Fracture mechanics life analytical methods verification testing

The objective was to evaluate NASCRAC (trademark) version 2.0, a second generation fracture analysis code, for verification and validity. NASCRAC was evaluated using a combination of comparisons to the literature, closed-form solutions, numerical analyses, and tests. Several limitations and minor errors were detected. Additionally, a number of major flaws were discovered. These major flaws were generally due to application of a specific method or theory, not due to programming logic. Results are presented for the following program capabilities: K versus a, J versus a, crack opening area, life calculation due to fatigue crack growth, tolerable crack size, proof test logic, tearing instability, creep crack growth, crack transitioning, crack retardation due to overloads, and elastic-plastic stress redistribution. It is concluded that the code is an acceptable fracture tool for K solutions of simplified geometries, for a limited number of J and crack opening area solutions, and for fatigue crack propagation with the Paris equation and constant amplitude loads when the Paris equation is applicable

Probabilistic Fatigue Damage Prognosis Using a Surrogate Model Trained Via 3D Finite Element Analysis

Utilizing inverse uncertainty quantification techniques, structural health monitoring can be integrated with damage progression models to form probabilistic predictions of a structure's remaining useful life. However, damage evolution in realistic structures is physically complex. Accurately representing this behavior requires high-fidelity models which are typically computationally prohibitive. In the present work, a high-fidelity finite element model is represented by a surrogate model, reducing computation times. The new approach is used with damage diagnosis data to form a probabilistic prediction of remaining useful life for a test specimen under mixed-mode conditions

Heptametallic, Octupolar Nonlinear Optical Chromophores with Six Ferrocenyl Substituents

New complexes with six ferrocenyl (Fc) groups connected to ZnII or Cd^(II) tris(2,2′-bipyridyl) cores are described. A thorough characterisation of their BPh_(4)− salts includes two single-crystal X-ray structures, highly unusual for such species with multiple, extended substituents. Intense, visible d(Fe^(II))→π* metal-to-ligand charge-transfer (MLCT) bands accompany the π→π* intraligand charge-transfer absorptions in the near UV region. Each complex shows a single, fully reversible Fe^(III/II) wave when probed electrochemically. Molecular quadratic nonlinear optical (NLO) responses are determined by using hyper-Rayleigh scattering and Stark spectroscopy. The latter gives static first hyperpolarisabilities β_0 reaching as high as approximately 10^(−27) esu and generally increasing with π-conjugation extension. Z-scan cubic NLO measurements reveal high two-photon absorption cross-sections σ2 of up to 5400 GM in one case. DFT calculations reproduce the π-conjugation dependence of β_0, and TD-DFT predicts three transitions close in energy contributing to the MLCT bands. The lowest energy transition has octupolar character, whereas the other two are degenerate and dipolar in nature

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

Energy dissipation in the mixed mode growth of cracks at the interface between brittle materials

In the present paper we compare the propagation of a crack in a homogeneous linear elastic material and the propagation of a geometrically identical crack located at the interface between two ideally brittle materials. Whereas the former crack is free to kink, the evolution of an interface crack results in a competition among the relative toughnesses of the surrounding layers and of the interface. By constraining cracks in homogeneous materials to propagate straight, as along an imaginary interface in a continuum, significant insights on the mixed mode growth of cracks at the interface between brittle materials are provided. It is shown that the collinear elongation in homogeneous materials under mixed mode conditions requires a higher amount of energy, which turns out to be dependent on the mode mixity. Such a surplus of energy has the same mathematical form of the expression widely used to model the increment of the fracture energy in layered materials. One can thus argue about which roles are played by thermodynamics constitutive prescriptions and which roles are played by geometrical constraints

High order boundary and finite elements for 3D fracture propagation in brittle materials

The quasi-static propagation of fracture in brittle materials was studied in several recent publications. A variational formulation (Salvadori, 2008; Salvadori and Carini, 2011; Salvadori and Fantoni, 2013) led to three-dimensional crack tracking strategies (Salvadori and Fantoni, 2014 [2,3]; Salvadori and Fantoni, 2016). One of the complexities of this new class of algorithms is the evaluation of high-order terms of the expansion of the crack opening and sliding. In this paper, new types of finite and boundary elements are formulated that capture the near crack-front asymptotical displacement behavior up to the order 3/2 . The use of these elements with the quasi-static crack propagation algorithms of the above references is demonstrated for a simple crack configuration

Evaluation of Galerkin Singular Integrals for Anisotropic Elasticity: Displacement Equation

Algorithms for the direct evaluation of singular Galerkin boundary integrals for three-dimensional anisotropic elasticity are presented. The integral of the traction kernel is defined as a boundary limit, and (partial) analytic evaluation is employed to compute the limit. The spherical angle components of the Green's function and its derivatives are not known in closed form, and thus the analytic integration requires a splitting of the kernel, into 'singular' and 'non-singular' terms. For the coincident singular integral, a single analytic evaluation suffices to isolate the potentially divergent term, and to show that this term self-cancels. The implementation for a linear element is considered in detail, and the extension to higher order curved interpolation is also discussed. Results from test calculations establish that the algorithms are successful

Evaluation of Galerkin Singular Integrals for Anisotropic Elasticity: Displacement Equation

Algorithms for the direct evaluation of singular Galerkin boundary integrals for three-dimensional anisotropic elasticity are presented. The integral of the traction kernel is defined as a boundary limit, and (partial) analytic evaluation is employed to compute the limit. The spherical angle components of the Green's function and its derivatives are not known in closed form, and thus the analytic integration requires a splitting of the kernel, into 'singular' and 'non-singular' terms. For the coincident singular integral, a single analytic evaluation suffices to isolate the potentially divergent term, and to show that this term self-cancels. The implementation for a linear element is considered in detail, and the extension to higher order curved interpolation is also discussed. Results from test calculations establish that the algorithms are successful