Dimensional Stress State Research Articles

Three dimensional stress and strain state of the offshore fill during the one-dimensional consolidation process

Evaluating the filling soil strain and stress behaviors during offshore reclamation and consolidation processes is crucial in forming a stable marine engineering foundation. While, the one-dimensional stress-strain testing technology cannot reflect the three-dimensional (3D) characteristics of the large site, which poses a potential disaster to the uneven settlement of the site. In this study, we construct a platform for 3D testing of strain and stress state during soil consolidation process on the basis of the novel 3D strain rosette and 3D earth stress sensor. Subsequently, the platform was used in a consolidation model test of the Dalian Offshore Airport filling soil, which consists of red clay and stone powder in a mass ratio of 1:4. The results indicate that self-weight consolidation mainly involves an increase in isotropic spherical strain, while load consolidation results in significant shear strain. During soil consolidation process, stress increases first and then dissipates, while vertical compression occurs due to the self-weight of the soil. The evolution law of the principal strain is direction-independent, whereas that of the principal stress remains comparatively stable when the principal stress increases steadily. This study provides a reference for the consolidation deformation and soil strength evaluation of soil fill.

An Elementary Derivation of the Maximum Shear Stress in a Three Dimensional State of Stress

An Elementary Derivation of the Maximum Shear Stress in a Three Dimensional State of Stress

Щодо розрахунку релаксації напружень в тонкостінних циліндричних оболонках із лінійно-в'язкопружних матеріалів

The problems of stress relaxation analysis in thin-walled cylindrical shells made of linear viscoelastic materials under uniaxial and biaxial loading have been solved. The analysis is based on a there-dimensional model of viscoelasticity starting from the hypothesis of the deviators proportionality. The viscoelastic properties of a material are given with relationships that establish the dependence between stress and strain intensities as well as between the mean stress and volumetric strain by the Bolzmann-Volterra type equation. The kernels of relaxation intensity and volumetric relaxation are given with the Rabotnov exponential-fractional functions. The parameters of relaxation kernels are determined from creep test result using the relationships between creep kernels under the complex stress state and creep kernels under the one- dimensional stress state. The problems of the analysis of normal and tangential stresses relaxation in thin-walled cylindrical shells made of high density polyethylene “ПЭВП” under uniaxial tension, pure torsion and combined tension with torsion loading have been solved and experimentally approved.

Analytical calculation method for the axial equivalent elastic modulus of laminated FRP pipes based on three dimensional stress state

In engineering design, the axial equivalent elastic modulus of laminated FRP pipe was mostly calculated by the average elastic modulus method or the classical laminated plate theory method, which are based on relatively simplified assumptions, and may be not accurate enough sometimes. A new analytical calculation method for the axial equivalent elastic modulus of laminated FRP pipe was established based on three-dimensional stress state. By comparing the results calculated by this method with those by the above two traditional analytical methods and the finite element method, it is found that this method for the axial equivalent elastic modulus fits well not only for thin-walled pipes with orthotropic layers, but also for thick-walled pipes with arbitrary layers. Besides, the influence of the layer stacking on the axial equivalent elastic modulus was studied with this method. It is found that a proper content of circumferential layer is beneficial for improving the axial equivalent elastic modulus of the laminated FRP pipe with oblique layers, and then can reduce its material quantity under the premise that its axial stiffness remains unchanged. Finally, the meso-mechanical mechanism of this effect was analyzed. The improving effect of circumferential layer on the axial equivalent elastic modulus of the laminated FRP pipe with oblique layers is mainly because that, the circumferential fibers can restrain the rigid body rotations of the oblique fibers, which tend to cause the significant deformations of the pipe wall units and the relatively low axial equivalent elastic modulus of the pipe.

Study of residual stress and microstructural evolution in as-deposited and inter-pass rolled wire plus arc additively manufactured Inconel 718 alloy after ageing treatment

The manufacture of structural components made from nickel-based super alloys would benefit from the commercial advantages of Wire + Arc Additive Manufacturing (WAAM), as it is commonly expensive to process using other conventional techniques. The two major challenges of WAAM are process residual stress and undesired microstructure. Residual stress causes part distortion and build failures, while the as-deposited microstructure does not allow the common heat-treatment to be effective in achieving the desired mechanical properties. This paper focuses on understanding the microstructural features, phase formation and three-dimensional residual stress state variation in as-deposited and inter-pass rolled conditions and after solutionising, quenching and ageing. The thermal history from successive deposition and cold working were correlated to the phase formation and macro residual stress formation and subsequent evolution. The {311} family of crystallographic planes were used as atomic strain gauge to determine the macrostrain and analysis of three dimensional stress state in different processing conditions. The measured strain were corrected for the compositional variation by measuring EDM machined d0 specimens manufactured under similar processing conditions. While the as-deposited part show significant stress redistribution and distortion after removal from the main fixture, inter-pass rolling was found to reduce part distortion significantly, the residual stress profile after inter-pass rolling showed highest tensile magnitude near the substrate while near the top of the deposit it was compressive as can be expected from the rolling process. The other two beneficial effects of inter-pass rolling on the microstructure are mitigation of the formation of undesired Laves-phase, thereby improving the response to solution treatment and aging together with significantly reduced grain size and texture. The application of inter-pass rolling reduces the potential part complexity, which however does not prevent the manufacture of common candidate parts, which are typically 1-to-1 replacements of forged, cast or machined from solid.

Resilient behavior of coarse granular materials in three dimensional anisotropic stress state

The coarse granular materials in the pavement base and subbase layers are generally in the stress state of three dimensional anisotropy, while most previous experimental researches regarding the base and subbase materials focused on the isotropic or axisymmetric K0 stress conditions. In this study, the resilient characteristics of unbound granular materials in initial three dimensional anisotropic stress states were investigated through an electro-mechanical true triaxial apparatus. The influences of initial shear stress, qini, coefficient of intermediate principal stress, b, amplitude of cyclic major principal stress, σ1ampl, and moisture content on the resilient responses of granular materials were investigated. Test results reveal that the resilient response of unbound granular materials is strongly affected by the three dimensional stress anisotropy in the saturated condition. With the increase of b from 0 to 0.8, a significant reduction of Mr occurs, and this reduction becomes intensified as qini increases. It is also found that Mr is increased by the increase of qini for almost all tests, and the increasing rate varies at different σ1ampl, b and moisture content values. Based on the experimental results, an empirical model to predict resilient modulus is proposed incorporating the effects of initial three dimensional stress anisotropy, which is expected to serve as a basic model to calculate the resilient modulus of granular materials in three dimensional stress state.

Evaluation of the creep crack growth behavior in 9Cr–1Mo steel under different stress conditions

Creep crack growth (CCG) behaviors of 9Cr–1Mo heat resistant steel under different stress states, such as the different initial crack lengths, two/three dimensional stress states, different side groove depths and angles are investigated by the numerical method. The results show that decreasing the initial crack length can increase the specimen life. Affected by the higher stress tri-axiality in the specimen, the side groove specimen life is greater than that the plain CT specimen. Crack front straightness extent increases with the increasing of value of d/B0 or magnitude of the α. The side groove depth of d/B0 = 0.1 and side groove angle of α = 80° meet the crack front straightness requirement, and it can be used to predict the CCG rate of the 9Cr–1Mo steel. The CCG rate of the plane strain specimen is greater than that the plane stress specimen for both the same loading condition of initial stress intensity factor and reference stress. On the whole, all the CCG rate data are dropped into the 95% prediction band of fitting curve, demonstrating that the CCG rate of 9Cr–1Mo heat resistant steel can be reasonably calculated by C*.

Triaxial behavior of granular material under complex loading path by a new numerical true triaxial engine

A new numerical true triaxial engine based on discrete element method accounting for rolling resistance contact is developed. By this engine, we have simulated mechanical behavior of granular materials under complex stress loading path in this study. Stress-strain responses of a kind of typical granular sand under several stress loading path in meridian and deviatoric stress space are provided. The results show that the three dimensional effects like the intermediate principal stress play an important role in the modeling processes. Theoretical analysis in strength characteristic implies the strength criteria with three parameters such as unified strength criterion and van Eekelen strength criterion are capable of describing cohesionless granular material behaviors in three dimensional stress states. Moreover, the case study for Chende sand further demonstrates the numerical true triaxial engine, is a potential tool. As compared to conventional triaxial compression test, this new developed apparatus could be widely used to “measure” elastic-plastic behavior in three dimensional stress space for finite element analysis in geotechnical problems.

Three-dimensional stress analysis in torsion of laminated composite bar with general layer stacking

Abstract A general laminated composite bar with rectangular cross-section which is subjected to torsional torque is studied and the three dimensional stress state, specially the out of plane stresses is investigated. A reduced displacement field is obtained for the long laminated bar in which the global and local deformation response of the laminate are separated. This reduced displacement field is obtained from integration of the strain components. In order to obtain the three dimensional stress state and free edge effect, the displacement based layer-wise method is employed for formulation of the problem and the governing equations are solved analytically. The numerical results are compared with the predictions of multi-term extended Kantorovich method and mixed-field multi-term extended Kantorovich method which is available in the open literature and with an analytical series solution, and very good agreements are achieved. The twisting, extension, and bending of laminate due to torsion torque, and the out of plane and in-plane stresses are studied for various layers stacking. In order to increase the accuracy, the out of plane stresses are obtained by integrating the equilibrium equations.

Normalization of fatigue characteristics for asphalt mixtures under different stress states

The fatigue test methods under different test conditions have strong impact on the test results, which obstructs a precise evaluation of fatigue characteristic for asphalt mixtures. Different test conditions means different stress states. Fatigue characteristic of a material is an objective attribute, and it should not vary with test methods and conditions. In order to accurately and objectively evaluate the fatigue properties of asphalt mixtures, a normalization model of fatigue characteristics for asphalt mixtures under different stress states was established based on the yield criterion in 3 dimensional stress states and the patterns of variation between the strength and the loading rate. The compressive, tensile and indirect tensile strength and fatigue tests were carried out respectively in different loading rates. The yield surface of strength for asphalt mixture was put forward based on the strength tests results and the yield criterion. Then, the normalization model of fatigue characteristics for asphalt mixtures under different stress states was established based on the yield criterion in 3 dimensional stress states. The results show that the differences of the fatigue tests results of asphalt mixtures under different test condition are large. It is difficult to evaluate the fatigue performance in different stress states of asphalt mixtures by using the conventional S-N fatigue equation. However, these differences can be reduced or even eliminated by using the normalization model, which considered the influence of the stress state and the strength corresponding to the fatigue loading frequency and stress level. The unified expression of fatigue characteristics under different test conditions for asphalt mixtures was realized. The fatigue behavior of asphalt mixture under different stress conditions can be objectively evaluated by using the normalized model.

Failure criterion of an asphalt mixture under three-dimensional stress state

A self-developed triaxial test method was adopted to characterize mechanical behavior of the asphalt mixture under three-dimensional stress states in this study. The conventional uniaxial tests and triaxial tests were conducted in the laboratory to verify the triaxial test results obtained using the technique developed. It is shown that the three dimensional stress states affect significantly the ultimate failure strength of AC-13 asphalt mixture and the failure modes are mainly represented both for the tensile failure and shear failure. The nonlinear strength criterions, as well as a linear engineering model of asphalt mixture under three-dimensional stress states in σoct-τoct space, were established based on the triaxial compressive/tensile tests, the plane tensile and compressive/axial tensile tests. In addition, a new method to carry out the strength design of asphalt pavement under the three-dimensional stress state was given to consider the failure effect of each stress component to the asphalt pavements.

02.04: Experimental and numerical analyses of butt‐welded S460 joints

ABSTRACTFor the development of reliable calculation approaches regarding the load bearing capacity of welded steel components, knowledge about stress‐strain relations in the weld and the heat affected zone is required. A three dimensional stress state, particularly in case of highly divergent material properties in the spatially concentrated areas of welded connections, mainly influences the response of the structure. This paper presents the experimental and numerical study of single‐pass butt‐welded joints under tensile loading. Furthermore, it depicts the determination of material properties in the weld and heat affected zone by means of miniature tensile tests. Miniature specimens are taken from the base material, the weld and the heat affected zone of connections with matching base and filler material by water jet technology. The varying material ductility, yield stress and ultimate strength, are illustrated experimentally depending on the origin of the miniature specimen (weld, heat affected zone, base material) and using a modified single‐pass butt‐welded joint under tensile load. The stress‐strain‐curves obtained by means of miniature tensile tests are used for the numerical simulation of a welded connection under tensile loading. The comparison of numerical results of welded connections with local strain measurements shows good agreement.

A fracture angle based three‐dimensional damage model for unidirectional fibre‐reinforced plastics

AbstractSince the failure analysis of fibre‐reinforced plastics is not limited to the first‐ply failure, it is mandatory to use adequate damage models to simulate the failure process. The paper describes a damage model for three‐dimensional stress states, which uses the crack orientation of the inter‐fibre fracture (IFF). The fracture angle describes the crack orientation and can be obtained by using Puck's IFF criterion. The fracture angle enables the possibility to take the causal stress situation for the IFF into account. This means that each Young's or shear modulus has its own damage function, which depends on the stress state and the fracture angle. Therefore, the stress‐strain extrapolation method of Schürmann and Weber for two dimensional stress states was advanced and modified for the three‐dimensional stress space. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

3D Finite Element Model as a Tool for Analyzing the Structural Behavior of a Railway Track

The rising public and commercial demands on railway network increases the need to improve systems that comprise the railway network. Especially in case of mixed corridors, the demands for track smoothness and load carrying capacity increase simultaneously. From this perspective, the optimization of track design creates efficiency and reduction of life-cycle costs. Hence, there is a great need for a tool which enables designing the load-carrying capacity of a railway track structure as a whole and simultaneously evaluates the stress and/or strain levels of each track component such that the life cycle of the track structure is optimized. The main focus of this study was to create a three dimensional structural model in which the stress-strain behavior of different railway track components could be evaluated realistically. The created model is based on finite element method using PLAXIS 3D software which is specialized in geotechnical problems. Differing from most of the traditional methods, which are based on a theory of linear elasticity, Finite Element Method-based approach with the chosen tool provides a non-linear solution and a three dimensional stress state. As features, the created structural model enables variation in structural layer thickness, rail size, sleeper type (wood/concrete) and material properties of rail pad, ballast, subballast layers and subgrade.

Distribution of stress state in the Nankai subduction zone, southwest Japan and a comparison with Japan Trench

To better understand the distribution of three dimensional stress states in the Nankai subduction zone, southwest Japan, we review various stress-related investigations carried out in the first and second stage expeditions of the Nankai Trough Seismogenic Zone Experiment (NanTroSEIZE) by the Integrated Ocean Drilling Program (IODP) and compile the stress data. Overall, the maximum principal stress σ1 in the shallower levels (<~1km) is vertical from near the center of forearc basin to near the trench and; the maximum horizontal stress SHmax (interpreted to be the intermediate principal stress σ2) is generally parallel to the plate convergence vector. The exception to this generalization occurs along the shelf edge of the Nankai margin where SHmax is along strike rather than parallel to the plate convergence vector. Reorientation of the principal stresses at deeper levels (e.g., >~1km below seafloor or in underlying accretionary prism) with σ1 becoming horizontal is also suggested at all deeper drilling sites. We also make a comparison of the stress state in the hanging wall of the frontal plate-interface between Site C0006 in the Nankai and Site C0019 in the Japan Trench subduction zone drilled after the 2011 Mw 9.0 Tohoku-Oki earthquake. In the Japan Trench, a comparison between stress state before and after the 2011 mega-earthquake shows that the stress changed from compression before the earthquake to extension after the earthquake. As a result of the comparison between the Nankai Trough and Japan Trench, a similar current stress state with trench parallel extension was recognized at both C0006 and C0019 sites. Hypothetically, this may indicate that in Nankai Trough it is still in an early stage of the interseismic cycle of a great earthquake which occurs on the décollement and propagates to the toe (around site C0006).

Locally resolved stress and strain analysis of sinter-joined micro valves using synchrotron X-ray diffraction and conical slit apertures

For assessing the quality of the joining area as well as researching the influence of joining parameters in combination with different materials, the principal stress components of sinter-joined micro valves were analysed. Transmission experiments have been conducted at the high-energy material science (HEMS) beamline P07 at PETRA III, DESY. Due to the dimensions of the samples, a high spatial resolution of the measurements was required. Of special interest was the distribution of residual stress in the joining area of the valves, which demanded a depth resolved measurement using a conical slit. Strains were deduced from the obtained Debye---Scherrer rings of the {200}, {211}, and {220}-planes of the ?/??-phase involving reference measurements on non-sintered powder of the specimen materials. The grain statistics have been improved by integrating over slices of the diffraction rings and by calculating a mean lattice parameter taking into account all lattice planes. From the strain data, the hydrostatic and the deviatoric stress were calculated for the three dimensional stress state.

Experimental Research on Flexural Behavior of Precast Thin-Wall Steel and Spun Concrete Composite Pile

The flexural load-bearing performance prototype test has been made on the precast thin-wall steel and spun concrete composite pile with a diameter of 1000 mm (TSC pile). The load deflection curve and pile deflection curve at each loading step have been obtained. The bending test results show that the deformation of large diameter TSC pile experienced elastic, elastic-plastic and plastic three phases under the load of bending moment, the damage of pile was caused by the tension stress of steel in tension zone exceeded the yield strength, which belongs to the ductile damage. As for the TSC pile ultimate flexural bearing capacity, the measured value agreed with the theoretical calculation value, which shows that the existing thin-wall centrifugal concrete filled steel tube structure ultimate flexural bearing capacity calculation theory and method is suitable for large diameter TSC pile. Preface Precast Thin-wall Steel and spun Concrete composite Pile (TSC pile) is in the use of type Q235B or Q345B plate (strip) pouring of concrete filled steel tube made of crimping forming and welding, the centrifugal casting[1]. The compressive strength of concrete is not less than 80MPa, with a new pile products bear large vertical load and horizontal load. Concrete pile has the characteristics of high compressive strength, flexural capacity is weak; While the flexural capacity of steel pipe pile is strong, has good plasticity, But easy buckling occurs when the axial compression, loss of compression capability. TSC pile is a steel - concrete composite structure between steel pile and centrifugal concrete pipe pile, not only can give full play to the advantages of the both, can also overcome the shortcomings of its own when used alone[2]: With the inner wall of the concrete pipe, the outer pipe can enhance its stability ;and the inner concrete pipe with steel " confining effect", by the uniaxial stress state into three dimensional stress state, which greatly improves the compressive strength, With high anti-hammering capability, high penetration, pile sinking speed, good durability, pile quality, materials and low cost[3]. The TSC pile has been successfully applied to industry, electric power, transportation and other areas, commonly used in port engineering pile type of larger diameter, and by the wind, wave and other horizontal load, to put forward higher requirements of flexural performance of pile body. Therefore it is necessary to study the flexural behavior of large diameter pile TSC. Model test is usually the most useful method to study the pile loading behavior[4, 5].In this paper, the diameter 1000mm of TSC pile bending prototype test has been conducted, and the test is a research on the large diameter pile in TSC subjected to pure bending bearing capacity. Experimental Study of Pure Bending of TSC Pile

Statistics of ductile fracture surfaces: the effect of material parameters

The effect of material parameters on the statistics of fracture surfaces is analyzed under small scale yielding conditions. Three dimensional calculations of ductile crack growth under mode I plane strain, small scale yielding conditions are carried out using an elastic-viscoplastic constitutive relation for a progressively cavitating plastic solid with two populations of void nucleating second phase particles represented. Large particles that result in void nucleation at an early stage are modeled discretely while small particles that require large strains to nucleate are homogeneously distributed. The three dimensional analysis permits modeling of a three dimensional material microstructure and of the resulting three dimensional stress and deformation states that develop in the fracture process region. Material parameters characterizing void nucleation are varied and the statistics of the resulting fracture surfaces is investigated. All the fracture surfaces are found to be self-affine over a size range of about two orders of magnitude with a very similar roughness exponent of $$0.56\,\pm \,0.03$$ . In contrast, the full statistics of the fracture surfaces is found to be more sensitive to the material microscopic fracture properties: height fluctuations are shown to crossover from a Student’s distribution with power law tails at small scales to a Gaussian behavior at large scales, but this transition occurs at a material dependent length scale. Using the family of Student’s distributions, this transition can be described introducing an additional exponent $$\mu = 0.15\,\pm \,0.02$$ , the value of which compares well with recent experimental findings. The description of the roughness distribution used here gives a more complete quantitative characterization of the fracture surface morphology which allows a better comparison with experimental data and an easier interpretation of the roughness properties in terms of microscopic failure mechanisms.

Modeling combined extrusion process to assess the limit of forming blanks from different materials

This article considers a method of modeling combined extrusion process based on the hypothesis of force and kinematic similarity of deformation parameters. It also shows the expediency calculation of plasticity resource in the combined extrusion through failure criterion that takes into account the influence of the third invariant of the stress tensor on the plasticity of blanks deformed under three dimensional stress state.

Prediction of Ductile Fracture Surface Roughness Scaling

Experimental observations have shown that the roughness of fracture surfaces exhibit certain characteristic scaling properties. Here, calculations are carried out to explore the extent to which a ductile damage/fracture constitutive relation can be used to model fracture surface roughness scaling. Ductile crack growth in a thin strip under mode I, overall plane strain, small scale yielding conditions is analyzed. Although overall plane strain loading conditions are prescribed, full 3D analyses are carried out to permit modeling of the three dimensional material microstructure and of the resulting three dimensional stress and deformation states that develop in the fracture process region. An elastic-viscoplastic constitutive relation for a progressively cavitating plastic solid is used to model the material. Two populations of second phase particles are represented: large inclusions with low strength, which result in large voids near the crack tip at an early stage, and small second phase particles, which require large strains before cavities nucleate. The larger inclusions are represented discretely and various three dimensional distributions of the larger particles are considered. The scaling properties of the predicted thickness average fracture surfaces are calculated and the results are discussed in light of experimental observations.