Determination Of Stress Field Research Articles

Eigenstrain and Fourier series for evaluation of elastic local fields and effective properties of periodic composites

The elastic stress and strain fields and effective elasticity of periodic composite materials are determined by imposing a periodic eigenstrain on a homogeneous solid, which is constrained to be equivalent to the heterogeneous composite material through the imposition of a consistency condition. To this end, the variables of the problem are represented by Fourier series and the consistency condition is written in the Fourier space providing the system of equations to solve. The proposed method can be considered versatile as it allows determining stress and strain fields in micro-scale and overall properties of composites with different kinds of inclusions and defects. In the present work, the method is applied to multi-phase composites containing long fibers with circular transverse section. Numerical solutions provided by the proposed method are compared with finite element results for both unit cell containing a single fiber and unit cell with multiple fibers of different sizes.

Determination of the First Stress Tensor Invariant of a Complex Steel Sheet Structure from Thermoelastic Stress Analysis

The determination of welded steel sheet assemblies high cycle fatigue properties is a prior concern of the automotive industry. Such assemblies are designed as high-safety parts, for which any fatigue failure is supposed to be prevented. Thus, the determination of complex structures stress field is necessary to design them. Even though finite element models are more and more accurate, experimental methods for the stress field tensors measurement under cyclic loadings are useful to validate those models. The purpose of this work is the experimental determination of the first stress tensor invariant amplitude at the surface of a complex structure under cyclic loading, a car wishbone, with a method based on thermal measurements, the Thermoelastic Stress Analysis (TSA). Parameters which have an influence on the measured temperature at the surface of the structure are studied, including the non-adiabatic behaviour of specimens due to a heterogeneous stress field and the influence of the paint used to measure the temperature with an infra-red camera. All these parameters are taken into account to determine successfully the wishbone stress tensor amplitude during a cyclic test.

Experimental-computational methods for determination of the stress-strain state of structural components

Results of scientific achievements in the development of experimental and computational methods for study of stress-loading parameters of structural components are reported. Special attention is paid to theoretical and long-term developments based on the methods of inverse problems of experimental mechanics. The paper provides examples of solutions of transient thermal conductivity problems with a limited amount of experimental data on determination of high-gradient inhomogeneous residual stress fields and flaw detection in structural components.

Determination of Stress Fields and Identification of Thermomechanical Parameters in a Thermally Grown Oxide under Thermal Cycling Loadings, Using Advanced Models

The presence of residual stresses in thermal oxide layers has been recognized for a long time. In the present work, the mechanical fields for chromium oxide are investigated. An extended model is established to take into account the effects of temperature and thermal cycling for the calculation of oxide stress. Numerical results are given in order to predict the influence of different parameters, especially the dependence of some material parameters with temperature. This enables to make comparison with experimental results.

Determination of Residual Stress Fields in a Thermally Grown Oxide under Thermal Cycling Loadings, Using XRD and Raman Spectroscopy — Correlations with Microstructural States

The presence of residual stresses in thermal oxide layers has been recognized for a long time. In the present work, the mechanical fields for chromia oxide are determined either by XRD or Raman spectroscopy. In addition, the microstructure of the chromia films is investigated ant its influence on the evolution of the stress release processes is analyzed.

Calculation of viscous energy dissipation in asphalt pavements

This paper presents a method to evaluate the energy dissipation in the pavement, induced by the viscous behaviour of bituminous constituents. The introduced method starts from the experimental characterization of each material and goes to the determination of stress and strain field, as well as viscous dissipated energy, in a pavement structure under a rolling wheel. A classical French pavement structure is considered as an application example. First, the behaviour of bituminous materials is characterized with advanced complex modulus tests. Second, a rheological model is used to describe the linear visco-elastic behaviour of bituminous materials. This model was previously developed at the Civil Engineering and Buildings Department of University of Lyon/ENTPE and has already shown its ability to describe completely and precisely the observed behaviour of bituminous materials. In order to make calculation the Finite Element software is then used in a third step, with the previous material model. Detailed hypotheses to perform the simulation of a rolling wheel on the pavement structure are explained. Results of the simulation are presented in terms of dissipated energy inside the pavement for a 40 ton truck. To give an order of magnitude, an estimation of the fuel consumption excess is given. Different temperature and vehicle speeds are considered. The Time Temperature Superposition Principle has been applied to estimate the dissipated energy at any temperature and vehicle speed. The simulation results show that energy dissipation in bituminous pavement due to the rolling weight of the considered 40 ton truck may induce a fuel consumption excess of a few percent for very unfavourable climatic conditions.

Late Cenozoic east–west crustal shortening in southern Longmen Shan, eastern Tibet: Implications for regional stress field changes

Abstract The co-seismic slip sense of the 2008 Wenchuan earthquake (Mw 7.9) has resulted in the present east–west (E–W) crustal shortening and oblique thrusting across Longmen Shan, which are inconsistent with southeast-directed thrusting that occurred during the late Triassic. Although the two major periods of compressional deformations in Longmen Shan have long been recognized, the fault slip rate of the late Cenozoic deformation and the initial E–W crustal shortening remain poorly investigated. This study confirms the fault slip rate in the Dayi Thrust Fault System (DYFS) based on data from the petroleum industry and shallow seismic reflection profiles, and well data. Folded late Pliocene to present strata are analyzed and yield with an average slip rate of 0.2 mm/yr on the DYFS. An average fault slip rate of 0.25 mm/yr is then obtained from the late Pliocene to present for the range front thrust of Longmen Shan. The E–W crustal shortening is investigated by using 3-D seismic reflection data, interpreting satellite image, and conducting a field investigation in the DYFS to determine stress field changes during the late Cenozoic. Two-period tectonic deformations during the late Cenozoic are found in the DYFS, which correspond to the NE- and NS-trending structures, respectively. The activities of the DYFS may reflect a change in the field direction of the regional stress—from NW–SE during the Oligocene to early Pliocene to E–W during the late Pliocene to Holocene, which is consistent with the present stress measurements. The 120 km NS-trending structures in the southern Longmen Shan range front as well as the Wenchuan earthquake co-seismic ruptures are assumed to reflect the active, E–W crustal shortening in Longmen Shan.

On the Determination of Biaxial Residual Stress Fields from Global Indentation Quantities

In the present study, quantitative relations for the determination of surface residual stresses, using sharp indentation testing, are presented. The relations are based on previous results for equi-biaxial residual fields but further developed to apply also for a general situation. The present analysis relies on theoretical methods, but the results are validated using previous experimental and numerical findings. Cone indentation of classical Mises elastoplastic material behavior is assumed throughout the investigation for clarity but not out of necessity. Further development for a complete characterization of a general residual stress field is discussed in some detail.

A review of methods for determining stress fields from earthquakes focal mechanisms; Application to the Sierentz 1980 seismic crisis (Upper Rhine graben)

AbstractThe inversion of earthquake focal mechanisms is one of the few tools available for determining principal stress directions at seismogenic depths. Various methods have been proposed for performing such inversions. For three of the most commonly used methods, including one that has been proposed by Jacques Angelier, we discuss the physical assumptions and the error determination and then we propose an extension for one of the methods. All four methods are then applied for evaluating the stress field in the Upper Rhine graben. They are applied to seismic data recorded with a temporary monitoring network that was deployed 12 hours after the magnitude Mw = 4.4 Sierentz earthquake, which occurred on July 15, 1980. While differences in principal stress directions can be as much as 28° depending on the method used for the principal stress direction determination (orientation of the minimum principal stress has been found to range from N051°E with a 27° plunge to N090° E with a 20° plunge), the 90% confidence level associated with each method varies from 11° to 27°. Moreover, these various methods yield fairly diverse values for the R factor that characterizes relative differences between principal stress magnitudes (from R = 0.7 with a 0.2 90% confidence level to R = 0.3 with a 0.2 90% confidence level). Furthermore all three methods leave some focal mechanisms unexplained. These are then declared to be the result of heterogeneity and are not considered for the inversion. It is concluded that earthquake focal mechanisms inversions lack resolution for stress field evaluation at depth if no proper attention is given to the event independence hypothesis. When proper attention is given to this hypothesis, a resolution of the order of 15° may be achieved. The minimum principal stress orientation derived with these various focal mechanisms inversions differs by 4 to 36° from the orientation determined from borehole breakouts observed in Basel, in a 5 km deep well (N054°E ± 14°), located some 20 km from Sierentz. The solution that fits best borehole breakout observations is that which satisfies the minimum number (three) of prerequisite physical assumptions.

Sicily and southern Calabria focal mechanism database: a valuable tool for local and regional stress-field determination

<p>In this work, we present a new catalog of focal mechanisms calculated for earthquakes recorded in Sicily and southern Calabria. It comprises about 300 solutions, for events with magnitudes ranging from 2.7 to 4.8 that occurred from 1999 to 2011. We used P-wave polarities to compute the fault-plane solutions. Two main goals are achieved. For the first, the catalog allows the stress regime and kinematics characterizing the studied area to be depicted at a regional and more local scale. In particular, moving along the tectonic lineament that extends from the Aeolian Islands to the Ionian Sea, there is a change from a regime characterized by sub-horizontal P-axes, ca. NW-SE directed, to an extensive one in the Calabro-Peloritan Arc, where T-axes striking in a NW-SE direction prevail. Our results also show that part of the seismicity is clustered along the main active seismogenic structures, of which the focal mechanisms indicate the kinematics. Finally, in the Etna volcano area, different stress fields act at different depths due to the combination of the regional tectonics, the strong pressurization of the deep magmatic system, and the dynamics of the shallower portion of the volcano. As a second goal, we highlight that the catalog also represents a valuable tool, through the data distribution on the internet, for further studies directed towards improving our understanding of the geodynamic complexity of the region, and for a better characterization of the seismogenic sources.</p>

Computational model for determination of dynamic load capacity of large three-row roller slewing bearings

In the presented paper a calculation procedure for determination of dynamic load capacity of large three-row roller slewing bearings is presented. The calculation procedure consists of three main parts: (i) determination of internal contact force distribution in a large three-row roller slewing bearing with consideration of bearing clearances and ring support deformations, (ii) determination of stress field in the contact area between raceway and rollers as a consequence of contact forces and (iii) determination of the bearing’s fatigue life due to contact fatigue of the raceway. The internal contact force distribution is determined numerically by using a symmetry 3D FEM-model of a large three-row roller slewing bearing. Another numerical procedure is used to determine the stress field in the contact area between rollers and raceway. This problem is studied on different roller types: cylindrical roller (without profile correction), fully crowned roller (logarithmic-profile) and partially crowned roller (ZB-profile). Numerically determined contact stresses then serve as a basis for fatigue analyses, where the bearing’s service life of the bearing is determined by using the stress-life approach, considering typical material parameters of the bearing’s raceway.

Influence of Errors of Determination of Stresses Near a Crack Tip on the Accuracy of Computation of the Coefficients of the Williams Series Under Mode II Loading

We model and analyze the influence of errors of the determination of stress fields on the accuracy of computation of the coefficients of the Williams expansion and reconstruction of stress fields under mode ІІ loading.

Finite element analysis to determine stress fields at the apex of V-Y flaps

After performing a V-Y advancement flap, we observed an unusually shaped necrosis, resembling a keyhole at the apex of the flap. As high closing tensions are an accepted cause of skin necrosis, we developed a mathematical model based on the finite element analysis in order to determine the stress field by simulating the mechanical behavior of human skin during suture and to explain this particular shape of necrosis. For the modeling, a planar nonlinear two-dimensional finite element model was used. The numerical simulation was carried out with Ansys® v12 software. Results are expressed in numerical and graphic form. The shape of the vertical iso-stress line for a stress equal to 18.8 kPa was similar to the necrosis observed in our clinical case. Similarities between the shape of necrosis and the calculated stress field at the apex of the V-Y advancement flap indicate the major role of skin tension in this necrosis. Finite element analysis is an original approach for describing the particular shape of a necrosis. Although many factors can be implicated in skin necrosis, the modeling confirms the role of tension in the necrosis of this particular case. Level of Evidence: Level V, risk/prognostic study

Analysis of laser shock waves and resulting surface deformations in an Al–Cu–Li aluminum alloy

Laser shock processing is now a recognized surface treatment for improving fatigue or corrosion behaviour of metallic materials through the generation of a compressive stress field. In turn, the analysis of shock wave propagation is of primary importance to predict numerically morphological and mechanical surface modifications.Considering experimental and numerical analyses of shock wave propagation, and surface deformations induced by single impacts, a 2050 aluminum alloy having different microstructures was investigated under laser-shock loading. In a first step, the evolution of shock wave attenuation and elastic precursor amplitude was correctly reproduced by finite element simulations, and in a second step, surface deformations induced by 1–6 local impacts were also compared satisfactorily with experiments. This allowed us to validate mechanical loading and materials' constitutive law, but did not allow accurate determination of residual stress fields on a single impact.

Mathematical simulation of metal deformation using horizontal foundry-forging module

The mathematical model of the deformation process using a horizontal foundry-forging module of a solidified metal is presented. The numerical solution of the three-dimensional problem results in the determination of stress fields, movement rates, temperatures, and strains in the plastic flow area of the metal at a given time step of loading.

Residual stress field determination in welds by means of X‐ray, synchrotron and neutron diffraction

AbstractTo what extent the welding residual stresses influence fatigue is still unclear and matter of debate. An important reason for this lack of clarity is that the exact determination of residual stress fields in welds is complicated which leads to conservative assumptions about these stresses in the fatigue design codes. The advances in the diffraction analysis of materials offer the opportunity for the full‐field residual strain mapping in welds albeit at the cost of time and technical complexity. In this work residual stress field determination in welded S1100QL specimens by means of the x‐ray, synchrotron and neutron diffraction techniques was undertaken. The results revealed that the maximum values of surface residual stresses are not as frequently assumed, as high as the yield strength in small scale specimens. At the weld toe which could serve as a fatigue crack initiation site, even lower residual stresses than the weld centreline could be present. The in‐depth measurements revealed that the effective part of the residual stress field which could be decisive for the fatigue failure initiation is concentrated at the surface of the weld.

Application of synchrotron X-ray diffraction and nanoindentation for the determination of residual stress fields around scratches

Residual stresses and plastic deformation around scratches or scribe marks in ductile materials can affect fatigue life. Scratches of the order of tens of microns may convert into propagating cracks driven by tensile residual stresses at the scratch root. Probing such stresses on a small scale is experimentally challenging in engineering materials. Here we present results of a combined study using synchrotron X-ray diffraction and nanoindentation to determine the residual stresses around scratches in aluminium alloys. The extraction of residual stresses in metallic materials where there is work hardening is challenging using indentation methods, but a method is presented by which this has been achieved, and a good correlation is obtained between the results obtained using diffraction and nanoindentation. The advantage of synchrotron X-ray measurement is that it allows validation of the stresses at the same spatial scale as nanoindentation. It was found that scratches produced by a “ploughing” mechanism where there was significant plastic deformation beneath the scratch showed higher work hardening and tensile residual stresses than those produced by a “cutting” mechanism where there was little plastic deformation of the material. Little effect of fatigue cycling was seen on the peak stresses at the scratch tip.

General approach to the development of mathematical models of nondestructive stress control. I. Methodological and physical substantiation and a kinematic model

It is shown that nondestructive stress control is not a part of the classical mechanics of deformable bodies by either the phenomenological basis or by the methodology. In a general case (separate component determination of inhomogeneous triaxial three-dimensional stress fields under conditions of natural and induced anisotropy), the theoretical development of closed mathematical models of nondestructive control is possible only with the use of a special approach of free deformation, which is based on additional facts on the relation of stresses to strain, which are unnecessary and neglected in classical mechanics.

Residual Stresses in Beams (With and Without Prior History) Numerically Assessed by the Crack Compliance Method

Abstract: This work assesses the Crack Compliance Method (CCM) by the Finite Element Method (FEM). The CCM is a very powerful method that is based on Fracture Mechanics Theory. Its experimental application and set up is validated by this work. The numerical assessment of the CCM is performed on bending beams with and without prior straining history, to determine the best position and orientation of strain gauges, as well as the optimum number of readings. The prior straining history condition, in the analyzed components, is induced by an axial pulling before the beam is bent. Three levels of preloading are considered: low, medium and high (which are related to the yield strain of the simulated material); Isotropic and Kinematic hardening rules are also considered. Additionally, an experimental evaluation is also presented by introducing a new supporting system to cut a slot in the beams. The results obtained in this work, provide a quantitative demonstration of the effect of hardening strain on the distribution of the residual stress in beams. In the same manner, the theoretical formulation of the CCM has been evaluated validating the application of this method for the determination of residual stress fields in mechanical components.

Stressandstrain reconstruction for the eastern segment of the Baltic shield

Stressandstrain reconstruction for the eastern segment of the Baltic shield