Pure Hydrostatic Loading Research Articles

Vertical velocity at hydrostatic and anisotropic stresses

Sonic and dipole wireline tools measure Vp and Vs along the vertical direction. The state of stress in the subsurface is predominantly anisotropic, while most laboratory experiments measuring the dynamic elastic properties are conducted under hydrostatic stress. The question we ask is whether such laboratory experiments provide the velocities that are close to those measured in the vertical wellbore where the stresses are anisotropic. To address this question, we conducted ultrasonic pulse transmission experiments on several room-dry rock samples. The comparison was made between the P- and S-wave velocities obtained at pure hydrostatic loading conditions and those at a smaller hydrostatic stress with added axial stress, so that the total stress along the axis of a cylindrical plug was the same as under pure hydrostatic loading. These differences were significant in the extreme case of only 1 MPa hydrostatic confining stress with the axial stress increasing up to 40 MPa. However, as the hydrostatic (confining) stress increased, the differences between the velocities along the axis of the sample became smaller and smaller. For example, at 1 MPa confining and 30 MPa axial stress, the relative difference in Vp was about 10%, while that in Vs was about 20%. However, at 10 MPa confining stress, these differences became about 3% and 6%, respectively, and further decreased as the confining stress increased. This means that even at strong in-situ contrasts between the vertical and horizontal stresses, the results of laboratory hydrostatic experiments can be used for in-situ velocity estimates. These results also appear to be consistent with a theoretical model that predicts the directional velocities at any triaxial stress conditions from those measured versus hydrostatic stress.

Approximate plastic yield criteria of geomaterials with pores and grains embedded in a porous matrix

Mineral grains and porosity are two common properties of geomaterials. This study focuses on establishing a macroscopic yield criterion for geomaterials having pores and mineral grains at the mesoscale which is embedded in a porous matrix. At the microscale, the solid phase is pressure-sensitive and obeys to the Drucker–Prager criterion which considers the asymmetric property between tension and compression. Based on a two-step homogenization procedure and the modified secant method, a macroscopic yield criterion is firstly derived which takes into account the effects of microstructure on the macroscopic mechanical behaviors of the studied material, such as the meso-porosity and mineral grains content at the mesoscale, the micro-porosity and the pressure-sensitive of the solid phase at the microscale. However, it overestimates the material strength in compressive loading by comparing with the Fast Fourier Transform (FFT) based numerical results. Then, this criterion is improved by considering the exact solution in pure hydrostatic loading of a porous medium with a Drucker–Prager matrix. By comparing to the numerical results with different microstructures and to experimental data, the new macroscopic yield criterion is estimated and validated. The main features of the studied geomaterial are well captured by this criterion.

ALTERNATIVE METHOD FOR QUALIFICATIONS OF GLASS FIBRE REINFORCED EPOXY PIPES (GRE)

This paper discusses the Ultimate Elastic Wall Stress (UEWS) test for GRE pipes under pure hydrostatic loading. UEWS appears to provide an attractive alternative to the currently used procedure laid down in ISO 14692, which involves an expensive series of long term constant pressure tests, as described in ASTM 2992, running for a period in excess of 10,000 hours.
 The pipes were subjected to biaxial loading, which was attained by combinations of hoop and axial stress. Loads were applied as groups of cycles which, were gradually increased until the UEWS had been determined. UEWS test has proved to be one of the most effective in terms of accuracy and speed. Moreover, it has been found to be sensitive to changes in key manufacturing and raw material parameters.
 Modelling results are also showed a harmonic approach and accepted to that obtained experimentally. This encourages to apply the proposed modelling for further biaxial load ratios.

Shakedown of porous material with Drucker-Prager dilatant matrix under general cyclic loadings

This paper is concerned with the shakedown limit states of porous ductile materials with Drucker-Prager matrix under cyclically repeated loads. Using the hollow sphere model and Melan’s shakedown theorem based on time-independent residual stress fields, a macroscopic fatigue criterion is derived for the general conditions of cyclic loads. First, the case of the hollow sphere subjected to pure hydrostatic loading is studied and the limit states of collapse by fatigue or by development of mechanism are derived. Then, the general case involving shear effects with any arbitrary cyclic load fluctuations ranging from the pulsating load to the alternating one is considered. The key idea is in two steps: (i) the choice of appropriate trial stress and trial residual stress fields and (ii) then maximizing the size of the load domain in the spirit of the standard lower shakedown theorem. The new macroscopic shakedown criterion depends on the porosity, the friction angle, Poisson’s ratio, the two stress invariants of the effective stress tensor and the sign of the third one. Together with the limit analysis-based yield criterion corresponding to the sudden collapse by development of a mechanism at the first cycle, it defines the safety domain of porous materials subjected to cyclic load processes. Interestingly, it is found that the safe domain is little sensitive to variations of the friction angle, however, it is considerably reduced compared to the one under monotonic loads obtained by limit analysis. Finally, a comparative study between the analytical results and numerical predictions performed by micromechanics-based finite element simulations is conducted for different porosities and friction angles.

Failure prediction of ±55° glass/epoxy composite pipes using system identification modelling

Black-box modelling using system identification method to predict the performance of glass fibre reinforced epoxy (GRE) composite pipe under multiaxial loading stress ratio is presented. In this study, both linear and nonlinear models were derived namely; linear time-invariant parametric model and artificial neural network model. The models derived are to approximate the pure hydrostatic loading performance using GRE pipes with winding angles of ±55°. Three different linear model structures were derived, and the best fit model achieved at 96.64% of best fit. On the other hand, the Artificial Neural Network (ANN) modelling showed better accuracy with the best fit of 99.82%. Finally, the point of failure at which first damage takes place predicted by the models derived was validated using experimental data.

Shakedown of porous materials

The paper is devoted to the determination of shakedown limit states of porous ductile materials under cyclically repeated loads by considering the hollow sphere model with von Mises matrix. We adopt Melan's statical approach based on time-independent residual stress fields. First of all, we determine the exact solution for the pure hydrostatic loading. It turns out that the collapse occurs by fatigue. Next, suitable trial stress fields are built with additional terms to capture the shear effects. This theoretical fatigue criterion of porous materials agreed with numerical simulations and experimental results provided in literature according to which, in ductile metals, the strain to fracture under cyclic loading is considerably lower than the one reached monotonically. Finally, the built criterion is compared to numerical simulations derived by both shakedown direct method and incremental simulations.

Effects of winding angle on the behaviour of glass/epoxy pipes under multiaxial cyclic loading

The effects of winding angle on the behaviour of glass/epoxy composite tubes under multiaxial cyclic loading were investigated. The performance of such composite tubes was studied using an indigenous automated test procedure that is compatible with the internal qualification requirements of the composite pipe manufacturers. Glass fibre reinforced epoxy (GRE) composite pipes with three winding angles, namely, [±45°]4, [±55°]4, and [±63°]4, were tested. A novel automated test rig was fabricated to accommodate five stress ratios, ranging from pure axial to pure hoop loadings. The cyclic pressure test was conducted until droplets of water were seen on the outer surface of the pipe. Failure envelopes were then constructed based on the first ply failure (FPF) points determined from the axial stress to hoop strain response at five stress ratios. Three functional failure modes, namely, tensile axial, weepage, and local leakage failures, were observed during the tests. The results indicate that each winding angle dominates a different optimum pressure loading condition, namely, [±55°]4 for pure hydrostatic loading, [±45°]4 for hoop to axial loading, and [±63°]4 for quad hoop to axial loading. The envelopes show a strong dependence on the stress ratio and winding angle.

A simulation-based determination of cap parameters of the modified Drucker–Prager cap model by considering specimen barreling during conventional triaxial testing

Two types of cap parameters were determined by fitting the experimentally obtained triaxial deviator stress curves found in the literature using the modified Drucker–Prager cap model. The two types of parameters were extracted using the specimen model that deforms uniformly or non-uniformly (barreling). The parameter set extracted from the non-uniformly deforming specimen model reasonably predicted the experimental deviator stress curves obtained from the barreling specimen. However, when the parameter set extracted from the uniformly deforming specimen model was used to simulate the experimental curves from the barreling specimen, the prediction was inferior to the set from the non-uniformly deforming model. Considering versatile types and properties of particulate materials (e.g., ceramic, metal, pharmaceutical powders and soils), we suggest to verify the prediction capabilities of the parameter sets from each specimen model. The stress path of the barreling specimen during the conventional triaxial test was fairly complex depending on the position in the specimen. Pure hydrostatic loading was not achieved even during the hydrostatic loading stage. In the shear loading stage, the position-averaged stress path showed a lower slope in the meridional plane than that of the uniformly deforming specimen with a slope of 3.

A set of enhanced formulations for existing nonlinear homogenization schemes and their evaluation

Abstract On the basis of non-biased comparative evaluations of various linearization procedures used in nonlinear homogenization, performed both at the global and local scales for power-law composites (Rekik et al., 2005, 2007, 2012), we propose in this paper six ad hoc enhancements of some of the linearization procedures considered in Rekik et al. (2007). Both “stress–strain” approaches (the secant and affine formulations) or “variational formulations” (the tangent second-order method (Ponte Castaneda, 1996)) are considered. The main idea consists in proposing alternatives for the usual reference strains used by the secant, affine and tangent second-order procedures. The new linear comparison composites generated by the linearization step around the chosen alternative descriptors of the strain field statistics explicitly account for either intraphase strain fluctuations or both inter- and intraphase strain fluctuations. As a first illustration, the relevance and limitations of the enhanced linearization procedures are tested for rigidly-reinforced and porous power-law composites. For isochoric loadings, it is shown that two variants of the enhanced tangent second-order formulation lead to accurate estimates of the exact effective response which are in good agreement with the efficient second-order scheme of Ponte Castaneda (2002a). Further, the modified secant formulation provides good results for strongly nonlinear rigidly-reinforced composites away from low particulate volume fraction and the percolation threshold; however some new inherent limitations of secant formulations are also established. At last, a very discriminant situation is tested: it consists of a porous medium submitted to a pure hydrostatic loading at low pore concentrations. It is shown that one variant of the proposed enhanced second-order formulations leads to accurate estimates alike the efficient and more sophisticated formulations proposed in Bilger et al. (2002); Danas et al. (2008).

A stress-based variational model for ductile porous materials

The main objective of this paper is to formulate a very new statically-based model of ductile porous materials having a von Mises matrix. In contrast to the Gurson’s well known kinematical approach applied to a hollow sphere, the proposed study proceeds by means of a statical limit analysis procedure. Its development and implementation require the choice of an appropriate trial stress field. The starting point is Hill’s variational principle for rigid plastic matrix. The use of a lagrangian multiplier allows to satisfy the plastic criterion in an average sense. The proposed trial stress field, complying with internal equilibrium, is composed of an heterogeneous part (exact solution for the stress field in the hollow sphere under pure hydrostatic loading) to which is added a uniform deviatoric stress field. Owing to this choice, the stress vector conditions on the void boundary are relaxed. By solving the resulting Saddle point problem, we derive closed form formula which depends not only on the first and second invariant of the macroscopic stress tensor but also on the sign of the third invariant of the stress deviator. The obtained results are fully discussed and compared to existing models, available numerical data and to Finite Elements results obtained from cell calculation carried out during the present study. Finally, we provide for the new model the macroscopic flow rule as well as the porosity evolution equations which also show very original features. Some of these features are illustrated.

Comprehensive analyses of syntactic foam behaviour in deepwater environment

Over the past 10 years, numerous studies were performed to better understand the behaviour of the glass syntactic foams used as thermal insulation of pipes for deepwater production. The obtained results outlined some specific behaviour of polymeric syntactic foams reinforced by glass microballoons in service conditions: both water uptake and mechanical stress have a key impact on thermal properties. This article focuses first on the wet behaviour of glass syntactic foams. The effect of water is investigated to better model the nature of water diffusing in syntactic foams with and without a topcoat protection. Secondly, the effect of hydrostatic pressure on coated structure is addressed by using a confined compression test. As polymer material is bonded to the steel surface, it is not submitted to pure hydrostatic loading but to non-spherical loading in the vicinity of the pipe. The confined compression test is then chosen to represent these non-spherical loadings of material. The rupture of glass microballoons is monitored by acoustic emission for different matrices and attempts are made to quantify the resulting acoustic emission signals by comparison with prior tomography results. These experimental analyses provide a better understanding of the main factors affecting the functional properties of syntactic foams.

The Imperfection Sensitivity of Isotropic Two-Dimensional Elastic Lattices

The imperfection sensitivity of the effective elastic properties is numerically explored for three planar isotropic lattices: fully triangulated, the Kagome grid, and the hexagonal honeycomb. Each lattice comprises rigid-jointed, elastic Euler–Bernoulli beams, which can both stretch and bend. The imperfections are in the form of missing bars, misplaced nodes, and wavy cell walls. Their effect on the macroscopic bulk and shear moduli is numerically investigated by considering a unit cell containing randomly distributed imperfections, and with periodic boundary conditions imposed. The triangulated and Kagome lattices have sufficiently high nodal connectivities that they are stiff, stretching dominated structures in their perfect state. In contrast, the perfect hexagonal honeycomb, with a low nodal connectivity of 3, is stretching dominated under pure hydrostatic loading but is bending dominated when the loading involves a deviatoric component. The high connectivity of the triangulated lattice confers imperfection insensitivity: Its stiffness is relatively insensitive to missing bars or to dispersed nodal positions. In contrast, the moduli of the Kagome lattice are degraded by these imperfections. The bulk modulus of the hexagonal lattice is extremely sensitive to imperfections, whereas the shear modulus is almost unaffected. At any given value of relative density and level of imperfection (in the form of missing bars or dispersed nodal positions), the Kagome lattice has a stiffness intermediate between that of the triangulated lattice and the hexagonal honeycomb. It is argued that the imperfections within the Kagome lattice switch the deformation mode from stretching to a combination of stretching and bending. Cell-wall waviness degrades the moduli of all three lattices where the behavior of the perfect structure is stretching dominated. Since the shear response of the perfect hexagonal honeycomb is by bar bending, the introduction of bar waviness has a negligible effect on the effective shear modulus.

Molecular dynamics simulations of the shape-memory behaviour of polyisoprene

Full-atomistic molecular dynamics simulations are used to study the shape-memorybehaviour of a representative amorphous polymer. A virtual polyisoprene was constructedand subjected to uniaxial stretch and hydrostatic compression thermomechanicalcycles. Uniaxial stretch loading results demonstrate that a temporary shape canbe stored at low temperature and that the original shape can be recovered athigh temperature due to the entropy effect involved in a change of shape at hightemperature. The material volume change during pure hydrostatic loading resultedin a change of internal energy. The volume change could not be stored at lowtemperature without applying hydrostatic stresses. These results shed light on thefundamental mechanisms driving shape memory and recovery in amorphous polymers.

Eshelby tensors for an ellipsoidal inclusion in a microstretch material

Eshelby tensors for an ellipsoidal inclusion in a microstretch material are derived in analytical form, involving only one-dimensional integral. As micropolar Eshelby tensor, the microstretch Eshelby tensors are not uniform inside of the ellipsoidal inclusion. However, different from micropolar Eshelby tensor, it is found that when the size of inclusion is large compared to the characteristic length of microstretch material, the microstretch Eshelby tensor cannot be reduced to the corresponding classical one. The reason for this is analyzed in details. It is found that under a pure hydrostatic loading, the bulk modulus of a microstretch material is not the same as the one in the corresponding classical material. A modified bulk modulus for the microstretch material is proposed, the microstretch Eshelby tensor is shown to be reduced to the modified classical Eshelby tensor at large size limit of inclusion. The fully analytical expressions of microstretch Eshelby tensors for a cylindrical inclusion are also derived.

Yield Functions and Flow Rules for Porous Pressure-Dependent Strain-Hardening Polymeric Materials

To characterize the response of progressively damaged glassy polymers due to the presence and evolution of voids, yield functions and flow rules were developed systematically for a pressure-dependent matrix following the modified von Mises criterion. A rigid-perfectly plastic material was first assumed. The upper bound method was used with a velocity field which has volume preserving and shape changing portions. Macroscopic yield criterion in analytical closed form was first obtained for spherical voids which is valid for all possible macroscopic strain rate fields. Macroscopic yield criteria in analytical closed form were then obtained for cylindrical voids for the special cases of axisymmetric and plane-strain modes of deformation. The upper-bound solutions were subsequently improved to better match analytical solutions for pure hydrostatic loading. Characteristics of the yield function as a function of pressure dependency and void fraction were studied in detail. Generalization of the model for spherical voids to include elasticity as well as strain hardening of the matrix was then obtained. An example for the uniaxial response of a progressively damaged material was then used to illustrate one possible application of the full set of constitutive equations. [S0021-8936(00)02902-0]

A theory of viscoplasticity based on infinitesimal total strain

A viscoplasticity theory based upon a nonlinear viscoelastic solid, linear in the rates of the strain and stress tensors but nonlinear in the stress tensor and the infinitesimal strain tensor, is being investigated for isothermal, homogeneous motions. A general anisotropic form and a specific isotropic formulation are proposed. A yield condition is not part of the theory and the transition from linear (elastic) to nonlinear (inelastic) behavior is continuous. Only total strains are used and the constant volume hypothesis is not employed. In this paper Poisson's ratio is assumed to be constant. The proposed equation can represent: initial linear elastic behavior; initial elastic response in torsion (tension) after arbitrary prestrain (prestress) in tension (torsion); linear elastic behavior for pure hydrostatic loading; initial elastic slope upon large instantaneous changes in strain rate; stress (strain)-rate sensitivity; creep and relaxation; defined behavior in the limit of very slow and very fast loading. Stress-strain curves obtained at different loading rates will ultimately have the same “slope” and their spacing is nonlinearly related to the loading rate. The above properties of the equation are obtained by qualitative arguments based on the characteristics of the solutions of the resulting nonlinear first-order differential equations. In some instances numerical examples are given. For metals and isotropy we propose a simple equation whose coefficient functions can be determined from a tensile test [Eqs. (31), (35), (37), (38)]. Specializations suitable for materials other than metals are possible. The paper shows that this nonlinear viscoelastic model can represent essential features of metal deformation behavior and reaffirms our previous assertion that metal deformation is basically rate-dependent and can be represented by piecewise nonlinear viscoelasticity. For cyclic loading the proposed model must be modified to account for history dependence in the sense of plasticity.

A theory of thermoviscoplasticity based on infinitesimal total strain

A theory of three-dimensional infinitesimal isotropic thermoviscoplasticity is proposed and investigated in several homogeneous deformations. The theory is represented by both a mechanical constitutive equation and a constitutive assumption for the heat equation; these equations are separately postulated but are coupled through their common linear dependence upon the stress rate and strain rate tensors and the time rate of temperature change, and through their common nonlinear dependence upon the stress and strain tensors and the absolute temperature. Throughout this theory total strain is used and the strain tensor is not decomposed into a sum of elastic and inelastic contributions. The concept of the yield surface is not employed and the transition from initially linear thermoelastic behavior to nonlinear inelastic behavior is continuous.Through qualitative discussion and quantitative examples, this proposed system of constitutive equations is shown to represent: initial linear thermoelastic behavior followed by inelastic rate sensitive work hardening; linear thermoelastic behavior between stress, strain and temperature in pure hydrostatic loading; initial cooling in uniaxial tension, initial heating in uniaxial compression, and initial isothermal behavior in torsion prior to inelastic deformation; subsequent self-heating in any monotonie loading following the onset of inelastic behavior; axial stress (strain) build-up due to temperature change uniformly induced by monotonic and cyclic torsional loading. Also represented are stress (strain) rate sensitivity; temperature rate sensitivity; creep and relaxation; and nonlinear dependence of the spacing between stress-strain curves at different stress (strain) rates upon the value of the stress (strain) rate tensor in constant-rate loading. Stress-strain curves corresponding to different constant strain (stress) rate loadings ultimately attain the same slope. Defined and physically meaningful limits are obtained in the cases of very slow and very fast loading rates in monotonie radial loading. Associated with limitingly slow loading is an equilibrium stress-strain curve, and in relaxation the stress relaxes to an equilibrium value associated with this curve.Illustrative specializations to cases of uniaxial, torsional, pure hydrostatic and radial deformation histories are considered and numerical results are obtained by postulating specific choices of material functions, and by numerically integrating the resulting system of first-order nonautonomous, nonlinear stiff differential equations. Results are presented in terms of graphs to show the influence of various test histories and material parameters as well as the capability of the model.In cyclic deformation the proposed equations of the model are modified according to previously established concepts to account for history dependence in the sense of plasticity. This is accomplished by updating a material parameter associated with the equilibrium stress-strain curves in such a manner that the material response predicted by the model remains continuous .and smooth. The ability to represent hardening in materials is illustrated. In torsional cycling a significant net increase in temperature can be induced. A possible thermoinelastic explanation for the Ronay effect is given.