automation tools read the corresponding input and output files, use the spring forces and deformations to obtain the adhesive stresses and strains, sort the stresses and strains in descending order, and generate plot files for 3D visualisation of the stress and strain fields. Grids (nodes) and elements can be numbered in any order that is convenient for the user. Using the automation tools, trade-off studies, which are needed for design of adhesively bonded joints, can be performed very quickly.

Tahmasebi, Farhad↗

DOE OSTI2021

Evaluating Effects of Shear Processing on 2D Crystalline Materials in 3D Metal Matrices: Atomistic Understanding of High Shear Deformation of Copper Graphene Composites

Composites made of copper and graphene demonstrate high strength, lubricity and enhanced electrical and thermal conductivity compared pure copper. However, manufacturing these composites at bulk volumes for industrial applications has been a big challenge. Shear deformation assisted processing is an effective method for manufacturing materials such as copper-graphene composites demonstrating ultra-fine grain structures and compositional homogeneity. Nevertheless, microstructural evolution of the composites and their property development under such conditions is not clearly understood currently. To rectify this gap in literature, high strain shear deformation of copper coated graphene foils was performed using a tribometer pin in this study. Changes in microstructure of the composite as well as the constituent components under shear deformation was correlated to process conditions. A sharp increase in the coefficient of friction attributed to rupture and smearing of graphene layer into copper substrate was observed during the shear processing. The coefficient of friction of the sheared copper/graphene composite was lower than that of pure copper, suggesting that partially worn graphene is effectively lubricious at the macroscale. A multimodal characterization of the processed region further revealed a shear deformation-induced ultrafine two-phase grain-structure consisting of copper and graphitic domains. Shear deformation reduced the copper grain size from around 50 – 100 µm to ~200 nm on an average and ~2 – 5 nm in some locations. The semicrystalline graphene films were observed to fracture into 10 – 50 µm size flakes. Oxygen enrichment was observed in the processed region. Finally, graphitic domain were identified for the first time in the copper matrix and not just at the grain boundaries providing evidence for a metastable composite microstructure as a result of solid phase processing at room temperature.

36 MATERIALS SCIENCE↗

NASA NTRS2002

Three-Dimensional Postbuckling Analysis of Curved Beams

Presented here is a method of solving highly flexible curved beam undergoing huge static or quasi-static deformations. A geometrically exact beam theory based on the use of Jaumann stresses and strains and exact coordinate transformation is presented in terms of 17 first-order ordinary differential equations, and a multiple shooting method is used to solve the corresponding nonlinear two-point boundary value problems. The geometrically exact beam theory accounts far large rotations, large displacements, initial curvatures, extensionality, and transverse shear strains. Four examples are used to demonstrate this method, including a rotating clamped-free beam under the influence of gravity and centrifugal forces, an L-frame subjected to an in-plane tip load, a circular arch subjected to a concentrated load, and a clamped-hinged helical spring subjected to an axial displacement. Results show that the combination of the multiple shooting method and the geometrically exact beam theory works very well. Moreover, the obtained numerically exact solutions can be used to verify the accuracy of nonlinear finite element codes for nonlinear analysis of complex structures.

Pai, P. Frank↗

NASA NTRS1972

Magnetostriction and magnetoelastic quantum oscillations in P-type lead telluride

A detailed experimental and theoretical study of quantum oscillations in the magnetostriction and Young's modulus of p-PbTe is presented. The valance band of PbTe is approximated by a spheroidal, nonparabolic model in which the effects of strain on the valance band parameters are described by a deformation potential model. Using appropriate thermodynamic derivatives of the modified Lifshitz-Kosevich expression for the oscillatory parts of the electronic free energy, it is shown that both types of oscillations arise mainly from relative shifts of the valance band maxima due to shear strains, accompanied by intervalley charge transfer. Band parameters derived from the periods, phases, and spin splitting of the oscillations are in generally good agreement with values reported by other workers. A detailed comparison is made of the experimentally observed oscillation amplitudes with those predicted by theory, and satisfactory agreement is found. The ratio of the amplitudes of the two effects yields a value of the valance band deformation potential in good agreement with a value found from piezoresistance experiments by Burke.

Thompson, T. E.↗

NASA NTRS1972

Aspect of cumulative fatigue damage under multiaxial strain cycling.

The concept of order of loading and its effect on cumulative fatigue damage under multiaxial strain cyclings was investigated. The effect is illustrated through nonlinear relationships between biaxial fatigue damage and cycle-ratio diagrams. Uniaxial theories such as Miner's method, the convergence method, and the double linear damage rule in its special and generalized form, were examined and extended to the biaxial case through the octahedral shear strain theory. The generalized double linear damage rule was found more applicable to biaxial cumulative fatigue damage.

Zamrik, S. Y.↗

NASA NTRS1990

A semi-micromechanic interlaminar strain analysis on curved-beam specimens

Experimental analyses were performed for determination of interlaminar strains in circumferentially unidirectional curved beam specimens. Semi-circular and semi-elliptic carbon-epoxy specimens were subjected to opening mode tensile loadings. Whole field measurements were recorded at load levels from about 5 to more than 90 pct of failure loads. Contour maps of displacement fields were obtained by using moire interferometry, using reference gratings of 2400 lines/mm or 60,690 lines/in. Whole field contour maps of circumferential and interlaminar strains were obtained by using moire interferometry in a semi-micromechanic scale. Various anomalous effects were observed in the displacement fields. The zig-zag fringe patterns indicated that the fiber orientation in each layer was not truly circumferential. This deviation from the unidirectionality caused free-edge effects, such as interlaminar shear strains even at the axis of symmetry and the altered normal strains in the thickness direction. In the resin rich zones between layers, the tensile interlaminar strain was excessively large due to the large compliance. As the result of the combined effect of these anomalous behaviors, the values of the interlaminar tensile strains were larger than those predicted analytically. The modulus E sub 3 was actually smaller than the assumed value E sub 2 by 20 pct.

Joh, Duksung↗

NASA NTRS1974

Time-dependent, non-Newtonian behavior of viscoelastic materials

A kinetic model for characterizing the shear stress or shear strain rate of thixotropic materials is developed and combined with Oldroyd's viscoelastic model (1953) modified in this paper in order to predict the first normal stress difference. In order to test the method, transient and steady state data have been obtained with a Weissenberg rheogoniometer used to measure the constant stress and constant shear rate of a solution of polymethyl methacrylate in diethylphthalate. A computer was used to facilitate data acquisition.

Jachimiak, P. D.↗

NASA NTRS1978

Determining crustal strain rates with spaceborne geodynamics ranging system data. 1: Baseline analysis

A satellite-borne laser ranging system is proposed that is capable of making highly precise geodetic measurements over baselines ranging from a few tens of kilometers to several hundred kilometers. The precision with which crustal strain rates are derived from measurements made with this system is analyzed by using simple site configurations, intersite distances of about 25-70 kilometers, and measurement programs ranging from a few years to fifteen years. It is concluded that precisions of several parts in 10 to the 9th power per year are achievable. Compared to the expected shear strain rates of about 7 x 10 to the minus 7th power yr/1, this produces very favorable signal-to-noise ratios.

Cohen, S. C.↗

DOE OSTI2021

Molecular dynamics simulation of vacancy and void effects on strain-induced martensitic transformations in Fe-50 at.% Ni model concentrated solid solution alloy

Strain-induced martensitic transformations can improve the strength and ductility of some face centered cubic (FCC) metals and alloys. Irradiation-induced defects such as vacancies, dislocation loops, and voids activate martensitic transformations over a wider range of mechanical loading conditions than in pristine material. Furthermore, the mechanisms underlying irradiation-enabled martensite transformations remain unclear. In this work, we use molecular dynamics simulations to study the effect of vacancies and voids on strain-induced martensitic transformations in a model concentrated solid solution alloy Fe-50 at.% Ni. It has been found that single vacancies have no resolvable effect on the transformation because they reduce the stacking fault energy by a relatively insignificant margin and do so only if the vacancy is located on the stacking fault plane. Voids, however, activate the martensite transformation through shear strain accumulation around the void due to dislocation pileup. The larger the void, the more pronounced this effect.

36 MATERIALS SCIENCE↗

NASA NTRS1978

Behavior of a turbulent boundary layer subjected to sudden transverse strain

Data from two experiments on the development of the components of the Reynolds stress tensor after a sudden application of transverse strain are compared. Computations were based on four different turbulence models: a first-order mixing length model, a second-order two-equation eddy viscosity model, and two second-order Reynolds stress models. The second-order models do not produce dramatic improvements over the simple mixing length model. The Reynolds stress models still need development to represent the physics of shear-strained turbulence well. Finally, it is demonstrated that the assumption of a scalar eddy viscosity, often used in engineering calculations of three-dimensional boundary layers, is quite reasonable.

Higuchi, H.↗

NASA NTRS1982

Cracked shells under skew-symmetric loading

A shell containing a through crack in one of the principal planes of curvature and under general skew-symmetric loading is considered. By employing a Reissner type shell theory which takes into account the effect of transverse shear strains, all boundary conditions on the crack surfaces are satisfied separately. Consequently, unlike those obtained from the classical shell theory, the angular distributions of the stress components around the crack tips are shown to be identical to the distributions obtained from the plane and antiplane elasticity solutions. Extensive results are given for axially and circumferentially cracked cylindrical shells, spherical shells, and toroidal shells under uniform inplane shearing, out of plane shearing, and torsion. The effect of orthotropy on the results is also studied.

Lelale, F.↗

DOE OSTI2024

Unveiling Structural Heterogeneity and Imbalance of Gold Decahedral Nanoparticles using Four-dimensional Scanning Transmission Electron Microscopy

Multi-twinned structures have been observed in technologically important crystal systems, for example diamond cubic and face-centered cubic (FCC) lattices, that include materials such as diamond, silicon, a wide range of noble metals, and their nanoscale counterparts. Beyond atomic building blocks, the special arrangements also occur in the self-assembly of nanoparticles (NP) and μm-sized colloidal particles and occupy parts of their phase diagrams. Spanning a wide range of length scales, the universality of the structures arises when the systems attempt to achieve multitwinned structures by overcoming geometric misfits during minimizing surface energies with entirely {111} or close-packing facets. While it is fundamental to understand how strain is sustained upon twinned structures and symmetry breaking, the knowledge will be paramount in practical aspects such as guiding and controlling the thin film growth, anisotropic NP growth, and self-assembly of NPs. Au decahedral (Dh) NP, as the most prevalent multi-twinned model system, fits five tetrahedral motifs into a circle by sharing an axis resulting in a geometric misfit angle of 7.35°, or a disclination with power of -7.35°. Postulating how Au FCC lattice adopts the misfit, theoretical models have been developed to address the underlying lattice symmetry and inhomogeneous strain distribution separately. Yet, experimental reports regarding the former have been limited due to the relatively large X-ray beam sizes that do not fit the sizes of NPs. On the other hand, though the latter has been widely adapted in the thermodynamics of small (<10 nm) multi-twinned nanoparticles, previous literature has shown that, at edge length of 17 nm, the theory’s is invalidated by shear strain that is observed in a defect-free Au Dh NP by high-resolution transmission electron microscopy (HR-TEM) imaging. Though the advancement of aberrationcorrected scanning transmission electron microscopy (AC-STEM) imaging and ab initio calculation techniques brings new opportunities, along with challenges in complicated image analysis and limitation in particle size (usually below 10 nm), the gap between nanoscale and mesoscale has never been extended to gain insight from atomic system with straightforward interaction potentials.

4D-STEM↗