Crack tip stress study for elastic-perfectly plastic materials with some applications

The problems of plasticity and non-linear fracture mechanics have been generally recognized as the most difficult problems of solid mechanics. The present dissertation is devoted to some problems on the intersection of both plasticity and non-linear fracture mechanics. The crack tip is responsible for the crack growth and therefore is the focus of fracture science. The problem of crack has been studied by an army of outstanding scholars and engineers in this century, but has not, as yet, been solved for many important practical situations. The aim of this investigation is to provide an analytical solution to the problem of plasticity at the crack tip for elastic-perfectly plastic materials and to apply the solution to a classical problem of the mechanics of composite materials.^ In this work, the stresses inside the plastic region near the crack tip in a composite material made of two different elastic-perfectly plastic materials are studied. The problems of an interface crack, a crack impinging an interface at the right angle and at arbitrary angles are examined. The constituent materials are assumed to obey the Huber-Mises yielding condition criterion. The theory of slip lines for plane strain is utilized. For the particular homogeneous case these problems have two solutions: the continuous solution found earlier by Prandtl and modified by Hill and Sokolovsky, and the discontinuous solution found later by Cherepanov. The same type of solutions were discovered in the inhomogeneous problems of the present study. Some reasons to prefer the discontinuous solution are provided. The method is also applied to the analysis of a contact problem and a push-in/pull-out problem to determine the critical load for plasticity in these classical problems of the mechanics of composite materials.^ The results of this dissertation published in three journal articles (two of which are under revision) will also be presented in the Invited Lecture at the 7$\rm\sp{th}$ International Conference on Plasticity (Cancun, Mexico, January 1999). ^

Modeling of shape memory alloys with plasticity

Shape memory alloys are a special class of metals that can undergo large deformation yet still be able to recover their original shape through the mechanism of phase transformations. However, when they experience plastic slip, their ability to recover their original shape is reduced. This is due to the presence of dislocations generated by plastic flow that interfere with shape recovery through the shape memory effect and the superelastic effect. A one-dimensional model that captures the coupling between shape memory effect, the superelastic effect and plastic deformation is introduced. The shape memory alloy is assumed to have only 3 phases: austenite, positive variant martensite and negative variant martensite. If the SMA flows plastically, each phase will exhibit a dislocation field that permanently prevents a portion of it from being transformed back to other phases. Hence, less of the phase is available for subsequent phase transformations. A constitutive model was developed to depict this phenomena and simulate the effect of plasticity on both the shape memory effect and the superelastic effect in shape memory alloys. In addition, experimental tests were conducted to characterize the phenomenon in shape memory wire and superelastic wire. ^ The constitutive model was then implemented in within a finite element context as UMAT (User MATerial Subroutine) for the commercial finite element package ABAQUS. The model is phenomenological in nature and is based on the construction of stress-temperature phase diagram. ^ The model has been shown to be capable of capturing the qualitative and quantitative aspects of the coupling between plasticity and the shape memory effect and plasticity and the super elastic effect within acceptable limits. As a verification case a simple truss structure was built and tested and then simulated using the FEA constitutive model. The results where found to be close the experimental data. ^

Elastic modulus study of gold thin film for use as an actuated membrane in a superconductive radio frequency (RF) microelectromechanical (MEM) switch

The objective of this research was to find Young's elastic modulus for thin gold films at room and cryogenic temperatures based on the flexional model which has not been previously attempted. Electrical Sonnet simulations and numerical methods using Abacus for the mechanical responses were employed for this purpose. A RF MEM shunt switch was designed and a fabrication process developed in house. The switch is composed of a superconducting YBa2 Cu3O7 coplanar waveguide structure with an Au bridge membrane suspended above an area of the center conductor covered with BaTiO3 dielectric. The Au membrane is actuated by the electrostatic attractive force acting between the transmission line and the membrane when voltage is applied. The value of the actuation force will greatly depend on the switch pull-down voltage and on the geometry and mechanical properties of the bridge material. Results show that the elastic modulus for Au thin film can be 484 times higher at cryogenic temperature than it is at room temperature. ^

Plasma and cold sprayed aluminum carbon nanotube composites: Quantification of nanotube distribution and multi-scale mechanical properties

Carbon nanotubes (CNT) could serve as potential reinforcement for metal matrix composites for improved mechanical properties. However dispersion of carbon nanotubes (CNT) in the matrix has been a longstanding problem, since they tend to form clusters to minimize their surface area. The aim of this study was to use plasma and cold spraying techniques to synthesize CNT reinforced aluminum composite with improved dispersion and to quantify the degree of CNT dispersion as it influences the mechanical properties. Novel method of spray drying was used to disperse CNTs in Al-12 wt.% Si prealloyed powder, which was used as feedstock for plasma and cold spraying. A new method for quantification of CNT distribution was developed. Two parameters for CNT dispersion quantification, namely Dispersion parameter (DP) and Clustering Parameter (CP) have been proposed based on the image analysis and distance between the centers of CNTs. Nanomechanical properties were correlated with the dispersion of CNTs in the microstructure. Coating microstructure evolution has been discussed in terms of splat formation, deformation and damage of CNTs and CNT/matrix interface. Effect of Si and CNT content on the reaction at CNT/matrix interface was thermodynamically and kinetically studied. A pseudo phase diagram was computed which predicts the interfacial carbide for reaction between CNT and Al-Si alloy at processing temperature. Kinetic aspects showed that Al4C3 forms with Al-12 wt.% Si alloy while SiC forms with Al-23wt.% Si alloy. Mechanical properties at nano, micro and macro-scale were evaluated using nanoindentation and nanoscratch, microindentation and bulk tensile testing respectively. Nano and micro-scale mechanical properties (elastic modulus, hardness and yield strength) displayed improvement whereas macro-scale mechanical properties were poor. The inversion of the mechanical properties at different scale length was attributed to the porosity, CNT clustering, CNT-splat adhesion and Al 4C3 formation at the CNT/matrix interface. The Dispersion parameter (DP) was more sensitive than Clustering parameter (CP) in measuring degree of CNT distribution in the matrix.

An energy based nanomechnical properties evaluation method for cementitious materials

Advances in multiscale material modeling of structural concrete have created an upsurge of interest in the accurate evaluation of mechanical properties and volume fractions of its nano constituents. The task is accomplished by analyzing the response of a material to indentation, obtained as an outcome of a nanoindentation experiment, using a procedure called the Oliver and Pharr (OP) method. Despite its widespread use, the accuracy of this method is often questioned when it is applied to the data from heterogeneous materials or from the materials that show pile-up and sink-in during indentation, which necessitates the development of an alternative method. ^ In this study, a model is developed within the framework defined by contact mechanics to compute the nanomechanical properties of a material from its indentation response. Unlike the OP method, indentation energies are employed in the form of dimensionless constants to evaluate model parameters. Analysis of the load-displacement data pertaining to a wide range of materials revealed that the energy constants may be used to determine the indenter tip bluntness, hardness and initial unloading stiffness of the material. The proposed model has two main advantages: (1) it does not require the computation of the contact area, a source of error in the existing method; and (2) it incorporates the effect of peak indentation load, dwelling period and indenter tip bluntness on the measured mechanical properties explicitly. ^ Indentation tests are also carried out on samples from cement paste to validate the energy based model developed herein by determining the elastic modulus and hardness of different phases of the paste. As a consequence, it has been found that the model computes the mechanical properties in close agreement with that obtained by the OP method; a discrepancy, though insignificant, is observed more in the case of C-S-H than in the anhydrous phase. Nevertheless, the proposed method is computationally efficient, and thus it is highly suitable when the grid indentation technique is required to be performed. In addition, several empirical relations are developed that are found to be crucial in understanding the nanomechanical behavior of cementitious materials.^

Plasma And Cold Sprayed Aluminum Carbon Nanotube Composites: Quantification Of Nanotube Distribution And Multi-Scale Mechanical Properties

Carbon nanotubes (CNT) could serve as potential reinforcement for metal matrix composites for improved mechanical properties. However dispersion of carbon nanotubes (CNT) in the matrix has been a longstanding problem, since they tend to form clusters to minimize their surface area. The aim of this study was to use plasma and cold spraying techniques to synthesize CNT reinforced aluminum composite with improved dispersion and to quantify the degree of CNT dispersion as it influences the mechanical properties. Novel method of spray drying was used to disperse CNTs in Al-12 wt.% Si pre-alloyed powder, which was used as feedstock for plasma and cold spraying. A new method for quantification of CNT distribution was developed. Two parameters for CNT dispersion quantification, namely Dispersion parameter (DP) and Clustering Parameter (CP) have been proposed based on the image analysis and distance between the centers of CNTs. Nanomechanical properties were correlated with the dispersion of CNTs in the microstructure. Coating microstructure evolution has been discussed in terms of splat formation, deformation and damage of CNTs and CNT/matrix interface. Effect of Si and CNT content on the reaction at CNT/matrix interface was thermodynamically and kinetically studied. A pseudo phase diagram was computed which predicts the interfacial carbide for reaction between CNT and Al-Si alloy at processing temperature. Kinetic aspects showed that Al4C3 forms with Al-12 wt.% Si alloy while SiC forms with Al-23wt.% Si alloy. Mechanical properties at nano, micro and macro-scale were evaluated using nanoindentation and nanoscratch, microindentation and bulk tensile testing respectively. Nano and micro-scale mechanical properties (elastic modulus, hardness and yield strength) displayed improvement whereas macro-scale mechanical properties were poor. The inversion of the mechanical properties at different scale length was attributed to the porosity, CNT clustering, CNT-splat adhesion and Al4C3 formation at the CNT/matrix interface. The Dispersion parameter (DP) was more sensitive than Clustering parameter (CP) in measuring degree of CNT distribution in the matrix.

Elastic modulus study of gold thin film for use as an actuated membrane in a superconductive radio frequency (RF) MicroElectroMechanical (MEM) switch

The objective of this research was to find Young's elastic modulus for thin gold films at room and cryogenic temperatures based on the flexional model which has not been previously attempted. Electrical Sonnet simulations and numerical methods using Abacus for the mechanical responses were employed for this purpose. A RF MEM shunt switch was designed and a fabrication process developed in house. The switch is composed of a superconducting YBa2Cu3O7 coplanar waveguide structure with an Au bridge membrane suspended above an area of the center conductor covered with BaTiO3 dielectric. The Au membrane is actuated by the electrostatic attractive force acting between the transmission line and the membrane when voltage is applied. The value of the actuation force will greatly depend on the switch pull-down voltage and on the geometry and mechanical properties of the bridge material. Results show that the elastic modulus for Au thin film can be 484 times higher at cryogenic temperature than it is at room temperature.

Physical, Geochemical, Geomechanical, Geophysical and Hydrodynamic Characterization and Anisotropy Assessment of Corvio Sandstone

Corvio sandstone is a ~20 m thick unit (Corvio Formation) that appears in the top section of the Frontada Formation (Campoó Group; Lower Cretaceous) located in Northern Spain in the southern margin of the Basque-Cantabrian Basin. Up to 228 plugs were cored from four 0.3 x 0.2 x 0.5 m blocks of Corvio sandstone, to perform a comprehensive characterization of the physical, mineralogical, geomechanical, geophysical and hydrodynamic properties of this geological formation, and the anisotropic assessment of the most relevant parameters. Here we present the first data set obtained on 53 plugs which covers (i) basic physical and chemical properties including density, porosity, specific surface area and elementary analysis (XRF - CHNS); (ii) the curves obtained during unconfined and confined strengths tests, the tensile strengths, the calculated static elastic moduli and the characteristic stress levels describing the brittle behaviour of the rock; (iii) P- and S-wave velocities (and dynamic elastic moduli) and their respective attenuation factors Qp and Qs, electrical resistivity for a wide range of confining stress; and (iv) permeability and transport tracer tests. Furthermore, the geophysical, permeability and transport tests were additionally performed along the three main orthogonal directions of the original blocks, in order to complete a preliminary anisotropic assessment of the Corvio sandstone.

(Table 1) Sample characteristics, test consolidations and calculated elastic parameters of ODP Sites 194-1193 and 194-1196

This study is based on rock mechanical tests of samples from platform carbonate strata to document their petrophysical properties and determine their potential for porosity loss by mechanical compaction. Sixteen core-plug samples, including eleven limestones and five dolostones, from Miocene carbonate platforms on the Marion Plateau, offshore northeast Australia, were tested at vertical effective stress, sigma1', of 0-70 MPa, as lateral strain was kept equal to zero. The samples were deposited as bioclastic facies in platform-top settings having paleo-water depths of <10-90 m. They were variably cemented with low-Mg calcite and five of the samples were dolomitized before burial to present depths of 39-635 m below sea floor with porosities of 8-46%. Ten samples tested under dry conditions had up to 0.22% strain at sigma1' = 50 MPa, whereas six samples tested saturated with brine, under drained conditions, had up to 0.33% strain. The yield strength was reached in five of the plugs. The measured strains show an overall positive correlation with porosity. Vp ranges from 3640 to 5660 m/s and Vs from 1840 to 3530 m/s. Poisson coefficient is 0.20-0.33 and Young's modulus at 30 MPa ranged between 5 and 40 GPa. Water saturated samples had lower shear moduli and slightly higher P- to S-wave velocity ratios. Creep at constant stress was observed only in samples affected by pore collapse, indicating propagation of microcracks. Although deposited as loose carbonate sand and mud, the studied carbonates acquired reef-like petrophysical properties by early calcite and dolomite cementation. The small strains observed experimentally at 50 MPa indicate that little mechanical compaction would occur at deeper burial. However, as these rocks are unlikely to preserve their present high porosities to 4-5 km depth, further porosity loss would proceed mainly by chemical compaction and cementation.

Fabricação e caracterização de um compósito hibrido com resíduo lignocelulósico

This work aims to manufacture and characterize a hybrid plastic composite with the matrix isophthalic polyester resin base and having as reinforcing glass fiber and the dry endocarp of coconut (Coco nucifera Linn) in the form of particles as filler. The composite was made industrially in Tecniplas Industry and Trade LTDA. in the form of plate, and was manufactured process made by the manual lamination (Hand Lay Up). From the plate they were prepared test specimens for testing density, water absorption, uniaxial traction in dry and wet states, and testing of bending, as well as studies on the behavior of the generated fractures, macroscopic and microscopic, in mechanical tests through. All tests were performed in order to find the most viable applications the hybrid composite manufactured. The tensile and bending tests were analyzed last tensile properties, elasticity and deformation module. After the studies, it is observed that the percentage moisture absorbed was 3.03%. The presence of moisture in the tensile test meant a decrease of 19.77% from last stand, and 5.26% in the elastic modulus. For bending tests gave an average value of 69.13 MPa flexural strength. The results show the application of hybrid composite studied in lightweight structures, indoors, which require low / medium performance traction demands, and which involve flexural requests.

Magnetic ordering in Er₂Ti₂O₇ and elastic softening in Tb₂Ti₂O₇

Geometric frustration occurs in the rare earth pyrochlores due to magnetic rare earth ions occupying the vertices of the network of corner-sharing tetrahedra. In this research, we have two parts. In the first one we study the phase transition to the magnetically ordered state at low temperature in the pyrochlore Er₂Ti₂O₇. The molecular field method was used to solve this problem. In the second part, we analyse the crystal electric field Hamiltonian for the rare earth sites. The rather large degeneracy of the angular momentum J of the rare earth ion is lifted by the crystal electric field due to the neighboring ions in the crystal. By rewriting the Stevens operators in the crystal electric field Hamiltonian ᴴCEF in terms of charge quadruple operators, we can identify unstable order parameters in ᴴCEF . These may be related to lattice instabilities in Tb₂Ti₂O₇.

Distinguishing tectonically-and gravity-driven synsedimentary deformation structures along the Apulian platform margin (Gargano Promontory, southern Italy)

Acknowledgements This work has been supported by Reservoir Characterisation Project (www.rechproject.com) and FAR Project 2014 "Characterisation and modelling of natural reservoirs of geofluids in fractured carbonate rocks", funded by the University of Camerino, coordinator Emanuele Tondi.

Internal deformation and kinematic indicators within a tripartite Mass Transport Deposit, NW Argentina

Acknowledgments This work was carried out with support from CNPq (Conselho Nacional de Desenvolvimento Científico e Tecnológico) – Brazil, BG-Brazil and the University of Aberdeen. We would like to thank the following geologists for their support, camaraderie and countless hours of fieldwork: Claus Fallgatter, Victoria Valdez, Carla Puigdomenech, Guilherme Bozetti, Roberto Noll Filho and Arthur Giovannini, and we thank Lorena Moscardelli and an anonymous reviewer, whose constructive comments helped to improve the manuscript.

Vibrations of 1D non-conservative elastic continuum due to passage of a MDOF damped oscillator

Peer reviewed