Deformation microstructures and recrystallization in heavily worked copper

Deformation microstructures in two batches of commercially pure copper (A and B) of allnost similar composition have been studied after rolling reductions from 5% to 95%. X- ray diffraction, optical metallography, scanning electron microscopy in the back-scattered mode, transmission and scanning electron microscopy have been used to examine the deformation microstructure. At low strains (~10 %) the deformation is accommodated by uniform octahedral slip. Microbands that occur as sheet like features usually on the {111} slip planes are formed after 10% reduction. The misorientations between rnicrobonds ond the matrix are usually small (1 - 2° ) and the dislocations within the bands suggest that a single slip system has been operative. The number of microbands increases with strain, they start to cluster and rotate after 60% reduction and, after 90 %, they become almost perfectly aligned with the rolling direction. There were no detectable differences in deformation microstructure between the two materials up to a deformation level of 60% but subsequently, copper B started to develop shear bands which became very profuse by 90% reduction. By contrast, copper A at this stage of deformation developed a smooth laminated structure. This difference in the deformation microstructures has been attributed to traces of unknown impurity in D which inhibit recovery of work hardening. The preferred orientations of both were typical of deformed copper although the presence of shear bands was associated wth a slightly weaker texture. The effects of rolling temperature and grain size on deformation microstructure were also investigated. It was concluded that lowering the rolling temperature or increasing the initial grain size encourages the material to develop shear bands after heavy deformation. Recovery and recrystallization have been studied in both materials during annealing. During recrystallization the growth of new grains showed quite different characteristics in the two cases. Where shear bands were present these acted as nucleation sites and produced a wide spread of recrystallized grain orientations. The resulting annealing textures were very weak. In the absence of shear bands, nucleation occurs by a remarkably long range bulging process which creates the cube orientation and an intensely sharp annealing texture. Cube oriented regions occur in long bands of highly elongated and well recovered cells which contain long range cumulative micorientations. They are transition bands with structural characteristics ideally suited for nucleation of recrystallization. Shear banding inhibits the cube texture both by creating alternative nuclei and by destroying the microstructural features necessary for cube nucleation.

Deformation and failure of welded steels used in offshore constructions

Hydrocarbons are the most common form of energy used to date. The activities involving exploration and exploitation of large oil and gas fields are constantly in operation and have extended to such hostile environments as the North Sea. This enforces much greater demands on the materials which are used, and the need for enhancing the endurance of the existing ones which must continue parallel to the explorations. Due to their ease in fabrication, relatively high mechanical properties and low costs, steels are the most widely favoured material for the construction of offshore platforms. The most critical part of an offshore structure prone to failure are the welded nodal joints, particulary those which are used within the vicinity of the splash zones. This is an area of high complex stress concentrations, varying mechanical and metallurgical properties in addition to severe North Sea environmental conditions. The main are of this work has been concerned with the durability studies of this type of steel, based on the concept of the worst case analysis, consisting of combinations of welds of varying qualities, various degrees of stress concentrations and the environmental conditions of stress corrosion and hydrogen embrittlement. The experiments have been designed to reveal significance of defects as sites of crack initiation in the welded steels and the extent to which stress corrosion and hydrogen embrittlement will limit their durability. This has been done for various heat treatments and in some experiments deformation has been forced through the welded zone of the specimens to reveal the mechanical properties of the welds themselves to provide data for finite element simulations. A comparison of the results of these simulations with the actual deformation and fracture behaviour has been done to reveal the extent to which both mechanical and metallurgical factors control behaviour of the steels in the hostile environments of high stress, corrosion, and hydrogen embrittlement at their surface.

A micro-compression study of shape-memory deformation in U-13 at.% Nb

Microcompression specimens, 10–15 µm in diameter by 20–30 µm in height, were produced from individual parent grains in a polycrystalline U–13 at.%Nb shape-memory alloy using the focused ion beam technique. The specimens were tested in a nanoindentation instrument with a flat diamond tip to investigate stress–strain behavior as a function of crystallographic orientation. The results are in qualitative agreement with a single-crystal accommodation strain (Bain strain) model of the shape-memory effect for this alloy.

The influence of composition, temperature and strain rate on the deformation of F.C.C. metals and alloys

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Radial deformation measurement of a cylinder under compression using multicore fibre

A multicore fibre (MCF) sensor to measure the radial deformation of a compliant cylinder under compression is presented. The sensor is connectorised and need not be permanently bonded to the test object. A differential measurement technique using FBGs written into the MCF makes the sensor temperature insensitive. FBG measurement of axial strain of a cylinder under compression is also reported.

Deformation microstructure under nanoindentations in Cu using 3D x-ray structural microscopy

We have used a recently developed x-ray structural microscopy technique to make nondestructive, submicron-resolution measurements of the deformation microstructure below a 100mN maximum load Berkovich nanoindent in single crystal Cu. Direct observations of plastic deformation under the indent were obtained using a ~0.5 µm polychromatic microbeam and diffracted beam depth profiling to make micron-resolution spatially-resolved x-ray Laue diffraction measurements. The local lattice rotations underneath the nanoindent were found to be heterogeneous in nature as revealed by geometrically necessary dislocation (GND) densities determined for positions along lines beneath a flat indent face and under the sharp Berkovich indent blade edges. Measurements of the local rotation-axes and misorientation-angles along these lines are discussed in terms of crystallographic slip systems.

Deformation Lemma, Ljusternik-Schnirellmann Theory and Mountain Pass Theorem on C1-Finsler Manifolds

∗Partially supported by Grant MM409/94 Of the Ministy of Science and Education, Bulgaria. ∗∗Partially supported by Grant MM442/94 of the Ministy of Science and Education, Bulgaria.

Minimum Mean Square Error Approach in Images Processing for Full-field Displacements and Deformation Measurements

A vision system is applied to full-field displacements and deformation measurements in solid mechanics. A speckle like pattern is preliminary formed on the surface under investigation. To determine displacements field of one speckle image with respect to a reference speckle image, sub-images, referred to Zones Of Interest (ZOI) are considered. The field is obtained by matching a ZOI in the reference image with the respective ZOI in the moved image. Two image processing techniques are used for implementing the matching procedure: – cross correlation function and minimum mean square error (MMSE) of the ZOI intensity distribution. The two algorithms are compared and the influence of the ZOI size on the accuracy of measurements is studied.

Radial deformation measurement of a cylinder under compression using multicore fibre

A multicore fibre (MCF) sensor to measure the radial deformation of a compliant cylinder under compression is presented. The sensor is connectorised and need not be permanently bonded to the test object. A differential measurement technique using FBGs written into the MCF makes the sensor temperature insensitive. FBG measurement of axial strain of a cylinder under compression is also reported.

Characterizing permanent deformation and fracture of asphalt mixtures by using compressive dynamic modulus tests

Permanent deformation and fracture may develop simultaneously when an asphalt mixture is subjected to a compressive load. The objective of this research is to separate viscoplasticity and viscofracture from viscoelasticity so that the permanent deformation and fracture of the asphalt mixtures can be individually and accurately characterized without the influence of viscoelasticity. The undamaged properties of 16 asphalt mixtures that have two binder types, two air void contents, and two aging conditions are first obtained by conducting nondestructive creep tests and nondestructive dynamic modulus tests. Testing results are analyzed by using the linear viscoelastic theory in which the creep compliance and the relaxation modulus are modeled by the Prony model. The dynamic modulus and phase angle of the undamaged asphalt mixtures remained constant with the load cycles. The undamaged asphalt mixtures are then used to perform the destructive dynamic modulus tests in which the dynamic modulus and phase angle of the damaged asphalt mixtures vary with load cycles. This indicates plastic evolution and crack propagation. The growth of cracks is signaled principally by the increase of the phase angle, which occurs only in the tertiary stage. The measured total strain is successfully decomposed into elastic strain, viscoelastic strain, plastic strain, viscoplastic strain, and viscofracture strain by employing the pseudostrain concept and the extended elastic-viscoelastic correspondence principle. The separated viscoplastic strain uses a predictive model to characterize the permanent deformation. The separated viscofracture strain uses a fracture strain model to characterize the fracture of the asphalt mixtures in which the flow number is determined and a crack speed index is proposed. Comparisons of the 16 samples show that aged asphalt mixtures with a low air void content have a better performance, resisting permanent deformation and fracture. © 2012 American Society of Civil Engineers.

Caputo Derivatives in Viscoelasticity: A Non-Linear Finite-Deformation Theory for Tissue

Mathematics Subject Classification: 26A33, 74B20, 74D10, 74L15

Melt inclusions from volcan de Colima, Mexico: complex examples of magmatic differentiation

Melt inclusions are minute magma bodies trapped within growing crystals. Their chemical compositions are useful in deciphering pre-eruptive conditions and magma evolution. The present study examined melt inclusions trapped in phenocrysts from the 3rd and 4th magmatic cycles (1869-1988) at Volcan de Colima, Mexico. Melt inclusions have highly evolved chemical compositions: 65-77% SiO2, >12% A12O3, 3-6% Na2O and K20 and less than 5.5% Fe and Mg. Major element compositions suggest that they are strongly differentiated magmas controlled by fractionation of plagioclase, opx, cpx and hornblende. Water concentrations were measured to be 2.7-3.5 wt. % in cpx hosted inclusions and 0.3-0.7 wt % in opx and plagioclase. Trace element compositions are anomalously low and inversely correlate with water. From this we deduce that Colima lavas and scorias simultaneously differentiate and degas. Moreover, hornblende rim growth rates constrain the ascent of the Colima magmas to -100 days for passive eruptions and >4 days for plinian eruptions.