Nonuniform Stress State Research Articles

The strength of the Brazilian fracture test

Since its introduction in the 1940s until present times, the so-called Brazilian test has been embraced by practitioners worldwide as a method of choice to indirectly measure the tensile strength of concrete, rocks, and other materials with a large compressive strength relative to their tensile strength. This is because of the ease that the test affords in both the preparation of the specimen (a circular disk) and the application of the loads (two platens compressing the specimen between them). Yet, this practical advantage has to be tempered by the fact that the observations from a Brazilian test — being an indirect experiment in the sense that it involves not uniform uniaxial tension but non-uniform triaxial stress states throughout the specimen — have to be appropriately interpreted to be useful. The main objective of this paper is to carry out a complete quantitative analysis of where and when fracture nucleates and propagates in a Brazilian test and thereby establish how to appropriately interpret its results. We do so by deploying the phase-field fracture theory of Kumar et al. (2020), which has been recently established as a complete theory of fracture capable of accurately describing the nucleation and propagation of cracks in linear elastic brittle materials under arbitrary quasistatic loading conditions. The last section of this paper puts forth a new protocol to deduce the tensile strength of a material from a Brazilian test that improves on the current ISRM and ASTM standards.

Influence of the Straining Path during Cold Drawing on the Hydrogen Embrittlement of Prestressing Steel Wires

Cold drawing is a commonly used technique for manufacturing the prestressing steel wires used as structural elements in prestressed concrete structures. As a result of this manufacturing process, a non-uniform plastic strain and residual stress states are generated in the wire. These stress and strain fields play a relevant role as the main cause of the in-service failure of prestressing steel wires in the presence of an aggressive environment, hydrogen embrittlement (HE). In this paper, hydrogen susceptibility to HE is compared in two different commercial cold-drawn wires with the same dimensions at the beginning and at the end of manufacturing that follow different straining paths. To achieve this goal, numerical simulation with the finite element (FE) method is carried out for two different industrial cold-drawing chains. Later, the HE susceptibility of both prestressing steel wires was estimated in terms of the hydrogen accumulation given by FE numerical simulations of hydrogen diffusion assisted by stress and strain states, considering the previously obtained residual stress and plastic strain fields generated after each wire-drawing process. According to the obtained results, the hardening history modifies the residual stress and strain states in the wires, affecting their behavior in hydrogen environments.

Finite-Element Modeling of FRP-Confined Noncircular Concrete Columns Using the Evolutionary Potential-Surface Trace Plasticity Constitutive Model for Concrete

The compressive behavior of fiber-reinforced polymer (FRP)-confined concrete columns with a noncircular cross section has been investigated through extensive experimental, analytical, and numerical research, but a unified theoretical/numerical approach that can accurately predict both their section-average behavior and local concrete behavior is not yet available. In noncircular columns under axial compression, the concrete is typically under a nonuniform stress state of three-dimensional (3D) compression, with the lateral compressive stresses being the reactive stresses from the confining device (i.e., passive confinement). The authors of the present paper recently developed a plasticity constitutive model for concrete under general 3D compressive stresses, which possesses a potential surface with an evolutionary deviatoric trace that can accurately capture the results of existing compression tests of concrete cubes under nonuniform, passive confinement. This paper explores the application and capability of this evolutionary potential-surface trace (EPT) plasticity constitutive model in finite-element (FE) analysis of FRP-confined square, rectangular, and elliptical plain-concrete columns under concentric compression. The section-average behavior of all the selected noncircular columns predicted by these FE analyses was close to the existing experimental data. The numerical results obtained with the EPT plasticity constitutive model were then examined in detail to achieve an improved understanding of local concrete behavior in FRP-confined noncircular columns.

Estimating ductile crack initiation in structural steel under combined tension and shear stress using a modified void growth model

Ductile fracture initiation is one of the important issues in recent research on structural steels. Many models have been established to simulate the mechanism of ductile fracture and predict the ductile crack initiation in different loading conditions. The void growth model is one of the most successful micro-models that is originally developed to estimate ductile crack initiation in the first mode of fracture under monotonic loading. However, one of the main shortcomings of these types of uncoupled void growth models is the incapability of them in capturing the behavior of steels under shear stress and the effect of it on the resulting voids and the process of ductile fracture in low and moderate-stress triaxialities. A newly proposed modified void growth model represented in this article is able to overcome this issue by introducing normalized maximum shear stress. A series of scanning electron microscopy examinations and experimental and numerical monotonic tensile examinations have been carried out on the notched round bar and flat groove plate specimens with different notch radii to calibrate the represented fracture model. Steel-holed plates with symmetric notches around the hole and notched shear plates have been tested and analyzed to demonstrate the application and validation of the represented void growth model in predicting the initiation of ductile fracture in various combinations of tension and shear under monotonic loading. Different angles of notches were used in the specimens to achieve diverse stress states to examine the application of the represented micro-model in non-uniform stress state fields. Finally, the role of the characteristic length, as the representative of the density of the inclusions in the material, on the accuracy of the model has been discussed in this article.

Probability of failure and weibull size-scaling parameters for thin glass subjected to two-point bending

The two-point bending test is a valuable test for estimating the strength of the thin and flexible glass/ceramic parts that are increasingly used in next-generation flexible electronics devices. We present closed-form expressions for determining Weibull material scale parameters and probability of failure for the two-point bending test. The presented solution, tested on Corning® Willow® glass samples, eliminates the need for iterative and often time-consuming approaches (e.g., Finite Element Analysis) for estimating scale parameters. Considering the strength-controlling flaw distribution on a surface or inside a volume, the solution assumes that the Weibull modulus (m) and scaling modulus (mAor mV) are distinct quantities to ensure the scale parameter is independent of the applied load. This condition reveals a special relationship between the moduli that is unique to two-point bending given its highly non-uniform state of stress, which contrasts with other uniaxial bending tests (such as three and four-point bending) in which both moduli have the same numerical value.

Effects of Geometry and Loading Mode on the Stress State in Asphalt Mixture Cracking Tests.

Currently, a variety of asphalt mixture cracking characterization tests are available as screening tools for the better selection of high-quality raw materials and also for the optimization of mixture design for different applications. However, for a same evaluation index, using different sample geometries and loading modes might lead to obtaining different values, which prevents the application of the evaluation index as a fundamental parameter in pavement design. In this paper, the effects of geometry and loading mode on the stress state in the experimental characterization of asphalt mixture cracking were discussed using numerical simulation. The results showed that applying thermally-induced load in restrained uniaxial test configuration should be considered when performing an asphalt mixture cracking test. Compared with direct tensile configuration, compressive stress clearly existed in other common test configurations, which may prevent the initiation and propagation of cracks. Moreover, it was revealed that nonuniform stress state exists in the dog-bone geometry, which makes it possible to know the failure plane in advance and place gauges at the failure plane for measuring fundamental deformation-related properties.

Geosynthetic Interface Friction at Low Normal Stress: Two Approaches with Increasing Shear Loading

The evaluation of geosynthetic interface friction is a key parameter for the stability of coupled geosynthetics, as in landfill capping liner. At the present time, few types of tests are suitable for measuring the interface friction at low normal stress: one of these is the inclined plane, usually carried out under a vertical stress of 5 kPa. This type of test is not without critical aspects, mainly due to the nonuniform normal stress state induced by the inclination of the plane, but, on the other hand, the most widespread direct shear test generally cannot be performed at such low values of normal stress. After a short discussion on the pros and cons of these two types of test, the paper presents a comparison of the interface friction angles obtained, for three interfaces, by means of an inclined plane and an unconventional direct shear apparatus, under the same low normal stress. The peculiarity of this latter device is of ensuring a gradual increase of the mobilized strength, in a way similar to what occurs during the inclined plane test. The good correspondence of the results of the two types of tests confirmed the validity of both the test approaches.

Investigation of the influence of gas fracturing on fracturing characteristics of coal mass and gas extraction efficiency based on a multi-physical field model

Coal seam gas recovery is a critical way to achieve clean energy development and reduce greenhouse gas emissions. Gas fracturing, as a necessary and advantageous stimulation measure, can effectively achieve gas extraction from deep coal seams and ensure safe production in deep coal mines. In this study, a hydro-mechanical coupling model is established to analyze the damage characteristics of coal seams during gas fracturing. The model focuses on three aspects: (a). the fracture criterion of type-I fracture under the action of multiple stress states in the fracturing process; (b). the characteristics of post-peak strain softening of coal and its influence on coal permeability; (c). the influence of non-uniform stress state on directional compression deformation and directional permeability of coal. The difference between gas fracturing (nitrogen, CO2) and hydraulic fracturing is studied based on this coupling model. The development of fractures in coal seam gas reservoirs after gas fracturing is investigated, and the influences of the coal parameters of the gas extraction process after fracturing are determined. Results show that because of the different compression coefficients, viscosities of water and gas and the slippage effect, there are obvious differences in the fracturing pressure of gas and water. Under the same parameters, the hydraulic fracturing method needs larger fracture initiation pressure than the gas fracturing method (nitrogen, CO2). For two kinds of media (nitrogen, CO2) in gas fracturing, in addition to the parameter difference of gas itself, the adsorption of CO2 is also the main factor affecting the fracturing pressure. The increase of coal permeability and Biot's coefficient will reduce the fracture initiation pressure, and the increase of confining pressure will increase the fracture initiation pressure.

Transformation of concrete deforming diagrams in conditions of uniform and non-uniform stress states

The aim of the research is formulated, which is the theoretical substantiation, development and testing of the concrete state diagram, suitable for use to calculations of the strength of bended reinforced concrete elements based on the deformational model, as well as for more complete assessment of non-uniform stress-strain state of the cross-sections of elements at all stages of their loading up to the destruction directly on the values of the relative strains of concrete and the corresponding stresses.
 In this paper, an analytical method of converting the parameters of reference concrete deforming diagrams, which are determined experimentally during standard tests of concrete prismatic specimens by short-term axial compression and tension up to the destruction in «soft» mode of loading, into parameters of simulated transformed diagrams, which correspond to the «rigid» mode of loading of concrete, is developed. The way of simultaneous application of analytical expressions for the specified defoming diagrams, which describe the operation of concrete in conditions of uniform compression, for transition to the state diagram, which displays the functional relationship between the stresses and strains of the concrete compressed zone in bended concrete and reinforced concrete elements, cross-sections of which operate in conditions of non-uniform stress state, is proposed.
 The results of testing the obtained mathematical model of the concrete state diagram during the calculation by different methodics of strength of the normal cross-sections of bendable reinforced concrete elements are presented.
 It has been determined that a promising direction for further experimental and theoretical research is the study of the application of the developed methodics of graphical building and mathematical descripting of concrete deforming diagrams under conditions of uniform and non-uniform compression to the calculation of concrete and reinforced concrete elements that are operated under the action of long-term and short-term low-cycle loadings.

Effect of inherent microcrack populations on rock tensile fracture behaviour: numerical study based on embedded discontinuity finite elements

Inherent microcrack populations have a significant effect on the fracture behaviour of natural rocks. The present study addresses this topic in numerical simulations of uniaxial tension and three-point bending tests. For this end, a rock fracture model based on multiple intersecting embedded discontinuity finite elements is developed. The inherent (pre-existing) microcrack populations are represented by pre-embedded randomly oriented discontinuity populations. Crack shielding (through spurious locking) is prevented by allowing a new crack to be introduced, upon violation of the Rankine criterion, in an element with an initial crack unfavourably oriented to the loading direction. Rock heterogeneity is accounted for by random clusters of triangular finite elements representing different minerals of granitic numerical rock. Numerical simulations demonstrate the strength lowering effect of initial microcrack populations. This effect is substantially stronger under uniaxial tension, due to the uniform stress state, than in semicircular three-point bending having a non-uniform stress state with a clear local maximum of tensile stress.

On the reliability of residual stress measurements in unidirectional carbon fibre reinforced epoxy composites

The present work introduces a novel methodology to analyse non-uniform residual stresses in composite materials. For robust determination of stresses in complex structures made of different layers, it is first necessary to prove that residual stress analysis in a single layer structure can reliably be accomplished. In present work a unidirectional carbon fibre reinforced epoxy is investigated. For residual stress determination, the integral incremental hole drilling method is used. It is revealed that the standard evaluation formalism for non-uniform stress analysis in isotropic structures is not applicable. A novel methodology based on the formalism for uniform stress analysis in orthotropic materials is introduced and applied for determining non-uniform residual stress states in depth. For calibration, a known load is induced by bending of samples. By comparing data obtained with the known bending stresses, the reliability of measurements is analysed and the novel formalism introduced is validated.

Static strength of brittle materials under multiaxial nonuniform stress states: A novel statistical model for assessing size effects

AbstractIn this paper, a model for the assessment of size effects on quasi‐static strength of brittle materials subjected to applied load inducing a nonuniform stress distribution within the material volume is proposed. An equivalent stress computed through finite element analysis is introduced in the model to account for the effect of the stress gradient within the loaded volume. The defect size distribution is modelled, differently from the literature, with the largest extreme value distribution. The proposed model has been validated with datasets available in the literature and obtained through bending tests on concrete specimens. For each type of test, the model permits to properly assess size effects. Due to its general formulation, a model for the strength variation with respect to the loaded volume, regardless of the testing type, was also obtained, further proving its effectiveness.

Physical modeling of deformation and filtration processes in low-permeability reservoir rocks when implementing the directional unloading method

This article describes the results of physical modeling of deformation and filtration processes in low-permeability reservoir rocks of the Achimov deposits of the Urengoy gas condensate field. The experiments were carried out on a unique true Triaxial Independent Loading Test System (TILTS) of the Institute for Problems in Mechanics of the Russian Academy of Sciences. The effect of the non-uniform triaxial stress state on the character of deformation and filtration processes in rocks was studied. Real stresses that occur in the bottomhole formation zone when the pressure in the well decreases were created in the rock specimens. Experiments were carried out to simulate the stress state at the walls of the open hole and at the tip of the perforation hole. The geomechanical approach is shown to be promising for creating ways to improve the quality of wells; in particular, the adaptation of the directional unloading method for the conditions of a given reservoir is considered. These studies are essential both in fundamental scientific and practical terms to substantiate technological solutions in the development of fields with low-permeability reservoirs.

EXPERIMENTAL INVESTIGATION OF POROPERM PROPERTIES OF GEOMATERIALS IN NONUNIFORM STRESS FIELD

The research methodology for anisotropic permeability of geomaterials due to nonuniform stress state is theoretically justified and tested on a laboratory scale. The poroperm properties of fine grain sand and cryogel are investigated in diametral compression tests of cylindrical specimens with a center hole. The time-independent flow rate is measured in various areas of side surfaces of the specimens. The inverse coefficient problem on empirical permeability–effective stress relationship is formulated, and its solvability is demonstrated.

Analysis of non-uniform residual stress state in plates with in-plane and transverse heterogeneities

In the present paper, we describe a model of a prestressed inhomogeneous body and provide the variational and weak statements. On its basis, we study a problem of mixed vibrations of a non-uniform plate with inclusions and a sandwich-structured three-ply plate under the conditions of the residual stress-strain state. We build the numerical finite-element solution on the basis of the weak problem statement and analyze the effect of the prestress states on its frequency response functions. In addition, we identify the prestress level in the middle layer of the composite plate by the data on frequency characteristics measurements.

Effects of nonuniform initial stress state on apparent fracture toughness

We analyze the nonuniform stress state in the vicinity of the fracture tip and its impact on apparent fracture toughness. It is shown that prescribing the boundary conditions at the deformed fracture faces allows one to take into account the effect of nonuniform tectonic stresses acting in the plane of the fracture. We conclude that the fracture may take an ellipsoidal form (aspect ratio departs from unity) as a result of interactions with anisotropic distribution of initial stresses, which leads to nonuniform growth in longitudinal and vertical directions. An expression for the effective stress intensity coefficient (fracture toughness) is obtained as a function of the nonuniform initial stress state. A simplified asymptotic approximation to the solution for the effective apparent fracture toughness is given, which may be further implemented into the near-tip asymptotics used in the form of a tip element in the numerical implementation of a Planar3D approach to hydraulic fracture simulation.

Особенности процессов деформирования монокристаллического никелида титана при действии импульса всестороннего сжатия

Using the example of single-crystal titanium nickelide, the importance of taking into account the volume compressibility anisotropy when calculating the processes of elastoplastic deformation in materials with cubic symmetry of elastic properties is shown. It is shown that the process of uniform volumetric deformation corresponds to the process of non-uniform stress state for materials with cubic symmetry of properties for some orientations of the calculated coordinate system relative to the directions of the main crystallographic axes. The index surface of volume compressibility (or the reciprocal of it - the compression modulus) has a non-spherical shape and is a function of Euler angles. This is shown for the first time by solving a model problem - determining the stress and strain states of a spherical body made of single-crystal titanium nickelide under the action of a comprehensive compression pulse. In the general case of orienting the calculated coordinate system relative to the directions of the main crystallographic axes, an initially spherical body of single-crystal titanium nickelide is deformed into a biaxial ellipsoid under the influence of a comprehensive compression pulse.

Implementation of Incremental Yield Condition for Continual Problems with Singularity

The limit elastic state of an infinitely large half-plane under the action of concentrated vertical and horizontal forces has been considered. The gradient yield condition specifying the elasto-plastic material yielding initial moment at non-uniform stress state is used as the limit state criterion. The analytical expressions allowing to interpret the result in the singular point have been derived.

An Expanding Cavity Model for Indentation Analysis of Shape Memory Alloys

Abstract The mechanical and functional responses of shape memory alloys (SMAs), which are often used in small volume applications, can be evaluated using instrumented indentation tests. However, deciphering the indentation test results in SMAs can be complicated due to the combined effects of the non-uniform state of stress underneath the indenter and stress-induced phase transformation. To address this issue, an expanding cavity model (ECM) applicable to spherical indentation of SMAs is developed in this work based on an analytical solution for an internally pressurized hollow sphere. Analytical expressions for key indentation parameters such as the mean contact pressure and size of the transforming zone are obtained, whose validity is evaluated by recourse to finite element simulations and published experimental data for a Ni–Ti alloy. It is shown that the ECM predicts the above parameters reasonably well for indentation strains varying from 0.01 to 0.04. Also, a method is proposed to determine the critical stress required to initiate phase transformation under uniaxial compression based on the application of the ECM to interpret the indentation stress–strain response.

Experimental determination of the shear strength of peat from standard undrained triaxial tests: correcting for the effects of end restraint

Conventional triaxial tests on peats are strongly criticised due to the very high shear strength parameters obtained from standard data elaboration, leading to unrealistic factors of safety when used in geotechnical design and assessment. Various operational approaches have been proposed in the literature to overcome this difficulty; however, they seem to lack consistent mechanical background. Some of the issues related to the shear strength evaluation of peats from triaxial tests come from the non-uniform stress and strain states developing in the samples well before failure is attained, due to end restraint effects. Undrained triaxial compression tests were performed on reconstituted peat to examine the influence of end restraint on the deviatoric stress, excess pore pressure and deviatoric strain response. Samples were tested with standard rough end platens and with modified platens to reduce the friction between the sample and bottom and top caps. Four different initial height-to-diameter ratios were examined, to reduce the consequences of rough end platens on the sample response. The results indicate that end restraint contributes dramatically to overestimating the shear strength of peat, due to the increase in both the calculated deviatoric stress and the measured excess pore pressure at the bottom of the sample. Suggestions are given to quantify the influence of end restraint in the interpretation of standard data, in an attempt to suggest viable procedures to determine more reliable effective and undrained shear strength parameters from standard triaxial tests.