If Not Brittle: Ductile, Plastic, or Viscous?

2021 ◽  
Author(s):  
Kelin Wang
Keyword(s):  
Brittle Failure ◽  
Permanent Deformation ◽  
Research Community ◽  
Deformation Mechanisms ◽  
Basic Knowledge ◽  
Primary Reason ◽  
Brittle Deformation ◽  
Macroscopic Deformation ◽  
Microscopic Deformation ◽  
Shallow Part

Abstract Integrating earthquake studies with geodynamics requires knowledge of different modes of permanent deformation of rocks beyond seismic failure. However, upon stepping out of the realm of brittle failure, students find themselves in a zone of terminology conflict. Rocks below the brittle shallow part of the lithosphere are said to be ductile, plastic, or viscous, yet in many papers what is obviously brittle deformation is said to be plastic. In this EduQuakes article, I explain the origin of this conflict and how to handle it. The primary reason for the conflict is that the word plastic is used by one research community to describe viscous deformation but by another community to describe permanent deformation that is not viscous. To the former community, emphasis is on microscopic deformation mechanisms. To the latter community, emphasis is on whether the macroscopic deformation is time dependent. Using a Coulomb continuum to approximate the effects of numerous brittle faults adds another level of complexity. It is futile to expect a unification of terminology any time soon, but with some basic knowledge one can live with this situation without suffering scientific confusion.

A Damage Mechanics Model for Uniaxial Deformation of Ice

1985 ◽  
Vol 107 (3) ◽  
pp. 363-368 ◽  
Author(s):  
D. G. Karr
Keyword(s):  
Damage Mechanics ◽  
Deformation Mechanisms ◽  
Uniaxial Deformation ◽  
Brittle Deformation ◽  
One Dimensional ◽  
Mechanics Model ◽  
Polycrystalline Ice ◽  
Strain Relationship ◽  
Quantitative Results ◽  
Damage Law

A one-dimensional stress-strain relationship is developed for pure polycrystalline ice subjected to uniaxial compression. The model is based on the continuous damage theories and includes the effects of elastic, plastic and brittle deformation mechanisms. A damage law for ice is established based on a statistical model for internal microfracture. Quantitative results are presented by directly relating the formation of internal cracks to published acoustic emission response of ice samples subjected to compression.

Quantifying the precursors to brittle failure in rocks using synchrotron imaging and machine learning

2020 ◽  
Author(s):  
Francois Renard ◽  
Jessica McBeck ◽  
Benoît Cordonnier
Keyword(s):  
Machine Learning ◽  
Spatial Resolution ◽  
Brittle Failure ◽  
Strain Field ◽  
System Size ◽  
Rock Deformation ◽  
Brittle Deformation ◽  
X Ray ◽  
In Situ Conditions ◽  
Fracture Growth

<p>Predicting the onset of system-size failure in rocks represents a fundamental goal in assessing earthquake hazard. On the field, seismological, geodetic and other monitoring data may record precursors to earthquakes. In laboratory experiments, such precursors often rely on monitoring acoustic emissions and this technique has some limitations in terms of spatial resolution and the lack of detection of aseismic strain. To overcome these challenges, we have performed a series of forty rock deformation experiments where we imaged, using synchrotron X-ray microtomography, rock samples as they deformed until brittle failure, at in situ conditions of pressure, high spatial micrometer spatial resolution, and through time. On the one hand, direct processing of the X-ray tomograms allow visualizing how precursory microfractures nucleate, grow, and coalesce until failure. From these data, we propose to characterize brittle failure as a critical phase transition, with evidence of several power-laws that characterize fracture growth. On the other hand, digital volume correlation techniques quantify the evolution of the local strain field inside each sample. We analysed the statistical properties of these strain fields using several machine learning techniques to predict the main parameters that control fracture growth (length, volume, shape, distance to the nearest fracture), and the features of the strain field that best predict the distance to failure. Our rock deformation experimental results show that, under laboratory conditions, precursors to brittle deformation exist. These precursors show predictable evolution when approaching system-size brittle deformation and we demonstrate that specific components of the strain field characterize this evolution to failure.</p>

Stresses Caused by Bit Loading at the Center of the Hole

1961 ◽  
Vol 1 (03) ◽  
pp. 177-183
Author(s):  
J.B. Cheatham ◽  
J.C. Wilhoit
Keyword(s):  
Stress Distribution ◽  
Pore Pressure ◽  
Cylindrical Cavity ◽  
Brittle Failure ◽  
Permanent Deformation ◽  
Confining Pressure ◽  
Radius Of Curvature ◽  
Oil Well ◽  
Large Radius ◽  
Bit Loading

Abstract Although an oil well is a long cylindrical hole with an irregular bottom, it appears likely that the nature of the stress concentration at the bottom of the hole can be ascertained from an analysis of the stresses around a short cylindrical cavity with rounded corners and smooth bottom. Such a cavity is studied primarily because it leads more readily to a solution to the problem by the use of stress functions in this paper the stress distribution around a short cylindrical cavity subjected to bit loading, overburden and drilling fluid pressures is determined by means of an analytical solution which approximately satisfies the boundary conditions of the problem. From this solution the stresses at the corner of the hole are calculated to be about 35 per cent lower than comparable results obtained by photoelastic and relaxation analyses. This difference is apparently due to the large radius of curvature at the corner of the cavity in the present analysis. Since good agreement is obtained between the results of this analysis and the stresses calculated for a similar loading on a semi-infinite elastic solid, it is concluded that the bit action in the region near the center of the hole is not appreciably affected by the presence of the sides of the hole. Introduction Much has been written concerning drilling "under down-hole conditions" and pertaining to the stress distribution in the rock at the bottom of an oil well. For example, it is known that identical rocks can be drilled more rapidly at the surface than under subsurface conditions of pressure and stress. Information on the behavior of rocks under loading can be obtained from triaxial test data. From such tests it is found that rocks exhibit brittle failure when the confining pressure and pore pressure are equal, but the mode of failure may change to ductile as the difference between the confining pressure and the pore pressure is increased. Brittle failure implies that there is very little permanent deformation before fracture, whereas ductile failure indicates that permanent deformation takes place before fracture. Some rocks are ductile at differential pressures of 5,000 psi, but other rocks are brittle even at differential pressures of more than 50,000 psi.

Deformation of Inhomogeneous Elastic Solids With Two-Dimensional Damage

2001 ◽  
Vol 68 (4) ◽  
pp. 528-536
Author(s):  
J. J. Luo ◽  
I. M. Daniel
Keyword(s):  
Periodic Structures ◽  
Elastic Behavior ◽  
Two Dimensional ◽  
Elastic Solids ◽  
Inhomogeneous Materials ◽  
Linear Elastic ◽  
Reinforced Composite ◽  
Macroscopic Deformation ◽  
Microscopic Damage ◽  
Microscopic Deformation

A general correlation is derived between macroscopic stresses/strains and microscopic deformation on the damage surfaces for inhomogeneous elastic solids with two-dimensional damage. Assuming linear elastic behavior for the undamaged materials, the macroscopic deformation associated with nonlinear strains, or damage strains, is shown to be the weighted sum of the microscopic deformations on the damage surfaces. For inhomogeneous materials with periodic structures (laminated composites, for example) and various identifiable damage modes, simple relations are derived between the macroscopic deformation and microscopic damage. When the number of identifiable damage modes is less than or equal to the number of relevant measurable macroscopic strains, the correlation can be used to evaluate the damage progression from simple macroscopic stress and strain measurements. The simple case of a unidirectional fiber-reinforced composite under longitudinal load is used to show how the results can help detect and characterize the damage using macroscopic measurements, without resorting to assumptions of detailed microscopic deformation mechanisms.

In situ studies of deformation at interfaces

1989 ◽  
Vol 47 ◽  
pp. 616-617
Author(s):  
William A. T. Clark
Keyword(s):  
Electron Microscope ◽  
Dislocation Motion ◽  
The Other ◽  
Deformation Mechanisms ◽  
Complementary Information ◽  
Fundamental Interest ◽  
Dynamic Experiments ◽  
Macroscopic Deformation ◽  
Polycrystalline Solids

During the last twenty-five years there have been a number of studies of dislocation motion and interactions performed in the electron microscope. In general these observations have been limited by a number of technical shortcomings which have compromised their usefulness. In recent years, however, significant developments in the design and construction of specimen stages and in systems for recording in situ experiments in real time in the electron microscope have led to a renewed interest in dynamic experiments. One such application is the study of the interaction of dislocations with interfaces in polycrystalline solids, a topic which is of fundamental interest in understanding the laws which govern macroscopic deformation. It has been clearly demonstrated that in situ experiments are essential to this investigation, as they have provided direct observation of deformation mechanisms which conventional TEM analyses, in which the samples are deformed before they are put in the microscope, cannot. The two types of TEM observations provide complementary information, each greatly enhancing the value of the other.

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