Strain Fringe Research Articles

Superimposed structures, incremental strain and deformation path from field data to modelling: A case study from the Alpi Apuane metamorphic core complex (NW Tuscany, Italy).

In this study, superimposed folds and antitaxial strain fringes are investigated to unravel the deformation path of the core zones of the Alpi Apuane metamorphic complex (northwest Tuscany Italy). Detailed field mapping combined with microstructural analyses is used together with computer-modelling of a complex strain fringe system to disclose the main steps of the Alpi Apuane syn-metamorphic deformation history. A comparison between natural investigated fibres and those produced by paraffine wax experiments provides details of the relative core-object-fringe rotation allowing new insight on the growth kinematics of strain fringes. The results of our analyses show that our composite fringe system is characterized by a first set of fibres to be related with the main composite axial planar foliation of regional scale isoclinal non-cylindric folds. This first set of fibre fringes records a local non-coaxial strain with an absolute core-object rotation (relative to an external reference frame represented by the main foliation) of 140° and a calculated shear strain (γ) of about 4. The second set of fringes, developed after the tilting of the main foliation and the first fringe-set in a sub-vertical orientation, records a lower absolute rotation of the core-object (25°), a lower shear strain (γ) of about 1.4 and a coaxial strain associated with the vertical shortening. This part of the composite fringe system and the related structures may relate to the switch from the crustal scale contractional regime to the extensional one, which characterized the development of the inner northern Apennines orogen.

EBSD and CL Study of Deformed Quartz Grains in Rocks: An Example for one Strain Fringe Structure From Iron Quadrangle.

Kinematic indicators, including certain strain fringes, represent an important group of structures related to the progressive deformation in rocks. The evolution of these fibrous textures can be explained by the combination of multiple mechanisms of deformation and fluid flow, mainly controlled by the orientation of the strain field and the morphology of the grains. In general, the observations are done with an optical microscope and compared with computational models of growth. This work proposes a combination of crystallographic and cathodoluminescence data obtained in rocks from banded iron formations of the Iron Quadrangle in Brazil to represent an example of how complementary analytical techniques can be useful to understand geological problems. The chosen sample exhibits a strain fringe structure of quartz around a clast of magnetite partially transformed into goethite and hematite. Through the crystallographic data it was possible to identify the grain boundary morphology and domains of low deformation areas. On the other hand, the cathodoluminescence signal evidenced the occurrence of grains with a higher concentration of crystalline defects.

Texture, Microstructure and Geochemistry of Magnetite from the Banduhurang Uranium Mine, Singhbhum Shear Zone, India – Implications for Physico-chemical Evolution of Magnetite Mineralization

Abstract The Singhbhum Shear Zone in eastern India is one of the largest repositories of uranium and copper in India. Besides uranium and copper, apatite-magnetite mineralization is widespread in this shear zone. This study aims at deciphering the physico-chemical evolution of magnetite mineralization in relation to progressive shearing integrating field relations, micro-textures, structures and compositions of magnetite in the Banduhurang uranium mine. Apatite-magnetite ores occur as discrete patches, tongues, and veins in the strongly deformed, fine grained quartz-chlorite schist. Textures and microstructures of magnetite indicate at least three stages of magnetite formation. Coarse-grained magnetite (magnetite-1) with long, rotational, and complex strain fringes, defined by fibrous and elongate quartz, is assigned to a stage of pre-/early-shearing magnetite formation. Medium grained magnetite (magnetite-2), characterized by single non-rotational strain fringe equivalent to the youngest fringe of magnetite-1, grew likely at the mid-/late-stage of shearing. Fine grained magnetite (magnetite-3) is generally devoid of any pressure shadow. This indicates even a much later stage of formation of this magnetite, presumably towards the closing stage of shearing. Some of the magnetite-1 grains are optically heterogeneous with a dark, pitted Cr-Ti-bearing core overgrown by lighter, fresh rim locally containing pyrite, chalcopyrite, and chlorite inclusions. The cores are also locally characterized by high Al and Si content. Homogeneous magnetite-1 is optically and compositionally similar to the overgrowth of heterogeneous magnetite-1. This homogeneous magnetite-1 that grew as separate phase is contemporaneous with the overgrowth on pitted core of heterogeneous magnetite-1. Magnetite-2 is compositionally very similar to homogeneous magnetite-1, but is devoid of sulfide inclusion. Magnetite-3 is generally devoid of any silicate or sulfide inclusion and is most pure with least concentrations of trace/minor elements. The high Al and Si content in some magnetite can be explained by coupled substitution that involves substitution of Si4+ for Fe3+ in the tetrahedral sites and Fe2+ for Fe3+ in the octahedral sites, with a simple substitution of Al3+ for Fe3+ in the octahedral sites. The mode of occurrences of apatite-magnetite ores indicates a predominantly hydrothermal origin of most magnetite. However, the Cr-Ti-bearing magnetite-1 cores and inferred mafic nature of the original protolith indicates that some magnetite was inherited from the original igneous rock. We propose that the pre-/early-shearing hydrothermal event of magnetite formation was associated with sulfide mineralization and alteration of existing magmatic magnetite. The second stage of magnetite formation at the mid-/late-stage of shearing was not associated with sulfide formation. Finally, fine-grained compositionally pure magnetite formed at the closing stage of shearing likely due to metamorphism of Fe-rich protolith.

Analysis and Simulation on Dynamic Stress of Tracked Vehicle Sprocket Based on Rigid-Flexible Coupling

This paper established a high-speed tracked vehicle dynamics model, and simulated the transient response of sprocket when the vehicle is running at 60km/h on the D class road. the finite element model of the single tooth in mesh is established in Ansys and the rigid-flexible coupling model of "trackboard- sprocket" is established in RecurDyn. The dynamic stress and strain fringe of the sprocket’s gear ring is achieved by analysis. Simulation results show that the stress of tracked vehicle sprocket gear root and the fixed gear bolt hole is larger, and the stress concentration is detected at the edge of contacted tooth. The simulation results provide the calculation basis for the optimization of the high-speed tracked vehicle system and its lifespan prediction.

Animations of progressive fibrous vein and fringe formation

Abstract: We developed two programs, Vein Growth and Fringe Growth, to investigate progressive growth ofcrystals in dilation sites (veins and strain fringes). Even though these models are based on a simple anisotropicgrowth function, they produce complex textures that compare well with natural examples of veins and strainfringes. In our simulations the most important factor that controls the crystal shape in the dilation site is theroughness of the growth surface (defined by asperities on the wall-rock of veins or core-object of fringe structures)and the amplitude of these asperities relative to the width of the dilation site after an opening-event. Fibrouscrystals (crystals with a high length to width ratio) which can track the opening trajectory of the dilation site willdevelop if grain boundaries of crystals are locked to asperities on the wall-rock of veins or core-object of fringes.This happens only if the amplitude of the asperities is large relative to single opening steps of the dilation site andif crystals grow fast enough to close the site. The width of fibres depends on the number of initial nuclei and onthe distance of adjacent asperities on the wall-rock- or core-object surface. Our simulations suggest that singlefibres should not be used for structural analysis especially in the case of strain fringes since relative rotationbetween fringes and core-object influences fibre-growth directions. We discuss the implications of our modellingresults for the use of crystal textures in veins and strain fringes for structural analysis. keywords: vein, strain fringe, texture, fibre, crack-seal

Isotopic Dating of Strain Fringe Increments: Duration and Rates of Deformation in Shear Zones

The time scales over which deformation in the Earth's crust remains localized in shear zones are poorly known, as are the associated strain rates. We have determined the longevity and rates of deformation using rubidium-strontium (Rb-Sr) microsampling dating of increments of fibrous strain fringes from a Pyrenean shear zone. The fibers grew quasi-continuously through a protracted deformation history between 87 and 50 million years ago, over a period comparable to that of an orogeny. During a short interval between 66 and 62 million years, a rise in strain rate from 1.1 x 10(-15) to 7. 7 x 10(-15) seconds(-1) occurred. This acceleration correlates with an abrupt change in fiber-growth direction and a stress-field inversion from gravitational collapse to renewed horizontal crustal shortening.

Photomechanical behavior of cellulose acetate under viscoelastoplastic deformation

To confirm the possibilities of cellulose acetate as a material for a model analysis during viscoelastoplastic deformation, the time-dependent photomechanical properties of the material were examined by means of creep tests under constant stress and recovery tests after removal of stress. Consequently, though the strain and the fringe order of cellulose acetate during creep and recovery are greatly influenced by stress and room temperature, both of them can be described simply by a power function of time, and the coefficient of each of these formulas can be represented by a function of the ratio of active stress to yield stress only. The effect of temperature is included in the formulation of the yield stress. In addition, the strain and the fringe order can be represented by the viscous-viscoelastic model proposed by Findleyet al.,1,2 in which both of them are divided into four components: elastic, plastic, time-dependent irrecoverable viscous and time-dependent recoverable viscoelastic. The relation between viscoelastic strain and viscoelastic fringe order, and the relation between viscous strain and viscous fringe order were verified to be equivalent to that between plastic strain and plastic fringe order, all of which do not depend on stress, temperature or time. Therefore, the strain distribution of cellulose acetate under viscoelastoplastic deformation can be determined directly from the value of the fringe order measured.

Holographic moiré for strain fringe patterns

New holographic-moire methods are presented to obtain strain fringe patterns. To introduce two carriers of different directions, two kinds of recording procedures are proposed: (1) triple-exposure recording by two object beams and one reference beam (all of these beams are identical in polarization state) and (2) double exposure or real-time recording by two orthogonally polarized object beams and two corresponding reference beams. In these recordings, the carriers are introduced by changing the directions of the reference beams and are modulated by deformation. Separated in-plane displacement derivative patterns are then obtained by optical processings. Both the principles and the experimental results are shown in the paper.

Polarized shearing-moire interferometry for separated 3-D strain fringe patterns

Utilizing laser's properties of both polarization and temporal coherence, a real time method of moire interferometry is proposed to obtain the separated 3-D displacement derivative fringe patterns. For dual beams that contain identical polarization components, the optical-path difference is larger than that of the coherent length to eliminate the interaction between the wavefronts due to the shearing. For dual beams that contain no identical components of polarization, the vibration planes are perpendicular to each other to have the frame-separation of the in-plane derivative patterns. The out-of-plane displacement derivative patterns are achieved by the shearing of the zero-order diffractions of the grating.

A new real-time method of moiré interferometry for displacement derivative fringe patterns

A new method of moiré interferometry is proposed in this paper to obtain the strain fringe pattern in real time. The specimen grating is illuminated by dual beams whose optical path-difference is larger than the coherence length of the laser. The diffractions of the grating are sheared by a glass wedge to fulfil the optical differentiation. The principles based on wavefront analysis are shown and an experimental verification is reported.

Polarized shearing holographic-moirè interferometry

A new holographic-moire method is presented to obtain the in-plane strain fringe patterns. During the recording, double object beams and dual reference beams of orthogonally polarized state are used to illuminate the object and the holographic plate, respectively. Two carriers modulated by deformation are obtained through double-exposure or in real time. Pure in-plane displacement derivative patterns are then obtained through twice filtering.

A Photoelastic Approach to Transient Stress Problems Employing Low-Modulus Materials

Abstract The objective of the program discussed in this paper was to develop a method, using photoelasticity and low-modulus materials, for studying dynamic stress distributions. Early in the program a number of low-modulus materials were studied and Hysol 8705 (a urethane-rubber compound) was selected as the most promising. A complete study of its mechanical and optical properties was made under static and dynamic loadings. It was established, that Poisson’s ratio ν is independent of rate of loading, the stress fringe value fσ is independent of rate of loading for strain rates greater than 8 in/in/ sec, and both the modulus of elasticity E and the strain fringe value fϵ were dependent oil the rate of loading. The specific energy loss for the material was about 10 per cent for the stress ranges associated with photoelastic determinations. Experimental observations of photoelastic fringe patterns in a rectangular strut subjected to axial impact were made to illustrate the potential of the method. Three different end conditions were imposed on the unloaded end of the strut: (a) A free end normal to the axis; (b) a fixed end normal to the axis; and (c) a free end inclined 45 deg to the axis. For the cases where the ends were normal to the axis it was found that the fringes followed the same law of reflection as the law for stresses given by elementary wave theory.

A photoelastic technique for strain measurement on flat aluminium alloy surfaces

A technique is described for bonding layers of an epoxy resin on flat aluminium alloy surfaces. Joints which withstood more than 4% strain were obtained by carefully controlled preparation of the metal and the adhesive. Initial birefringence was avoided by curing the joint without external pressure and by slow cooling after finish curing at 65° C. The different types of reflexion polariscopes are discussed, the strain fringe values for the reflecting layer and for the adhesive are estimated. A test of a lug describes an application of the method.