Critical Stress State Research Articles

UH model considering temperature effects

The influences of temperature on the mechanical behavior of saturated clays are discussed first. Based on the concept of true strength and the revised calculation method of the potential failure stress ratio, the equation of the critical state stress ratio for saturated clays under different temperatures is deduced. Temperature is introduced as a variable into the UH model (3-dimensional elastoplastic model for overconsolidated clays adopting unified hardening parameter) proposed by Yao et al. and then the UH model considering temperature effects is proposed. By means of the transformed stress method proposed by Yao et al., the proposed model can be applied conveniently to 3-dimensional stress states. The strain-hardening, softening and dilatancy behavior of overconsolidated clays at a given temperature can be described using the proposed model, and the volume change behavior caused by heating can also be predicted. Compared with the modified Cam-clay model, the proposed model requires only one additional parameter to consider the behavior of the decrease of preconsolidation pressure with an increase of temperature. At room temperature, the proposed model can be changed into the original UH model and the modified Cam-clay model for overconsolidated clays and normally consolidated clays, respectively. The considered temperature range here is from the melting point to the boiling point of the pore water (e.g. the experimental temperatures (20°C-95°C) mentioned in this paper are within this range). Comparison with existing test results shows that the model can reasonably describe the basic mechanical behavior of overconsolidated clays under various temperature paths.

Direct Shear Tests on JSC-1A Lunar Regolith Simulant

A series of direct shear tests were conducted on the JSC-1A lunar regolith simulant in a 101.6-mm- (4-in.-) diameter container. The direct shear test provides a unique mode of failure that aids the development of excavation tools for the Moon. Relative density and normal load were varied to study the strength behavior of such granular material at peak and critical state conditions. The values of the internal friction angle ranged from 30 to 70°. A relationship between the internal friction angle of the direct shear and the published triaxial compression test results is presented. Additionally, the measured dilatancy angle is related to the difference in peak and critical state stress friction angles.

Stiffening of smectite buffer clay by hydrothermal effects

Smectite clay is a major engineered “buffer” barrier in repositories for high-level radioactive waste since it provides the waste canisters with a low-permeable embedment that minimizes canister stresses caused by earth shocks and tectonics by being ductile and homogeneous. The hydrothermal conditions prevailing in deep repositories cause some loss and degradation of the buffer and stiffening by precipitation of cementing matter, like quartz, cristobalite and iron compounds emanating from the clay or from the canisters. Thus, chemical reactions leading to cementation can prevent self-sealing of fissures caused by desiccation in the early stage of maturation of the buffer and increase its stiffness so that critical stress conditions may be generated in the canisters.

Characterization of the Elastic-plastic Region Based on Magnetic Memory Effect

Detecting stress concentration, especially critical stress state leading to structure damage or failure, is one of the most important tasks of equipment diagnosis. Metal magnetic memory technique needs further research to evaluate stress concentration quantitatively due to ambiguous physical mechanism, though it has potential to detect early defects in ferromagnetic materials. Mild Q235 steel defective specimens in demagnetization state were loaded in tension up to visible necking, with magnetic memory signals measurement made at increasing stress levels. Magnetic signals varied greatly under first several loadings and subsequently tended to stability in the elastic region, which showed that the magnetization always approaches the anhysteretic magnetization curve and was explained by the theory of magnetomechanical effect. In the plastic stage, an abnormal wave occurred in the stress concentration zone and its height value was sensitive to plastic deformation levels and dependent on the distance between the probe and defect, in accordance with the simulation results based on the magnetic dipole model. Different magnetic signal characteristics in the elastic-plastic region indicate that the magnetic memory technique can identify macroyielding and early damage, which is of profound significance for ensuring safe operation of equipment in service.

Sites of Rupture in Human Atherosclerotic Carotid Plaques Are Associated With High Structural Stresses

It has been hypothesized that high structural stress in atherosclerotic plaques at critical sites may contribute to plaque disruption. To test that hypothesis, 3D fluid-structure interaction models were constructed based on in vivo MRI data of human atherosclerotic carotid plaques to assess structural stress behaviors of plaques with and without rupture. In vivo MRI data of carotid plaques from 12 patients scheduled for endarterectomy were acquired for model reconstruction. Histology confirmed that 5 of the 12 plaques had rupture. Plaque wall stress (PWS) and flow maximum shear stress were extracted from all nodal points on the lumen surface of each plaque for analysis. A critical PWS (maximum of PWS values from all possible vulnerable sites) was determined for each plaque. Mean PWS from all ulcer nodes in ruptured plaques was 86% higher than that from all nonulcer nodes (123.0 versus 66.3 kPa, P<0.0001). Mean flow maximum shear stress from all ulcer nodes in ruptured plaques was 170% higher than that from all nonulcer nodes (38.9 versus 14.4 dyn/cm2, P<0.0001). Mean critical PWS from the 5 ruptured plaques was 126% higher than that from the 7 nonruptured ones (247.3 versus 108 kPa, P=0.0016 using log transformation). The results of this study show that plaques with prior ruptures are associated with higher critical stress conditions, both at ulcer sites and when compared with nonruptured plaques. With further validations, plaque stress analysis may provide additional stress indicators helpful for image-based plaque vulnerability assessment.

Microscopic phase-dependent residual stresses in the machined surface layer of two-phase alloy

Residual stresses in the machined surface layer, which affect fatigue crack nucleation and stress corrosion cracking especially in aerospace engines and gas turbines for power generation, depend on microstructures in case of machining a multiple-phase alloy. Hence, the microscopic phase-dependent residual stresses should be known when a machined part is used under critical stress conditions and circumstances. In the present paper, finite element modeling of machining two-phase alloys has been developed for obtaining the residual stresses in the machined surface layer. Iron and steels, which consist of different volume fractions of ferrite and eutectoid pearlite, were selected as work materials to be machined. First, it was confirmed that the calculated results agree well in chip formation and cutting forces with experimental ones. Then, residual stresses in the machined surface layer were obtained for different carbon contents and regular/random arrangements of microstructure. As a result, it is found that the microstructure of the workpiece has a great influence on the residual stress distribution on the machined surface and that tensile surface residual stress on pearlite is much larger than that on ferrite. Finite element machining of the work material with stripe arrangement of ferrite and pearlite revealed that the peak of residual stress would be reduced by decreasing the width of stripes of ferrite and pearlite.

A volume–stress model for sands under isotropic and critical stress states

A simple volume–stress model for granular soils under isotropic and critical stress states is presented. The model is formulated in the double logarithmic space of void ratio versus mean stress. It has the same number of parameters as used in the Cam Clay models to describe isotropic compression, with one additional parameter to define the critical state curve. The model can qualitatively describe a number of unique features of sand behaviour. Comparison with experimental data indicates that the model is able to predict well the volume change of a range of different sands subjected to isotropic and triaxial compression.

Finite element analysis of cancellous bone failure in the vertebral body of healthy and osteoporotic subjects

The aim of this work is to assess the fracture risk prediction of the cancellous bone in the body of a lumbar vertebra when the mechanical parameters of the bone, i.e. stiffness, porosity, and strength anisotropy, of elderly and osteoporotic subjects are considered. For this purpose, a non-linear three-dimensional continuum-based finite element model of the lumbar functional spinal unit L4-L5 was created and strength analyses of the spongy tissue of the vertebral body were carried out. A fabric-dependent strength criterion, which accounts for the micro-architecture of the cancellous bone, based on histomorphometric analyses was used. The strength analyses have shown that the cancellous bone of none of the subject types undergoes failure under loading applied during normal daily life like axial compression; however, bone failure occurs for the osteoporotic segment, subjected to a combination of the compression preloading and moments in the sagittal or in the frontal plane, which are conditions that may not be considered to occur 'daily'. In particular, critical stress conditions are met because of the high porosity values in the horizontal direction within the cancellous bone. The computational approach presented in the paper can potentially predict the material fracture risk of the cancellous bone in the vertebral body and it may be usefully employed to draw failure maps representing, for a given micro-architecture of the spongy tissue, the critical loading conditions (forces and moments) that may lead to such a risk. This approach could be further developed in order to assess the effectiveness of biomedical devices within an engineering approach to the clinical problem of the spinal diseases.

Modelling unsaturated soil behaviour during normal consolidation and at critical state

An analysis of results from published laboratory tests on Jossigny silt and Barcelona clayey silt is presented to confirm the existence of a unique capillary bonding function linking the quotient between unsaturated and saturated void ratio, at the same mean average skeleton stress, to a single capillary bonding scalar variable. The analysis confirms that the same capillary bonding function applies to both normally consolidated and critical stress states. The above two experimental sets with the addition of further published data for Speswhite Kaolin are also used to study the relationship between unsaturated critical shear strength, mean average skeleton stress and capillary bonding variable. The results of such analysis are assessed in the light of a similar modelling framework proposed in the literature.

Atomistic Formation Mechanism of Multiple Shear Bands in Amorphous Metals

At room temperature, plastic deformation of amorphous metals is localized in narrow bands, so called shear bands (SBs), which is a key issue of their brittle/ductile deformations. The extremely disordered structure and the abrupt fracture obtained in the experiments hinder us from making clear the nature and dynamics of SBs. In this study, atomistic modeling to produce the multiple shear bands (MSBs), not single shear band, was proposed, and the evolution process of MSBs including their coalescence and stationary was investigated using molecular dynamics simulations. We prepared a plate of Cu-Zr binary amorphous alloy model by the melt-quench process, and then performed uniaxial tensile and compressive tests under plane stress condition. During the loading, the deformation was suddenly localized in narrow bands shortly after the onset of yielding. The propagation of SBs was accompanied with drastic stress drop and significant local heating caused by the friction of atoms. Also, critical stresses of SB nucleation considerably differed between under tension and compression. This result indicates that Tresca or von Mises criterion, commonly used as a yield condition in the crystalline metals, is not appropriate to describe the yielding of the amorphous metals. The SB angles to the loading axis are observed to be 45∼57° under tension, while 40∼46° under compression. These angles agree well with the fracture angles observed in the experiments with multi-component metallic glasses. It is concluded that the critical stress state of SB nucleation is dependent on not only the shear stress but also the stress normal to the SB, and it can be described by Mohr-Coulomb criterion.

Dynamics of a spherical viscoelastic shell: Implications to a criterion for fragmentation/expansion of bubbly magma

This paper investigates dynamics of a spherical bubble surrounded by a viscoelastic fluid. The purpose of the study is to understand the parameters which control expansion and fragmentation of bubbly magma by decompression. In particular, we focus on which occurs first, fragmentation or expansion. Supposing that rupture of the bubble wall occurs in a critical stress condition, we calculate the change of the bubble radius and tensile stress at the bubble wall for various decompression rates. Conditions in which tensile stress is stored in the shell are represented in terms of dimensionless parameters. The results are interpreted as follows: when magma viscosity is larger than a critical value, and the decompression time is shorter than viscous expansion time, tensile stress is stored before expansion; when magma viscosity is smaller than the critical value, tensile stress is not stored, no matter how rapid the decompression. Although it is a generally accepted theory that fragmentation is effected by stress conditions and decompression time, exactly how decompression time ( t 1) effects the fragmentation is not yet fully understood. This study demonstrates that the stress condition is controlled by the length of the decompression time not relative to the viscoelastic relaxation time ( t 1 / τ), but relative to the viscous expansion time ( t 1 / τ l rlx). As suggested by recent experimental studies, the decompression time relative to viscoelastic relaxation time ( t 1 / τ) is also significant to the fragmentation process itself. It indicates that the decompression time effects the fragmentation not through the stress condition. However more work must be completed to fully understand the particular relationship between the decompression time and relaxation time in terms of its influence on fragmentation.

Differential influence of open surgery and sepsis on the circulating insulin-like growth factors and their binding proteins as representative metabolic markers

Objectives: In critical illnesses and stress conditions many endocrine systems are disturbed. In the current study we determined the influence of open surgery, post-operative sepsis and its early therapy on the components of the insulin-like growth factor (IGF) system in patients with malignant gastric or pancreatic tumors. Design and methods: Twenty-one patients and eighty-one age- and sex-matched healthy subjects were included in this study. IGF-I, IGF-II, IGF binding proteins (IGFBPs), cortisol, insulin and protein concentrations (total, albumin and IgG) were determined pre-operatively, post-operatively, when sepsis was diagnosed and 48 h after initiating therapy. Results: The concentrations of circulating IGF-I, IGF-II and IGFBP-3 were significantly lower in pre-operative patients compared to healthy subjects. Sepsis caused a further decrease in IGF-I and IGFBP-3 but an increase in IGFBP-1, IGFBP-2 and IGFBP-4 resulting in a redistribution of IGF molecules from ternary to binary complexes. Conclusions: The presence of malignant gastric or pancreatic tumors followed by post-operative sepsis caused a serious misbalance in components of the IGF system which failed to recover during the time of our longitudinal study.

Fracture properties of notched and pre-cracked specimens of a tempered martensitic steel at low temperature

The fracture properties of the 9CrWVTa reduced-activation tempered martensitic steel Eurofer97 were studied in the lower ductile to brittle transition. Sub-sized pre-cracked compact tension and notched tensile specimens were tested. Finite element simulations were undertaken to supplement the mechanical tests and to calculate the local stress/strain fields around the stress concentrators. Based upon a local approach of quasi-cleavage, a critical stress state was calibrated on the fracture toughness data measured with the compact tension specimens. This critical stress state was shown to predict the evolution with temperature of the lower bound curve of fracture toughness data. It was also found to predict very well the failure load and failure displacement of the notched specimens.

Coupled fluid/structure analyses of the MEGAPIE spallation source target during transients

The paper describes some R&D activities undertaken in support of the design and safe operation of MEGAPIE (MEGAwatt PIlot Experiment) spallation source target, which is scheduled to be irradiated by a proton beam in the SINQ facility at the Paul Scherrer Institute in 2006. The target material is lead bismuth eutectic (LBE), which also acts as the primary coolant. As a consequence of the spallation reactions, about 600 kW of heat would be deposited in the target during operation, and considerable R&D effort is being expended to demonstrate continuing coolability and structural integrity under a variety of operational and abnormal conditions. The paper gives three examples of transient analyses carried out as part of the safety assessment of the target: (1) a beamline trip and recovery; (2) failure of the primary electro-magnetic pump (EMP); (3) failure of the secondary EMP (used to cool the base of the target). The study involves the simultaneous application of a system-analysis code, in our case a version of RELAP5, a computational fluid dynamics (CFD) tool (CFX-4), and a structural analysis code (ABAQUS). The RELAP5 code is used to provide transient boundary conditions for a localized conjugate heat transfer analysis of the lower target region, undertaken using CFD, and includes the feed-back effects arising from the secondary cooling and control systems. A conjugate heat transfer problem is then solved using CFD, which provides time-dependent thermal and flow data within the LBE, together with the thermal and mechanical loads to the target structures. Finally, an in-house interface program is employed to transfer mesh geometry, model topology and (time-dependent) thermal/mechanical data to enable stress analysis of the principal lower-target structural components to be performed. It is demonstrated that none of the transients considered result in critical stress conditions occurring in the target components, but that further operation is not recommended unless both pumps are fully operational.

Work of adhesion in laser-induced delamination along polymer-metal interfaces

Laser-induced delamination is a recent technique aimed at characterizing adhesive strength of thin polymer coatings on metal substrates. A laser pulse is used to create a blister that initiates further delamination of the film under pressure. To process the experimental data a simple elastic model was developed. The model predicts values for the blister height and pressure in fair agreement with the experimental findings. The critical stress state required for delamination and the work of adhesion are derived. To account for possible plastic deformation computer simulations using finite elements with a mixed mode cohesive zone were carried out. The polymer coating is described with a constitutive law that includes an elastic response, yielding and hardening with increasing strain. The stress fields calculated with finite element model are in agreement with those predicted by the elastic model and it suggests that the contribution of plastic deformation to the work of adhesion is rather limited. Comparative analysis of these two approaches is presented. The theoretical predictions are compared to experimental results obtained for the 40μm thick polyethylene terephthalate film on steel substrate.

Hydromechanical modeling of critically stressed and faulted reservoirs

A critical stress state around a faulted reservoir prior to production and injection is an important factor in the hydromechanical responses during production. The purpose of this article is to show how the long-range correlations of production rates observed in several oil fields can be reproduced with hydromechanical modeling of a faulted reservoir subjected to a critical stress state prior to production operations. The modeling implies that the permeability distribution in a reservoir that is in a critical stress state is time dependent. A finite-element model with fully coupled geomechanics and flow was used. The modeling has been applied to an approximation of the complex structure of the Gullfaks reservoir in the North Sea, including the far-field stress regimes and fault systems, although the model is considerably simplified in the search for generic, instead of field-specific, principles. Under a critical stress state, a small change of the effective stress caused by fluid-pressure changes in the reservoir is likely to trigger reservoirwide hydromechanical reactions, irrespective of whether the change was at a local scale or a reservoir scale. Such responses include fault reactivations, volumetric and shear strain changes, induced deformation evolution, and permeability changes. With a permeability enhancement model, permeability increase is expected if fault reactivation and shear strain change occur. In contrast, if the in-situ stress is not at a critical state, the reservoir reacts locally. In this case, the deformation is mainly elastic, and no permeability enhancements occur. Therefore, the impact of inelastic geomechanical interactions (particularly shear deformation) at a critical point is likely to be very influential on reservoir fluid flow. This critical-point behavior gives explanation to the widespread field observations of long-range correlations in well rates, which are inferred to be manifestations of reservoir-scale mechanical responses involving faults, instead of the local hydraulic links that Darcy flow between wells implies. Permeability changes occur during inelastic deformation despite injection pressures being much lower than the confining stress (the minimum total principal stress). The increase in permeability in the reservoir rocks is caused by the dilation normal to the surface of the faults and/or fractures, which is caused by the shearing along the faults and/or fractures, instead of hydrofracturing. This confirms that dilational shearing can develop despite the effective stress regime being compressive. Dilational shearing has a major impact on the deformation of reservoir rock during production and is an important mechanism for generating conductivity on fractures under a fluid pressure that is lower than the confining stress, possibly even in reservoirs under depletion.

Coupled geomechanics–flow modelling at and below a critical stress state used to investigate common statistical properties of field production data

Abstract An areal model of a fractured/faulted reservoir with 49 wells is developed that incorporates fully-coupled geo-mechanics and fluid flow. It is a generic example of a pattern waterflood although it is inspired by a parallel study of the Gullfaks reservoir in the North Sea, in which stress-related, fault-related and long-range correlations in rate fluctuations are observed. Based on this model, three scenarios are examined in terms of different initial stress states prior to production, each of which involves 36 months of production and injection in the presence of fracture sets and faults. The results support the concept that the long-range, stress-related and fault-related characteristics of correlations in rate fluctuations, observed not only in the Gullfaks data, but also in several other fields worldwide, are symptomatic of a system near a geomechanical critical point. These characteristics are not observed in models that are sub-critical. Short-range rate correlations are likely to exist where there are highly permeable zones between producers and injectors. Long-range rate correlations occur only within critically-stressed regions where there is active shearing or fault reactivation. The modelling results are consistent with field evidence suggesting that incipient shearing is an important mechanism coupled with reservoir flow behaviour.

Cohesive Zone Description and Quantitative Analysis of Glassy Polymer Fracture

Crazing is described with a viscoplastic cohesive zone which accounts for its initiation for a critical stress state, the thickening of the craze surfaces up to the failure of the craze fibrils which corresponds to the nucleation of a crack locally. A calibration of the parameters of such a cohesive zone is presented for PMMA (Polymethyl methacrylate). The rate dependent formulation of the cohesive zone is shown necessary to capture the rate dependency of the glassy polymer toughness.

Calibration of a viscoplastic cohesive zone for crazing in PMMA

In a numerical analysis of mode I fracture in amorphous polymers, Estevez et al. [Estevez R, Tijssens MGA, Van der Giessen E. Modelling of the competition between shear yielding and crazing in glassy polymers. J Mech Phys Solids 2000;48:2585–617] have shown that the material toughness is governed by the competition between the time scales related to shear yielding and crazing. The present study aims at calibrating the parameters involved in this description, for a commercial PMMA. An elastic–viscoplastic constitutive law featuring softening upon yielding and hardening at continued deformation is used for the bulk while crazing is described with a viscoplastic cohesive zone. The three steps of crazing with initiation for a critical stress state, thickening of the craze surfaces and breakdown of the craze fibrils for a critical opening are characterized separately. In particular, it is demonstrated that the use of a viscoplastic cohesive zone is necessary to capture the variation of the toughness with loading rate. For PMMA, the related energy release rate is shown to depend primarily on the craze critical opening and the craze thickening kinetics while craze initiation is of minor importance for the quasi-static loading conditions under consideration here.

Local Maximal Stress Hypothesis and Computational Plaque Vulnerability Index for Atherosclerotic Plaque Assessment

It is believed that atherosclerotic plaque rupture may be related to maximal stress conditions in the plaque. More careful examination of stress distributions in plaques reveals that it may be the local stress/strain behaviors at critical sites such as very thin plaque cap and locations with plaque cap weakness that are more closely related to plaque rupture risk. A "local maximal stress hypothesis" and a stress-based computational plaque vulnerability index (CPVI) are proposed to assess plaque vulnerability. A critical site selection (CSS) method is proposed to identify critical sites in the plaque and critical stress conditions which are be used to determine CPVI values. Our initial results based on 34 2D MRI slices from 14 human coronary plaque samples indicate that CPVI plaque assessment has an 85% agreement rate (91% if the square root of stress values is used) with assessment given by histopathological analysis. Large-scale and long-term patient studies are needed to further validate our findings for more accurate quantitative plaque vulnerability assessment.