Creep Instability Research Articles

Low Cycle Fatigue and Creep-Fatigue Interaction Behaviour of Reduced Activation Ferritic Martensitic (RAFM) Steels with Varying W and Ta Contents

Reduced activation ferritic/martensitic (RAFM) steels are candidate materials for the test blanket modules of ITER. Several degradation mechanisms such as thermal fatigue, low cycle fatigue, creep fatigue interaction, creep, irradiation hardening, swelling and phase instability associated irradiation embrittlement must be understood to estimate the component lifetime. The current work focuses on the effect of tungsten and tantalum on low cycle fatigue (LCF) and creep-fatigue interaction (CFI) behavior of four RAFM steels with varying W and Ta contents. Total strain controlled LCF experiments were performed under various strain amplitudes in the range +0.25% to +1% and temperatures (300 K to 873 K) in air at a constant strain rate of 3×10-3s-1 using a servo hydraulic fatigue testing system. CFI experiments were carried out at total strain amplitude of +0.6% and by applying strain hold of different durations (10 min and 30 min) in peak tension and peak compression. Both LCF and CFI life of the RAFM steels improved with the increase in tungsten and tantalum contents. Based on the amount of softening during continuous cycling, tungsten content was optimized at 1.4 wt. % and the tantalum content at 0.06 wt%. Stress relaxation obtained during creep-fatigue interaction studies showed close relation with the chemical composition of the RAFM steels. Other damaging parameters influencing fatigue life were dynamic strain ageing (DSA) occurring in the intermediate temperature regime and oxidation at elevated temperatures. Keywords: RAFM steel, low cycle fatigue, dynamic strain ageing, creep-fatigue interaction, oxidation

Transient creep and convective instability of the lithosphere

SUMMARY Laboratory experiments with rock samples show that transient creep, at which strain grows with time and strain rate decrease at constant stress, occurs while creep strains are sufficiently small. The transient creep at high temperatures is described by the Andrade rheological model. Since plate tectonics allows only small deformations in lithospheric plates, creep of the lithosphere plates is transient whereas steady-state creep, described by non-Newtonian power-law rheological model, takes place in the underlying mantle. At the transient creep, the effective viscosity, found in the study of postglacial flows, differs significantly from the effective viscosity, which characterizes convective flow, since timescales of these flows are very different. Besides, the transient creep changes the elastic crust thickness estimated within the power-law rheology of the lithosphere. Two problems of convective stability for the lithosphere with the Andrade rheology are solved. The solution of the first problem shows that the state, in which large-scale convective flow in the mantle occurs under lithospheric plates, is unstable and must bifurcate into another more stable state at which the lithospheric plates become mobile and plunge into the mantle at subduction zones. If the lithosphere had the power-law fluid rheology, the effective viscosity of the stagnant lithospheric plates would be extremely high and the state, in which large-scale convection occurs under the stagnant plates, would be stable that contradicts plate tectonics. The mantle convection forms mobile lithosphericplatesiftheeffectiveviscosityoftheplateisnottoomuchhigherthantheeffective viscosity of the underlying mantle. The Andrade rheology lowers the plate effective viscosity corresponding to the power-law fluid rheology and, thus, leads to instability of the state in which the plates are stagnant. The solution of the second stability problem shows that the state, in which the lithospheric plate moves as a whole with constant velocity, is stable but smallamplitude oscillations are imposed on this motion in regions of thickened lithosphere beneath continental cratons (subcratonic roots) where the thickness of the lithosphere is about 200 km. These oscillations create small-scale convective cells (the horizontal dimensions of the cells are of the order of the subcratonic lithosphere thickness). Direction of motion within the cells periodically changes (the period of oscillations is of the order of 10 8 yr). The small-amplitude convective oscillations cause small strains and do not destroy the thickening of the lithosphere beneath cratons. Thus, the transient creep of the lithosphere explains not only mobility of the lithospheric plates but longevity of subcratonic roots as well.

The Micro-Mechanism Analysis on Rock Creep Damage

Rock creep is a hot topic and key point in engineering geology. Based on renormalization group theory, the rock creep instability of micro-mechanism can be described as follow: with the expanding and interaction of micro-cracks and the main fault forms, which leads to failure. Comparing with the similarity of rock creep and rock compression process, and combining results of rock creep process, it is shown that there a distinct pertinence between different stages of rock creep. The relationship characteristics of different evolutionary stages can be used to provide scientific foundation for rock creep.

Temperature-dependent shear flow and the absence of thermal runaway in valley glaciers

We propose a two-dimensional model of a valley glacier in order to reconsider the question of whether thermal runaway could be a viable mechanism for the onset of creep instability in surging glaciers. We do this by providing an approximate solution for the temperature field based on the idea that shear is concentrated at the glacier bed. With this assumption, we show that a closed-form evolution equation for the glacier profile exists. While this is well known for isoviscous flows, it has not been previously derived for variable viscosity flows. During the process of deriving this equation, we show that thermal runaway does not occur. We provide numerical solutions of the model, and are led to infer that enhanced basal heating owing to refreezing of surface meltwater is an essential constituent in raising the bed temperature to the melting point.

Zonal disintegration phenomenon in enclosing rock mass surrounding deep tunnels — mechanism and discussion of characteristic parameters

The mechanism of the zonal disintegration phenomenon (ZDP) was realized based on the analysis of the stressed-strained state of the rock mass in the vicinity of the maximum stress zone, which resides in the creep instability failure of rock mass due to the development of a plastic zone and transfer of the maximum stress zone within the rock mass. Some characteristic parameters of the ZDP are discussed theoretically. In first instance, the analytical critical depth condition for the occurrence of ZDP was obtained, which depends on the characteristics and stress concentration coefficient of the rock mass. Secondly, based on creep theory, the expression of the outer radius of the undisturbed zones in the deep rock mass was obtained with the use of an improved Burgers rheological model, which indicated that the radius depends on the characteristics of the rock mass and the depth of excavation and increases quasi-linearly with the rise of creep compliance of the rock mass. Finally, the formula for the distance of the most remote fissured zone away from the working periphery was derived, which increases logarithmically with the increase in the ratio of the in-situ stress and ultimate strength of rock mass. The distances between fissured zones are discussed in qualitative terms.

Mechanism of zonal disintegration phenomenon in enclosing rock mass around deep tunnels

In order to study the mechanism of the zonal disintegration phenomenon (ZDP), both experimental and theoretical investigations were carried out. Firstly, based on the similarity law, gypsum was chosen as equivalent material to simulate the deep rock mass, the excavation of deep tunnel was modeled by drilling a hole in the gypsum models, two circular cracked zones were measured in the model, and ZDP in the enclosing rock mass around deep tunnel was simulated in 3D gypsum model tests. Secondly, based on the elasto-plastic analysis of the stressed-strained state of the surrounding rock mass with the improved Hoek-Brown strength criterion and the bilinear constitutive model, the maximum stress zone occurred in vicinity of the elastic-plastic interface due to the excavation of the deep tunnel, rock material in maximum stress zone is in the approximate uniaxial loading state owing to the larger tangential force and smaller radial force, the mechanism of ZDP was explained, which lay in the creep instability failure of rock mass due to the development of plastic zone and transfer of the maximum stress zone within the rock mass. Thirdly, the analytical critical depth for the occurrence of ZDP was obtained, which depended on the mechanical indices and stress concentration coefficient of rock mass.

Zonal disintegration phenomenon in rock mass surrounding deep tunnels

Zonal disintegration is a typical static phenomenon of deep rock masses. It has been defined as alternating regions of fractured and relatively intact rock mass that appear around or in front of the working stope during excavation of a deep tunnel. Zonal disintegration phenomenon was successfully demonstrated in the laboratory with 3D tests on analogous gypsum models, two circular cracked zones were observed in the test. The linear Mohr-Coulomb yield criterion was used with a constitutive model that showed linear softening and ideal residual plastic to analyze the elasto-plastic field of the enclosing rock mass around a deep tunnel. The results show that tunneling causes a maximum stress zone to appear between an elastic and plastic zone in the surrounding rock. The zonal disintegration phenomenon is analyzed by considering the stress-strain state of the rock mass in the vicinity of the maximum stress zone. Creep instability failure of the rock due to the development of the plastic zone, and transfer of the maximum stress zone into the rock mass, are the cause of zonal disintegration. An analytical criterion for the critical depth at which zonal disintegration can occur is derived. This depth depends mainly on the character and stress concentration coefficient of the rock mass.

Influence of channelling on heating in ice‐sheet flows

Ice‐sheet flows can be channelled by perturbations in the basal topography or in the sliding coefficient. These lead to spatial variation in the steady profile, the flux and the dissipative heating. This paper examines the linearized theory of heating variations, showing that the map plane aspect ratio of the basal perturbation has a dominating effect on the qualitative behaviour. For ribbing transverse to the direction of flow, maximum heating occurs over bedrock and sliding viscosity highs. When flow‐parallel channelling occurs maximum heating occurs over bedrock lows and sliding viscosity lows. These results are used to examine symmetry‐breaking behaviour of numerical thermoviscous ice‐sheet models in terms of a dissipation‐driven creep instability.

A Possible Mechanism of Crustal Deformation Before the Xingtai Earthquake in 1966

The medium of crust model is treated as Maxwell medium, and the model includes hard inclusion, soft inclusion, and deep-seated fault. By using three-dimensional finite element method and differential method, the change of disturbed average stress and disturbed maximum shear stress with time and the crustal deformation on the surface of the model is calculated. (1) At the depth of 11 km in crust, the change of disturbed maximum shear stress caused by the speedup creep of the deep-seated fault is accelerated by hundreds of times. The beginning of the deep-seated fault instability is the beginning of forming the core of the Xingtai large earthquake in 1966. This character is very favorable to quickly transfer shear strain energy from the lower crust to the upper and middle crust. (2)The character of deformation on the surface of the model is very similar to that in Xingtai area before large earthquake in 1966. We may conclude that the precursor is connected not only with the dilation of rock but also with the creep instability along the deep-seated fault before large earthquake.

Intergranular structure in dental amalgams

The existence of an intergranular precipitate that provides a structural basis of creep, intergranular corrosion and thermal instability in dental amalgams has been in dispute. Also in dispute is a related matter concerning the solid solubility of Sn in ϒ1. Both these aspects have been examined in this differential scanning calorimetry (DSC) study using the following materials: (a) a conventional ϒ2−containing amalgam, (b) six ϒ2−free amalgams, and (c) a series of ϒ1 specimens with up to 4 wt% Sn. It has been observed that the solid solubility of Sn in ϒ1 is about 1.0 wt%. Above this Sn concentration, an intergranular precipitate, identified as the δ2 phase of the SnHg system, appears in ϒ1. This phase is characterized by a low melting temperature (∼90°C). The existence of this phase in the conventional dental amalgam has been confirmed. It has been observed further that the ϒ2−free dental amalgams, depending on their nature and Hg contents, may contain δ2 either as a transient or a permanent phase.

Observations on source time functions of earthquakes obtained from inversion of teleseismic body waveforms

SUMMARY An interesting aspect of the nucleation of large Eastern Mediterranean earthquakes is the emergent nature of their source time functions. Several large and shallow, normal, strike-slip and thrusting events, which occurred in other parts of the world, and broke the surface for which the source time functions have been determined using the same inversion procedure, exhibit similar characteristics. These emergent source time functions may reflect a difficulty in breaking barriers, the localized region of the fault which remains unbroken at the completion of the dynamic fault process, at which ruptures nucleated, or some particular physical process (e.g. creep instability) that may commonly occur during the rupture of large earthquakes. Earthquakes in similar tectonic settings with similar source mechanisms reflect common patterns.

Effect of the choice of creep instability criterion on the solution of the problem of optimizing rod-shaped structures

Effect of the choice of creep instability criterion on the solution of the problem of optimizing rod-shaped structures

Evolution of the East Antarctic Ice Sheet: A Numerical Study of Thermo-Mechanical Response Patterns With Changing Climate

An efficient numerical ice-sheet model, including time dependence and full thermo-mechanical coupling, has been developed in order to investigate the thermal regime and overall configuration of a polar ice sheet with respect to changing environmental conditions.From basic sensitivity experiments, in which a schematic East Antarctic ice sheet is forced with a typical glacial–interglacial climatic shift, it is found that: (i) the mutual interaction of temperature and deformation has a stabilizing effect on its steady-state configuration; (ii) in the transient mode, this climatic transition initially leads to increased ice thickness due to enhanced accumulation, after which this trend is reversed due to a warmer base. Time-scales for this reversal are of the order of 103 years in marginal zones and of 104 years in interior regions; (iii) horizontal heat advection plays a major role in damping possible runaway behaviour due to the dissipation – strain-rate feed-back, suggesting that creep instability is a rather unlikely candidate to initiate surging of the East Antarctic ice sheet.The model is then applied to four East Antarctic flow lines. Only the flow line passing through Wilkes Land appears to be vulnerable to widespread basal melting, due to enhanced basal warming following climatic warming. Time-dependent modelling of the Vostok flow line indicates that the Vostok Station area has risen about 95 m since the beginning of the present interglacial due to thermo-mechanical effects, which is of particular interest in interpreting the palaeoclimatic signal of the ice core obtained there.

Evolution of the East Antarctic Ice Sheet: A Numerical Study of Thermo-Mechanical Response Patterns With Changing Climate

An efficient numerical ice-sheet model, including time dependence and full thermo-mechanical coupling, has been developed in order to investigate the thermal regime and overall configuration of a polar ice sheet with respect to changing environmental conditions. From basic sensitivity experiments, in which a schematic East Antarctic ice sheet is forced with a typical glacial–interglacial climatic shift, it is found that: (i) the mutual interaction of temperature and deformation has a stabilizing effect on its steady-state configuration; (ii) in the transient mode, this climatic transition initially leads to increased ice thickness due to enhanced accumulation, after which this trend is reversed due to a warmer base. Time-scales for this reversal are of the order of 103 years in marginal zones and of 104 years in interior regions; (iii) horizontal heat advection plays a major role in damping possible runaway behaviour due to the dissipation – strain-rate feed-back, suggesting that creep instability is a rather unlikely candidate to initiate surging of the East Antarctic ice sheet. The model is then applied to four East Antarctic flow lines. Only the flow line passing through Wilkes Land appears to be vulnerable to widespread basal melting, due to enhanced basal warming following climatic warming. Time-dependent modelling of the Vostok flow line indicates that the Vostok Station area has risen about 95 m since the beginning of the present interglacial due to thermo-mechanical effects, which is of particular interest in interpreting the palaeoclimatic signal of the ice core obtained there.

The origin of large or great thrust-type earthquakes along subducting plate boundaries

Seismicity, deformation, state of stress, and abundance of fluids along subducting plate boundaries are reviewed, and the origin of large or great thrust-type earthquakes is discussed based on the recent experimental results on the slip behavior of halite and serpentine gouges. Shallow subducting plate boundaries above 20–25 km in depth are characterized by low seismicity, low tectonic stress, inter-plate decoupling, ductile deformation associated with the formation of metamorphic schistosity (except at very shallow depths), metamorphism suggesting solution processes on massive scale, and presence of abundant H 2O. It is argued that these unique features are due to pressure-solution processes, to high fluid pressure, to low strength and stable behavior of clayey sediments under wet environments, and/or to the deformation of soft, unconsolidated sediments at very shallow depths. The low seismicity in this zone is in marked contrast with major strike-slip faults along which large earthquakes occur at depths shallower than 15–20 km. It is emphasized that these unique features are expected only for restricted regions where there is constant supply of H 2O due to progressive metamorphism or where fluids in the rocks are trapped and cannot escape to the surface. Large or great thrust-type earthquakes in subduction zones initiate at depths of 30–50 km, below the shallow decoupled zone. In this focal depth range, the supply of H 2O during progressive metamorphism perhaps diminishes downwards, the overriding and subducting plates are coupled and stick to each other during much of the inter-seismic period, and the resistance to slip (or shear stress) is presumably high. It is suggested that these earthquakes begin to occur at a depth where the plate-boundary zone becomes fairly dry. Deformation at these depths appears to be predominantly ductile, so that the earthquakes cannot be regarded simply as a brittle phenomenon. (1) Creep instability i.e., instability associated with plastic deformation, and (2) dehydration-induced instability are the most likely mechanisms for initiating the earthquakes, and both have some experimental support. Stick-slip of halite gouge while undergoing ductile deformation primarily by intracrystalline gliding is described and discussed as a supporting evidence for (1). Shear resistance of halite gouge increases with increasing confining pressure in stick-slip regimes. Hence the observed stick-slip may be a semi-brittle phenomenon with respect to the pressure dependence of the shear resistance, although the deformation texture cannot be distinguished from that formed by pressure-insensitive flow. Serpentine gouge exhibits violent stick-slip upon its decomposition under dry, not wet, environments, supporting the mechanism (2) above. Exact mechanisms which lead to the unstable fault motion are poorly understood as yet, but stick-slip of both halite and serpentine gouges is recognized only when the slip-rate dependence of friction is negative i.e., lower friction at faster slip rate, consistent with the theoretical prediction of Rice and Ruina (1983). There is a possibility that the thrust-type earthquakes can be explained essentially within the framework of fault constitutive laws developed by Dieterich (1979) and Ruina (1983).

Initiation of ice ages by creep instability and surging of the East Antarctic ice sheet

Creep or shear heating instability is shown to be a plausible means of initiating a surge of the East Antarctic ice sheet and plunging the Earth into an ice age. The occurrence of this instability requires only that the ice thickness exceed a critical value which may not be much larger than the present ice dome thickness. Creep instability can occur on the fast time scale of 100–1,000 yr required by inferences of past rapid cooling events and sudden rises of sea level before the onset of Northern Hemisphere glaciations.

A creep instability analysis of the Antarctic and Greenland ice sheets

Creep instability, the runaway increase of temperature and deformation due to internal strain heating, is analysed with a very simple model of one-dimensional heat transfer to estimate the stability of the Antarctic and Greenland ice sheets. Derived stability maps indicate that for the assumed rheology both ice sheets are completely stable; however, the stability of the coastal region of Wilkes Land in Antarctica is only marginal and cannot be accurately determined because of uncertainties in the data, especially basal shear stress.

Strain heating and creep instability in glaciers and ice sheets

Creep instability, the runaway increase of internal temperature and deformation rate, may affect the boundary condition at the base of glaciers and ice sheets and thus influence their flow and dimensions. We consider a simple slab model of heat transport in which three dimensionless parameters determine the relative importance of strain heating, ice advection normal to the surface, and boundary conditions. We find that an ice mass will be unstable if the strain‐heating parameter exceeds a critical value which depends strongly on advection and boundary conditions. Critical values over the range of parameters appropriate to natural ice masses are presented. Accumulation (downward advection) or ablation (upward advection) affects the critical value by up to 5 orders of magnitude: ablation tends to reduce stability, and accumulation increases it. For an ice mass frozen to its bed, instability eventually raises the basal ice to melting point. This can restore thermal stability, but the ice mass will start to slide over its bed. If the strain‐heating parameter exceeds a second, higher critical value, a layer of basal ice at melting point will form. We find that the conditions for instability are likely to exist in the accumulation and ablation zones of certain glaciers and ice sheets. However, times calculated for instability to develop are in the range 102–103 yr for glaciers and 103–104 yr for ice sheets. As these times exceed the normal residence time for ice in the ablation zone, it appears that instability is most likely to develop in the accumulation zone. This conclusion is reinforced by the fact that ablation increases the growth time for instability, whereas accumulation decreases it. The growth times quoted above are longer than the periods of most glacier surges, and thus creep instability is an unlikely surge mechanism. Unstable conditions may, however, obtain in East Antarctica and may have existed in the central part of ice age ice sheets. Surges of ice sheets triggered by creep instability may be possible.

Creep Instability of Ice Sheets

Abstract The equation governing the growth or decay of a temperature perturbation T’ in an ice slab under shear stress σ xy is where K and k are respectively the thermal conductivity and diffusivity of ice, KB-v is the advection velocity normal to the bed and is the rate of increase of strain heating with temperature assuming a power law for flow. For a slab of infinite thickness under constant stress and at constant ambient temperature, T Fourier analysis gives -k2+a/k < o as the condition for stability where k is the wave number of a sinusoidal perturbation. When the slab has finite thickness the stability depends on the sign of the eigenvalues λm of the perturbation equation and on the boundary condition at the ice-rock interface. In general the eigenfunctions and eigenvalues must be found by approximate methods such as the Rayleigh-Ritz procedure but in the case where the stress and ambient temperature are constant over the slab thickness and there is no advection the eigenfunctions are either sines or cosines depending on the boundary conditions. In this special case the stability condition is if the bed is frozen and if it is at the melting point. The eigenvalue associated with the smallest value of m is the least stable so the maximum stable thickness is thus h = ½ π(a/K)1/2 if the bed is frozen or h = π (a/K)1/2 if it is at the melting point. For typical flow-law parameters these depths are around 250 m and 500 m respectively. The eigenvalues are related in a simple way to the growth or decay rates of the eigenfunctions: (K λm)–1 is the time constant for the mth eigenfunction. Depth-dependent stress, temperature, and advection have a marked effect on stability. A slab in which stress and temperature increase to values B and T B at the bed is considerably more stable than a slab held at constant stressσB and a constant temperature T B. Advection normal to the bed also has a major influence on stability. If the advection velocity is taken to vary linearly with depth and the bed is frozen, the effect of upward advection is to decrease stability and of downward advection to increase it. When the bed is temperate the effect of advection is more complex: downward advection increases stability but upward advection may increase or decrease it depending on the magnitude of the advection velocity.

Creep Instability of Ice Sheets

AbstractThe equation governing the growth or decay of a temperature perturbation T’ in an ice slab under shear stress σxy iswhere K and k are respectively the thermal conductivity and diffusivity of ice, KB-v is the advection velocity normal to the bed andis the rate of increase of strain heating with temperature assuming a power law for flow. For a slab of infinite thickness under constant stress and at constant ambient temperature, T Fourier analysis gives -k2+a/k < o as the condition for stability where k is the wave number of a sinusoidal perturbation. When the slab has finite thickness the stability depends on the sign of the eigenvalues λm of the perturbation equation and on the boundary condition at the ice-rock interface. In general the eigenfunctions and eigenvalues must be found by approximate methods such as the Rayleigh-Ritz procedure but in the case where the stress and ambient temperature are constant over the slab thickness and there is no advection the eigenfunctions are either sines or cosines depending on the boundary conditions.In this special case the stability condition isif the bed is frozen andif it is at the melting point. The eigenvalue associated with the smallest value of m is the least stable so the maximum stable thickness is thus h = ½ π(a/K)1/2 if the bed is frozen or h = π (a/K)1/2 if it is at the melting point. For typical flow-law parameters these depths are around 250 m and 500 m respectively. The eigenvalues are related in a simple way to the growth or decay rates of the eigenfunctions: (K λm)–1 is the time constant for the mth eigenfunction.Depth-dependent stress, temperature, and advection have a marked effect on stability. A slab in which stress and temperature increase to values B and TB at the bed is considerably more stable than a slab held at constant stressσB and a constant temperature TB. Advection normal to the bed also has a major influence on stability. If the advection velocity is taken to vary linearly with depth and the bed is frozen, the effect of upward advection is to decrease stability and of downward advection to increase it. When the bed is temperate the effect of advection is more complex: downward advection increases stability but upward advection may increase or decrease it depending on the magnitude of the advection velocity.