Paul A. Wawrzynek

Quasi-automatic simulation of crack propagation for 2D LEFM problems

A strategy for quasi-automatic simulation of propagation of arbitrary cracks in two-dimensional, linear elastic finite element models is presented. This strategy has been implemented in FRANC2D (FRacture ANalysis Code 2D). An underlying winged-edge data structure enables automatic local modifications of the mesh along the propagation path without loss of any unaffected structural information. The finite element mesh is locally regenerated after each step of propagation by means of a robust remeshing algorithm. The propagation process is driven by linear elastic fracture mechanics concepts which are used to calculate mixed-mode stress intensity factors, predict incremental changes in trajectory, and assess local crack stability. Crack trajectories, obtained for different techniques of stress intensity factor calculation, and for different mixed-mode interaction theories, are presented and favorably compared to experimentally obtained paths.

Interactive finite element analysis of fracture processes: An integrated approach

Abstract A fracture analysis program has been developed which incorporates the concepts of finite element analysis, fracture mechanics, computer graphics, finite element postprocessing, automatic mesh generation, and data base design. The program FRANC (FRacture ANalysis Code) is a tool which allows a practicing engineer or a researcher to perform an incremental fracture analysis at his desk. The program draws on a substantial experience base and this paper describes the philosophy of the program and the integration of its parts. Also, a number of example problems will be presented which show some results of incremental fracture analyses.

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.

An interactive approach to local remeshing around a propagating crack

Abstract When performing a finite element analysis of a discrete crack propagating through a structure, one must modify the element mesh to reflect the current configuration of the crack. This can be a tedious and time consuming task if the analyst must create a new finite element mesh at each crack step manually. It is much more desirable to have a computer automatically remesh the problem every time the crack is lengthened. Unfortunately, it is very difficult to produce an algorithm which will produce a satisfactory mesh for all structures for all crack configurations. An approach to overcoming this difficulty is to allow the computer to make its best try at remeshing the problem and then, through the use of computer graphics, show those results to the analyst. At this point, the analyst can accept the mesh created by the computer or he can, through the use of interactive graphics, indicate to the computer the parts of the mesh that are unsatisfactory and allow the computer to try again. This process can be repeated until a satisfactory mesh is created. This strategy was implemented in the FRANC (FRacture ANalysis Code) program and is described by means of an example problem in this paper.

Simulating Fatigue Crack Growth in Spiral Bevel Gears

Abstract The boundary element method and linear elastic fracture mechanics theories are used to predict three dimensional fatigue crack trajectories in a spiral bevel pinion under a moving load. It is found that the moving load produces a non-proportional load history in a gear’s tooth root. An approach that accounts for fatigue crack closure effects is developed to propagate the crack front under the non-proportional load. The predictions are compared to experimental results. The sensitivity of the predictions to variations in loading conditions and crack growth rate model parameters is explored. Critical areas that must be understood in greater detail prior to predicting more accurate crack trajectories and crack growth rates in three dimensions are identified.

Arbitrary crack representation using solid modeling

This paper describes the fundamental modeling approaches adopted for crack nucleation and propagation in a software system that is specifically designed to simulate problems with evolutionary geometry. Only the topological and geometrical aspects of crack modeling, and how these aspects affect the database representation in the system, are addressed in the present discussion. The following are the innovative features of the present crack modeling approach: (a) crack simulation is done with a true geometric representation of the structure, via solid modeling; (b) crack modeling relies on the sophisticated, topology-based data structure of this system to support linkage to the solid model, fast interaction and accurate representation of evolving flaw shapes; (c) the system provides the ability to specify flaws of arbitrary shape (including non-planar flaws), size and orientation at arbitrary locations in the geometric model; (d) the flaw is specified at the desired location in the actual structure geometry, rather than at a location in the mesh; (e) the system uses all its automatic and local remeshing capabilities for the simulation of flaw initiation and growth.

On the virtual crack extension method for calculation of the rates of energy release rate

Abstract This paper generalizes the analytical virtual crack extension method presented by Lin and Abel by providing the higher order derivatives of energy release rate due to crack extension for multiply cracked bodies. It provides derivations and verifications of the following: extension to the general case of multiple crack systems, extension to the axisymmetric case, inclusion of crack-face and thermal loading, and evaluation of the second derivative of energy release rate. The salient feature of this method is that the energy release rate and its higher order derivatives for multiple crack systems are computed in a single analysis. It is shown that the number of rings of elements surrounding the crack tip that are involved in the mesh perturbation due to the virtual crack extension has an effect on the solution accuracy. Maximum errors for the mesh density used in the examples are about 0.2% for energy release rate, 2–3% for its first derivative, and 5–10% for its second derivative.

Finite element modelling of fracture propagation in orthotropic materials

Abstract This paper presents a simple method for the analysis of fracture propagation in orthotropic materials. The method is applicable to a wide range of materials such as steel which may have anisotropic toughness characteristics, rock which often has anisotropic stiffness and toughness properties, and woods and composites where the toughness and stiffness can vary by orders of magnitude. Several theories of fracture propagation in anisotropic materials are reviewed with regard to their application to various materials. It is shown that isoparametric quarter-point elements can be used to obtain accurate stress intensity factors using orthotopic displacement correlation equations. An example of fracture propagation analysis in an orthotropic structure is presented and conclusions are drawn with regard to the relative influence of anisotropic strength and orthotropic stiffness properties.

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.

Consideration of Moving Tooth Load in Gear Crack Propagation Predictions

Abstract : Robust gear designs consider not only crack initiation, but crack propagation trajectories for a fail-safe design. In actual gear operation, the magnitude as well as the position of the force changes as the gear rotates through the mesh. A study to determine the effect of moving gear tooth load on crack propagation predictions was performed. Two dimensional analysis of an involuted spur gear and three-dimensional analysis of a spiral-bevel pinion gear using the finite element method and boundary element method were studied and compared to experiments. A modified theory for predicting gear crack propagation paths based on the criteria of Erdogan and Sih was investigated. Crack simulation based on calculated stress intensity factors and mixed mode crack angle prediction techniques using a simple static analysis in which the tooth load was located at the highest point of single tooth contact was validated. For three-dimensional analysis, however, the analysis was valid only as long as the crack did not approach the contact region on the tooth.