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Strain Gradients (strain + gradient)
Selected AbstractsNacre in Mollusk Shells as a Multilayered Structure with Strain GradientADVANCED FUNCTIONAL MATERIALS, Issue 7 2009Boaz Pokroy Abstract How do living organisms attain the complicated shapes of grown bio-composites? This question is answered when studying the mechanics of the nacre layer in the bivalve mollusk shells. In this study, the internal strains/stresses across the shell thickness are profiled as a function of depth by strain gauge measurements during controlled etching in the selected areas. Measurements of stress release under etching provide clear evidence that the investigated shells, in fact, are strained multilayered structures, which are elastically bent due to the forces evolving at the organic/inorganic interfaces. The stresses are mostly concentrated in the "fresh" nacre sub-layers near the inner surface of the shell adjacent to the mollusk mantle. This analysis unexpectedly shows that the elastic bending of the nacre layer is due to strain gradients which are originated in the gradual in-depth changes of the thickness of ceramic lamellae. The changes mentioned were directly observed by scanning electron microscopy. By this sophisticated design of the ultra-structure of the nacre layer, the bowed shape of the bivalve shells is apparently achieved. [source] Structural Transformations during Formation of Quasi-Amorphous BaTiO3,ADVANCED FUNCTIONAL MATERIALS, Issue 7 2007D. Ehre Abstract A model of structural transformations of amorphous into quasi-amorphous BaTiO3 is suggested. The model is based on previously published data and on X-ray photoelectron spectroscopy data presented in the current report. Both amorphous and quasi-amorphous phases of BaTiO3 are made up of a network of slightly distorted TiO6 octahedra connected in three different ways: by apices (akin to perovskite), edges, and faces. Ba ions in these phases are located in the voids between the octahedra, which is a nonperovskite environment. These data also suggest that Ba ions compensate electrical-charge imbalance incurred by randomly connected octahedra and, thereby, stabilize the TiO6 network. Upon heating, the edge-to-edge and face-to-face connections between TiO6 octahedra are severed and then reconnected via apices. Severing the connections between TiO6 octahedra requires a volume increase, suppression of which keeps some of the edge-to-edge and face-to-face connections intact. Transformation of the amorphous thin films into the quasi-amorphous phase occurs during pulling through a steep temperature gradient. During this process, the volume increase is inhomogeneous and causes both highly anisotropic strain and a strain gradient. The strain gradient favors breaking those connections, which aligns the distorted TiO6 octahedra along the direction of the gradient. As a result, the structure becomes not only anisotropic and non-centrosymmetric, but also acquires macroscopic polarization. Other compounds may also form a quasi-amorphous phase, providing that they satisfy the set of conditions derived from the suggested model. [source] Feasibility of complementary spatial modulation of magnetization tagging in the rat heart after manganese injectionNMR IN BIOMEDICINE, Issue 1 2008J.-N. Hyacinthe Abstract It has been shown that manganese-enhanced MRI (MEMRI) can safely depict the myocardial area at risk in models of coronary occlusion,reperfusion for at least 2,h after reperfusion. To achieve this, a solution of MnCl2 is injected during coronary occlusion. In this model, the regional function quantification deficit of the stunning phase cannot be assessed before contrast injection using MR tagging. The relaxation effects of manganese (which remains in normal cardiac myocytes for several hours) may alter the tags by increasing tag fading and hence the quality of strain measurement. Therefore, we evaluated the feasibility of cardiac MR tagging after manganese injection in normal rats. Six normal Sprague,Dawley rats were imaged in vivo using complementary spatial modulation of magnetization (C-SPAMM) at 1.5,T, before and 15,min after intraperitoneal injection of MnCl2 solution (,17.5,µmol,kg,1). The contrast-to-noise ratio of the tag pattern increased significantly (P,<,0.001) after injection and remained comparable to the control scan in spite of the higher myocardial relaxation rate caused by the presence of manganese. The measurements of circumferential strain obtained from harmonic phase imaging analysis of the tagged images after MnCl2 injection did not differ significantly from the measurements before injection in the endocardial, mid-wall, and epicardial regions. In particular, the transmural strain gradient was preserved. Thus, our study suggests that MR tagging could be used in combination with MEMRI to study the acute phase of coronary artery disease. Copyright © 2007 John Wiley & Sons, Ltd. [source] Phase modulation effects in X-ray diffraction from a highly deformed crystal with variable strain gradientACTA CRYSTALLOGRAPHICA SECTION A, Issue 5 2009M. Shevchenko The X-ray interbranch scattering by lattice distortions is studied for a thin crystal whose thickness is appreciably less than the conventional X-ray extinction length. The concept of interbranch phase modulation of the X-ray wavefield is extended to the case of a large gradient which depends on depth inside the crystal. The prominent interbranch features of the diffracted intensity are also established within this concept. Numerical calculations of the diffracted intensity are presented for an exponential strain gradient model to illustrate this. Diffraction (extinction) contrast is discussed for a strongly deformed specimen containing a single dislocation. It is predicted that for large values of the X-ray extinction length the extinction contrast may arise even in the case of a very thin crystal. This effect, owing to the interbranch phase changes of the waves scattered in the deformed matrix, is observed in experiments with protein crystals. [source] A Fourier optics approach to the dynamical theory of X-ray diffraction , continuously deformed crystalsACTA CRYSTALLOGRAPHICA SECTION A, Issue 4 2004Giovanni Mana X-ray diffraction in continuously deformed crystals is considered by application of Fourier optics and from the viewpoint of the analogy between X-ray dynamics and the motion of two-level systems in quantum mechanics. Different forms of Takagi's equations are traced back to a common framework and it is shown that they are different ways to represent the same propagation equation. A novel way to solve Takagi's equations in the presence of a constant strain gradient is presented and approximation methods derived from quantum mechanics are considered. Crystal deformation in X-ray interferometry and two-crystal spectrometry are discussed and it is demonstrated that Si lattice-parameter measurements depend on the diffracting plane spacing on the crystal surface. [source] Fatigue damage analysis in a duplex stainless steel by digital image correlation techniqueFATIGUE & FRACTURE OF ENGINEERING MATERIALS AND STRUCTURES, Issue 2 2008A. EL BARTALI ABSTRACT Strain field measurements by digital image correlation today offer new possibilities for analysing the mechanical behaviour of materials in situ during mechanical tests. The originality of the present study is to use this technique on the micro-structural scale, in order to understand and to obtain quantitative values of the fatigue surface damage in a two-phased alloy. In this paper, low-cycle fatigue damage micromechanisms in an austenitic-ferritic stainless steel are studied. Surface damage is observed in real time, with an in situ microscopic device, during a low-cycle fatigue test performed at room temperature. Surface displacement and strain fields are calculated using digital image correlation from images taken during cycling. A detailed analysis of optical images and strain fields measured enables us to follow precisely the evolution of surface strain fields and the damage micromechanisms. Firstly, strain heterogeneities are observed in austenitic grains. Initially, the austenitic phase accommodates the cyclic plastic strain and is then followed by the ferritic phase. Microcrack initiation takes place at the ferrite/ferrite grain boundaries. Microcracks propagate to the neighbouring austenitic grains following the slip markings. Displacement and strain gradients indicate probable microcrack initiation sites. [source] Nacre in Mollusk Shells as a Multilayered Structure with Strain GradientADVANCED FUNCTIONAL MATERIALS, Issue 7 2009Boaz Pokroy Abstract How do living organisms attain the complicated shapes of grown bio-composites? This question is answered when studying the mechanics of the nacre layer in the bivalve mollusk shells. In this study, the internal strains/stresses across the shell thickness are profiled as a function of depth by strain gauge measurements during controlled etching in the selected areas. Measurements of stress release under etching provide clear evidence that the investigated shells, in fact, are strained multilayered structures, which are elastically bent due to the forces evolving at the organic/inorganic interfaces. The stresses are mostly concentrated in the "fresh" nacre sub-layers near the inner surface of the shell adjacent to the mollusk mantle. This analysis unexpectedly shows that the elastic bending of the nacre layer is due to strain gradients which are originated in the gradual in-depth changes of the thickness of ceramic lamellae. The changes mentioned were directly observed by scanning electron microscopy. By this sophisticated design of the ultra-structure of the nacre layer, the bowed shape of the bivalve shells is apparently achieved. [source] An experimental method for determining the effects of strain gradients in a granular materialINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 8 2003Matthew R. Kuhn Abstract The paper presents an algorithm for use with the discrete element method to study possible strain-gradient effects in granular materials. The algorithm produces an intentionally non-uniform displacement pattern by applying external (body) forces to the particles within a simulated granular assembly. The paper describes a method for adjusting the external forces to attain the intended gross displacement pattern, but while allowing individual particles to be in equilibrium among neighbouring particles. The performance of the algorithm is tested in an example of quasi-static deformation, and the algorithm's performance is measured in three respects. The algorithm is shown to enforce the intended displacement pattern, to allow particles to equilibrate among neighbouring particles, and to produce a smooth distribution of the external forces among particles. Copyright © 2003 John Wiley & Sons, Ltd. [source] On the C1 continuous discretization of non-linear gradient elasticity: A comparison of NEM and FEM based on Bernstein,Bézier patchesINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 10 2010P. Fischer Abstract In gradient elasticity, the appearance of strain gradients in the free energy density leads to the need of C1 continuous discretization methods. In the present work, the performances of C1 finite elements and the C1 Natural Element Method (NEM) are compared. The triangular Argyris and Hsieh,Clough,Tocher finite elements are reparametrized in terms of the Bernstein polynomials. The quadrilateral Bogner,Fox,Schmidt element is used in an isoparametric framework, for which a preprocessing algorithm is presented. Additionally, the C1 -NEM is applied to non-linear gradient elasticity. Several numerical examples are analyzed to compare the convergence behavior of the different methods. It will be illustrated that the isoparametric elements and the NEM show a significantly better performance than the triangular elements. Copyright © 2009 John Wiley & Sons, Ltd. [source] Nucleation and growth of myrmekite during ductile shear deformation in metagranitesJOURNAL OF METAMORPHIC GEOLOGY, Issue 7 2006L. MENEGON Abstract Myrmekite is extensively developed along strain gradients of continuous, lower amphibolite facies shear zones in metagranites of the Gran Paradiso unit (Western Alps). To evaluate the role of stress, strain energy and fluid phase in the formation of myrmekite, we studied a sample suite consisting of weakly deformed porphyric granites (WDGs), foliated granites (FGs) representative of intermediate strains, and mylonitic granites (MGs). In the protolith, most K-feldspar is microcline with different sets of perthite lamellae and fractures. In the WDGs, abundant quartz-oligoclase myrmekite developed inside K-feldspar only along preexisting perthite lamellae and fractures oriented at a high angle to the incremental shortening direction. In the WDGs, stress played a direct role in the nucleation of myrmekites along interfaces already characterized by high stored elastic strain because of lattice mismatch between K-feldspar and albite. In the FGs and MGs, K-feldspar was progressively dismembered along the growing network of microshear zones exploiting the fine-grained recrystallized myrmekite and perthite aggregates. This was accompanied by a more pervasive fluid influx into the reaction surfaces, and myrmekite occurs more or less pervasively along all the differently oriented internal perthites and fractures independently of the kinematic framework of the shear zone. In the MGs, myrmekite forms complete rims along the outer boundary of the small K-feldspar porphyroclasts, which are almost completely free of internal reaction interfaces. Therefore, we infer that the role of fluid in the nucleation of myrmekite became increasingly important as deformation progressed and outweighed that of stress. Mass balance calculations indicate that, in Al,Si-conservative conditions, myrmekite growth was associated with a volume loss of 8.5%. This resulted in microporosity within myrmekite that enhanced the diffusion of chemical components to the reaction sites and hence the further development of myrmekite. [source] | |||||||||||||