Failure zone of rock associated with crack growth mine working

Abstract A theory of viscoelastic crack growth developed nearly five decades ago is generalized to allow traction in the so-called failure zone that is a function of the crack opening displacement (COD). In earlier work, except for a minor exception, traction was specified. The current model leads to a nonlinear double integral that has to be solved for the COD before crack growth can be predicted. First, a closed-form, accurate approximation is found for a linear elastic body. We then show that this COD may be easily and accurately extended to linear viscoelasticity using a realistic, broad spectrum creep compliance. An analytical relationship between stress intensity factor and crack speed then follows. Consistent with earlier work, it is defined almost entirely by creep compliance. Five different failure zone tractions are employed; their differences are shown to have little effect on the crack growth other than through a speed shift factor. The Appendix discusses initiation of growth.

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Generalized functions in determining the stress field and convergence of a single mine working surrounded by a failure zone

Soviet Mining Science ◽

10.1007/bf02500780 ◽

1991 ◽

Vol 27 (4) ◽

pp. 310-313

Author(s):

A. A. Pimenov

Keyword(s):

Stress Field ◽

Mine Working ◽

Generalized Functions ◽

Failure Zone

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A theory of viscoelastic crack growth-Revisited

10.21203/rs.3.rs-733371/v4 ◽

2021 ◽

Author(s):

Richard A Schapery

Keyword(s):

Crack Growth ◽

Creep Compliance ◽

Process Zone ◽

Crack Opening ◽

Shift Factor ◽

Analytical Relationship ◽

Failure Zone ◽

Opening Displacement ◽

Linear Elastic ◽

Linear Elastic Body

Abstract A theory of viscoelastic crack growth developed nearly five decades ago is generalized to express traction in the so-called fracture process zone or failure zone as a function of the crack opening displacement (COD). In earlier work, except for minor exceptions, traction was specified as a function of location. The new model leads to a nonlinear double integral that has to be solved for the COD before crack growth can be predicted. First, a closed-form, accurate approximation is found for a linear elastic body. We then show that this COD may be easily and accurately extended to linear viscoelasticity using a realistic, broad spectrum creep compliance. An analytical relationship connecting the stress intensity factor to crack speed then follows. Consistent with earlier work, it is defined almost entirely by the creep compliance. Five different failure zone tractions are employed; their differences are shown to have little effect on crack growth other than through a speed shift factor. The Appendix discusses initiation of growth.

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A theory of viscoelastic crack growth-Revisited (Revised)

10.21203/rs.3.rs-733371/v2 ◽

2021 ◽

Author(s):

Richard A Schapery

Keyword(s):

Crack Growth ◽

Creep Compliance ◽

Process Zone ◽

Crack Opening ◽

Shift Factor ◽

Analytical Relationship ◽

Failure Zone ◽

Opening Displacement ◽

Linear Elastic ◽

Linear Elastic Body

Abstract A theory of viscoelastic crack growth developed nearly five decades ago is generalized to express traction in the so-called fracture process zone or failure zone as a function of the crack opening displacement (COD). In earlier work, except for minor exceptions, traction was specified as a function of location. The new model leads to a nonlinear double integral that has to be solved for the COD before crack growth can be predicted. First, a closed-form, accurate approximation is found for a linear elastic body. We then show that this COD may be easily and accurately extended to linear viscoelasticity using a realistic, broad spectrum creep compliance. An analytical relationship connecting the stress intensity factor to crack speed then follows. Consistent with earlier work, it is defined almost entirely by the creep compliance. Five different failure zone tractions are employed; their differences are shown to have little effect on crack growth other than through a speed shift factor. The Appendix discusses initiation of growth.

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A theory of viscoelastic crack growth-Revisited

10.21203/rs.3.rs-733371/v3 ◽

2021 ◽

Author(s):

Richard A Schapery

Keyword(s):

Crack Growth ◽

Creep Compliance ◽

Process Zone ◽

Crack Opening ◽

Shift Factor ◽

Analytical Relationship ◽

Failure Zone ◽

Opening Displacement ◽

Linear Elastic ◽

Linear Elastic Body

Abstract A theory of viscoelastic crack growth developed nearly five decades ago is generalized to express traction in the so-called fracture process zone or failure zone as a function of the crack opening displacement (COD). In earlier work, except for minor exceptions, traction was specified as a function of location. The new model leads to a nonlinear double integral that has to be solved for the COD before crack growth can be predicted. First, a closed-form, accurate approximation is found for a linear elastic body. We then show that this COD may be easily and accurately extended to linear viscoelasticity using a realistic, broad spectrum creep compliance. An analytical relationship connecting the stress intensity factor to crack speed then follows. Consistent with earlier work, it is defined almost entirely by the creep compliance. Five different failure zone tractions are employed; their differences are shown to have little effect on crack growth other than through a speed shift factor. The Appendix discusses initiation of growth.

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A Possible Way of Applying Schapery's Viscoelastic Fracture Model to Creep Crack Growth in Carbon-epoxy Composites

Advanced Composites Letters ◽

10.1177/096369359300200302 ◽

1993 ◽

Vol 2 (3) ◽

pp. 096369359300200

Author(s):

V. Delauménie ◽

J. Chaoufi ◽

D. Gamby

Keyword(s):

Crack Growth ◽

Creep Crack Growth ◽

Epoxy Composites ◽

Fracture Model ◽

Failure Zone ◽

Creep Crack ◽

Transverse Cracking ◽

Second Stage ◽

Viscoelastic Fracture

Schapery and Christensen's models of viscoelastic fracture have been adapted to describe the phenomenon of transverse cracking in composites. In a second stage, the application of both models to a known composite allowed to determine the size of the “failure zone”, which is one of key parameters in Schapery's model.

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Examination of Fracture Interfaces in Silicon Nitride

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100113925 ◽

1975 ◽

Vol 33 ◽

pp. 60-61

Author(s):

Nancy J. Tighe

Keyword(s):

Silicon Nitride ◽

Grain Boundary ◽

Crack Growth ◽

Subcritical Crack Growth ◽

Slow Crack Growth ◽

Ceramic Materials ◽

Grain Boundary Sliding ◽

Boundary Phase ◽

Turbine Engines ◽

Boundary Sliding

Silicon nitride is one of the ceramic materials being considered for the components in gas turbine engines which will be exposed to temperatures of 1000 to 1400°C. Test specimens from hot-pressed billets exhibit flexural strengths of approximately 50 MN/m2 at 1000°C. However, the strength degrades rapidly to less than 20 MN/m2 at 1400°C. The strength degradition is attributed to subcritical crack growth phenomena evidenced by a stress rate dependence of the flexural strength and the stress intensity factor. This phenomena is termed slow crack growth and is associated with the onset of plastic deformation at the crack tip. Lange attributed the subcritical crack growth tb a glassy silicate grain boundary phase which decreased in viscosity with increased temperature and permitted a form of grain boundary sliding to occur.

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