B.J. Carter

Automated 3-D crack growth simulation

SUMMARY Automated simulation of arbitrary, non-planar, 3D crack growth in real-life engineered structures requires two key components: crack representation and crack growth mechanics. A model environment for representing the evolving 3D crack geometry and for testing various crack growth mechanics is presented. Reference is made to a specific implementation of the model, called FRANC3D. Computational geometry and topology are used to represent the evolution of crack growth in a structure. Current 3D crack growth mechanics are insufficient; however, the model allows for the implementation of new mechanics. A specific numerical analysis program is not an intrinsic part of the model; i.e., finite and boundary elements are both supported. For demonstration purposes, a 3D hypersingular boundary element code is used for two example simulations. The simulations support the conclusion that automatic propagation of a 3D crack in a real-life structure is feasible. Automated simulation lessens the tedious and time-consuming operations that are usually associated with crack growth analyses. Specifically, modifications to the geometry of the structure due to crack growth, re-meshing of the modified portion of the structure after crack growth, and re-application of boundary conditions proceeds without user intervention.

The effect of strain rate on rock strength

SummaryThe effect of the strain rate on strength has been evaluated for two widely different rock types, a brittle limestone (Tyndallstone) and a ductile salt rock (Lanigan potash rock).Results of static and dynamic fatigue tests on Tyndallstone, a dolomitic limestone, show an increase in strength with increasing strain or stressing rate although the rate effect is very small. Although the static and dynamic fatigue tests are expected to yield the same stress corrosion parameter, no such agreement has been observed.Dynamic fatigue tests of the more ductile salt rock showed a substantial rate effect. The usual strength criteria, that consider the influence of confining pressure alone, are no longer adequate to describe the strength of Lanigan potash. A general strength criterion, that incorporates the effect of both the confining pressure and the strain rate, is proposed.

Size and Stress Gradient Effects on Fracture Around Cavities

SummaryThe effect of hole size on fracture initiation around cavities in rock is examined through physical model tests on Tyndall limestone. Twenty five models, employing nine different hole sizes, ranging from 3.2 to 62 mm in diameter were tested in uniaxial compression. Strain gauges placed both on the face of the model block and inside the cylindrical cavity were used to record the state of fracture.Fracture initiation data for primary, remote and sidewall fractures were determined using the stress-strain curves from the respective strain gauge locations. For all three fracture types, the initiation stress decreases with increasing hole size and appears to approach a horizontal asymptote for large cavity sizes. The fracture mechanics formulations and the stress averaging method give the best fit to the primary fracture initiation except for very small cavity sizes. The stress averaging method also provides a very good fit to the sidewall fracture initiation data.

Criteria for brittle fracture in compression

Abstract Fracture nucleation and propagation in the compressive stress field of the geological and the mining environment is considered with the purpose of formulating an empirical, but general fracture criterion that is in agreement with experimental evidence. Present fracture criteria are inadequate for compressive loading. The boundary stress-based theories ignore the effect of the stress gradient while the critical stress intensity concept of fracture mechanics neglects the normal stress that acts parallel with the direction of fracture propagation. A new, empirical crack resistance (CR) function is defined based on experimental data and then combined with an ‘averaged’ state of stress in front of the cracktip to formulate a ‘crack driver’ (CD) function. The crack driver is analogous to the safety factor, but with values greater than unity representing the fractured state. The crack driver concept is implemented to predict the nucleation and propagation of fracture in a compressive environment. The evolution of the failure process around underground openings is then described, with special reference to the primary, the remote and the slabbing types of fracture of rock mechanics and mining terminology.

The sandia fracture challenge: Blind round robin predictions of ductile tearing

Existing and emerging methods in computational mechanics are rarely validated against problems with an unknown outcome. For this reason, Sandia National Laboratories, in partnership with US National Science Foundation and Naval Surface Warfare Center Carderock Division, launched a computational challenge in mid-summer, 2012. Researchers and engineers were invited to predict crack initiation and propagation in a simple but novel geometry fabricated from a common off-the-shelf commercial engineering alloy. The goal of this international Sandia Fracture Challenge was to benchmark the capabilities for the prediction of deformation and damage evolution associated with ductile tearing in structural metals, including physics models, computational methods, and numerical implementations currently available in the computational fracture community. Thirteen teams participated, reporting blind predictions for the outcome of the Challenge. The simulations and experiments were performed independently and kept confidential. The methods for fracture prediction taken by the thirteen teams ranged from very simple engineering calculations to complicated multiscale simulations. The wide variation in modeling results showed a striking lack of consistency across research groups in addressing problems of ductile fracture. While some methods were more successful than others, it is clear that the problem of ductile fracture prediction continues to be challenging. Specific areas of deficiency have been identified through this effort. Also, the effort has underscored the need for additional blind prediction-based assessments.

Fitting strength criteria to intact rock

SummaryRock strength data covering the full range of possible stress conditions are presented for three rocks: a granite, a limestone and a salt rock. The Hoek and Brown square root parabola and the Johnston criteria are fitted to the strength data coming from around 500 laboratory tests. The fitting procedure is facilitated by a specially built PC code, ROCKER, which is available to anyone on request.The Hoek and Brown criterion is modified through the inclusion of a third parameter to account for the low tensile strength of the salt rock. A new criterion, the Rocker function is formulated to follow strength data closely in the tension-low confining pressure region.

The Sandia Fracture Challenge: blind round robin predictions of ductile tearing

Existing and emerging methods in computational mechanics are rarely validated against problems with an unknown outcome. For this reason, Sandia National Laboratories, in partnership with US National Science Foundation and Naval Surface Warfare Center Carderock Division, launched a computational challenge in mid-summer, 2012. Researchers and engineers were invited to predict crack initiation and propagation in a simple but novel geometry fabricated from a common off-the-shelf commercial engineering alloy. The goal of this international Sandia Fracture Challenge was to benchmark the capabilities for the prediction of deformation and damage evolution associated with ductile tearing in structural metals, including physics models, computational methods, and numerical implementations currently available in the computational fracture community. Thirteen teams participated, reporting blind predictions for the outcome of the Challenge. The simulations and experiments were performed independently and kept confidential. The methods for fracture prediction taken by the thirteen teams ranged from very simple engineering calculations to complicated multiscale simulations. The wide variation in modeling results showed a striking lack of consistency across research groups in addressing problems of ductile fracture. While some methods were more successful than others, it is clear that the problem of ductile fracture prediction continues to be challenging. Specific areas of deficiency have been identified through this effort. Also, the effort has underscored the need for additional blind prediction-based assessments.

Tensile fracture from circular cavities loaded in compression

When a block of rock containing an equi-dimensional void is loaded in compression, the resulting fracture may form at one of three basic positions: at the tensile stress concentration of the perimeter (primary fracture), at the compressive stress concentration of the perimeter (slabbing fracture), or off the perimeter, remote to the cavity (remote fracture). All three are genetically similar; they form and propagate parallel to the direction of the maximum compressive stress. The location of the fracture with respect to the cavity is controlled by the cavity size and the confining pressure.Although LEFM solutions exist for the primary fracture, the mathematical crack of fracture mechanics is ill-suited to analyze fractures that form in a primarily compressive state of stress (remote and slabbing fractures); the mathematical crack is independent of the compressive stress acting along its plane. A stress-based solution is proposed that incorporates the effect of both the maximum and the minimum principal stress. The major shortcoming of conventional stress-based techniques, the lack of size dependence, is removed by a procedure of stress averaging over a constant distance or area. For the case of the cylindrical cavity, stress averaging along the primary fracture path can be built into a closed-form solution. Averaging stresses over a constant area requires numerical techniques.Physical experiments, involving the compression loading of cylindrical cavities in three rocks: a granite, a limestone and a salt rock provide data for the comparison and the calibration of the theoretical criteria. Stress averaging over a constant area gave the best agreement with the test data.

Universal crack closure integral for SIF estimation

Abstract Numerical analysis of cracked structures often involves numerical estimation of stress intensity factors (SIFs) at a crack tip/front. A newly developed formulation called universal crack closure integral (UCCI) for the evaluation of potential energy release rates (PERRs) and the corresponding SIFs is presented in this paper. Unlike the existing element dedicated forms of crack closure integrals (MCCI, VCCI) with application limited to finite element analysis, this new numerical SIF/PERR estimation technique is independent of the basic stress analysis procedure, making it universally applicable. The second merit of this procedure is that it avoids the generally error-producing zones close to the crack tip/front singularity. The UCCI procedure, based on Irwin’s original CCI, is formulated and explored using a simple 2D problem of a straight crack in an infinite sheet. It is then applied to some three-dimensional crack geometries with the stresses and displacements obtained from a boundary element program.

En echelon crack-arrays in potash salt rock

SummaryThere are two types of fracture patterns in the yield pillars of the potash mines of Saskatchewan. The individual members of both patterns are tensile (extension) fractures that propagate parallel with the maximum principal stress trajectory (perpendicular to the minimum principal stress). The difference between the two patterns lies in the arrangement of the member fractures. In theen echelon tensile crack-array, the macroscopic fracture consists of individual tensile cracks that are slightly offset from each other. They have only a small overlap and the child crack seems to form randomly on either side of its parent. Consequently, the en echelon tensile crack-array inherits the axial orientation of its members. In contrast, the tensile cracks of anen echelon shear crack-array, have a larger overlap and their lateral displacement from each other is biased in one direction. Therefore, the crack-array is no longer axial but inclined 20–25 degrees from the maximum principal stress direction. With increasing stress, the shear crack-array often collapses, forming theenvelope orhourglass structures of the potash mines.