Total Stress Field Research Articles

Gravitational potential energy and regional stress and strain rate fields for continental plateaus: Examples from the central Andes and Colorado Plateau

The commonly observed extension in areas of elevated and thickened crust is an expected consequence of having excess gravitational potential energy (GPE) compared to the low GPE of the surrounding crust. While this conceptual model is well founded, it is less clear how well GPE-related stress orientations compare quantitatively to observed stress and strain rate orientations and what any inconsistency tells us about the presence of other competing forces. We estimate the GPE distribution for the central Andes and the greater Colorado Plateau area using topography and crustal thickness variations, respectively, and compare the related stress fields with the World Stress Map as well as with a geodetic strain rate field (for the Colorado Plateau only). In both areas, deviatoric stresses associated with GPE variations alone cannot fully account for the observed deformation rate field. For the central Andes only a combination of deviatoric stresses associated with GPE and relative plate motions can account for the near N–S tensional stress observed in the Peruvian Andes and the margin–normal compressional stress along the eastern Cordillera and sub-Andean fold-and-thrust belt. The observed deformation field around the Colorado Plateau shows E–W extension, largely inconsistent with the deviatoric stresses associated with GPE variations except for the area east of the Rio Grande Rift. The NE–SW oriented stress observed on the southwestern Colorado Plateau is consistent with the orientations of tensional deviatoric stresses associated with GPE variations. We argue that this consistency could be haphazard; stress observations may not reflect the current state of stress due to inherited structure, or could result from the relative high strength of Colorado Plateau that allows for regional GPE variations (and possibly basal shear) to be more significant forces than far-field plate interactions. For the central Andes and Colorado Plateau, stresses associated with GPE variations have a strong influence on the total stress field, and can thus be used to calibrate the overall level of deviatoric stress acting within the lithosphere.

Mechanical/thermal stress intensification for mode II crack tip: Fracture initiation behavior of steel, aluminum and titanium alloys

A macroscopic crack would be diathermanous for heat. The heat flow would partly pass the crack surface. The crack is called as the uninsulating crack. An insulating crack implies that the heat flow cannot pass the crack surface completely. The proposed crack model includes both insulating and uninsulating crack cases. The problem of a line crack under the combination of remote uniform heat flow and mechanical shear loading is solved by the complex function method. Obtained are the analytical solutions including the temperature distribution, thermal stress intensity factor, total stress field and strain energy density function. It is found that if the temperature gradient perpendicular to the crack line on the upper and lower crack surfaces remains constant, the mode II thermal stress intensity factor prevails while the mode I thermal stress intensity factor vanishes. It is a typical mode II crack problem. Moreover, the mode II thermal stress intensity factor only depends on the temperature gradient perpendicular to the crack. The temperature gradient parallel to the crack line has no influence on the thermal stresses. The diathermanous feature of the crack would affect the thermal stress field. Three materials, say steel alloy 38Cr2Mo2VA, aluminum alloy LY12 and titanium alloy TC6, are selected to perform the numerical calculations. Their fracture behaviors under thermal and mechanical loading are discussed and compared by application of strain energy density theory. It is found that for an insulating crack, the positive temperature gradient would kill the mechanical loading that would impede the crack growth. However, the uninsulating crack behaves quite different. For the uninsulating crack, the positive temperature gradient would enhance the mechanical loading or the crack growth. The results are useful for the safety assessment of structural members, especially in the pressurized vessels and pipes and nuclear power plants.

Stress Partitioning: a Practical Concept for Analysing Boundary Conditions of Brittle Deformation

Although conjugate fault systems cannot accommodate three-dimensional strain, the notion of stress-driven fracturing based upon Mohr-Coulomb's failure criterium can be reconciled with any kinematic boundary condition if a non-static scenario is considered. The concept of stress partitioning is proposed as a tool for understanding the mechanisms allowing such compatibility. It describes stress changes that occur in response to failure events, giving the appearance that the total stress field is decoupled into distinct, independent components. It can be mainly applied to biaxial horizontal loading conditions (e.g. multidirectional tension or multidirectional compression in intraplate regions). Swapping of horizontal stress axes, caused by stress drop subsequent to failure, can result in two distinct stress events and two, either tensile or shear fracture systems with nearly orthogonal strikes. Each fracture event develops according to Mohr-Coulomb's and Griffith's failure criteria, but the resulting overall deformation is three-dimensional.

Separation of Primary Stress in Finite Element Analysis of Pressure Vessel with the Principle of Superposition

A key problem in engineering application of “design by analysis” approach is how to decompose a total stress field obtained by the finite element analysis into different stress categories defined in the ASME Code III and VIII-2. In this paper, we suggested an approach to separate primary stress with the principle of superposition, in which the structure does not need to be cut into primary structure but analyzed as a whole only with decomposed load. Taking pressurized cylindrical vessel with plate head as example, the approach is demonstrated and discussed in detail. The allowable load determined by the supposed method is a little conservative than that determined by limited load analysis.

Three-dimensional strain and temperature monitoring of composite laminates

This paper discusses a new sensor design based on optical fibre Bragg gratings which is being developed in the framework of the MASSFOS-project ('Multi-Axial Stress and Strain sensing of thermo hardened composite elements using Fibre Optic Sensors'-project). The main technical objective of this ESA co-funded project is the development of a monitoring system which measures dynamically the multi-axial stress and strain in thermo hardened composite elements (made of space qualified material). The sensor consists of a 'High Birefringence '-fibre (HiBi-fibre) in which two gratings are inscribed; each grating yields two distinct Bragg peaks. The first grating is sensitive to the total stress field in the material, while the second one is isolated from transverse stress components. By measuring the four Bragg peaks of the sensor, it is possible to determine the total strain field, plus the temperature inside a composite material. Theoretical simulations have indicated a good strain resolution of the proposed design. Experimental calibration of the sensor gave similar results.

Cone model for two surface foundations on layered soil

In this paper, the cone model is applied to the vibration analysis of two foundations on a layered soil half space. In the analysis, the total stress field in the subsoil is divided into the free-field and the scattering field. Seed’s simplified method is adopted for the free-field analysis, while the cone model is proposed for analyzing the dynamic scattering stress wave field. The shear stress field and the compressive stress field in the layered stratum with two scattering sources are calculated by shear cone and compressive cone, respectively. Furthermore, the stress fields in the subsoil with two foundations are divided into six zones, and the P wave and S wave are analyzed in each zone. Numerical results are provided to illustrate features of the added stress field for two surface foundations under vertical and horizontal sinusoidal force excitation. The proposed cone model may be useful in handling some of the complex problems associated with multi-scattering sources.

Elastic and inelastic triggering of earthquakes in the North Anatolian Fault zone

Deformation models used to explain the triggering mechanism often assume pure elastic behaviour for the crust and upper mantle. In reality however, the mantle and possibly the lower crust behave viscoelastically, particularly over longer time scales. Consequently, the stress field of an earthquake is in general time-dependent. In addition, if the elastic stress increase were enough to trigger a later earthquake, this triggered event should occur instantaneously and not many years after the triggering event. Hence, it is appropriate to include inelastic behaviour when analysing stress transfer and earthquake interaction. In this work, we analyse a sequence of 10 magnitude M s > 6.5 events along the North Anatolian Fault between 1939 and 1999 to study the evolution of the regional Coulomb stress field. We investigate the triggering of these events by stress transfer, taking viscoelastic relaxation into account. We evaluate the contribution of elastic stress changes, of post-seismic viscoelastic relaxation in the lower crust and mantle, and of steady tectonic loading to the total Coulomb stress field. We analyse the evolution of stress in the region under study, as well as on the rupture surfaces of the considered events and their epicentres. We study the state of the Coulomb stress field before the 1999 İzmit and Düzce earthquakes, as well as in the Marmara Sea region. In general, the Coulomb stress failure criterion offers a plausible explanation for the location of these events. However, we show that using a purely elastic model disregards an important part of the actual stress increase/decrease. In several cases, post-seismic relaxation effects are important and greater in magnitude than the stress changes due to steady tectonic loading. Consequently, viscoelastic relaxation should be considered in any study dealing with Coulomb stress changes. According to our study, and assuming that an important part of the rupture surface must be stressed for an earthquake to occur, the most likely value for the viscosity of the lower crust or mantle in this region is 5 · 10 17–10 18 Pa · s. Our results cannot rule out the possibility of other time-dependent processes involved in the triggering of the 1999 Düzce event. However, the stress increase due to viscoelastic relaxation brought 22% of the 1999 Düzce rupture area over the threshold value of Δ σ c ≥ 0.01 MPa (0.1 bar), and took the whole surface closer to failure by an average of 0.2 MPa. Finally, we argue that the Marmara Sea region is currently being loaded with positive Coulomb stresses at a much faster rate than would arise exclusively from steady tectonic loading on the North Anatolian Fault.

Intraslab seismicity and thermal stress in the subducted Cocos plate beneath central Mexico

We present a model of the subducting Cocos slab beneath Central Mexico, that provides an explanation for stresses causing the occurrence of the majority of the intraslab earthquakes which are concentrated in a long flat segment. Based on the recently developed thermal models for the Central Mexico subduction zone, the thermal stresses due to non-uniform temperature contrast in the subducting slab are calculated using a finite element approach. The slab is considered purely elastic but due to high temperature at its bottom the behavior is considered as ductile creep. The calculation results show a ∼ 20 km slab core characterized by a tensional state of stress with stresses up to 70 MPa. On the other hand, the top of the slab experiences high compressive thermal stresses up to 110 MPa, depending on the elastic constants used and location along the flat part of the subducting plate. These compressive stresses at the top of the slab are not consistent with the exclusive normal fault intraslab earthquakes, and two different sources of stress are proposed. The trenchward migration of the Mexican volcanic arc for the last 7 Ma indicates an increase of the slab dip through time. This observation suggests that the gravity torque might exceed the suction torque. Considering the flat slab as an embedded plate subject to an applied clockwise net torque of 0.5 × 10 16–1.5 × 10 16 N m, the upper half would exhibit tensional stresses of 40–110 MPa that can actually balance the compressive thermally induced stresses. An alternative stress source might come from the slab pull force caused by the slab positive density anomaly. Based on our density anomaly estimations (75 ± 20 kg/m 3), a 350 km slab length, dipping at 20° into the asthenosphere, induces a slab pull force of 1.7 × 10 12–4.6 × 10 12 N m. This force produces a tensional stress of 41–114 MPa, sufficient to balance the compressive thermal stresses at the top of the flat slab. The linear superposition of the thermally and torque or slab pull induced stresses shows tensile stresses up to 60–180 MPa inside the flat slab core. Also, our results suggest that the majority of the intraslab earthquakes inside the flat slab are situated where the resultant stresses are larger than 40–80 MPa. This study provides a reasonable explanation for the existence of exclusively normal fault intraslab earthquakes in the flat slab beneath Central Mexico, and also it shows that thermal stresses due to non-uniform reheating of subducting slabs play a considerable role in the total stress field.

Contact Analyses for Bodies With Frictional Heating and Plastic Behavior

The stress field within machine components is an important indicator for contact failures. Since both thermal stresses due to frictional heating and plasticity are significant in engineering application, it is critical to predict the total stress field. In this work, the steady-state thermal effect is considered and a thermo-elastic–plastic contact model is developed. The model is applicable for rolling and/or sliding contact problem, as far as small equivalent plastic strain hypothesis is respected. Influence coefficients for surface normal displacement, temperature, and strain and stress tensors are used with the discrete convolution and fast Fourier transform algorithm. The single-loop conjugate gradient iteration scheme is also applied to achieve fast convergence speed. Simulations are presented for several academic examples ranging from elastic to thermo-elastic–plastic. The thermo-elastic–plastic analyses show that the heat factor in a contact situation has significant effect not only on the critical Hertzian pressure and on the pressure distribution, but also on the magnitude and depth of the maximum von Mises stress during loading and the residual ones found after unloading.

Measurement of residual stress distributions in Al 2O 3/3Y-TZP multilayered composites by fluorescence and Raman microprobe piezo-spectroscopy

Microscopic distributions of residual stresses were evaluated in multilayered composite specimens consisting of Al 2O 3/3 mol% Y 2O 3-stabilized ZrO 2 (3Y-TZP) layers with different compositions and thicknesses. Residual stress measurements were performed both by Raman and fluorescence piezo-spectroscopy, and they revealed the existence of tensile and compressive hydrostatic stresses in the zirconia and alumina phases, respectively. Residual stresses mainly arose from thermal expansion and elastic mismatch between the constituent ceramic phases. However, the overall residual stress field consisted of two separate components: (i) a microscopic stress field originating on the microstructural scale from grain-to-grain thermal and elastic mismatches between Al 2O 3 and 3Y-TZP phases; and, (ii) a macroscopic stress field, which is established to obey equilibrium conditions between adjacent layers. From a comparison between stress data collected according to different piezo-spectroscopic techniques (i.e., based on fluorescence and Raman band shift for Cr 3+-doped Al 2O 3 and 3Y-TZP, respectively), a reliability assessment of the stress measurement could be also obtained. The macroscopic stress field piled up among different layers could be separated from the microscopic grain-to-grain stress field and quantitatively evaluated to a degree of precision by employing a calibration procedure using chromophoric Al 2O 3 phase as a “stress sensor”. Some fine details of the internal stress distribution were also revealed, as for example the existence of a parabolic stress profile within 3Y-TZP layers with substantial stress intensification nearby the junctions between neighbouring layers. The total stress field was found to remarkably depend on layer thickness for given constant dimensions of the multilayered structure.

Development of Displacement-Softening Model for Interface Shear Behavior Between Geosynthetics

This paper presents two kinds of constitutive model applicable for geosynthetic interfaces, namely a combined model (MODEL 1) and DSC model (MODEL 2). In order to verify the performance of the two models, back­ predictions were carried out on smooth geomembrane (S-GM) and textured geomembrane (T-GM) interfaces with geotextile (GT), namely S-GM/GT and T-GM/GT interface using the parameters obtained from test results For the combined model (MODEL 1), the total stress field is divided into two regions, i.e. pre-peak and post-peak region, to take into account the displacement-softening effect on the interface shear behavior. The DSC model (MODEL 2) was also considered to model the interface shear behavior between geosynthetics. This model is comprised of two reference states, namely the relative intact (RI) and the fully adjusted (FA) state, and one function, namely the disturbance function. Though the comparisons between measured data and back-prediction results for MODEL 1 and MODEL 2 (DSC model) showed good agreements with each other, MODEL 1 has a critical limitation related to the boundary value problem as it is inconvenient to implement this model into FEM. Finally, DSC model (MODEL 2) was suggested as an appropriate model for simulating large-displacement shear behaviors with the characteristics of plasticity because the DSC model has been widely implemented in FEM process by many researchers.

Atomistic study of the interaction between a microcrack and a hard inclusion inβ−SiC

We present an atomistic investigation on mechanical loading effects in a model fiber-reinforced $\ensuremath{\beta}\text{\ensuremath{-}}\mathrm{Si}\mathrm{C}$ monocrystal where a crack is present. Our simulations are both consistent with the basic results of elementary continuum mechanics and provide a deeper physical insight at the nanoscale. In particular, we propose an effective renormalization of some basic quantity (e.g., the crack length), which reconcile continuum theory to atomistics. Finally, we prove that the interaction between the microcrack and the hard inclusion (fiber) is able to increase the strength of the $\ensuremath{\beta}\text{\ensuremath{-}}\mathrm{Si}\mathrm{C}$ lattice and falls beyond the linear regime. We consistently provide a corresponding constitutive equation for the total stress field for an interacting crack-fiber pair.

Residual stresses deriving from holographic interferometry data on a base of inverse problem solution

A transition model, which is capable of obtaining both membrane and bending residual stress components from initial experimental information, is developed for thin-walled plane structures. The determination of residual stresses is based on the combined implementing of the hole-drilling method and reflection hologram interferometry. Required input data are obtained by simultaneous measurements on through hole distortions in two principal strain directions on opposite sides of thin plane specimen. These sides are faces of the drill entrance and exit. Superimposed residual stresses field, which consists of both membrane and bending components, is a reason for the various deviations of each specific fringe pattern from an ideal form. This fact is a clear experimental indication of the bending stress contribution in a total stress field. Two ways of decomposition of superimposed residual stresses field are proposed and analysed in detail. Emphasis is laid on a careful quantitative formulation of the inverse problem needed for an accurate deriving both membrane and bending residual stress components. It is shown that an availability of two-side initial data is both an essential and necessary condition of such a formulation. Detailed analysis of an accuracy of the results obtained is performed. This analysis is based on a wide set of both actual interferograms and analogous reference fringe patterns related to superimposed residual stress field under study. Comparing residual stress values obtained proceeding from one-side and two-side data are presented for different types of superimposed field of interest.

Classification of holographic fringe patterns inherent in through hole drilling in residual stress field

Comparative analysis of actual fringe patterns, which are induced by combined implementing the hole drilling method and reflection hologram interferometry for residual stresses determination, is presented. Involved considerations are related to plane thin-walled structural elements. A set of interferograms of perfect (ideal) form is selected proceeding from one-side measurements. A base for recognising each specific ideal configuration is a fine coincidence between actual interferograms and analogous reference fringe patterns constructed for the same stress state. Perfect (ideal) both actual and reference fringe patterns are defined as a response of pure membrane 2D stress field on through hole drilling between exposures. Main principles of creating the regular catalogue of reference fringe patterns inherent in through hole drilling in thin-walled components are formulated. Emphasis is made on a careful collecting and classifying actual interferograms with clear indications of bending stress presence in total residual stress field. Evidences needed for a reliable classification of the type of residual stresses field of interest are established and verified. A response of superimposed residual stress field, which consists of both membrane and bending components, is characterised by various deviations of each specific fringe pattern from an ideal form. More deep analysis of fringe patterns related to superimposed residual stress field is based on specially designed technique. The main essence of the approach developed is simultaneous measurements of through hole distortions in two principal strain directions on opposite sides of thin plane specimen. These sides are faces of the drill entrance and exit. Sophisticated optical set-up that is capable of obtaining high-quality fringe patterns in the course of two-side measurements is developed and implemented. Typical set of fringe patterns obtained for single probe hole on opposite specimen faces is presented.

DYNAMIC THERMOELASTIC PROCESSES IN MICROPERIODIC COMPOSITES

The aim of this article is to present (i) a formulation of the field equations characterizing a "refined averaged model" describing the dynamical thermoelastic processes in microperiodic composite materials, (ii) an analysis of particular models, and (iii) an application of an "effective modulus model" to solve a boundary initial value problem for a microperiodic layered semispace. Using a modeling procedure proposed in papers by Wo niak et al. [1,2], the fundamental field equations of coupled thermoelasticity for general microperiodic composite materials are derived and a one-dimensional layered composite model is obtained. The fundamental field equations involve the functions \\eqalign{{\\bf u}({\\bf x}, t) = {\\bf U} ({\\bf x}, t)+h^a({\\bf x}){\\bf V}^a({\\bf x}, t)\\cr \\vartheta({\\bf x}, t) =\\Theta({\\bf x}, t)+h^a({\\bf x})\\Phi^a({\\bf x}, t)\\qquad a=1,\\ldots ,n} where h a are the microshape functions; u and are the displacement and temperature fields, respectively; U , V a , , and | a are the basic unknown V-macrofunctions (V means a representative volume element). In a general case, a refined averaged model is described by a system of four partial differential equations for the displacement and temperature macrofunctions U and , coupled with a system of 4 n partial differential equations for the displacement and temperature microcorrectors V a and | a . In this case, the microstructure length-scale effect on the macrobehavior ofthecompositeistaken into account. In the framework of an effective modulus model the dynamical problem of thermal stresses for a composite semispace, corresponding to thermal shock on the surface x =0, has been formulated and solved in a closed form by a Laplace transform technique proposed by Ignaczak and the author [3]. The solutions obtained for the total temperature and stress fields are analyzed numerically and graphically. A survey of papers devoted to modeling layered thermoelastic composites including various homogenization theories is presented, among others, by Wo niak and Wierzbicki [2].

Two-Step Approach of Stress Classification and Primary Structure Method

A key problem in engineering applications of “design by analysis” approach is how to decompose a total stress field obtained by the finite element analysis into different stress categories defined in the ASME Code III and VIII-2. In this paper, we suggest a two-step approach (TSA) of stress classification and a primary structure method (PSM) for identification of primary stress. Together with the equivalent linearization method (ELM), the stress classification problem is well solved. Some important concepts and ideas discussed by Lu and Li [Lu, M. W., and Li, J. G., 1986, ASME PVP-Vol. 109, pp. 33–37; Lu, M. W., and Li, J. G., 1996, ASME PVP-Vol. 340, pp. 357–363] are introduced. They are self-limiting stress, multi-possibility of stress decomposition, classification of constraints, and primary structures. For identification of peak stress, a modified statement of its characteristic and a “1/4 thickness criterion” are given. [S0094-9930(00)00201-8]

Methodology for service life increase of hot forging tools

Hot forging is widely used in the manufacturing of automotive components. The high production rate induces severe thermomechanical stresses in the tools. The lifetime of dies is commonly driven either by wear or thermal cracking. This paper describes the methodology that has been applied to gain understanding of the thermomechanical stress field in a cemented carbide punch used for the manufacture of airbag container type parts. The stresses are the result of a combination of purely mechanical stresses due to the forging process , and thermomechanical stresses induced by the thermal cycling of the punch surface during successive hot forging and waiting periods. Simulation results have been validated as a result of experimental investigations. The results show that in the critical area subjected to thermal cracking, the thermomechanical stress contribution is as high as 75% of the total stress field. As a consequence, it has been determined that an increased tool life could be expected by a global modification of the nominal hot-forging process parameters, i.e. by the modification of billet temperature and forging rate.

Micromechanical modeling of stress distribution in undulated composites under axial loading

The previously developed micromechanical model to predict the thermoelastic response of unidirectionally reinforced fibrous composites ( Nayfeh and Abdelrahman, 1997) is extended for the case of undulated fiber reinforcement under axial loading. For the present purposes, the composite is modeled as a concentric cylindrical system laterally constrained such that it satisfies the periodicity condition of the unidirectionally reinforced composites. The field equations, combined with the interface, boundary and symmetry conditions, are first solved for the stress distribution in the system for cases involving straight fibers. Based upon local directions (slopes) of the undulated fibers, the linear transformation is used to obtain local stress distributions along the undulated fibers. The total stress field is found to be combinations of these local stresses and the inherent contributions obtained from the transformations of the normal loads along the undulated directions in the absence of reinforcement. The results of this modeling are compared with finite element computations for a variety of situations.

A Maxwell Stress for Material Interactions

A Maxwell stress is identified to quantify the continuum average effect of molecules arising from two-particle central force interactions. The negative of the divergence of the Maxwell stress gives the body force due to such interactions. Such a stress was introduced previously but was interpreted as a surface traction to represent these effects (C. Argentoet al., J. Mech. Phys. Solids45, 1161 (1997)). The spatial scale of body force interactions among molecules is determined by the size of the bodies interacting and the size of the gaps between them, so that the Maxwell stress approach is necessary since forces of attraction cannot be guaranteed to isolate themselves to a vanishingly thin layer at the free surface. The Maxwell stress is directly useful in calculations of the total stress field within the body. A few examples for simple geometries are given.

A Layer-Wise Laminate Theory Rationally Deduced From the Three-Dimenstonal Elasticity

A layer-wise theory of laminated plates, which accounts for piecewise constant shear strain in the thickness, is derived from the three-dimensional elasticity theory by imposing suitable constraints on the strain and stress fields. At this aim, the functional of the three-dimensional elasticity is modified according to the Lagrange multipliers theory. In fact, a nonstandard application of the Lagrange theory is presented, because of the simultaneous presence of constraints on dual spaces. The imposed constraints make reactive strain and stress fields arise. Thus, it is necessary to distinguish between elastic and total strain and stress fields. The difference between them is emphasized in a numerical application.