Simultaneous Shearing Research Articles

Micromechanical modeling of three-dimensional open-cell foams using the matrix method for spatial frames

A micromechanics model for three-dimensional (3D) open-cell foams is developed by using the matrix method for spatial frames and tetrakaidecahedral unit cells. The effective elastic properties of foams are determined utilizing unit cells subjected to loadings of three different modes. The newly obtained member stiffness submatrices for a 3D frame member undergoing simultaneous axial, transverse shearing, flexural and torsional deformations and having a circular or non-circular cross-section are employed. The use of these stiffness submatrices enables the incorporation of all four deformation mechanisms (i.e., stretching, shearing, bending and twisting) possible under the specified loadings and the treatment of four different strut cross-section shapes (i.e., circle, square, equilateral triangle and Plateau border) in a unified manner. The formulas for determining the effective Young's moduli, Poisson's ratios and shear moduli of open-cell foams are derived using the composite homogenization theory. The new formulas, in which the cell displacements are obtained employing the matrix method, include all necessary microstructural and material parameters, unlike those provided by existing models. It is shown that the foam elastic properties depend on the relative foam density, the shape and size of the strut cross-section, and the Young's modulus and Poisson's ratio of the strut material. By applying the new model, a parametric study of sample cases involving the three loading modes and the four strut cross-section shapes is conducted for carbon foams, whose modeling motivated this work. The predicted values of the effective properties agree favorably with those based on existing models and experimental data for the Mode I loading case, which is the only case that has been well studied. For the Mode II and Mode III loading cases, the formulas and the subsequent sample results are presented in a systematic manner for the first time. Comparisons of the predicted effective elastic properties for the three loading cases quantitatively show that carbon foams exhibit certain degrees of anisotropy.

Analysis of simultaneous sheet metal forming operations using elastomer technique

The main aim of this paper is to investigate the feasibility of this technique for the simultaneous forming, embossing and shearing of sheet metals to produce special panels. In the present work the confined system was adopted, where the elastomer was housed in a container. Sheet metal operations consist of different geometries. However, in this work special steel dies were chemically machined to produce the desired shape. Sheet materials with different work hardening behaviour and elastomer of 70–75 Shore hardness were used for the experiments. A simplified analytical treatment is presented for predicting the applied load and the total ram movement required for the forming process. These values are mainly governed by the tool geometry, sheet material and the physical properties of the elastomer pad employed. Other relevant parameters will also be examined.

HRTEM and EELS Studies on the Amorphization of Hexagonal Boron Nitride Induced by Ball Milling

We present a new approach, namely ball milling, to synthesize amorphous boron nitride (a‐BN). The amorphization kinetics are revealed by X‐ray diffractometry (XRD), high‐resolution transmission electron microscopy (HRTEM), and electron energy loss spectroscopy (EELS). HRTEM investigations indicate that, in the early stage of milling, the thick sp2 layers are sliced into many thinner sheets because of cleavage along the basal planes. In the intermediate stage of milling, deformation is accommodated primarily by simultaneous shearing along the basal planes. As a result of sustained shearing, a number of defects, such as stacking faults, (0002) [11¯20] twinning, simultaneous shearing of lattice planes, and half Frank loops with Burgers vectors of 1/2[0001], are introduced in the hexagonal BN (h‐BN) grains. Simultaneous shearing also causes significant change in the lattice symmetry of most grains. In the final stage of milling, the fiberlike tightly bonded sp2 sheets are broken and refined further, until a nanocrystalline and amorphous mixture is formed. XRD of the sample milled for 180 h exhibits an amorphous halo pattern; nevertheless, HRTEM demonstrates that the end product is essentially a nanocrystalline and amorphous mixture. The grain sizes of the nano‐crystals are <3 nm, and their stacking is turbostratic. EELS investigations of the a‐BN indicate that bonding is primarily sp2, but a small fraction of sp3a‐BN is also found, which is assumed to be the nuclei of the cubic phase (c‐BN) in the high‐pressure and high‐temperature experiments and thus facilitates the hexagonal to cubic transition. The present a‐BN fabrication method can provide an effective way to facilitate the synthesis of sintered bulk c‐BN materials.

Stacking disordering in hexagonal BN induced by shearing under ball milling

Significant stacking-disordering within basal planes, such as heavy stacking faults, basal plane twinning or even entirely disordered stackings and shearing of lattice planes, delamination and kink bands were frequently found in most hexagonal BN (h-BN) grains after milling. It is evident that most of these highenergy defect structures are created by simultaneous shearing rather than by dissociation of a perfect dislocation. As a result of frequent shearing, the unitcell shape of the [1120] lattice image changes from a rectangle to a rhombi. Nonbasal plane defects such as half Frank loops, and interstitial and vacancy loops with high-energy stacking configurations were also frequently found. These deformation structures stem inherently from the structural characteristic of h-BN and are significantly different from those observed in fcc metals such as copper.

HRTEM and EELS studies of defects structure and amorphous-like graphite induced by ball-milling

Deformation structures and amorphization kinetics of graphite with high crystallinity upon ball-milling (BM) are studied by high-resolution transmission electron microscopy (HRTEM) and electron energy-loss spectroscopy (EELS). Basal plane stacking disorder, cleavage, delamination cracks, misorientation bands and low-angle (0002) twist boundaries are observed. The basal plane stacking disorder is probably produced by simultaneous shearing of all the lattice planes involved. Other defects such as half Frank loops or interstitial loops and significant bending and buckling of the basal planes are also frequently observed. Sustained shearing of (0002) planes acting in parallel with the increase of the Frank loops finally leads to the breakage of the hexagonal network in a very fine scale until an amorphous-like structure results. Although the amorphous-like phase exhibits amorphous halo diffraction patterns, HRTEM investigations indicate that it consists of highly curled small flakes with average basal plane diameter less than 5 nm and thickness (normal to the basal planes) less than 2 nm. EELS investigations demonstrate that its bonding is essentially sp 2. The present study clarifies the defect configuration appearing in heavily deformed graphite and also shows evidence that the amorphization of graphite is a defect-controlled process.

Fluid pressure and effective stress in sandbox models

Abstract We have done a series of simple tests on sandpacks, involving upward flow of compressed air through the pores and its effect on the yield strength. The ultimate objective is to model deformation coupled with fluid flow in sedimentary basins. For all tests, we used a single batch of Fontainebleau sand, sieved to a grain size between 0.200 and 0.315 mm, poured into a cylindrical container and then fluidized. The density of this sand was 1.585 g/cm3, irrespective of sand thickness. The lithostatic pressure was proportional to the thickness of the sandpack. A yield envelope was obtained by shearing the sandpack horizontally. Compressed air entered the base of the sandpack and flowed upwards through the pore spaces. For 69 measurements on air flow without shearing, a plot of discharge velocity versus gradient of fluid pressure is close to a straight line, verifying Darcy's law and yielding an intrinsic permeability of about 1.7 darcy for the sand. For 72 tests on simultaneous shearing and fluid flow, the estimated effective stress (lithostatic stress minus estimated pore fluid pressure) ranged from 0 to 1600 Pa and the pore fluid ratio (between air pressure and lithostatic pressure) from 0.0 to 1.0. A plot of shear stress versus effective stress at failure is almost linear, verifying Terzaghi's principle of effective stress. The best-fit slope (coefficient of internal friction) is about 0.55 and the intercept on the shear stress axis (cohesion) is less than 85 Pa. The tests show that it is feasible to use compressed air within sandpacks, as a means of modelling deformation coupled with fluid flow. The next step will be to build sandbox models of layered sequences and to investigate detachments caused by abnormal fluid pressures.

Kinetic process of mechanical alloying inFe50Cu50

It is shown that mechanical alloying in the immiscible Fe-Cu system is governed by the atomic shear event and shear-induced diffusion process. We found that an alpha-to-gamma phase transformation, as evidenced by the Nishiyama-Wasserman orientation relationship, occurs by simultaneous shearing process when the grain size reduces to about 20 nm and Cu content reaches 20 at. % in bcc-Fe(rich)Cu grains in the intermediate stage of milling of Fe(50)Cu(50). Further milling promotes the interdiffusion between fcc-Fe(rich)Cu and fcc-FeCu(rich), which is favored because of the similarity of the lattice structures, until a complete fee Fe-Cu solid solution is formed. The results provide significant insight into the understanding of recent experiments showing that chemical mixing of immiscible elements can bd induced by mechanical alloying. [S0163-1829(98)51342-2].

Ductile extrusion of the Higher Himalayan Crystalline in Bhutan: evidence from quartz microfabrics

Quartz textures measured from deformed quartz tectonites within the Lesser Himalaya and Higher Himalaya Crystalline of Bhutan show similar patterns. Orientation and distribution of the quartz crystallographic axes were used to confirm the regional shear sense: the asymmetry of c-axis and a-axis patterns consistently indicates top-to-the-south shearing. The obliquity of the texture and the inferred finite strain (plane strain to moderately constrictional), suggest the strain regime had a combination of rotational and irrotational strain path. In most of the samples from the Bhutan Himalaya, the inferred deformation mechanisms suggest moderate- to high-temperature conditions of deformation that produced the observed crystallographic preferred orientation. Much higher temperature of deformation is indicated in the quartz veins from a leucogranite.The observed ductile deformation is pervasively developed in the rocks throughout the investigated area. The intensity of deformation increases only slightly in the vicinity of the Main Central Thrust. Simultaneous southward shearing within a large part of the Higher Himalaya Crystalline near and above the Main Central Thrust and normal faulting across the South Tibetan Detachment, is explained by the tectonically induced extrusion of a ductily deforming wedge. The process of extrusive flow suggested here can be approximated quantitatively by channel flow models that have been used to describe subduction zone processes. Channel flow accounts for some observed phenomena in the Himalayan orogen such as inverted metamorphic sequences near the Main Central thrust, not related to an inversion of isotherms, and the syntectonic emplacement of leucogranites into the extruding wedge, locally leading to an inversion of isotherms due to heat advection.

The deformation matrix for simultaneous simple shearing, pure shearing and volume change, and its application to transpression-transtension tectonics

Simultaneous simple shearing and pure shearing, with or without additional volume change, can be combined into a single, upper triangular deformation matrix. The off-diagonal term, Γ, is named the effective shear strain, and is a simple function of the pure shearing and simple shearing components. A three-dimensional deformation matrix for the simultaneous combination of coaxial deformation, with or without additional volume change, and up to three simple shearing systems with mutually orthogonal shear planes is also presented. By using this matrix, one can easily extract the various properties of incremental as well as finite strain, and the progressive as well as finite rotation of passive markers during deformation. The case of transpression-transtension is revised, using the unified deformation matrix. The orientation of the major axis of the strain ellipsoid ( λ 1) is always horizontal if the deformation is transtensional, switches from horizontal to vertical during transpressional wrenching (1 > W k > 0.81 for constant vorticity deformations), and is always vertical for highly transpressional deformations ( W k ⩽ 0.81). For transpression, material lines initially rotate towards the horizontal shearing direction, but generally turn to rotate towards the vertical axis after a certain strain. For transtension, all material lines rotate towards a direction in the horizontal plane which is oblique to the shearing direction.