Showing papers on "Hydrostatic stress published in 2021"

Stress sensitivity of porosity and permeability under varying hydrostatic stress conditions for different carbonate rock types of the geothermal Malm reservoir in Southern Germany

Abstract: In geothermal reservoir systems, changes in pore pressure due to production (depletion), injection or temperature changes result in a displacement of the effective stresses acting on the rock matrix of the aquifer. To compensate for these intrinsic stress changes, the rock matrix is subjected to poroelastic deformation through changes in rock and pore volume. This in turn may induce changes in the effective pore network and thus in the hydraulic properties of the aquifer. Therefore, for the conception of precise reservoir models and for long-term simulations, stress sensitivity of porosity and permeability is required for parametrization. Stress sensitivity was measured in hydrostatic compression tests on 14 samples of rock cores stemming from two boreholes of the Upper Jurassic Malm aquifer of the Bavarian Molasse Basin. To account for the heterogeneity of this carbonate sequence, typical rock and facies types representing the productive zones within the thermal reservoir were used. Prior to hydrostatic investigations, the hydraulic (effective porosity, permeability) and geomechanical (rock strength, dynamic, and static moduli) parameters as well as the microstructure (pore and pore throat size) of each rock sample were studied for thorough sample characterization. Subsequently, the samples were tested in a triaxial test setup with effective stresses of up to 28 MPa (hydrostatic) to simulate in-situ stress conditions for depths up to 2000 m. It was shown that stress sensitivity of the porosity was comparably low, resulting in a relative reduction of 0.7–2.1% at maximum effective stress. In contrast, relative permeability losses were observed in the range of 17.3–56.7% compared to the initial permeability at low effective stresses. Stress sensitivity coefficients for porosity and permeability were derived for characterization of each sample and the different rock types. For the stress sensitivity of porosity, a negative correlation with rock strength and a positive correlation with initial porosity was observed. The stress sensitivity of permeability is probably controlled by more complex processes than that of porosity, where the latter is mainly controlled by the compressibility of the pore space. It may depend more on the compaction of precedented flow paths and the geometry of pores and pore throats controlling the connectivity within the rock matrix. In general, limestone samples showed a higher stress sensitivity than dolomitic limestone or dolostones, because dolomitization of the rock matrix may lead to an increasing stiffness of the rock. Furthermore, the stress sensitivity is related to the history of burial diagenesis, during which changes in the pore network (dissolution, precipitation, and replacement of minerals and cements) as well as compaction and microcrack formation may occur. This study, in addition to improving the quality of input parameters for hydraulic–mechanical modeling, shows that hydraulic properties in flow zones largely characterized by less stiff, porous limestones can deteriorate significantly with increasing effective stress.

Hydrostaticity in high pressure experiments: some general observations and guidelines for high pressure experimenters

Abstract: The characteristics of hydrostatic stress conditions are discussed and compared with real experimental observations made under high pressure with a diamond-anvil cell. While fluid pressure-transmit...

Photothermal Excitation Process during Hyperbolic Two-Temperature Theory for Magneto-Thermo-Elastic Semiconducting Medium

Abstract: A novel technique is used to study the magnetic field influence in the free surface of an elastic semiconductor medium for a one-dimensional (1D) deformation. The problem is formulated during the hyperbolic two-temperature theory to study the coupled between the plasma, thermo-elastic waves. The investigation is conducted during a photothermal transport processes with the effects of both initial hydrostatic stress and some mechanical force. Using the Laplace transform method, the governing equations of the elastic waves, carrier density, quasi-static electric field, heat conduction equation, hyperbolic two temperature coefficient and constitutive relationships are obtained for the thermo-magnetic-electric medium. The mechanical stresses, thermal and plasma boundary conditions are applied on the interface adjacent to the vacuum to obtain the basic physical quantities in Laplace domain. The inversion of Laplace transform with numerical method is applied to obtain the complete solutions in time domain for the main physical fields under investigation. The effects of thermoelectric, thermoelastic and hyperbolic two temperature parameters of the applied force on the displacement component, carrier density, force stress and temperature distribution have been discussed graphically.

Machine Learning Based Methods for Obtaining Correlations between Microstructures and Thermal Stresses

Abstract: The microstructure–property relationship is critical for parts made using the emerging additive manufacturing process where highly localized cooling rates bestow spatially varying microstructures in the material. Typically, large temperature gradients during the build stage are known to result in significant thermally induced residual stresses in parts made using the process. Such stresses are influenced by the underlying local microstructures. Given the extensive range of variations in microstructures, it is useful to have an efficient method that can detect and quantify cause and effect. In this work, an efficient workflow within the machine learning (ML) framework for establishing microstructure–thermal stress correlations is presented. While synthetic microstructures and simulated properties were used for demonstration, the methodology may equally be applied to actual microstructures and associated measured properties. The dataset for ML consisted of images of synthetic microstructures along with thermal stress tensor fields simulated using a finite element (FE) model. The FE model considered various grain morphologies, crystallographic orientations, anisotropic elasticity and anisotropic thermal expansion. The overall workflow was divided into two parts. In the first part, image classification and clustering were performed for a sanity test of data. Accuracies of 97.33% and 99.83% were achieved using the ML based method of classification and clustering, respectively. In the second part of the work, convolution neural network model (CNN) was used to correlate the microstructures against various components and measures of stress. The target vectors of stresses consisted of individual components of stress tensor, principal stresses and hydrostatic stress. The model was able to show a consistent correlation between various morphologies and components of thermal stress. The overall predictions by the model for all the microstructures resulted into R2≈0.96 for all the stresses. Such a correlation may be used for finding a range of microstructures associated with lower amounts of thermally induced stresses. This would allow the choice of suitable process parameters that can ensure that the desired microstructures are obtained, provided the relationship between those parameters and microstructures are also known.

Damage propagation in short fiber thermoplastic composites analyzed through coupled 3D experiments and simulations

Abstract: Due to the complex nature of the heterogeneous microstructures of short fiber composites, computationally predicting their mechanical behavior, especially past the elastic regime and into the damage initiation and progression regimes, is very challenging. Matrix cracking has notably been difficult to predict because it can propagate in different manners, such as fiber mediated interfacial cracking and conoidal cracking, which have not been well understood. Therefore, this work couples in-situ X-ray micro tomography experiments with a finite element simulation of the exact microstructure to enable a sub-fiber 3D microstructural study by tracking damage propagation and computing the local stresses and strains in the microstructure. Here we show the role of shear stress in interfacial cracking (and how it differs from debonding), the role of hydrostatic stress in conoidal cracking, and the role of environmental damage in longitudinal fiber breakage. In doing so, this work gives insight into the stress states resulting in non-linear damage propagation in thermoplastic fiber composites.

Elastic waves in particulate glass-rubber mixtures

Abstract: We investigate the propagation of waves in dense static granular packings made of soft and stiff particles subjected to hydrostatic stress. Physical experiments in a triaxial cell equipped with bro...

On Unstable Isostatic Stratifications of Heavy Geomasses

Abstract: The conditions for the onset of instability of stratified heavy geomasses are analytically investigated in the work. The geomaterial forming a geomass is supposed to be elastic and to possess both bulk and shear stiffnesses. The unperturbed equilibrium state of the geomass is isostatic, i.e., characterized by hydrostatic stress field. The depth stratification of density and elastic properties of geomaterial is considered as continuous. The characteristics of stratifications of elastic and density parameters, that surely lead to the onset of instability, are obtained. The obtained sufficient conditions for instability are compared with obtained earlier by the authors the sufficient conditions for stability. Possible geophysical applications of the results are considered.

Investigation on the forming limit diagram of AA5754-O alloy by considering strain hardening model, strain path, and through-thickness normal stress

Abstract: This study clarified the effects of the chosen hardening model, through-thickness normal stress, and non-linear strain path on the precision of forming limit diagram (FLD). The Marciniak-Kuczynski (M-K) instability theory was employed to calculate the FLD of AA5754-O based on the different hardening models. Swift, Voce, modified Voce, Kim-Tuan, and modified Kim-Tuan hardening models were adopted to predict the forming limits, and their constant parameters were presented. Predicted FLDs indicate that modified Kim-Tuan has a better agreement with experimental data than other models. After that the influences of through-thickness normal stress on the forming limit diagram were examined. The three-dimensional stress state was converted to plane-stress condition according to the assumption that hydrostatic stress is ineffective on the plastic deformation. The results show that formability improves when normal stress increases. However, the effect of the normal stress on FLD for various hardening models is different. Due to the complexity of sheet metal forming, the strain path of the material may change during the deformation process. The results indicated that strain path has a significant effect on the FLD, and the path dependence of the forming limit stress diagram (FLSD) will be examined in detail. Finally, the forming limits were computed to analyze the effect of the normal stress on the non-linear loading path deformation. It was observed that by increasing the amount of pre-strain, the effect of the normal stress on the formability will diminish. Moreover, results showed that normal stress will affect the path dependence of the FLSD.

Numerical Study of Coupled Elasto-Plastic Hydrogen Diffusion at Crack Tip Using XFEM

Abstract: Hydrogen absorption can deteriorate the mechanical properties of the material at high temperature and high pressure. This deterioration phenomenon, termed as hydride-induced embrittlement, involves the simultaneous operation of diffusion of hydrogen, precipitation of hydride, mechanical deformation, and fracture in the material. In this work, hydride-induced embrittlement is modeled at the crack tip by coupling of the hydrogen diffusion and mechanical deformation in the extended finite element method (XFEM) framework. XFEM is the most suitable method to model the cracks in the coupled problems because it does not require conformal mesh and re-meshing for crack growth. The chemical potential required for hydrogen diffusion in the crack tip region depends on the hydrostatic stress gradients. The effect of hydride-induced embrittlement on the crack tip of edge crack specimen is performed in the present work. The formulation consists of two steps—first step is to determine the hydrostatic stress field from the mechanical deformation process which is used in second step to evaluate the hydrogen concentration, hydride fraction, and stress triaxiality. This is an iterative process applied at each time interval until the solution converges. The numerically obtained values of stress trace in the hydride precipitation zone are compared with the literature, and are found in good agreement.

Deformation of Rock Mass in the Vicinity of Underground Opening at Great Depth

Abstract: The article discusses natural stress field variation with depth. Rocks are assumed to be elastic. Increase in the stress level results in higher principal shear stresses but causes no failure. It is stated that failure is only possible at the increased lateral earth pressure coefficients, which induce hydrostatic stress redistribution at great depths. It is shown that Poisson’s ratio tends to 1/2 in isotropic rock mass.

A new analytical model to predict the formation of necking instabilities in porous plates subjected to dynamic biaxial loading

Abstract: In this paper, we have developed a linear stability analysis to predict the formation of necking instabilities in porous ductile plates subjected to dynamic biaxial stretching. The mechanical behavior of the material is described with the Gurson–Tvergaard–Needleman constitutive relation for progressively cavitating solids (Gurson 1977; Tvergaard 1981, 1982; Tvergaard and Needleman 1984) which considers the voids to be spherical and the matrix material isotropic with yielding defined by the von Mises (1928) criterion. The analytical model is formulated in a two-dimensional framework in which the multiaxial stress state that develops inside the necked region is approximated with the Bridgman (1952) correction factor, superimposing a hydrostatic stress state to the uniform stress field that develops in the plate before localization. As opposed to the linear stability models published so far to model dynamic necking in ductile plates, which consider the material to be fully dense and incompressible, the approach developed in this paper provides new insights into the interplay between porosity and inertia on plastic localization. In addition, the predictions of the theoretical model for the critical strain leading to necking formation have been compared with unit-cell finite element calculations performed in ABAQUS/Explicit (2019). Satisfactory quantitative and qualitative agreement has been found between the theoretical and the computational approach for loading paths ranging from plane strain tension to nearly equibiaxial tension, loading rates varying from 100 to $$10{,}000~\text {s}^{-1}$$ , and different values of the initial void volume fraction ranging from 0.01 to 0.1. Both analytical and finite element results suggest that the influence of porosity on necking localization increases, due to voids coalescence, as the loading rate increases and the loading path approaches equibiaxial tension. The original formulation developed in this paper serves as a basis for analytically modeling the dynamic formability of porous ductile plates, and it can be readily extended to consider more complex porous plasticity theories, e.g. constitutive models which consider the anisotropy of the material (Benzerga and Besson 2001) and/or voids with different shapes (Gologanu et al. 1993; Monchiet et al. 2008).

Assessment of Hydrostatic Stress and Thermo Piezoelectricity in a Laminated Multilayered Rotating Hollow Cylinder

Abstract: In this paper, we built a mathematical model to study the influence of the initial stress on the propagation of waves in a hollow infinite multilayered composite cylinder. The elastic cylinder assumed to be made of inner and outer thermo piezoelectric layer bonded together with Linear Elastic Material with Voids (LEMV) layer. The model described by the equations of elasticity, the effect of the initial stress and the framework of linearized, three-dimensional theory of thermo elasticity. The displacement components obtained by founding the analytical solutions of the motion’s equations. The frequency equations that include the interaction between the composite hollow cylinders are obtained by the perfect-slip boundary conditions using the Bessel function solutions. The numerical calculations carried out for the material PZT-5A and the computed non-dimensional frequency against various parameters are plotted as the dispersion curve by comparing LEMV with Carbon Fiber Reinforced Polymer (CFRP). From the graph, it is clear that those are analyzed in the presence of hydrostatic stress is compression and tension.

Hydrostatic Stress and Fatigue Crack Growth of Notched Ti6Al4V in Aggressive Media

Abstract: The behavior of structures, machine or components made of composite materials or light high-performance alloys is still a great concern for applications in which high strength-to-mas-ratio is a fundamental requirement. Procedures to detect flaws of small initial cracks and evaluate fatigue crack growth are nowadays essentials for high performance flying or ground machines (airplanes, automobiles,...). Structural reliability and structural health monitoring are considered in this paper and the surface replica method is deepened. Numerical FEM models were developed to assist the surface replica method analysis of the results.Ti6Al4V alloy was considered. This paper is a short technical communication

An Extended Ductile Fracture Prediction Model Considering Hydrostatic Stress and Maximum Shear Stress

Abstract: An uncoupled ductile fracture model, based on Mu–Zang model, is extended by incorporating a hydrostatic stress term. An aluminum alloy material (Al 6016-T6) is selected with a series of static ductile fracture tests performed on four different specimens, which can cover a wide range of stress states. A robust simulation-experiment approach is adopted to characterize the correlation between the material’s ductility and distinct stress states. The extended model is then calibrated using least-squares optimization. The resulting 3D fracture surface demonstrates acceptable deviations from the tested data, manifesting a promising capability of the extended model to describe the ductility of the considered material within a wide stress state range. In addition, the comparison against other representative ductile fracture models further confirms a good prediction performance of the model proposed.

Experimental Investigations on Microstructure, Properties and Workability Behavior of Zinc Oxide Reinforced Al–Si–Mg Matrix Composites

Abstract: Al-Si based alloy matrix composites are now broadly utilized by the industrial sectors like automobile, structural, aerospace and more practical industrial applications due to its noncompetitive economy range, good mechanical properties and less density. In order to widen its applications, it is very significant to improve its mechanical and workability behavior. So, in this work, an effort has been taken to develop a ZnO microparticles (3, 4.5 & 6 %) reinforced with Al-Si-Mg (AA6061) alloy by stir casting route.Scanning electron microscopy (SEM), energy dispersive spectroscopy (EDS) and X-ray diffraction analysis (X-RD) were employed for characterization studies of the composites. Tensile and hardness of the composites are investigated, compared and analyzed its effects. Another novel finding of the work is determining the workability behavior of the prepared samples with aspect ratio of 1 by incremental compressive loading of 25 kN through cold upsetting technique. For all developed samples, true axial stress (σz), hoop stress (σө), hydrostatic stress (σm), effective stress (σeff), formability stress index (β) and stress ratio parameters [(σz/σeff), (σө/σeff), (σm/σeff)] were determined and the results are correlated with the axial strain (ez). The results clearly infers that increasing weight contributions of ZnO particles increase the mechanical properties, all the stresses and stress ratio parameters of the composites.

Experimental and Numerical Study on Ductile Fracture Prediction of Aluminum Alloy 6016-T6 Sheets Using a Phenomenological Model

Abstract: A phenomenological ductile fracture model is proposed by a careful consideration of void nucleation, growth and coalescence during plastic deformation. Within the model framework, void nucleation is controlled by an equivalent plastic strain function. Void growth takes place through two ways, namely void dilation and void elongation, which are characterized by the normalized hydrostatic stress and normalized maximum shear stress, respectively. Void coalescence is characterized by the maximum shear stress. Aluminum alloy (AA) 6016-T6 sheets are selected to conduct ductile fracture (DF) experiments on specimens with different geometries, which can cover a wide range of stress states from simple shear to balanced biaxial tension. Subsequently, the new DF model is calibrated by using a robust hybrid numerical-experimental approach with a three-dimensional (3D) fracture surface constructed for AA 6016-T6. Ductile fracture data of other two aluminum alloys (AA 2024-T351 and AA 5083-O) are also used to evaluate DF model performance by establishing their 3D fracture surfaces. Finally, a cup drawing test is conducted and simulated as a case study showing how an applicable way of using the new model. Furthermore, the predictive accuracy of the proposed DF model for fracture initiation is compared with other three uncoupled models (modified Mohr–Coulomb criterion (MMC), Lou-Yoon-Huh model and Mu-Zang model) by ABAQUS/Explicit with a user subroutine (VUMAT), which shows a good performance of the proposed DF model.

An Elastic Solution for Twin Circular Tunnels’ Stress in Hydrostatic Stress Field

Abstract: In order to present an elastic solution for twin circular tunnels’ stress distribution in hydrostatic stress field, based on the complex variable theory and the superposition principle, the stress field of twin tunnels under static hydraulic pressure is decomposed into two parts: the original stress field and the secondary stress field. According to the symmetry of the structural form and the load distribution, the secondary stress filed can be simplifyed into a half-plane model. Therefore, the stress filed can be analyzed with the complex variable theory conveniently. Finally, the elastic solution of the twin tunnels under static hydraulic pressure is demonstrated by the superposition of the original stress field and the secondary stress field. In order to verify the analytical solution, a finite element model is adopted as the comparative test.. The result of the finite element simulation shows that the stress concentration at the middle rock wall is most obvious. And the stress concentration factor keeps increasing when the twin tunnels’ spacing distance and supporting pressure are decreasing. Besides, the maximum tangential stress appears at the tunnel boundary. The farther away from the tunnel’s boundary, the tangential stress gets lower. Furthermore, the supporting pressure leads to the increasing of radial stress and the decreasing of tangential stress. The analytical results are highly consistent with the numerical results with finite element method.

Numerical simulation of void growth in front of a blunting crack-tip in plastically compressible solids

Abstract: Effect of plastic compressibility on void growth ahead of a moving crack-tip is investigated numerically for a mode I crack subjected to plane strain deformation with small-scale yielding. Exploration is made for quasi-static finite deformations of isotropic hardening elastic–viscoplastic solids. For comparison purpose, both plastically incompressible and plastically compressible solids are considered to study the crack-tip deformation, void growth and interaction between the crack-tip and a nearby void by examining the near tip distributions of plastic strain, hydrostatic stress, effective stress and stress triaxiality. The plastic compressibility is found to have strong effect on the crack-tip deformation and stress–strain fields in the ligament and void region. The shape of void growth in front of the crack-tip is significantly influenced by the plastic compressibility. The present results show that in the case of plastically compressible solids, the rate of void growth in the direction perpendicular to the crack plane is more than the corresponding in the direction parallel to the crack and this observation is in sharp contrast to the void growth behavior observed in plastically incompressible solids. The predictions of the crack-tip and void interaction in the presence of plastic compressibility may be very helpful in understanding the crack growth and void coalescence in some relatively newer materials having very high energy absorption capacity, highly desired electrical and thermal as well as radiation-resistant properties, properties of bioimplants, etc.

Numerical simulation of hydrogen distribution around a crack tip in a high-Mn steel

Abstract: Hydrogen transport ahead of a crack tip is critical to understand the hydrogen-assisted cracking in steels. With this objective, a micromechanics-based model (Taylor relation) has been applied for finite element simulations of hydrogen transport in high-Mn steel. A sensitivity analysis regarding the influence of boundary condition, crack-tip radius, and initial hydrogen concentration on the hydrogen distribution is performed. The results indicate that stress-dependent boundary condition realistically presents the hydrogen transport, which is influenced by hydrostatic stress gradient and trap multiplication during plastic deformation. With strong plastic strain (small crack-tip radius) or deep traps (deformation twin), the total hydrogen peak moves towards the crack tip due to the dominant role of trapped hydrogen. However, the effect of trapped hydrogen will decrease with an increase of initial hydrogen concentration in the specimen. The simulations show useful implications for hydrogen embrittlement in high-Mn steels.

Stress–strain prediction of dual phase steels using 3D RVEs considering both interphase hardness variation and interface debonding at grain boundaries

Abstract: The numerical study on the complex failure mechanism in dual phase steels is significant because of their intricate microstructure. Their mechanical behavior depends on the volume fraction of martensite/ferrite and microstructural morphology, such as size, aspect ratio, interconnectivity, and mechanical behavior of individual phases. Like all multiphase materials, the connectivity between different phases and possible changes in mechanical properties near the interface (interphases) play significant roles in microstructural damage initiation and propagation and, therefore, affect the overall mechanical response. This study focused on the stress–strain behavior of DP-800 steel using finite element analysis of three-dimensional representative volume elements. Based on experimental results, local hardening was considered in the ferrite matrix near the martensite islands. Also, various volume fractions and material properties for different hardening zones were implemented to study the stress–strain behavior of DP steels. Interface elements based on cohesive zone modeling were considered to simulate the damage on the ferrite and martensite interface numerically. Furthermore, hydrostatic stress distribution which is known as an indicator to show the void initiation was used to predict damage zones and the stress distribution is compared with the results obtained from the cohesive zone method. The mechanical behaviors of the finite element models by the proposed methodology, considering cohesive elements and hardening zones in three-dimensional representative volume elements, indicated a better adaptation to the experimental results.