Behavior of a Fluid Filled Subsurface Crack Under Moving Hertzian Loading

2007 ◽  
Author(s):  
Xiaoqing Jin ◽  
Leon M. Keer ◽  
Qian Wang
Keyword(s):  
Crack Propagation ◽  
Energy Release Rate ◽  
Energy Release ◽  
Release Rate ◽  
Crack Opening ◽  
Fluid Pressure ◽  
Elastic Strain Energy ◽  
Strain Energy Release ◽  
Energy Criterion ◽  
Subsurface Crack

Cracking of a fluid filled subsurface crack is studied by the distributed dislocation technique within the framework of two-dimensional linear elastic fracture mechanics. The opening volume of the horizontal Griffith crack is fully occupied by an incompressible fluid. In the presence of friction, a moving Hertzian line contact load is applied at the surface of the half plane. The induced hydrostatic fluid pressure inside the crack is calculated through an iterative scheme with the restriction that due to the fluid incompressibility there is no change of the crack-opening volume (COV). The stress intensity factors at the tips of the fluid filled crack are analyzed and the effective quadrature formulae are given for the evaluation of the COV. A hypothesis is introduced that the crack propagation is initiated when the elastic strain energy release rate reaches the critical fracture toughness and is arrested when the energy release rate is below the arrest toughness. Based on the energy criterion, predictions will be attempted for determining the load position where the crack propagation/kink commences as well as the growth increment of the branch crack before it is arrested. A step-by-step crack path is constructed for various loading conditions.

Shape and energies of a dynamically propagating crack under bending

2003 ◽  
Vol 18 (10) ◽  
pp. 2379-2386 ◽  
Author(s):  
Dov Sherman ◽  
Ilan Be'ery
Keyword(s):  
Crack Propagation ◽  
Energy Release Rate ◽  
Energy Release ◽  
Release Rate ◽  
Crack Front ◽  
Three Dimensional ◽  
Strain Energy Release ◽  
Governing Parameter ◽  
Propagating Crack ◽  
Front Shape

We report on the exact shape of a propagating crack in a plate with a high width/thickness ratio and subjected to bending deformation. Fracture tests were carried out with brittle solids—single crystal, polycrystalline, and amorphous. The shape of the propagating crack was determined from direct temporal crack length measurements and from the surface perturbations generated during rapid crack propagation. The shape of the crack profile was shown to be quarter-elliptical with a straight, long tail; the governing parameter of the ellipse axes is the specimen's thickness at most length of crack propagation. Universality of the crack front shape is demonstrated. The continuum mechanics approach applicable to two-dimensional problems was used in this three-dimensional problem to calculate the quasistatic strain energy release rate of the propagating crack using the formulations of the dynamic energy release rate along the crack loci. Knowledge of the crack front shape in the current geometry and loading configuration is important for practical and scientific aspects.

Nonlinear Approach for Strain Energy Release Rate in Micro Cantilevers

2010 ◽  
Author(s):  
Arash Kheyraddini Mousavi ◽  
Seyedhamidreza Alaie ◽  
Maheshwar R. Kashamolla ◽  
Zayd Chad Leseman
Keyword(s):  
Surface Roughness ◽  
Crack Propagation ◽  
Energy Release Rate ◽  
Energy Release ◽  
Release Rate ◽  
Strain Energy ◽  
Strain Energy Release Rate ◽  
Strain Energy Release ◽  
Rigid Substrate ◽  
Micro Cantilever

An analytical Mixed Mode I & II crack propagation model is used to analyze the experimental results of stiction failed micro cantilevers on a rigid substrate and to determine the critical strain energy release rate (adhesion energy). Using nonlinear beam deflection theory, the shape of the beam being peeled off of a rigid substrate can be accurately modeled. Results show that the model can fit the experimental data with an average root mean square error of less than 5 ran even at relatively large deflections which happens in some MEMS applications. The effects of surface roughness and/or debris are also explored and contrasted with perfectly (atomically) flat surfaces. Herein it is shown that unlike the macro-scale crack propagation tests, the surface roughness and debris trapped between the micro cantilever and the substrate can drastically effect the energy associated with creating unit new surface areas and also leads to some interesting phenomena. The polysilicon micro cantilever samples used, were fabricated by SUMMIT V™ technology in Sandia National Laboratories and were 1000 μm long, 30 μm wide and 2.6 μm thick.

Efficient Computation of Strain Energy Release Rate in Crack Growth Simulation

1999 ◽  
Author(s):  
D. J. Chen
Keyword(s):  
Finite Element ◽  
Crack Propagation ◽  
Energy Release Rate ◽  
Energy Release ◽  
Release Rate ◽  
Strain Energy ◽  
Strain Energy Release Rate ◽  
Strain Energy Release ◽  
Error Estimator ◽  
Efficient Computation

Abstract This paper utilizes an automated process to simplify the calculation of the strain energy release rate (SERR) during the crack propagation. The convergence of a finite element solution is achieved by adaptive re-meshing scheme with an error estimator of the linear strain triangular (LST) elements. As the desired mesh density is achieved, computation of the SERR using virtual crack closure technique (VCCT) can be obtained by using the static condensation scheme without re-analyzing the finite element models. Thus, the amount of computational and modeling time can be significantly reduced in the analysis of the crack propagation.

scholarly journals Combined Effect of Pressure and Shear Stress on Penny-Shaped Fluid-Driven Cracks

2018 ◽  
Vol 85 (3) ◽  
Author(s):  
Wenhao Shen ◽  
Ya-Pu Zhao
Keyword(s):  
Stress Intensity Factor ◽  
Shear Stress ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Crack Propagation ◽  
Energy Release Rate ◽  
Energy Release ◽  
Release Rate ◽  
Crack Opening ◽  
Effect Of Pressure

Penny-shaped fluid-driven cracks are often detected in many fluid–solid interaction problems. We study the combined effect of pressure and shear stress on the crack propagation in an impermeable elastic full space. Boundary integral equations are presented, by using the integral transform method, for a penny-shaped crack under normal and shear stresses. The crack propagation criterion of stress intensity factor is examined with the strain energy release rate. Dominant regimes are obtained by using a scaling analysis. Asymptotic solution of the toughness-dominant regime is derived to show the effect of shear stress on the crack opening, crack length, and pressure distribution. The results indicate that a singular shear stress can dominate the asymptotic property of the stress field near the crack tip, and the stress intensity factor cannot be calculated even though the energy release rate is finite. Shear stress leads to a smaller crack opening, a longer crack, and a slightly larger wellbore pressure. A novel dominant-regime transition between shear stress and pressure is found. Unstable crack propagation occurs in the shear stress-dominant regime. This study may help in understanding crack problems under symmetrical loads and modeling fluid–solid interactions at the crack surfaces.

A Study of Crack Growth in Sandwich Composite Beams

2001 ◽  
Author(s):  
Sami I. El-Sayed ◽  
Srinivasan Sridharan
Keyword(s):  
Energy Release Rate ◽  
Energy Release ◽  
Release Rate ◽  
Strain Energy ◽  
Strain Energy Release Rate ◽  
Crack Opening ◽  
Strain Energy Release ◽  
Beam Specimen ◽  
Crack Kinking ◽  
Interfacial Delamination

Abstract The paper proposes models to track the face-core interfacial delamination growth and crack kinking into the sandwich core, respectively. The models consist in interposing a cohesive layer along a pre-existing delamination or an identified plane of crack propagation. The former, designated as CLD (cohesive layer delamination model) is investigated first in detail using an example of a restrained beam specimen. The Influence of the key parameters of the model, viz. the thickness of the cohesive layer and the strength and stiffness of the cohesive layer material, have been studied. It is found that the model is fairly robust and is not sensitive to changes in parameters other than the critical strain energy release rate. The second model is a highly simplified one, but it is nevertheless a comprehensive model which can track the crack path by identifying crack planes in various elements using a maximum tensile stress criterion. This is designated as CLDK model as it deal with delamination and crack kinking — whichever is the preferred mode of fracture. The models are constructed ensuring that the crack opening is controlled by the critical value of strain energy release rate in mode I fracture. Experimental results of two sandwich specimens, viz. bottom restrained beams with 0° and −10° tilt angle respectively were used for comparison. The results indicate that the both the models are able to capture the initiation and track the growth of the interfacial delamination. The CLDK model tracks the crack kinking into the core, and its subsequent return to the facesheet-core interface.

scholarly journals Moving interfacial Griffith crack between bonded dissimilar media

2005 ◽  
Vol 2005 (3) ◽  
pp. 289-299 ◽  
Author(s):  
S. Mukherjee ◽  
S. Das
Keyword(s):  
Energy Release Rate ◽  
Energy Release ◽  
Crack Opening Displacement ◽  
Release Rate ◽  
Strain Energy ◽  
Strain Energy Release Rate ◽  
Crack Opening ◽  
Strain Energy Release ◽  
Griffith Crack ◽  
Opening Displacement

The plane strain problem of determining strain energy release rate, crack energy, and crack-opening displacement (COD) for a moving Griffith crack at the interface of two dissimilar orthotropic half-planes is considered. The problem is reduced to a pair of singular integral equations of second kind which have finally been solved by using Jacobi polynomials. Graphical plots of the strain energy release rate, crack energy, and crack-opening displacement for the problem in different particular cases are presented.

The Effect of Local Yielding on the Strain-Energy Release Rate

1969 ◽  
Vol 91 (4) ◽  
pp. 852-854
Author(s):  
P. L. Key
Keyword(s):  
Energy Release Rate ◽  
Energy Release ◽  
Correction Factor ◽  
Release Rate ◽  
Strain Energy ◽  
Strain Energy Release Rate ◽  
Elastic Strain Energy ◽  
Strain Energy Release ◽  
Finite Width ◽  
Dugdale Model

In a recent paper in the Journal of Basic Engineering [1], Forman presented numerical results for the strain-energy release rate of a crack in a finite width plate using the Dugdale model [2] of a yielded crack to describe the effects of local plastic flow. However, there appear to be several errors in the formulation of the problem by Forman. In addition, it is believed that an analytical rather than numerical approach to this problem would be more useful for applications. In this Note, an analytical form for a correction factor due to yielding is obtained for the elastic strain-energy release rate from an exact expression for the strain-energy release rale of the Dugdale model of a yielded crack in an infinite sheet. The effect of finite sheet width is treated as a separate correction factor.

Strength Determination Based on the Results of Modeling the Crack Propagation in a Nanostructured Hard Alloy

2019 ◽  
Vol 806 ◽  
pp. 45-50
Author(s):  
Maksim Dvornik ◽  
Elena Mikhailenko
Keyword(s):  
Crack Propagation ◽  
Energy Release Rate ◽  
Energy Release ◽  
Release Rate ◽  
Volume Fraction ◽  
Strain Energy Release ◽  
The Finite Element Method ◽  
Intermediate Layers ◽  
Cobalt Layer ◽  
Co Alloys

The process of crack propagation from the initial pore in the microstructures of WC-Co alloys with different volume fraction of the cobalt phase was studied by simulation of the stressed state by the finite element method. A calculation of the energy release rate during the propagation of crack through sections which consist of the carbide grains and the cobalt phase was made. It is shown that the strain energy release rate increases with crack propagation in WC grains and decreases with crack propagation in the intermediate layers of cobalt. The maximum stresses required for the destruction of the cobalt layer determine the strength of the entire microstructure. The strength of the alloy increases when decreasing pore diameter and increasing the cobalt phase fraction.

scholarly journals A New Bursting Liability Evaluation Index for Coal –The Effective Elastic Strain Energy Release Rate

Energies ◽  
2019 ◽  
Vol 12 (19) ◽  
pp. 3734
Author(s):  
Zhiguo LU ◽  
Wenjun JU ◽  
Fuqiang GAO ◽  
Youliang FENG ◽  
Zhuoyue SUN ◽  
...  
Keyword(s):  
Energy Release Rate ◽  
Energy Release ◽  
Release Rate ◽  
Elastic Strain ◽  
Strain Energy ◽  
Strain Energy Release Rate ◽  
Elastic Strain Energy ◽  
Strain Curve ◽  
Strain Energy Release ◽  
Stress Strain Curve

Because both faults and cleats exist in coal, sharp stress drops occur during loading when coal is deformed. These drops occur during the pre-peak stage and are accompanied by sudden energy releases. After a stress drop, the stress climbs slowly following a zigzag path and the energy accumulated during the pre-peak stage is unstable. A stress–strain curve is the basic tool used to evaluate the bursting liability of coal. Based on energy accumulation in an unsteady state, the pre-peak stress–strain curve is divided into three stages: pre-extreme, stress drop, and re-rising stage. The energy evolution of the specimen during each stage is analyzed. In this paper, an index called the effective elastic strain energy release rate (EESERR) index is proposed and used to evaluate the coal’s bursting liability. The paper shows that the propagation and coalescence of cracks is accompanied by energy release. The stress climb following a zigzag path prolongs the plastic deformation stage. This causes a significant difference between the work done by a hydraulic press during a laboratory uniaxial compression experiment and the elastic strain energy stored in the specimen during the experiment, so the evaluation result of the burst energy index would be too high. The determination of bursting liability is a comprehensive evaluation of the elastic strain energy accumulated in coal that is released when the specimen is damaged. The index proposed in this paper fully integrates the energy evolution of coal samples being damaged by loading, the amount of elastic strain energy released during the sample failure divided by the failure time is the energy release rate. The calculation method is simplified so that the uniaxial compressive strength and elastic modulus are included which makes the new index more universal and comprehensive. Theoretical analysis and physical compression experiments validate the reliability of the evaluation.

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