Showing papers on "Hydrostatic stress published in 2006"

Shear modulus reconstruction in dynamic elastography: time harmonic case

Abstract: This paper presents a direct inversion approach for reconstructing the elastic shear modulus in soft tissue from dynamic measurements of the interior displacement field during time harmonic excitation. The tissue is assumed to obey the equations of nearly incompressible, linear, isotropic elasto-dynamics in harmonic motion. A finite element discretization of the governing equations is used as a basis, and a procedure is outlined to eliminate the need for boundary conditions in the inverse problem. The hydrostatic stress (pressure) is also reconstructed in the process, and the effect of neglecting this term in the governing equations, which is common practice, is considered. The approach does not require iterations and can be performed on sub-regions of the domain resulting in a computationally efficient method. A sensitivity study is performed to investigate the detectability of abnormal regions of different size and shear modulus contrast from the background. The algorithm is tested on simulated data on a two-dimensional domain, where the data are generated on a very fine mesh to get a near exact solution, then downsampled to a coarser mesh that is similar to the spatial discretization of actual data, and noise is added. Results showing the effect of the hydrostatic stress term and noise are presented. A reconstruction using MR measured experimental data involving a tissue-mimicking phantom is also shown to demonstrate the algorithm.

Discrete crack modelling of ductile fracture driven by non-local softening plasticity

Abstract: A combined approach towards ductile damage and fracture is presented, in the sense that a continuous material degradation is coupled with a discrete crack description for large deformations. Material degradation is modelled by a gradient enhanced damage-hyperelastoplasticity model. It is assumed that failure occurs solely due to plastic straining, which is particularly relevant for shear dominated problems, where the effect of the hydrostatic stress in triggering failure is less important. The gradient enhancement eliminates pathological localization effects which would normally result from the damage influence. Discrete cracks appear in the final stage of local material failure, when the damage has become critical. The rate and the direction of crack propagation depend on the evolution of the damage field variable, which in turn depends on the type of loading. In a large strain finite element framework, remeshing allows to incorporate the changing crack geometry and prevents severe element distortion. Attention is focused on the robustness of the computations, where the transfer of variables, which is needed after each remeshing, plays a crucial role. Numerical examples are shown and comparisons are made with published experimental results. Copyright © 2005 John Wiley & Sons, Ltd.

Mechanical stresses in cellular structures under high hydrostatic pressure

Abstract: Mechanical stresses and deformation of cellular structures due to the application of high hydrostatic pressure (HHP) is analysed for two cases. In the first case, a liquid-filled spherical shell with linear elastic material properties is considered as first approximation of a biological cell. The theoretical analysis reveals the existence of severe non-hydrostatic mechanical stresses in the wall of the structure. As second case, a nonlinear model of a yeast cell (Saccharomyces cerevisiae) under high hydrostatic pressure is assessed by use of the finite-element method. It is observed that hydrostatic stress conditions are preserved in the interior part of the cell, while nonhydrostatic stress is encountered in the cell wall. There, von-Mises stress reaches its critical value upon failure (70 T4 MPa) at a pressure load between 415 MPa and 460 MPa. This confirms observations of cell wall damage at this pressure as reported earlier by other authors.

Shock-induced crystal-plastic deformation and post-shock annealing of quartz microstructural evidence from crystalline target rocks of the Charlevoix impact structure, Canada

Abstract: Two distinct types of shock-induced quartz microstructure in charnockitic target rocks and quartz veins of the Charlevoix impact structure are described. The dominant shock effects in the type 1 microstructure in charnockites at ∼2–4 km from the centre of the structure are planar deformation features (PDFs) parallel to rhombohedral planes of quartz. The abundance of different sets of these PDFs indicates a high hydrostatic component of the shock wave-associated stress (∼10–15 GPa). Evidence of crystal-plastic deformation due to high deviatoric stresses is absent. In contrast, PDFs parallel to the basal plane are predominant in the type 2 microstructure developed in rocks at ∼4–9 km from the centre of the structure, whereas rhombohedral PDFs are rare. This indicates a lower hydrostatic stress component (∼7–8 GPa), which correlates with a radial decrease in recorded peak shock pressure. The basal PDFs are revealed by transmission electron microscopy to represent mechanical Brazil twins, which record crystal-plastic deformation at high deviatoric stresses (McLaren et al. , 1967). These findings imply that the deviatoric component of the shock wave-associated stress increases relative to the hydrostatic component with increasing distance from the centre of the impact structure. In the type 2 microstructure, numerous deformation bands, strong undulose extinction and cataclastic zones at the optical scale, as well as glide-dislocations and microcracks at the TEM scale, occur in association with basal PDFs, and are therefore also interpreted to be shock-induced. This is consistent with the observation that quartz from the outer part of the impact structure is devoid of similar features. Thus, the highly heterogeneous and localised glide-controlled deformation accompanied by mechanical twinning and microcracking recorded by the type 2 microstructure is suspected to be induced by the high deviatoric stresses and high loading rates during shock. Post-shock recovery is indicated in the type 1 microstructure by the actual microstructure of rhombohedral PDFs, dislocations in climb configuration and well-ordered low angle grain boundaries, as well as in the type 2 microstructure by the occurrence of small elongate subgrains with low angle grain boundaries paralleling low-index planes. This has probably taken place during annealing shortly after the impact event at quasi-static conditions and still sufficiently high post-shock temperatures, rather than during a separate regional thermal event.

Modelling of Ag3Sn coarsening and its effect on creep of Sn-Ag eutectics

Abstract: A new constitutive model, which can account for the solder's microstructure and its evolution, is proposed to describe the creep behaviour of the Sn–Ag eutectic phase. In this model, the threshold stress, being a function of the particle size, volume fraction and distribution of Ag 3 Sn intermetallic compound (IMC), is introduced to build the relationship between the creep behaviour of the Sn–Ag solder and its microstructure. Evolution of the eutectic phase's microstructure is accounted for in terms of the coarsening model. Both the creep strain rate and hydrostatic stress's influence are taken into account in the IMC coarsening model. The proposed model is implemented into the commercial finite element code ABAQUS. The creep deformation due to the applied stress and IMC coarsening are discussed in the case of a flip chip solder joint. The obtained results show that the shape of the solder joint influences the particle distribution caused by heterogeneous coarsening. The solder joint is softened due to microstructure evolution over a long range of time.

Microstructure evolution of SIMA processed Al2024

Abstract: In this paper, the strain induced melt activated (SIMA) process of A2024 was investigated systematically in order to provide a basis for semi-solid forming of the alloy. To delete the hydrostatic component of stress, the uniform uniaxial compression process is performed. The relation between the grain size and strain before heating is presented and a microstructure evolution model for SIMA is proposed on the basis of experiment. There include two steps in SIMA process. In the first step of plastic deformation, there are two mechanisms to control the deformation, slip or cross-slip or twinning in grain and grain rotation. The deviatory stress will benefit to slip or cross-slip or twinning in grains, and the hydrostatic stress will benefit to rotation of gain. In the second step of heating, the grain boundary will melt first and the shape of the grains will be globe.

Residual stresses in a quenched superalloy turbine disc: Measurements and modeling

Abstract: A series of neutron diffraction measurements have been carried out to determine the elastic residual strains deep within a large, 40-cm-diameter, forged and water-quenched IN718 aeroengine compressor disc. Neutron path lengths of up to 6 cm were necessary to probe the thickest parts of the forging, and three-dimensional strain and stress components have been derived for the first time in such a large superalloy specimen. Measurements have been compared with the results from a coupled thermal-mechanical finite-element model of the quenching process, based upon appropriate temperature-dependent material properties, with some success. The general residual stress state in the disc is one of near-surface compression, balanced by tension within the disc interior. The steepest stress and strain gradients occur in the transition region from compression to tension, about 1 cm below the surface all around the disc. The largest stress component is in the disc tangential direction and reaches a magnitude of 400 to 500 MPa near the disc surface and at its core. This exceeds the effective yield stress because of the presence of significant hydrostatic stress.

Linewidth dependence of grain structure and stress in damascene Cu lines

Abstract: Damascene Cu interconnects show significant differences in both their microstructural and stress behavior as compared to those of Al interconnects patterned using the etching process. Thermal stresses build up during the successive thermal cycles due to the differences in the coefficients of thermal expansion of the component materials. Other than these thermal stresses, growth stresses originating from grain growth develop in damascene Cu interconnects as well. In this study, the linewidth dependence of the stress in damascene Cu was examined experimentally, as well as by numerical simulation. The stresses of damascene Cu with widths ranging from 0.13to2μm were measured using x-ray diffraction, and the measured hydrostatic stress was found to increase with increasing linewidth, in contrast to the typical behavior of Al interconnects. Microstructure analysis using transmission electron microscopy revealed that the grain sizes increased with increasing line dimensions. The increase in stress in the interco...

Finite-element simulation of inclusion size effects on copper shaped-wire drawing

Abstract: The effects of inclusion size on copper shaped-wire drawing were investigated. For this purpose, an experimental investigation for optimal die half-angle was conducted. Based on experimental data of optimal die half-angle, the deformation and the hydrostatic stress of the copper shaped-wire that contain an inclusion were calculated by two-dimensional finite element analysis. As the FEA results, while the leading edge of the inclusion passed through the die, the necking due to inclusion wire drawing occurred on some parts of the copper wire surface in front of and near the leading edge of the inclusion. The effects of inclusion size on drawing stress, tensile stress in front of inclusion and contact compressive stress while copper shaped-wire drawing were carried out.

Theory for Electromigration Failure in Cu Conductors

Abstract: A model for electromigration failure is proposed where the criterion for damage is not classical nucleation forming a void, but is a delamination at an interface. In addition, the anisotropy in the elastic constants of Cu metal is responsible for a bimodal failure distribution recognizing that the driving force for mass transport depends on the hydrostatic stress whereas the failure criterion depends on a normal stress. The agreement with published data is reasonably good.

Hydrostatic stress and hydrostatic stress gradients in passivated copper interconnects

Abstract: A numerical evaluation of the effects of geometrical factors on the hydrostatic stress and hydrostatic stress gradients in passivated copper interconnects was performed. These values were correlated with experimental values in the literature on the location of voids in the interconnect. Copper interconnects of aspect ratios between 0.1 and 10 were studied. Numerical work using the commercial ANSYS software and analytical work based on the Eshelby and Wikstrom models were performed. Comparison is made between the analytical, numerical and experimental results (obtained from the literature). It was found that for an interconnect with no pre-existing voids, maximum hydrostatic stress gradients occurred at the corners of the interconnects suggesting that void growth is most probable at the corners of the interconnect. The stress gradient within the interconnect with aspect ratio of 10 is about 10 times larger than that in interconnects of aspect ratios 0.1 and 1. This suggests that the narrowest interconnects are most likely to undergo voiding. This study found that it is insufficient to look only at the hydrostatic stress at the centre of the interconnect and that stress gradient also needs to be taken into consideration to assess reliability.

Fractographic and numerical study of hydrogen–plasticity interactions near a crack tip

Abstract: This paper offers a fractographic and numerical study of hydrogen–plasticity interactions in the vicinity of a crack tip in a high-strength pearlitic steel subjected to previous cyclic (fatigue) precracking and posterior hydrogen-assisted cracking (HAC) under rising (monotonic) loading conditions. Experiments demonstrate that heavier cyclic preloading improves the HAC behaviour of the steel. Fractographic analysis shows that the microdamage produced by hydrogen is detectable through a specific microscopic topography: tearing topography surface or TTS. A high resolution numerical modelling is performed to reveal the elastoplastic stress–strain field in the vicinity of the crack tip subjected to cyclic preloading and subsequent monotonic loading up to the fracture instant in the HAC tests, and the calculated plastic zone extent is compared with the hydrogen-assisted microdamage region (TTS). Results demonstrate that the TTS depth has no relation with the active plastic zone dimension, i.e., with the size of the only region in which there is dislocation movement, so hydrogen transport cannot be attributed to dislocation dragging, but rather to random-walk lattice diffusion. It is, however, stress-assisted diffusion in which the hydrostatic stress field plays a relevant role. The beneficial effect of crack-tip plastic straining on HAC behaviour might be produced by the delay of hydrogen entry caused by residual compressive stresses and by the enhanced trapping of hydrogen as a consequence of the increase of dislocation density after cyclic plastic straining.

Contributing Factors to the Increased Formability Observed in Electromagnetically Formed Aluminum Alloy Sheet

Abstract: This paper summarizes the results of an experimental and numerical program carried out to study the formability of aluminum alloy sheet formed using electromagnetic forming (EMF). Free-formed and conical samples of AA5754 aluminum alloy sheet were studied. The experiments showed significant increases in formability for the conical samples, but no significant increase for the free-formed parts. It was found that relatively little damage growth occurred and that the failure modes of the materials changed from those observed in quasi-static forming to those observed in high hydrostatic stress environments. Numerical simulations were performed using the explicit finite element code LS-DYNA with an analytical EM force distribution. The numerical models revealed that a complex stress state is generated when the sheet interacts with the tool, which is characterized by high hydrostatic stresses that create a stress state favourable to damage suppression increasing ductility. Shear stresses and strains are also produced at impact with the die which help the material achieve additional deformation. The predicted peak strain rates for the free formed parts were on the order of 1000 s and for the conical parts the rates are on the order of 10,000 s. Although aluminum is typically considered to be strain-rate insensitive, the strain rates predicted could be playing a role in the increased formability. The predicted strain paths for the conical samples were highly non-linear. The results from this study indicate that there is an increase in formability for AA5754 when the alloy is formed into a die using EMF. This increase in formability is due to a combination of high hydrostatic stresses, shear stresses, high strain rates, and non-linear strain paths.

Ion-irradiation induced stress relaxation in metallic thin films and multilayers grown by ion beam sputtering

Abstract: The stress state of Mo layers in Ni/Mo multilayers was investigated and its evolution under ion beam irradiation was monitored using the “sin2 ψ” method. The growth stress in the Mo sub-layers was found to be consistent with a hydrostatic state of stress, accounting for the local deformations due to point defects induced during the sputter growth process. The hydrostatic stress is also responsible for a biaxial stress component appearing in the multilayer that is attached to the substrate, an additional stress component which is superimposed to the coherency stress developed due to epitaxial growth of the multilayers. Ion-irradiation of multilayers results in partial stress relaxation at low fluences, as the growth stress can be almost fully relaxed, while the coherency stresses remain unchanged. That is due to the system’s state, the growth stress is far from thermodynamic equilibrium, the coherency stress is close-to-equilibrium. The employed method, combining X-ray diffraction strain analysis and ion irradiation-induced relaxation, in addition to identifying the chemical effects contribution, proved to be a unique tool for recognising and distinguishing stress contributions.

Fracture Assessment of Carbon Fibre/Epoxy Reinforcing Rings through a Combination of Full-Scale Testing, Small-Scale Testing and Stress Modeling

Abstract: Carbon fibre/epoxy rings are used as radial reinforcement for polymer bearing elements with nominal diameter 250 mm functioning under 150 MPa. Full- scale static and dynamic testing revealed no catastrophic failure for loading to 400 MPa, although there was circumferential splitting of carbon fibres at the machined top edge causing counterface wear under sliding. A combined numerical- experimental analysis was applied for design improvement with a representative small-scale qualification test on the real ring geometry, inducing additional stress concentrations compared to ASTM standards. Full-scale modelling revealed high radial-axial shear stresses (33 MPa) in non-hydrostatically loaded zones, while it increased towards 104 MPa under hydrostatic load conditions. The former is the most critical and should be simulated either on a small-scale unidirectional com- pression test or on a representative short beam shear test, respectively, measuring the radial-axial or radial-tangential shear strength. A relation between both small- scale states of stress was experimentally and numerically studied, experiencing that the composite ring has lower radial-tangential shear stress compared to radial-axial shear stress as a different hydrostatic stress state is observed in the bulk of the composite ring. As a compressive test is however more difficult to perform than a short-beam-shear test, a representative design criterion for shear fracture is determined from failure at 27 kN normal load in a short-beam-shear test. Finally,