Transverse shear deformation in exact buckling and vibration of composite plate assemblies
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Anderson, Melvin S.↗
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Influence of shear deformation of the cross section on torsional frequencies of box beams
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Davenport, William W↗
Transverse vibrations of hollow thin-walled cylindrical beams
The variational principle, differential equations, and boundary conditions considered appropriate to the analysis of transverse vibrations of hollow thin-walled cylindrical beams are shown. General solutions for the modes and frequencies of cantilever and free-free cylindrical beams of arbitrary cross section but of uniform thickness are given. The combined influence of the secondary effects of transverse shear deformation, shear lag, and secondary effects of transverse shear deformation, shear lag, and longitudinal inertia is shown in the form of curves for cylinders of rectangular cross section and uniform thickness. The contribution of each of the secondary effects to the total reduction in the actual frequency is also indicated. (author)
Budiansky, Bernard↗
Approximate Stress Analysis of Multistringer Beams with Shear Deformation of the Flanges
The problem of the skin-stringer combinations used as axially loaded panels or as covers for box beams is considered from the point of view of the practical stress analyst. By a simple substitution the problem is reduced to the problem of the single-stringer structure, which has been treated in NACA Report no. 608. The method of making this substitution is essentially empirical; in order to justify it, comparisons are shown between calculations and strain-gage tests of three beams tested by the author and of one compression panel and three beams tested and reported elsewhere.
Kuhn, Paul↗
Buckling of sandwich cylindrical shells with shear deformable core through nondimensional parameters
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Ines Uriol Balbin↗
Pressure–strain interaction. I. On compression, deformation, and implications for Pi-D
The pressure–strain interaction describes the rate per unit volume that energy is converted between bulk flow and thermal energy in neutral fluids or plasmas. The term has been written as a sum of the pressure dilatation and the collisionless analog of viscous heating referred to as Pi–D , which isolates the power density due to compressible and incompressible effects, respectively. It has been shown that Pi–D can be negative, which makes its identification as collisionless viscous heating troubling. We argue that an alternate decomposition of pressure–strain interaction can be useful for interpreting the underlying physics. Since Pi–D contains both normal deformation and shear deformation, we propose grouping the normal deformation with the pressure dilatation to describe the power density due to converging/diverging flows, with the balance describing the power density purely due to shear deformation. We then develop a kinetic theory interpretation of compression, normal deformation, and shear deformation. We use the results to determine the physical mechanisms that can make Pi–D negative. We argue that both decompositions can be useful for the study of energy conversion in weakly collisional or collisionless fluids and plasmas, and implications are discussed.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Single-Step Shear-Based Deformation Processing of Electrical Conductor Wires
Commercial electrical conductor wires are currently produced from aluminum alloys by multi-step deformation processing involving rolling and drawing. These processes typically require 10 to 20 steps of deformation, since the plastic strain or reduction that can be imposed in a single step is limited by material workability and process mechanics. Here, we demonstrate a fundamentally different, single-step approach to produce flat wire aluminum products using machining-based deformation that also ensures adequate material workability in the formed product. Two process routes are proposed: (1) chip formation by free-machining (FM), with a post-machining, light drawing reduction (<20%) to achieve desired finish and (2) constrained chip formation by large strain extrusion machining (LSEM). Using commercially pure aluminum conductor alloys (Al 1100 and EC1350) as representative material systems, we demonstrate key features of the machining-based processing, including (a) single-step processing to achieve flat wire geometries, (b) surface finish (Ra = 0.2 to 1.0 μm) comparable to that of commercial wire products made by drawing/rolling, (c) deformation control independent of wire size, and (d) hardness increases of 50–150% over that of annealed wires, while retaining high electrical conductivity (>56% IACS). Here, the wire microstructure, which can also be varied via the large-strain deformation parameters, is correlated with mechanical and electrical properties. Implications for commercial manufacture of flat wire products are discussed.
36 MATERIALS SCIENCE↗
Shear-based deformation processing of age-hardened aluminum alloy for single-step sheet production
Shear-based deformation processing by hybrid cutting-extrusion and free machining are used to make continuous strip, of thickness up to one millimeter, from low-workability AA6013-T6 in a single deformation step. The intense shear can impose effective strains as large as 2 in the strip without pre-heating of the workpiece. The creation of strip in a single step is facilitated by three factors inherent to the cutting deformation zone: highly confined shear deformation, in situ plastic deformation-induced heating and high hydrostatic pressure. The hybrid cutting-extrusion, which employs a second die located across from the primary cutting tool to constrain the chip geometry, is found to produce strip with smooth surfaces (S a < 0.4 μm) that is similar to cold-rolled strip. The strips show an elongated grain microstructure that is inclined to the strip surfaces – a shear texture – that is quite different from rolled sheet. Furthermore, this shear texture (inclination) angle is determined by the deformation path. Through control of the deformation parameters such as strain and temperature, a range of microstructures and strengths could be achieved in the strip. When the cutting-based deformation was done at room temperature, without workpiece pre-heating, the starting T6 material was further strengthened by as much as 30% in a single step. In elevated-temperature cutting-extrusion, dynamic recrystallization was observed, resulting in a refined grain size in the strip. Implications for deformation processing of age-hardenable Al alloys into sheet form, and microstructure control therein, are discussed.
36 MATERIALS SCIENCE↗
Postbuckling of long thick plates in compression including higher order transverse shearing effects
Aluminum plates of various length/width ratios loaded in compression are examined analytically in terms of buckling and postbuckling for comparison with classical theory. The plates are considered to be subjected to longitudinal compressive displacement with no edge stress and are assumed to be simply supported at the side edges. The average longitudinal direct stresses are computed to plot characteristic curves by means of the following theories: 3D flexibility, higher-order shear deformation, first-order shear deformation, and classical von Karman. The 3D flexibility approach yields the lowest results with more unknowns than the higher-order shear-deformation method. The 3D flexibility approach is considered to be the most accurate, and it is shown that the calculated resultants and displacements tend to vary when consideration is given to the effects of transverse shear.
Stein, Manuel↗
Postbuckling response of long thick isotropic plates loaded in compression including higher order transverse shearing effects
Buckling and postbuckling results for aluminum plates loaded in compression are presented. The buckling results were plotted to show the effects of thickness on the stress coefficient. Buckling results are given for various length-to-width ratios. Postbuckling results for plates with transverse shearing flexibility are compared to results from classical theory for various width-to-thickness ratios. The plates are considered to be long with side edges simply supported, with edges free of stress and the plates are subjected to longitudinal compressive displacement. Characteristic curves indicating the average longitudinal direct stress resultant as a function of the applied displacements are calculated based on four different theories: Classical von Karman, first-order shear deformation, higher-order shear deformation, and three-dimensional flexibility. Present results indicate that the three-dimensional flexibility theory gives the lowest and therefore, most accurate results. The higher-order shear deformation theory has fewer unknowns than the three-dimensional flexibility but is not as accurate. The figures presented show that small differences occur in the maximum stress resultants and the transverse displacements calculated when the effects of transverse shear are included.
Stein, Manuel↗
Microstructural evolution in shear-punch tests: A comparative study of pure Cu and Cu-Cr alloy
Understanding the mechanisms behind microstructural evolution during shear deformation has been a long-standing area of interest. However, establishing a connection between microstructure, mechanical properties, and extent of shear deformation is challenging and requires refined experimental approaches. Shear-punch testing (SPT) provides a controlled method to introduce shear into small volumes of material that later can be subjected to detailed microstructural characterization. In this study, we utilize an SPT device to induce shear deformation to pure copper and a binary copper-chromium alloy. Electron backscatter diffraction and transmission electron microscopy were used to study the mechanisms of plastic deformation after SPT. Our results indicate that shear deformation of pure Cu produces a dense network of intercepting microshear bands upon sustained deformation. Twin boundaries undergo degradation into high angle grain boundaries due to simultaneous deviation from the axis-angle pair condition of 60° misorientation on [111] direction. The presence of 50% volume Cr particles in the soft Cu matrix fundamentally altered the shear deformation mechanism. Preferential deformation of the Cu matrix led to accelerated shear-induced formation of low and high angle grain boundaries, and subsequent grain refinement. Comparatively, no grain refinement occurred in pure Cu at a strain ~10 times larger (ϵ = 4.73) than that of the copper-chromium case (ϵ = 0.42). Overall, our study sheds light on the microstructural evolution during shear deformation and highlights the significant influence of particle reinforcements on the shear deformation mechanisms of metals.
36 MATERIALS SCIENCE↗
Postbuckling response of long thick plates loaded in compression including higher order transverse shearing effects
Buckling and postbuckling results are presented for compression-loaded simply-supported aluminum plates and composite plates with a symmetric lay-up of thin + or - 45 deg plies composed of many layers. Buckling results for aluminum plates of finite length are given for various length-to-width ratios. Asymptotes to the curves based on buckling results give N(sub xcr) for plates of infinite length. Postbuckling results for plates with transverse shearing flexibility are compared to results from classical theory for various width-to-thickness ratios. Characteristic curves indicating the average longitudinal direct stress resultant as a function of the applied displacements are calculated based on four different theories: Classical von Karman theory using the Kirchoff assumptions, first-order shear deformation theory, higher-order shear deformation theory, and 3-D flexibility theory. Present results indicate that the 3-D flexibility theory gives the lowest buckling loads. The higher-order shear deformation theory has fewer unknowns than the 3-D flexibility theory but does not take into account through-the-thickness effects. The figures presented show that small differences occur in the average longitudinal direct stress resultants from the four theories that are functions of applied end-shortening displacement.
Stein, Manuel↗
Postbuckling response of long thick plates loaded in compression including higher order transverse shearing effects
This paper presents buckling and postbuckling results for compression-loaded simply-supported aluminum plates and composite plates with a symmetric lay-up of thin +/-45-deg plies composed of many layers. Buckling results for aluminum plates of finite length are given for various length-to-width ratios. Asymptotes to the curves based on the buckling results give N(XCr) for plates of infinite length. Postbuckling results for plates with transverse shearing flexibility are compared to results from classical theory for various width-to-thickness ratios. Characteristic curves indicating the average longitudinal direct stress resultant as a function of the applied displacements are calculated based on four different theories: classical von Karman theory using the Kirchhoff assumptions, first-order shear deformation theory, higher-order shear deformation theory, and three-dimensional flexibility theory. Present results indicate that the three-dimensional flexibility theory gives the lowest buckling loads. The higher-order shear deformation theory has fewer unknowns than the three-dimensional flexibility theory but does not take into account through-the-thickness effects. The figures presented show that small differences occur in the average longitudinal direct stress resultants from the four theories that are functions of applied end-shortening displacement.
Stein, Manuel↗
The effects of transverse shearing and anisotropy on vibration frequencies of laminated cylinders
The natural vibration frequencies of orthotropic and anisotropic, simply supported right circular cylinders are predicted using a theory which takes into account higher-order transverse shear deformation effects. A comparison between results based on first-order transverse shear deformation theory and the higher-order theory indicates that an additional allowance for transverse shear deformation has a negligible effect on the predicted natural vibration frequencies associated with long wavelengths, but significantly reduces the natural vibration frequencies associated with short wavelengths. Results of a parametric study of ply orientation for two classes of laminates indicates that while stacking sequence affects natural vibration frequencies, cylinder geometry and mode shape are more important in accurately predicting transverse shear deformation effects. Transverse shearing effects are less important in predicting natural vibration frequencies associated with long wavelength than in predicting axial compressive buckling loads.
Jegley, D. C.↗
Isotropic seismic radiation from rock damage and dilatancy
SUMMARY We present semi-analytical and numerical results on isotropic radiation expected to be generated by seismic sources with damaged dilatant materials that sustain during failure an overall shear deformation. The results are derived for inclusions with different stiffness components, including those responsible for shear-volumetric coupling in dilatant material, and different geometries, in a surrounding elastic solid. The obtained relations indicate that the isotropic seismic potency and seismic moment components are proportional to the shear potency components multiplied by the aspect ratio between the thickness and length of the source zone. For a typical rupture zone with a thin tabular geometry, the expected small aspect ratio explains the general seismological observations of small isotropic radiation. However, isotropic radiation induced by dynamic dilation for short and thick sources is more pronounced and may reach for spherical sources sustaining shear deformation 18 per cent of the shear components. Sources that include also tensile components and explosions can produce larger isotropic radiation. The results provide rigorous relations that can be used to estimate different source properties in numerical simulations, experiments and field studies.
Geochemistry & Geophysics↗
A higher-order theory for geometrically nonlinear analysis of composite laminates
A third-order shear deformation theory of laminated composite plates and shells is developed, the Navier solutions are derived, and its finite element models are developed. The theory allows parabolic description of the transverse shear stresses, and therefore the shear correction factors of the usual shear deformation theory are not required in the present theory. The theory also accounts for the von Karman nonlinear strains. Closed-form solutions of the theory for rectangular cross-ply and angle-ply plates and cross-ply shells are developed. The finite element model is based on independent approximations of the displacements and bending moments (i.e., mixed finite element model), and therefore, only C sup o -approximation is required. The finite element model is used to analyze cross-ply and angle-ply laminated plates and shells for bending and natural vibration. Many of the numerical results presented here should serve as references for future investigations. Three major conclusions resulted from the research: First, for thick laminates, shear deformation theories predict deflections, stresses and vibration frequencies significantly different from those predicted by classical theories. Second, even for thin laminates, shear deformation effects are significant in dynamic and geometrically nonlinear analyses. Third, the present third-order theory is more accurate compared to the classical and firt-order theories in predicting static and dynamic response of laminated plates and shells made of high-modulus composite materials.
Reddy, J. N.↗
Decoupling of strain and temperature effects on microstructural evolution during high shear strain deformation
The interplay between defect generation by shear strain and defect annihilation by local heating is difficult to predict in shear-assisted processing techniques. In this study, we decoupled the effects of high shear strain and external heating in an immiscible Cu-Nb alloy using a pin-on-disk tribometer to mimic the microstructural evolution of material during solid-phase processing. The change in sub-surface deformation, strain distribution, and redistribution of the second phase as a function of temperature were examined using transmission electron microscopy and atom probe tomography. Zener-Hollomon parameter is used to semi-quantify the deformation of Cu-Nb alloys as a function of strain and temperature.
36 MATERIALS SCIENCE↗