Semi Empirical Stress Analysis of a Brittle Material in a Vicinity of a Stress Concentrator

2006 ◽  
Vol 3-4 ◽  
pp. 243-252 ◽  
Author(s):  
M. Chabaat ◽  
S. Djouder ◽  
M. Touati
Keyword(s):  
Stress Field ◽  
Main Crack ◽  
Process Zone ◽  
Crack Opening ◽  
Damage Zone ◽  
Local Stress ◽  
Complex Problem ◽  
Solution Procedure ◽  
Semi Empirical ◽  
Interaction Problem

In this study, interaction of a main crack with its surrounding damage, which consists of continuous lines of discontinuities, is analysed. To solve this complex problem, a Semi-Empirical Approach (SEA), which relies on experimentally measured crack opening displacements as the solution to this multiple crack interaction problem is suggested. The solution procedure is illustrated, first, for a particular case of the interaction of an array of horizontal and vertical crazes with a main crack, and second, for the generalized case to include the whole damage of crazing patterns surrounding the main crack. The results show that the crack Damage Zone (DZ) or the socalled Process Zone (PZ) interaction may either amplify or suppress the resulting stress field depending on the crack damage configuration. Green’s function for the Stress Intensity Factor (SIF) is employed to quantify the effects on a crack of the damage of continuous patterns of discontinuities. It follows from the analysis that an increase in the number of crazing patterns will amplify the stress at the main crack. It is also shown throughout this study that the overall effect of the damage is identified, as being an amplifying one and that the resulting local stress field would direct the propagation of the main crack since there is no toughening.

Interacting Crazing Patterns Near the Tip in the Damage Zone of a Crack

2010 ◽  
Vol 123-125 ◽  
pp. 555-558
Author(s):  
H. Seddiki ◽  
M. Chabaat
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Stress Field ◽  
Main Crack ◽  
Damage Zone ◽  
Numerical Approach ◽  
Mode I ◽  
The One ◽  
Linear Propagation

The present paper investigates interactions between a main crack and a surrounding layer of crazing patterns. Analysis of the stress field distribution as well as the energy induced during these interactions is based on the resolution of some equations along with appropriate boundary conditions and the use of a numerical approach. The effect of amplification and shielding on the resulting stress field is shown through a study of mode I Stress Intensity Factor (SIF). Besides, to quantify the effects of this damage on the main crack, it is shown that the Energy Release Rate (ERR) is defined as being a superposition of the energy released due to the linear propagation of the main crack as well as the one due to the translational change in the growth of the damage. It is also proven that crazes closer to the main crack dominate the resulting interaction effect and reflect an anti-shielding of the damage while a reduction constitutes a material toughness.

The STIMTEC-X hydraulic stimulation campaign at the URL Reiche Zeche Mine, Germany

2021 ◽  
Author(s):  
Carolin Boese ◽  
Joerg Renner ◽  
Georg Dresen ◽  
Keyword(s):  
Acoustic Emission ◽  
High Resolution ◽  
Stress Field ◽  
Stress Measurement ◽  
Damage Zone ◽  
Local Stress ◽  
Seismic Monitoring ◽  
Underground Laboratory ◽  
Small Scale ◽  
Hydraulic Stimulation

<p>In 2018-2019, the STIMTEC hydraulic stimulation experiment was conducted at the Reiche Zeche underground laboratory in Freiberg, Saxony/Germany, to investigate the role of hydro-mechanical processes for the often required enhancement of hydraulic properties in deep geothermal projects. We applied the same injection protocol to each of the ten stimulated intervals in the 63 m-long injection borehole. Yet, we observed significant small-scale variability in the seismic and hydraulic responses to stimulation and in parallel stress field heterogeneity on the meter scale. While acoustic emission (AE) activity was high in the upper part of the injection borehole, no AE events were detected in its deepest part, ending in a high-permeability damage zone.</p><p>To investigate the stress field and seismic variability throughout the experimental volume and their interrelation further, we started the follow-on experiment STIMTEC-X. The initial phase involved eleven local stress measurements performed in October 2020 in three existing boreholes, previously used for monitoring purposes, with varying orientations and lengths. This phase of the experiment was seismically monitored in real-time using an adaptive, high-resolution seismic monitoring network comprising six AE-type hydrophones, six regular AE sensors and four accelerometers. The hydrophones were installed in combination with hydraulic gauges or the double packer probe used for localized injection to make best use of the existing infrastructure. Hydrophones were optimally placed for each measurement configuration anew with at least one deployed in the direct vicinity (~3-4 m) of the injection interval. We detected low-magnitude AE activity (M<-3.5) at high resolution, spatially distributed between distinct clusters identified previously during the STIMTEC experiment. Overall, these records indicate a doubling of the seismically active volume. We also performed eight dilatometer tests to determine deformation characteristics of induced hydrofracs and pre-existing fractures. A circulation experiment between the injection borehole and two newly drilled boreholes of 23 m and 30 m depth is pending. Here, we present the seismicity associated with the STIMTEC and STIMTEC-X hydraulic stimulation campaigns and focal mechanism solutions. We focus on how they contribute to 3-D volumetric stress field characterisation between local stress measurement points.</p><p><img src="https://contentmanager.copernicus.org/fileStorageProxy.php?f=gnp.5069b42fb60064884501161/sdaolpUECMynit/12UGE&app=m&a=0&c=928e8094105ded0e25c2a2da4e49946e&ct=x&pn=gnp.elif&d=1" alt=""></p><p>Figure 1: Borehole layout (cyan - injection borehole, yellow: seismic monitoring boreholes, green: hydraulic monitoring borehole, red: mine-back validation boreholes) and acoustic emission (AE) events during the STIMTEC (yellow and orange circles) and STIMTEC-X (purple circle) experiments at the Reiche Zeche underground laboratory in Freiberg, Germany. Damage zones (transparent red) and hydraulically stimulated (dark blue rings) and/or hydraulically tested intervals (light blue rings) are shown. Stimulation of the intervals resulted in >11000 AE events with most events occurring during the periodic pumping sequences following the hydrofracturing. The seismic clouds extend about 5 m radially around the boreholes.</p>

Crack-Extension Force for a Part-Through Crack in a Plate

1962 ◽  
Vol 29 (4) ◽  
pp. 651-654 ◽  
Author(s):  
G. R. Irwin
Keyword(s):  
Stress Field ◽  
Crack Extension ◽  
Crack Opening ◽  
Elliptical Crack ◽  
Field Parameter ◽  
Experimental Measurements ◽  
Boundary Points ◽  
Crack Extension Force ◽  
Extension Force

The crack stress-field parameter K and crack-extension force G at boundary points of a flat elliptical crack may be derived from knowledge that normal tension produces an ellipsoidal crack opening. Rough correction procedures can be employed to adapt this result for application to a part-through crack in a plate subjected to tension. Experimental measurements suggest this adapted result has a useful range of accuracy.

Prediction of the Initial Crack Tip Microstructure in a Single Crystal of CuAlNi

1999 ◽  
Author(s):  
Galyna M. Vasko ◽  
Perry H. Leo ◽  
Thomas W. Shield
Keyword(s):  
Stress Field ◽  
Single Crystal ◽  
Crack Opening ◽  
Crack Tip ◽  
Initial Crack ◽  
Single Edge ◽  
Opening Displacement ◽  
Elastic Crack ◽  
Maximum Work ◽  
Anisotropic Elastic

Abstract The austenite to martensite pseudoelastic transformation induced by the anisotropic elastic crack tip stress field in a single crystal of shape memory alloy is considered. It is proposed that the orientation of the initial austenite-martensite interface that forms can be predicted based on knowledge of the stress field, the crystallography of the transformation and one of two selection criteria. These criteria are based on the work of formation of the martensite in stress field and the crack opening displacement the martensite causes at the crack. Predictions of the criteria are compared to experiments on three single edge notched CuAlNi single crystal specimens. Results indicate that the maximum work criterion accurately predicts the orientation of the austenite-martensite interfaces that initially form near a crack.

scholarly journals Local stress fields in solids estimated by acoustical emission method

2021 ◽  
Vol 2103 (1) ◽  
pp. 012064
Author(s):  
V L Hilarov ◽  
E E Damaskinskaya
Keyword(s):  
Time Series ◽  
Acoustic Emission ◽  
Stress Field ◽  
Estimation Method ◽  
Local Stress ◽  
Stress Fields ◽  
Emission Method ◽  
Macroscopic Fracture ◽  
Stress Estimation ◽  
Kinetic Concept

Abstract Based on the Zhurkov’s kinetic concept of solids’ fracture a local internal stress estimation method is introduced. Stress field is computed from the time series of acoustic emission intervals between successive signals. For the case of two structurally different materials the time evolution of these stresses is examined. It is shown that temporal changes of these stresses’ accumulation law may serve as a precursor of incoming macroscopic fracture.

scholarly journals Air-temperature control on diurnal variations in microseismicity at Laohugou Glacier No. 12, Qilian Mountains

2019 ◽  
Vol 60 (79) ◽  
pp. 125-136 ◽  
Author(s):  
Tao Zhang ◽  
Yuqiao Chen ◽  
Min Ding ◽  
Zhongyan Shen ◽  
Yuande Yang ◽  
...  
Keyword(s):  
Short Duration ◽  
Crack Opening ◽  
Low Frequency ◽  
Local Stress ◽  
Stress Concentrations ◽  
Night Time ◽  
Strong Negative Correlation ◽  
Near Surface ◽  
Temperature Change Rate ◽  
Trigger Algorithm

ABSTRACTWe conducted a 9-d seismic experiment in October 2015 at Laohugou Glacier No. 12. We identified microseismic signals using the short-term/long-term average trigger algorithm at four stations and classified them as long and short-duration events based on waveform, frequency, duration and magnitude characteristics. Both categories show systematical diurnal trends. The long-duration events are low-frequency tremor-like events that mainly occurred during the daytime with only several events per day. These events lasted tens of seconds to tens of minutes and are likely related to resonance of daytime meltwater. The dominant short-duration events mostly occurred during the night time with a peak occurrence frequency of ~360 h−1. Their short-duration (<0.2 s), high frequency (20–100 Hz) and dominance of Rayleigh waves are typical of events for near-surface crack opening. A strong negative correlation between the hourly event number and temperature change rate suggests that the occurrence of night-time events is controlled by the rate of night-time cooling. We estimated the near-surface tensile stress due to thermal contraction at night to be tens of kilopascals, which is enough to induce opening of surface cracks with pre-existing local stress concentrations, although we cannot exclude the effect of refreezing of meltwater produced during the day.

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