A program to calculate the state of stress in the vicinity of an inclined borehole through an anisotropic rock formation

Geophysics ◽  
2019 ◽  
Vol 84 (5) ◽  
pp. F103-F118 ◽  
Author(s):  
Wei Li ◽  
Douglas R. Schmitt ◽  
Maria Tibbo ◽  
Changchun Zou
Keyword(s):  
Stress Concentration ◽  
Stress Distribution ◽  
Elastic Anisotropy ◽  
Inverse Function ◽  
Elastic Stiffness ◽  
Far Field ◽  
Anisotropic Rock ◽  
Anisotropic Formation ◽  
Sign Convention ◽  
Inclined Borehole

A borehole existing in any geologic formation concentrates the far-field tectonic and overburden stresses amplifying the magnitudes of certain stress components near the borehole. It is important to understand the magnitudes and patterns of this stress concentration because these lead to damage and can even collapse the borehole if sufficiently strong. The solution of the stress distributed near a borehole can be complicated considering the elastic anisotropy of rocks. We have developed programs (ASCIB3D) in MATLAB and Python to model the stress distribution around an inclined borehole in an arbitrarily oriented anisotropic medium. The program is built on the Lekhnitskij-Amadei solution. The input orientation of the far-field stresses and the elastic stiffness matrix of the medium into the program are geology angles instead of the rotation angles shown in previous studies, making the code more convenient for users. The sign convention for the inverse function, which is ignored in previous studies, is discussed in detail. The results indicate that the program ASCIB3D is a useful tool for modeling the stress distributed around an inclined borehole in the anisotropic formation and analyzing the effect of anisotropy and borehole inclination on stress distribution. The inclination and azimuth of the borehole and the anisotropy of the rocks affect the orientation and strength of the stress concentration.

scholarly journals Stress analysis of infinite laminated composite plate with elliptical cutout under different in plane loadings in hygrothermal environment

2021 ◽  
Vol 8 (1) ◽  
pp. 1-12
Author(s):  
Ashok Magar ◽  
Achchhe Lal
Keyword(s):  
Stress Concentration ◽  
Stress Distribution ◽  
Composite Plate ◽  
Volume Fraction ◽  
Elliptical Hole ◽  
Laminated Composite ◽  
Laminated Composite Plate ◽  
Concentration Changes ◽  
Hygrothermal Environment ◽  
Plate Analysis

Abstract This paper presents the solution of stress distribution around elliptical cutout in an infinite laminated composite plate. Analysis is done for in plane loading under hygrothermal environment. The formulation to obtain stresses around elliptical hole is based on Muskhelishvili’s complex variable method. The effect of fibre angle, type of in plane loading, volume fraction of fibre, change in temperature, fibre materials, stacking sequence and environmental conditions on stress distribution around elliptical hole is presented. The study revealed, these factors have significant effect on stress concentration in hygrothermal environment and stress concentration changes are significant with change in temperature.

scholarly journals Determination of the Elastic Tensor of a Textured Low-Carbon Steel

1993 ◽  
Vol 21 (1) ◽  
pp. 3-16 ◽  
Author(s):  
P. Spalthoff ◽  
W. Wunnike ◽  
C. Nauer-Gerhard ◽  
H. J. Bunge ◽  
E. Schneider
Keyword(s):  
Carbon Steel ◽  
Elastic Anisotropy ◽  
Low Carbon Steel ◽  
Elastic Stiffness ◽  
Ultrasonic Pulse ◽  
Grain Structure ◽  
Maximum Deviation ◽  
Low Carbon ◽  
The Hill ◽  
Pulse Echo

The components of the elastic stiffness tensor of hot rolled low-carbon steel were determined using an ultrasonic pulse-echo-method. They were also calculated on the basis of X-ray texture measurements using the Hill approximation. The maximum deviation between experimental and calculated values is 3.5%. An influence of the slightly anisotropic grain structure on the elastic anisotropy could not be seen.

Stress Distribution in Be Compact Tension Specimen

2007 ◽  
Vol 561-565 ◽  
pp. 2033-2036
Author(s):  
Rui Wen Li ◽  
Ping Dong
Keyword(s):  
Finite Element ◽  
Stress Concentration ◽  
Stress Distribution ◽  
Compact Tension ◽  
Compact Tension Specimen ◽  
Tension Specimen ◽  
X Ray ◽  
Measured Stress ◽  
Local Stresses ◽  
Fracture Behaviors

Beryllium (Be) is susceptible to introduce stress because it is a brittle metal with a high elastic modular. The compact tension (CT) specimens of beryllium were designed to determinate stress and fracture behaviors. Stress distribution near notch in CT beryllium was measured by the combination of an X-ray stress analysis and a custom-designed load device. The results show that local stresses near notch tip are much higher than those on other area. Thus, stress concentration lead the CT specimens fracture along the notch direction. Residual stresses due to machining are remained. A finite element ( FE ) calculation on the same loaded geometry was made, and the result is agreement with the measured stress distribution near notch.

Analysis of Stress in Aircraft Components Using Lock-In Thermography

2010 ◽  
Vol 663-665 ◽  
pp. 1073-1076 ◽  
Author(s):  
Xun Liu ◽  
Jun Yan Liu ◽  
Xu Dong Li ◽  
Guang Yu Zhang
Keyword(s):  
Stress Concentration ◽  
Stress Distribution ◽  
Stress Analysis ◽  
Aluminium Alloys ◽  
Thermoelastic Effect ◽  
Load Frequency ◽  
Effect Theory ◽  
Lock In ◽  
The Relationship

This paper describes a theoretical and experimental analysis on full-filed stress distribution from thermoelastic measurements and its application to determination of stress concentration. The sum of the principle stress can be measured by Thermal Stress Analysis (TSA). Lock-in Thermography is very effective tool to measure the structure stress distribution by its high thermal resolving. In this study, the thermoelastic effect theory is described and the relationship between the temperature and the applied stress is developed in an elastic material. Experiments were carried out with 2A12 aluminium alloys plate and ones with hole structure under cyclic load. The thermoelastic effect coefficient is obtained for 2A12 aluminium alloys materials, and the effect law is analyzed that the stress value measured was affected by load frequencies. The optional load frequency is obtained, and that is, the load frequency is selected greater than 3.5Hz for 2Al12 materilas, and it was found that the structure stress can be evaluated with good accuracies by the lock in thermography. The experiment was carried out for aircraft components stress distribution measurement and structure stress analysis. The experimental results show the stress concentration position is easy found from stress distribution by lock-in thermography.

scholarly journals Force Transfer and Stress Distribution in an Implant-Supported Overdenture Retained with a Hader Bar Attachment: A Finite Element Analysis

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Preeti Satheesh Kumar ◽  
Kumar K. S. Satheesh ◽  
Jins John ◽  
Geetha Patil ◽  
Ruchi Patel
Keyword(s):  
Finite Element ◽  
Stress Concentration ◽  
Stress Distribution ◽  
Maximum Stress ◽  
Alveolar Bone ◽  
Von Mises Stress ◽  
Element Analysis ◽  
Finite Element Software ◽  
Force Transfer ◽  
Edentulous Mandible

Background and Objectives. A key factor for the long-term function of a dental implant is the manner in which stresses are transferred to the surrounding bone. The effect of adding a stiffener to the tissue side of the Hader bar helps to reduce the transmission of the stresses to the alveolar bone. But the ideal thickness of the stiffener to be attached to the bar is a subject of much debate. This study aims to analyze the force transfer and stress distribution of an implant-supported overdenture with a Hader bar attachment. The stiffener of the bar attachments was varied and the stress distribution to the bone around the implant was studied. Methods. A CT scan of edentulous mandible was used and three models with 1, 2, and 3 mm thick stiffeners were created and subjected to loads of emulating the masticatory forces. These different models were analyzed by the Finite Element Software (Ansys, Version 8.0) using von Mises stress analysis. Results. The results showed that the maximum stress concentration was seen in the neck of the implant for models A and B. In model C the maximum stress concentration was in the bar attachment making it the model with the best stress distribution, as far as implant failures are concerned. Conclusion. The implant with Hader bar attachment with a 3 mm stiffener is the best in terms of stress distribution, where the stress is concentrated at the bar and stiffener regions.

Shear Stress Discontinuities in Adhesive Joints

2015 ◽  
Vol 1088 ◽  
pp. 758-762
Author(s):  
Xiao Cong He
Keyword(s):  
Shear Stress ◽  
Stress Concentration ◽  
Stress Distribution ◽  
Three Dimensional ◽  
Adhesive Layer ◽  
Adhesive Joints ◽  
Shear Stress Distribution ◽  
Element Analysis ◽  
Dimensional Finite Element ◽  
Three Dimensional Finite Element

This paper deals with the stress discontinuities in shear stress distribution of adhesive joints. The three-dimensional finite element analysis (FEA) software was used to model the joints and predict the shear stress distribution along the whole beam. The FEA results indicated that there are stress discontinuities existing in the shear stress distribution within adhesive layer and adherends at the lower interface and the upper interface of the boded section. The numerical values of the shear stress concentration at key locations of the joints and the stress concentration ratio are discussed.

Microstructure Design for a Rotating Disk: With Application to Turbine Engines

2005 ◽  
Author(s):  
Stephen D. Sintay ◽  
Brent L. Adams
Keyword(s):  
Design Space ◽  
Elastic Anisotropy ◽  
Material Design ◽  
Rotating Disk ◽  
Material Model ◽  
Elastic Stiffness ◽  
Fiber Texture ◽  
Material Parameters ◽  
Extension Force ◽  
Order Of Magnitude

Through the use of generalized spherical harmonic basis functions a spectral representation is used to model the microstructure of cubic materials. This model is then linked to the macroscopic elastic properties of materials with Cubic Triclinic and Cubic Axial-symmetric symmetry. The influence that elastic anisotropy has on the fatigue response of the material is then quantified. This is accomplished through using the effective elastic stiffness tensor in the computation of the crack extension force, G. The resulting material model and macroscopic property calculations are the foundation for a software package which provides an interface to the microstructure. The Microstructure Sensitive Design interface (MDSi) enables interaction with the material design process and provides tools needed to incorporate material parameters with traditional design, optimization, and analysis software. The microstructure of the material can then be optimized concurrently other engineering models to increase the overall design space. The influence of microstructure on the performance of a spinning disc is explored. The additional design space afforded by inclusion of the material parameters show that for both Cubic Triclinic and Cubic Axial-symmetric material symmetry conditions G can be reduced by more than an order of magnitude. For the Cubic Axial-symmetric condition a Cube <001> fiber texture and a <111> fiber texture are identified as the best performing orientation distributions.

Effect of variations in microstructure on clay elastic anisotropy

Geophysics ◽  
2020 ◽  
Vol 85 (2) ◽  
pp. MR73-MR82 ◽  
Author(s):  
Colin M. Sayers ◽  
Lennert D. den Boer
Keyword(s):  
Elastic Properties ◽  
Volume Fraction ◽  
Elastic Anisotropy ◽  
Rock Physics ◽  
Elastic Stiffness ◽  
Single Domain ◽  
Model Parameters ◽  
Stiffness Tensor ◽  
Elastic Stiffness Tensor ◽  
Clay Platelets

Rock physics provides a crucial link between seismic and reservoir properties, but it requires knowledge of the elastic properties of rock components. Whereas the elastic properties of most rock components are known, the anisotropic elastic properties of clay are not. Scanning electron microscopy studies of clay in shales indicate that individual clay platelets vary in orientation but are aligned locally. We present a simple model of the elastic properties of a region (domain) of locally aligned clay platelets that accounts for the volume fraction, aspect ratio, and elastic-stiffness tensor of clay platelets, as well as the effective elastic properties of the interplatelet medium. Variations in clay anisotropy are quantified by examining the effects of varying model parameters upon the effective transverse-isotropic (TI) elastic-stiffness tensor of a domain. Statistics of these distributions and correlations between stiffnesses and anisotropy parameters enable the most probable sets of stiffnesses to be identified for rock physics calculations. The mean of these distributions is on the order of twice the mode for in-plane stiffnesses ([Formula: see text], [Formula: see text], [Formula: see text]), but it is of the same order as the mode for out-of-plane stiffnesses ([Formula: see text], [Formula: see text], [Formula: see text]). Despite random sampling, well-defined relations emerge, consistent with similar shale relations reported in the literature. Expressing these relations in terms of [Formula: see text] for a single domain of aligned clay platelets facilitates their general application. In the limit that the volume fraction approaches unity, the elastic stiffnesses thus derived reproduce those of the clay mineral assumed as platelets. Given the elastic-stiffness tensor of a single domain of aligned clay platelets, the effective TI elastic-stiffness tensor of clay is obtained by integrating over the clay-platelet orientation-distribution function.

Analytical solutions of a spherical nanoinhomogeneity under far-field unidirectional loading based on Steigmann–Ogden surface model

2020 ◽  
Vol 25 (10) ◽  
pp. 1904-1923
Author(s):  
Youxue Ban ◽  
Changwen Mi
Keyword(s):  
Flexural Rigidity ◽  
Elastic Stiffness ◽  
Surface Model ◽  
Far Field ◽  
Stress Concentrations ◽  
Equilibrium Equations ◽  
Legendre Series ◽  
Simple Method ◽  
Shear Moduli ◽  
Special Cases

For a solid surface or interface that is subjected to transverse loading, the influence of its flexural resistibility to bending deformation becomes significant. A spherical inhomogeneity or void embedded in an infinite elastic medium under the application of nonhydrostatic loads represents a typical example. In this work, we consider the most fundamental loading of a far-field unidirectional tension. Analytical displacements and stresses are developed by the coupling of a Steigmann–Ogden surface mechanical model, the simple method of Boussinesq displacement potentials, the semi-inverse method of elasticity, and Legendre series representations of spherical harmonics. The problem is then solved by converting the equilibrium equations of displacement into a linear system with respect to the Legendre series coefficients. The developed solutions are general in the sense that they may reduce to their classical or Gurtin–Murdoch counterparts as special cases. Analytical expressions reveal that the derived solution depends on four dimensionless ratios from among surface material parameters, shear moduli ratio, and inhomogeneity or void radius. In particular, instead of depending on both flexural parameters in the moment–curvature relation, one fixed combination is sufficient to represent the surface flexural rigidity. This is in contrast with the influence of the in-plane elastic stiffness, in which both surface Lamé parameters matter. Parametric studies further demonstrate that, for metallic inhomogeneities or voids with radii between 10 nm and 100 nm, the effects of surface flexural rigidity on stress distributions and stress concentrations are significant.

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