Non-homogeneous Stress Field Research Articles

Forecasting the Strength Gaining Kinetics of the Concrete Hardening in the Abnormal Conditions

Introduction. During construction of the massive monolithic reinforced concrete structures, concrete hardening takes place in the unsteady abnormal temperature conditions, which, along with the massiveness of the structure and concrete recipe features, influence significantly on the concrete strength gaining kinetics. The non-homogeneity of the temperature field leads to the difference of the hardening concrete strength and deformation indicators in the different points of a structure at one and the same time, eventually resulting in formation of the non-homogeneous stress field. Due to the insufficient number of publications dedicated to the topic of forecasting the dependence of the strength of concrete on the time and temperature conditions of its hardening and recipe features, the research in this field becomes a relevant objective. Thus, the aim of the work is to determine a mathematical dependence of the strength gaining kinetics of different concretes on the reduced time of hardening parameter, the dependence which is necessary for calculating the thermal stress of the massive reinforced concrete structures at early-age hardening in the unsteady temperature conditions.Materials and Methods. The data received during the authors’ experiments and calculations, as well as the data available in the existing publications and regulatory documents was used. Theoretical assessment of the concrete strength gaining kinetics, depending on the cement type hardening kinetics, was done. The assessment took into account the actual heat of hydration of the hardening concrete and its temperature, including the unsteady one, and was based on the following provisions: the kinetics of cement heat of hydration can be considered as the cement hydration degree and strength gaining indicator; the cement hydration degree in a given moment of time determines the porosity of a cement brick, and the strength of a cement brick and concrete is determined by the porosity thereof.Results. The dependence of the relative strength of concrete on the reduced time of hardening parameter in the unsteady temperature conditions is determined for the concretes having different kinetics of hardening in the normal conditions. The good convergence of the proposed dependence with the results of experimental studies and some normative documents is shown.Discussion and Conclusion. The scientific concepts on the relative strength assessment of the concrete, hardening in the abnormal temperature conditions, have been further developed based on the hypothesis of the concrete hardening kinetics dependence on the kinetics of cement heat of hydration, taking into account the degree of concrete aging per "reduced time of hardening". It’s worth to use this dependence for calculating the thermal stress of the massive reinforced concrete structures at early-age hardening. The efficiency of assessing the strength gaining kinetics of the various concretes, hardening in the unsteady temperature conditions, by using the "reduced time" parameter, has been shown and substantiated. The heat of hydration kinetics and the total porosity magnitude, determined by the hydration degree indicator, have been taken into account. The application of the "reduced time of hardening", depending on the concrete aging degree to assess the relative strength of concrete, with regard to its recipe features, has been substantiated.

The calculation of the parameters of disc-shaped hydraulic fracturing crack propagating in hard rock roofs of a coal seam near the in-seam working

The model of geomechanical state of the disc-shaped hydraulic fracturing crack that propagates in hard rocks near the in-seam working was developed. The peculiarity of the model is in non-homogeneous stress field which is conditioned by the presence of the working. This field plays an important role in calculating the trajectory of the crack propagation and under certain conditions it drastically changes the direction of the initial crack. The problem of the rock massif stress state in the vicinity of the in-seam working is narrowed to the second exterior boundary value problem of the elasticity theory for integrated singular equation. It can be reached by substituting limit stress coal seam marginal zones by their acting stresses. Analyzing the results it is defined that when the ratio of the working liquid pressure to the gravitational hard rock pressure equals four units the trajectory of the crack is linear and coincides with the direction of the initial crack. If the ratio of the working liquid pressure to the gravitational pressure changes from three to four units the trajectory of the crack looks as a gently sloping curve that insignificantly changes its direction towards the initial crack.

Synergistic impeding of phonon transport through resonances and screw dislocations

Improving the control of heat flow at the nanoscale is essential for promoting its applications in many fields, such as energy conversion, thermal informatics, and communication technologies. Here we perform a systematic study on the synergistic effect of screw dislocations and surface resonators on thermal transport of Si nanowires and the corresponding mechanisms based on molecular dynamics simulations. We uncover that screw dislocations reduce the thermal conductivity by enhancing the anharmonicity of nanowires due to the nonhomogeneous stress field. For resonant structures, we demonstrate that the suppression of relaxation time is the main mechanism for thermal conductivity reduction. The suppression of relaxation time by more than two orders of magnitude below 4 THz dramatically reduces the resonant structure thermal conductivity, while the previously proposed group velocity reduction mechanism can only impede phonon transport beyond 4 THz slightly. By comparing the mechanisms produced by dislocations and resonators, we find that the resonators have a stronger effect over screw dislocations in impeding the phonon transport at low frequencies while it becomes opposite at high frequencies. As a result, they can be combined together to manipulate phonon transport synergistically at all frequencies. Our findings not only provide insights into the mechanisms of thermal conductivity engineering by screw dislocations and surface resonators, but they also illustrate a paradigm for ultralow thermal conductivity design through the tailoring of the entire frequency range of phonon transport.

Spatially Varying Small-strain Stiffness in Soils Subjected to K0 Loading

Grain-scale characteristics and formation history determine spatial variability in granular masses. We investigate the effect of spatially varying stiffness on the load-deformation response under zero-lateral strain conditions using numerical simulations of correlated random fields, where the granular medium is represented by a non-linear stress-dependent meso-scale model. Results show that stiffness heterogeneity results in higher global compressibility as compared to the homogeneous medium with the same arithmetic mean stiffness. Furthermore, the non-homogeneous stress field that develops inside the granular mass is characterized by focused load transfer along columnar regions, higher stress anisotropy and lower horizontal-to-vertical stress ratio K0 than in a granular medium of homogenous stiffness. As the applied stress increases, the inherent stress-dependent response of the granular material leads to a more homogenous stress field. While greater variance in stiffness causes lower global stiffness, a longer correlation length results in greater variance in global mechanical response among multiple realizations.

Combined notch and size effect modeling in a local probabilistic approach for LCF

In recent years a local probabilistic model for low cycle fatigue (LCF) based on the statistical size effect has been developed and applied on engineering components. Here, the notch support extension based on the stress gradient effect is described in detail, as well as an FEA-based parameter calibration. An FEA is necessary to simulate non-homogeneous stress fields in non-smooth specimens which exhibit gradients and determine size effects. The hazard density approach and the surface integration over the FEA stress lead to geometry-independent model parameters. Three different materials (superalloys IN-939, Rene80, steel 26NiCrMoV14-5) and three different geometry types (smooth, notch, cooling hole specimens) are considered for a more comprehensive validation of the probabilistic LCF model and to demonstrate its wide application range. At the same time, a reduced testing effort is needed compared to deterministic model predictions with notch support.

Effect of micro-cracks in nonhomogeneous stress field on fracture instability in structural components

The paper analyses the effects of statistical distribution in sizes of micro-cracks on scatter of fracture toughness of steels under brittle conditions. The results are utilized for reliability assessment of selected functional parts. The reliability considered as a complementary probability of brittle fracture initiation is discussed in dependence on the character of statistical distribution of micro-crack sizes, mechanical properties of steel, mechanisms of energy dissipation during cracks propagation, variation of loading, stress state of functional part and its service life. This probability approach is compared with deterministic reliability access originating from computation of safety factor. Its rational evaluation as a function of acceptable probability of fracture instability provides high economical effects saving materials and energy.

A stochastic differential equations approach for the description of helium bubble size distributions in irradiated metals

A rate theory model based on the theory of nonlinear stochastic differential equations (SDEs) is developed to estimate the time-dependent size distribution of helium bubbles in metals under irradiation. Using approaches derived from Itô’s calculus, rate equations for the first five moments of the size distribution in helium–vacancy space are derived, accounting for the stochastic nature of the atomic processes involved. In the first iteration of the model, the distribution is represented as a bivariate Gaussian distribution. The spread of the distribution about the mean is obtained by white-noise terms in the second-order moments, driven by fluctuations in the general absorption and emission of point defects by bubbles, and fluctuations stemming from collision cascades. This statistical model for the reconstruction of the distribution by its moments is coupled to a previously developed reduced-set, mean-field, rate theory model. As an illustrative case study, the model is applied to a tungsten plasma facing component under irradiation. Our findings highlight the important role of stochastic atomic fluctuations on the evolution of helium–vacancy cluster size distributions. It is found that when the average bubble size is small (at low dpa levels), the relative spread of the distribution is large and average bubble pressures may be very large. As bubbles begin to grow in size, average bubble pressures decrease, and stochastic fluctuations have a lessened effect. The distribution becomes tighter as it evolves in time, corresponding to a more uniform bubble population. The model is formulated in a general way, capable of including point defect drift due to internal temperature and/or stress gradients. These arise during pulsed irradiation, and also during steady irradiation as a result of externally applied or internally generated non-homogeneous stress fields. Discussion is given into how the model can be extended to include full spatial resolution and how the implementation of a path-integral approach may proceed if the distribution is known experimentally to significantly stray from a Gaussian description.

Ab initiocontinuum model for the influence of local stress on cross-slip of screw dislocations in fcc metals

We develop a model of cross-slip in face-centered cubic (fcc) metals based on an extension of the Peierls-Nabarro representation of the dislocation core. The dissociated core is described by a group of parametric fractional Volterra dislocations, subject to their mutual elastic interaction and a lattice-restoring force. The elastic interaction between them is computed from a nonsingular expression, while the lattice force is derived from the $\ensuremath{\gamma}$ surface obtained directly from ab initio calculations. Using a network-based formulation of dislocation dynamics, the dislocation core structure is not restricted to be planar, and the activation energy is determined for a path where the core has three-dimensional equilibrium configurations. We show that the activation energy for cross-slip in Cu is $1.9\phantom{\rule{4pt}{0ex}}\text{eV}$ when the core is represented by only two Shockley partials, while this value converges to $1.43\phantom{\rule{4pt}{0ex}}\text{eV}$ when the core is distributed over a bundle of 20 Volterra partial fractional dislocations. The results of the model compare favorably with the experimental value of $1.15\ifmmode\pm\else\textpm\fi{}0.37\phantom{\rule{4pt}{0ex}}\text{eV}$ [J. Bonneville and B. Escaig, Acta Metall. 27, 1477 (1979)]. We also show that the cross-slip activation energy decreases significantly when the core is in a particular local stress field. Results are given for a representative uniform ``Escaig'' stress and for the nonuniform stress field at the head of a dislocation pileup. A local homogeneous stress field is found to result in a significant reduction of the cross-slip energy. Additionally, for a nonhomogeneous stress field at the head of a five-dislocation pileup compressed against a Lomer-Cottrell junction, the cross-slip energy is found to decrease to $0.62\phantom{\rule{4pt}{0ex}}\text{eV}$. The relatively low values of the activation energy in local stress fields predicted by the proposed model suggest that cross-slip events are energetically more favorable in strained fcc crystals.

Analysis of Dynamic Response of Concrete Using a Mesoscale Model Incorporating 3D Effects

Shock and impact loading often generates stress waves in the responding structural object with a drastic time and spatial variation. Consequently the transient response of the material involves not only high strain rate, but also a highly non-homogeneous stress field with respect to the mesoscale heterogeneity of the concrete-like materials. To comprehensively capture the material response and the underlying mechanisms under such loading conditions, the use of a mesoscale model is desirable. This paper discusses the development of a mesoscale model that describes reasonably the random mesoscopic structure of concrete materials and at the same time allows for the simulation of response under complex dynamic loads. Due to the complexity in the generation and meshing of the random aggregate structure of concrete, at the present stage the random mesoscale geometry is generated within a 2D plane. The use of a 2D representation of a concrete is common and may be acceptable in lower loading rate applications, however, under high rate loading a 2D model for concrete in compression could introduce noticeable errors due to an inability to fully capture the crucial lateral inertia confining effect. This special phenomenon is investigated in this paper, and a remedial modelling scheme is proposed to minimize the inaccuracy in a 2D mesoscale model for high strain rate loading. Finally, the experimentally observed strain rate increase factor is discussed in light of the mesoscale numerical modeling results.

Identification of non-homogeneous stress fields in dynamic experiments with a non-parametric method

Stress and strain fields are generally assumed homogeneous in high strain rate experiments. Therefore, only mean stress and strain are measured. However, this assumption is not valid for soft materials and/or very high strain rates. For heterogeneous dynamic tests, inverse techniques are usually proposed to identify the stress and strain fields. In this paper, a non-parametric method to identify the stress field is presented. This method is based on a force measurement on the specimen boundary and a displacement (strain) field measurement carried out by a digital image correlation technique. It is applied to measure the strain rate sensitivity of a synthetic rubber (Criblex 80). This new technique estimates the stress field with good accuracy.

Geometry and distribution of regional joint sets in a non-homogeneous stress field: case study in the Ebro basin (Spain)

Three regional joint sets striking N–S, E–W and WNW–ESE affect the Tertiary rocks of the central Ebro basin. From analysis of their chronological relationships and spatial distribution, it is concluded that they correspond to two different tectonic events. The N–S set (oldest) and the E–W set (younger) are present in the southern and central sectors, while the WNW–ESE joint set predominates in the northern one. The N–S joints propagated in response to joint-normal and fluid loads under an intraplate stress field with S Hmax oriented near N–S (related to forces caused by the convergence of Africa, Iberia and Europe and rifting at the Valencia trough) during the sedimentary infilling of the basin. These joints are only present in the southern part of the area. The E–W joint set in the southern-central sector records the same fracturing event as the WNW–ESE set does in the northern one. Its orientation was modified by the presence of the older N–S set in the south, which perturbed the regional stress field. The younger WNW–ESE and E–W joint sets are interpreted as unloading joints. These propagated as a consequence of flexural uplift and exhumation related to isostatic rebound at the Pyrenees and the Ebro foreland basin. A numerical approach is used to explain the inhomogeneous distribution of the N–S joint set in terms of their absence being controlled by the depth of the water table at the time of their formation.

Assessment of Internal Damping in Uniaxially Stressed Metals: Exponential and Autoregressive Methods

When a metallic material is highly stressed, its internal specific damping capacity increases showing a nonlinear behavior. In spite of this, the most part of experimental methods employ nonhomogeneous stress fields measuring only a volumetric average, often called structural damping. To overcome this problem the procedure herein presented extends the applicability of the plain traction or compression methods to higher frequency range (up to 300 Hz). The introduced methodology corrects for elastic energy and dissipated energy relative to the test machine and to the fixtures. The experimental procedure is based on the acquisition of a decay signal when the test machine excitation force has been removed. Two different methods to extract the pattern of internal damping versus material strain have been compared: one is based on least square exponential fitting while the other employs an autoregressive model. Best results have been obtained combining the two techniques taking into account also the variation of Young’s modulus with strain. The resulting curves of the loss factor as a function of strain amplitude for three steels and two cast irons are presented.

Stress tensor determination in France and neighbouring regions

The tectonic behaviour of different seismic regions of France is inferred from the properties of the local stress tensor obtained from focal mechanisms of regional earthquakes. Polarities of P-wave arrivals for several earthquakes are used in the inversion of the stress tensor and individual focal mechanisms. The principal axes and the shape of the tensor are closely related to the forces which generate seismic ruptures on pre-existing faults. We analyse 142 earthquakes of magnitude above 3.7 which occurred between 1965 and 1989. Good results are obtained for some regions. The northern Alps and the southern end of the Upper Rhinegraben show a quasi-compressive, strike-slip tectonic regime, with a maximum stress-axis oriented NW-SE. The tectonic regime changes to an extensional strike-slip type in the Rhenish Massif and the Lower Rhinegraben, the direction of the minimum stress-axis being NNE-SSW. The central and western regions of France (Central and Armorican Massifs) exhibit an extensional tectonic regime combined with strike-slip faulting. The minimum stress-axis strikes in a NE-SW direction. A strongly non-homogeneous stress field seems to be present in the southwestern Alps, and no unique stress tensor could be obtained for that region. This problem is likely to be related to a rapid variation of the stress field in space which could be expected, given the arc-like geometry of the mountain range. The Pyrenean domain is unresolved due to lack of data and, moreover, existing focal mechanisms are globaly inconsistent. Nevertheless, those mechanisms which are well constrained suggest a NNW-SSE to NW-SE direction of maximum stress in the western part of the Pyrenees. Thus, the stress field in France is fairly homogeneous at a regional scale for most of the territory except for the highly deformed belts.

Adaptive remeshing for shear band localization problems

Failure of earth structures or laboratory specimens of soils is often characterized by the existence of bands or surfaces at which strain localizes. Numerical simulation of shear band development has attracted the attention of many research groups during past years. Here it is proposed that adaptive remeshing techniques can be applied to better simulate strain localization problems in geotechnique. The algorithm has been previously applied to compressible fluid dynamics problems to capture discontinuities such as shocks. A new refinement functional has been introduced to improve quality of produced meshes. Finally, the algorithm is applied to solve inception and development of shear bands on both homogeneous stress fields and non-homogeneous stress fields.

Dynamic interaction of a propagating crack with an oblique fault

The behaviour of a fast running crack against an internal oblique fault in a brittle material (polymethylmethacrylate) was investigated by the use of high-speed photography and caustics. This problem is significant in rock mechanics, where the whole failure of the rock mass is often due to such dynamic interaction phenomena during earthquake activities. Interesting effects were disclosed when the rapidly moving crack was approaching the internal fault. The non-homogeneous stress field, which was created by the internal slant crack, forced the main propagating crack to a curved path, and simultaneously, to a deceleration of its velocity and eventually its arrest, as well as the variation of the only effective K I -stress intensity factor along almost all the field of propagation of the crack. The purpose of this paper is to investigate the conditions which govern the development of such phenomena.