Interactive color display of 3-D engineering analysis results

A general approach to three-dimensional postprocessing of engineering analyses is presented. The approach is versatile and may handle the results from a wide range of engineering analysis methods which involve the discretization of continua. To facilitate the understanding of complex three-dimensional numerical models, advanced interactive color postprocessing techniques are introduced. Finite element, finite difference, and boundary element models are evaluated with the prototype postprocessor. The existing color graphics program (POSTPRO3D) was ported to a high-resolution device. Interactive graphic tools were implemented to facilitate qualitative mesh evaluation from a single analysis. A postprocessing environment was design for workstation technology

FRANC2D: A two-dimensional crack propagation simulator. Version 2.7: User's guide

FRANC 2D (FRacture ANalysis Code, 2 Dimensions) is a menu driven, interactive finite element computer code that performs fracture mechanics analyses of 2-D structures. The code has an automatic mesh generator for triangular and quadrilateral elements. FRANC2D calculates the stress intensity factor using linear elastic fracture mechanics and evaluates crack extension using several methods that may be selected by the user. The code features a mesh refinement and adaptive mesh generation capability that is automatically developed according to the predicted crack extension direction and length. The code also has unique features that permit the analysis of layered structure with load transfer through simulated mechanical fasteners or bonded joints. The code was written for UNIX workstations with X-windows graphics and may be executed on the following computers: DEC DecStation 3000 and 5000 series, IBM RS/6000 series, Hewlitt-Packard 9000/700 series, SUN Sparc stations, and most Silicon Graphics models

Um método numérico para a modelagem de fraturamento coesivo em 3D

Neste trabalho apresenta-se um método que estende o modelo de fraturamento coesivo proposto por Hillerborg et ~ 1 . ~ 3 ' para problemas tri-dimensionais. O principal objetivo é o estudo do efeito das dimensóes absolutas de elementos de materiais ceramicos em seu comportamento estrutural. As hipóteses básicas e limitacóes de tal método sáo apresentadas e discutidas. O novo modelo obtido é entáo apresentado através da formulacáo matricial do problema coesivo. Esta formulacáo fornece um sistema de equacóes nao-lineares que pode ser resolvido com o algoritmo de Newton-Raphson. O modelo é capaz de representar a evolucáo das zonas de processos inelásticos e das de fissura verdadeira para diferentes geometrias estruturais2. A implementacáo computacional do modelo é feita utilizando-se técnicas de programacáo orientada para objetos e computacáo gráfica. Finalmente, apresenta-se um exemplo em que uma soluqáo tri-dimensional gerada com este modelo matemático é comparada com a solucao bi-dimensional conhecida na literatura.Peer Reviewe

On the Effects of Modeling As-Manufactured Geometry: Toward Digital Twin

Asimple, nonstandardized material test specimen,which fails along one of two different likely crack paths, is considered herein.The result of deviations in geometry on the order of tenths of amillimeter, this ambiguity in crack pathmotivates the consideration of asmanufactured component geometry in the design, assessment, and certification of structural systems.Herein, finite elementmodels of as-manufactured specimens are generated and subsequently analyzed to resolve the crack-path ambiguity. The consequence and benefit of such a "personalized" methodology is the prediction of a crack path for each specimen based on its as-manufactured geometry, rather than a distribution of possible specimen geometries or nominal geometry.The consideration of as-manufactured characteristics is central to the Digital Twin concept. Therefore, this work is also intended to motivate its development

A Method for Combining Experimentation and Molecular Dynamics Simulation to Improve Cohesive Zone Models for Metallic Microstructures

Fracture processes within a material begin at the nanometer length scale at which the formation, propagation, and interaction of fundamental damage mechanisms occur. Physics-based modeling of these atomic processes quickly becomes computationally intractable as the system size increases. Thus, a multiscale modeling method, based on the aggregation of fundamental damage processes occurring at the nanoscale within a cohesive zone model, is under development and will enable computationally feasible and physically meaningful microscale fracture simulation in polycrystalline metals. This method employs atomistic simulation to provide an optimization loop with an initial prediction of a cohesive zone model (CZM). This initial CZM is then applied at the crack front region within a finite element model. The optimization procedure iterates upon the CZM until the finite element model acceptably reproduces the near-crack-front displacement fields obtained from experimental observation. With this approach, a comparison can be made between the original CZM predicted by atomistic simulation and the converged CZM that is based on experimental observation. Comparison of the two CZMs gives insight into how atomistic simulation scales

Discrete crack growth analysis methodology for through cracks in pressurized fuselage structures

A methodology for simulating the growth of long through cracks in the skin of pressurized aircraft fuselage structures is described. Crack trajectories are allowed to be arbitrary and are computed as part of the simulation. The interaction between the mechanical loads acting on the superstructure and the local structural response near the crack tips is accounted for by employing a hierarchical modeling strategy. The structural response for each cracked configuration is obtained using a geometrically nonlinear shell finite element analysis procedure. Four stress intensity factors, two for membrane behavior and two for bending using Kirchhoff plate theory, are computed using an extension of the modified crack closure integral method. Crack trajectories are determined by applying the maximum tangential stress criterion. Crack growth results in localized mesh deletion, and the deletion regions are remeshed automatically using a newly developed all-quadrilateral meshing algorithm. The effectiveness of the methodology and its applicability to performing practical analyses of realistic structures is demonstrated by simulating curvilinear crack growth in a fuselage panel that is representative of a typical narrow-body aircraft. The predicted crack trajectory and fatigue life compare well with measurements of these same quantities from a full-scale pressurized panel test

Residual Strength Prediction of Fuselage Structures with Multiple Site Damage

This paper summarizes recent results on simulating full-scale pressure tests of wide body, lap-jointed fuselage panels with multiple site damage (MSD). The crack tip opening angle (CTOA) fracture criterion and the FRANC3D/STAGS software program were used to analyze stable crack growth under conditions of general yielding. The link-up of multiple cracks and residual strength of damaged structures were predicted. Elastic-plastic finite element analysis based on the von Mises yield criterion and incremental flow theory with small strain assumption was used. A global-local modeling procedure was employed in the numerical analyses. Stress distributions from the numerical simulations are compared with strain gage measurements. Analysis results show that accurate representation of the load transfer through the rivets is crucial for the model to predict the stress distribution accurately. Predicted crack growth and residual strength are compared with test data. Observed and predicted results both indicate that the occurrence of small MSD cracks substantially reduces the residual strength. Modeling fatigue closure is essential to capture the fracture behavior during the early stable crack growth. Breakage of a tear strap can have a major influence on residual strength prediction

A phase-field model for cohesive fracture

In this paper, a phase-field model for cohesive fracture is developed. After casting the cohesive zone approach in an energetic framework, which is suitable for incorporation in phase-field approaches, the phase-field approach to brittle fracture is recapitulated. The approximation to the Dirac function is discussed with particular emphasis on the Dirichlet boundary conditions that arise in the phase-field approximation. The accuracy of the discretisation of the phase field, including the sensitivity to the parameter that balances the field and the boundary contributions, is assessed at the hand of a simple example. The relation to gradient-enhanced damage models is highlighted, and some comments on the similarities and the differences between phase-field approaches to fracture and gradient-damage models are made. A phase-field representation for cohesive fracture is elaborated, starting from the aforementioned energetic framework. The strong as well as the weak formats are presented, the latter being the starting point for the ensuing finite element discretisation, which involves three fields: the displacement field, an auxiliary field that represents the jump in the displacement across the crack, and the phase field. Compared to phase-field approaches for brittle fracture, the modelling of the jump of the displacement across the crack is a complication, and the current work provides evidence that an additional constraint has to be provided in the sense that the auxiliary field must be constant in the direction orthogonal to the crack. The sensitivity of the results with respect to the numerical parameter needed to enforce this constraint is investigated, as well as how the results depend on the orders of the discretisation of the three fields. Finally, examples are given that demonstrate grid insensitivity for adhesive and for cohesive failure, the latter example being somewhat limited because only straight crack propagation is considered

Multiscale Modeling of Damage Processes in Aluminum Alloys: Grain-Scale Mechanisms

This paper has two goals related to the development of a physically-grounded methodology for modeling the initial stages of fatigue crack growth in an aluminum alloy. The aluminum alloy, AA 7075-T651, is susceptible to fatigue cracking that nucleates from cracked second phase iron-bearing particles. Thus, the first goal of the paper is to validate an existing framework for the prediction of the conditions under which the particles crack. The observed statistics of particle cracking (defined as incubation for this alloy) must be accurately predicted to simulate the stochastic nature of microstructurally small fatigue crack (MSFC) formation. Also, only by simulating incubation of damage in a statistically accurate manner can subsequent stages of crack growth be accurately predicted. To maintain fidelity and computational efficiency, a filtering procedure was developed to eliminate particles that were unlikely to crack. The particle filter considers the distributions of particle sizes and shapes, grain texture, and the configuration of the surrounding grains. This filter helps substantially reduce the number of particles that need to be included in the microstructural models and forms the basis of the future work on the subsequent stages of MSFC, crack nucleation and microstructurally small crack propagation. A physics-based approach to simulating fracture should ultimately begin at nanometer length scale, in which atomistic simulation is used to predict the fundamental damage mechanisms of MSFC. These mechanisms include dislocation formation and interaction, interstitial void formation, and atomic diffusion. However, atomistic simulations quickly become computationally intractable as the system size increases, especially when directly linking to the already large microstructural models. Therefore, the second goal of this paper is to propose a method that will incorporate atomistic simulation and small-scale experimental characterization into the existing multiscale framework. At the microscale, the nanoscale mechanics are represented within cohesive zones where appropriate, i.e. where the mechanics observed at the nanoscale can be represented as occurring on a plane such as at grain boundaries or slip planes at a crack front. Important advancements that are yet to be made include: 1. an increased fidelity in cohesive zone modeling; 2. a means to understand how atomistic simulation scales with time; 3. a new experimental methodology for generating empirical models for CZMs and emerging materials; and 4. a validation of simulations of the damage processes at the nano-micro scale. With ever-increasing computer power, the long-term ability to employ atomistic simulation for the prognosis of structural components will not be limited by computation power, but by our lack of knowledge in incorporating atomistic models into simulations of MSFC into a multiscale framework