Showing papers on "Stress field published in 2009"

Annular shear of cohesionless granular materials: from the inertial to quasistatic regime.

Abstract: Using discrete simulations, we investigate the behavior of a model granular material within an annular shear cell. Specifically, two-dimensional assemblies of disks are placed between two circular walls, the inner one rotating with prescribed angular velocity, while the outer one may expand or shrink and maintains a constant radial pressure. Focusing on steady state flows, we delineate in parameter space the range of applicability of the recently introduced constitutive laws for sheared granular materials (based on the inertial number). We discuss the two origins of the stronger strain rates observed near the inner boundary, the vicinity of the wall and the heteregeneous stress field in a Couette cell. Above a certain velocity, an inertial region develops near the inner wall, to which the known constitutive laws apply, with suitable corrections due to wall slip, for small enough stress gradients. Away from the inner wall, slow, apparently unbounded creep takes place in the nominally solid material, although its density and shear to normal stress ratio are on the jammed side of the critical values. In addition to rheological characterizations, our simulations provide microscopic information on the contact network and velocity fluctuations that is potentially useful to assess theoretical approaches.

On the anti-plane shear of an elliptic nano inhomogeneity

Abstract: The elastic field of an elliptic nano inhomogeneity embedded in an infinite matrix under anti-plane shear is studied with the complex variable method. The interface stress effects of the nano inhomogeneity are accounted for with the Gurtin–Murdoch model. The conformal mapping method is then applied to solve the formulated boundary value problem. The obtained numerical results are compared with the existing closed form solutions for a circular nano inhomogeneity and a traditional elliptic inhomogeneity under anti-plane. It shows that the proposed semi-analytic method is effective and accurate. The stress fields inside the inhomogeneity and matrix are then systematically studied for different interfacial and geometrical parameters. It is found that the stress field inside the elliptic nano inhomogeneity is no longer uniform due to the interface effects. The shear stress distributions inside the inhomogeneity and matrix are size dependent when the size of the inhomogeneity is on the order of nanometers. The numerical results also show that the interface effects are highly influenced by the local curvature of the interface. The elastic field around an elliptic nano hole is also investigated in this paper. It is found that the traction free boundary condition breaks down at the elliptic nano hole surface. As the aspect ratio of the elliptic hole increases, it can be seen as a Mode-III blunt crack. Even for long blunt cracks, the surface effects can still be significant around the blunt crack tip. Finally, the equivalence between the uniform eigenstrain inside the inhomogeneity and the remote loading is discussed.

Novel anisotropic continuum‐discrete damage model capable of representing localized failure of massive structures: Part I: theoretical formulation and numerical implementation

Abstract: Purpose – The purpose of this paper is to discuss the identification of the model parameters for constitutive model capable of representing the failure of massive structures, from two kinds of experiments: a uniaxial tensile test and a three‐point bending test.Design/methodology/approach – A detailed development of the ingredients for constitutive model for failure of massive structures are presented in Part I of this paper. The salient feature of the model is in its ability to correctly represent two different failure mechanisms for massive structures, the diffuse damage in so‐called fracture process zone with microcracks and localized damage in a macrocrack. The identification of such model parameters is best performed from the tests under heterogeneous stress field. Two kinds of tests are used: the simple tension test and the three‐point bending test. The former allows us illustrate the non‐homogeneity of the strain field at failure even under homogeneous stress, whereas the latter provides a very good...

Strain on ferroelectric thin films

Abstract: Strain engineering aims to take advantage of the stress field imposed by substrates on thin films It requires an understanding of the consequences of stress fields on the physical properties of the deposited materials This is achieved in ferroelectric thin films through the use of misfit-strain phase diagrams that show the stability regions for the possible phases These encompass bulk phases as well as new ones exhibiting symmetries that are not present in the bulk For the solid solution lead zirconate–lead titanate, Pb(Zr1−xTix)O3, monoclinic phases found in the bulk morphotropic phase boundary region and associated to concentrations exhibiting the highest properties can be stabilized on a wider range of composition in thin films In addition, phases of lower symmetry can be stabilized through the use of anisotropic biaxial stress fields, generated by orthorhombic substrates for example Another crucial aspect of the influence of biaxial stress fields is the generation of domain structures Theoretical tools as well as experimental verifications have provided much insight on the underlying physics We, therefore, present here an overview of the influence of both iso- and anisotropic biaxial stress fields on the structures and properties of ferroelectric thin films exemplified on Pb(Zr1−xTix)O3

Inferring the coseismic and postseismic stress changes caused by the 2004 Mw = 6 Parkfield earthquake from variations of recurrence times of microearthquakes

Abstract: [1] Kinematic models of coseismic stress, inverted from ground motion data, do not usually find good correlation between the location of aftershocks and high-stress patches. In particular, numerous earthquakes are recorded in areas of the fault where the stress decreases. However, most of coseismic slip distributions have limited spatial resolution (typically not better than ∼1 km). Here we investigate the stress changes produced by the 2004 Mw = 6 Parkfield earthquake on and near its rupture zone, at the scale of magnitude 2 earthquake asperities (approximately tens of meters). After relocating earthquakes in this zone between 1984 and 2007, we form repeating, highly similar earthquake sequences and study how the quasiperiodicity of occurrence at each sequence, observed during the 20 years preceding the 2004 main shock, is perturbed by this event. We apply a simple model of the seismic cycle to infer the coseismic and postseismic stresses experienced by the repeatedly failing asperities. Despite being spatially sparse, these stress distributions have resolutions only limited by the typical scale of an asperity. We propose that the high spatial variability of the seismicity patterns following the Mw = 6 earthquake, results from an heterogeneous coseismic stress field. The emergence of the Omori-Utsu law observed at large-scale (greater than kilometers) at Parkfield is simply the outcome of averaging such quasi-deterministic patterns over many sequences. The fact that the coseismic stress can significantly change over distances of the order of 100 m adds credence to the hypothesis that earthquake rupture is intrinsically very heterogeneous.

Contribution of gravitational potential energy differences to the global stress field

Abstract: SUMMARY Modelling the lithospheric stress field has proved to be an efficient means of determining the role of lithospheric versus sublithospheric buoyancies and also of constraining the driving forces behind plate tectonics. Both these sources of buoyancies are important in generating the lithospheric stress field. However, these sources and the contribution that they make are dependent on a number of variables, such as the role of lateral strength variation in the lithosphere, the reference level for computing the gravitational potential energy per unit area (GPE) of the lithosphere, and even the definition of deviatoric stress. For the mantle contribution, much depends on the mantle convection model, including the role of lateral and radial viscosity variations, the spatial distribution of density buoyancies, and the resolution of the convection model. GPE differences are influenced by both lithosphere density buoyancies and by radial basal tractions that produce dynamic topography. The global lithospheric stress field can thus be divided into (1) stresses associated with GPE differences (including the contribution from radial basal tractions) and (2) stresses associated with the contribution of horizontal basal tractions. In this paper, we investigate only the contribution of GPE differences, both with and without the inferred contribution of radial basal tractions. We use the Crust 2.0 model to compute GPE values and show that these GPE differences are not sufficient alone to match all the directions and relative magnitudes of principal strain rate axes, as inferred from the comparison of our depth integrated deviatoric stress tensor field with the velocity gradient tensor field within the Earth's plate boundary zones. We argue that GPE differences calibrate the absolute magnitudes of depth integrated deviatoric stresses within the lithosphere; shortcomings of this contribution in matching the stress indicators within the plate boundary zones can be corrected by considering the contribution from horizontal tractions associated with density buoyancy driven mantle convection. Deviatoric stress magnitudes arising from GPE differences are in the range of 1–4 TN m−1, a part of which is contributed by dynamic topography. The EGM96 geoid data set is also used as a rough proxy for GPE values in the lithosphere. However, GPE differences from the geoid fail to yield depth integrated deviatoric stresses that can provide a good match to the deformation indicators. GPE values inferred from the geoid have significant shortcomings when used on a global scale due to the role of dynamically support of topography. Another important factor in estimating the depth integrated deviatoric stresses is the use of the correct level of reference in calculating GPE. We also elucidate the importance of understanding the reference pressure for calculating deviatoric stress and show that overestimates of deviatoric stress may result from either simplified 2-D approximations of the thin sheet equations or the assumption that the mean stress is equal to the vertical stress.

A new methodology based on X-ray micro-tomography to estimate stress concentrations around inclusions in high strength steels

Abstract: This work aims at improving the calculation of stress fields around non-metallic inclusions in high strength bearing steels. A new methodology is proposed, based on: (i) the determination of 3D morphologies of inclusions by X-ray micro-tomography imaging; (ii) the characterization of the mechanical properties of the inclusion by nano-indentation, and (iii) finite element (FE) calculations of the stress concentration induced by the inclusions. The methodology is applied to a calcium aluminate inclusion with cavities, located in a Hertzian stress field. The stress concentration appears to be strongly dependent on the orientation of the inclusion-cavity considered. The stress concentration fields obtained from realistic 3D shapes are compared to those obtained from simplified shapes of inclusions.

Numerical/experimental analysis of the stress field around miniscrews for orthodontic anchorage.

Abstract: SUMMARY The aims of this study were to analyse the stress distribution developing around an orthodontic miniscrew (OM) inserted into the maxilla and to determine the stress fi eld changes for different screw lengths and for different levels of osseointegration occurring at the bone/screw interface. An integrated experimental/numerical approach was adopted. Using the photoelastic technique, the stress fi eld arising in the bone after screw insertion and the application of the initial orthodontic load was assessed. The fi nite element (FE) method was used to determine the stress acting in the bony tissue after a given time following screw application, when, for the viscoelastic relaxation effects, the only stress fi eld remaining was that due to the application of the orthodontic load. Different levels of osseointegration were hypothesized. Photoelastic analyses showed that stress distribution does not change signifi cantly for moderate initial orthodontic loads. From the FE simulations, it was found that critical conditions occur for screws 14 mm long with an orthodontic load of 2 N. The optimal screw length seems to be 9 mm. For such a dimension, small stress values were found as well as low risk of lesion to the anatomical structures. found remarkable differences between the stress distribution computed for models with and without abutment teeth. Studies of stress allow optimization of the shape of the screw and of its geometric parameters such as length, diameter, and thread pitch. Furthermore, analysis of the stress arising around miniscrews could be utilized in computational mechano-biological models ( Pauwels, 1960 ; Prendergast et al. , 1997 ; Carter et al. , 1998 ; Gomez-Benito et al. , 2005 ) in order to study bone remodelling and the tissue differentiation processes occurring in the vicinity of the screw. A comprehensive analysis of the mechanical behaviour of miniscrews and of the bone structural response during the period from insertion to when a given level of osseointegration is achieved at the bone/screw interface has yet to be carried out. The aim of this research was to analyse the stress distribution which develops around a miniscrew due both to the insertion of the screw in the maxillary bone, producing the stress fi eld ( s insertion ), and to the application of the orthodontic load on the miniscrew head, producing the stress fi eld ( s load ). An integrated numerical/experimental approach was adopted in order to investigate how the load transfer at the bone/screw interface changes for screws of different lengths and for different levels of osseointegration.

Three-dimensional numerical modeling of slip rate variations on normal and thrust fault arrays during ice cap growth and melting

Abstract: [1] Changes in the volumes of ice caps considerably alter the stress state of the lithosphere by generating a transient signal that is added to the tectonic background stress field These stress field changes, in turn, affect crustal deformation and in particular the slip behavior of existing faults Here we use three-dimensional finite element models to investigate how arrays of normal and thrust faults near a growing and subsequently melting ice cap are influenced in their slip evolution The results show that regardless of fault dip, both types of faults experience a decrease in their slip rate during ice cap advance and an increase in their slip rate during ice cap retreat if they are located beneath the ice cap In contrast, faults outside the ice cap that are loaded on their footwall or hanging wall only show the opposite pattern: their slip rate increases during glacial loading and decreases during subsequent unloading If the load is located along strike of the fault; that is, at one of its tips, the slip behavior of normal and thrust faults is different: The normal fault shows a slip rate increase during unloading, the thrust fault during loading Our results explain the location and timing of deglaciation-induced paleoearthquakes in Scandinavia and the contrasting slip histories reported from normal faults in the Basin and Range Province, which are located at different positions relative to the former Yellowstone ice cap More generally, our findings imply that a uniform slip behavior of faults in formerly glaciated regions should not be expected

Stress evolution and fault stability during the Weichselian glacial cycle

Abstract: In this report we examine how the waxing and waning of an ice sheet during a glacial cycle affects the state of stress in the Earth, and how those changes in stress influence the stability of faults. We focus on the stresses at repository depth in Forsmark and Oskarshamn, and on the stability field at seismogenic depth at the proposed repository sites and at the Paervie endglacial fault in northern Sweden. This study is a modelling study, where we use 3-dimensional ice and earth models to calculate the glacial isostatic adjustment (GIA), i.e. the response of the Earth to an ice load, examining both displacements and stresses. We use a flat-earth finite element approach, based on Wu with some modifications. The result presented here is a continuation of previous studies in 2 dimensions and complement those studies in assessing how the 3-dimensionality of the problem affects the conclusions. We use the Fennoscandian ice model of Naeslund, which is a dynamic ice sheet model based on climate reconstructions with constraints from geological observations. The ice model spans the entire Weichselian glaciation but we only use the last 68 kyr, which includes the 2 major periods of ice cover as depicted in this ice sheet reconstruction. For the GIA calculation we use a number of different earth models, both with flat horizontal layers and with various 3D structures of lithosphere thickness. We don't include lateral variations in the viscosity of the mantle. Comparing the current day rebound velocities predicted by our models with GPS observations from the BIFROST project, we note that in general, we can obtain a reasonable fit to the observations with our models, and that the results are rather sensitive to the assumed viscosity of the mantle. We find that the differences between data and model results, for all earth models, have common features which we interpret as due to the ice model. These observations are in agreement with numerous other GIA studies. Our flat layered models tend to fit the data better than the few models with laterally varying lithosphere thickness, where especially the horizontal velocities vary significantly between models and between the models and the data. The regional patterns of stress distribution and stress directions are remarkably similar for all earth models, while the magnitude of the induced stresses vary significantly between models, mainly due to variations in the stiffness of the uppermost layer. The temporal stress evolution at 500 m depth in Forsmark and Oskarshamn is determined by the ice sheet evolution whereas the magnitude of the induced stresses depend on the earth model. For models with realistic stiffness distributions, the induced horizontal stresses both in Forsmark and in Oskarshamn are similar to the magnitude of the vertical stress of the ice load. Stress histories for the Paervie fault, which is located close to the western edge of the ice sheet, show that although the Paervie fault is the largest known endglacial fault, the induced stress magnitudes are not very high, which is due to the relatively modest thickness of the ice sheet here all through the glacial history. In the fault stability analysis we use mainly two synthetic background stress fields, one reverse and one strike-slip. In agreement with previous studies we find that the background stress field is important for the resulting stability field. We show that in a reverse state of stress at 9.5 km depth, with a glacially induced pore pressure head of 50% of the local ice weight, both Forsmark and Oskarshamn would experience fault instability at the end of glaciation. In a strike-slip stress state, the stability field is more sensitive to variations in the direction of the background field, but for our reference field both Forsmark and Oskarshamn show mostly stable conditions. Stability analysis at the Paervie fault shows that in a strike-slip background field the Paervie fault would be stable all through the glaciation while in a reverse faulting background stress field our models show unstable conditions at the end of the glaciation, in general agreement with the observations. The assumed background stress field, with the direction of maximum horizontal stress in the direction of local plate motion, predicts a fault orientation in general agreement with the overall strike of the Paervie fault. Our simulations of fault stability show a very strong dependence of fault stability on the glacially induced excess pore pressure. Increasing the pressure head to 90% of the local ice weight will cause wide-spread instability during ice covered conditions in a strike-slip background field, while in a reverse field instability is promoted earlier in the glacial cycle. Our approach to estimating the induced pore pressure in this study has been one of very simple static conditions and high permeability, implying an immediate propagation of pressures at the base of the ice sheet to the studied depth.

Eigenstrain analysis of residual strains and stresses

Abstract: Experimental stress evaluation procedures often rely on the measurement of some component(s) of elastic strain followed by point-wise calculation of stress based on continuum elasticity assumptions. Such point-wise assessments are, however, incomplete and not entirely satisfactory, as calculations conducted for different points can easily give rise to values that may not satisfy requirements of global force balance. The real purpose of experimental data interpretation is in fact to obtain a reasonably internally consistent description of the state of stress everywhere in the object to the greatest possible level of detail. What is usually being sought is a residual-stress-admissible (RS-admissible) field, i.e. such that would satisfy boundary conditions imposed both in terms of tractions and displacements, and would correspond to a divergence-free stress field (i.e. such that satisfies stress equilibrium conditions everywhere). Note, however, that elastic strains are no longer required to be compatible. T...

Investigation of stress induced by CO2 laser processing of fused silica optics for laser damage growth mitigation

Abstract: Laser damage mitigation' is a process developed to prevent the growth of nanosecond laser-initiated damage sites under successive irradiation. It consists of re-fusing the damage area with a CO2 laser. In this paper we investigate the stress field created around mitigated sites which could have an influence on the efficiency of the process. A numerical model of CO2 laser interaction with fused silica is developed. It takes into account laser energy absorption, heat transfer, thermally induced stress and birefringence. Residual stress near mitigated sites in fused silica samples is characterized with specific photoelastic methods and theoretical data are compared to experiments. The stress distribution and quantitative values of stress levels are obtained for sites treated with the CO2 laser in various conditions of energy deposition (beam size, pulse duration, incident power). The results provided evidence that the presence of birefringence/residual stress around the mitigated sites has an effect on their laser damage resistance.

Modelling dislocations in a free-standing thin film

Abstract: We present a set of efficient numerical algorithms to accurately compute the forces on dislocations in free-standing thin films. We first present a spectral method for computing the image stress field of dislocations in an isotropic elastic half space and a free-standing thin film. The traction force on the free surface is decomposed into Fourier modes by a discrete Fourier transform and the resulting image stress field is obtained by superimposing analytic solutions in the Fourier space. Dislocations intersecting free surfaces are discussed, including the use of virtual segments and the associated uniqueness of their solutions. The efficiency of the algorithm is enhanced by incorporating the analytical solutions for straight dislocations intersecting free surfaces. A comprehensive algorithm, including a flow diagram, is formulated and the numerical convergence of these algorithms discussed. As a benchmark, we compute the equilibrium orientation of a threading dislocation in a free-standing thin film. Good agreement is observed between the predictions from the dislocation dynamics model and those from molecular static simulations and the line tension model.

Prediction of the Fatigue Life of Cast Steel Containing Shrinkage Porosity

Abstract: A simulation methodology for predicting the fatigue life of cast steel components with shrinkage porosity is developed and validated through comparison with previously performed measurements A X-ray tomography technique is used to reconstruct the porosity distribution in 25 test specimens with average porosities ranging from 8 to 21 pct The porosity field is imported into finite element analysis (FEA) software to determine the complex stress field resulting from the porosity In the stress simulation, the elastic mechanical properties are made a function of the local porosity volume fraction A multiaxial strain-life simulation is then performed to determine the fatigue life An adaptive subgrid model is developed to reduce the dependence of the fatigue life predictions on the numerical mesh chosen and to account for the effects of porosity that is too small to be resolved in the simulations The subgrid model employs a spatially variable fatigue notch factor that is dependent on the local pore radius relative to the finite element node spacing A probabilistic pore size distribution model is used to estimate the radius of the largest pore as a function of the local pore volume fraction It is found that, with the adaptive subgrid model and the addition of a uniform background microporosity field with a maximum pore radius of 100 μm, the measured and predicted fatigue lives for nearly all 25 test specimens fall within one decade Because the fatigue lives of the specimens vary by more than four orders of magnitude for the same nominal stress amplitude and for similar average porosity fractions, the results demonstrate the importance of taking into account in the simulations the distribution of the porosity in the specimens