Showing papers on "Hydrostatic stress published in 2013"

On stress-dependent elastic moduli and wave speeds

Abstract: On the basis of the general non-linear theory of a hyperelastic material with initial stress, initially without consideration of the origin of the initial stress, we determine explicit expressions for the stress-dependent tensor of incremental elastic moduli. In considering three special cases of initial stress within the general framework, namely hydrostatic stress, uniaxial stress and planar shear stress, we then elucidate in general form the dependence of various elastic moduli on the initial stress. In each case, the effect of initial stress on the wave speed of homogeneous plane waves is studied and it is shown how various special theories from the earlier literature fit within the general framework. We then consider the situation in which the initial stress is a pre-stress associated with a finite deformation and, in particular, we discuss the specialization to the second-order theory of elasticity and highlight connections between several classical approaches to the topic, again with special reference to the influence of higher-order terms on the speed of homogeneous plane waves. Some discrepancies arising in the earlier literature are noted.

Cavitation in materials with distributed weak zones: Implications on the origin of brittle fracture in metallic glasses

Abstract: Several experimental studies have shown that fracture surfaces in brittle metallic glasses (MGs) generally exhibit nanoscale corrugations which may be attributed to the nucleation and coalescence of nanovoids during crack propagation. Recent atomistic simulations suggest that this phenomenon is due to large spatial fluctuations in material properties in a brittle MG, which leads to void nucleation in regions of low atomic density and then catastrophic fracture through void coalescence. To explain this behavior, we propose a model of a heterogeneous solid containing a distribution of weak zones to represent a brittle MG. Plane strain continuum finite element analysis of cavitation in such an elastic-plastic solid is performed with the weak zones idealized as periodically distributed regions having lower yield strength than the background material. It is found that the presence of weak zones can significantly reduce the critical hydrostatic stress for the onset of cavitation which is controlled uniquely by the local yield properties of these zones. Also, the presence of weak zones diminishes the sensitivity of the cavitation stress to the volume fraction of a preexisting void. These results provide plausible explanations for the observations reported in recent atomistic simulations of brittle MGs. An analytical solution for a composite, incompressible elastic-plastic solid with a weak inner core is used to investigate the effect of volume fraction and yield strength of the core on the nature of cavitation bifurcation. It is shown that snap-cavitation may occur, giving rise to sudden formation of voids with finite size, which does not happen in a homogeneous plastic solid.

Stress relaxation through interdiffusion in amorphous lithium alloy electrodes

Abstract: At high guest (lithium) atom concentrations, the diffusion of host (e.g., silicon) atoms may become significant in amorphous Li-alloy-based solid electrodes. The effect of this diffusion mechanism on stress development is in addition to guest atom diffusion, stress-induced enhancement of guest atom diffusion and plasticity. The effect of the diffusive migration of host atoms in amorphous Li-alloy-based electrodes is investigated using a continuum model. A mixed-form finite element framework is developed to simulate the full coupling between stress development and interdiffusion. This framework overcomes the challenges associated with the numerical evaluation of the hydrostatic stress gradient. The analysis focuses on the relative importance of the mechanical driving force and chemical driving force for host migration. Calculations show that host migration can cause stress reductions of up to ∼20% in Li–Si electrodes at stress levels below the yield threshold of the material. Analyses also show that the long-term steady state of stress distribution is independent of the host diffusivity and the thermodynamic factor of diffusion which quantifies the tendency of the two species of atoms to chemically mix, even though the transient behavior (in particular, the peak stresses during charging being important quantities) does depend on the thermodynamic factor and the host diffusivity. The diffusion of Si (host) introduces a time scale which, along with the time scale for Li (guest) diffusion, controls the diffusional response of electrodes.

Characterization and modelling of the 3D elastic-plastic behaviour of an adhesively bonded joint under monotonic tension/compression-shear loads: influence of three cure cycles

Abstract: Characterization and modelling of the 3D elastic-plastic behaviour of ductile adhesive materials are all but straightforward. Advanced models and significant experimental work are required in order to achieve good accuracy over a wide range of different loading conditions combining tension or compression with shear. Indeed, advanced constitutive laws taking into account hydrostatic stress dependency and non-associated formalism have to be defined. As a consequence, the experimental characterization of an adhesive within a bonded assembly has to include different load combinations. In this study, a modified Arcan specimen is used to obtain a large experimental data base covering tension, tension-shear, shear and compression-shear results for a bi-component epoxy-based adhesive (Huntsman™ Araldite 420 A/B). Three different bonding conditions are considered; the curing temperature (50 or 110 °C) and aged time at the test (within a week or after a 6 months storage at room temperature) being the two parameters investigated. A simplified inverse identification method based on these results is proposed for the identification of a 3D elastic-plastic model proposed by Mahnken and Schlimmer. In particular, the number of identification steps involving coupled finite element analysis and optimization software is considerably reduced. The comparison between the predicted and experimental results demonstrates the good capabilities of the model and underlines its limitations considering the flow rule definition in a specific case. Results show that both the curing temperature and the aged time have a substantial influence on the yield surface and final strength of the adhesive whereas the hardening curve seems less affected. Some possible improvements in the modelling of the adhesive under monotonic proportional loads are proposed as a conclusion.

Effect of hydrostatic initial stress on a fiber-reinforced thermoelastic medium with fractional derivative heat transfer

Abstract: Purpose – The purpose of this paper is to investigate the influences of fractional order, hydrostatic initial stress and gravity field on the plane waves in a linearly fiber-reinforced isotropic thermoelastic medium. Design/methodology/approach – The problem has been solved analytically and numerically by using the normal mode analysis. Findings – Numerical results for the temperature, the displacement components and the stress components are presented graphically and analyzed the results. The graphical results indicate that the effect of fractional order, hydrostatic initial stress and gravity field on the plane waves in the fiber-reinforced thermoelastic medium are very pronounced. Comparisons are made with the results in the absence and presence of hydrostatic initial stress and gravity field. Originality/value – In the present work, the authors shall formulate a fiber-reinforced two-dimensional problem under the effect of fractional order, hydrostatic initial stress, and gravity field. The normal mode...

Pressure-sensitive plasticity of lithiated silicon in Li-ion batteries

Abstract: Lithiation-induced plasticity is a key factor that enables Si electrodes to maintain long cycle life in Li-ion batteries. We study the plasticity of various lithiated silicon phases based on first-principles calculations and identify the linear dependence of the equivalent yield stress on the hydrostatic pressure. Such dependence may cause the compression-tension asymmetry in an amorphous Si thin film electrode from a lithiation to delithiation cycle, and leads to subsequent ratcheting of the electrode after cyclic lithiation. We propose a yield criterion of amorphous lithiated silicon that includes the effects of the hydrostatic stress and the lithiation reaction. We further examine the microscopic mechanism of deformation in lithiated silicon under mechanical load, which is attributed to the flow-defects mediated local bond switching and cavitation. Hydrostatic compression confines the flow defects thus effectively strengthens the amorphous structure, and vice versa.

Investigation of shear damage considering the evolution of anisotropy

Abstract: The damage that occurs in shear deformations in view of anisotropy evolution is investigated. It is widely believed in the mechanics research community that damage (or porosity) does not evolve (increase) in shear deformations since the hydrostatic stress in shear is zero. This paper proves that the above statement can be false in large deformations of simple shear. The simulation using the proposed anisotropic ductile fracture model (macro-scale) in this study indicates that hydrostatic stress becomes nonzero and (thus) porosity evolves (increases or decreases) in the simple shear deformation of anisotropic (orthotropic) materials. The simple shear simulation using a crystal plasticity based damage model (meso-scale) shows the same physics as manifested in the above macro-scale model that porosity evolves due to the grain-to-grain interaction, i.e., due to the evolution of anisotropy. Through a series of simple shear simulations, this study investigates the effect of the evolution of anisotropy, i.e., the rotation of the orthotropic axes onto the damage (porosity) evolution. The effect of the evolutions of void orientation and void shape onto the damage (porosity) evolution is investigated as well. It is found out that the interaction among porosity, the matrix anisotropy and void orientation/shape plays a crucial role in the ductile damage of porous materials.

Modeling the behavior of sandstone based on generalized plasticity concept

Abstract: SUMMARY With the concept of generalized plasticity, a constitutive model for describing the deformation behavior of sandstone is proposed in this paper. This proposed model is characterized by the following features: (i) nonlinear elasticity under hydrostatic and shear loading; (ii) associated flow rule for pre-peak simulation; (iii) substantial plastic deformation during shear loading; and (iv) significant shear dilation and distortion prior to the failure state. This model requires 10 material parameters, including three for elasticity and seven for plasticity. All of the parameters can be determined, in a straightforward manner, by the suggested procedures. The proposed model has been validated by comparing the triaxial test results of the Mushan sandstone under different hydrostatic stress, different stress paths, and cyclic loading condition. It is also versatile in simulating the deformation behaviors of two other sandstones. Upon slight modification of the model, the post-peak behavior of sandstone can be reasonably predicted using proposed model. Copyright © 2012 John Wiley & Sons, Ltd.

Stress-Dependent Flow, Mechanical, and Acoustic Properties for an Unconventional Oil Reservoir Rock

Abstract: Summary Accurate estimation of rock properties has significant impact on reservoir simulation, geophysical interpretation, hydraulic fracture design, and geomechanical analysis. B ecause reservoirs are buried at depth, measurement of these properties should consider a s tress environment that is as close to in-situ as possible. Stress-dependence of permeability, pore volume compressibility, elastic moduli, and acoustic anisotropy has been widely studied in conventional reservoirs. H owever, due to challenges in sample preparation and laboratory setup, most measurements of unconventional rock are still limited to hydrostatic stress conditions. This paper investigates a nano-Darcy unconventional oil reservoir rock under triaxial stress conditions. Rock permeability and pore volume compressibility, strength and Young’s modulus, acoustic velocities, six stiffness coefficients, and Thomsen anisotropy parameters are measured under different levels of loading and confining stresses. The relationship of these properties to the differential stress between loading and confining stresses is identified and compared with conventional hydrostatic tests. The differential stress level reaches as high as 20,000 psi for rock mechanics tests and 10,000 psi for flow tests. S teady pressure and pulse decay methods have been applied to measure permeability with gas or oil fluid flows. Despite high rock strength (greater than 10,000 psi), the rock permeability and acoustic anisotropy strongly depend on the differential stress level. Following a typical slow permeability reduction with increasing stress, a distinguished stage of accelerated permeability reduction is observed when the differential stress exceeds 3,160 psi. Interestingly the initial pore volume compressibility of the strong rock is measured as high as 50×1/Mpsi. After slight decreases until the differential stress reaches a certain level, the compressibility reverses the trend and increases significantly. Both rock strength and Young’s modulus vary greatly with the angles to bedding planes. The stress-strain curves under different confining stresses challenge the traditional modulus-based brittleness. Thomsen anisotropy parameters reduce as much as 80% with the differential stress after observing an initial increase of anisotropy when the stress is low. Among the six stiffness coefficients, the two shear components along vertical and horizontal directions (C12 and C13) vary much more than the others. T his highlights the necessity of applying differential stress, rather than hydrostatic stress, in the laboratory. It also indicates that the studied nano-Darcy rock may be much more compressible and stress-dependent than its strength suggests.

X-ray micro-beam diffraction determination of full stress tensors in Cu TSVs

Abstract: We report the first non-destructive, depth resolved determination of the full stress tensor in Cu through-silicon vias (TSVs), using synchrotron based micro-beam X-ray diffraction. Two adjacent Cu TSVs were studied; one deliberately capped with SiO2, the other without (uncapped). Both Cu TSVs were found to be in a state of tensile hydrostatic stress that fluctuated considerably with depth. The average hydrostatic stress across the capped and the uncapped Cu TSVs was found to be (99 MPa ± 13 MPa) and (118 MPa ± 18 MPa), respectively. This apparent disparity between the mean hydrostatic stresses is attributed to local differences in their microstructure, and not to the differences in capping.

Prediction of void closure in steel slabs by finite element analysis

Abstract: Closure of a spherical voids in a steel slab under plane-strain deformation was investigated using the rigidplastic finite-element method. Variations in the major and minor axes of a void from finite element analysis of a void model were related to the minimum principal strain and hydrostatic stress from finite element analysis of a non-void model. The correlation curves were obtained and a method using these curves to predict the void closure progress was proposed. The method was successfully applied to deformation processes such as simple compression, forging and rolling. Since hydrostatic stress also influenced void closure, the effective strain by itself was not sufficiently capable of predicting void closure. However, the effective strain was used to predict void closure for a specific process because it reached about 0.7 in compression or forging and about 0.78 during rolling as the void completely closed.

Study of Ground Response Curve (GRC) Based on a Damage Model / Badanie Krzywej Odpowiedzi Gruntu (Grc) W Oparciu O Model Pękania Skał

Abstract: Analysis of stresses and displacements around underground openings is necessary in a wide variety of civil, petroleum and mining engineering problems. In addition, an excavation damaged zone (EDZ) is generally formed around underground openings as a result of high stress magnitudes even in the absence of blasting effects. The rock materials surrounding the underground excavations typically demonstrate nonlinear and irreversible mechanical response in particular under high in situ stress states. The dominant cause of irreversible deformations in brittle rocks is damage process. One of the most widely used methods in tunnel design is the convergence-confinement method (CCM) for its practical application. The elastic-plastic models are usually used in the convergence-confinement method as a constitutive model for rock behavior. The plastic models used to simulate the rock behavior, do not consider the important issues such as stiffness degradation and softening. Therefore, the use of damage constitutive models in the convergence-confinement method is essential in the design process of rock structures. In this paper, the basic concepts of continuum damage mechanics are outlined. Then a numerical stepwise procedure for a circular tunnel under hydrostatic stress field, with consideration of a damage model for rock mass has been implemented. The ground response curve and radius of excavation damage zone were calculated based on an isotropic damage model. The convergence-confinement method based on damage model can consider the effects of post-peak rock behavior on the ground response curve and excavation damage zone. The analysis of results show the important effect of brittleness parameter on the tunnel wall convergence, ground response curve and excavation damage radius.

Hydrostatic Stress Effect on the Yield Behavior of Inconel 100

Abstract: Classical metal plasticity theory assumes that hydrostatic stress has no effect on the yield and postyield behavior of metals. Recent reexaminations of classical theory have revealed a significant effect of hydrostatic stress on the yield behavior of notched geometries. New experiments and nonlinear finite element analyses (FEA) of Inconel 100 (IN 100) equal-arm bend and double-edge notch tension (DENT) test specimens have revealed the effect of internal hydrostatic tensile stresses on yielding. Nonlinear FEA using the von Mises (yielding is independent of hydrostatic stress) and the Drucker-Prager (yielding is linearly dependent on hydrostatic stress) yield functions was performed. In all test cases, the von Mises constitutive model, which is independent of hydrostatic pressure, overestimated the load for a given displacement or strain. Considering the failure displacements or strains, the Drucker-Prager FEMs predicted loads that were 3% to 5% lower than the von Mises values. For the failure loads, the Drucker Prager FEMs predicted strains that were 20% to 35% greater than the von Mises values. The Drucker-Prager yield function seems to more accurately predict the overall specimen response of geometries with significant internal hydrostatic stress influence.

A note on the modeling of incompressible fluids with material moduli dependent on the mean normal stress

Abstract: In incompressible materials, both fluids and solids, a part of the stress is not prescribed by constitutive specification, that is, the part of the stress is not determined in terms of kinematical quantities, temperature, et cetera. This “indeterminate” part of the stress is variously referred to as the “constraint stress”, the “reaction stress” or the “Lagrange multiplier” enforcing the constraint. In the case of an incompressible Navier–Stokes fluid, the part of the stress, that is a consequence of the constraint, also happens to coincide with the mean value of the stress which is referred to as the “mechanical pressure”. However, in general non-Newtonian fluids this is not the case, and, unfortunately, in view of the widespread use of the Navier–Stokes equation, the terminology “pressure” is used interchangeably for both the part of the stress that is not constitutively specified and the mean value of the stress, leading to considerable confusion with regard to important issues concerning non-Newtonian fluids. Recognizing the distinction between the mean value of the stress and the part of the stress that is not constitutively specified becomes critical in materials whose moduli depend on the mean value of the stress. An example of the same concerns the viscosity, which depending on whether it is a function of the indeterminate part of the stress or the mean value of the stress could lead to different flow characteristics. In this short note we discuss an error that is a consequence of not recognizing the distinction between these different quantities but misidentifying them as being the same, the mechanical “pressure”.

Influence of carbon content on workability behavior in the formation of sintered plain carbon steel preforms

Abstract: Complete experimental investigation on the workability behavior of sintered plain carbon steel cylindrical preforms with carbon contents of 0%, 0.35%, 0.75%, and 1.1%, under cold upsetting, has been studied in order to understand the influence of carbon content on the workability process. The abovementioned powder metallurgy sintered preforms with constant initial theoretical density of 84% and aspect ratio of 0.4 were prepared using a suitable die set assembly on a 1 MN capacity hydraulic press and sintered for 90 min at 1,200°C. Each sintered preform was cold upset under nil/no frictional constraint. Under triaxial stress state condition, densification, axial stress, hoop stress, hydrostatic stress, effective stress, and formability stress index against axial strain relationship were established and presented in this work. Further, attained density is considered to establish formability stress index and various stress ratio parameters’ behavior.

Analysis of Metallic Ductile Fracture by extended Gurson models

Abstract: Ductile fracture of metallic materials is usually the result of void nucleation, growth and coalescence. The original Gurson-Tvergaard (GT) model deals with the homogenous deformation related to void nucleation and growth. However, it takes no consideration on the localized deformation due to the void coalescence. In this paper extended GT damage models incorporating two different void coalescence criteria are developed, respectively. One of the void coalescence criteria is based on the plastic limit load model by Thomason; the other decides the onset of void coalescence by a critical equivalent plastic strain as a power law of stress triaxiality (defined by the ratio of the hydrostatic stress over the equivalent stress). Hence, void coalescence is controlled by physical mechanisms, rather than by a critical void volume fraction which cannot be taken as a constant. The extended constitutive models are implemented into an implicit finite element code via a user defined material subroutine (UMAT) in ABAQUS. Detail analyses are performed for a series of notched round tensile bars. The predictions of the fracture behavior based on the proposed approach, from void nucleation to final material failure, are compared with experiment data. Both results agree pretty well. In the end, the effects of stress triaxiality are discussed.

Theoretical and numerical modeling of rock hysteresis based on sliding of microcracks

Abstract: Nonlinearity and hysteresis are two key features of elastic rock deformation. This behavior can be attributed to the presence of cracks and crack-like voids. The hysteretic behavior of rocks is related to the concept of unrecovered energy. Two main processes lead to the existence of unrecovered energy in the sliding crack model: (i) the work of frictional forces and (ii) the strain energy trapped in the solid. In this paper, a theoretical and numerical analysis will be presented to extend the work of David et al. [1] to consider 3D penny-shaped cracks. A 3D finite element analysis is used to evaluate the sliding crack model numerically. In this approach, the penalty method is used to simulate the contact behavior of the crack faces. The stick-slip condition of the crack faces is simulated by employing the constitutive frictional law of Amontons. The results show that no residual strain is developed in the body containing randomly oriented cracks if one assumes a uniform stress over all the crack cells. The energy loss is therefore equal to the work of frictional forces on the crack faces. mechanisms and sources. The cracks were generally considered to be initially closed, as well. In addition, no numerical simulation has been carried out to verify the theoretical results. There remains a need for a more precise constitutive model that can capture the nature of the micro-structured materials by considering the frictional contact behavior of initially open interacting cracks in a general loading condition. Table 1. Constitutive models of microstructured materials based on frictional contact of microcracks. Loading condition Crack specifications Frictional constitutive law Walsh [6] Uniaxial compression (loading only) Noninteracting closed 2D cracks Coulomb Kachanov [5] Triaxial asymmetric compression (loading only) Noninteracting closed pennyshaped cracks Coulomb (μ=0.6) Horry and NematNasser [4] Biaxial plane strain (loading only) open pennyshaped cracks interacting based on selfconsistent approach Coulomb (μ=0, ∞) Lawn and Marshall [7] Uniaxial compression (loading and unloading) Noninteracting closed pennyshaped cracks friction coefficient together a cohesion term David et al. [1] Uniaxial compression (loading and unloading) Noninteracting open 2D cracks Coulomb The hysteretic behavior of rocks introduces the concept of unrecovered energy. Two main processes lead to the existence of unrecovered energy in the sliding crack model: (i) the work of frictional forces, and (ii) the strain energy trapped in the solid. Whereas the work of the frictional forces is lost as heat energy, strain energy is available in the solid, and may be recovered at a later loading stage. Given that shear stress plays an important role in frictional sliding, hysteretic behavior under triaxial loading is expected to be different from the uniaxial case. For example, according to the sliding crack model, the hysteresis vanishes for the pure hydrostatic stress state. The classic work of Walsh [6], described the role of microcracks in inducing nonlinear and hysteretic behavior. David et al. [1] extended Walsh’s formulation to consider initially open cracks, and analyzed the behavior of the rock during both loading and unloading, under uniaxial compression. They compared a twodimensional analytical formulation against experimental data on sandstones and thermo-mechanically loaded granite specimens, and concluded that the elastic deformation of the rock subjected to uniaxial compression can be fully characterized by four microstructural parameters: the modulus of the uncracked rock, the crack density, an initial crack aspect ratio, and a friction coefficient. In the present paper, a theoretical and numerical analysis will be presented to extend the work of David et al. [1] to consider 3D penny-shaped cracks. A 3D finite element analysis is also used to evaluate the sliding crack model numerically. 2. THEORETICAL MODELING OF ROCK HYSTERESIS 2.1. Solid Containing a Single Crack Assuming a cube of edge length containing a penny-shaped crack with the orientation of relative to the direction of the uniaxial applied stress σ, the effective modulus in the direction of applied load ( ) is determined by applying Betti’s reciprocal theorem [6]: