Bulk Deformation Research Articles

Study of Deformation Rule of Ordovician Limestone in Unloading of High Confining Compress

Under unloading condition, the characteristics of rock are different from them under loading condition. This paper talks about the characteristics of Ordovician limestone under loading and unloading condition of high compress which were taken from North Tian Mountain. The testing results indicated that: The lateral deformation and bulk deformation of rock sample are clearly in the process of unloading. Plastic deformation is not notability in the unloading condition. After the peak value in the stress-strain curve, the stress decrease quickly, it is showed that the brittleness characteristic is the better remarkable under unloading condition than loading condition. Under unloading condition, deformation modulus E50 and Possion ratio μ is quadric with the confining compress.

Finite Element Based Contact Analysis of Fractal Surfaces – Effect of Varying Elastic Modulus

The present finite element simulation describes the influence of varying elastic modulus in a non-adhesive frictionless bulk deformation contact between isotropic self-affine fractal surface and a rigid flat covering elastic, elastic-plastic and the plastic region. The nature of rough surface is non-stationary and random. The scale independent characteristics can only describe the multi scale behavior of the rough surfaces. Fractal geometry describes the disordered chaos multitude behavior of rough surfaces in an ordered manner through two characteristics namely; fractal dimension D and fractal roughness G. Three-dimensional rough surfaces are generated using a modified two-variable Weierstrass-Mandelbrot function with specific fractal parameters in ANSYS environment. The present findings are validated with the experimental results available in the literature.

Timescales in creep and yielding of attractive gels

The stress-induced yielding scenario of colloidal gels is investigated under rough boundary conditions by means of rheometry coupled with local velocity measurements. Under an applied shear stress σ, the fluidization of gels made of attractive carbon black particles dispersed in a mineral oil is shown to involve a previously unreported shear rate response γ dot above(t) characterized by two well-defined and separated timescales τc and τf. First γ dot above decreases as a weak power law strongly reminiscent of the primary creep observed in numerous crystalline and amorphous solids, coined the "Andrade creep". We show that the bulk deformation remains homogeneous at the micron scale, which demonstrates that whether plastic events take place or whether any shear transformation zone exists, such phenomena occur at a smaller scale. As a key result of this paper, the duration τc of this creep regime decreases as a power law of the viscous stress, defined as the difference between the applied stress and the yield stress σc, i.e. τc ∼ (σ - σc)(-β), with β = 2-3 depending on the gel concentration. The end of this first regime is marked by a jump of the shear rate by several orders of magnitude, while the gel slowly slides as a solid block experiencing strong wall slip at both walls, despite rough boundary conditions. Finally, a second sudden increase of the shear rate is concomitant with the full fluidization of the material which ends up being homogeneously sheared. The corresponding fluidization time τf robustly follows an exponential decay with the applied shear stress, i.e. τf = τ0 exp(-σ/σ0), as already reported for smooth boundary conditions. Varying the gel concentration C in a systematic fashion shows that the parameter σ0 and the yield stress σc exhibit similar power-law dependences with C. Finally, we highlight a few features that are common to attractive colloidal gels and to solid materials by discussing our results in the framework of theoretical approaches of solid rupture (kinetic, fiber bundle, and transient network models).

Influence of spark plasma sintering temperature on the densification, microstructure and mechanical properties of Al-4.5 wt.%Cu alloy

The effect of sintering temperature on the densification mechanisms, microstructural evolution and mechanical properties of spark plasma sintered (SPS) compacts of a gas atomized Al-4.5 wt.%Cu alloy was investigated. The powder particles whose size varied between 10 to 500 µm was subjected to SPS at 400, 450 and 500 °C at a pressure of 30 MPa. The compact sintered at 500 °C exhibited fully dense microstructure which was characterized by a uniform distribution of the secondary phase, free of dendrites and micro-porosity. Microscopy and the SPS data reveal that the events such as particle rearrangement, localized deformation and bulk deformation appear to be the sequence of sintering mechanisms depending on the size range of powder particles used for consolidation. The compact sintered at 500 °C exhibited the highest hardness and compression strength since the microstructure was characterized by fine distribution of precipitates, large fraction of submicron grains and complete metallurgical bonding.

Modeling of pipe-drawing tool for drawing the multifaceted pipes of nonferrous metals on an immediate arbor

A method of mathematical modeling of a pipe-drawing tool for drawing the multifaceted pipes of nonferrous metals and alloys using the vector-matrix apparatus, which can be applied for the analytical description of the bulk deformation region, is presented. Arbors with various geometries of the reduction zone are considered. As a result of modeling the deformation region, which appears when manufacturing the profiled multifaceted pipes by arbor drawing using all types of considered arbors, it is established that the best result with the smallest rounding radii is attained for arbors with a pyramidal input into the reduction zone.

Coupling effects of nonlocal and surface energy on vibration analysis of nanobeams

This paper is proposed to study the coupled effects of surface properties and nonlocal elasticity on vibration characteristics of nanobeams by using a finite element method. Nonlocal differential elasticity of Eringen is exploited to reveal the long-range interactions of a nanoscale beam. To incorporate surface effects, Gurtin–Murdoch model is proposed to satisfy the surface balance equations of the continuum surface elasticity. Euler–Bernoulli hypothesis is used to model the bulk deformation kinematics. The surface layer and bulk of the beam are assumed elastically isotropic. Galerkin finite element technique is employed for the discretization of the nonlocal mathematical model with surface properties. An efficiently finite element model is developed to descretize the beam domain and solves the equation of motion numerically. The output results are compared favorably with those published works. The effects of nonlocal parameter and surface elastic constants on the vibration characteristics are presented. Also, the effectiveness of finite element method to handle a complex geometry is illustrated. The present model can be used for free vibration analysis of single-walled carbon nanotubes with essential, natural and nonlinear boundary conditions.

Studying the Mechanism behind Stress Corrosion Cracking of Non Sensitized 304L Austenitic Stainless Steel

The susceptibility of non sensitized 304L stainless steel (SS) components towards stress corrosion cracking (SCC) has been studied here in the light of the significant role played bysurface working operations. The plant experience shows that the fracture surfaces of non sensitized 304L stainless steel components have no signs of carbide precipitation. However, heavy plastic deformation has been evidenced in the form of high density of slip bands on the surface up to a depth of about 100 μm with high tensile residual stresses near the surface. The present study has established that the primary cause of the increase in SCC susceptibility is the heavy plastic deformation near the surface and high magnitude of tensile residual stresses which is a consequence of the surface finishing operations like machining and grinding. In this study, solution annealed 304L stainless steel has been subjected to a) surface working operations like machining and grinding and b) bulk deformation operations such as 10 % cold rolling operation. The materials in different conditions where then subjected to detailed a) microstructural characterisation, b) electrochemical characterisation and c) tests for determining the stress corrosion cracking susceptibility. The distinct differences in the micro structure as a result of bulk deformation vs. surface deformation of 304L austenitic stainless steel were highlighted and correlated to the susceptibility towards stress corrosion cracking. The effect of surface working on the nature and composition of high temperature (300 °C and 10 MPa) oxide formed on 304L stainless steel has been studied in-situ by contact electric resistance (CER) and electrochemical impedance spectroscopy measurements using controlled distance electrochemistry technique in high purity water (conductivity < 0.1 μScm-1) at 300 °C and 10 MPa in an autoclave connected to a recirculation loop system. The results highlighted the distinct differences in the oxidation behaviour of surface worked material as compared to solution annealed material in terms of specific resistivity and low frequency Warburg impedance.

Failure Analysis of a Jet Engine Gearbox Drive Gearshaft Ball Bearing

The case study presented in this article details the failure investigation of an M50 alloy steel bearing used in a jet engine gearbox drive assembly. It discusses the investigative steps and analytic tools used to determine the root cause, highlighting the importance of continuous, thorough questioning by the investigating activity. The combined analyses demonstrated that the bearing failed by a single event overload as evidenced by bulk deformation and traces of foreign material on the rolling elements. The anomalous transferred metal found on the rolling elements subsequently led to the discovery of overlooked debris in an engine chip detector, and thus resulted in a review of several maintenance practices.

A structural model of passive skeletal muscle shows two reinforcement processes in resisting deformation

Passive skeletal muscle derives its structural response from the combination of the titin filaments in the muscle fibres, the collagen fibres in the connective tissue and incompressibility due to the high fluid content. Experiments have shown that skeletal muscle tissue presents a highly asymmetrical three-dimensional behaviour when passively loaded in tension or compression, but structural models predicting this are not available. The objective of this paper is to develop a mathematical model to study the internal mechanisms which resist externally applied deformation in skeletal muscle bulk. One cylindrical muscle fibre surrounded by connective tissue was considered. The collagenous fibres of the endomysium and perimysium were grouped and modelled as tension-only oriented wavy helices wrapped around the muscle fibre. The titin filaments are represented as non-linear tension-only springs. The model calculates the force developed by the titin molecules and the collagen network when the muscle fibre undergoes an isochoric along-fibre stretch. The model was evaluated using a range of literature based input parameters and compared to the experimental fibre-direction stress–stretch data available. Results show the fibre direction non-linearity and tension/compression asymmetry are partially captured by this structural model. The titin filament load dominates at low tensile stretches, but for higher stretches the collagen network was responsible for most of the stiffness. The oblique and initially wavy collagen fibres account for the non-linear tensile response since, as the collagen fibres are being recruited, they straighten and re-orient. The main contribution of the model is that it shows that the overall compression/tension response is strongly influenced by a pressure term induced by the radial component of collagen fibre stretch acting on the incompressible muscle fibre. Thus for along-fibre tension or compression the model predicts that the collagen network contributes to overall muscle stiffness through two different mechanisms: (1) a longitudinal force directly opposing tension and (2) a pressure force on the muscle fibres resulting in an indirect longitudinal load. Although the model presented considers only a single muscle fibre and evaluation is limited to along-fibre loading, this is the first model to propose these two internal mechanisms for resisting externally applied deformation of skeletal muscle tissue.

Tuning the Light Emission from GaAs Nanowires over 290 meV with Uniaxial Strain

Strain engineering has been used to increase the charge carrier mobility of complementary metal-oxide-semiconductor transistors as well as to boost and tune the performance of optoelectronic devices, enabling wavelength tuning, polarization selectivity and suppression of temperature drifts. Semiconducting nanowires benefit from enhanced mechanical properties, such as increased yield strength, that turn out to be beneficial to amplify strain effects. Here we use photoluminescence (PL) to study the effect of uniaxial stress on the electronic properties of GaAs/Al0.3Ga0.7As/GaAs core/shell nanowires. Both compressive and tensile mechanical stress were applied continuously and reversibly to the nanowire, resulting in a remarkable decrease of the bandgap of up to 296 meV at 3.5% of strain. Raman spectra were measured and analyzed to determine the axial strain in the nanowire and the Poisson ratio in the <111> direction. In both PL and Raman spectra, we observe fingerprints of symmetry breaking due to anisotropic deformation of the nanowire. The shifts observed in the PL and Raman spectra are well described by bulk deformation potentials for band structure and phonon energies. The fact that exceptionally high elastic strain can be applied to semiconducting nanowires makes them ideally suited for novel device applications that require a tuning of the band structure over a broad range.

Cholesteric pitch transitions induced by mechanical strain

We investigate thickness and surface anchoring strength influence on pitch transitions in a planar cholesteric liquid crystal layer. The cholesteric-nematic transition is also investigated. We assume planar boundary conditions, with strong anchoring strength at one interface and weak anchoring strength at the other. The surface anchoring energy we consider to describe the deviation of the surface twist angle from the easy axis induced by a bulk deformation is a parabolic potential or Rapini and Papoular periodic potential, respectively. We show that under strain, all pitch transitions take place at a critical thickness that is equal to the quarter of the natural cholesteric pitch. The latter result does not depend on the anchoring strength, the particular surface potential, or material properties. The twist angle on the limiting surface characterized by weak anchoring varies with strain either by slipping and or in a discontinuous manner according to the thickness of the sample. The position of the bifurcation point depends only on the ratio of the extrapolation length over the layer thickness, but its value is model dependent. Multistability and multiplicity of the transition are discussed.

Mechanisms of Creep Deformation in Pure Sn Solder Joints

The work reported here concerns the creep of pure Sn solder joints with Cu metallization (Cu||Sn||Cu). Steady-state creep tests in shear are combined with electron backscatter diffraction (EBSD) analysis of the evolution of the microstructure during creep to clarify the deformation mechanism and the nature of the microstructural evolution. The creep behavior of the joint changes significantly with temperature. At low temperature (65°C), two distinct creep mechanisms are observed. Low-stress creep is apparently dominated by grain boundary sliding, as evidenced by the low stress exponent (n ≈ 4), low activation energy (Q ≈ 42 kJ/mole), and significant grain rotation during creep. High-stress creep is dominated by bulk deformation processes, evidenced by a high stress exponent (n ≈ 9), an activation energy like that for bulk diffusion (Q ≈ 70 kJ/mole), and a relatively fixed microstructure. At high temperature all aspects of its behavior are consistent with deformation by bulk creep mechanisms; the stress exponent and activation energy are high (n ≈ 5 to 7, Q ≈ 96 kJ/mole), and despite significant grain coarsening, the microstructure retains (and strengthens) a fixed [001] texture. The results suggest that a “segmented” constitutive equation of Dorn type is most suitable for the low-temperature behavior, while a “hyperbolic” constitutive equation may be preferable at high temperature.

Correlation between Surface Stress and Apparent Young’s Modulus of Top-Down Silicon Nanowires

In this work, we report experimental evidence of surface stress effects on the mechanical properties of silicon nanostructures. As-fabricated, top-down silicon nanowires (SiNWs) are bent up without any applied force. This self-buckling is related to the surface relaxation that reaches an equilibrium with bulk deformation due to the material elasticity. We measure the SiNW self-deformation by atomic force microscopy (AFM), and we apply a simple physical model in order to give an estimation of the surface stress. If the equilibrium is altered by a nanoforce, applied by an AFM tip, nanowires find a new equilibrium condition bending down (mechanical bistability). In this work, for the first time, we report a clear and quantitative relationship between the SiNWs' apparent Young's modulus, measured by force-deflection spectroscopy, and the estimated value of surface stress, obtained by self-buckling measurements taking into account the Young's modulus of bulk silicon. This is an experimental confirmation that the surface stress is fundamental in determining mechanical properties of SiNWs, and that the elastic behavior of nanostructures strongly depends on their surfaces.

Static analysis of nanobeams including surface effects by nonlocal finite element

In reality, there are two phenomena should be considered to describe behaviors of nanostructures adequately and accurately. The first one is the surface properties, especially for a relatively high ratio of the surface area to the volume of structural. The second phenomenon is the information about bulk material, which contains the forces between atoms and the internal length scale. Therefore, the objective of the current work is to study the coupled effects of surface properties and nonlocal elasticity on the static deflection of nanobeams. Surface elasticity is employed to describe the behavior of the surface layer and the Euler-Bernoulli beam hypothesis is used to state the bulk deformation kinematics. Both, the surface layer and bulk volume of the beam are assumed elastically isotropic. Information about the forces between atoms, and the internal length scale are proposed by the nonlocal Eringen model. Galerkin finite element technique is employed for the discretization of the nonlocal mathematical model with surface properties. The present results are compared favorably with those published results. The effects of nonlocal parameter and surface elastic constants are figured out and presented.

Physical and chemical properties of flaxseed

A b s t r a c t. Physical and chemical properties of flaxseed were studied as a function of moisture content. The geometric properties increased with increasing moisture content. The bulk density, rupture force, deformation and energy absorbed decreased linearly while true density, porosity, thousand seed mass, angle of repose and static coefficient of friction increased linearly with increasing moisture content. K e y w o r d s: flaxseed, physical properties, chemical properties

High-rate bulk and shear responses of bovine brain tissue

This experimental study systematically investigates the dynamic response of bovine brain tissue under uniaxial strain and pure shear loading conditions. The combination of such stress states and strain rates are representative in the brain under blast loading in which both bulk and shear deformation may be involved. The dynamic uniaxial strain experiments (bulk response) were conducted on a modified Kolsky compression bar with an aluminum confinement collar. Bovine brain samples were sealed in the collar and loaded by the Kolsky bars so that the specimen only deformed in the axial direction. The resultant stress-strain curves reflected the pressure–volume relations from which the bulk modulus were obtained. The dynamic shear response was determined by using a recently developed Kolsky torsion bar technique for tissue materials characterization. Quasi-static torsion experiments were also conducted on an MTS system to construct a full set of shear stress-strain curves over a wide range of shear strain rates (0.01–700 s−1). The experimental results show that the dynamic bulk modulus of brain is in the range of 1.68–2.33 GPa which is close to the low rate values reported in the literature, while the shear responses show significant rate sensitivity over the tested strain rate range.

Chiral effect in plane isotropic micropolar elasticity and its application to chiral lattices

In continuum mechanics, the non-centrosymmetric micropolar theory is usually used to capture the chirality inherent in materials. However, when reduced to a two dimensional (2D) isotropic problem, the resulting model becomes non-chiral. Therefore, influence of the chiral effect cannot be properly characterized by existing theories for 2D chiral solids. To circumvent this difficulty, based on reinterpretation of isotropic tensors in the 2D case, we propose a continuum theory to model the chiral effect for 2D isotropic chiral solids. A single material parameter related to chirality is introduced to characterize the coupling between the bulk deformation and the internal rotation, which is a fundamental feature of 2D chiral solids. Coherently, the proposed continuum theory is applied for the homogenization of a triangular chiral lattice, from which the effective material constants of the lattice are analytically determined. The unique behavior in the chiral lattice is demonstrated through the analyses of a static tension problem and a plane wave propagation problem. The results, which cannot be predicted by the non-chiral model, are verified by the exact solution of the discrete model.

Analysis of the fault pattern in the Lower Lanzo Valley (italian Western Alps): a multi-scale integrated approach

This work combines, at different scales, field mapping, detailed structural analysis, satellite images (Landsat TM and ASTER) and aerial photos interpretation for the study of the fault network affecting the Lower Lanzo Valley (Turin), a key-area of the inner Western Alps bordered by two major post-Oligocene tectonic discontinuities: the Canavese Line and the Col del Lis-Trana Deformation Zone. In the study area, where both the Sesia-Lanzo Zone (Austroalpine Domain) and the Lanzo Ultramafic Complex (Piemonte Zone) crop out, this integrated approach allowed distinguishing an E-W-striking major dextral transcurrent/transpressive fault system. E-W faults, usually sub-parallel, are arranged at times in en-echelon left stepped geometric pattern and linked by minor NE-SW faults. The transcurrent activity of these structures, consistent with a bulk NW-SE shortening direction with a NE-SW extension, occurred under brittle-ductile to brittle structural conditions. Rare mesoscale kinematic data also suggest a transtensive/extensional reactivation for these faults under brittle conditions. Dextral transcurrent/transpressive movements along the E-W fault system analysed in this study could be considered roughly coeval with the dextral activity along the N-S striking Col del Lis-Trana Deformation Zone, consistent with a NE-SW to E-W shortening direction, as their transcurrent activity occurred under similar structural conditions. These different shortening directions may be the result of a complex strain partitioning, in time and space, of the bulk deformation induced, since the Oligocene, in the Western Alps by the NW-SE convergence, coupled with the anticlockwise rotation, of the Adria plate with respect to the European plate. In this kind of scenario the E-W dextral faults affecting the Lower Lanzo Valley accommodated the NW-SE directed convergence whereas the N-S dextral faults, like the Col del Lis-Trana Deformation Zone, adsorbed the rotational component between the two colliding plates. The subsequent normal reactivation of the E-W faults may be related to the extensional regime that affected the inner Western Alps since the Early(?) Miocene, due to the progressive decrease of the convergence between the two plates and the subsequent prevailing of gravitational body forces inside the chain. Seismological data indicate that this stress regime is still ongoing.

Multiple direct extrusion: A new technique in grain refinement

A novel high-straining bulk deformation technique based on repeating conventional direct extrusion is presented. This technique, named multiple direct extrusion (MDE), uses a square container with a rectangular die aperture that can achieve a minimum 50% reduction/pass in the cross section of the billet. After extrusion, the new billet is cut perpendicular to the longitudinal axis. The resulting halves are then joined to obtain a square shape again so that the direct extrusion process can be repeated. Two processing routes are possible before reintroducing the billet into the container: no rotation and 90° rotation around the longitudinal axis. During each cycle, the billets change their geometrical shape and as a result, the cross section area gets smaller. A mechanism of grain fragmentation during MDE based on the analysis of velocity discontinuities along slip lines in the deformation zone is suggested. Four cycles of MDE were applied to commercial copper and the potential for grain refinement, and the improvement in mechanical properties were evaluated.

Asperity micro-contact models as applied to the deformation of rough line contact

Different statistical micro-contact models including Greenwood–Williamson (GW), Chang–Etsion–Bogy (CEB), Zhou–Maietta–Chang (ZMC), Kogut–Etsion (KE) and Jackson–Green (JG) are employed together with the bulk deformation of the bounding solids to predict dry rough line-contact characteristics such as the apparent pressure profile, contact width and real area of contact. The approach involves solving the micro-contact models and separation formulas simultaneously. Comparison of different contact models reveals that the use of elastic–plastic micro-contact models predicts a lower maximum normal pressure and a greater contact width and real contact area compared to the GW model. Further, based on the results of numerical simulations, useful relationships are provided for the prediction of the maximum contact pressure, contact width, real area of contact and pressure distribution.